Table of Contents

001

Title page

002

Author

003

Preface

004

Part 1 - Title page - Relativity -Map

005

Part 1 -Introduction - The fundamental considerationsThe fundamental considerations

006

Part 1 - The transformation equations of the length and time

007

Part 1 - The derived transformation equations

008

Part1 - The spacetime density

009

Part 1 - The speed superposition

010

Part 1 - Acceleration - Length and time dilation and contraction

011

Part 1 - Space Flow - Mass

012

Part 1 - Linear Momentum - Force

013

Part 1 - Kinetic Energy

014

Part 1 - Author

015

Part 2 - Title page - Gravity - Map

016

Part 2 - Gravity of the Mass Point - Basic relations

017

Part 2 - Spacetime Density

018

Part 2 - Speed of a spacetime structure falling into a singularity

019

Part 2 - Transformation equations of the radia in a gravitational field

020

Part 2 - Acceleration of the spacetime structure falling into a singularity

021

Part 2 - Gravity of Earth globe - Gravity above the earth surface

022

Part 2 - Measurement of the radia above Earth globe surface

023

Part 2 - Gravity of a common cosmic object - Gravity at zero speed above the surface of a common cosmic object

024

Part 2 - Free motion of the object in a spaceflow line - Light speed in a spaceflow line

025

Part 2 - Speed and acceleration of the free object in a spaceflow line

026

Part 2 - Kinetic energy - Gravitational potential - Potential energy

027

Part 2 - Common free motion in gravitational field - Spherical and linear geometry

028

Part 2 - Equations of common free motion - The apparent change of the space density due to orbital motion -

Orbital and vertical speeds in Zcr frame - Confrontation Keppler's laws with the space-flow theory of gravity

029

Part 2 - Influence of relativity factor on common free motion - Influence of relativity factor on basic parameters of gravitational field -

Deformation of geometry of gravitational field

030

Part 2 - The example of calculation of orbital trajectories in solar system - Basic parameters of the sun's gravitational field -

Calculation example for the planet Mercury

031

Part 2 - Trajectories of objects in revolution around Sun

032

Part 2 - The shape of orbital trajectories in solar system

033

Part 2 - Orbital trajectories round the characteristic radius of gravitational field

034

Part 2 - Analysis of the common motion in gravitational field - Culminating radia - The shift of culminating points -

The energy of free object in free motion - How long does it take sun's light to reach earth - The dark matter

035

Part 2 - Author

036

Part 3 Title page - Gravity inside Mass - Map

037

Part 3 - Mass object in gravitationald field of another object - Interface area - Gravitational acceleration due to external objects

038

Part 3 - Mass distribution of gravitational objects -

Mass distribution of gravitational object created of the mass of constant frame intrinsic mass density

039

Part 3 - Mass distribution of gravitational object created of several layers of different frame intrinsic mass density

040

Part 3 - Gravitational acceleration created by object itself

041

Part 3 - Gravitational acceleration created by other object

042

Part 3 - Summary

043

Part 3 - Author

044

Epilogue

045

Epilogue in slovak language

046

Epilogue in italian language

001

THE SPACETIME PHENOMENA

SPACE FLOW THEORY

The work deals with alternative physics, based on the idea of a quantized and oscillating space.

The fundamental attribute of such spacetime structure is spacetime density, defining dimension and time.

by Frantisek Stefanko

The work consists of the three subsequent sections:

- RELATIVITY

- GRAVITY DUE TO SPACE FLOW

- GRAVITY AND MASS DISTRIBUTION

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PREFACE

EPILOGUE

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AUTHOR

F. Stefanko

Skautska 1

04001 Kosice

Slovakia

E-mail address : fstefanko@gmail.com

I am obliged to inform the public that I am not a professional physicist, and, that , to start this work, I had to pluck up courage at first, to forget about many warning fingers of my teachers of physics.

The thought became perhaps the only suitable instrument for people doing fundamental research. But in case only, that it is selfpossessed and independent enough, to penetrate through spacetime structures, not affecting them,and being not affected by them.. This is the Way.

Copyright: A user may download, copy and reproduce this article, but this activity is limited to ten copies of the article. Otherwise author must be contacted. In case of citations of the article, the source must be clearly indicated.

003

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PREFACE

Thinking over the second Newton's law and Einstein's GR, we must come to the question what the reference frames or, what background are to be considered, in relation to which the acceleration of a respective accelerated mass object should be taken.

That is to say not only from mathematical, but also from physical point of view. Located far from the respective mass object, we will of course believe, that the best object to connect the reference frames system with it, will be some stable cosmic object (like a star), since it gives us chance to define exactly the object's trajectory (mathematical standpoint).

In case however, we were located somewhere in a free space, closely to the object, we would prefer to connect the reference frames system with our position (we can of course define our position with the relation to the stable cosmic objects). Besides, located closely to the object, we are much more aware of the fact that the force we need to accelerate the object serves not to overcome the resistance of the remote cosmic objects, but to overcome the accelerating resistance of the space (spacetime structure) itself. That is, the accelerating force is not required to increase the object's speed with respect to the remote objects, but to increase its speed with respect to the spacetime structure (substance) in that it is immersed and, of that is created (physical standpoint).

The space itself therefore must be understood as an entity that really exists. Not only as the background, but also as the substance responsible for all space-time phenomena (we shall see later, that the mass must be considered as one of them). Under these circumstances, although we do not see it, the space becomes the natural place, where we may locate the systems of the reference frames, to study the motion of the objects. In some cases (for instance inside gravitational fields) the motion of the mass objects cannot be detected if the reference frame will be connected with the cosmic objects, but it will have to be connected with the space.

At that time already, when the Special relativity was acknowledged, admitting the time dilation and length contraction, even long before, when the theories admitting various space geometries (or the space curvature) were accepted by scientists, the fact that the spacetime continuum has its own structure was accepted. We can hardly imagine the curvatured spacetime without the idea that the things deformed in a curvatured spacetime are firmly bound up with it.

We can conceive the space as the continuum created by the standing undulation of the primary substance. It would look like a collection of the oscillating wave packets (spacetime cells). The number of space-time cells in a predefined distance (space density) and the frequency of the cells (time density) are the quantities responsible not only for the space-time curvature, but for the whole physics. The following three works are based on such quantized conception of the space (space flow theory):

THE SPACETIME PHENOMENA part one

Relativity

dealing with

interpretation of the length contraction (or dilation) as a consequence of the change of the density of the spacetime cells,

interpretation of the time dilation (contraction) as a consequence of the change of the frequency of the standing waves of the spacetime cells,

interpretation of mass by means of the flowing spacetime structure,

interpretation of the mass particles by means of a very dense spacetime structure flowing into singularity.

THE SPACETIME PHENOMENA part two

Gravity due to Space Flow

dealing with

interpretation of gravity as an accelerated motion of the spacetime structure into a mass and

THE SPACETIME PHENOMENA part three

Gravity and Mass Distribution inside Gravitational Objects

showing

how gravity, space density and mass distribution inside gravitational objects are influenced by mass specific density of the individual mass layers under the surface of the gravitational objects.

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004

THE SPACETIME PHENOMENA PART ONE

The paper deals with the interpretation of the relativistic phenomena on the principle of the variable space and time density.

RELATIVITY

by F.Stefanko

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The inertial and gravitational forces are of the same nature, defined by the same laws. This principle was formulated by Albert Einstein, in consequence of the discovery of the equality of inertial and gravitational mass. The obvious conclusion from the principle was drawn and applied in this work : In fact, the gravitational force is caused by the change of speed of spacetime structure, falling into a mass. The idea gives chance to explain gravity and to look differently into inside of space, time and mass.

This is Part one of the work, bringing mainly calculations of the galileian projections of the basic physical quantities into different reference frames.

In Part two of the work gravity is explained by means of the spacetime structure falling into a mass.

Part three deals with gravity and mass distribution under the surface of the gravitational objects.

PART 1 MAP

INTRODUCTION

TRANSFORMATION EQUATIONS OF LENGTH AND TIME

DERIVED TRANSFORMATION EQUATIONS

AREA, VOLUME, SPEED

SPACETIME DENSITY

SPEED SUPERPOSITION

ACCELERATION, LENGTH AND TIME CONTRACTION AND DILATION

SPACEFLOW, MASS

LINEAR MOMENTUM, FORCE

KINETIC ENERGY

Author

March 17th 2001

AUTHOR

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1.Introduction

There are two inertial reference frames shown in Fig 1, defined as follows:

Fig1 Two inertial reference frames with relative speed vo along x direction

- the unprimed frame,with the starting point 0

- the primed ( ' ) frame with the starting point 1. The coordinate x, of the frame is in the same line with the coordinate x of the unprimed frame. We take the primed system to be moving at a speed vo in the positive x direction with respect to the unprimed frame. The other two carthesian coordinates (y,z,y',z') are not shown.

Suppose the starting points 0 and 1 are identical at time t = 0. A flash of light is iniciated at t=0 in the two starting points in x direction. The light beam reaches point 2 at time t. The distance the beam travels in the unprimed frame is c*t, where c= 2,9997··· *10^8 ms-1 is the speed of light in a vacuum, considered by scientists to be constant in all inertial reference frames. Within the same time interval the primed system starting point 1 has passed the displacement vo*t, and the light inside the primed system has passed the displacement given by the length of the abscissa 1 - 2. This displacement however is of vo*t shorter than the displacement passed by the beam of light inside the unprimed system. The problem and great surprise arises when performing the speed measurement, because the same light speed magnitude is measured in both reference frames. Albert Einstein, perhaps the most famous scientist of the twentieth century, published his Special theory of relativity based on two postulates:

- The laws of physics are the same in all inertial systems. No preffered inertial system exists.

- The speed of light in a vacuum is the same in all inertial systems.

Using the two postulates and Lorenz transformation of coordinates Einstein derived a set of equations to apply when transforming variables between two reference frames in a relative motion. They give rise to some fascinating relationships and phenomena, like time dilation, length contraction and the mass increase, as viewed by observers in two different reference frames.

Now, despite the Special relativity is supported by experimental evidence, people find that Special relativity is not so difficult to understand , as it is hard to believe. Partly because its conclusions and predictions are outside of everyday experience and partly because it does not offer explanation.

2. The fundamental considerations

Space and time of the primed system differ from the space and time of the unprimed system. The space in direction 1 - 2 seems to be of higher density.The following conclusions can be derived from Fig 1 if the change of the space (or spacetime) density is taken as a reason making to keep constant speed of light in a vacuum possible.

2.1 The 1cm long abscissa, or bar (made of a material breathing with space) in a primed frame will be measured shorter than 1cm provided that the measurement is performed by the ruler from the unprimed system, that does not adapt on the space density of the primed system (or does not breathe with the space). And, the 1cm abscissa in an unprimed frame will be measured longer than 1cm if the ruler is calibrated in the primed frame and does not breathe with the space. However when the bar is measured by the ruler which breathes with space, the 1cm abscissa will stay 1cm long in both cases.

In case, however, when the 1cm abscissa (or bar) made of a material not breathing with space and calibrated for unprimed system was removed into a system of a higher space density, its length would be measured there :

- longer , if measured by the ruler breathing with space

- the same , if measured by the ruler not breathing with space and calibrated for the system of the lower space density (unprimed system now),

- and shorter , if measured by the ruler not breathing with space and calibrated for the system of a higher space density (primed system now).

And, of course, when 1cm abscissa (or bar) , made of a material not breathing with space and calibrated for primed system (system with higher space density now) was removed into unprimed system (system of a lower space density now), its length would be measured there:

- shorter, if measured by the ruler breathing with space,

- the same, if measured by the ruler not breathing with space and calibrated for the system of the higher density (primed system now),

- and longer, if measured by the ruler not breathing with space and calibrated for the system of a lower space density (unprimed system now).

This "gedanken" experiment could be carried out by the only ruler as well, equipped for three modes of the measurement:

a

In the 1st position of the control switch of this sophisticated meter, the ruler breathes with the space. By means of the ruler switched to this mode, the 1cm abscissa breathing with space is calibrated in both frames, and the following measurement are carried out:

aa

the length of the 1cm bar breathing with space, in both frames. The measurement shows 1cm in both cases.

ab

the length of the 1cm bar not breathing with space and calibrated for the system of lower space density. The measurement shows :

aba

the length of the bar =1cm in a frame system of lower space density

abb

the length of the bar > 1cm in a frame system of higher space density.

ac

the length of the 1cm bar not breathing with space and calibrated for the system of higher space density. The results show :

aca

the length of the bar < 1cm in a frame system with lower space density

acb

the length of the bar =1cm in a frame system with higher space density.

b

To the 2nd position the ruler is switched in a frame system with lower space density. In this mode the ruler stops breathing with the space, and keeps the scale calibration for the system of lower density. Then the following measurement is carried out :

ba

the length of the bar =1cm if the bar breathing with space is measured in a frame system of lower density,

bb

the length of the bar < 1cm if the bar breathing with space is measured in a frame with higher density,

bc

the length of the bar =1cm, if the bar not breathing with space and calibrated for the frame with lower space density is measured,

bd

the length of the bar < 1cm, if the bar not breathing with space and calibrated for the frame with higher density is measured.

c

To the 3rd position the ruler is switched in the higher space density. Now again the ruler stops breathing with the space,however it keeps the scale calibration for the system of higher density. The length,s measurement shows the following results :

ca

the length of bar > 1cm if the bar breathing with space is measured in a frame of lower density,

cb

the length of bar =1cm if the bar breathing with space is measured in a frame of higher density,

cc

the length of bar > 1cm, if the bar not breathing with space and calibrated for the frame of lower space density is measured,

cd

the length of bar > 1cm, if the bar not breathing with space and calibrated for the frame of higher space density is measured.

2.2 Considering that the basic physical laws of motion and gravitation are pointing at a close connection of the mass and spacetime, we may expect that all material objects do breathe with the spacetime structure. All physical phenomena not only take place in the spacetime continuum, but they are directly connected with the spacetime structure. This is why all physical quantities and the laws of physics may be considered as the same inside of all inertial systems, in a similar way as the 1cm abscissa length is measured (by the meter breathing with space of course,because it is made of a material breathing with space) the same in the space of different density.In case only when one physical phenomenon (or quantity) is influenced by the phenomena (or quantities) from different reference frames, and contemporary or "con-space" events are necessary to be determined, the physical quantities have to be transformed to the same scale. The typical example of such case is the resultant speed of the speed components from different reference frames. Another phenomena that might be considered as a reason to modify the laws of physic are:

- possible existence of another (or paralel) spacetime continuum. This theme is not delt with in the paper. The possible existence of another spacetime continuum however, especially the spacetime of a very low density, gives an advice how to travel at a speed many times exceeding the speed of light.

- the existence of the modified spacetime structures, like for instance in a gravitational field.

The distance "l" the light has travelled in a spacetime structure within given time interval can be defined as a number of the spacetime cells travelled by photon within time unit, and lined up in a direction of the speed vector, which is the same in all reference frames. This is why the distance "l" is the same in all reference frames, not depending on the space density (see par. 2.1/aa) . Looking at the distance "l" however from the frame system of another density, we can see, or measure the distance < l or > l, acc. to par. 2.1/bb or 2.1/ca.

The bar or the ruler not breathing with space, as they are described in the "gedanken experiment" can hardly be made of a material substance. Therefore probably the only substance that can be used to construct the bar not breathing with space is the space structure itself. We can imagine that the abscissa 0-1 in Fig1 is defined :

- by the length dimension L' of the primed system density space

- or by the length dimension L of the unprimed system density space.

Then, looking from the unprimed system, we can understand L' as a bar not breathing with space and calibrated for the primed system. And, looking from the primed system, L can be understood as the bar not breathing with space and calibrated for the unprimed system.

There is one known way only how to detect the change of the spacetime density and how to detect or measure the length of the bar in scale of the reference frame system of a different space density. It is light (or any other suitable) radiation. For the reason only that the light beam travels on the shortest way between two points of the space, we can construct the telemetering ruler not breathing with space.

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3. The transformation equations of the length and time

3.1 Length

Length of the abscissa breathing with space

l' = l

(1)

l'··· the length of the abscissa breathing with space in the primed frame

l··· the length of the abscissa breathing with space in the unprimed frame

or, in general, lm = ln.

(2)

{lm}n

stands for the length of the abscissa in a frame "m", measured by the ruler not breathing with the space and calibrated for the frame "n".

stands for the density of the space. This quantity is applied instead of the "space curvature",frequently used to indicate the spacetime change. It means the number of the spacetime cells, or the wave packets, divided by the volume, they occupy. When measured by the instruments breathing with the space, the density would stay the same, and it is . We can take this density. For our considerations the third root of the ratio of the "m" to "n" systems space densities is used, when measured by the instruments not breathing with the space and calibrated for "n" system , designated as .

Remark: The other relevant explanation of the space density or space curvature would not abolish the equation (2).

3.2 Time

Time events breathing with spacetime

t' = t

(3)

The equation (3) says that flow of time is the same in different spacetime structures when measured by instruments breathing with spacetime structures.In other words, any physical quantity in course of the same physical phenomenon, taking place in different spacetime structures, reaches the same value at the same time, measured by the instrument breathing with spacetime structure. However when time is measured by instrument not breathing with spacetime, the time intervals at which the physical quantity mentioned reaches the same values, are different (are not contemporary).

t'··· time in the primed frame

t'··· time in the unprimed frame

or, in general, tm = tn.

(4)

{tm}n

··· time elapsed in the frame "m", measured by the clock not breathing with the time (or spacetime) and calibrated for the "n" frame.

··· the time density. It means the number of the spacetime oscillations in the frame "m" within the time unit that has elapsed in the frame "n", divided by number of the spacetime oscillations fixed to define the time unit.

Remark: The other relevant explanation of the time density would not abolish the equation (4).

Taking the time unit equal to one oscillation , we have :

when time (number of oscillations) is measured by the clock breathing with time,

does not equal 1 in general, when detecting the number of the spacetime oscillations in frame "m" within the time unit measured by the clock not breathing with time and calibrated for "n" frame time unit.

For our considerations the ratio of the "m" to "n" systems time densities is used, when measured by the instruments not breathing with time and calibrated for "n" system , designated as .

3.3 Motion of one object in two reference frames

< It seems, the space and time in two of more spacetime structures occurring in the same place, appear to be not breathing with the other spacetime structures, in a similar way as an abscissa not breathing with space is defined in paragraphs 2.1 and 2.2. The following illustration shows that the length of abscissa lm of the system M , not breathing with the space of the system N can be measured as the length Lnm in the system N (by the instrument from system N, breathing with space), and that similarly the abscissa ln can be measured as Lmn in the system M. In the same way the time intervals Tnm and Tmn can be determined.

To discuss more thoroughly the con-spacetime events, imagine the motion of the objects in two the following reference frame systems (see Fig2 ) :

- Reference frame system M, moving at a constant speed vm/o with respect to a primed system,

- And the frame system N, of the same space and time density as there are in an unprimed system, but moving at the same speed vn/o = vm/o together with M system.

Let the object M move in M-frame at a speed vm = 0,5 m/s. The motion covers the distance lm = 2m at time interval 4s. The same distance ln might be travelled at time interval tn = 4s by another object, N, moving in N-frame at the same speed vn = 0,5 m/s. The two object mentioned however are not found on the same place at the same time, because

and therefore, looking from frame N, we can find :

- object N on the distance 2m at time tn = 4s

- and object M on the distance 1m at timetm = 4s

Looking for the object M in N-frame, we have to take into consideration that

1. at time interval tm = 4s in M-frame, the time interval only

has elapsed in N-frame , and therefore

(5a)

where

Tnm (Tmn) is the time interval in frame N (M) , corresponding to time interval in frame M (N).

2. and, that the distance lm =2m in M-frame is detected as

Fig 2 Motion of one object in two reference frames

in N-frame, and

(5b)

where

Lnm (Lmn) is the distance in frame N (M), corresponding to the distance in frame M (N).

Now , starting from time interval Tmn = 4s in M-frame we can see that object has travelled the distance

in M-frame, and the same object is found in frame N :

- at the distance

- and at time

Taking:

where means speed in frame N, corresponding to the speed in frame M(it may be used in frame N for superposition, as a galileian increment) we have

and, in general,

(5c)

The equations (5a), (5b) and (5c) represent the transformation equations between M and N reference frames. The frame N, moving at the same speed with frame M, but having the same spacetime density as the unprimed frame, is imaginary only. But it will become real, if we put it into unprimed system, and take quantities Lnm, Tnm, and as suitable for galileian transformation in N-frame.

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4. The derived transformation equations.

4.1Area (s)

ds' = ds, or, in general, dsm = dsn

(6)

Con-space area:

(6a)

4.2Volume ()

or, in general,

(7)

Con-space volume (V):

(7a)

<

4.3 Speed (v)

v' = v or, in general, vm = vn

To precede possible misunderstanding , the meaning of the speed v or v' is the following:

1. When a body is moving at a speed v in the unprimed frame, the observer from the primed frame can perform the measurement of this speed (not the resultant speed) by the instruments breathing with the spacetime :

1. from the primed frame, after the primed frame has been accelerated or braked, to eliminate the relative motion between the frames,

2. or after the observer has accelerated, or braked, to eliminate the relative motion between the frames.

In both cases the measurement shows the same magnitude of the speed, now designated as v'.

2. If a body was moving at a speed v' in the primed frame, and the observer from the unprimed frame performed the similar measurement of the speed v, he would find out, that v' = v as well.

The speed in a frame M, measured by the instruments not breathing with space and time and calibrated for the time and length units of the N frame, may be expressed :

(8)

and the con-spacetime speed calculated from con-spacetime length and time is defined by equation (5c).

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4.4 The spacetime density.

Taking into consideration paragraphs 3.3 and 4.3 we are now able to find out, that we may transform the distance and speed from the primed reference frame M to the reference frame N, moving together with the frame M at the same speed with regard to the unprimed frame, but unlike with it, having the same spacetime density as the unprimed reference frame. These transformed quantities may be dealt with in the unprimed reference frame in accordance with well-known galileian transformation. In this paragraph the reference frame N is taken as an unprimed frame and the transformed quantities Lnm and nm (see equations (5b) and (5c)) as galileian increments to the distance and speed in frame N.

The light propagation in common case, in unprimed and primed reference frames is shown on Fig 3 (below). The primed reference frame M moves at a speed vm/n with respect to the unprimed frame N. At time t=0 the starting points of the frames N and M are identical. At that moment the light beam is iniciated from the starting point (no matter whether from N- or M-point) at an angle n in anticlockwise direction from the vector of the speed vm/n. The light beam travels at the same angles n= m in both frames,when measured by the instruments breathing with the spacetime. If the leading of the light beam photons was strong enough, we could make it to pull two silk threads, one from starting point N and another from starting point M. Let the threads are of the same quality, breathing with spacetime and marked by the scale of length.

Fig 3 The length transformation

The observer from the frame N would see the dragging photon at the point X after time tn has elapsed. He would measure at that moment (by the instruments breathing with spacetime)

- the length of the distance NX amounting to the value ctn (product of the speed of light and the time elapsed )

- the distance NX directly red on the scale of silk thread, amounting to the same value ctn

- the angle n between speed vector vm/n and the silk thread NX

- the length of the silk thread MX of the value

where

t/m/n and s/m/n

are the space and time densities in direction MX

m/n

is defined as spacetime density,

- the length of the distance NM, amounting to vm/n*tn

- The angle nm between vm/n and the thread MX, different from n (higher in this case) in general,

- And he could calculate the speed of light photon travelling in M-frame (that of course equals to the value c in M-frame), transformed to N-frame, as

The observer from the frame M would see the thread MX at an angle m= n with respect to vm/n. This is why the dragging photon is situated in point P for the M-observer. In fact, points P and X are identical and M-observer does not see angle nm. He would measure at the same moment (by the instruments breathing with spacetime)

- the length of the silk thread MX = MP of the value Lmn= Lnm* s/m/n=ct*t/m/n=ct

- the distance MX = MP, directly red on the scale of silk thread, amounting to the same value

- the angle between vm/n and thread MX = MP of the value m = n, as mentioned above.

Looking back to starting point N, he would see

- the distance NM of the length vm/ntn*s/m/n (vm/ntn*s/m/n=Lmn - the distance travelled by the point N with regard to frame M).

Remark : s/m/n here is the spacetime density in direction MN.

- the distance NX = NP of the length ctn*s/m/n ( ctn*s/m/n=Lmn - the distance ctn transformed from N to M reference frame)

In general the speeds

- vm/n , expressing the relative motion of the primed system with respect to the unprimed system,

- and vx/m , expressing the speed of the object inside of the primed reference frame,

give the resultant speed vr/x/n , defined as galileian vector superposition of the speeds vm/n and vx/m / m/n/ nm ,

where

(9)

is the spacetime density defined as ratio of the space to time density in the frame M at the angle m in anticlockwise direction from the vector of the speed vm/n. In N frame the angle nm corresponds to the angle m.

We can simply derive from Fig 3 that

(10)

Respecting the triangle NMX in Fig 3 , we may write :

and eliminating time, we obtain

(11)

and hence

(12)

Now substituting for the angle from equation (10) in equation (12), we obtain:

(12a)

The equations (12) and (12a) say that the spacetime density of the primed system spacetime continuum depends on the angle. We may state that the spacetime of the primed reference frames is anisotropic for the observer from another reference frame. The equations (14) and (14a) give the following solutions for the four basic directions :

a/

(13a)

(13b)

b/

(13c)

(13d)

c/

>

(13e)

(13f)

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4.5 The speed superposition

It can be derived from Fig 4:

and,

(14)

wherem/n/nm is the spacetime density acc. to formula (12), or (12a).

Substituting for angle from equation (10), we obtain :

(14a):

(14a)

where m/n/n is the spacetime density acc. to formula (12) or (12a).

It can be derived

and therefore,

(15)

The equation (14) and (14a) give the following resultant speed for the four basic directions:

(16a)

(16b)

(16c)

(16d)

(16e)

It can be shown that:

Substituting c for vx/m

we obtain vr/x/n =c

Substituting c for vm/n we have

Taking vr/x/n=0 in the equation (16e), it is vx/m=vn/m , and we obtain:

(17)

where

vn/m

is the speed of the N reference frame relative movement with respect to the M reference frame, and,

vm/n

is the speed of the M reference frame relative movement with respect to the N reference frame.

Considering the equation (17) and looking from the unprimed systems N at objects M, moving at speed vm/n with respect to the N systems and comparing this speed with the speed vn/m of the frames N with respect to the objects M, measured by observers staying in objects M, we can find out the reference frames systems at which in any case (at very low speeds as well) the inequality vm/n > vn/m stays true. Such reference frames systems do not move with respect to the spacetime structure and may be considered as preferred (or basic). This discovery is in contradiction with one of the fundamental principles on which the Special theory of relativity is based.

Respecting the derived equations, we may say, that while speed of light in a common reference frame reaches value c in all directions, the galileian projection of the speed of light from one reference frame to another reaches different value in general, depending on an angle of a light beam with respect to direction of a respective frame speed with reference to a frame into which the light speed c is projected.

In consequence of anisotropic distribution of the spacetime density in a primed frame it is necessary to remind, that the calculation of the spacetime densities and resultant speeds derived for motion of a reference frame M in the preferred frame N may be used for any two reference frames, provided that calculating relations between frames N and M, orientation stays the same. The angles must be related to the same speed vector. The results of calculations however do not give results explicit enough for critics of the Special relativity, because the speeds vm/n and vn/m must be exchanged one with another when M is taken as a reference frame instead of N. In case the spacetime densities in common frames N and M and the speed of their relative motion were calculated with relation to a preferred reference frame, the results would become explicit. There are evidently quantities and phenomena requesting to be calculated with reference to the preferred frame, as potential energy and gravitation. On the contrary, another quantities, like acceleration, force, linear momentum and kinetic energy, in a primed frame, do not depend on a primed reference frame speed with respect to the preferred frame. The problem will be dealt with perhaps in part two of this work.

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4.6 Acceleration (a)

A physical mechanism gives (by means of the force fm ) the acceleration am within time tm to the object of the mass mm in M reference frame. The same physical mechanism applied in N reference frame gives the acceleration an=am at time tn=tm (by means of the force fn=fm ) to the object of the mass mn= m m .

(18)

It means, that the same physical actions in different reference frames will cause the same acceleration: The physical actions mentioned however are not contemporary. Looking from frame N at the object M just accelerating in frame M, we can observe this action as a con-spacetime event, characterized by the fact that

in general, due to different space and time densities in reference frame M. We obtain:

(19)

or,

(20)

At t/m/n / m/n not changing with time we obtain:

(21)

The contemporary event's time interval Tmn = tn * t/m/n in M-frame is corresponding to time interval tn in N-frame. If acceleration an in N-frame is applied, the object is accelerated to speed vn within time tn . Looking from frame M, the object is accelerated to speed mn = Amn * Tmn = vn * m/n within contemporary time Tmn . At time tm = tn however, the speed vm = vn is reached in M-frame:

vm = Amn tm = an tm = vn

Amn tm = an tm

Amn = an

(22)

The equation (22) says, that acceleration of a mass object is the same with respect to any inertial reference frames.

Respecting equations (19) we may write:

(23)

And we obtain the following equations defining relations between space, time and spacetime densities :

(24)

(25)

4.7 Length and time dilation and contraction

Length and time dilation and contraction in primed reference frames

According to equations (12a) and (25) we have

(26)

(27)

Equations (26) and (27) give :

Substituting t for n , and m/n/n from equation (12a) for m/n/nmi n equation (10), we obtain

where nm now represents an angle in N-frame corresponding to the angle t in M-frame. Using the equivalent marking t for this angle, we obtain

(28)

The angle t in M-frame is detected in N-frame as t and vice versa, in consequence of differrent geometry.

