The study of the form, function, and composition of matter has been, and
continues to be, one of the greatest intellectual challenges of all time. In ancient
times the Greek Empedocles (495-435 B.C.) came up with the idea that matter is
composed of earth, air, fire, and water. In 430 B.C. the idea of Empedocles was
rejected by, the Greek, Democritus of Abdera. Democritus believed that the
substances of the creation are composed of atoms. These atoms are the smallest
bits into which a substance can be divided. Any additional subdivision would
change the essence of the substance. He called these bits of substance "atomos"
from the Greek word meaning "indivisible". Democritus was, of course, correct in
his supposition, however, at the time, no evidence was available to confirm this
idea. Ancient technology was primitive and could not to confirm or contest any of
these ideas. Various speculations of this sort continued to be offered and rejected
over the next 2,000 years.

The scientific revolution began in the seventeenth
century. With this revolution came the tools to test the theories of matter. By the
eighteenth century these tools included methods of producing gases through the use
of chemical reactions, and the means to weigh the resultant gases. From his studies
of the gaseous by-products of chemical reactions, French chemist Antoine Lavoisier
(1743-1794) discovered that the weight of the products of a chemical reaction
equals the weight of the of the original compound.
The principle of "the conservation of mass" was born. For his achievements
Lavoisier is today known as the father of modern chemistry.

Pg_2
UP

Late in the eighteenth
century, the first use of another new tool began to be applied to test the theories of
matter. This tool is electrical technology. The first electrical technology to be
applied to the study of matter, electrolysis, involves the
passing of an electrical
current through a conductive solution. If an electrical current is passed through a
conductive solution, the solution tends to decompose into its elements. For example,
if an electric current is passed through water, the water decomposes, producing
the element hydrogen at the negative electrode and the element oxygen at the positive
electrode. With the knowledge obtained from the use of these new technologies,
English schoolteacher, John Dalton (1766-1844) was able to lay down the
principles of modern chemistry. Dalton's theory was based on the concept that,
matter is made of atoms, all atoms of the same element are identical, and atoms
combine in whole number ratios to form compounds.

Electrical technology became
increasingly more sophisticated during the nineteenth century. Inventions such as
the cathode ray tube (a television picture tube is a cathode ray tube) allowed atoms
to be broken apart and studied. The first subatomic particle to be discovered was
the electron. In 1897, J.J. Thomson demonstrated that the beams seen in cathode
ray tubes were composed of electrons. In 1909, Robert Millican measured the
charge of the electron in his, now famous, oil drop experiment.
Two years later, Ernest Rutherford ascertained the properties of the atomic nucleus
by observing the angle at which alpha particles bounce off of the nucleus. Niels
Bohr combined these ideas and in 1913, placed the newly discovered electron in
discrete planetary orbits around the newly discovered nucleus. The planetary model
of the atom was born. With the appearance of the Bohr model of the atom, the
concept of the quantum nature of the atom was established.

Pick the icon to view the Bohr model of the atom.

As the temperature of matter is increased, it emits correspondingly shorter wavelengths of electromagnetic energy. For example, if a metal poker is heated it will become warm and emit long wavelength infrared heat energy. If the heating is continued the poker will eventually become red hot. The red color is due to the emission of shorter wavelength red light. If heated hotter still, the poker will become white hot emitting even shorter wavelengths of light. An astute observer will notice that there is an inverse relationship between the temperature of the emitter and the wavelength of the emission. This relationship extends across the entire electromagnetic spectrum. If the poker could be heated hot enough it would emit ultra-violet light or X-rays.

The German physicist Max Karl Ludwig Planck studied the light emitted from matter and came to a profound conclusion. In 1900, Planck announced that light waves were given off in discrete particle-like packets of energy called quanta. Today Planck's quanta are know known as photons. The energy in each photon of light varies inversely with the wavelength of the emitted light. Ultraviolet, for example, has a shorter wavelength than red light and, correspondingly, more energy per photon than red light. The poker, in our example, while only red hot cannot emit ultraviolet light because its' atoms do not possess enough energy to produce ultraviolet light. The sun, however, is hot enough to produce ultraviolet photons. The ultraviolet photons emitted by the sun contain enough energy to break chemical bonds and can "sun" burn the skin. The radiation spectrum cannot be explained by any wave theory. This spectrum can, however, be accounted for by the emission of a particle of light or photon. In 1803, Thomas Young discovered interference patterns in light. Interference patterns cannot be explained by any particle theory. These patterns can, however, be accounted for by the interaction of waves. How can light be both a particle and a wave?