Applying equations (5a) and (5b) we have (see Fig 5):

(29)

(30)

The inequalities (29) show that time and length in a primed (unprimed) frame are contracted (dilated) for the observer from unprimed (primed) frame at

or, at

The inequalities (30) show that time and length in an unprimed (primed) frame are dilated (contracted) for the observer from primed (unprimed) frame at

or, at

Length and time dilation in moving reference frames

A bar-stick X_1-X_2 breathing with space, not moving with respect to M-frame, is situated in this frame at an angle a with reference to a vector of the speed at which M-frame moves with reference to an N-frame (see Fig 6). The length X_1-X_2 is drawn in units of the N-frame.

Fig 6

All points of the bar-stick X_1-X_2 are moving at a speed nm=vm/n with reference to N-frame, and, the frame N is moving at a speed (see equation 17)

(m/n/ is the spacetime density at an angle )

with reference to frame M.

At an angle nm (in N-frame) however, all bar-stick points are moving at a speed nm=vm/nCos( nm) in direction of the bar-stick line with reference to N-frame, and frame N is moving at a speed

in this direction with reference to frame M. Spacetime density m/n/(+) stands for density at angle + :

The length of the bar-stick in N-frame:

The con-spacetime length of the bar-stick in M-frame:

We can see that Lmn < Lnm for Cos > 0 .

In Fig6: Lmn = MX_2 = NX_3 = Lnm. This is for the reason only that the bar-stick X_1 - X_2 in M-frame is drawn in units of the N-frame. In fact (Lmn = MX_2) < (Lnm = NX_3).

Space and time densities

Designating M -frame space density as

and taking into consideration that spacetime is symetrical with reference to the axis x, we obtain

(31)

The equation (31) is valid for

(31a)

Substituting Cosnm = 0 for nm = /2 in equation (10), we can modify the interval of the validity for equation (31):

(31b)

We also have:

acc. to equation (25),

Designating M- frame linear time density as

and, taking into consideration that spacetime is symetrical with reference to the axis x, we obtain

(32)

where the variable is defined acc. to equations (31a) and (31b).

Obviously the linear time density is not only difficult to understand, but also to measure. The clocks used in our primed system do not distinguish the anisotropic behaviour of the time flow. This is why we may assume that these clocks are showing the average time. We may designate the primed frame average time density as

(33)

Solving the integral in eq. (33) we receive

(34)

Length and time contraction and dilation

Assuming N-frame reference point is passing point X_2 in the very same contemporary moment when M-frame reference point is passing point M, we can find out, that within contemporary time interval (ending at the same contemporary moment in both frames)

- when the N-frame reference point is just passing point M (still continuing on its way through the bar-stick)

- the M-frame reference point is just passing the point X_2 (just leaving the bar-stick)

The reason is that the bar-stick is breathing with spacetime, and consequently it is dilated in M-frame, since the spacetime structure in M-frame is dilated due to lower space and time densities.

In fact, if the bar-stick length in N-frame is taken as ln = vntn = vm/ntn , then real bar-stick length ( not con-spacetime) in M-frame is the same:

lm = vmtm = vntn = ln, because vn = vm, and, tn = tm

(35)

The length lm observed from frame N can be expressed as

(36)

where s/m/n is defined by equation (31) and is defined by equation (31b).

Applying equation (32), we have

(37)

where t/m/n is defined by equation (32).

Respecting fact, that space and time densities acc. to equations (31) and (32) are lower than 1, the equations (36)and (37) say, that

- The dimensions and time, measured by the instruments breathing with spacetime, are dilated with reference to the frame own dimensions and time. It means, that the dimensions of the moving object are detected longer from our frame, than from moving object own frame. And, that the clock situated in a moving object own frame are lagging with respect to the clock in our frame.

- As observers from any inertial reference frame, we are detecting, as contemporary, the events from the past of all reference frames moving with respect to our frame.

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1st Revision : August 8th 2003 (the extent of theme not changed)

The subject of revision :

- The more thorough explanation of the theme

- Modification of the indexing

4.8 Space flow

At that time already, when the Special relativity was acknowledged, admitting the time dilation and length contraction, even long before, when the theories admitting various space geometries (or the space curvature) were accepted by scientists, the fact that the spacetime continuum has its own structure was accepted. We can hardly imagine the curvatured spacetime without the idea that the things deformed in a curvatured spacetime are firmly bound up with it.

The imagination of the spacetime structure makes possible to define the Unit flow of the space, as the number of the spacetime cells that has passed through the unit area perpendicular to the vector of the speed, within a time unit. Because the number of the spacetime cells is proportional to the volume, it is :

(29)

the unit space flow in the unit of volume per time unit

v

the speed of the spacetime cells with respect to the unit area

We have :

(30)

ds

the area differential

dQ

the space flow passing through an area differential.

Determining the space flow in the frame M with regard to frame N, the "contemporary" speed mn = v*m/n has to be used instead of v , to obtain speed proportional to the spacetime density. The speed mn defines the number of spacetime cells of the M-frame spacetime structure, that has passed in direction of its speed through a perpendicular reference area, within time unit of N-frame.

The change of the space (or, spacetime) density however brings the change of the frequency of the spacetime structure. Applying the definition of the time density from chapter 3.2, we can easily derive that the frequency of the spacetime structure must be directly proportional to the time (or spacetime) density. The higher (lower) frequency must be understood as the sign of the higher (lower) energy of the spacetime cell. From this point of view we may consider one spacetime cell as n spacetime quanta if the time density (frequency) became n-times higher (lower). This is why now the spaceflow speed (marked (v)tn) has to be considered as t/m/n times higher (lower), and we have :

(31)

where speed (v)tn

defines the distance in units of M-frame, travelled within time unit of N-frame, if the distance was defined as the lined up series of the spacetime quanta.

See Fig7a :

Fig7a The speed of the space flow

Thus

(32)

(32a)

(32b)

where

dQmn

stands for the differential of the space flow cells in M-frame, recalculated for the time unit of the reference (N) frame, and,

dQemn

stands for the differential of the space flow quanta in M-frame, recalculated for the time unit of the reference (N) frame

Space flow into a mass point

Admitting possibility of the existence of the space flow brings us to idea of the spacetime flowing from all directions to a mass point, giving chance to explain the mass point as a spacetime structure of a very high spacetime density, and, to explain the acceleration due to gravity as an acceleration due to change of the speed of the space falling into a mass point. The question where from and to is the spacetime travelling on its way to a mass point cannot be ignored in general, but may be disregarded in this work.

At an angle = the spaceflow speed v is orientated in direction with the speed vm/n at which mass point is moving with respect to N-frame. The equation (12a) must be modified for this configuration:

Respecting equation (25), we have:

(33)

Substituting for s/m/n to equation (32) from (33), we obtain:

(34)

(34a)

The area differential on the spherical area of the radius r (see Fig7b):

Fig7b

Thus

(35)

(35a)

where ln stands for natural logarithm.

We can simply derive that Qmn = Qm = Qn = 4r^2v in equation (35) represents the frame own space flow (reaches the same value in all frames).

Thus

(36)

4.9 Mass (m)

In Special relativity the following transformation equation for the mass was derived:

(37)

where M is mass of an object as measured by an observer moving at a speed v with respect to the object, and m, called rest mass, is the object's mass as measured in its own frame. This transformation equation is considered as verified, because it was confirmed by many laboratory experiments, especially on synchrotrons and synchrocyclotrons.

We can see that curve spaceflow-speed of the mass-point according to equation (36) is very similar to the curve mass-speed according to equation (37). This is why we may say that quantity of a mass is proportional to quantity of a spacetime flowing into it. The equation (36) therefore may be modified to express also mass- speed dependence:

(38)

(39)

The derived formula (38) gives the following results in comparison with formula (37) accepted by Special relativity:

vm/n / c

Mass acc. to equation (37)

Mass acc. to equation (38)

Ratio m_2 / m_1

m_1

m_2

0,01

1,000033mo

1,00005mo

1,000017

0,05

1,000835mo

1,001252mo

1,000417

0,2

1,013663mo

1,020621mo

1,006864

0,5

1,098612mo

1,154701mo

1,051054

0,8

1,373265mo

1,66667mo

1,213652

0,95

1,9281mo

3,2056mo

1,660916

0,99

2,67338mo

7,088812mo

2,651323

0,9999

4,95221mo

70,7124mo

14,27896

In common case, when object X of the mass m moves in frame M at a speed vx/m , and frame M at a speed vm/n in frame N, using equation (38) we may write

For mass of the object X, moving at a resultant speed vx/n, as detected from frame N:

(40)

For mass of the object X, moving at a speedvm/n in N frame, as detected from N frame:

(41)

For mass of the object X, moving at a speed vx/m in M frame, as detected from N frame ( it means the mass we detect moving in M frame at a speed vx/m/ m/n ) :

(42)

Solving relations between equations (40), (41) and (42), we obtain the following formulas:

(43)

(44)

(45)

The mass m of the object X, moving in M-frame at a speed vx/m reaches value Mxm when detected from M-frame:

(46a)

Dividing equation (44) by Mxm we obtain

(46)

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4.10 Linear momentum (p)

In general, it is accepted

where

dP

is the differential of the linear momentum,

v and dv

are the speed and its differential,

M and dM

are the mass and its differential.

Travelling together with an object X of the mass m moving in frame M at a speed vx/m , we cannot detect speed vx/m. Our speed with respect to spacetime structure is now vm/x. Thus the linear momentum of the object X of the rest mass m, motionless with respect to frame X, but moving at a speed vm/x with respect to the spacetime structure of the frame M may be defined as pm/x. It is the same linear momentum, as if the object X of a non-relativistic mass m was moving at a speed vx/m with respect to frame X :

(47)

Looking from frame M, we can see our own frame M moving at a contemporary speed

It means, vx/m represents galileian projection in M-frame, corresponding to the speed vm/x in X-frame. Further we obtain (see also equation (17)):

(47a)

Consequently,

(47b)

Equations (47) and (47b) define the linear momentum of the object in its own reference frame. In spite of the fact, that object is without motion with reference to its own frame, it moves with respect to spacetime structure of any other reference frame, and all kinds of interactions influencing motion of the object, are realized by affecting of this relative motion.

With reference to frame M :

where

dpx/m

stands for the linear momentum differential of the object X in M-frame, and,

Mmx and dMmx

stand for galileian projection of the mass and its differential from X to M-frame.

Substituting for Mmx from equation (46a), we can derive

(48):

(48)

In case when dvx/m is in line with vx/m, we obtain

(49)

The galileian projection of the linear momentum from M- into N-frame:

Substitution for Mn(mx) from equation (42), and for

yields :

(50):

(50)

Applying equation (12), we can express dm/n / (m/n )2 in equation (50) :

(50b)

It is dvm/n = 0 at vm/n = const., if M-frame moves without acceleration, and without rotation with reference to N-frame, and, d = 0 if the acceleration of the object X in M-frame is in line with the speed vx/m . Under these circumstances, we receive:

(50c)

Substitution for

in equation (50c), yields:

(50d)

Applying equation (49), we have in common case:

(51)

(52)

In common motion configuration X/M/N, we may write

(53)

Under the circumstances that M-frame moves without acceleration and without rotation with reference to N-frame, and that acceleration of the object X in M-frame is in line with the speed vx/m , we receive

(54)

4.11 Force (f)

The force is defined as

(55)

Dividing equation (47) by time differential dtx, we receive the force responsible for acceleration of the object in its own frame.

(56)

Dividing equation (47b) by time differential dtx yields

Since

we have

(56a)

Comparing equations (56) and (56a), we receive:

(56b)

The force acting on the object moving in M-frame, derived from equation (48):

(57):

(57)

If acceleration is acting in direction of the speed, equation (57) gives :

(57a)

If acceleration is acting in opposite to direction of the speed, equation (57) gives :

(57b)

The galileian projection of the force from M- to N-frame, derived from equation (50) :

(58):

(58)

Applying equation (50b), we obtain :

(58a):

(58a)

where (in equations 58 and 58a)

Fn(x/m)

stands for the galileian projection of the force from M- to N-frame. Direction of the force is defined by the angle nm according to equation (10), giving galileian projection of the angle from M- to N-frame resulting from vectors' superposition in equation (58),

ax/m

stands for acceleration of the object X in M-frame,

am/n

stands for acceleration of the frame M with reference to N-frame,

vx/m

stands for speed of the object X in M-frame at the angle a from vm/n,

vm/n

stands for speed of the frame M with reference to frame N,

m/n

stands for spacetime density at angle a in M- with reference to N-frame, and,

stands for angular speed of the speedvx/m vector in M-frame

Under the circumstances that M-frame moves without acceleration and without rotation with reference to N-frame, and that acceleration of the object X in M-frame is in line with the speed vx/m, we receive(see equation 50d) :

(58b)

Applying equations (51) and (52) :

(59)

(60)

In comon motion configuration X/M/N :

(62)

And finally, under the circumstances that M-frame moves without acceleration and without rotation with reference to N-frame, and that acceleration of the object X in M-frame is in line with the speed vx/m, we receive:

(62)

Remark: Direction of the vector ax/m is defined by the angle nm according to equation (10).

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4.12 Kinetic energy (w)

(63)

where

stands for scalar product of the vectors f and dl.

Applying equation (56) in case when force is acting on the object X in direction of the speed vx/m , we have

(64)

We may substitute in equation (64):

am/x

acc. to equation (56b),

dtm/x

and the following solution:

Since

for the motion at a constant acceleration ax/m in frame M it must be:

Thus

(65)

The equation (65) determines kinetic energy of an object X in its own frame, with reference to a M-frame, moving at a speed vm/x with reference to an object X.

Common equation for kinetic energy in frame M can be obtained by substitition for the force from equation (57) to equation (63) and by solving of respective integral. In case when acceleration is in line with the speed, applying equations (57a), (57b), and (63), we obtain :

(66)

Remark: We can derive :

Common equation for galileian projection of the kinetic energy from M- to N-frame can be obtained by substitution for the force from equation (58) to equation (63).Under the circumstances that M-frame moves without acceleration and without rotation with reference to N-frame, and that acceleration of the object X in M-frame is in line with the speed vx/m , we may substitute for the force in equation (63) from equation (58b), and we have:

(67)

There are two con-spacetime accelerating mechanisms bringing an object to the same speed with reference to any reference frame:

- By using the means of the object own reference frame. Energy required to reach the speed is lower (see equation 65).

- By using the means of any inertial reference frame . Energy required to reach the speed is higher now (see equation 66). Braking the object X that has been accelerated to a speed vx/m using the means of the object own reference frame, in a reference frame M, brings gain of kinetic energy.

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F. Stefanko

Skautska 1

04001 Kosice

Slovakia

E-mail address : fstefanko@gmail.com

I am obliged to inform the public that I am not a professional physicist, and, that , to start this work, I had to pluck up courage at first, to forget about many warning fingers of my teachers of physics.

The thought became perhaps the only suitable instrument for people doing fundamental research. But in case only, that it is selfpossessed and independent enough, to penetrate through spacetime structures, not affecting them,and being not affected by them.. This is the Way.

Copyright: A user may download, copy and reproduce this article, but this activity is limited to ten copies of the article. Otherwise author must be contacted. In case of citations of the article, the source must be clearly indicated.

015

GRAVITY DUE TO SPACE FLOW

The paper deals with the interpretation of gravity on the principle of the spacetime structure falling into mass particles.

THE SPACETIME PHENOMENA part two

by F.Stefanko

2 nd Revision

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- PART 2 MAP

- HOME - INTRODUCTION (just displayed page)

- GRAVITY

- Gravity of the mass point

- Basic relations

- Spacetime density

- Speed of a spacetime structure falling into a singularity

- Transformation equations of the radia in gravitational field

- Acceleration of the spacetime structure falling into a singularity

- Gravity of Earth globe

- Gravity above Earth surface

- Measurement of the radia above Earth globe surface

- Gravity of a common cosmic object

- Gravity at zero speed above the surface of a common cosmic object

- Free motion in a spaceflow line

- Light speed in a spaceflow line

- Speed of the free object in a spaceflow line

- Kinetic energy, Gravitational potential, Potential energy

- Common free motion in gravitational field

- Spherical and linear geometry

- Equations of common free motion

- The apparent change of space density

- Orbital and vertical speeds

- Confrontation Keppler's laws with space-flow theory

- Influence of relativity factor on common free motion

- Influence of relativity factor on basic parameters

- Deformation of geometry of gravitational field

- The example of calculation of orbital trajectories in solar system

- Basic parameters of sun's gravitational field

- Calculation example for planet Mercury

- Trajectories of objects in revolution around Sun

- The shape of orbital trajectories in solar system

- Orbital trajectories round characteristic radius of gravitational field

- Analysis of common motion in gravitational field

- Culminating radia

- The shift of culminating points

- The energy of free object in free motion

- How long does it take sun's light to reach Earth

- The dark matter

- Author

The paper has been published within the work The Spacetime Phenomena, and proceeds with the paper The Spacetime Phenomena Part one, bringing new concept of gravity, based on idea of the spacetime structure of a varying density and frequency.

In the paper the gravity is explained by means of a space flow falling into a mass, and on the idea of the gravitational acceleration identical with the acceleration of the spaceflow speed. This explanation of the gravitational phenomenon is in conformity with the Principle of equivalency, and besides it brings the answer on a question about the essence of a gravitational and inertial mass :

The mass, defined by means of the flow of the space is a physical quantity complying with both inertial and gravitational properties of the mass.

Detecting from any point of a gravitational field, the spacetime structure in this point flows into a mass at a constant speed. However, detecting it from one chosen orbit, the spacetime structure is accelerated, respecting the two principal conditions:

- the space flow must stay constant (proportional to a quantity of a mass into which it flows)

- the space density is increased more quickly than the time density, along with decreasing distance from the centre of gravity.

Flowing into a mass, the spacetime structure creates its own space geometry, influenced by relativistic character of its thickening. The equations only defining the gravitational field above the surface of the cosmic object are published in this paper. These equations are in compliance with the acknowledged contemporary theories as long as in the respective theory the change mentioned of the space and time densities along with radius has been implemented.

Briefly, the spaceflow theory brings the following new knowledge :

- The imagination of the variable space and time densities as mentioned.

- Gravitational field is defined

- by the frame intrinsic space flow speed (measured inside orbital reference frame the space flow is just passing through), proportional to the cube root of the mass of the gravitational object, designated as vm/x, which is identical with the escaping speed from the gravitational field.

- by the frame intrinsic radius, proportional to the cube root of the mass of the gravitational object, designated as rx. Observed from a chosen orbital reference frame, the frame intrinsic radius is measured as the common radius (rlmx), as we know and use it in our imagination of the space of the constant space density.

- The ratio Tg = rx / vm/x = 570,48 seconds may be considered to be constant in relatively weak gravitational fields (like at planets). In stronger gravitational field it is influenced by relativistic relationships.

- The acceleration of the free object in general depends not only on radius, but also on its free fall and orbital speed. The maximum acceleration of the object in pure free fall (without orbital speed) is reached at the zero speed (in the culminating point). With the increasing speed the acceleration is decreased, reaches zero when the escaping speed is reached, and becomes positive (acting in direction out of the gravitational field) in case if the object due to outer force overcomes the escaping free fall speed.

Publishing date : March 17th 2001

1st Revision : February 15th 2003

2nd Revision : February 14th 2006

The 2nd Revision offers more profound look into a common free motion, as well as it corrects some errors in the 1st Revision on this subject.

Author

- Thus the frame intrinsic speed of the free object at zero orbital speed

- moving into centre of gravity at the frame intrinsic speed lower than the escaping speed,

is accelerated with decreasing radius and at the zero radius (if possible to reach it) the object reaches the frame intrinsic speed equalling to escaping speed.

- moving into centre of gravity at the frame intrinsic speed matching the escaping speed,

stays moving at the same frame intrinsic speed.

- moving into centre of gravity at frame intrinsic speed exceeding the escaping speed,

is slowed down with decreasing radius and at zero radius (if possible to reach it) reaches the escaping speed.

- moving out of the centre of gravity at the frame intrinsic speed lower than the escaping speed,

is slowed down until it reaches the culminating point.

- moving out of the centre of gravity at the frame intrinsic speed matching the escaping speed,

stays moving at the same frame intrinsic speed.

- moving out of the centre of gravity at the frame intrinsic speed exceeding the escaping speed,

becomes accelerated with the increasing radius.

- For many reasons (like it is the comparison of kinetic and potential energy) it is important to express the speed of the object in time units of the chosen reference frame, and the length units of the reference frame which is the object just passing through (frame intrinsic length units). Such speed, designated as Zct speed (Zct - Zone of contemporary frames) is in general Sqrt(rx / rlmx) times lower (higher) than the frame intrinsic speed mentioned. It appears to be the closest to the classical understanding of the free fall speed in gravitational field.

- For the reason of the today's human imagination, enabling also to define the method 'how to measure the world', the Zcr reference frames were defined (Zcr - zone of the constant ratio of space to time density), giving posibility to express physical quantities in time and length units of a chosen reference frame. The speed expressed in such reference frames is in general Sqrt(rlmx / rx) times higher (lower) than the frame intrinsic speed mentioned.

- The motion in a direction of the gravitational acceleration as described above, must be understood as motion in line geometry. The orbital motion however is a typical phenomenon of the spherical geometry. In the paper the different time flow of the orbital motion is found with respect to the time flow of the vertical motion. Respecting this fact, the equations of the common motion in gravitational field have been derived and verified by calculation of the Earth globe motion in the solar system. The equations show that the certain shift of the culminating points of the orbiting objects appears to be the general attribute of the common motion in a gravitational field. The perihelion advance of the planet Mercury was presented as the phenomenon confirming the theory of general relativity.

- The speed of light in gravitational field appears to be :

- Zct speed : approximatelly constant, equalling to its value on Earth surface, except of the gravitational fields of extremly great or extremly small size,

- Frame intrinsic speed : inversely proportional to the square root of space density,

- Zcr speed : inversely proportional to the space density.

- The spaceflow theory of gravity brings very optimistic opinion for travelling out of a solar system. Since the time density decreases proportionally with the square root of the distance from the Sun (in direction of space flow speed), the galilean projection of a traveller speed from this interstelar space into our space (the speed in our units) is increased proportionally with the square root of the distance from the Sun in interval to approx. one half of the distance between the stars.

- Comparing the spaceflow theory and the general theory of relativity, we can tell:

- Both theories are respecting the Principle of equivalency.

- Instead of the spacetime curvature in general relativity, the changes of the space and time density have been derived in spaceflow theory, causing the relativity effects.

- In spaceflow theory different change of the time flow is derived, belonging to the respective change of length, than it is assumed in theory of general relativity.

- The spaceflow theory is not based on the constancy of the speed of light. The derived equations show, that the speed of light (except of extreme cases) stays constant only in contemporary (Zct) frame. The general relativity is based on Postulate of the frame intrinsic speed of light constancy.

- The two principal experiments confirming the theory of general relativity, the bending of the light rays, and, the shift of the culminating points of the free objects, in gravitational field, are confirmed by the spaceflow theory as well.

The work Gravity and Mass Distribution inside Gravitational Objects (as a Part three of the work The Spacetime Phenomena) has been published by now. The presented results are unexpected, amazing and shocking, invoking the phenomena from science fiction story.

Copyright: A user may download, copy and reproduce this article, but this activity is limited to ten copies of the article. Otherwise author must be contacted. In case of citations of the article, the source must be clearly indicated.

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5.GRAVITY

5.1 Gravity of the Mass Point

5.1.1 Basic relations

We came to conclusion, in chapter 4.9, that the mass of the mass particle is proportional to the flow of space into it. Admitting the existence of the flow of the space into a singularity, we can explain the gravitational acceleration by means of this flow, being accelerated on its way to the mass particle.

Travelling in a reference frame X together with its spacetime structure into the mass particle M, situated in a reference frame M, the observer can detect the speed vm/x (or vxm , emphasizing that it is the galileian projection of the speed vx/m ) of the mass particle M moving in a direction opposite to the speed vx/m of the frame X(or to the flow of the space) moving with reference to the mass particle.

Fig.8 The spaceflow speed in a gravitational field

The spacetime density of the own frame (or, the frame intrinsic spacetime density) must be detected the same in all reference frames, as discussed in chapter 2. Travelling together with the flow of space, the observer in frame X detects the spaceflow as

(101)

(102)

where rx

stands for the distance MX (between the gravitational singularity point M and the falling orbital area X), in units of the X frame, as if the globe defined by the centre point M and radius rx was filled in by the space of constant space density, the same as on the spherical area of the radius rx ,

and Q

stands for the flow of the space into a singularity M.

Fig.9

The spacetime structure falling into a singularity

Evidently must be Q = const, defined by a quantity of the mass in the mass point, if we take spaceflow as the flow of the basic (preferred) reference frame spacetime structure, because there is no reason to expect that the flow of the spacetime structure may increase, or decrease on its way into singularity. In case, however, when Q is constant, the speed vm/x, representing the movement of the mass point with respect to frame X -connected with spacetime structure, will have to be constant too, because change of speed vm/x would cause change of the flow of the space (see equation (36)). Consequently, the radius rx must be constant too (see equation 101). This consequence, ridiculous at first sight, can be explained very simply, by means of change of the space density, as shown on Fig.9.

This is why we may say, that, travelling together with the spacetime structure into a mass singularity, we are detecting constant speed vm/x, constant radius rx, and, of course, constant spacetime density as well.

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5.1.2 Spacetime density

Being situated in a chosen orbit (in a chosen frame, not moving with respect to a singularity point M, and trying to measure radius rx of the spacetime structure passing through any another common orbit ), we must find out that we can measure only the galileian projection of the respective radius rx into our chosen orbit, because the instruments, we use, are usually breathing with the spacetime structure. See Fig.10.

Fig.10 Space density in gravitational field

Generalizing the relation between radia rmx and rx rx = rxm, because it is galileian projection of the radius rm into the frame X of the falling spacetime structure) from Fig.10, we obtain:

(103)

where stands for the space density due to geometry of the spacetime structure in a gravitational field.

In common case the following circumstances have to be taken into consideration:

- The spacetime density depends on direction in general. For our considerations a radius suitable to calculate the orbit surface in equation (101) must be used, determined by the space density in a direction perpendicular to a vector of speed vx/m. To calculate the speed vx/m, the space and time densities in a speed direction must be known.

- The relativistic behavior of the spacetime structure must be implemented.

Respecting equation (5b), we may write:

(104)

where

rtmx

stands for a radius in units of a chosen frame, determining the orbital surface of a common orbit,

rlmx

stands for a radius in units of a chosen frame, determining the distance between the singularity point and the common orbit,

stands for a relativistic space density in a direction perpendicular to a speed direction, and,

stands for a relativistic space density in a direction of the spaceflow speed.

Substituting the space density at an angle and 0 acc. to equation (31) for the relativistic density in equation (104), we obtain:

(105)

where

vm/x

is defined by equation ((102)), and

cg

stands for the speed of light in a respective common orbital frame M (we do not know yet, whether the speed of light stays constant, or varies along with the space density).

And, substituting from equation (105) to (104) we have:

(106)

(107)

The equation (107) defines the space density of the spacetime structure tn the gravitational field. The space density is increased with the decreasing radius. Respecting the equation (23), we can derive, that the spacetime (or time,) density of the spacetime structure in the gravitational field equals to the square root of its space density acc. to equation (107).

The space density of the own frame (frame intrinsic space density) equals to 1. This is why we can modify the equation (106) to obtain the radia measured inside of the own frame (the frame intrinsic radia):

(107a)

where

rtm

stands for the frame intrinsic radius determining the frame intrinsic surface of a common orbit, and,

rlm

stands for the frame intrinsic radius, determining the frame intrinsic distance between singularity point and a common orbit.

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5.1.3 Speed of a spacetime structure falling into a singularity

Definition 1

The Zone of constant ratio of space to time density (Zcr) represents the zone of orbital frames of the space density as it is defined by equation (107), but of the time density following the course of the space density (not the course of its square root). The ratio space to time density stays constant for all Zcr frames. The significant atribute of the Zcr zone appears the fact, that the frame intrinsic speed of the object in inertial motion stays constant (the inertial motion in gravitational field exists in direction perpendicular to gravitational acceleration only), due to constant ratio of the length and time units.

Definition 2

The Zone of contemporary frames (Zct) represents the zone of orbital frames of the space density as it is defined by equation (107), but of the constant time density of the chosen frame.

Designating vox/m as the Zcr spaceflow speed through a common M frame, vzx/m as the Zct spaceflow speed through a common M frame, and vx/m as a frame intrinsic spaceflow speed, it must be:

(108)

Since

(109):

(109)

where

lm

stands for the distance passed through in a common M frame,

lo

stands for the distance passed through in a chosen M frame,

tm

stands for the time interval elapsed in a common M frame,

to

stands for the time interval elapsed in the chosen M frame,

we may declare, that the Zct speed vzx/m is defined as the speed of the spacetime structure of a common space density(in a common orbit) in its own length units within time unit of the chosen frame (the spaceflow speed contemporary with the chosen frame) and, that the Zcr speed vox/m is defined as the speed of the spacetime structure of a common space density(in a common orbit), expressed in length and time units of the chosen frame.

In accordance with equation (47a), respecting that frame M moves in a preferred frame X, and in opposite direction to the motion of the frame X with reference to frame M, we have

(110)

Thus, the equation (110) may be modified into equation (111):

(111)

Substituting for gravitational space density from equation (107), we receive:

(112)

And, since it follows from equation (106) :

(113)

we also have:

(114)

Substituting for rx from equation (107a), and, for vm/x from equation (110), we obtain:

(115)

The frame intrinsic speed vm/x - the speed of the frame M motion with respect to frame X connected with the spacetime structure, measured inside respective frame X - stays constant in all orbits. The Zct speed of a common frame M through a common frame X may be expressed similarly to the equation (108):

(116)

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5.1.4 Transformation equations of the radia in a gravitational field.

There are three orbital frames of the gravitational field outlined in Fig11. In all three frames the same frame intrinsic radius (or, the frame intrinsic distance from the gravity centre) rlm must be measured, according to equation (107a):

Fig11

The relations between radia in a gravitational field

By the instrument not breathing with space, and calibrated :

For frame 1, we can measure radia :

- r1lmx2, defining position of the frame 2 in units of the frame 1

- r1lmxn, defining position of the frame N in units of the frame 1

For frame 2, we can measure radia :

- r2lmx1, defining position of the frame 1 in units of the frame 2

- r2lmxn, defining position of the frame N in units of the frame 2

For frame N, we can measure radia :

- rnlmx1, defining position of the frame 1 in units of the frame N

- rnlmx2, defining position of the frame 2 in units of the frame N

In accordance with equation (107a):

(117)

where

stands for the space density of the frame 2 with reference to frame 1.

Therefore:

(118)

Again, in accordance with equation (107a):

(119)

where

stands for the space density of the frame 1 with reference to frame 2.

It must be:

(120)

Substituting for the space density from equation (120) into equation (119), we receive:

(121)

And again, according to equation (107a):

(122)

It must be:

(123)

Substituting from equations (118) and (122) to equation (123), we receive:

(124)

Since acc. to equation (107a):

(125)

substituting for space density from equation (124) to equation (125) we have:

(126)

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5.1.5 Acceleration of the spacetime structure falling into a singularity

(Gravitational acceleration)

Standing (means: not moving with respect to a singularity point) in a common distance rlmx from a singularity, we can detect, in our own frame, that the spacetime structure is falling into a singularity at a speed vx/m (frame intrinsic spaceflow speed), and is beeing just accelerated at an acceleration g (frame intrinsic acceleration of the spaceflow speed).

Again, standing in a common frame (in a distance rlmx from singularity), and observing the spacetime structure flowing through our own frame, we could detect (if, for example, the quantum of the spacetime structure was dyed) by the length instrument calibrated on our frame (frame of the observer), and the clock calibrated on the chosen frame (frame corresponding to the distance rlm from the singularity point), that the spacetime structure is falling into a singularity at a speed vzx/m, following the equation (114),or, (115) different than the frame intrinsic speed according to equation (110). This speed may be considered as a real con-spacetime speed of the spacetime structure through a common orbital frame (in its own units), respecting changes of the space and time densities relating to a chosen reference frame.

The acceleration of the motion of the spacetime structure in frames of the Zct zone (contemporary with the chosen frame) may be defined as a derivation of the speed vzx/m by time of the chosen frame:

(127)

where

gzx/m

stands for the Zct spaceflow acceleration.

The speed vzx/m is defined by equation (114). To calculate the derivation dvzx/m/drlmx, however, we would have to know the derivation of the speed of light , cg, by the radius. For the time being we do not know it.

The derivation dvzx/m/drlmx can be resolved in a following way:

- in case of a constant speed of light cg:

(128)

- in case the speed of light cg varies along with a radius (space density):

(129)

The derivation drlmx/dto may be expressed:

(130)

Solving the equations (114), (127), (128), (129) and (130), we have:

in case of a constant speed of light cg:

(131)

in case the speed of light cg varies along with a radius (space density):

(132)

The three spaceflow speeds we have been dealing with in chapter 5.1.3, may be expressed as the speed of the space flow that has passed the same distance lm expressed in the same frame intrinsic units, within the same frame intrinsic time interval tm, but expressed as:

galilean projection of the time interval tm into Zct frame, giving time interval

for the speed vzx/m,

frame intrinsic time interval

tm

for the speed vx/m,

galilean projection of the time interval tm into Zcr frame, giving time interval

for the speed vox/m

That is,

(133)

In a similar way as the acceleration gzx/m was defined, we may define:

- gx/m

as the frame M intrinsic spaceflow acceleration, and,

- gox/m

as the Zcr spaceflow acceleration (the acceleration of the space flow, expressed in length and time units of a chosen frame).

We came to conclusion, in chapter 5.1.1, that the speed vm/x does not change with the radius. Respecting the equation (110), we can say, that

- the frame M intrinsic space flow gravitational acceleration in case of a constant speed of light will be:

(133a)

- the frame M intrinsic space flow gravitational acceleration, in case the speed of light varies with the radius,

will depend on the derivation dcg/drlmx

According to equations (133) and (107) we have

(134)

Respecting the definition formula of the Zcr spaceflow acceleration,

(135)

and the derivation (from equation (134))

(136)

we receive, by substitution from eq. (134) and (136) to equation (135), the equation defining the Zcr spaceflow acceleration:

(137)

Summarizing the results of the chapter, we can say:

1. Measuring the acceleration of the space flow by means of the meter calibrated on the spacetime structure belonging to a respective point (radius), and by means of the clock calibrated on a spacetime structure of the chosen frame (like of the frame on Earth surface), we obtain the results corresponding to equation (131) or (132). This acceleration acts in direction of the space flow (accelerating it).

2. Measuring the acceleration of the space flow by means of both, the meter and clock, calibrated on spacetime structure belonging to a respective point (radius), we would come to conclusion, that the space flow moves without acceleration, or, with acceleration (if any) due to change of the speed of light with the radius.

Note: The spaceflow acceleration due to change of the speed of light might become significant in gravitational fields of the big cosmic bodies (like stars) or in gravitational fields of the bodies of a very high mass density (like nucleons).

3. Measuring the acceleration of the space flow by means both meter and clock calibrated on the chosen frame, we would find out that the acceleration is constant (acc. to equation (137)), but acting in opposite to the direction of the space flow (slowing down the spaceflow speed).

Note: The acceleration of the body moving in gravitational field will be described in subsequent chapters.

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5.2 Gravity of Earth globe

5.2.1 Gravity above the earth surface

Assuming the even distribution of the Earth mass along with a space angle, we may consider the Earth mass as concentrated into a singularity in the middle of the Earth globe, for the investigation about the gravity over the Earth surface. The formula, derived by Sir Isaac Newton, defining the acceleration due to gravity in the Earth globe gravitational field is generally accepted:

(138)

In this formula, however, the change of the space and time density was not taken into account. The space and time were considered as the homogenous quantities, not deformed by the thickening of the spacetime structure with the decreasing radius. To speak in words of this paper, in Newton's theory it is assumed gzx/m =gx/m=gox/m. In fact, the theory of the spacetime geometry presented in this work is quite new idea, and was not yet verified. Such verification is simple in principle. It might be carried on by comparison of the contemporary time intervals in the different orbital frames, and, by comparison of the height above Earth, measured by the mechanical instrument, with the same height measured by light ray (or better, by means of the angular measurement as presented in next chapter).

Anyhow, we can tell that the Newton's formula was verified in a relatively small region above Earth surface, where the consequence of the change of the space and time densities hardly can be found out. During the space research within last 40 - 50 years however many informations have been available, confirming inaccuracy of the Newton's formula in higher heights.

The Zct spaceflow acceleration gzx/m according to equations (131) and (132) must be identical with the frame intrinsic acceleration influencing an object situated in a chosen frame (at the radius rlmx = rlm), but in case only, we are dealing with the frame intrinsic acceleration acting on the object of a zero speed with respect to a chosen frame. This is because the frame intrinsic gravitational acceleration of the object depends not only on radius, but also on object's speed (we came to conclusion in chapter 5.1.5, that the frame intrinsic acceleration of the object approaching the speed vx/m reaches zero.)

This is why we may express the frame intrinsic gravitational acceleration of an object situated at a zero speed in the chosen frame (this gravitational acceleration will be indicated go) by means of the equations (131) and (132), applying the substitution rlmx = rlm :

at cg = const:

(138a)

at cg variable:

(138b)

Since any common orbital frame may be declared as a chosen one, we are coming to conclusion that the frame intrinsic acceleration influencing the objects, not moving with respect to the gravitational object, is defined by equations (138a) and (138b). The speed of light dependency on radius, in equation (138b) however, evidently must be applied with reference to the space density, since it might give the only physical reason for the change of the speed of light. It means that, examining the gravitational field of the object different from Earth globe, the same speed of light c = 2,997924 * 10 8 ms-1 has to be expected in the orbit of the same space density as it is on Earth surface. It will be derived in the chapter chapter 5.3.2.2 that for the Earth globe gravitational field the equation (138a) may be applied with sufficient accuracy.

Our meters for direct measurement evidently do breathe with spacetime structure. Therefore considering the fact that the radius of the Earth globe was determined from the Earth globe circumference length (not by direct measurement through the globe), we may consider the radius of the Earth globe on its equator, Re=6,378x10^6m as a radius rtm (see equation (107a)):

(139)

Respecting that cg=c on Earth surface, it must be:

(140)

The acceleration due to gravity on Earth surface is considered as verified in general:

(141)

where

Me

stands for the mass of the Earth globe. It is accepted Me=5,977x10^24 kg

stands for gravitational constant =6,673x10-11m^3kg-1 s-2

Solving the equations(138a), (140) and (141), we receive:

(142)

The equations(140) and (142) show the basic parameters of the Earth gravitational field. These parameters may be modified for practical calculations in a following way:

Respecting that:

we have:

(143)

being equal to the escape speed of the Earth gravitational field,

and, respecting that:

we have:

(144)

representing the radius considered as a radius of the Earth surface orbit.

Substituting for vm/x from equation (143) and for rx from equation (144) to equations (114) and (131) and respecting that:

and, consequently rlmx=rtmx=Re, we obtain

(145)

(145a)

Further, respecting the equations (108), (110), (133), (137) and (138a), we receive:

(146)

(146a)

(146b)

(147)

(147a)

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5.2.2 Measurement of the radia above Earth globe surface

Situated in any orbital spherical area in a gravitational field, we may define our position:

1. By means of a radius rtmx, corresponding to an orbital space density in a direction perpendicular to a spaceflow speed, with reference to a chosen orbit. Radius rtmx of the same orbit reaches different value, depending on a chosen orbit in which the radius is measured (see chapter 5.1.4). The size of an orbital spherical area (in units of a chosen reference orbit) may be calculated:

(149)

The radius may be measured by means of an instrument not breathing with space.
We can hardly measure radius rtmx by direct measurement, except of its value rtmx=Re on earth surface. Since the speed vm/x have been found many times smaller than the speed of light, we may consider the equation rtmx=rlmx=Re as sufficiently accurate on earth surface, and, equation rtmx=rlmx as sufficiently accurate for orbits above earth surface.

2. By means of a radius rlmx, corresponding to an orbital space density in a line of a spaceflow speed, with reference to a chosen orbit. This radius stands for the distance between singularity point and respective orbit, expressed in units of a chosen orbit, and reaches different value, depending on a chosen orbit in which it is measured (see chapter 5.1.4). It could be measured in a corridor only, made through the Earth globe, in which the same space density had been created as it is a longitudinal space density in a respective orbit.
We can measure the radius rlmx by the same way as the distance between Earth and its Moon had been measured, and brought Sir Isaac Newton to a diccovery of the law of universal gravitation, which conforms with equation (130) for the earth gravitation. See Fig.11.

Fig.11 Measurement of the radius rlmx

Knowing the radiusRe, distance AB, and angle alpha, we can simply calculate the distance CD and the radius rlmx.

Despite we provide measurement with instruments breathing with space, we measure the distance AB with a very high accuracy, because it practically lays in a spacetime structure and the same space density as which our instrument is calibrated for.
Also the angle alpha is measured with sufficient accuracy, considering that our speed vm/x is very small with respect to speed of light.

3. By means of a frame intrinsic radius rtm. This radius is measured (and calculated) by means of measuring of the length of line of an orbit circumference, by an instrument breathing with space. The size of an orbital area (in scale of the orbit own space density) may be calculated:

(150)

Any our orbital spherical area is constantly passed through, by X-frame spacetime structure, falling into a singularity. The observer from X-frame, just passing our orbital area, detects that M-frame is moving in opposite direction at a speed vm/x. The relativistic spacetime density in a direction perpendicular to the spaceflow speed is determined by equation (105). Therefore the galilean projection of the radius rx into our orbital frame will be:

(151)

Taking into consideration very low ratio vm/x/cg, we may write for the space above earth surface:

(152)

4. By means of a radius rlm measured by an instrument not breathing with space, in a line of a spaceflow speed. This radius stands for the distance between singularity point and respective orbit, expressed in units of an orbit itself.
The relativistic density in a line of a spaceflow speed is determined by equation (105). We can derive in a similar way as in c), that:

(153)

and, for earth gravitational field:

(154)

5. By means of a frame intrinsic radius Rlm, standing for the distance between singularity point and respective orbit, measured by the instrument calibrated in the chosen frame, but breathing with the spacetime structure in all points of the radius line. See Fig.12.
Fig.12 The example of a spacetime structure of which radius Rlm consists

The structure of the radius Rlm is shown exaggerating the principle of the matter. In fact, the size of the spacetime structure packet is innumerably times lower with respect to the radius. This size is constant, of course, if measured by an instrument breathing with space. In accordance with equation (153) it may be expressed as:

(155)

Note: The equation (155) says, that, if an increment's length of the rlmx (representing certain number of the spacetime packets) is measured, by the ruler, in the chosen frame, and then, the same number of the spacetime packets, in the same line, is measured in a common orbit by the same ruler, it will show the same increment's length.

But, creating radius Rlm, every spacetime packet must contribute to the radius by the same percentage of its magnitude. It means, the contribution of the packet from any orbit to the radius Rlm must be understood as a galilean projection of a packet's size into M-frame of a chosen orbit. Therefore:

(156)

where

stands for the total space density in a spaceflow line (having its origin both in relativistic and geometric reasons) in a respective orbit,

stands for the total space density in a spaceflow line in a chosen orbit.
The total space densities may be derived from equations (105) and (107):

(157)

(158)

These space densities may be applied in case only, if all mass of which gravitational field we are examining, is concentrated in a singularity. In case we were searching for a radius in a gravitational field of a cosmic object of a real size, like Earth, we should have to take into consideration, that the basic parameters of a gravitational field, rx and vm/x are decreasing under cosmic body surface along with decreasing mass into which the spaceflow structure flows.

Substituting for the total space densities from equations (157) and (158) to equation (156), we receive:

(159)

Taking delta increments as differentials, and, assuming the constant speed of light, or, restricting the validity of the equation on the interval of a constant speed of light, we obtain by integration of equation (159):

(160)

where
Llm

stands for the distance between the radia rlmxk and rlmx, measured by means of a measuring tape, that was calibrated inside of the chosen frame (that is, in the horizontal direction on the chosen orbit).

rlmxk

stands for the lower limit of the measured interval
Taking into consideration the influence of the prospective change of the speed of light, we would have to solve the integral:

(160a)

Trying to find out the height Llmx above the Earth surface (rlmxk= rlm=rx), we usually measure it by the method described on (Fig 11). By this method we receive the difference between radius rlmx and radius rlm=rx on Earth surface:

Llmx=rlmx-rlm
In case, however, if measuring tape was used, calibrated in a horizontal position on Earth surface, and then one its end was taken up to a height Llmx, we could read on its scale, just reaching the Earth surface, the value of the height Llm. Above Earth surface (in general, at rlmx > rlm) it must be :

(161)

The equation (161) gives the following results for rlm= Re=6,378 * 10^6 m:

Llmx(m)

10^3

10^5

10^6

2*10^6

4*10^6

6*10^6

8*10^6

1*10^7

5*10^7

1*10^8

Llm(m)

9992,2

99224

928943

1739629

3105025

4229036

5184323

6014992

13899093

17948612

Llmx/Llm

1,00078

1,00782

1,07649

1,14967

1,28823

1,41876

1,54311

1,662513

3,59736

5,57146

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5.3 Gravity of a common cosmic object

5.3.1 Gravity at zero speed above the surface of a common cosmic object

In the chapter 4.9 we found quantity of a mass to be proportional to a spaceflow quantity. Therefore the equation (101) may be modified:

(162)

where

K

is constant, and,

m

stays for mass of the gravitational object

Applying equation (138b) at rlmx=rlm, we can derive:

(163)

It will be shown later, that, except of the case when vm/x approaches very closely the speed of light (in the orbital frame of the space density = 1), the equation (163)may be used in form:

(163a)

This is why (see also equations (138a) and (146b) ) we may write:

(164)

Applying equations (162) and (164) we can derive:

(165)

Since K is constant, the ratio rx/vm/x must be constant as well. Applying equations (142) and (144), we receive:

(166)

(167)

where Tg

stands for the time constant of a gravitational field. This constant must be considered as an universal constant not dependent neither on a mass, nor on a spacetime density of a spacetime structure surrounding mass. Physically may be interpreted as a time interval, the any orbit of the spacetime structure would take to meet singularity point, provided that the respective orbital spacetime density remained the same on its way to a singularity.

Applying equations (165) and (166) the equation (162) may be rewriten to an universal form:

(168)

Solving the equations (166) and (168), we obtain:

(169)

(170)

Remark:

Generalizing the equation (162), we may write:

Applying equations (165), (166) and (167) we can calculate the proportionality factor between mass and the flow of the space falling into it:

The validity of equations (169) and (170) is usually restricted on a relatively small region around a cosmic object. This is because the spacetime density in a system to which a cosmic object belongs is determined by a dominant cosmic object of the system, as it is Sun in the solar system.

The equations defining the spaceflow speed and its acceleration above the surface of a common gravitational object, can be derived by substitution of the basic gravitational parameters:

rx from equation (169), and

vm/x from equation (170),

to equations (114), (108) (131), (132), (137), (138a), and (138b) .

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5.3.2 Free motion of the object in a spaceflow line

5.3.2.1 Light speed in a spaceflow line

To explain and solve the motion of an object in a direction of the space flow we may use the relativistic factor derived for the space flow, since it was derived for this direction. However to resolve the motion of an object in the opposite direction we have to define the downward direction as a chosen relativistic frame, and express the upward motion as its the galilean projection into it. Designating

vzn/m acc. to equation (108)

as the Zct downward object speed,

vzn/m+

as the Zct upward object speed,

vn/m

as the frame intrinsic downward object speed, and,

vn/m+

as the frame intrinsic upward object speed,

we have:

(171)

The equation (171) shows that to express the upward quantities, the space density

(171a)

has to be applied instead of the space density as defined by equation (107) for the downward quantities.

On this condition, and, being aware of the fact that in the equation (132) defining the Zct downward spaceflow acceleration, the quantity cg express, in fact, the absolute value of the speed of light, we can derive, by the same way as in the chapter (5.1.5) the common equation for the Zct acceleration of the free object in the spaceflow line :

(171b)

To express the gzn/m-, the negative value of the light speed cg and, to express the gzn/m+, the positive value of the light speed cg has to be substituted to the equation (171b),

In a common orbital reference frame we may write:

(172)

where

dvzn/m

stands for the differential of the Zct speed of the common object moving in the spaceflow line( the speed of an object in a common orbital frame, in length units of the common orbital frame, within time unit of the chosen frame)

dto

stands for the frame time differential in a chosen orbital frame.

We may substitute for gx/m from equation (132), and for dto

(172a)

where

drlm

stands for the frame intrinsic length differential

Applying equation (160a), and taking drlm=dLlm, we may write:

(173)

Now, substituting to equation (172) for:

gzn/m from equation (172),

dto from equation (172a),

drlm from equation (173),:

we receive :

(174):

(174)

The equation (174) may be used to find out the speed of light cg dependence along with the radius rlmx. To do that, we have to take:

Solving the equation (174) by substitution mentioned, we receive:

(175)

Integration of the differential equation (175) is not simple.However, accepting the condition

,

we may ignore this expression, and, in a such way we obtain :

(176):

(176)

The solution of the equation (176) for cg < differs from the solution for cg > at the same radius rlmx. This is why we may expect, that on Earth surface, as well, the downward value of the speed of light differs from its upward value. We may assume that this feature is caused due to different relativistic spacetime deformation in the upward direction. In fact, the space density (see equation (107) ) for the upward motion should be modified :

(176a)

and, consequently, the equation (107a) should be modified for the upward frame intrinsic radius :

(176b)

Thus, looking for the boundary conditions to solve the equation (176), we may accept the following procedure:

Accepting c g< =c at rlmx = rlmo ,

where

(176c)

stands for the frame intrinsic radius in the space density on Earth surface,

the speed cg> = c will be reached at the radius rlmxo1 :

(176d)

Thus we obtain the solutions :

> for the downward direction (cg < 0 ) :

(177):

(177)

where

(177a)

for the upward direction (cg > 0 ):

(178):

(178)

where

(178a)

Applying the equations (169) and (170) to calculate the basic parameters of the gravitational fields, rx and vm/x, we can analyse the equations (177), (177a), (178) and (178a), and derive simplified equations for :

- c g < ..... the downward speed of light, and,

- c g > ..... the upward speed of light in the gravitational field,

which are exact enough for gravitational objects of the mass up to 10^32 kg :

(179)

(179a)

and,

(179b)

The basic parameters of the gravitational fields of some chosen objects, and their respective constants k and k 1< , are shown in the following table:

Tab1

Object

Mass (kg)

rx (m)

vm/x (m/s)

k (m/s)

k_1 (m/s)

k /k_1

Proton

1,672*10-27

4,17211*10-11

7,31334*10-14

10035,3

8,95037*10^12

0,11212*10-8

Earth

5,997*10^24

6,37928*10^6

1,11823*10^4

10035,5

8,95121*10^12

0,11211*10-8

Sun

1,989*10^30

4,42068*10^8

7,74905*10^5

10048,7

9,00861*10^12

0,11154*10-8

Common

2*10^33

4,42881*10^9

7,76331*10^6

10205,7

1,27507*10^13

0,08004*10-8

We can easily derive, that for the objects like planets and smaller, the equations (179) and (179a) may be simplified once more:

(180)

(180a)

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5.3.2.2 Speed and acceleration of the free object in a spaceflow line

We can judge from Tab1 that for gravitational objects up to 10^33 kg due to small value of the ratio vm/x/c the relativistic factors may be neglected for practical calculations (perhaps except of the calculations of the long-term gravitational influence).

Differentiating the equations (179a) and (179b), we have :

(181)

(181a)

Substituting from equations (180) and (181) to equation (171b), and neglecting the relativistic factors, we receive:

(181b)

where

gzn/m-

stands for the Zct acceleration of the object on its downward motion

And, substituting in a similar way from equations (180a) and (181a) to equation (171b), we receive :

(181c)

where

gzn/m+

stands for the Zct acceleration of the object on its upward motion

Now, designating :

(181d)

we can derive :

(181e)

(181f)

Applying c=2,997*10^8 m/s and the data from Tab1, we are able to calculate that even for the gravitational object of the mass of 2*10^33 kg the ratios g2+/1 and g2-/1 do not exceed the value of 5,1 %. This is why we can say, that for practical calculations (except of the calculations of the long-term gravitational influence) the equations (181b) and (181c) may be modified, and the Zct object acceleration defined as :

(182)

Neglecting the relativistic factors and applying the equation (182), we can rewrite the equation (174):

(183)

Resolving the differential equation (183) for the boundary condition vzn/m=vzn/mk at rlmx=rlmxk, we receive the common formula for the Zct speed of the object moving in a spaceflow line:

(184)

Applying the equation (108) for the speeds:

vzn/m

the object's Zct speed (speed of the object in length unit of the space density that the object is just passing through, within time unit of the chosen frame),

vn/m

the object's frame intrinsic speed (speed of the object in length and time units of the space density that the object is just passing through), and,

von/m

the object's Zcr speed (object,s frame intrinsic speed, expressed in length and time units of the chosen frame),

we can write:

(185)

(185a)

Since, neglecting the relativity factor,

(185b)

substituting from the equations (184) and (185b) to the equation (185) we obtain:

(186)

where

vn/mk

stands for the object's frame intrinsic speed, corresponding to its Zct speed vzn/mk, at the radius rlmxk (the boundary condition).

(186a)

and, substituting from equations (186) and (185b) to equation (185a), we obtain:

(187)

where

von/mk

stands for the object's Zcr speed, corresponding to its frame intrinsic speed vn/mk, and to its Zct speed vzn/mk, at the radius rlmxk (the boundary condition).

(187a)

The equations (186) and (187) make possible to derive the respective frame intrinsic and Zcr acceleration, applying the following equations:

(188)

(188a)

Resolving the equations (186) and (188) we obtain :

(189)

Remark 1 :

Once the object has reached the frame intrinsic speed vn/mk=-vm/x at any radius rlmxk it moves in its following course without its relative motion with respect to the spacetime structure. Therefore it must be gn/m=gx/m=0. We can see, that in this case the equation (189) gives gn/m=0. This result is in accordance with the equation (133a).

Once the object has reached the frame intrinsic speed vn/mk=vm/x (in a drection out of the gravitational field), its frame intrinsic acceleration again becomes gn/m=0 (see equation 189), and the speed vn/m=vm/x will not come back below the limit vm/x without being braked by the outward force (see equation (186). The speed vm/x therefore represents the frame intrinsic escaping speed from the gravitational field.

Resolving the equations (187) and (188a) we have :

(190)

Remark 2 :

The object moving at the frame intrinsic speed vn/mk=vm/x (without motion with respect to the spacetime structure), that is, at the Zcr speed

(190a)

does not appear to move without acceleration in Zcr frame. In fact in this frame it appears to be braked, since in this case the equation (190) gives the acceleration

(190b)

This result is in accordance with the equation (137).

Remark 3 :

Resolving the equation (190) for gon/m=0, we receive:

(190c)

This equation defines radius rlmx at which the Zcr acceleration, or braking of the object in free fall reaches zero, that is, the radius at which the object's Zcr accelelation or braking in course of its free fall has been reduced to zero and the object now begins to be braked or accelerated.

Remark 4 :

Substituting for vn/mk=0 to equation (189), we receive:

(190d)

The equation (190d) says, that the frame intrinsic acceleration of the object not moving with respect to M-frames (or, with respect to the gravitational object) is constant at rlmx = rlmxk (that is at the moment when vn/m = 0), and then becomes decreasing with decreasing radius (since vn/m goes up).

Remark 5 :

Substituting for von/mk=0 to equation (190), we receive the equation

(190e)

defining the course of the Zcr acceleration of the object along with radius rlmxk, the speed of that has become zero at the radius rlmxk (at the radius rlmxk the object has not been moving with respect to M-frames).

The examples of the object free fall acceleration calculated in accordance to the equations (182), (188) and (188a) are shown on Fig13 and Fig14.

Fig13

Fig14

Resolving the equation (186) for vn/m=0, we can derive the radius rc at which the object culminates if its motion has begun at the radius rlmxk and at the speed vn/mk of a positive value:

(191)

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5.3.2.3 Kinetic energy, Gravitational potential, Potential energy

Applying the equation (66), we can derive the equation defining the kinetic energy of the free object moving in a line of the spaceflow speed :

(192)

where

m

stands for the object's rest mass,

czg

stands for the speed of light in the Zct zone, and,

Wkn/m

stands for the object's kinetic energy with respect to the chosen frame.

Obviously it must be :

(193)

Further substituting from equation (193) and (184) to equation (192), we obtain :

(194)

Since

(194a)

we also have:

(194b)

and,

(194c)

Defining the boundary condition in equation (194) : vzn/mk=0 at rlmxk approaching the infinity,

we can derive from equation (194):

(195)

The equation (195) gives the kinetic energy with respect to the chosen M-frame, of the object of the rest mass m, falling from infinity, that is, of the object moving at the same speed as the speed of the falling spacetime structure (the speed of the spacetime structure is the upper limit of the speed the free object may reach, but in a sufficiently long distance from the infinity this limit may be considered to be achieved). Neglecting the relativity factors this speed (vx/m) may be determined vx/m= vm/x. Respecting the equation (186), we can see that vn/mk=+ vm/x at radius rlmxk. It means, to leave the gravitational field the object needs the same kinetic energy as defined by the equation (195). This is why we may define the gravitational potential as :

(196)

and the gravitational potential energy of the orbit rlmx2 with respect to the orbit rlmx1 as :

(197)

where

U_2

stands for the gravitational potential at the radius rlmx2 and,

U_1

stands for the gravitational potential at the radius rlmx1.

Thus :

(198)

The potential and potential energy calculated according to the equations (196) and (198), give results close to the results calculated in accordance with the conform physics. Unlike to the conform physics however, the difference of the kinetic energy of the object in free fall, between two orbits (rlmx2 and rlmx1) does not match the respective difference of the potential energy in general. Applying the equation (194b), we can derive :

(199)

where

Wk2-1

stands for the difference of the kinetic energy of the object in free fall, between the two orbits (rlmx2 and rlmx1), and,

vn/m1

stands for the frame intrinsic object's speed at the radius rlmx1.

The equation (199) shows that the difference of the kinetic energy depends not only on the radia of the respective orbits, but also on the initial speed vn/m1 (or, in general, vn/mk ) of the object at the initial radiusrlmx1 (or, in general, rlmxk). In case only, when vn/mk=vm/x, the difference of the kinetic energy matches with the difference of the potential energy, since in this case we have :

(200)

Analysing the equation (194b), we can derive that for the gravitational objects from nucleons to stars this equation may be simplified, with sufficient accuracy, in the following way :

(201)

We can derive from the equation (201) the difference of the kinetic energy between two orbits (the orbit at the common radius rlmx and the orbit at the radius rlmx1) :

(202)

The equation (198) may be modified in the same way as the equation (201) was derived from equation (194b) :

(203)

We can see from equation (202), that, accepting a very low inaccuracy, the difference of the kinetic energy of the free object, between two orbits, may be considered as defined by the position only of the two orbits. (The analysis shows, that this equality cannot be applied to the gravitational objects of a very high mass along with a very high mass density). The difference of the kinetic energy of the free object matches with the potential energy between the same orbits (see equation 203).