Pg_4 UP

In 1924, Prince Louis de Broglie proposed that matter possess wave-like properties.

Pick the icon to view one form of the Germar Davisson experiment.

Throw a stone in a lake and watch he waves propagate away from the point of impact. Listen to a distant sound that has traveled to you from its source. Shake a rope and watch the waves travel down the rope. Tune in a distant radio station, the radio waves have traveled outward from the station to you. Watch the waves in the ocean as they travel into the shore. In short, waves propagate, its their nature to do so, and that is what they invariably do. Maxwell's equations unequivocally demonstrate the fields propagate at light speed. Matter waves, however, remain "stuck" in the matter. Why do they not propagate? What "sticks" them? An answer to this question was presented by Erwin Schrödinger and Werner Heisenberg at the Copenhagen conventions. The Copenhagen interpretation states that elementary particles are composed of particle-like bundles of waves. These bundles are know as a wave packets. The wave packets move at velocity V. These wave packets are localized (held is place) by the addition of an infinite number of component waves. Each of these component waves has a different wavelength or wave number. An infinite number of waves each with a different wave number is required to hold a wave packet fixed in space. This argument has two major flaws. It does not describe the path of the quantum transition and an infinite number of real waves cannot exist within a finite universe.

Max Born attempted to side step these problems by stating that the wave packets of matter are only mathematical functions of probability. Only real waves can exist in the real world, therefore an imaginary place of residence, called configuration space, was created for the probability waves. Configuration space contains only functions of kinetic and potential energy. Forces are ignored in configuration space.

Ordinary rules, including the rules of wave propagation, do not apply in configuration space. The propagation mystery was supposedly solved. This solution sounds like and has much in common with those of the ancient philosophers. It is dead wrong!"Forces of constraint are not an issue. Indeed, the standard Lagrangian formulation ignores them...In such systems, energies reign supreme, and it is no accident that the Hamiltonian and Lagrangian functions assume fundamental roles in a formulation of the theory of quantum mechanics.."Grant R. Fowles University of Utah

Einstein also believed that something was amiss with the whole idea. His remark,"Schrödinger never accepted this view, but registered his concern and disappointment that this transcendental, almost psychical interpretation had become universally accepted dogma."

Modern PhysicsSerway, Moses, Moyer; 1997

indicates that he placed little confidence in these waves of probability. For the most part, the error made little difference, modern science advanced, and bigger things were discovered. It did, however, make at least one difference; it forestalled the development of gravitational and low level nuclear technologies for an entire Century."God does not play dice"

Pg UP

Matter is composed of energy and fields of force. Matter can be mathematically modeled but a mathematical model does not make matter. Matter waves are real, they contain energy, are the essence of mass, and convey momentum.

"Matter does not disperse because it is held together by forces. These forces generate the gravitational field of matter, establish the inertial properties of matter, and set matter's dynamic attributes. The remainder of this chapter will be spent qualifying these forces and the relationship that they share with matter. The ideas to follow are central to this author's work. Reader's who have no interest in math may skip to the conclusion without missing the essential details of this chapter. Essentially the math shows that forces within matter are responsible for many of the properties of matter.This result is rather surprising... since electrons are observed in practice to have velocities considerably less than the velocity of light it would seem that we have a contradiction with experiment."

Paul Dirac, his equations suggested that the electron propagates at light speed._{11}

This concept will be extended in Chapter 10. The various fields that compose matter have radically different ranges and strengths. The force, that pins the various fields within matter, will be explored. An understanding of the structure of the restraining forces has revealed the path of the quantum transition.