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5.3.3 Common free motion in gravitational field

5.3.3.1 Spherical and linear geometry

We can see the relations between the size of the cells of the spacetime structure on Fig15 in two orbital frames:

- In a common orbital frame at the radius rlmx, and,

- In the chosen orbital frame at the radius rx

Fig 15 The spacetime structure in gravitational field

where represents

Cm

the real spacetime structure cell in the common frame,

Cmo

the galileian projection of the cell Co from the chosen into the common reference frame,

Co

the real spacetime structure cell in the chosen frame,

Com

the galileian projection of the cell Cm from the common into the chosen frame

Do

Diameter of the cell in the chosen frame, and,

Dm

Diameter of the cell in the common frame, measured by meter not breathing with spacetime structure and calibrated on the chosen frame.

It must be:

(204)

Observing, from the chosen orbital frame at the radius rx, the object revolving at the radius rlmx around the gravitational object, we will measure (by the meter breathing with the spacetime structure) the circumference length lo within the angle alpha:

(205)

the same, as the observer from the orbital frame at the radius rlmx would measure (lm=lo) in his own frame within the same angle. This feature appears to be principal for the comprehension of the difference between the spherical and linear geometry, since in linear geometry the observer in the chosen frame will measure the con-space circumference length (galilean projection to lm):

(206)

and, the galilean projection of the frame intrinsic circumference length travelled by the revolving object in the common orbital frame at the radius rlmx into the chosen orbital frame will be:

The length interval in the chosen frame, however, corresponding to one turn of the revolving object in the common frame, equals to the value:

The object in orbital motion (perpendicular to the spaceflow speed) is passing the frame intrinsic length differential dlm within the frame intrinsic time differential dtm. Respecting the linear geometry, we may write for the galilean projection dto of the time differential dtm into the chosen reference frame :

(207)

In a spherical geometry however, since now the galilean projection of the length interval into a chosen frame is rx/rlmx times lower (higher) than it is in linear geometry, the respective galilean projection of the time differential dt'o of the time differential dtm into a chosen frame must be rx/rlmx times lower (higher) :

(207a)

Thus, we can derive for the Zct speed (speed in frame intrinsic length units of the common frame and time units of the chosen frame):

a/ in linear geometry

(207b)

b/ in spherical geometry

(207c)

The equations 207 - 207a (and, subsequently also 207b - 207c) seems to be in conflict with one another, since of course, the time differential of the common orbital motion must be uniquely determined as the one value (hence the real geometry is just one). In fact however, this contradiction is apparent only. The equation (207) has been derived for case only of the zero orbital speed, because to derive it, it was presupposed the gravitational space density same as for the motion in a space-flow line :

(208)

The equation (207a) has been derived for case only when the revolving object reaches such orbital speed (vzocr), that maintains him in a circle, without vertical motion. We can easily derive from the equations (207b) and (207c) that the Zct orbital speed for the motion in a circle will be :

in linear geometry

(209)

in spherical geometry

(209a)

where To indicates period of rotation.

Considering the equation (209a) and Fig15 we certainly must come to a conclusion, that speed v'zo = 2*PI*rlmx / To can be explained by two ways :

- The length of the trajectory l passed by the revolving object on the circle of the radius rlmx is rlmx / rx times greater (in units of the chosen reference frame) than the length lo of the trace, marked by the line connecting the revolving object with the centre of gravity, on a circle of the radius rx (the chosen reference frame). Both paths (l and lo) are passed within the same time interval.

The real frame intrinsic length of the trajectory passe by the object however is lm=l*rx/rlmx and the respective Zct speed would reach v'zo=2*PI*rx/To in a line geometry. The motion however takes place in a spherical geometry. That is why the Zct speed of the revolving object vzo=2*PI*rlmx/To must be taken into consideration.

- Thus, if we put the common circumference of the circle of the radius rx (the circle from the chosen frame of space density = 1) close to the circle of a common radius rlmx, we will have to discover that these two lines are created of the spacetime structure of the same space density (that is of the space density in a linear geometry). Let us designate this space density as the apparent gravitational space density for the calculations concerning orbital motion. For the motion in a circle (on condition that vertical speed = 0) it will then be :

(209b)

and,

(209c)

Starting common motion of the object in a gravitational field at the radius rlmx=rk and at the orbital Zct speed vzo=vzok (see Fig 15a), assuming of course some vertical displacement of the object after certain time interval, we can expect the following scenario :

- The frame intrinsic speed of the object in an apparent gravitational space density = 1 must stay constant.

- The time interval measured in a chosen reference frame (at the radius rx), within it the object passes the same path, must be inversely proportional to the radius rlmx, because the period of rotation of the revolving object, providing that its vertical shift was stopped at a radius rlmx, would be rk/rlmx times smaller than such period of rotation at the radius rk. Consequently must be :

(210)

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5.3.3.2 Equations of common free motion

Applying the equation (202) we may write the equation acceptable in a linear geometry :

(211)

where

Wkr-k

stands for the difference of the kinetic energy between the orbits at the common radius rlmx and the initial radius rk due to their motion in reference to the spacetime structure

m

mass of the object

vm/x

parameter of the gravitational field: the frame intrinsic speed of the spacetime structure

rx

parameter of the gravitational field: the frame intrinsic radius defining the geometry of the gravitational field

rlmx

common radius in a gravitational field

rk

the initial radius of just observed motion in a gravitational field

vzo

stands for the Zct orbital speed according to equation (210)

vzok

stands for the initial Zct orbital speed at the radius rk

vzl

stands for the Zct free fall speed

vzlk

stands for the initial Zct free fall speed

Substituting to equation (211) for vzo from equation (210), we receive :

(212)

Thus :

(213)

The equation (213) shows the free fall speed on condition that the time flow is not influenced by the orbital speed (at the orbital speed approaching zero). We can see, that substituting vzok=0 the equation (213) is transformed into equation (184).

To make our equations more simplified, we shall consider the initial vertical speed vzlk at a radius rk as zero. Let us find out radia at which the speed vzl reaches the zero value (the experience shows us that at common motion the zero value of the vertical speed is reached at two radia):

Under condition vzl=0, we have

(214)

Solving this quadratic equation, we receive:

(215)

(216)

The equations (215) and (216) define two radia, R_1=rk (the initial radius) and R_2=rf (the final radius), between which takes place common motion in a gravitational field.

The excentricity of the object's trajectory in a gravitational field is defined as :

(216a)

Starting its motion at vzl=0 (zero vertical motion) and, at initial radius rk, the object arrives at a final radius rf, which may be smaller, greater, or equal as the initial radius rk, depending on the size of the initial orbital speed vzok. To determine the critical value of the orbital speed vzok = vzocr, at which rf = rk, that is at which the object revolves in the circle around the centre of gravity, we have to expect, that:

(217)

(218)

In a common case rk=rlmx, since of course, each radius may become the initial one for our start of the common motion.

Thus

(219)

Hence, comparing the initial orbital speed (at vertical speed = 0) with the critical orbital speed at the radius rk (R_1), we find what kind of the common motion will follow:

In case vzok > vzocr :

The proceeding vertical speed will be set in opposite direction to the gravitational acceleration. The upward motion will stop at the radius rf > rk .

In case vzok = vzocr :

The motion will continue in a circle of radius rk.

In case vzok < vzocr :

The proceeding vertical speed will be set in direction of the gravitational acceleration. The downward common motion will stop at the radius rf < rk .

The apparent change of the space density due to orbital motion

Looking newly at Fig15a we can come to the following significant conclusion:

The greater (less) is the Zct orbital speed of the object in a common motion, the more (less) times the circumference of the imaginary circle, that might be created by one revolution of the object's trajectory on condition that its instantaneous orbital speed became constant and its vertical speed became zero, might encircle the circumference of the circle in the chosen frame (2*PI*rx).

Consequently we can tell that

at rlmx > rx

the apparent gravitational density is directly proportional to the Zct orbital speed. At the critical speed vzocr it reaches the value "1" (we already know that the motion in a circle is possible at the critical speed only) and, at the zero orbital speed it reaches the value "rx/rlmx" (the natural space density of the gravitational field)

at rlmx < rx

the apparent gravitational density is inversely proportional to the Zct orbital speed. At the critical speed vzocr it reaches the value "1" and, at the zero orbital speed it reaches the value "rlmx/rx" .

It must be therefore :

at rlmx > rx

(220)

(221)

Hence:

(222)

where k is constant. Respecting equation (221), we have

(223)

and,

(224)

Substituting for vzo fron equation (210) and for vzocr from equation (219) to the equation (224), we have :

(224-1)

at rlmx < rx

(220a)

(221a)

Hence:

(222a)

where k is constant. Respecting equation (221), we have

(223a)

and,

(224a)

Substituting for vzo fron equation (210) and for vzocr from equation (219) to the equation (224), we have :

(224-1a)

Orbital and vertical speeds in Zcr frame (in units of a chosen frame)

At rlmx > rx :

At rlmx > rx the circumference of the circle, passed by an object at the common radius rlmx, is longer (in units of the chosen frame) than the corresponding circumference in the chosen frame. Therefore it must be:

(225)

Respecting the equations (224) and (225), we have:

(226)

Angular speed

(226b)

Observing the common motion, we can detect the Zcr orbital speed (voo) rather than its Zct value (vzo or, vzok). The Zct speed can be derived from the quadratic equation (226). The following equation shows the calculation of the initial Zct speed vzok from the initial Zcr speed vook (at rlmx=rk):

(227)

Applying the equations (185) and (185a), we can derive the equation for the Zcr vertical speed vol (the vertical speed of the object in a common motion, expressed in units of a chosen frame):

(228)

Substituting from equations (210), (213) and (224) and, presuming the initial speed vzlk=0 (at the radius rk), we receive:

(229)

At rlmx < rx :

At rlmx < rx the circumference of the circle, passed by an object at the common radius rlmx, is shorter (in units of the chosen frame) than the corresponding circumference in the chosen frame. Therefore it must be:

(225a)

Respecting the equations (224) and (225), we have:

(226a)

Again, observing the common motion, we can detect the Zcr initial orbital speed (vook) rather than its Zct value (vzok). Substituting for voo=vook and rlmx=rk, we can derive from the equation (226a):

(227a)

Since the Zcr orbital speed (voo) goes down with the apparent space density, the Zcr vertical speed (vol) must go up:

(228a)

(229a)

Confrontation Keppler's laws with the space-flow theory of gravity

First Keppler's law

Statutory text: The shape of the orbit of any body orbiting the sun is an ellipse with the sun at one of the foci.

Comparison with space-flow theory: This law does not conform to a space-flow theory, even if at the orbital speeds not differring much with the critical orbital speeds the shapes of orbits are very similar to the ellipses.

Derivation: The law was derived for the motion in a spacetime structure of a constant space density. This condition can be considered as approximately fulfilled in case only of the orbital speeds not differring much with the critical orbital speeds.

Second Keppler's law

Statutory text: The line joining the planet to the sun sweeps out equal areas in equal times.

Comparison with space-flow theory: This law does not conform to a space-flow theory.

Derivation:The law was derived as a consequence of the conservation of angular momentum. We have :

(230)

where

L...stands for angular momentum

I...stands for moment of inertia

Omega...stands for angular speed

m...stands for object's mass

Substituting for voo from equation (226), we have:

(231)

We can see from equation (231) that the angular momentum is not constant, but varies with radius in a common motion.

Note: However substituting the Zct orbital speed vzo from the equation (210) instead the Zcrspeed voo into equation (230), we receive

(232)

The law of conservation of angular momentom in spaceflow theory stays valid in Zct frames only (that is, in frames in which the length units are expressed in units of the spacetime structure, where the motion takes place, and time units are expressed in a chosen frame).

Third Keppler's law

Statutory text: The square of the sidereal orbital periods of the planets are proportional to the cube of the planets' mean distance from the sun.

Comparison with space-flow theory: The law conforms to the spaceflow theory in case only when the objects (planets) are orbiting around the sun at critical speeds (in a circular trajectories). The more the initial orbital speed differs from the critical value, the more the law is incorrect.

Derivation: For the sidereal orbital period of the object orbiting around the centre of gravity at the critical initial orbital speed, we have

(233)

By comparison of the sidereal periods T_1 and T_2 of the objects orbiting at critical speeds at the radia r_1 and r_2, we receive

(234)

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5.3.3.3 Influence of relativity factor on common free motion

Influence of relativity factor on basic parameters of gravitational field

All equations defining common free motion in a gravitational field has bee derived in previous chapters on condition that the influence of the relativity of the motion (expressed by the relativity factor) was ignored. The routine calculations of the parameters of free motion are sufficiently accurate even if the relativity factor is ignored. For many calculations however, especially for gravitational fields of the objects characterized by considerably greater mass than the mass of the planet Earth, the influence of the relativity factor must be taken into consideration.

The gravitational acceleration in Zct frame (length units in a frame of the observed object, time units in a chosen frame) is defined by the equation (138b). Applying the equation (180a), we have :

(235)

where

cg

stands for speed of light in a spaceflow line,

c

stands for speed of light on Earth surface and,

rx

stands for the gravitational frame intrinsic radius.

Substituting from the equation (235) to (138b), we receive :

(236)

where

gzx/m

stands for the Zct gravitational acceleration

Let us designate factor p :

(237)

In a chosen reference frame (rlmx = rx) :

(238)

Factor p determines how the gravitational acceleration is influenced by the relativistic behaviour of the spacetime structure in a gravitational field. Unfortinately the factor p is not the constant, neither in a gravitational field of one specific gravitational object (like the Sun). Its size is affected not only by the mass of the gravitational object, but also by the distance from the centre of gravity (radius rlmx)

This fact could result in a very complicated equations describing common motion in a gravitational field. However for calculations of trajectories related to motion, taking place in a relatively narrow orbital zones, like move planets, the mean value of the factor p, taken from its values at the limit radia (rk, rf), may be considered as constant, with a sufficient accuracy.

It should be :

(239)

Alternatively to the equation (163a) we have :

(240)

So, alternatively to equation (165) we have :

(241)

In the equation (162) we presupposed that K, expressing the coefficient of proporcionality between the space flow and mass, is the universal constant. Now we can see that due to influence of the relative motion of the space flow with regard to the speed of light, the parameter K cannot be considered as universal constant, but it varies with the mass of the gravitational object. Therefore the new ratio Tg between the gravitational frame intrinsic radius and the frame intrinsic space flow speed will be :

(242)

where

Tg

stands for the new constant, influenced by the relativity factor; this constant must be calculated for each gravitational body,

T'g

stands for the original constant calculated when the relativity factor was ignored; T'g = 570,48 seconds,

rx

stands for the new gravitational frame intrinsic radius, influenced by the relativity factor,

r'x

stands for the original gravitational frame intrinsic radius, not influenced by the relativity factor,

vm/x

stands for the new frame intrinsic space flow speed, influenced by the relativity factor and,

v'm/x

stands for the original frame intrinsic space flow speed, not influenced by the relativity factor.

We can derive from the equation (168) :

(243)

(244)

and, from the equation (170) :

(245)

(246)

Deformation of geometry of gravitational field

We can derive from the equation (113) :

(247)

where

rtmx

stands for the charactaristic radius of gravitational field calculated from the circumference of any orbital circle (meaured in place of the respective orbit) with its centre identical with the centre of gravity and,

rlmx

stands for the charactaristic radius of gravitational field, defined by the distance between any point inside gravitational field and the centre of gravity, on condition that the space between this point and the centre of gravity was created by spacetime structure of the same gravitational space density (not the apparent gravitational space density) as it is in the respective point.

Substituting for cg from the equation (235) :

(248)

Since rtmx is a radius calculated from the circumference length of the circle with its centre identical with the centre of gravity and, rlmx represents the distance from the centre of gravity, the equality of these two radia should be expected. In a weaker gravitational fields they really may be considered equal. With greater mass of the gravitational body however the ratio rtmx / rlmx rises up. In a gravitational field of the Sun it has to be taken into consideration.

The growth of the ratio rtmx / rlmx in principle means that the space density in a horizontal direction of the gravitational field becomes lower than the space density in a vertical direction. Subsequently the lower horizontal space density brings, in fact, the equivalent reduction of the angle of the meridian circle in a gravitational field, below its primary value of 360 grades. Therefore reaching the angle in this deformed spacetime structure will be registered, in the non-deformed geometry (of the equal space density in both vertical and horizontal directions), at an angle greater than 360 grades. For our calculations of the Zcr orbital speed in this deformed spacetime structure therefore, we shall use (as derived before) the spacetime deformation density (as the square root of the space deformation density):

(248a)

From this point of view the equations (226) and (226a), defining the Zcr orbital speed have to be modified. The Zcr speed vood (that is the speed expressed in length and time units of a chosen frame) for the deformed spacetime structure shall be used :

At rlmx>rx, modifying the equation (226) :

(249)

At rlmx<rx, modifying the equation (226a) :

(250)

Consequently the angle speed according to the equation (226b) has to be modified :

(250a)

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5.3.3.4 The example of calculation of orbital trajectories in solar system

Basic parameters of the sun's gravitational field

The basic parameters of the Sun's gravitational field, namely its frame intrinsic radius and space-flow speed, not influenced by the relativistic relationships, should be calculated fro the equations (169) and (170). Using these equations we have :

(253):

(253)

(254):

(254)

where

r 'x

stands for the frame intrinsic radius of the Sun's gravitational field, not influenced by relativistic relationships,

v 'm/x

stands for the frame intrinsic space-flow speed of the Sun's gravitational field, not influenced by relativistic relationships,

stands for gravitational constant = 6,673x10-11m3kg-1 s-2 ,

T 'g

stands for the time constant of the Sun's gravitational field, not influenced by relativistic relationships = 570,48 seconds and,

m

stands for the mass of the Sun = 1,989*10^30 kilograms

The relativistic behaviour of the space-flow mechanism, creating gravitational field, results in a slight modification of the basic parameters, that could be neglected in common calculations, but not in the precise calculations. This "relativistic modification" is defined by means of the factor p, by the equations (237), (244) and (246). Since the factor p varies with the radius, it must be determined for each orbital zone (e.g. for the mean radius of the planet's trajectory) separately. See Tab13b-1.

Tab13b-1

Planet

Mean radius (m)

p

rx (m)

vm/x (m/sec)

Mercury

5,897000E+10

0,999104

4,423318E+08

7,746738E+05

Venus

1,082070E+11

0,999339

4,422626E+08

7,747343E+05

Earth

1,496000E+11

0,999437

4,422335E+08

7,747599E+05

Mars

2,286600E+11

0,999545

4,422019E+08

7,747876E+05

Jupiter

7,787600E+11

0,999753

4,421404E+08

7,748414E+05

Saturn

1,429000E+12

0,999818

4,421214E+08

7,748581E+05

Uranus

2,872000E+12

0,999872

4,421056E+08

7,748719E+05

Neptune

4,497600E+12

0,999897

4,420980E+08

7,748786E+05

Pluto

6,045000E+12

0,999911

4,420939E+08

7,748822E+05

Comet Halley

1,005740E+13

0,999931

4,420880E+08

7,748873E+05

Calculation example for the planet Mercury

Given parameters

The initial radius at which the planet Mercury reaches the upper culminating point (Aphelion)

rk=7,1740*10^10m

The initial Zcr vertical speed (Zcr ... in units of the chosen frame)

vol=0

The initial Zcr orbital speed (Zcr ... in units of the chosen frame)

vook=3,37220*10^4m/sec

Calculated parameters

Substituting for rx, vm/x, rk and vook to equation (227), we can calculate the initial Zct orbital speed (Zct ... length units in the frame at the radius at which Mercury occurs, time units in the chosen reference frame)

vzok= 3,806988*10^4

Substituting for rx, vm/x, rk and vzok to equation (216), we can calculate the final radius rf at which planet Mercury reaches the lower culminating point (Perihelion)

(255):

(255)

Since rk > rf, the radius rk represents aphelion (determining the greatest distance from the Sun) and, the radius rf represents perihelion (determining the minimal distance from the Sun).

Applying equation (216a) we receive for the excentricity of the Mercury's trajectory :

(256)

The apparent space density.

Applying the equation (224-1) we can calculate the apparent space density in the range of radia between rk and rf. See Fig16.

Since the gravitational space density rx/rlmx in range of radia rk - rf reaches values 6,1680*10-3 - 9,5758*10-3 (rx/rk - rx/rf), that is smaller than the apparent space density, the condition (224b) is fulfilled. Therefore the apparent density as shown on Fig16 stays valid all over the Mercury's trajectory.

The orbital Zct speed (the speed expressed in length units of the frame of the radius at which Mercury takes place and in time units of the chosen frame)

Applying equation (210) we can calculate the Zct orbital speed vzo for the range of radia rk - rf. See Fig16a.

The space deformation density.

Applying the equation (248), we can determine the space deformation density in range of radia rk - rf. See Fig16b.

The Zcr orbital speed (that is, orbital speed in length and time units of a chosen frame) in a deformed spacetime structure.

The Zcr orbital speed in a deformed spacetime structure is defined by the equation (249). The curve of Zcr, orbital speed (vood) vs radius, in the range of radia rk - rf, is shown on Fig16a.

The angle speed in a deformed spacetime structure is defined by the equation (250a). The curve angle speed vs radius, in the range of radia rk - rf, is shown on Fig16c.

The vertical Zct vzl speed (that is, the speed expressed in length units of the frame of the radius at which Mercury takes place and in time units of the chosen frame), on condition that the initial speed vzlk=0, according to the equation (213), is shown on Fig16d in the range of radia rk - rf.

The vertical Zcr speed vol

The vertical Zcr speed vol (that is, orbital speed in length and time units of a chosen frame) according to the equation (229), is shown on Fig16d in the range of radia rk - rf.

Time interval Tod of motion from the aphelion rk to the perihelion rf

Since the integral

is very complicated, it was calculated by the numerical method :

Tod=3,80125*10^6 seconds

The angle , the radius Sun - Mercury carries out during motion from the aphelion rk to the perihelion rf.

Since the integral

is very complicated, it was calculated by the numerical method :

Calculation of the parameters of Mercuru's trajectory for the motion from perihelion to aphelion

For the upward motion of the planet Mercury, from the perihelion to the aphelion, the initial Zcr orbital speed vook in non deformed spacetime structure shall be calculated from the parameters of downward motion, as the speed voo according to the equation (226) at the perihelion :

The radius rf from the calculation of the downward motion shall be now declared as the initial radius - rk.

rk=4,619260*10^10 m

Applying the equation (227) we receive

vzok=5,912491*10^4 m/sec

Applying the equation (216) we receive

rf=7,1740*10^10 m

All other parameters as calculated fot the downward motion will become identical with those fot the upward motion, including:

- The time interval Tou of the motion from the perihelion to the aphelion,

Tou=3,801025*10^6 sec

- The angle , the radius Sun - Mercury carries out during motion from the perihelion rk to the aphelion rf,

Siderical period of Mercury (period of rotation)

(257)

The advance of culminating points (perihelion or aphelion advance) within one revolution

(258)

The advance of culminating points (perihelion or aphelion advance) within 100 years

(258a)

The trajectory of the planet Mercury

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5.3.3.5 Trajectories of objects in revolution around Sun

In the calculation example of Mercury we used the speed vook (the speed voo at the initial radius rk) as the initial parameter. In fact however, the speed voo represents the Zcr orbital speed in a non deformed spacetime structure, and cannot be directly measured, because the spacetime structure in gravitational field is more or less deformed due to different space (spacetime) densities in vertical and horizontal directions. It should be preferable therefore to use the speed vood as the initial parameter, instead of voo, since it represents the real, measurable Zcr orbital speed in the deformed spacetime structure.

So, for the next calculations the initial parameters shall be defined as follows :

- the basic parameters of the Sun's gravitational field, rx and vm/x, according to Tab13b-1,

- the initial radius rk - aphelion,

- the initial Zcr vertical speed vol=0 and,

- the initial Zcr orbital speed voodk (that is, the real orbital speed vood at the radius rk).

The calculation will start by the determination of the initial value of the space deformation density (at the radius rk), in conformity with the equation (248):

(259)

Applying the equation (248a), we can calculate the initial speed vook (the speed voo at the radius rk) :

(260)

The next continuance of the calculation stays the same as in the example for the planet Mercury. Calculated parameters parameters of all planets of the solar system are shown in Tab13c-1 and Tab13c-2. It is advisable to remind that the credibility of calculated parameters might be influenced by the not quite correct choice of the initial parameters rk and voodk.

Tab13c-1

Trajectory

parameters

Mercury

Venus

Earth

Mars

Jupiter

Sun's grav. field

radius rx (m)

4,423318*10^8

4,422627*10^8

4,422336*10^8

4,422019*10^8

4,421405*10^8

Sun's grav. field

speed vm/x (m/sec)

7,746738*10^5

7,747343*10^5

7,747598*10^5

7,747876*10^5

7,748414*10^5

Initial radius rk

(Aphelion) (m)

7,174000*10^10

1,090000*10^11

1,520505*10^11

2,492341*10^11

8,160848*10^11

Initial Aphelion orbital

speed voodk (m/sec)

3,374684*10^4

3,464646*10^4

2,906995*10^4

2,101049*10^4

1,214440*10^4

Initial space

deformation density

0,999594

0,999671

0,999721

0,999782

0,999880

Radius rf

-perihelion (m)

4,619260*10^10

1,074146*10^11

1,471770*10^11

2,801013*10^11

7,414499*10^11

Excentricity

0,216627

0,007326

0,01628

0,089940

0,047919

Perihelion orbital

speed vood (m/sec)

6,517342*10^4

3,541456*10^4

3,052287*10^4

2,752682*10^4

1,402123*10^4

Siderical period (secs)

7,60205*10^6

1,941214*10^7

3,155690*10^7

5,936459*10^7

3,743278*10^8

Siderical period (years)

0,240899

0,615551

1

1,882439

11,861987

Perihelion advance

per 1 revolution (grade)

3,853734*10-4

5,944308*10-2

5,042625*10-2

3,760662*10-2

2,191771*10-2

Perihelion advance

within 100 years (grades)

0,159972

9,656825

5,042625

1,997760

0,184773

Time per 360 grades

advance (years)

2,250385*10^5

3728,9

7139,134

18020,18

1,94834*10^5

Tab13c-2

Trajectory

parameters

Saturn

Uranus

Neptune

Pluto

Comet Halley

Sun's grav. field

radius rx (m)

4,421214*10^8

4,421057*10^8

4,420981*10^8

4,420939*10^8

4,420880*10^8

Sun's grav. field

speed vm/x (m/sec)

7,748581*10^5

7,748719*10^5

7,748786*10^5

7,748822*10^5

7,748830*10^5

Initial radius rk

(Aphelion) (m)

1,520000*10^12

3,018000*10^12

4,545000*10^12

7,50000*10^12

2*10^13

Initial Aphelion orbital

speed voodk (m/sec)

8,752046*10^3

6,296608*10^3

5,347304*10^3

3,195624*10^4

29,456780

Initial space

deformation density

0,999911

0,999937

0,999949

0,999960

0,999975

Radius rf

-perihelion (m)

1,338164*10^12

2,726822*10^12

4,450205*10^12

4,588750*10^12

1,148093*10^11

Excentricity

0,063620

0,050685

0,001054

0,240751

0,988584

Perihelion orbital

speed vood (m/sec)

1,059317*10^4

7,330520*10^3

5,518890*10^3

6,673403*10^3

6,754823*10^4

Siderical period (secs)

9,296020*10^8

2,651208*10^9

5,201713*10^9

7,837128*10^9

2,376908*10^9

Siderical period (years)

29,477487

84,0135

164,8358

248,5137

75,3212

Perihelion advance

per 1 revolution (grade)

1,613383*10-2

1,1479*10-2

9,226582*10-3

7,27981*10-3

-3,595870*10-1

Perihelion advance

within 100 years (grades)

0,054733

0,013663

0,005597

0,00293

-0,477043

Time per 360 grades

advance (years)

6,577418*10^5

2,6348*10^6

3,573*10^6

6,1447*10^6

7,5408*10^4

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5.3.3.6 The shape of orbital trajectories in solar system

The shape of the orbital trajectory was in general considered by physicists as circular, elliptical or, not differring much from elliptical so far. The trajectories calculated in accordance with this spaceflow theory varies from the circular through egg-like to pear-like shape, along with the increasing excentricity.

We can see on the following images how the shape of the trajectories with the same aphelion and different perihelion varies. For our example the single aphelion was choosen rk=1,52*10^12 m (the aphelion of the planet Saturn).

Fig13d-1

Trajectory

e=0,063620

Trajectory

e=0,304444

Parameters

rk=1,52*10^12 m

voodk=8,752046*10^3 m/sec

rf=1,33816*10^12 m

e=0,063620

To=9,296020*10^8 secs

DeltaAlpha=1,613383*10-2 grade

Parameters

rk=1,52*10^12 m

voodk=6,504840*10^3 m/sec

rf=8,104947*10^11 m

e=0,304444

To=6,495800*10^8 secs

DeltaAlpha=1,066802*10-2 grade

Trajectory

e=0,67903

Trajectory

e=0,893049

Parameters

rk=1,52*10^12 m

voodk=3,003776*10^3 m/sec

rf=2,905724*10^11 m

e=0,67903

To=3,335930*10^8 secs

DeltaAlpha=-6,211542*10-2 grade

Parameters

rk=1,52*10^12 m

voodk=1,001461*10^3 m/sec

rf=8,587478*10^10 m

e=0,893049

To=1,650563*10^8 secs

DeltaAlpha=-4,174293*10-1 grade

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5.3.3.7 Orbital trajectories round the characteristic radius of gravitational field

As it was derived, while at radia greater than the characteristic radius rx the free motion of an object in a gravitational field is defined by equations (225).....(229), at radia less than the radius rx, the free motion is governed by equations (225a).....(229a). The parameters and appearance of the trajectories are considerably influenced by this fact, especially due to different distribution of the space density in that two cases.

On Fig13e-1 we can see four trajectories, all starting at the same aphelion rk=4*10^8 m (below radius rx), with the different excentricities, reaching down to the radius rf=1,1837*10^7 m (that is, below rx). It is to be pointed that such motion would be realistic only provided that the mass of the Sun was compressed into the volume of sphere of the radius less than rf. The actual radius of the Sun is 6,959*10^8 m.

Fig13e-1

Trajectory

e=0,0976

Trajectory

e=0,4192

Parameters

rk=4*10^8 m

vook=5,5*10^5 m/sec

rf=3,288599*10^8 m

e=0,0976

To=3,790650*10^3 secs

DeltaAlpha=-0,2508 grades

Parameters

rk=4*10^8 m

vook=4,5*10^5 m/sec

rf=1,636793*10^8 m

e=0,4192

To=2,606312*10^3 secs

DeltaAlpha=-10,9299 grades

Trajectory

e=0,7565

Trajectory

e=0,975952

Parameters

rk=4*10^8 m

vook=3*10^5 m/sec

rf=5,544063*10^7 m

e=0,7565

To=2,069060*10^3 secs

DeltaAlpha=+1,3941 grades

Parameters

rk=4*10^8 m

vook=1,5*10^4 m/sec

rf=1,183759*10^7 m

e=0,9425

To=2,080688*10^3 secs

DeltaAlpha=+106,966 grade

On Fig13e-2 we can see two trajectories, both starting at the same aphelion rk=1*10^9 m (over radius rx), with the different excentricities, reaching down to the radius rf=3,94444*10^7 m (that is below rx). It is to be pointed that such motion would be realistic only provided that the mass of the Sun was compressed into the volume of sphere of the radius less than rf.

Fig13e-2

Trajectory

e=0,5491

Trajectory

e=0,9241

Parameters

rk=1*10^9 m

vook=3*10^5 m/sec

rf=2,910727*10^8 m

e=0,5491

To=8,010336*10^3 secs

DeltaAlpha=-43,8802 grades

Parameters

rk=4*10^8 m

vook=6*10^4 m/sec

rf=3,944432*10^7 m

e=0,9241

To=4,918258*10^3 secs

DeltaAlpha=-33,2072 grades

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5.3.3.8 Analysis of the common motion in gravitational field

Culminating radia

Analyzing the equations (213), we are coming to conclusion that the free fall speed reaches zero under the following circumstances:

1. In case when vzo = vzocr according to equation (218) (the critical or, the 1st cosmic speed is reached), and the free fall speed reaches zero (vzlk = 0) at the radius rk. In this case the examined object becomes circulating around the gravitational object in a circle of the radius rk.

2. In a common case, the examined object does not circulate in the circle, but in the ellipse-like, egg-like or pear-like curve. In this case the vertical speed reaches zero in two points (radia):

1. At the upper initial radius rk, provided that the horizontal (orbital) initial speed fulfills the condition:

(261)

2. And, at the lower final radius rf,

(262)

Remark :

Of course, the lower culminating radius rf may be reached in case only, if it exceeds the radius of the surface of gravitational body.

1. Or, in a similar way:

1. At the lower initial radius rk, provided that the initial orbital speed fulfills the condition:

(263)

2. And, at the upper final radius rf according to the equation (262). The upper culminating point however exists on condition only, that :

(264)

If the equation (264) is not fulfilled, the object escapes from the gravitational field. The equation (264) defines the orbital escaping speed for the case, when the extent of the gravitational field is not restricted by another (superior) gravitational field.

The shift of culminating points

We can see from Tab13b-1, Tab13b-2, Fig13d-1 and Fig13e-1 that at the same time when the object makes one turn from the upper to the lower culminating point and back to the upper culminating point, the radius vector of the object turns by the angle , differring from 360 degrees by . The angle would be expected of 360 degrees in a common geometry. General relativity derives slight advance (that is > 0) of culminating points

Observations have revealed that the major axis of the Mercury's orbit rotates in space with respect to stars, covering angle of about 16 degrees every 10000 years, that is 1,38758 seconds of arc within one turn of Mercury's rotation around Sun (Perihelion advance of Mercury). The Einstein,s theory of general relativity predicts perihelion advance of Mercury of 0,10358 seconds of arc within one turn. The example of the calculation of the Mercury's orbital trajectory in Tab13b-1 shows that accordind to space-flow theory the whole observed value of the perihelion advance of Mercury might be explained by the relativistic phenomena and the related deformation of the gravitational field. In this example the perihelion advance of 3,8537*10-4 degrees per one turn is calculated, corresponding to 1,38733 seconds of arc per one turn. So, the perihelion advance by space-flow theory is 13,396 times greater than the perihelion advance by the theory of general relativity for planet Mercury.

It has become of common knowledge that the seasons on Earth and, probably on any planet, are caused by the tilt of the earth's rotation, that is, due to the deflection 23,4 degrees (for the Earth) of the axis from a direction perpendicular to the earth's orbital plane. The direction of the axis stays nearly the same with regard to stars, even as the Earth revolves around the Sun. As a result, when the Earth is at a certain place in its orbit, the northern hemisphere is tilted towards the Sun, and there is summer on the northern hemisphere. Half a year later the northern hemisphere is tilted away from the Sun and there is winter on northern hemisphere. Two days during year, when the earth's axis is most directly toward or away from the Sun are named the solstices and they are also the longest and shortest days of the year.

The earth's orbit however is not a perfact circle. It is somewhat elliptical and the distance between the Earth and the Sun varies during the year. Since the variation of the distance is relatively small, this effect is too weak to cause seasons, but it might have some influence over their intensity.

The Earth reaches perihelion - the point when it is closest to the Sun on January 4th in this era. The date of perihelion does not remain fixed. As we can see in Tab13c-1, the perihelion is constantly delayed, it will be reached gradually on all days of the year, and reaches again the january 4th within about 7139 years. Even if this period cannot be considered as verified (tha data in Tab13c-1 should be considered as the results of calculation examples), the real time of Earth per 360 degrees perihelion advance would not probably differ much from this value. This discovery might be significant for the evaluation of the global development of weather, since the balance of conditions determining weather is pretty subtle. Up to now scientific sources determine the period of the 360 degrees perihelion advance of Earht to more than 50000 years.

The energy of free object in free motion

The unit kinetic energy (kinetic energy on unit of mass) of the object in free motion in Zct reference frame, on condition that the relativistic influence is ignored, is defined (see equation 211):

(265)

Substituting for rx and vm/x from equations 169 and 170, we can derive:

(266)

This is the same energy as it was derived by Sir Isaac Newton:

(267)

In a space-flow theory energy can be expressed yet in another two reference frames, Zcr and intrinsic, that is in frames differring from the Zct frame by different length or time units. Respective equations are rather complicated and that is why they are not included in this paper.

The relativistic influence caused by increasing speed of the space flow in gravitational field (defined by mass of gravitational body) has no consequences on energy. Say if we apply parameters rx from the equation (244) and vm/x from the equation (246), which have already been modified regarding the relativistic influence mrntioned, the equation (267) stays unchanged. So, the unit kinetic energy is not influenced by relativistic phenomena. The energy of the object however varier with the relativistic increase of its mass, as it is was defined by the equation (192).

How long does it take sun's light to reach earth

To determine the time interval within it the photon from the Sun passes over the distance Sun - Earth, it is necessary to consider the following entries :

- initial Zct speed of light c = 2,997*10^8 m/sec

- distance Sun - Earth : 1,496*10^11 m

- radius of the sun's surface rk = 6,959*10^8 m

- period of sun's rotation: 2,12544*10^6 secs

- corresponding Zcr radial speed on sun's surface vook = 2057,206 m/sec

- basic parameters of the sun's gravitational field:

rx = 4,43776*10^8 m

vm/x = 7,73412*10^5 m/sec

In case the photon starts from the centre of the sun's disc

Applying the equation 227 for the vook = 2057,206 m/sec we can calculate the Zct initial orbital speed vzok on sun's surface:

vzok = 3,212548*10^3 m/sec

Since it must be

(268)

where vzlk stands for the initial vertical speed of the photon, we have:

(269)

Substituting for vzlk in equation 213, we have for the Zct vertical speed:

(270)

Applying equations 228 and 224-1, we have :

(271)

Ignoring motion of the photon in earth's gravitational field (we can afford it, since earth's gravitational field is significantly weaker than the sun's gravitational field), we can calculate (numerically) time interval Tse within it sun's light reaches the Earth:

(272)

In case the photon starts from the limb of the sun's disc

By reason that now photon starts from the sun's surface horizontally, must be:

vzok = c = 2,997*10^8 m/sec

vzlk = 0

Applying the equation 229, we have :

(273)

and

(274)

Up to now calculations, based on the idea of the space-time of constant space density (homogenous and heterogenous space) and, on the idea of constant speed of light, result in an explicit value of the time interval Tse = 8 minutes: 18 seconds. According to space-flow theory the time interval Tse varies with distance of the place of the photon's launch from the centre of sun's disc, reaching 52,45 seconds for the photon starting from the centre of sun's disc and 11 hours: 9 minutes: 57 seconds for the photon starting from the limb of sun's disc. The dependence Tse vs distance from the centre os sun's disc is not directly proportional. The greatest growth of the time Tse comes from photons starting nearby the sun's limb.

The dark matter

By measuring Doppler shifts in our galaxy (Milky Way) scientists determined orbital speeds of stars. This in turn allows them to calculate the mass of galaxy. However the mass calculated in such a way is much larger than the mass of all stars and gas, that can be seen in galaxy. That is how scientists came to a conclusion that at least 90% of the mass of any galaxy, and perhaps 99% of the mass of the universe do exist in the form of matter that cannot be seen (dark matter).

Space-flow theory can significantly contribute to the solution of this great cosmological problem, especially in a disc-shaped galaxies. The unit space flow (space flow per unit space angle) in a narrow space angle close to the plane of galactic disc is much greater than the unit space flow in the remaining space angle. The space flow in the narrow disc angle therefore reaches much higher value than it would correspond to this angle in case of uniform distribution of the mass. Since space flow is directly proportional to the mass, this implies conclusion that gravitational field in this space angle is as strong as if it was created by the such much times greater gravitational mass how much times is the unit space flow in this narrow space angle greater than it would be there in case of the uniform distribution of the mass.

Orbital speeds of the stars in galaxies are approaching their critical values according to equation (218), since the trajectories of the stars are approximately circular. By substitution for rx and vm/x from equations (169) and (170) to equation (218) we can derive:

(275)

where are

M

stands for the mass of galaxy under radius rlmx at which orbits the respective star.

vzo

orbital speed of the star in galaxy

rlmx

distance of the star from the centre of galaxy

kapa

gravitational constant

In case the unit space flow in a narrow disc angle is 10 times greater than in a uniform distribution, corresponding mass of (imaginary) gravitational body will be also 10 times greater, and the orbital speed will have to be:

(276)

Resume:

Too high orbital speed observed at the stars in galaxies can be explained by unequal distribution of the mass in galaxy. There is no need to look for dark matter for that reason.

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Author

Frantisek Stefanko

Skautska 1

04001 Kosice

Slovakia

E-mail address :

fstefanko@gmail.com

The work Gravity and Mass Distribution inside Gravitational Objects (as a Part three of the work The Spacetime Phenomena) has been published by now. The presented results are unexpected, amazing and shocking, invoking the phenomena from science fiction story.

036

Gravity and Mass Distribution inside Gravitational Objects

The Spacetime Phenomena part 3

by F. Stefanko

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- PART 3 MAP

- HOME - GRAVITY AND MASS DISTRIBUTION INSIDE GRAVITATIONAL OBJECTS (just displayed page).

- 5.3.4 Mass object in gravitational field of another object

- 5.3.4.1 Interface Area

- 5.3.4.2 Gravitational acceleration due to exterior objects

- 5.3.5. Mass distribution in gravitational objects

- 5.3.5.1 Mass distribution in gravitational object, created of the mass of a constant frame intrinsic mass density

- 5.3.5.2 Mass distribution in gravitational object, created of the several layers of a different frame intrinsic mass density

- 5.3.6. Gravitational acceleration inside gravitational objects

- 5.3.6.1 Gravitational acceleration created by object itself

- 5.3.6.2 Gravitational acceleration created by other object

- Summary

- Author

The images below show how the academic science expounds the architecture of the mass distribution under Earth's surface. We may ask if this scheme is true. The work presented argues for much more options how to design such cosmic body like the Earth.

Preface

The paper has been created within the scope of the work The Spacetime Phenomena, as its Part three. The reader should become acquainted with the Part One and Part Two of the work, which are available free on internet (listed in Open Directory Project).

It seems (and it will be confirmed i the next chapters), that the space (spacetime) density defining the material world (at least all what is consisting of the mass particles), is determined by that gravitational object, which is causing its highest value in a respective spacetime particular point. In other words, we can tell, that every gravitational object, manifesting itself by its own (in the next chapters we shall use "open") gravitational field, must be surrounded by the interface area, inside which the space (spacetime) density is defined by its gravitational field, in accordance with the equation (107).

Also it seems (and it will be confirmed i the next chapters), that the spacetime continuum inside the open gravitational field of the mass object, despite it is defined by its own space density, makes in its place possible the real existence of the spacetime structure manifested by the space density as defined by any another existing mass object,with its respective speed, as defined by the equation (115).

In this work we shall derive the parameters of the interface area in the most simple case, when the inferior object is nested inside the open gravitational field of the dominant object, and, no another object is close enough to the inferior object, to share the same part of the interface area with it.

The gravitational acceleration induced by the object M_2 in object's M_1 gravitational field, must be re-calculated for the space density of the object's M_1 space density.

The mass distribution inside gravitational body is solved on principle that the mass differential must be considered directly proportional not only to the mass density, but also to the space density.

The gravitational acceleration inside gravitational object is derived on the principle that the inner spheres of the object are contributing to the gravitational acceleration above the higher spheres by their gravitational acceleration, as derived in the chapter 5.3.2.2, but re-calculated for the respective space density, determined by the mass distribution of the gravitational object.

Note. The Spaceflow Theory seems to be in good train. I came to opinion, that it brings quite new way how to look on space and time, and that it might become the background, I had always looked for in all phenomena. The theory is in progress, so I hope each year will be refilled. Or, of course revised, since this concept of doing science is not simple. At least not simple for me "to be able always to find the chosen reference frame". In case of revision all will be published on Internet. Using the keywords like "space flow, spacetime density" everybody should find the site, or my address.

Author

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5.3.4 Mass object in gravitationald field of another object

5.3.4.1 Interface area

If a mass object orbits around cosmic object, or anyhow is situated in its gravitational field, it has its own open gravitational field, if its specific mass is high enough, to create the gravitational space density on its surface higher than the gravitational space density of a respective position in a gravitational field of a dominant gravitational object. If its specific mass is not high enough, it is without its own open gravitational field, despite its individual parts, like atoms and nucleons, have always their own open gravitational fields (because of their very high specific mass).

Note : To explain the fact that an object does not have its own open gravitational field, we must remind that the gravitational effects of such object are manifested by means of the hidden gravitational field (that is, the gravitational field of the respective object in a space of the density defined by the dominant object). The matter will be dealt with later.

The boundary between gravitational field of the object Ml and the superior gravitational field of the object M is defined as the interface area. See Fig18.

Fig18

Fig18 shows that the open part of the gravitational field, if any, of the mass object in a gravitational field of a dominant gravitational object is enclosed in an egg-shaped interface area, defined by:

Dl

lower interface limit

Du

upper interface limit

Da

central interface limit

Applying equations (107) and (170), we can derive conditions of the equality of a gravitational space density:

for lower interface limit

for upper interface limit

for central interface limit

where

M (M_1)

stands for mass of a superior (inferior) object

rxm (rxm1)

stands for radius according to equation (169) of an object M (M_1)

Rorl

stands for radius rlmx of an orbit around object M, at which object M_1 is located.

Substituting for rx and vm/x from equations (169) and (170) into the equation (114), we can easily derive :

(501)

It means, the expression vzx/m represents the Zct (contemporary) speed of the spacetime structure, when the relativistic effect is ignored.Therefore, except of case when the mass of the gravitational object approaches zero, or infinity, we may write :

(502)

Applying the equation (502) and the derived conditions of equality of the gravitational space density, we can determine the interface limits :

(503)

(504)

(505)

5.3.4.2 Gravitational acceleration due to exterior objects.

The gravitational interaction originated by the exterior object M_1 (M_2) has to be added to the gravitational interaction of the examinated object M_2 (M_1), to calculate the resultant gravitational interaction in the gravitational field of the object M_2 (M_1).

In case, the object M_2 is situated inside the gravitational field of the dominant object M_1, we can find out the contribution of the gravitational field of the object M_1 to the acceleration caused by the gravitational object M_2, according to equations derived in chapter 5.3.2.2. However this calculation is based on condition that the space density of the respective point in the gravitational field M_2 is defined by gravitational field of the object M_1 (not M_2). Since the space density due to gravitational field of the object M_2 becomes higher now than the space density that is originated by the object M_1, the gravitational field of the object M_1 becomes hidden in this zone. Therefore the acceleration due to gravitational field of the object M_1 must be re - calculated on space density of the gravitational field of the object M_2.

Let us imagine the two following events :

1. An object or a spacetime structure itself moves in a background of the spacetime density (consequently, in a time density ) at the frame intrinsic speed v_1.

2. The same object or a spacetime structure itself passes from the background of the space density to the space density , without being affected by gravitational (or any other) interaction.

Under these circumstances we must admit that if an object, or a spacetime structure itself in a background of the spacetime density passes distance l_1 frame intrinsic meters within t_1 frame intrinsic seconds, it will pass

in the background of the space density .

Therefore the inertial passage from the background of the space density to the background of the space density brings the change of the frame intrinsic speed v_1 to v_2:

(506)

Examining gravitational effects of the dominant object M_1 (of the mass M_1) in point P, situated in a gravitational field of the inferior object M_2 (of the mass M_2) (see Fig19), we can derive :

Fig 19

(506a)

(506b)

Applying the equation (169) for rx1 and rx2, we receive :

(506c)

and, substituting from (506c) to (242), we have:

(507)

Examining the speed of the spacetime structure in point P, it must be :

(507a)

where

vx/m1

stands for the frame intrinsic speed, in direction P-M_1, of the spacetime structure of the gravitational field of the object M_1 ,in case, if the point P was situated in the space density g1. This speed is defined by equation (170).

vx/m1-2

stands for the frame intrinsic speed, in direction P-M_1, of the spacetime structure of the gravitational field of the object M_2 (due to gravitational field of the object M_1), that would have to be added (in vector superposition) to speed vm/x2, (representing the frame intrinsic speed in direction P-M_2, caused by gravitational field of the object M_2), if we wanted to know the total frame intrinsic speed of the spacetime structure in point P,

rlmx1

stands for the distance P-M_1 in length units of the chosen frame, and,

rlmx2

stands for the distance P-M_2 in length units of the chosen frame.

Thus, respecting the equation (108), it must be :

(508)

where vzx/m1-2

- stands for the Zct speed (speed in frame intrinsic length units and the time unit of the chosen reference frame), of the spacetime structure of the gravitational field of the object M_2 (due to gravitational field of the object M_1), that would have to be added (in vector superposition) to speed vm/x2, (representing the frame intrinsic speed in direction P-M_2, caused by gravitational field of the object M_2), if we wanted to know the total frame intrinsic speed of the spacetime structure in point P of the gravitational field M_2.

We may write, respecting also the equations (169), (170), and (242a) :

- where rx2, defined by equation (169), stands for the radius in units of the orbital frame of the point P in gravitational field of the object M_2,

(509)

- Remark :

Applying the equations (169), (170) and (114) (or (115)), we can derive that the Zct speed (in a direction P - M_2), of the spacetime structure inside gravitational field M_2, may be expressed as :

(509a)

Comparing the equations (509) and (509a) we can easily derive, that inside the interface area of the gravitational field M_2 (like Earth) in a dominant gravitational field M_1 (like Sun) the spacetime structure Zct speed vzx/m1-2 reaches higher values than the M_2 gravitational field own spacetime structure Zct speed vzx/m2. If these two speeds were acting in the same (contemporary) spacetime structure, they would result (due to vector superposition) to the resulting speed approaching the Zct speed of the gravitational field M_1, and, the gravitational field M_2 would be deformed so much, that the parameters of the M_2 gravitational field should be considerably changed, in contradiction to the chapters 5.2.1, 5.2.2 and 5.3.1. This is why we must admit that the spacetime continuum makes the partial flows of the spacetime structure of the different densities (of the different time flows) possible to exist inside the same space zone, not affecting one another. The acceleration however, acting on mass in such space zone, is defined as the vector superposition of the partial accelerations from all partial spacetime flows.

The acceleration of the space flow, manifested by the speed vzx/m1-2 in gravitational field of the object M_2 can be expressed as

(509b)

Since

- (510)

where vox/m1-2 stands for the Zcr speed,

and (see equation (509)),

(511)

substituting from equations (510) and (511) to equation (509), we receive :

(512)

The gravitational acceleration gzx/m1-2 represents the Zct gravitational acceleration in gravitational field of the object M_2, due to gravitational field of the object M_1, that has to be added to the Zct gravitational acceleration in gravitational field M_2, in vector superposition, to calculate the total Zct acceleration. The negative sign in equation (512) define the direction P-M_1 of the acceleration.

In case when rlmx2 / rx2 = rlmx1 / rx1, occuring in all points of the interface area between gravitational fields M_1 andM_2, the gravitational acceleration reaches

(513)

According to equations (170) and (166) :

(514)

Applying rx1/rx2=vm/x1/vm/x2= rlmx1/rlmx2, we can derive for the ratio of the gravitational acceleration induced from object M_1 (in direction P - M_1) to gravitational acceleration caused by object M_2 (in direction P - M_2) in points of the interface area (like the ratio of the components of the gravitational acceleration on from Sun and Earth on the interface area around Earth):

(514a)

The equation (251) is identical with the equation (182), confirming that the Zct acceleration gzx/m1-2 becomes identical with acceleration gzx/m1 of the gravitational field M_1 in all points of interface area.

In case when rlmx2 = rx2, occurring, for instance on Earth surface ( if the reference frame on Earth surface was taken as the chosen one), the equation (512) becomes

(515)

and, applying the equation (138), we can derive for the ratio of the gravitational acceleration induced from object M_1 (in direction P - M_1) to gravitational acceleration caused by object M_2 (in direction P - M_2) in the chosen reference frame (like the the ratio of the components of the gravitational acceleration from Sun and Earth on the Earth surface):

(515a)

This result is in compliance with the Newton's theory of universal gravitation, confirming that the gravitational effects of the Sun's gravitational field on Earth surface, calculated by spaceflow theory, are in correspondence with experiment. The contribution of the gravitational acceleration of the Sun to the gravitational acceleration of the Earth according to the equation (249) however, differs from the acceleration expected by Newton's theory along with the height above Earth.

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5.3.5 Mass distribution of gravitational objects

To examine the mass distribution under the surface of the gravitational object, let us have a look on the relativistic phenomenon (how much the total mass exceeds the rest mass due to its motion with respect to the spacetime structure falling into mass). According to equation (38) we can express the relativistic mass :

(516)

where

m

stands for the relativistic mass

mo

stands for the rest mass

Designating

(517)

as the relativity factor, and applying the equations (170) and (180), we can derive :

(518)

We can derive from the equation (516) that even at the relativity factor kr = 0,1 it will be m = 1,00335 mo. Designating kr = 0,1 as sufficient to apply the equation (516) without the relativistic modification, that is in form

(519)

we can derive from equation (516)

(520)

where

mk

stands for maximum gravitational mass (evenly spread under the respective radius), at which the relativity effect causing mass increase may be neglected, and the equation (519) may be considered as sufficiently precise.

The equation (520) can be modified using the average mass density instead of mass;

(520a)

The curve "average mass density vs radius" acc. to equation (520a) is shown on Fig20, for kr=1,005.

Fig20

The maximum mass mk under radius rlmx that may be considered as not influenced by relativistic mass increase.

Fig20 shows that, to derive the equation of the mass distribution, the relativistic mass increase due to the motion of the mass inside gravitational objects with respect to the falling spacetime structure need not be taken into consideration, since even at the objects of the radius 2*10^11 m (higher than the distance Sun - Earth) the average mass density about 6000 kg/m^3 (the mass density occurring at planets) is allowable at the relativity factor kr < 1,005. This relativistic mass increas however plays the significant role for the cosmic objects created of the mass of high mass density, like the neutron stars.

Another factor interacting the space flow streaming into a mass, that is also the mass quantity, is the space (spacetime) density, that may influence the mass by the similar way like we derived it in chapter 4.8. The space density inside the gravitational object may be significantly influenced by the mass distribution (depends on mass and radius). However now we are speaking about the space density inside gravitational field of the mass, that is located under the respective radius, not about the space density inside atomic nucleus, nucleon or similar mass particle. In chapter 4.8, respecting the postulate of the constancy of the speed of light, we have derived that the relative speed, with respect to the chosen frame, induces the variation of the space density inside the gravitational field of the mass particle, giving rise to the mass increase (relativity effect). In chapter 5.3.4.2 however, we have derived that any gravitational object is able to influence the space density inside the mass particle in case only, if the object reaches, by its own gravitational field, in position of the mass particle, the space density higher than it is induced by the mass particle itself. This effect may occur in case only, when the gravitational field of the influencing object is extremely intensive, since the space density on the proton's surface reaches the value about

and we can derive that, to reach such high space density in proton, the object of the Earth mass (concentrated in a very small volume) should be situated in a distance from the proton not longer than

This is why, deriving the mass distribution in gravitational object, we need not take into consideration the relativistic mass increase (decrease) due to increase (decrease) of the space density in the gravitational field inside the gravitational object.

Ignoring both the relativistic mass increase due to speed, and the relativistic increase (decrease) due tu change of the space density, the mass distribution under surface of the gravitational object may be considered depending on the mass density dustribution, and on this feature of the space density that is responsible for the mass distribution Note:observing from the chosen reference frame, like from the earth surface, the constant cube vulume, not breathing with the space, we would have to find out that the quantity of mass in this cube differs depending on the position of the cube inside gravitational object, in consequence of the change of the space density.

Between radia rlmx and rlmx+drlmx the mass differential dm may be expected :

(521)

where

stands for the frame intrinsic space density (measured by the instruments breathing with spacetime structure in a respective position inside gravitational object)

In general, we can tell, that under the common radius rlmx the mass m is situated, to which the gravitational radius rx is related according to equation (169):

The gravitational space density :

(522)

Solving the equations (521) and (522) we receive the common equation of the mass distribution vs radius inside gravitational objects :

(523)

5.3.5.1 Mass distribution of gravitational object created of the mass of constant frame intrinsic mass density.

At = o =const

At constant frame intrinsic space density the differential equation (523) gives the solution :

(524)

where

- (525)

- K is common constant.

At the boundary condition :

- at rlmx = Ro (the outer radius of the gravitational object) :

- m = Mo (the total mass of the gravitational object)

- the equation (524) becomes :

(526)

Substituting for m from equation (526) to equation (522), we recwive the equation defining the gravitational space density :

(527)

Applying the equation (526) we can express the average mass density under respective radius :

(528)

The examination of the equations (526), (527) and (528) leads to the following conclusions :

- The gravitational object can be created of the mass of any frame intrinsic mass density. The object of the mass Mo may be created of the low (high) mass density, since the low (high) mass density is compensated by high (low)space density to reach the requested average mass density.

Note The decision whether the object would be able to exist, made of any frame intrinsic mass density, depends on conditions of stability of the object (like gravitational acceleration,pressure, themperature and many others), and is not discussed in this chapter.

- At k = 3, or, acc. to equation (525) at the frame intrinsic mass density

(529)

- The mass distribution becomes directly proportional to the third power of the radius. See Fig21.

Fig21

- The gravitational space density becomes constant, not depending on radius :

(530)

- The average mass density under radius becomes constant, not depending on the radius :

(531)

- At k < 3, or, acc. to equation (525) at the frame intrinsic mass density

(532)

- The mass becomes directly proportional to the power lower than 3 of the radius.See Fig22

Fig22

- The space density becomes increasing with the decreasing radius. See Fig23.

Fig23

- The average mass density under radius becomes increasing with the decreasing radius. See Fig24.

Fig24

- At k > 3, or, acc. to equation (525) at the frame intrinsic mass density

(533)

- The mass becomes directly proportional to the power higher than 3 of the radius.See Fig25

Fig25

- The space density becomes decreasing with the decreasing radius. See Fig26.

Fig26

- The average mass density under radius becomes decreasing with the decreasing radius. See Fig27.

Fig27

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5.3.5.2 Mass distribution of gravitational object created of several layers of different frame intrinsic mass density.

In a common case let us have the gravitational object formed of the following layers of the frame intrinsic mass density :

1

on its surface, between radia Ro - R_1

2

between radia R_1 - R_2

3

between radia R_2 - R_3

n

between radia R(n-1) - Rn

Fig28

Gravitational object formed of 3 layers of different frame intrinsic mass density.