Pg_7 UP

The matter wave function is composed of various fields. Photons were employed to represent these various fields. Photons exhibit the underlying relationship between momentum and energy of a field (static or dynamic) in which disturbances propagate at luminal velocities. Consider photons trapped in a massless perfectly reflecting box. The photon in a box is a simplistic representation of matter. Light has two transverse modes of vibration and carries momentum in the direction of its travel. All three modes need to be employed in a three dimensional model. For the sake of simplicity this analysis considers only a single dimension. The photons in this model represents the matter wave function and the box represents the potential well of matter. As the photons bounce off of the walls of the box momentum "p" is transferred to the walls of the box. Each time a photon strikes a wall of the box it produces a force. This force generates the gravitational mass associated with the photon in the box. The general formula of gravitational induction, as presented in the General Theory of Relativity

Equation # 2 The gravitational field produced by a force

G = the gravitational constant

r = the gravitational radius

dp/dt = force

Each time the photon strikes the wall of the box it produces a gravitation field according to equation #2. The gravitational field produced by an impact varies with the reciprocal of distance "1/r". The gravitational field produced by matter varies as the reciprocal of distance squared "1/r

Pg_8 UP

L = The dimensions of the box

p = momentum

t = the time required for the photon to traverse the box= 2L/c

r = the distance to point X

The far gravitational field at point X is the vector sum of the fields produced by the impacts on walls A and B.

This field is given by below.

*E*_{g at x} = 1/r field from wall A - 1/r field from wall B

Equation 3 Showing the super-position of two fields.

*E*_{g at x} = (G / [ c^{2} (r+L) ] ) ( dp / dt ) - (G / [c^{2}r] ) (dp / dt)

Equation 4 Simplifying.

*E*_{g at x} = - (G / c^{2}) (dp / dt) [ L / (r^{2} + r L) ]

Equation 5 Taking the limit to obtain the far field.

*E*_{g at x} = lim_{as r>>L} - (G / c^{2}) (dp / dt) [ L / (r^{2} + r L) ]

The result , Equation #7, is the far gravitational field of matter. Far, in this example, means greater than the wavelength of an
elementary particle. In the case of a superconductor far
means longer than the length of the superconductor.

*E*_{g at x} = - (G / c^{2}) (dp / dt) L / r^{2} Equation #7

This momentum of an energy field that propagates at light speed is given by
the equation below _{2 }.

p = E / c

E = the energy of the photon

c = light speed

p = momentum (radiation pressure)

The amount of force (dp / dt) that is imparted to the walls of the box depends on the round trip travel time of the photon.
Equation 8 gives the force on the walls of the box.

dp / dt = Dp / Dt = (2E / c) / (2L / c) = E / L Equation #8 Note: *This force is 29.05 Newtons at the classical radius of the electron. *

Equation #8 was substituted into Equation #7. Equation 9 is the far gravitational field produced by energy bouncing in a box

*E*_{g at x} = - (G / c^{2}) (E / L) (L / r^{2}) Equation #9

Equation 10 is Einstein's relationship between matter and energy.

M = E / c^{2} Equation #10

Substituting mass for energy yileds Equation #11, Newton's formula for gravity _{5 }.

** E_{g at x} = - GM / r^{2} ** Equation #11

Forces are produced as energy is restrained. These forces induce the gravitational field of matter.

Pg_9 UP

In 1924 Prince Louis DeBroglie proposed that matter has a wavelength associated with it.

The manner in which an electron acquires and possesses its dynamic attributes is the subject of the quantum reality question. The fact of the matter is that nobody really these days knows how an electron, or any other quantum entity, actually possesses its dynamic attributes."

Louis deBroglie suggested that the electron may be a beat note.

Pick the icon to view an animation on the DeBroglie wavelength of matter.

The harmonic vibration of a quantum particle is expressed by its Compton wavelength.
Equation #1A expresses the Compton wavelength.

l_{c} = h / Mc

Equation #2A gives the relationship between frequency f and
wavelength l. Please note that the phase velocity of the
wave is c.

c = f l

Substituting Eq #2A into Eq. #1A yields Eq #3A the Compton
frequency of matter.

f_{c} = Mc^{2} / h

A doppler shifted component of the original frequency is
produced by the restraint of the wavefunction. Classical
doppler shift is given by Eq #4A.

f_{2} = f_{1} ( 1 +- v / c)

A beat note is formed by the mixing of the doppler shifted
and original components. This beat note is the deBroglie
wave of matter.

Equation #5A and the above express a
function "F" involving the sum of two sin waves.