In this common case the differential equation (523) must be solved for the different boundary condition in each layer :

- 1st layer

- (534)

Solution for R_1 < rlmx < Ro

(535)

where

(536)

Applying the equation (535) we can derive :

- The space density:

(535a)

The average mass density:

(535b)

- 2nd layer

- (537)

Solution for R_2 < rlmx < R_1

(538)

where

(539)

Applying the equation (538) we can derive :

- The space density:

(538a)

The average mass density:

(538b)

- 3rd layer

- (540)

Solution for R_3 < rlmx < R_2

(541)

where

(542)

Applying the equation (541) we can derive :

- The space density:

(541a):

(541a)

The average mass density:

(541b):

(541b)

- n-th layer

- (543):

(543)

Solution for Rn < rlmx< R(n-1)

(544)

where

(545)

Applying the equation (544) we can derive :

- The space density:

(544a):

(544a)

The average mass density:

(544b):

(544b)

- The example

- To calculate the mass distribution and related parameters under Earth surface, on condition that its outer radius Ro = 6,378*10^6 m, its total mass Mo = 5,977*10^24 kg, and, that the mass is created of the following 3 layers :

1st layer

Radia : Ro = 6,378*10^6 m, R_1 = 6,377*10^6 m

Frame intrinsic mass density: 1000 kg/m^3

2nd layer

Radia : R_1 = 6,377*10^6 m, R_2 = 6,378*10^3 m

Frame intrinsic mass density: 2700 kg/m^3

3rd layer

Radia : R_2 = 6,377*10^3 m, R_3 = 0 m

Frame intrinsic mass density: 7870 kg/m^3

Solution

Applying the derived equations, the mass distribution, the space density, and the average mass density under radius were calculated in each layer :

1st layer (See Fig29)

Fig29

Mass distribution, space density and average mass density under radius in 1st layer

2nd layer (See Fig30)

Fig30

Mass distribution, space density and average mass density under radius in 2nd layer

3rd layer (See Fig31)

Fig31

Mass distribution, space density and average mass density under radius in 3rd layer

We can see from Fig29, Fig30 and Fig31, that the space density is increasing with the decreasing radius in the upper two layers (1st and 2nd layer), causing, that, in spite of fact that the frame intrinsic density in upper two layers is much less than in the 3rd (inner) layer, the most of the Earth mass is situated in upper two layers. In the 3rd layer the space density becomes decreasing with decreasing radius. At the radius approaching to zero, the space density is comming to zero as well.

Note

At this low space density must exist the radius rlmx = Rcr, representing the radius of one spacetime cell (much bigger than the cell on Earth surface, when measured in units of the Earth surface frame). Summarizing the mass between radia Ro and Rcr, we have to come to conclusion, that the summarized mass Ms is less than the total mass Mt of the gravitational object. Under these circumstances we would have to admit, that the mass amount of Mt - Ms must be situated in this very last spacetime cell, or, more likely, in a different zone of the spacetime continuum, spreading from the centre of gravity out to infinity. To determine the radius Rcr (of course it must be very small with respect to Ro, and depending on the frame intrinsic mass density), however, we should have to know the frame intrinsic radius of the spacetime cell.

The average mass density under radius reaches its maximum 2,087*10^8 kg/m^3 at the radius R_2 (on spherical area between the 2nd and 3rd layers). This very high mass concentration arises both due to high frame intrinsic mass density and high space density.

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5.3.6 Gravitational acceleration inside gravitational objects

5.3.6.1 Gravitational acceleration created by object itself.

In a common case, when under the radius rlmx occurs the sphere of the mass m, the average mass density may vary in large extent. Due to this fact it might also happen that the certain layer under the radius rlmx becomes "hidden", e.g. situated out of the own interface area (of course the mass particles of which the object is consisting have their own interface area, because of their high mass density). Such event arrives when the space density in the layer becomes lower than the space density of other gravitational object. We can see on Fig26 and Fig31 that inside a cosmic body such condition arises in a space close to the centre of gravity, if this space is filled by the mass of the high mass density. In such case the mass distribution in a respective layer is governed by the space density originated now by other governing object, and the gravitational acceleration in such layer has to be re-calculated from the hidden gravitational field of the respective layer to the open gravitational field of the other object, in accordance with the chapter 5.3.4.2.

The gravitational acceleration on the surface of the spherical object of mass m, under the radius rlmx inside the major gravitational object must be in conformity with the equation (182):

(545)

or, substituting for vm/x from the equation (170) :

(546)

where

gzx

stands for the Zct gravitational acceleration at the radius rlmx of the object of mass m under radius rlmx.

Applying the equations (189) and (190) at vn/mk=0 (the mass under radius rlmx does not move with respect to the centre of gravity) and at rlmxk=rlmx (since rlmxk means the radius at which vn/mk=0), we receive :

- the frame intrinsic acceleration acting at a common radius rlmx :

(547)

- and, the Zcr acceleration, acting at a common radius rlmx or, at a respective mass m :

(548)

The equations (546), (547) and (548) define the gravitational acceleration in a spaceflow line not only under the surface of the gravitational body, but also above its surface, in a space at which the frame intrinsic mass density approaches zero, however in case only,when the respective object does not move with respect to the centre of gravity. We can see that the frame intrinsic gravitational acceleration (we can measure it directly in a respective depth) is identical with the Zct gravitational acceleration, that cannot be measured directly, however it represents the important quantity for calculation of the gravitational potential and energy.

The example

- To calculate the Zct gravitational acceleration under Earth surface, on condition that its outer radius Ro = 6,378*10^6 m, its total mass Mo = 5,977*10^24 kg, and, that the mass is created of the following 3 layers :

1st layer

Radia : Ro = 6,378*10^6 m, R_1 = 6,377*10^6 m

Frame intrinsic mass density: 1000 kg/m^3

2nd layer

Radia : R_1 = 6,377*10^6 m, R_2 = 6,378*10^3 m

Frame intrinsic mass density: 2700 kg/m^3

3nd layer

Radia : R_2 = 6,377*10^3 m, R_3 = 0 m

Frame intrinsic mass density: 7870 kg/m^3

Solution

Applying the results of the mass distribution according to example in chapter 5.3.5.2, the Zct gravitational acceleration was calculated for each layer, applying the equation (546). The results are shown on Fig32 :

At the radia defining the three layers the following values were calculated :

- At Ro : gzx = -9,80275 m/s^2

- At R_1 : gzx = -9,80373 m/s^2

- At R_2 : gzx = -11,0688 m/s^2

- At R_1 = 0 : gzx = 0

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5.3.6.2 Gravitational acceleration created by other object.

Applying the equation (512), and realising that the expression

(549)

means the space density at the radius rlmx2 of the object M_2, we may modify the equation (512):

(550)

Substituting for radius rx2 from the equation (169) to the equations (549) and (550), we get :

(551)

where

m_2

stands for the mass under the radius rlmx2 inside the gravitational object M_2.

The Zct gravitational acceleration, caused by the object M_1, in a point P under the surface of the gravitational object M_2 (see Fig19) in a distance rlmx1 from the object M_1, acting in direction P - M_1, is defined by the equation (551). The mass m_2 to be used in the equation (551) is defined by the equation (526) for the object created of the mass of the constant frame intrinsic mass density. For the object consisting of the more layers of the different mass density the equation must be derived for each layer, by the way shown in the chapter 5.3.5.2.

The example 1

To derive the equation for the total gravitational force attracting the object M_2 (created of the mass of a constant mass density) to the object M_1 situated far away from the object M_2. The object M_2 has its own open gravitational field.

Solution

- The total force attracting the object M_2 to the object M_1 is defined :

(552)

Applying the equation (526):

(553)

(554)

Substituting from the equations (553) and (554) to the equations (551) and (552), and considering the distance rlmx1 between the object M_1 and all particular points inside the object M_2 as identical, we can derive :

(555)

(556)

The example 2

To derive the equation for the total gravitational force attracting the object M_2 (created of the mass of a constant mass density) to the object M_1 situated far away from the object M_2. The object M_2 has not its own open gravitational field. Both objects are situated slightly above Earth surface.

- Solution

In this case the space density does not follow the equation (549), but the equation defining the space density of the object that governs in a respective zone. Usually its value will be constant for the objects of small volumes. For instance for the piece of a rock on Earth surface will be = 1. Also the mass distribution in such case will follow the conditions given by the governing object. Again for the piece of rock on Earth surface, the mass distribution will be homogenous. On such conditions the equation (552) becomes :

(557)

(558)

Analysing the equations (556) and (558), we can tell that the total force attracting object M_2 to object M_1 does not depend in general on mass of the objects and on the distance between them only, but also on the constant k_2 or, on the mass distribution inside the object M_2. The constant k_2 is defined by the equation (525) and is directly proportional to the frame intrinsic mass density. In a common case the two objects of the same total mass are attracted each by the different force, if the mass distribution inside the objects is not the same.

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Summary

In chapters 5.3.4, 5.3.5 and 5.3.6 the gravitational interaction between objects, as well as the mass distribution and gravitational field inside objects have been dealt with, from the viewpoint of the spaceflow theory. The principal feature the presented work is based on, appears to be the interface area, that creates the border between gravitational fields. Inside the object's interface area the spacetime structure is governed by the open gravitational field of the respective object (manifesting itself inside this interface area by the primary space density), since there are no another objects close (or big) enough to create higher space density in this space. Together with the spacetime structure governed by the object in its own interface area however, they do exist there also the hidden gravitational fields of the other objects, with their own configurations of the space density (lower then the primary space density). The objects occuring inside this interface area are subjected to the influence of its space (spacetime) density, they are connected with (and also created by) this primary space density. The reason of course, lies in the lowest gravitational potential, the gravitational field of the governing object offers (see chapter chapter 5.3.2.3).

Numbers of the existing objects (like piece of the rock on Earth surface) do not have their interface area. It does no mean that they are without gravitational field. Their mass lies in the volume created by the space density of the other(governing) object. The gravitational acceleration of such objects really exist, however it does not depend on the mass of the object only, but also on the magnitude of the forced primary space density. The higher the forced primary space density, the lower becomes the gravitational acceleration of the gravitational field of such object. We can easily derive the condition for the existence of the interface area of the spherical object :

(559)

where

stands for the universal constant,

stands for the gravitational constant,

m

stands for the mass of the object and,

r

the radius (in units of the chose frame) assigned to the mass m

stands for the space density of the primary spacetime structure

Defining the average mass density as:

(560)

we can derive from the equation (559) the following condition for the existence of the interface area (or, for the existence of the open gravitational field):

(561)

Taking into consideration the equation (561), we can tell, that in the space close to Earth surface (where space density of the primary spacetime structure = 1), the spherical objects only of the average mass density higher than 5496,5 kg/m^3 have their own open gravitational field (have their own interface area). The heavy objects, (e.g. ferrous) have their own open gravitational field, while the light objects (e.g. aluminic) are characterized by hidden gravitational field in a space close to Earth surface.

The determination whether the object has its own open gravitational field or not, might be interesting from many points of view. For the topic, we are dealing with, it plays role in the way how to calculate its gravitational acceleration. The derived equation (558) confirms that the theory is in correspondence with the experiment, since this formula was verified many times by scientists in experiments in order to measure the gravitational constant.

There is also another significant consequence of the existence of the hidden gravitational fields. The condition defining the uprise of the hidden gravitational field is based on comparison of the two values of the space density : the value originated by object itself, and the value "offered" by the other object. Taking into consideration the fact, that the distances of the cosmic bodies are varying in certain limits, and another fact, that the "offered" space density is inversely proportional to the distance of the other object foom the respective place, we must admit, that

- the attractive force between the cosmic objects becomes dependent not only on the distance between them, but also on the change of the space density due to change of the distance, in these layers of the objects in which the gravitational field has become hidden and that,

- the change of the object's layer from the open to the hidden state (and vice versa) is apparently the feedback process, and therefore it might give rise to oscillations of the gravitational acceleration (hence on Earth to the earquake) inside the object.

We came to the conclusion that the relativistic mass increase of the cosmic object due to the motion of the object's mass with respect to the spacetime structure (space flow) may be ignored, except of the case of the cosmic objects created of a very high mass density (like the neutron stars). Quite new mechanism of the relativistic mass increase has been derived in the work, based on the increase of the space density inside the mass particles. This phenomenon is set in case only, when the other mass object comes very close to the mass particle, causes the change of the zone inside the mass particle to the "hidden" zone, and replaces the space density of the hidden zone by the higher space density. Such physical action of course, can be done by another mass particle only, because the mass particle is the only object, which (its centre of gravity) is able to be close enough to another mass particle. The physics of the atomic nucleus or of the mass particles is off the point of this work, we understand however, that the mass increas of the mass particles due to their close vicinity is very similar to the well known mass increase of the nucleons in the atomic nucleus, and that, the sudden positive change of the mass of the interacting mass particles apparently can play significant role in nuclear forces.

Another important feature the work is based on, is the space density, that is directly proportional th the one third power of the mass and, inversely proportional to the radius above the respective mass. The differential of the mass therefore becomes directly proportional not only to the mass density and to the differential of the volume, but also directly proportional to the third power of the space density. This new approache leads to the consequence, that (theoretically) any object, defined by the total mass and the outer radius, can be created of the mass of any mass density.

Note : In fact the stability of the object depends also on another parameters, like the temperature, pressure and others.

The presented results of the mass, the average mass density and, the space density, for the objects made of mass of the constant frame intrinsic mass density, are the following :

- At the frame intrinsic mass density of 5496,5 kg/m_3 :

- the mass becomes directly proportional to the third power of the radius,

- the average mass density and the space density stay constant,

- At the frame intrinsic mass density lower than 5496,5 kg/m_3 :

- the mass is directly proportional to the power < 3 of the radius,

- the average mass density and the space density become increasing with the decreasing radius,

- At the frame intrinsic mass density higher than 5496,5 kg/m_3 :

- the mass is directly proportional to the power > 3 of the radius,

- the average mass density and the space density become decreasing with the decreasing radius.

The results of the calculation of the mass distribution of the object consisting of the several layers of the different frame intrinsic mass density are similar to the case above. In all layers the character of the curves described above stays the same.

The disclosure of the fact that inside the layers of the mass density higher than 5496,5 kg/m_3 the space density goes down with the decreasing radius is very remarkable from the viewpoint of the mutual influence of all material objects, as mentioned above.

Finding that the object may be created of the mass of any mass density is an inspiring disclosure, since it explains how the high average mass density in the centre of the object can be created without the iron, lead, or other heavy elements, and besides it explains how the high average mass density can be created in any layer of the object's volume or, how to create the centre of the object almost empty.

The gravitational acceleration inside the gravitational body is directly proportional to the ((2k/3)-1)power of the radius, where

Thus we can derive:

- Inside the layer of the mass of the frame intrinsic mass density lower than 2748,2 kg/m_3 :

gravitational acceleration increases with the decreasing radius,

- Inside the layer of the mass of the frame intrinsic mass density = 2748,2 kg/m_3 :

gravitational acceleration stays constant,

- Inside the layer of the mass of the frame intrinsic mass density higher than 2748,2 kg/m_3 :

gravitational acceleration decreases with the decreasing radius,

- Inside the layer of the mass of the frame intrinsic mass density = 5496,5 kg/m_3 :

gravitational acceleration is directly proportional to the radius.

On the end let us go through an example, explaining very simply the spaceflow theory. In the solar corona the scientists many times detected the incredibly high height, to which the material of corona had been fired. This feature can be easily explained by the difference between the space density on the surface of Sun and the space density on the surface of Earth (defined = 1). Applying the equations defining the parameters of the gravitational field, we can write for the space density on the surface of Sun :

(562)

where

the mass of Sun,

the radius of Sun

and, we receive :

(563)

It means, that if the material from Sun's surface is thrown up to the height 1 km (measured by local Sun's surface meter), we will have to measure this height from Earth surface (measured by Earth surface meter) as

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Author

F. Stefanko

Skautska 1

04001 Kosice

Slovakia

E-mail address : fstefanko@gmail.com

I am obliged to inform the public that I am not a professional physicist, and, that , to start this work, I had to pluck up courage at first, to forget about many warning fingers of my teachers of physics.

The thought became perhaps the only suitable instrument for people doing fundamental research. But in case only, that it is selfpossessed and independent enough, to penetrate through spacetime structures, not affecting them,and being not affected by them.. This is the Way.

Copyright: A user may download, copy and reproduce this article, but this activity is limited to ten copies of the article. Otherwise author must be contacted. In case of citations of the article, the source must be clearly indicated.

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Epilogue

I do not consider my work for finished, and surely not without mistakes. Nevertheless I want to declare my conviction that the space flow theory might be helpful on the way of physics to the theory of everything. It is however run for a long route to break through scientific authorities and to prove the perspective of the theory from the outside. Besides, I am getting into the age when the interior of the space-time quantum becomes more inviting than its exterior. Therefore, I would like to mention yet several interesting things, that follow or, that might follow from the space flow theory.

The background of space flow theory

The space flow theory is working on the presumption of Universe filled out by its primary matter, oscillating. and so creating space-time structure, consisting of huge number of space-time cells (or. wave packets). This space-time structure and succeeding development of the mass particles are the basic entities whose existence had to precede the following evolution of Universe. The determinant component of these initial entities is of course the primary matter. of which properties and behaviour we can only speculate. It is evident however, that it deals with the entity, that is filling the interior of the space-time quantum. We have already grasped from quantum physics that the interior of the quantum behaves unlocally, what means, that also the prime matter behaves unlocally, hence it is not structured. Thus we can see that the fundamental substance of the Universe must be quantum of the primary matter (QPM). Oscillations inside of the QPM are making thicker and thinner places (cells), like the waves in the sea. The density, dimension and the frequency of the cells create our space-time structure and so our known Universe. So, one may say that there does not exist nothing but the primary matter ,or "nomenon" as it is splendidly explained in "Ashtavakra Gita". The origin of the mass particles has to be in relation with the source of the oscillations in QPM, since mass in space flow theory is defined as a very dense space-time structure, that in the beginning of the universe evolution could be created only by a sharp change of the oscillations intensity. In the subsequent evolution the creation of the mass particles could be accelerated by collisions and gravitational fields. The condition for the existence of the stable mass particle of course, must lie in maintaining of the constant space flow, flowing from our space-time structure into another, paralel continuum, or another universe.

Lorentz transformation

In my work, I have not yet expressed my standpoint to the Special and the General Theory of Relativity. Especially since they ,as well as the quantum mechanics have a lot of my respect. They are, and for long time shall be the basis of scientific and technological development, but also of philosophical research. But there are also the subject of scientific discussion and disputes. Basic relationships Einstein's special relativity are derived from 4 Lorentz transformation equations between the reference frame S and reference frame S', moving at speed v with regard to the reference frame S (i.e. between two inertial systems):

1. x' = k(x - vt)

k... constant

x ... length in the system S

x'... length in the system S'

t... time in the system S

2. y' = y

3. z' = z

4. x = k (x' + vt')

t'... time in the system S'

We can see that in equation no. 4 the speed v' is replaced by the speed v. This follows from the so-called 1st postulate of the special theory of relativity: "All laws of physics can be expressed by equations of the same form in all reference systems moving with constant velocity with each other." This postulate is incorrect. If it is not yet clear at this stage of the solution, after completion of the the general theory of relativity, it was quite clear: system S' as a result of its relative movement with regard to the system S is now located in amended space-time. Therefore, the speed of the system S with regard to system S' need not be v' = -v . It depends on what proportion will change the length and time units. For the same reason, in the equation no. 4 the constant k' should be used instead of k, as it is evident that the k' is not equal to k . If these changes are applied, the Lorentz transformation would look quite different. It should be noted, however, that in order to make such changes, it is necessary to go deeper into space-time. That I have tried in this work. This can not be solved by pure mathematics.

Speed of light

My work began with the presumption of the its own constant speed of light (measured in the location of the light beam). Later I came to the realization that postulate of the constant speed of light applies only to the speed of light, expressed in units of length of the respective space (ie in length's units appropriate with the space-time density of the given location) and in units of time of the common chosen reference frame (e.g. on Earth's surface), that is in the so called system Zct.

Michelson-Morley Experiment

This experiment was carried out on the basis of incorrect theoretical assumptions:

1. Actually ether, or space-time structure, does not flow in the direction opposite the Earth's motion around the Sun on the Earth's surface, but in a direction perpendicular to the Earth's surface.

2. The speed of light, measured in the system Zct, depends on the space density in a given place and practically does not depend on the movement of the reference system with regard to the space-time (ether).

Paradoxes discovered by Quantum Physics

There are several paradoxes discovered by Quantum Physics of whose common nature is instantaneous interaction between the remote mass particles (like there is so called the EPR "Einstein-Podolski-Rosen" paradox). The existence of the quantum of primary matter mentioned, offers the way how to explain these paradoxes, because the interior of the QPM behaves unlocally, hence enabling the instantaneous interaction

Physical fields

All physical fields could be explained by the flow of the space-time structure into a charge due to the flow's respective acceleration, or, by the flow of the space-time structure out of a charge, due to the flow's respective deceleration.

Cosmology

Our look on the origin, structure and space-time relationships of the universe will differ, from the point of view of the space flow theory, with respect to the contemporary respected theories. The redshift measured on radiation coming from galaxies might be explained by the progressive reduction of the space (space-time) density, and respective increase of the speed of light, i.e. decrease of its frequency. If it is like this, the space density reduction is going on with the evolution of the universe, from the beginning. In case the evolution would have been realized in accordance with the Big Bang theory, it would have to be modified to respect the fact that also the space-time structure is expanding, and hence that the evolution is taking place in a gradually slowing down of the time flow (the time density decreases with the space expansion at a slower rate than the space density).This phenomenon is in accordance with the theory of cosmic inflation, explaining the extremly rapid expansion of the early universe, and with Hubble Space Telescope (HST) observations of very distant supernovae, confirming accelerated expansion of the universe.

It is very likely that what we call primary matter inside the space-time cells, although in a very diluted form, behaves gravitationally. This would mean that the universe is full of such matter, and that the long time seeked dark matter is hidden inside space-time structure.

From the equations derived in the description of orbital motion can be concluded that each space-time cell contains energy, of which source can be movement of the prime matter inside it. So we can say that the universe (quantum QPM) is full of such energy, and that also the long time seeked dark energy is hidden inside space-time structure.

Cosmic objects

The mass distributiuon inside gravitational objects (like planets and stars), according to space flow theory, is determined by frame intrinsic mass density, of the object's material, by space density distribution and gravity (of course also by other physical parameters, like pressure, temperature and mechanical properties, that need not be taken into account for the simple consideration). Frame intrinsic mass density means the mass density measured by respective device located in the position where the material is located. The real mass density as seen from the chosen reference frame (like from the frame of Earth surface) however, is influenced by the space density distribution and vice versa. This is very important disclosure of the space flow theory, that greatly extends the alternatives how cosmic objects can be created. The real mass distribution ,following from the respective differential equation, can be very complicated, depending also on distribution of the frame intrinsic mass density (if the object consists of several materials). In simple cases, for the objects of a constant frame intrinsic mass density lower, equal, or higher than 5496,5 kg/m^3, the mass under the respective radius is directly proportional to the power less than 3, =3, or more than 3 of the radius. Thus, at objects,

1. approx. like stars, composed of a mass of low frame intrinsic density, the mass located near center of gravity becomes very dense, as seen from the chosen reference frame.

2. like neutron stars, the most of the mass is located near the surface of the object, and its interior might be empty.

The gravitational acceleration inside the gravitational body is directly proportional to the ((2k/3)-1)power of the radius, where k= 5,4381*10-4θ (θ stays for the frame intrinsic mass density (kg/m^3)). Thus we can derive, that: Inside the layer of the mass of the frame intrinsic mass density lower, equal, or higher than 2748,2 kg/m^3, the gravitational acceleration is increasing, stays constant, or is decreasing with the decreasing radius. Inside the layer of the mass of the frame intrinsic mass density = 5496,5 kg/m^3 the gravitational acceleration is directly proportional to the radius. The results presented leads to the consequence, that

1. (in simple case mentioned) any object, defined by the total mass and the outer radius, can be created of the mass of any frame intrinsic mass density and,

2. to enable the existence of the life, as we know it, the planets have to be composed of the mass of the average mass density approximately 5496 kg/m^3 as seen from their surface and, of the frame intrinsic mass density of their outer layer approximately 2748 kg/m^3. The average mass density 5496 kg/m^3 generates the space density =1 on planet's surface and, the frame intrinsic mass density of the outer layer of 2748 kg/m^3 ensures relatively stable conditions for life on planet's surface.

Note 1: It seems that the health troubles of the cosmonauts might be caused not only due to low gravitational field or low intensity of the magnetic field, but due to the lower space density as well, because it can be assumed that the space density affects the human body.

Note 2: On the planet Mars, if we apply the basic parameters:

M = 6.4219 * 10 23 kg .... the mass of the planet

R_0 = 3.397 * 10^6 m .... radius of the planet's surface

rx = 3.0327 * 10^6 m .... radius at which the density of space = 1, if there was a whole mass of the planet below it,

we can calculate the space density = 0.892, ie 10.8% below the Earth's surface. This results in that the speed of light on the surface of Mars is of 5.88% higher than on the surface of the Earth. This circumstance can be very serious for stays of a human crew on Mars, especially during landing, since it may affect the operation of measuring devices, which determines the landing accuracy and the life of the crew.

Note 3: In this work it is assumed that the measuring instrumentss "breathe" in space-time, e.g. that their parts, responsible for measurement of the distance and time are always adapting themselves to the density of the area in which they are located. This statement may not be true for all measurement methods. It should be counted with this factor (urgently as well if necessary) when planning research or other uses of space objects.

Nonduality

The space flow theory says that there is nothing but the prime matter. All the other, that exists, is arising from it due to its oscillations (creating the space-time structure), due to thickening and thinning of the space-time structure and due to accelerated flow of the space-time structure. Looking from our space-time world into the depth of the space, we might see the space-time cells of the different space density. Looking deeper, we might see the ocean of the prime matter oscillating into huge number of the dense and thin spots. Going deeper we would become the prime matter and we would not see any dense nor thin spots, only the calm ocean. All actions are stopped, we do nothing, we ARE only .

The philosophy of Nonduality says that there is nothing but one Spirit in the Universe, and that everything living or inanimate is inseparable and indivisible part of this Spirit. The Vedas (sacred scriptures of Hinduism) are the oldest source of this philosophy. Very aptly is this principle interpreted in a short treatise, named Ashtavakra Gita.

To tell the truth, I got acquainted with this philosophy before I started to write the space flow theory. However I grasped only before completing the work what really nonduality means and, that the idea of the space flow theory corresponds with "Advaita Vedanta".

Theological coherence

Time is defined in the space flow theory as a succession of the moments of thickening (or thinning) of the space-time cells. From our Universe, for example from our place (frame) on the surface of Earth, we can imagine the QPM, mentioned above, in accordance with the space flow theory, and due its huge size, oscillating at frequency approaching zero (This frequency might be measured by the device located in our space-time structure. In fact, however, QPM is in extremely high energetic state due to the movement of primary matter, and our definition of time here fails inside it, because the primary matter is not quantized). So, if God would have dwelled in a space-time structure, formed of many QPM's (of many worlds), he would be really almost everlasting, as it is written in 2Pe 3:8 : "...But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years and a thousand years as one day." Omnipresence or ubiquity is the property of being present everywhere. According to eastern theism, God is present everywhere. Divine omnipresence is thus one of the divine attributes, although in western theism omnipresence has attracted less philosophical attention than such attributes as omnipotence, omniscience, or being eternal. The conception of the space flow theory, based on presumption of the existence of the quantum of the primary matter (QPM), with its unlocal behaviour, offers the possibility to be everywhere, at the same time. To tell the truth, we can imagine such "unbelievable" phenomenon from exterior of the QPM, because we can imagine the mass object as dissolved inside QPM, but it is difficult to identify with the idea of such a glancing from inside QPM. But it is God's business. For thousand of years, philosophers and sages, and for last decades many scientists, have come to the realization that there is only one substance and we are therefore all part of it. This substance can be called Awareness, Consciousness, Spirit, Advaita, Brahman, Tao, Nirvana, God, or even prime matter. It is constant, ever present, unchangeable and is the essence of all existence. From the common, scientific and theistic point of view, this entity could be named the Observer (or christian God the Father). It is the only entity that could manifest itself by such atributes like omnipotence, omniscience, omnipresence and eternity, although from a philosophical point of view, it is manifesting itself by attribute only resulting from the name "I am who I am" (Exodus 3:14), because this attribute contains all.

Kosice, November 1st 2012

Kosice, December 9th 2016 (Poznámky 2 a 3)

My respectable readers, please, take into account that this work, broadly speaking,

shows that the spacetime continuum is neither homogeneous nor isotropic,

which is mainly related to the ratio of space-time densities of the two compared space-time continua.

This means that the laws of physics, physical objects or properties, known in our space-time continuum,

are modified in a different space-time continuum in accordance with its the space-time density and,

at zero density (inside the QPM quantum) are most probably transformed into unity

with vast potential to become anything , with any property.

Therefore, the primary substance of the universe (of the quantum QPM),

which is discussed here in the theological sense, may really contain all existence

including all its features (material and immaterial), and even may manifest itself as live, creative, inspiring, full of love

and of the ability to be itself in every moment (because it exists in the eternal moment).

In this sense, it might be assumed that the following quotations from the Vedas, Koran and the Bible are talking about the same thing,

called Awareness, Consciousness, Spirit, Advaita, Brahman, Tao, Nirvana, God, or even prime matter.

Meditate on yourself as motionless awareness,

free from any dualism,

giving up the mistaken idea that you are just a derivative consciousness

or anything external or internal.