F(L,t)| = amplitude orig. wave + amplitude reflected wave | | L held constant F(t) = sin(2p fRefer to the figure above. A minimum in the beat note envelope occurs when the component waves are opposed in phase. At time zero the angles differ by p radians. Time zero is a minimum in the beat note envelope. A maximum in the beat envelope occurs when the component waves are aligned in phase. The phases were set equal, in Equation #7A, to determine the time at which the aligned phase q condition occurs._{c}t + p) + sin[ 2p f_{c}(1 +- v/c) t ] Substituting Eq #4A into Eq #5A yields Eq #6A. F(t) = sin[2p t(Mc^{2}/h)+ p] + sin[2p t(Mc^{2}/h)(1 +- v/c)]

q

2 p t ( M c

ct = (+ -) h / 2 Mv

The result, Equation #10A, is the deBroglie wavelength of matter. Reflections contain a luminal Comption wave. The superposition of these reflections is the deBroglie wave of matter.

Pg_10 UP

This energy in a containment model is a simplistic representation of matter. In this analysis no distinction will be made between baryonic, leptonic, and electromagnetic waves.________________ | \ | | P1 \ | | \| A| / B | P2 / | | / | |______________| |<---- L------>| Matter wave in a box

The wavelength of the energy represents the Compton wavelength of matter. The containment represents the surface of matter. The field propagates at light speed. Its momentum is equal to E/c. The containment is at rest. The energy is ejected from wall "A" of the containment, its momentum is p

p

The momentum of a flow of energy is given by equation #2C

p = E/c Eq #2 E = energy c = light speed p = momentum Substituting Eq. #2C into Eq. #1 yields Eq. #3C. pGiven the containment is at rest. The amount of energy in the containment remains fixed, the quantity of energy traveling in the forward direction equals the quantity of energy traveling in the reverse direction. This is shown in equation #4._{t}= [E_{1}/2c - E_{2}/2c] Eq. #3C

EEquation #5 is the total momentum of the system at rest. If an external force is applied to the system its velocity will change. The forward and the reverse components of the energy will then doppler shift after bouncing off of the moving containment walls. The momentum of a an energy flow varies directly with its frequency. Given that the number of quantums of energy is conserved, the energy of the reflected quantums varies directly with their frequency. This is demonstrated by equation #6C._{1}= E_{2}Eq #4C

Substituting Eq. #4C into Eq. #3C yields Eq #5C.

p_{t}= (E/2c)(1 - 1) Eq #5C

EEquation #7C is the momentum of the system after all of its energy bounces once off of the containment walls. Equation #7 shows a net flow of energy in one direction. Equation #7C is the momentum of a moving system. The reader may desire to analyze the system after successive bounces of its energy. This analysis is quite involved and unnecessary. Momentum is always conserved. Given that no external force is applied to the system after the first bounce of its energy, its momentum will remain constant._{2}= E(_{1}) [f_{f}/ f_{i}] Eq. #6C Substituting Eq. #6C into Eq #5C. yields eq. #7C. p_{t}= (E/2c)[(f_{f1}/f_{i1}) - (f_{f2}/f_{i2})] Eq #7C

Relativistic doppler shift is given by equation #8C.

(f

v = velocity with respect to the observer c = light speed fThe result, equation #14C is the relativistic momentum of moving matter. This first analysis graphically demonstrates that inertial mass is produced by a containment force at the surface of matter. A fundamental change in the frame of reference is produced by the force of containment. This containment force converts energy, which can only travel at light speed, into mass, which can travel at any speed less than light speed._{f}/f_{i}= frequency ratio + or - depends on the direction of motion Substituting equation #8 into equation #7C yields equation 9C - .5 .5 _ = E | (1-v^{2}/c^{2}) (1-v^{2}/c^{2}) | --- | ----------- - ---------- | Eq #9C 2c | (1-v/c) (1+v/c) | - _ _ - _ .5 .5_ = E | (1+v/c)(1-v^{2}/c^{2}) (1-v/c)(1-v^{2}/c^{2}) | --- | ---------------- - ----------------- | 2c | (1+v/c)(1-v/c) (1-v/c)(1+v/c) | - - - .5 - E | (1-v^{2}/c^{2}) (1+v/c-1+v/c) | -- | ----------------------- | 2C | (1-v^{2}/c^{2}) | - - ___ Ev________ .5 c^{2}(1-v^{2}/c^{2}) Substituting mass for energy, M = E/c^{2}= ___Mv______ .5 (1-v^{2}/c^{2})

Pg_11 UP

Note:

A version of this analysis has been published in

According to existing theory the matter wave emerges from the Fourier addition of component waves. This method requires an infinite number of component waves. Natural infinities do not exist within a finite universe. The potential and kinetic components of a wave retain their phase during a Fourier localization. The aligned phase condition is a property of a traveling wave. The Fourier process cannot pin a field or stop a traveling wave.

Texts in quantum physics commonly employ the Euler formula in their analysis. The late Richard Feynman said, "The Euler formula is the most remarkable formula in mathematics. This is our jewel." The Euler formula is given below:

e

The Euler formula describes the simple harmonic motion of a standing wave. The cos component represents the potential energy of a standing wave. The sin component represents the kinetic energy of a standing wave. The kinetic component is displaced by 90 degrees and has a i associated with it. The localization of a traveling wave through a Fourier addition of component waves is in error. To employ this method of localization and then to describe the standing wave with the Euler formula is inconsistent. This author corrected this error through the introduction of restraining forces. The discontinuity produced at the elastic limit of space restrains the matter wave. The potential and kinetic components of the restrained wave are displaced by 90 degrees. A mass bouncing on the end of a spring is a good example of this type of harmonic motion. At the end of it travel the mass has no motion ( kinetic energy = zero) and the spring is drawn up tight ( potential energy = maximum ). One quarter of the way into the cycle the spring is relaxed and the mass is moving at its highest velocity (kinetic energy = maximum). A similar harmonic motion is exhibited by the force fields. The energy of a force field oscillates between its static and magnetic components.

Mass energy ( E

/|\ | | E_{m}= Mc^{2}| | |_90^{o}

The phase of a standing wave is 90 degrees. All standing waves are localized by restraining forces.

A traveling wave has its kinetic and potential components aligned in phase. An ocean wave is a good example of this type of harmonic motion. The wave's height ( potential energy ) progresses with the kinetic energy of the wave.

The energy "E" contained by a wave carrying momentum "P" is expressed below.

E = Pc

The traveling wave expresses itself through its relativistic momentum "P".

P = Mv / (1- v

Substituting yields the amount of energy that is in motion "E

The vector sum of the standing ( EE_{q}= Mvc / (1- v^{2}/ c^{2})^{1/2}|----------------------> 0^{o}

[ E

[ E

E

The relativistic energy is represented by the length of the hypotenuse on a complex plain

The ratio of standing energy to the relativistic energy [ E

g = arc sin (1- v

The phase g expresses the angular separation of the potential and kinetic energy of matter. The physical length of a standing wave is determined by the spatial displacement of its potential and kinetic energy. This displacement varies directly with the phase g. The phase g varies inversely with the group velocity of the wave. This effect produces the length contraction associated with special relativity.

Time is represented on the Z (out of the plain) axis on a complex diagram. The rotation of a vector around the X axis into the Z axis represents the change in potential energy with respect to time. The rotation of a vector around the Y axis into the Z axis represents a change in potential energy with respect to position. Relativistic energy is reflected on both axes. The loss in time by the relativistic component E

The phase g of a wave expresses the displacement of its potential and the kinetic energy. When placed on a complex diagram the phase directly determines the relativistic momentum, mass, time, and length. These effects reconcile special relativity and quantum physics.

The analysis reveals information not provided by special relativity. The ratio of traveling energy to the relativistic energy ( E

This model requires a restrained luminal wave. What is the nature of this restraing force? Are forces beyond the four known forces required? This author will show that no addtional forces are required. The restraining force is produced throgh the action of the known forces. The nature of this restraining force will be presented in Chapter 10. An analysis of this restraining force, in Chapter 12, revealed the path of the quantum transition.

Kinetic and potential energy were represented as vectors on a two dimensional complex plain. The rotation of this complex plain through a third dimension added the element of time to the construct. The inclusion of additional dimensions should enable this model to be extended into the realm of high energy physics. The extended model would contain, at its core, a unification of relativity and quantum physics.

Pg_12 UP

Photons from the extremes of the universe have traveled side by side for billions of years. These photons do not agglomerate. The slightest agglomeration would result in a decrease in entropy. This decrease would be in violation of the laws of thermodynamics. Photons traveling in straight lines extert no gravitational influence.

Matter gives up energy during the process of photon ejection. The principle of the conservation of energy requires that the negative gravitational potential and the positive energy of the universe remain in balance. The ejected photon must carry a gravitational influence that is equivalent to the gravitational mass lost by the particle.