(Ashtavakra Gita 1.13)

In the heart of all things, of whatever there is in the universe, dwells the Lord.

(Isha Upanishad)

OM. This eternal word is all : what was, what is and what shall be, and what beyond is in eternity.

All is OM.

(Upanishads)

Wheresoever you turn, there is the face of God.

(Koran)

And when the Great Ra-M-Cha was irradiated

from the great Light of Joy,

the Great Flow of Inglie

(of the first Living Light)

burst from him.

(Vedas by Aryanic Slovieni,

Book of Light)

In the beginning was the Word, and the Word was with God, and the Word was God.

He was with God in the beginning. Through him all things were made;

without him nothing was made that has been made.

(John 1)

As a five-year boy, I knew that the most amazing things I met in the world were the starry sky above me, and the consciousness in me. (I know that many knew it, for example also Kant and Jung). I believe that those who know it today, will go even further. In particular because the understanding that the starry sky finds itself in space and in the consciousness of each of us, at the same time, can significantly contribute to evolutionary step of humanity. However in case only only, if we prove to realize each himself as the universal consciousness. This cognizance is a direct guidance on how to properly answer two questions: "Who are you, man?" and, "What to do" :

We already know that the entity that forms the essence of existence is in our spacetime invisible and undetectable (but perceptible), and fills the entire universe, as well as any mass particles in it. Each one of us can come to perceive this entity if he is looking for what's the smoothest, and perhaps the most empty in himself. In simple terms, it is the perception of signs of life within us (and particularly in the nerve centers), because in them or behind them it can be perceived this "nothing", which basically contains the whole existence. Already during the first flash of light during meditation you feel joy and enthusiasm, and those who carry their cross also great relief (my yoke is sweet and my burden is light - the words of Jesus Christ). Understanding this fact, that is, permanent identification with it, has an important positive effect through emotion (created by unconditional love) not only on man but also on life itself (the remote influence of consciousness on the state of matter has already been demonstrated). It does not matter how someone calls this dominant entity, the spirit, the brahman, the tao, the consciousness, or the primary substance. It is our creator. In its invisible light, it shows us the direction to our evolutionary step, and perhaps to the kingdom of God.

The meaning of the term unconditional love lies mainly in its logical content,

but at this time also in the feeling of enthusiasm, rapture, humility, astonishment and nonlocality,

arising in man by understanding the relationship between consciousness and quantum physics.

This can lead to a state that advanced spiritual authorities call enlightenment.

However, it is important to know that this advice will probably not allow everyone to start perceiving the spiritual essence, because the consciousness of many people is trapped in feelings or minds. It is always necessary to know who is aware of life. Devote the necessary time to be fully aware of your current experience and fully accepting all thoughts, emotions, feelings, everything that is present within and around you, without identifying with them. As noted above in this chapter, universal consciousness is apparently associated with space, even creating it. It is therefore necessary to know to connect our consciousness with the space of the universe (that is, the QPM quantum space, which is therefore nonlocal, that is, everything contained in it is virtually omnipresent and exists in the present). The quality of such identification is related to spiritual forwardness. However, after a brief workout, the vision of an extensive space can be achieved with the initial progress.

In fact, the advices for the cultivation of consciousness (evolutionary progress) actually lead to the transformation of human consciousness from the past into the present ("Be awake"- the words of Jesus Christ), because we have already understood that the essence of existence exists in a permanent presence. So if we look into our interior, we discover a lot of thoughts, feelings as well as emotional and other injuries from the past that create a barrier to us. Behind this barrier, which we only observe, is what we are looking for, God, the Entity that forms the essence of existence, or the Permanent Presence. A person at least slightly advanced in the spiritual sphere is able to perceive this entity, which gradually leads him to anchoring consciousness to the present. Those who do not have such perceptions will achieve the goal by faith and surrendering to him. But we did just the first step that brought us inspiration, and it turns into a positive emotion. This can be called "unconditional love". All, what is behind the barrier, has the character of a high-energy, or, even the high-frequency field, and suddenly opening the barrier could then damage our molecular or cellular structures. Again: Just look at the barrier. This process itself leads to a gradual increase in the frequency of our consciousness and possibly to the modification of the relevant body structures. He exists !!! We have been searching for this goal for centuries and millennia. And further? Our expectation could follow from the words of Jesus Christ "Blessed are the pure in heart, for they shall see God" (Ps 24).

(Please note that: Purity of heart lies in an inspiring, creative, wonderful, and intimate relationship with the Universe (Oneness, God.) A pure heart is the result of the path of maturation, through purification and renunciation of the way of life that leads to suffering).

Please keep communicating with the universe as follows:

You, the source of everything, thank you for filling me with your light.

Frantisek Stefanko

Kosice December 16th 2018

Epilogue slovak version

Epilogue italian version

It is likely that you, the man, will understand that you are an immaterial entity, whose home is a field of energy manifested by ruthless penetration, bringing joy, love, inspiration, creativity, spirituality, optimism, peace, intuition and divine abilities, and in particular the transparent presence of enormous life force. And when you get so far, you will have the opportunity to get rid of the ego (transform it) and advance higher, into unity. IEOUA!

Yes, one who has come this far must go on. However, it is not easy. Czech mystic Kvetoslav Minarik points out that the most difficult it's up to you to force yourself to be completely depersonalized and selfless, while maintaining the ability to act. It often lasts a lifetime. However, a great advantage is given to the one who, recognizing himself in everything, rejoices with his whole being

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Epilóg

Nepovažujem svoju prácu za hotovú, a určite nie bez chýb. Napriek tomu chcem vyjadriť presvedčenie, že teória toku priestoru by mohla byť užitočná na ceste fyziky k teórii všetkého. Je to však beh na dlhú cestu presvedčiť vedecké autority a preukázať perspektívu teórie zvonku. Okrem toho, dostávam sa do veku, kedy ma vnútro časopriestorového kvanta láka viac ako jeho zovňajšok. Preto by som sa chcel zmieniť ešte o niekoľkých zaujímavých veciach, ktoré vyplývajú, alebo, by mohli vyplynúť z teórie toku priestoru.

Pozadie Teórie Toku Priestoru

Teória toku priestoru vychádza z prezumpcie vesmíru vyplneného jeho primárnou hmotou, oscilujúcou. a vytvárajúcou tak časopriestorovú štruktúru, pozostávajúcu sa z obrovského množstva časopriestorových buniek (alebo vlnových balíkov). Táto časopriestorová štruktúra a z nej vzniknuté hmotné častice sú základné entity, ktorých existencia musela predchádzať nasledujúci vývoj vesmíru. Určujúcou zložkou týchto počiatočných entít je samozrejme primárna hmota. o ktorej vlastnostiach a správaní môžeme len špekulovať. Je však zrejmé, že sa jedná o entitu, ktorá vyplňuje vnútro časoprostorového kvanta. Už sme pochopili z kvantovej fyziky, že vnútro časopriestorového kvanta sa chová nelokálne, čo znamená, že aj primárna hmota sa chová nelokálne, a teda nie je štruktúrovaná. Tak možno vidieť, že základnou substanciou vesmíru musí byť kvantum primárnej hmoty (QPM, z anglického Quantum of Primary Matter). Oscilácie vo vnútri QPM vytvárajú hustejšie a redšie miesta (bunky), ako vlny v mori. Hustota, rozmer a frekvencia buniek vytvára našu časopriestorovú štruktúru a teda náš známy vesmír. Takže možno povedať, že neexistuje nič iné, ako primárna hmota, alebo "nomenon", ako je nádherne vysvetlené v "Ashtavakra Gita". Pôvod hmotných častic musí súvisieť so zdrojom oscilácií v QPM, pretože hmotnosť v teórii toku priestoru je definovaná ako veľmi hustá časopriestorová štruktúra, ktorá na začiatku vývoja vesmíru by mohla byť vytvorená iba ostrou zmenou oscilácie. V následujúcej evolúcii by vytváranie hmotných častíc byť mohlo byť urýchlené kolíziami a gravitačnými poliami. Podmienkou pre existenciu stabilnej hmotnej častice samozrejme musí byť udržiavanie konštantného toku priestoru, tečúceho z našej časopriestorovej štruktúry do iného, paralelného kontinua, alebo iného vesmíru.

Lorentzova transformácia

Vo svojej práci som sa doposiaľ nevyjadril k Špeciálnej a Všeobecnej Teórii Relativity. Najmä preto, lebo k nim ako aj ku kvantovej mechanike mám veľký rešpekt. Ony sú a dlho ešte budú základom vedeckého a technického rozvoja, ale aj filozofického bádania. Ale sú aj predmetom vedeckých diskuzií a sporov. Základné vzťahy Einsteinovej Špeciálnej relativity sú odvodené zo 4 Lorentzových transformačných rovníc medzi vzťažnou sústavou S a vzťažnou sústavou S', pohybujúcou sa vzhľadom na sústavu S rýchlosťou v (t.j. medzi dvoma inerciálnymi sústavami):

1. x' = k(x - vt)

k... konštanta

x... vzdialenosť v sústave S

x'... vzdialenosť v sústave S'

t... čas v sústave S

2. y' = y

3. z' = z

4. x = k(x' + vt')

t'... čas v sústave "S'"

Vidíme, že v rovnici č. 4 je rýchlosť v' nahradená rýchlosťou v. To vyplýva z tzv. 1. postulátu špeciálnej teórie relativity: "Všetky fyzikálne zákony možno vyjadriť rovnicami, ktoré majú rovnaký tvar vo všetkých vzťažných sústavách pohybujúcích se navzájom konštantnou rychlosťou." Tento postulát je však nesprávny. Ak to ešte nie je celkom zrejmé v tomto štádiu riešenia, po vypracovaní všeobecnej teórie relativity to bolo priamo pred očami: sústava S' sa v dôsledku jej pohybu vzhľadom na sústavu S nachádza v zmenenom časopriestore. Preto rýchlosť sústavy S vzhľadom na sústavu S' nemusí byť v' = -v. To závisí od toho, v akom pomere sa zmenia jednotky dlžky a času. Z rovnakého dôvodu by v rovnici č. 4 mala byť použitá konštanta k' namiesto k, lebo je evidentné, že k' sa nerovná k. Ak by sa aplikovali tieto zmeny, Lorentzova transformácia by vyzerala celkom odlišne. Treba však podotknúť, že aby bolo možné takéto zmeny urobiť, bolo by treba ísť hlbšie do časopriestoru. O to som sa pokúsil v tejto práci. To sa nedá urobiť iba pomocou samotnej matematiky.

Rýchlosť svetla

Moja práca začala s prezumpciou konštantnej vlastnej rýchlosti svetla (meranej v mieste pohybu svetla). Až neskôr som dospel k poznatku, že postulát konštantnej rýchlosti platí iba pre rýchlosť svetla vyjadrenú v jednotkách dlžky daného miesta (t. j. danej časopriestorovej hustoty) a v jednotkách času vzťažnej sústavy (napr. na povrchu Zeme), t. j. v tak zvanej sústave Zct.

Experiment Michelson Morley

Tento experiment bol vykonaný na základe nesprávnych teoretických predpokladov:

1. V skutočnosti éter, alebo časopriestorová štruktúra, na povrchu Zeme, neprúdi v smere pohybu Zeme okolo Slnka, ale v smere kolmom na povrch Zeme.

2. Rýchlosť svetla, meraná v sústave Zct, je daná hustotou priestoru v danom mieste a prakticky nezáleží na pohybu sústavy vôči časopriestoru (éteru).

Paradoxy objavené kvantovou fyzikou

Existuje niekoľko paradoxov objavených kvantovou fyzikou ktorých spoločnou podstatou je okamžitá interakcia medzi vzdialenými hmotnými časticami ako napríklad tzv EPR paradox (Einstein-Podolski-Rosen). Existencia zmieneného kvanta primárnej hmoty ponúka spôsob ako vysvetliť tieto paradoxy, pretože vnútro QPM sa chová nelokálne a umožňuje tak okamžitú interakciu.

Fyzikálne polia

Všetky fyzikálne polia možno vysvetliť tokom časopriestorovej štruktúry do náboja, v dôsledku zrýchlenia toku priestoru , alebo tokom časopriestorovej štruktúry von z náboja, v dôsledku spomalenia (záporného zrýchlenia) toku priestoru.

Kozmológia

Náš pohľad na pôvod, štruktúru a časopriestorové vzťahy vo vesmíre sa bude líšiť, z hľadiska teórie toku priestoru, v porovnaní so súčasne rešpektovanými teóriami. Červený posun meraný na žiarení prichádzajúcom z galaxií môže byť vysvetlený postupným znižovaním priestorovej (t.j. aj časopriestorovej) hustoty, a následne zvýšením rýchlosti svetla a znížením jeho frekvencie. Ak je to tak, k zníženiu hustoty priestoru dochádza s vývojom vesmíru od jeho začiatku. V prípade, že by evolúcia mala byť realizovaná v súlade s teóriu veľkého tresku, táto teória by musela byť upravená tak, aby rešpektovla skutočnosť, že aj časopriestorová štruktúra expanduje, čiže, že sa evolúcia uskutočňuje v postupne sa spomaľujúcom toku času (hustota času sa s expanziou priestoru znižuje pomalším tempom ako hustota priestoru). Tento jav je v súlade s teóriou vesmírnej inflácie, vysvetľúcou extrémne rýchlu expanziu raného vesmíru, a s pozorovaniami veľmi vzdialených supernov Hubbleovým Space Telescopom (HST ), potvrdzujúcimi zrýchlené rozpínanie vesmíru.

Je veľmi pravdepodobné, že to, čo nazývame primárnou hmotu vo vnútri časopriestorových buniek, aj keď vo veľmi zriedenej forme, sa chová gravitačne. To by znamenalo, že vesmír je plný takej hmoty, a že dlho hľadaná temná hmota je skrytá vo vnútri časopriestorovej štruktúry.

Z rovníc odvodených v popise orbitálneho pohybu možno dôjsť k záveru, že každá časopriestorová bunka obsahuje energiu, ktorej zdrojom môže byť pohyb primárnej hmoty v jej vnútri. To znamená, že vesmír (kvantum QPM) je plný takej energie, a že aj dlho hľadaná temná energia je skrytá vo vnútri časopriestorovej štruktúry.

Kozmické objekty

Rozloženie hmoty vnútri gravitačných objektov (ako planéty a hviezdy), je podľa teórie toku priestoru určené vlastnou hustotou hmoty materiálu kozmického objektu, rozložením priestorovej hustoty a gravitáciou (samozrejme aj inými fyzikálnymi parametrami, ako je tlak, teplota a mechanické vlastnosti, ktoré nemusia byť brané do úvahy pre jednoduchú úvahu). Termín vlastná hustota hmoty znamená hustotu meranú príslušným zariadením nachádzajúcom sa v mieste, kde sa nachádza meraný materiál. Avšak skutočná hustota hmoty, ako je videná zo zvolenej referenčnej sústavy (ako napr. zo sústavy odpovedajúcej hustote priestoru na zemského povrchu) je ovplyvnená rozložením hustoty priestoru, a naopak. Toto je veľmi dôležitý objav teórie toku priestoru, ktorý významne rozširuje alternatívy, ako možno vytvárať kozmické objekty. Skutočné rozloženie hmotnosti, vyplývajúce z príslušných diferenciálnych rovníc, môže byť veľmi komplikované, závisiace aj od rozloženia vlastnej hustoty hmoty (v prípade, že objekt sa skladá z niekoľkých materiálov). V jednoduchých prípadoch, pre objekty s konštantnou vlastnou hustotou hmoty nižšou, rovnakou, alebo väčšou ako 5496,5 kg/m^3, hmotnosť pod príslušným polomerom je priamo úmerná mocnine polomeru s mocniteľom menším ako 3, rovným 3, alebo väčším ako 3. Tak, pri objektoch,

1. -cca. ako hviezdy, zložených z hmoty s nízkou vlastnou hustotou, sa hmotnosť nachádzajúca sa v blízkosti stredu gravitácie stáva veľmi hustou vzhľadom k referenčnej sústave na povrchu objektu.

2. -ako neutrónové hviezdy, sa najviac hmoty sa nachádza v blízkosti povrchu objektu, a jeho vnútro môže byť prázdne.

Gravitačné zrýchlenie vo vnútri gravitačného objektu je priamo úmerné ((2k / 3) -1) mocnine polomeru, kde k = 5,4381*10-4θ (θ je vlastná hustota hmoty (kg/m^3)). Tak možno odvodiť, že: Vo vnútri vrstvy s hmotou o vlastnej hustote nižšou, rovnou alebo vyššou ako 2748,2 kg/m^3 gravitačné zrýchlenie rastie, zostáva konštantné alebo sa znižuje s klesajúcou polomerom. Vo vnútri vrstvy s hmotou o vlastnej hustote = 5496,5 kg/m^3 gravitačné zrýchlenie je priamo úmerné polomeru. Uvedené výsledky vedú k záveru, že

1. (v zmienenom jednoduchom prípade) akýkoľvek objekt, definovaný celkovou hmotnosťou a vonkajším priemerom, môže byť vytvorený z hmoty o akejkoľvek vlastnej hustote, a,

2. pre zabezpečenie existencie života, ako ho poznáme, planéty by mali byť zložené z hmotnosti o priemernej hustote hmoty, ako ju vidíme z povrchu objektu, približne 5496 kg/m^3, a o vlastnej hustote hmoty na ich povrchu približne 2748 kg/m3. Priemerná hustota hmoty 5496 kg/m^3 vytvára hustotu priestoru = 1 na povrchu planéty, a vlastná hustota hmoty vonkajšej vrstvy 2748 kg/m^3 zaisťuje relatívne stabilné podmienky pre život na povrchu planéty.

Poznámka 1: Zdá sa, že sa zdravotné problémy kozmonautov mohli byť spôsobené nielen slabým gravitačným poľom alebo nízkou intenzitou magnetického poľa, ale rovnako aj nižšou hustotou priestoru (napríklad na Mesiaci), lebo možno predpokladať, že hustota priestoru má vplyv na ľudské telo.

Poznámka 2: Na planéte Mars, ak aplikujeme jej základné parametre:

M = 6,4219*10^23 kg ....hmotnosť planéty,

R_0 = 3,397*10^6 m ....polomer povrchu planéty ,

rx = 3,0327*10^6 m .... polomer pri ktorom by bola hustota priestoru = 1, ak by bola celá hmotnosť planéty pod ním,

je hustota priestoru = 0,892, teda o 10,8% nižšia ako na povrchu Zeme. To má za následok, že rýchlosť svetla na povrchu Marsu je o 5,88% vyššia ako na povrch Zeme. Táto okolnosť môže byť veľmi závažná pri pobyte ľudskej posádky na Marse,ale najmä pri pristávaní, pretože môže ovplyvniť činnosť meracích prístrojov, od ktorých závisí presnosť pristávania a život posádky.

Poznámka 3: V tejto práci sa predpokladá, že meracie prístroje "dýchajú" s časopriestorom, t.j. že ich časti zodpovedné za meranie vzdialenosti a času sa prispôsobujú hustote priestoru v akej sa nachádzajú. Toto tvrdenie však nemusí byť pravdivé pre všetky meracie metódy. S touto okolnosťou však treba rátať (niekedy aj urgentne) pri plánovaní výskumu, alebo iného využitia kozmických objektov.

Neduálnosť

Teória toku priestoru hovorí, že niet ničoho, okrem primárnej hmoty. Všetko ostatné, čo existuje, vzniká z nej v dôsledku jej oscilácií (tvoriac tak časopriestorovú štruktúru), v dôsledku zahusťovania a zrieďovania časopriestorovej štruktúry a v dôsledku zrýchleného toku časopriestorovej štruktúry. Hľadiac z nášho časo-priestorového sveta do hĺbky priestoru, mohli by sme vidieť časopriestorové bunky rôznej časopriestorovej hustoty. Hľadiac hlbšie, mohli by sme vidieť oceán primárnej hmoty oscilujúci do obrovského množstva hustých a riedkých škvrn. Pokračujúc hlbšie, stali by sme sa primárnou hmotou a nevideli by sme žiadne husté, ani riedke miesta, len pokojný oceán. Všetok pohyb tu zaniká, my nerobíme nič, len SME.

Filozofia Neduálnosi hovorí, že vo vesmíre existuje len jeden Duch, a že všetko živé alebo neživé je neoddeliteľnou a nedeliteľnou súčasťou tohto Ducha. Védy (Sväté písma hinduizmu) sú najstarším zdrojom tejto filozofie. Veľmi výstižne je tento princíp vysvetlený v krátkom pojednaní, pod názvom Ashtavakra Gita. Aby som povedal pravdu, s touto filozófiou som sa zoznámil prv ako som začal písať teóriu toku priestoru. Avšak pochopil som až pred dokončením práce, čo skutočne Neduálnosť znamená, a že idea teórie toku priestoru zodpovedá filozófii "Advaita Vedanta".

Teologická súvislosť

Čas, v Teórii Toku Priestoru, je definovaný ako postupnosť momentov zahustenia (alebo zriedenia) časopriestorových buniek. Z nášho vesmíru, napríklad z nášho miesta (sústavy) na povrchu Zeme si môžeme predstaviť zmienene kvantum QPM, oscilujúce s frekvenciou blížiacou sa nule, v súlade s teóriou toku priestoru a v dôsledku jeho obrovskej veľkosti (Táto frekvencia môže byť meraná prístrojom umiestnenom v našej časopriestorovej štruktúre. V skutočnosti však QPM je vo veľmi vysokom energetickom stave v dôsledku pohybu primárnej hmoty, a naša definícia času tu vnútri zlyhá, pretože primárna hmota nie je kvantovaná). Teda, ak by Boh býval v časopriestorovej štruktúre tvorenej z mnohých QPM (z mnohých svetov), bol by naozaj takmer večný, ako je písané v 2Pe 3:8 : "Ale, nech však neuniká vašej pozornosti jedna skutočnosť, milovaní, že jeden deň je u Jehovu ako tisíc rokov a tisíc rokov ako jeden deň". Podľa východného theizmu, Boh je prítomný všade.Božská všadeprítomnosť je tak jedným z božských atribútov, aj keď v západnom theizme všadeprítomnosť priťahovala menej filozofickej pozornosti ako všemohúcnosť, vševedúcnosť, alebo večnosť. Koncepcia Teórie Toku Priestoru, založená na predpoklade existencie kvanta primárnej hmoty QPM, s jeho nelokálnym chovaním, ponúka mužnosť byť všade v rovnakom čase. Pravdupovediac, tento neuveriteľný fenomén si vieme predstaviť z vonkajšku kvanta QPM, pretože si vieme predstaviť hmotný objekt ako rozpustený v QPM, ale ťažko sa stotožňujeme s takouto predstavou hľadiac z vnútra QPM. Ale to je Božia záležitosť. Po tisíc rokov filozofi a mudrci, a v posledných dekádach mnohí vedci, dospeli k poznaniu, že existuje iba jedna substancia a preto my sme jej časťou. Táto substancia môže byť nazývaná Vedomie, Duch, Advaita, Brahman, Tao, Nirvána, Boh, alebo aj Primárna hmota. Je konštantná, večná, nemenná, a je esenciou všetkej existencie. Zo spoločného theistického aj vedeckého hľadiska táto entita môže byť nazývaná Pozorovateľ (alebo kresťanský Boh Otec). Je to jediná entita, ktorá sa môže prejavovať takými atribútami ako všemohúcnosť, vševedúcnosť, všadeprítomnosť a večnosť, aj keď z filozofického hľadiska by jej mal prislúchať iba atribút vyplývajúci z mena "Som ktorý Som" (Exodus 3:14), lebo tento atribút obsahuje všetko.

Košice, 17.November 2012

Košice, 9.December 2016 (Poznámky 2 a 3)

Moji vážení čitatelia, vezmite prosím do úvahy, že táto práca, všeobecne povedané,

ukazuje, že časopriestorové kontinuum nie je ani homogénne, ani izotropné,

čo súvisí najmä s pomerom časopriestorových hustôt dvoch porovnávaných časopriestorových kontinuí.

To znamená, že fyzikálne zákony, fyzikálne objekty, či vlastnosti, známe v našom časopriestore,

sú v inom časopriestore modifikované v súlade s jeho hustotou časopriestoru,

a pri nulovej hustote (vo vnútri kvanta QPM) sú teda zrejme transformované do jednoty,

s obrovským potenciálom stať sa čímkoľvek, s akoukoľvek vlastnosťou.

Z tohto dôvodu, primárna substancia v univerze (kvantum QPM),

o ktorej tu hovoríme v teologickom zmysle, môže naozaj obsahovať celú existenciu

vrátane všetkých jej vlastností (hmotných aj nehmotných), a dokonca sa môže prejavovať aj ako živá, tvorivá, inšpiratívna, plná lásky

a schopnosti byť sama sebou v každom okamžiku (lebo ona existuje vo večnom okamžiku).

V tomto zmysle by bolo možné predpokladať, že následujúce citácie z Véd, Koránu a Biblie hovoria o tej istej veci,

nazývanej vedomie, duch, Advaita, Brahman, Tao, Nirvana, Boh, alebo aj primárna hmota.

Medituj o sebe ako o nehybnom vedomí,

zbavenom akéhokoľvek dualizmu,

vzdávajúc sa mylnej predstavy že si len odvodené vedomie,

alebo niečo vonkajšie, či vnútorné.

(Aštavakra Gita 1.13)

V srdci všetkých vecí, nech sú z čohokoľvek vo vesmíre, prebýva Pán.

(Iša Upanišada)

ÓM. Toto večné slovo je všetko: čo bolo, čo je, čo bude, a čo iné je ešte vo večnosti.

Všetko je ÓM.

(Upanišady)

Kamkoľvek sa obrátiš, je tvár Božia.

(Korán)

A keď Veľký Ra-M-Cha bol ožiarený

veľkým svetlom radosti,

veľký tok Inglie

(prvého živého svetla)

vybuchol z neho.

(Kniha svetla Árijskych Slovienov)

Na počiatku bolo Slovo, to Slovo bolo u Boha a to Slovo bolo Boh.

Ono bolo na počiatku u Boha. Ním vzniklo všetko;

a bez neho nevzniklo nič z toho, čo jestvuje.

(Ján 1)

Ako päťročný chlapec som vedel, že to najúžasnejšie čo na svete stretávam, je hviezdna obloha nado mnou a vedomie vo mne (viem, že to vedeli skoro všetci, napr. aj Kant a Jung). Verím, že tí, ktorí to vedia dnes, pôjdu ešte ďalej. Najmä preto, lebo pochopenie skutočnosti, že tie hviezdy sa súčasne nachádzajú v kozmickom priestore aj vo vedomí každého z nás, môže významnou mierou prispieť k vývojovému kroku ľudstva. Avšak len ak si dokážeme uvedomiť každý sám seba ako univerzálne vedomie. Toto poznanie je priamy návod, ako správne odpovedať na dve otázky: "Kto si, človeče?" a "Čo robiť" :

Už vieme,že entita, ktorá tvorí podstatu existencie, je v našom časopriestore neviditeľná a nemerateľná (ale vnímateľná), a vyplňuje celé univerzum, ako aj každú hmotnú časticu v ňom. Každý z nás môže dospieť k vnímaniu tejto entity, ak sám v sebe hľadá to čo je najjemnejšie, a možno najprázdnejšie. Jednoduchšie povedané, ide o vnímanie prejavov života v našom vnútri (a najmä v nervových centrách), lebo v nich alebo za nimi možno vnímať to "nič", ktoré v podstate obsahuje celú existenciu. Už pri prvom záblesku svetla počas meditácie pocítite radosť a nadšenie, a tí čo nesú svoj kríž aj veľkú úľavu (moje jarmo je sladké a moje bremeno je ľahké - slová Ježiša Krista). Pochopenie tejto skutočnosti, t. j. trvalé stotožnenie sa s ňou vo vedomí má prostredníctvom emócie (vytváranej nepodmienenou láskou) významný pozitívny vplyv nielen na človeka ale aj na život sám (diaľkový vplyv vedomia na stav hmotnej častice už bol preukázaný). Je jedno ako tú dominantnú entitu kto nazve, či boh, duch, brahman, tao, vedomie, alebo primárna substancia. Ona je našim stvoriteľom. Ona nám svojim neviditeľným svetlom ukazuje smer k evolučnému kroku, a možno aj k Božiemu kráľovstvu.

Význam pojmu nepodmienečná láska spočíva najmä v jeho logickom obsahu,

ale súčasne aj v pocite nadšenia, vytrhnutia, pokory, úžasu a nelokálnosti,

vznikajúceho u človeka pochopením vzťahu medzi vedomím a kvantovou fyzikou.

To môže viesť k stavu, ktorý vyspelé duchovné autority nazývajú osvietením.

Treba však vedieť, že zmienená rada pravdepodobne neumožní všetkým ani naštartovať vnímanie duchovnej podstaty, pretože vedomie mnohých je uväznené v pocitoch alebo v mysli. Vždy treba vedieť kto si uvedomuje život. Venuj potrebný čas tomu, aby si si bol plne vedomý svojej aktuálne prežívanej skúsenosti a plne prijal všetky myšlienky, emócie, pocity, všetko, čo je práve prítomné vo tvojom vnútri aj okolo teba, bez toho, aby si sa s čímkoľvek stotožňoval. Ako bolo vyššie uvedené v tejto kapitole, univerzálne vedomie je zrejme spojené s priestorom, dokonca ho vytvára. Treba preto vedieť svoje vedomie spájať s priestorom univerza (ide o priestor kvanta QPM, ktorý sa teda chová nelokálne, t.j. všetko čo je v ňom obsiahnuté je v podstate všadeprítomné, a existuje v prítomnosti). Kvatita takého stotožnenia súvisí s vyspelosťou v duchovnej oblasti. Avšak po krátkom tréningu predstavy rozsiahleho priestoru sa dá dosiahnuť začiatočnícky pokrok.