These conditions are satisfied by a photon with a variable gravitational mass. This mass varies directly with the force (dp/dt) it experiences.

Hubbles' constant expresses the expansion space in units of (1/time). Ordinarily, the effects resulting for the Hubble expansion are quite tiny. At great distances and at high velocities significant effects do, however, take place. As a photon travels through space at the high velocity of light it red shifts. This red shift may be considered to be the result of an applied force. This force is produced by the acceleration given in equation #1D.

Acceleration = Hc Eq #1D H = Hubble's constant, given in units of (1/sec)To demonstrate the gravitational relationships of a photon the principle of the conservation of momentum will be employed. According to this principle exploding bodies conserve there center of gravitational mass. Mass M ejects a photon while over the pivot I. The gravitational center of mass must remain balanced over the pivot point I. Mass M

c = light speed

Force induces the gravitational field of matter and energy. The confinement of mass energy produces a field that drops off at a one over r squared rate. A gravitational field is also produced by the acceleration of energy through Hubble’s constant. This gravitational field drops off at a one over r rate. Both mechanisms produce a equivalent effect at the edge of the visible universe. The equivalance conserves the negative gravitational potential of the universe. The speed of light<---SThe center of mass of an exploding body is qualified by equation #2D. This center is both inertial and gravitational. M_{1}---> <---------S_{2}---------> Mass photon ---------------------------------------- I Matter and a energy on a balance beam_{1}S_{1}= M_{2}S_{2}Eq #2D The gravitational field of the particle was descirbed with Newton's formula of gravity, see 2C below left. The general formula of gravitational indiction, as presented in the General Theory of Relativity_{3, 4 }is given below. Induced grav. field = G/(c^{2}r) dp/dt This equation (as derived in Chapter 6 ) was describes the gravitational influence of the photon, see 2C below right. (Newton's grav. field)(displacement) = (Einstein's grav. influence)(displacement) Eq 2C (GM_{1}/r^{2}) S_{1}= G/(c^{2}r) force S_{2}(GM_{1}/r^{2})S_{1}= G/(c^{2}r) dp/dt S_{2}Substitutinhg vt and ct for displacement S and multiplying by r squared GM_{1}(v_{1}t) = (G/c^{2}) dp/dt (ct)r Eq #5D Substituting for force, dp/dt = Ma = MHc = (E_{2}/c^{2})Hc = E_{2}H/c Eq #6D G(M_{1}v_{1})t = (G/c^{2})( E_{2}/ c) Hctr Substituting momentum p for M_{1}v_{1}and E_{2}/c Gp_{1}t = (G/c^{2})p_{2}Hctr Setting the momentums equal. p_{1}= p_{2}c = HrEq #11D

Pg_13 UP

Schrödinger's wave equation is a basic tenement of low energy physics. It embodies all of chemistry and most of physics. The equation is considered to be fundamental and not derivable from more basic principles. The equation will be produced (not derived) using an accepted approach. Several assumptions are fundamental to this approach. The flaws within these assumptions will be exposed.

This author will derive Schrödinger's wave equation from a set of fundamental classical parameters. The Schrödinger's wave equation was fundamentally derived from the premice that the speed of sound with the nucleus is 1.094 million meters per second and that restraining forces confine a luminal wave. This author's approach is classical.

Pg_14 UP

Ñ

The wave equation describes a classical relationship between velocity, time, and position. The velocity of the wave packet is v.

Pg_15 UP

The exponential form of the sin function (e

Ñ

After the double integration the equation is reduced.

Frequency squared f divided by velocity squared v equals (1/l) squared.

The Schrödinger equation describes the deBroglie wave of matter. The deBroglie wave and Planck's constant were

"Schrödinger also had to explain how wave packets could hold together, elaborate the meaning of the wave function, and demonstrate how the discontinuities of quantum phenomena arise from a continuous wave processes."

The Great Equations, Robert P. Creese, Pg. 248

Ñ

Ñ

(Mv

Substituting

Ñ

Simplifying

Pg_16 UP

The electron's elastic constant was classically extracted from this velocity.

The frequency is known as the

The simple harmonic motion is of a restrained wave is given by. Please not the Compton angular velocity, not the deBroglie wavelength, was is used in the formulation.

d

In order to give a result in conventional units the classical value for the Compton angular velocity, below, was placed into the formulation.

Squaring and factoring.

The Compton angular velocity squared was substituted for w

Dividing by light speed squared.

H. Ziegler pointed out in a 1909 discussion with Einstein, Planck, and Stark that relativity would be a natural result if all of the most basic components of mass moved at the constant speed of light.

Mass energy is expressed as the difference between the total energy and the potential energy of the matter wave. U always equals 1/2 E there for a factor of two was employed to get the total positive energy.

Substituting

The result below is the time independent Schrödinger equation.

The time independent Schrödinger equation has been derived from a simple technique. The deBrobie wave was not incorporated ad-hoc into the solution. Disturbances within the matter wave propagate at luminal velocities. Restraining forces prevent dispersion. The deBroglie wave arose naturally from the restraint of the Compton wave.

Pg_17 UP

The movement of ordinary matter does not produce a net magnetic field. The movement of charged matter does produce a net magnetic field. Charged matter is produced by the separation of positive and negative charges. The derivation used to develop Newton's formula of gravity (Equation #3) shows that matter may harbor positive and negative near field gravitational components.

The wavefunctions of superconductors are collimated. The collimated wave functions act in unison like a single macroscopic elementary particle. The near field gravitational components of a superconductor are macroscopic in size. The rotation of these local gravitational fields is responsible for the gravitational anomaly observed at Tampere University.

Pg_18 UP

The nature of the bundling force will be presented in Chapters 10 & 11. An analysis of the bundling force revealed the path of the quantum transition.

Pg_19 UP

1.French aristocrat Louis de Broglie described the electrons wavelength in his Ph. D. thesis in 1924. De Broglie's hypothesis was verified by C. J. Davisson and L. H. Germer at Bell Labs.2.Gilbert N. Lewis demonstrated the relationship between external radiation pressure and momentum. Gilbert N. Lewis. Philosophical Magazine, Nov 1908.3.A. Einstein, Ann d. Physics 49, 1916.4.Einstein's principle of equivalence was experimentally confirmed by R.v. Eötös in the 1920's. R.v. Eötös, D. Pekar, and Feteke, Ann. d. Phys 1922. Roll, Krotkov and Dicke followed up on the Eötvös experiment and confirmed the principle of equivalence to and accuracy of one part in 10 11 in the 1960's. R.G. Roll, R. Krokow & Dicke, Ann. of Physics 26, 1964.5.Sir. Issac Newton, PHYILOSOPHICA NATURALIS PRINCIPIA MATHENATICA (1687).6.Jennison, R.C. "What is an Electron?" Wireless World, June 1979. p. 43."Jennison became drawn to this model after having experimentally demonstrated the previously unestablished fact that a trapped electromagnetic standing wave has rest mass and inertia."Jennison & Drinkwater Journal of Physics A, vol 10, pp.(167-179) 1977 Jennison & Drinkwater Journal of Physics A, vol 13, pp.(2247-2250) 1980 Jennison & Drinkwater Journal of Physics A, vol 16, pp.(3635-3638) 19837.B. Haisch & A. Rueda of The California Institute for Physics and Astrophysics have also developed the deBroblie wave as a beat note. Refer to: http://www.calphysics.org/mass.html http://xxx.lanl.gov/abs/gr-qc/99060848.Znidarsic F. "The Constants of the Motion" The Journal of New Energy Vol. 5, No. 2 September 20009."A Possibility of Gravitational Force Shielding by Bulk YBa2Cu307-x", E. Podkletnov and R. Nieminen, Physica C, vol 203 (1992), pp 441-444.10.Puthoff has shown that the gravitational field results from the cancellation of waves. This author's model is an extension version this idea. H.E. Puthoff, "Ground State Hydrogen as a Zero-Point-Fluctuation-Determined State" Physical Review D, vol 35, Number 3260, 1987 H. E. Puthoff "GRAVITY AS A ZERO-POINT FLUCTUATION FORCE", Physical Review A, vol 39, Number 5, March 198911.Ezzat G. Bakhoum "Fundamental disagreement of Wave Mechanics with Relativity"Physics EssaysVolume 15, number 1, 200212.John D. Barrow and John K. Webb "Inconstant Constants"Scientific AmericanJune 200513.Albert Einstein, "Development of our Conception of Nature and Constitution of Radiation,"Physikalische Zeitschrift 22, 1909.