V skutočnosti uvedené rady pre kultiváciu vedomia (evolučného pokroku) vlastne vedú k transformácii ľudského vedomia z minulosti do prítomnosti ("Buďte bdelí" - slová Ježiša Krista), lebo už sme pochopili, že podstata existencie jestvuje v trvalej prítomnosti. Ak teda hľadíme do svojho vnútra, objavíme množstvo myšlienok, pocitov, ako aj emočných a iných poranení, z minulosti, ktoré pred nami vytvárajú bariéru. Za touto bariérou, ktorú iba pozorujme, sa nachádza to, čo hľadáme, Boh, Entita tvoriaca podstatu existencie, či Trvalá prítomnosť. Človek aspoň mierne pokročilý v duchovnej sfére je schopný túto entitu vnímať, čo ho postupne privedie k zakotveniu vedomia do prítomnosti. Tí, ktorí nedisponujú takýmto vnímaním dosiahnu cieľ vierou a odovzdaním sa mu. Ale to sme urobili iba prvý krok, ktorý nám priniesol inšpiráciu, a tá sa premení na pozitívnu emóciu. Tú možno nazvať "nepodmienenou láskou". To, čo je na druhej strane má charakter vysoko-energetického, t.j. aj vysoko-frekvenčného poľa, a náhle otvorenie bariéry by následne mohlo poškodiť naše molekulárne, či bunkové štruktúry. Pteto opäť: bariéru iba pozorujme. Samotný tento proces vedie k postupnému zvyšovaniu frekvencie nášho vedomia a pravdepodobne k modifikácii uvedených telesných štruktúr. On existuje!!! Tento cieľ sme hľadali dlhé stáročia a tisícročia. A ďalej? Naše očakávanie by mohlo vyplývať zo slov Ježiša Krista "Blahoslavení čistého srdca, lebo oni uvidia Boha" (Ž 24).

(Prosím, uvedomme si, že: Čistota srdca spočíva v inšpiratívnom, kreatívnom, úžasnom a aj dôvernom vzťahu s Univerzom (Jednotou, Bohom). Čisté srdce je výsledkom cesty dozrievania, cez očisťovanie a zriekanie sa takého spôsobu života, ktorý vedie k utrpeniu).

Prosím, komunikujme neustále s univerzom, takto:

Tebe, prameň všetkého, ďakujem, že ma napĺňaš svojim svetlom.

František Štefanko

Košice, 16.Dec. 2018

Epilogue english version

Epilogue italian version

Je pravdepodobné, že ty, človek takto pochopíš, že si nehmotnou entitou, ktorej domovom je pole energie prejavujúce sa neľútostnou prenikavosťou, prinášajúce radosť, lásku, inšpiráciu, tvorivosť, duchovnosť, optimizmus, pokoj, intuíciu, božské schopnosti a najmä priehľadnú prítomnosť obrovskej životnej sily. A keď si sa dostal tak ďaleko, naskytne sa ti možnosť zbaviť sa ega (transformovať ho) a postúpiť vyššie, do jednoty. IEOUA!

Áno, kto sa dostal tak ďaleko, musí pokračovať. Nie je to však ľahké. Český mystik Květoslav Minařík upozorňuje,že najťažšie na tom je prinútiť sa k úplnéme odosobneniu a nesebeckosti, pri zachovaní akcieschopnosti. Často to trvá aj celý život. Veľkou výhodou je však obdarený ten, kto vo všetkom samého sebe poznávajúc, raduje sa celou bytosťou.

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Non ritengo il mio lavoro per finito, e sicuramente non senza errori. Tuttavia voglio dichiarare la mia convinzione che la teoria del flusso dello spazio potrebbe essere utile sulla via della fisica alla teoria del tutto. È però correre per un lungo percorso per sfondare autorità scientifiche e per dimostrare la prospettiva della teoria dall'esterno. Inoltre, io sono già in età in cui l'interno del quanto dello spazio-tempo diventa più invitante del suo esterno. Pertanto, vorrei citare ancora alcune cose interessante, che seguono, o che potrebbero scaturire dalla teoria del flusso dello spazio.

Lo sfondo della teoria del flusso dello spazio

La teoria del flusso dello spazio sta lavorando sulla presunzione dell'Universo riempito dalla sua materia prima, oscillante e così sta creando la struttura spazio-temporale, costituita di numero enorme di spazio-temporali cellule (oppure pacchetti d'onda). Questa struttura spazio-temporale e ne create particelle materiali sono le entità di base, le cui esistenza doveva precedere la seguente evoluzione dell'Universo. La componente determinante di queste entità iniziali è, naturalmente, la materia prima. di cui proprietà e il comportamento possiamo solo speculare. È evidente tuttavia che si tratta della entità, che riempe l'interno del quanto dello spazio-tempo. Abbiamo già capito dalla fisica quantistica che l'interno del quanto si comporta in modo non locale, il che significa, che anche la materia prima si comporta in modo non locale, quindi non è strutturata. Così possiamo vedere che la sostanza fondamentale dell'Universo deve essere il quanto della materia prima (QPM, dal inglese "Quantum of the Primary Matter"). Oscillazioni all'interno del QPM stanno facendo luoghi (cellule) più densi e più sottili , come le onde del mare. La densità, dimensione e la frequenza delle cellule creano la nostra struttura spazio-temporale e quindi il nostro Universo conosciuto. Quindi, si può dire che non esiste altro che la materia prima, o "nomenon", come è splendidamente illustrato in "Ashtavakra Gita". L'origine delle particelle materiali deve essere correlato con la fonte delle oscillazioni in QPM, poiché la massa in teoria del flusso dello spazio è definita come una struttura molto densa dello spazio-tempo, che all'inizio dell'evoluzione dell'universo poteva essere creato solo mediante un brusco cambiamento dell'intensità delle oscillazioni. Nella successiva evoluzione la creazione delle particelle materiali poteva essere accelerata dai collisioni mutui, e campi gravitazionali. La condizione per l'esistenza della particella materiale stabile, naturalmente, deve trovarsi nel mantenimento del flusso dello spazio costante, che fluisce dalla nostra struttura spazio-temporale in un altro continuo paralello, o altro Universo.

Trasformazione di Lorentz

Nel mio lavoro, non ho ancora espresso il mio punto di vista sulla teoria della relatività speciale e generale. Soprattutto perché, così come anche la meccanica quantistica hanno un sacco di mio rispetto. Essi sono, e per lungo tempo saranno alla base dello sviluppo scientifico e tecnologico, ma anche di ricerca filosofica. Ma ci sono anche oggetto di discussione scientifica e controversie. Equazioni base della relatività Speciale di Einstein sono derivati da quattro equazioni di trasformazione di Lorentz tra il sistema di coordinate S e sistema di coordinate S', che muove a velocità v rispetto al sistema di coordinate S (cioè tra due sistemi inerziali):

1. x '= k (x - vt)

k ... costante

x ... lunghezza nel sistema S

x '...lunghezza nel sistema S '

t ... tempo nel sistema S

2. y' = y

3. z' = z

4. x = k (x '+ vt')

t '... tempo nel sistema S'

Possiamo vedere che in equazione No. 4 la velocità v' è sostituita dalla velocità v . Ciò deriva dal cosiddetto Primo postulato della teoria della relatività speciale: "Tutte le leggi della fisica possono essere espresse da equazioni della stessa forma in tutti i sistemi di riferimento che si muovono con velocità costante con l'altro." Questo postulato non è corretto. Se non era ancora chiaro in questa fase della soluzione, dopo il completamento della teoria generale della relatività, è stato abbastanza chiaro: Il sistema S' a causa del suo movimento relativo per quanto riguarda il sistema di S si trova ora nel modificato spazio-tempo. Pertanto, la velocità del sistema S rispetto al sistema S' probabilmente non sarà v' = -v . Dipende da quale proporzione cambieranno le unità di lunghezza e di tempo. Per lo stesso motivo, in equazione No. 4 la costante k' dovrebbe essere utilizzata invece di k , in quanto è evidente che k' non è uguale a k. Se tali modifiche vengono applicate, la trasformazione di Lorentz sarebbe molto diversa. Va notato, tuttavia, che per effettuare tali modifiche si deve andare piú profondo nello spazio-tempo. Così ho provato in questo lavoro. Questo non può essere risolto con la matematica pura.

Velocità della luce

Il mio lavoro è iniziato con la presunzione della propria velocità costante della luce (misurata nella posizione del fascio di luce). Successivamente sono venuto alla realizzazione che postulato della velocità costante della luce applica solo alla velocità della luce, espressa in unità di lunghezza del rispettivo spazio (cioè nella densità dello spazio-tempo appropriata) e in unità di tempo del sistema comune di riferimento scelto (ad esempio sulla superficie terrestre), cioè nella cosidetta sistema Z ct.

Michelson-Morley esperimento

Questo esperimento è stato effettuato sulla base di errati presupposti teoretici:

1. Effettivamente etere, o struttura spazio-temporale, non scorre nella direzione opposta del movimento della Terra intorno al Sole, sulla superficie terrestre, ma in direzione perpendicolare alla superficie della Terra.

2. La velocità della luce, misurata nel sistema Z ct , dipende dalla densità spaziale in un determinato luogo e praticamente non dipende dal movimento dela sistema di coordinate rispetto allo spazio-tempo (etere) .

Paradossi scoperti dalla fisica quantistica

Ci sono diversi paradossi scoperti dalla fisica quantistica dei cui natura è la reciproca interazione istantanea tra le particelle materiali a distanza (come ce cosidetto l'EPR "Einstein-Podolski-Rosen" paradosso). L'esistenza del quanto di materia prima menzionato, offre il modo come spiegare questi paradossi, perché l'interno del QPM si comporta in modo non locale, consentendo quindi l'interazione istantanea.

Campi fisici

Tutti i campi fisici potrebbero essere spiegate dal flusso della struttura dello spazio-tempo in una carica, a causa della sua accelerazione o, dal flusso della structura dello spazio-tempo, orientato verso l' esterno della carica, a causa della sua decelerazione.

Cosmologia

Il nostro sguardo su origine, struttura e relazioni spazio-temporali nel universo sarà diverso, dal punto di vista dalla teoria del flusso dello spazio, rispetto alle teorie contemporanee rispettabile. Il "redshift" misurato sulla radiazione proveniente da galassie potrebbe essere spiegato con la progressiva riduzione di densità dello spazio (spazio-tempo), e rispettivo aumento della velocità della luce, cioè diminuzione della sua frequenza. Se è così, la riduzione della densità dello spazio si realizza continuamente dall' inizio dell' evoluzione del universo. Nel caso l'evoluzione era stata realizzata secondo la teoria del Big Bang, la teoria sarebbe dovuta essere modificata per rispettare il fatto che anche la struttura spazio-temporale è in espansione, e quindi che l'evoluzione si svolge in un graduale rallentamento del flusso del tempo (la densità del tempo decresce con l'espansione dello spazio ad una velocità inferiore rispetto alla densità dello spazio). Questo fenomeno è in accordo con la teoria dell'inflazione cosmica, che spiega l'espansione estremamente rapida del'universo primordiale, e con Hubble Space Telescope (HST) osservazioni di supernove molto distanti, che confermano l'espansione accelerata dell'universo.

E 'molto probabile che ciò che chiamamo materia prima all'interno delle cellule spazio-temporali, anche se in una forma molto diluita, si comporta gravitazionalmente. Ciò significa che l'universo è pieno di tale materia, e che la materia oscura, cosi lungo cercata, è nascosta all'interno di struttura spazio-temporale.

Dalle equazioni derivate nella descrizione del movimento orbitale si può concludere che ogni cellula spazio-temporale contiene energia, di che fonte può essere il movimento della materia prima nel suo interno. Quindi si puo dire che l'universo (quantum QPM) è pieno di tale energia, e che anche la energia oscura cosi lungo cercata, è nascosta all'interno di struttura spazio-temporale.

Oggetti cosmici

La distribuzione della massa all'interno di oggetti gravitazionali (come pianeti e stelle), secondo la teoria del flusso dello spazio, è determinata dalla densità intrinseca del materiale dell'oggetto, dalla distribuzione della densità spaziale e dalla gravità (naturalmente anche da altri parametri fisici, come la pressione, temperatura e le proprietà meccaniche, che non necessitano essere presi in considerazione per il semplice caso menzionato). Densità intrinseca significa la densità di materiale misurata dal rispettivo dispositivo, collocato nella posizione in cui si trova il materiale. La densità reale di materiale come vista dal frame di riferimento scelto (come dal frame collocato sulla superficie terrestre) tuttavia, è influenzata dalla distribuzione di densità spaziale e viceversa. Questo è molto importanta scoperta della teoria del flusso dello spazio, che estende notevolmente le alternative come gli oggetti cosmici possono essere creati. La distribuzione di massa reale, seguita dalla rispettiva equazione differenziale, può essere molto complicata, anche in funzione della distribuzione della densità intrinseca (se l'oggetto è costituito da materiali diversi). In casi semplici, per gli oggetti di una costante densità di massa intrinseca inferiore, uguale o superiore a 5496,5 kg/m^3, la quantità della massa sotto il rispettivo raggio è direttamente proporzionale alla potenza inferiore a 3, = 3, o più di 3 del raggio. Così, per oggetti

1. ca. come stelle, costituiti di una massa di densità intrinseca bassa, la massa situata vicino al centro di gravità diventa molto densa, come vista dal frame di riferimento scelto.

2. come stelle di neutroni, la maggior parte della massa si trova vicino alla superficie dell'oggetto, e il suo interno può essere vuoto.

L'accelerazione gravitazionale all'interno del corpo gravitazionale è direttamente proporzionale alla ((2k / 3) -1) potenza del raggio, dove k = 5,4381 * 10 -4 θ (θ è la densità intrinseca di massa (kg/m^3)). Così possiamo ricavare che: All'interno dello strato (del corpo gravitazionale) di densità intrinseca di massa inferiore, uguale o superiore a 2748,2 kg/m^3, l'accelerazione gravitazionale è in aumento, rimane costante o diminuisce con il raggio decrescente . All'interno dello strato di massa della densità intrinseca = 5496,5 kg/m^3 l'accelerazione gravitazionale è direttamente proporzionale al raggio. I risultati presentati portano alla conseguenza che

1. (nel caso semplice citato) qualsiasi oggetto, definito dalla massa totale e il raggio esterno, può essere creato della massa di qualsiasi densità intrinseca, e,

2. per permettere l'esistenza della vita, come la conosciamo, i pianeti devono essere composte dalla massa della densità media di massa circa 5496 kg/m^3 come vista dal loro superficie e, della densità intrinseca nel loro strato esterno di circa 2748 kg/m^3. La densità di massa media 5496 kg/m^3 genera la densità dello spazio = 1 sulla superficie del pianeta e, la densità intrinseca di massa dello strato esterno di 2748 kg/m^3 assicura condizioni relativamente stabili per la vita sulla superficie del pianeta.

Nota 1: Sembra che i problemi di salute dei cosmonauti potevano essere causati non solo a causa del basso campo gravitazionale o bassa intensità del campo magnetico, ma anche a causa della densità spaziale inferiore, perché si può presumere che la densità spaziale influisce corpo umano.

Nota 2: Per il pianeta Marte, se applichiamo i parametri di base:

M = 6,4219 * 10 23 kg .... la massa del pianeta

R 0 = 3.397 * 10 6 m .... raggio della superficie del pianeta

r x = 3,0327 * 10 6 m ....raggio in cui la densità di spazio = 1 se tutta massa del pianeta si trova sottostante,

siamo in grado di calcolare la densità spaziale = 0,892, vale a dire il 10,8% sotto la densità spaziale alla superficie della Terra. Ciò comporta che la velocità della luce è di 5,88% maggiore sulla superficie di Marte che sulla superficie della Terra. Questa circostanza può essere molto grave per i soggiorni di un equipaggio umano su Marte, in particolare durante l'atterraggio, perché questo può influire il funzionamento degli strumenti di misura che determinano la precisione di atterraggio e la vita dell'equipaggio.

Nota 3 : In questo lavoro si presume che apparecchi di misura "respirano" con lo spazio-tempo, cioè che i loro parti, responsabili della misurazione della distanza e del tempo sono adattati secondo la densità spaziale in cui si trovano. Questa asserzione non deve essere vera per tutti i metodi di misurazione. Con questo fattore, si deve contare (a volte con urgenza) durante la pianificazione di ricerca o per altre utilizzazioni dei oggetti cosmici.

Nondualità

La teoria del flusso dello spazio dice che non è altro che la materia prima. Tutto che esiste, è ne derivano per le sue oscillazioni (creando la struttura dello spazio-tempo), a causa di ispessimento e assottigliamento della struttura dello spazio-tempo e dovuto al flusso della struttura dello spazio-tempo accelerato. Guardando dal nostro mondo spazio-temporale nella profondità dello spazio, potremmo vedere le celle spazio-temporali della densità spaziale diversa. Guardando più in profondità, potremmo vedere l'oceano della materia prima oscillante nel numero enorme di punti densi e sottili. Approfondimento diventiamo la materia prima e non vediamo mai né densi, né sottili punti, solo il mare calmo. Tutte le azioni sono fermate, non facciamo niente, SIAMO solo.

La filosofia della Nondualità dice che non c'è niente, ma un solo Spirito nell'Universo, e tutto ciò che è vivente o inanimato è parte indivisibile e inseparabile di questo Spirito. I Veda (sacre scritture dell'induismo) sono la fonte più antica di questa filosofia. Molto opportunamente questo principio viene interpretato in un breve trattato, di nome Ashtavakra Gita.

A dire il vero, ho conosciuto questa filosofia prima di iniziare a scrivere la teoria del flusso dello spazio. Comunque ho capito solo prima di completare il lavoro che cosa significa realmente non-dualità, che l'idea della teoria del flusso dello spazio corrisponde con "Advaita Vedanta".

Coerenza teologica

Tempo è definito nella teoria del flusso dello spazio come una successione di momenti di ispessimento (o assottigliamento) delle cellule spazio-temporali . Dal nostro Universo, ad esempio, dal nostro posto (frame di riferimento) sulla superficie della Terra, ci possiamo immaginare il QPM, già citato, oscillante a frequenza tendente a zero, secondo la teoria del flusso dello spazio, e grazie le sue enormi dimensioni (Questa frequenza può essere misurata con il dispositivo collocato nella nostra struttura spazio-temporale. In realtà, però, QPM si trova nel estremamente alto stato energetico a causa del movimento della materia prima all interno, e la nostra definizione di tempo qui dentro fallisce, perché la materia prima non è quantizzata). Quindi, se Dio avrebbe abitato nella struttura spazio-temporale, costituita di molti QPM (di molti mondi), sarebbe davvero quasi eterno, come è scritto in 2Pietro 3:08: "... Ora, carissimi, non dimenticate quest'unica cosa: che un giorno è per il Signore come mille anni e mille anni come un giorno. " Onnipresenza, o ubiquità, è la proprietà di essere presente ovunque. Secondo teismo orientale, Dio è presente in ogni luogo. Onnipresenza divina è dunque uno degli attributi divini, anche se in teismo occidentale, onnipresenza ha attirato meno attenzione filosofica di attributi come l'onnipotenza, l'onniscienza, o di essere eterno. La concezione della teoria del flusso dello spazio, basata sulla presunzione dell'esistenza del quanto della materia prima (QPM), con il suo comportamento non locale, offre la possibilità di essere ovunque, allo stesso tempo. A dire il vero, possiamo immaginare questo fenomeno "incredibile" dall'esterno del QPM, perché siamo in grado di immaginare l'oggetto di massa come dissolto dentro QPM, ma è difficile identificarsi con tale idea guardando dall'interno QPM. Ma e 'cosa di Dio. Per migliaia di anni, filosofi e saggi, e per ultimi decenni molti scienziati, sono arrivati alla consapevolezza che esiste una sola sostanza e quindi siamo tutti sua parte. Questa sostanza può essere chiamata Consapevolezza, Coscienza, Spirito, Advaita, Brahman, Tao, Nirvana, Dio, o anche la Materia prima. E 'costante, sempre presente, immutabile ed è l'essenza di tutta l'esistenza. Dal punto di vista comune, scientifico e teistico , questa entità potrebbe essere chiamata l'osservatore (o cristiano Dio Padre). E l'unica entità che può manifestarsi da atributi tali come l'onnipotenza, l'onniscienza, l'onnipresenza e l'eternità, sebbene da un punto di vista filosofico si manifesta solo dal attributo derivato dal nome "Io sono colui che sono" (Esodo 3 : 14), perché questo attributo contiene tutti.

Kosice, 27 dicembre 2012

Kosice, 9 dicembre 2016 (le note 2 e 3)

I miei lettori rispettabili, si prega di tenere conto che questo lavoro, in senso lato,

mostra che il continuum spazio-temporale non è né omogeneo né isotropo,

che è principalmente legato al rapporto tra le densità spazio-temporali dei due spazio-temporali continua.

Ciò significa che le leggi della fisica, oggetti o proprietà fisiche, noti nel nostro spazio-tempo,

vengono modificate in un diverso spazio-tempo secondo la sua densità spazio-tempoporale e,

a densità zero (all'interno del quantum QPM) sono molto probabilmente trasformati in unità

con vasto potenziale per diventare qualsiasi cosa, con qualsiasi proprietà.

Pertanto, la sostanza prima dell'universo (del QPM quantum), di che parliamo qui in senso teologico,

può davvero contenere tutta l'esistenza compreso tutte le sue caratteristiche (materiali e immateriali),

e può anche manifestarsi come vivace, creativa, ispirante e piena di amore

e della capacità di essere sé in ogni momento (perché lei esiste nel momento eterno).

In questo senso, si potrebbe supporre che le seguenti citazioni di Veda, Corano e Bibbia parlano della stessa cosa,

chiamata Consapevolezza, Coscienza, Spirito, Advaita, Brahman, Tao, Nirvana, Dio, o anche la materia prima.

Medita su te stesso come consapevolezza immobile, libero da ogni dualismo,

abbandonando l'idea erronea di essere solo una coscienza limitata,

o qualunque cosa interna o esterna.

(Ashtavakra Gita 1.13)

Nel cuore di tutte le cose, di qualsiasi cosa ci cono, nell'universo, abita il Signore.

(Isha Upanishad)

ÓM. Questa parola eterna è tutto: ciò che è stato, ciò che è e ciò che sarà, e ciò che è al di là nell'eternità.

Tutto è OM.

(Upanishad)

Dovunque vi volgiate, là è il volto di Dio.

(Corano)

E quando il Grande Ra-M-Cha è stato irradiato

dalla grande Luce della Gioia,

il grande flusso di Inglie

(della prima Luce Vivente)

esplose da lui.

(Veda di Aryanic Slovieni,

Libro di Luce)

In principio era il Verbo, e il Verbo era presso Dio e il Verbo era Dio.

Egli era con Dio in principio. Per mezzo di lui tutte le cose sono state fatte;

senza di lui niente è stato fatto che è stato fatto.

(Giovanni 1)

Come un quinquennale ragazzo sapevo che le cose più meravigliose che incontravo nel mondo, erano il cielo stellato sopra di me, e la coscienza in me. (So che molti lo sapevano, anche Kant e Jung per esempio). Io credo che quelli che lo sanno oggi, vanno ancora più lontano. In particolare perché la comprensione che quelle stelle si trovano contemporaneamente nello spazio e nella coscienza di ognuno di noi, può contribuire in modo significativo al passo evolutivo dell'umanità. Ma solo se ognuno si realizza come la coscienza universale. Questa conoscenza è una guida diretta su come rispondere correttamente a due domande: "Chi sei, l'uomo?" e, "Cosa fare" :

Sappiamo già che l'entità che forma l'essenza dell'esistenza è nel nostro spazio-tempo invisibile e non rilevabile (ma percepibile) e riempe l'intero universo, così come le particelle di massa in esso contenute. Ognuno di noi può arrivare a percepire questa entità se sta cercando ciò che è il più fine e forse il più vuoto in se stesso. In termini semplici, è la percezione dei segni della vita dentro di noi (e in particolare nei centri nervosi), perché in essi o dietro di essi può essere percepito questo "nulla", che fondamentalmente contiene l'intera esistenza. Già durante il primo bagliore di luce durante la meditazione provate gioia ed entusiasmo, e coloro che portano la loro croce, anche grande sollievo (il mio giogo è dolce e il mio carico è leggero - le parole di Gesù Cristo). Comprensione di questo fatto, cioè identificazione permanente con esso, ha un importante effetto positivo attraverso l'emozione (creata dall'amore incondizionato) non solo sull'uomo ma anche sulla vita stessa (l'influenza remota della coscienza sullo stato della materia è già stata dimostrata). Non importa come qualcuno chiama questa entità dominante, lo spirito, il brahman, il tao, la coscienza o la sostanza primaria. È il nostro creatore. Nella sua luce invisibile, ci mostra la direzione verso il nostro passo evolutivo, e forse verso il regno di Dio.

Il significato del termine amore incondizionato risiede principalmente nel suo contenuto logico,

ma in questo momento anche nel sentimento di entusiasmo, rapimento, umiltà, stupore e nonlocalità,

che sorgono nell'uomo dalla comprensione del rapporto tra coscienza e fisica quantistica.

Questo può portare a uno stato che le autorità spirituali avanzate chiamano illuminazione.

Tuttavia, è importante sapere che questo consiglio probabilmente non permetterà a tutti di iniziare a percepire l'essenza spirituale, perché la coscienza di molte persone è intrappolata nei sentimenti o nelle menti. È sempre necessario sapere chi è consapevole della vita. Dedica il tempo necessario per essere pienamente consapevole della tua esperienza attuale e accettare pienamente tutti i pensieri, le emozioni, i sentimenti, tutto ciò che è presente dentro e intorno a te, senza identificarti con loro. Come notato sopra in questo capitolo, la coscienza universale è apparentemente associata allo spazio, persino a crearlo. È quindi necessario sapere di connettere la nostra coscienza con lo spazio dell'universo (cioè lo spazio quantico QPM, che è quindi non locale, cioè, tutto ciò che è contenuto in esso è virtualmente onnipresente ed esiste nel presente). La qualità di tale identificazione è correlata all'avanzamento spirituale. Tuttavia, dopo un breve allenamento, la visione di un ampio spazio può essere raggiunta con il progresso iniziale.

In realtà, i consigli per la coltivazione della coscienza (progresso evolutivo) portano effettivamente alla trasformazione della coscienza umana dal passato al presente ("Sii sveglio" - le parole di Gesù Cristo), perché abbiamo già capito che l'essenza di l'esistenza esiste in una presenza permanente. Quindi, se guardiamo nel nostro interno, scopriamo un sacco di pensieri, sentimenti, così come le ferite emotive e altre del passato che creano una barriera per noi. Dietro questa barriera, che osserviamo soltanto, è ciò che stiamo cercando, Dio, l'Entità che forma l'Esenza dell'esistenza o la Presenza permanente. Una persona almeno leggermente avanzata nella sfera spirituale è in grado di percepire questa entità, che gradualmente lo porta ad ancorare la coscienza al presente. Chi non ha una tale percezione raggiungerà l'obiettivo mediante la fede e cercando di arrendersi ad essa. Ma abbiamo fatto solo il primo passo che ci ha portato alla emozione positiva, che può essere considerata come "amore incondizionato". Tutto, che è dietro la barriera, ha il carattere di campo della energia alta, cioè di campo della frequenza alta, e l'apertura improvvisa della barriera potrebbe danneggiare le nostre strutture molecolari o cellulari. Ancora: Solo guarda la barriera. Questo processo stesso porta ad un graduale aumento della frequenza della nostra coscienza e forse alla modifica delle strutture corporee pertinenti. Lui esiste !!! Stiamo cercando questo obiettivo da secoli e millenni. E inoltre? La nostra attesa potrebbe derivare dalle parole di Gesù Cristo "Beati i puri di cuore, perché vedranno Dio" (Sal 24).

(Si prega di notare che: la purezza del cuore risiede in una relazione ispiratrice, creativa, meravigliosa e intima con l'Universo (Unicità, Dio). Un cuore puro è il risultato del percorso di maturazione, attraverso la purificazione e la rinuncia al stile di vita che porta alla sofferenza).

Continua a comunicare con l'universo come segue:

Tu, la fonte di tutto, grazie per avermi riempito della tua luce.

Frantisek Stefanko

Kosice, 16 dicembre 2018

Epilogue english version

Epilogue slovak version

È probabile che tu, l'uomo, capirai che sei un'entità immateriale, la cui casa è un campo di energia, manifestato da una penetrazione spietata, che porta gioia, amore, ispirazione, creatività, spiritualità, ottimismo, pace, intuizione, capacità divine, e in particolare la presenza trasparente di un'enorme forza vitale. E quando arriverai così lontano, avrai l'opportunità di sbarazzarti dell'ego (trasformarlo) e avanzare più in alto, nell'unità. IEOUA!

Sì, chi è arrivato fin qui deve andare avanti. Tuttavia, non è facile. Il mistico ceco Kvetoslav Minarik sottolinea che il più difficile sta a te sforzarti di essere completamente spersonalizzato e altruista, pur mantenendo la capacità di agire. Spesso dura tutta la vita. Tuttavia, un grande vantaggio è dato a colui che, riconoscendosi in tutto, gioisce con tutto il suo essere.

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Table of Contents

THE SPACETIME PHENOMENA PART ONE

PART 1 MAP

THE SPACETIME PHENOMENA part two

PART 2 MAP

The Spacetime Phenomena part 3

PART 3 MAP

Epilogue