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What follows is an old paper...
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| --------------| A COLLECTION OF IDEAS | by Raheman Velji |
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This paper is constantly being updated.
Last update: March 15, 2008.
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* * * [must use a fixed-width font to view diagrams properly] * * *
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CONTENTS:
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(1) Self-sufficient Propulsion
A) Invention - the Simple Newton Engine
An invention that will have a lasting effect on space transportation.
---------------------------------------
(2) Law of Conservation of Energy
A) Invention - the Gravitational-Membrane Dynamo
B) Potential Energy
C) Creating and Destroying Mechanical Energy
Ideas which clearly demonstrate that the Law of Conservation of Energy
is wrong. Includes a neat invention which may be a perpetual
motion dynamo.
---------------------------------------
(3) Work and Energy
A) Defining Force, Work and Mechanical Energy
B) Relative Views
Force, work and mechanical energy will be defined in more intuitive
ways. Observations of force, work, change in mechanical energy
and mechanical energy depend on the frame you claim is at rest.
---------------------------------------
(4) Special Relativity
A) Preliminary
B) A Reality Check
C) Simultaneity
D) The Constancy of the Speed of Light
E) Outsider System vs. Insider System
F) Understanding the Michelson-Morley Experiment
G) The Finale
Simultaneity is absolute, not relative. The speed of light is not
constant. How does light propogate? Why we get a null
result from the Michelson-Morley experiment will be explained.
Amongst other things..
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-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (1) SELF-SUFFICIENT PROPULSION -|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
Devices that use "self-sufficient propulsion"
work on Newton's law that "every action has an equal and opposite
reaction." The idea is to harness the "action" and eliminate the
"reaction", or convert the "reaction" into useable energy. Thus,
within the device, the "reaction" is lost allowing the "action" to
propel the device. All devices that use "self-suffiecient
propulsion" work without affecting the environment. That is, they
don't need a road to push off of like cars, they don't have to push air
like planes or spew out gases like space shuttles. Thus, they get
the name "self-sufficient propulsion" because they *are*
self-sufficient. In other words, you can put a box around the
entire device and the box would move, and nothing would enter or exit
the box, and the device itself wouldn't react with the environment that
comes inside the box. It only reacts to the environment in the
box, which it creates, which it uses to propel itself. Devices
that use "self-suffiicient propulsion" would look like UFOs if they are
strong enough. (I propose that any device that uses
"self-suffiecient propulsion" should have the name "Newton" added to
its full-name so that we remember how it relates to Newton's law.
I will use that convention here; whether this convention should be
adopted is debatable.) The idea of "self-suffiecient propulsion"
will have a lasting effect on space transportation.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= A) Invention - the Simple Newton Engine =-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
START:
\-----------\-----------\-----------\-----------\
Side-view (cross-section):
forward -->
| ___cylinder
|
||
|
\/
|/-------------
||
#X| <--magnet ("X")
|\-------------
| /\
|
||__piston ("#")
|
|
|<--start line
The engine is a cylinder with a piston in
it. The piston may require wheels to move inside the
cylinder.
"Every action has an equal and opposite
reaction." The main idea of the "Simple Newton engine" is to
harness the "action" by getting rid of the "reaction". How do we
get rid of the momentum of the "reaction"? One way is by using
friction, which is discussed in "STEP 3".
The idea is to force the piston in the
backward direction, down the cylinder. Since every action has an
equal and opposite reaction, the cylinder will then experience a force
in the forward direction. This force is ideally created by using
electromagnets. Let us say that there is an electromagnet on the
piston ("#") which repels the magnet ("X") that is connected to the
front of the cylinder. (Also, one could make this similar to a
"Linear Induction motor", with the piston as the projectile.)
/-----------/-----------/-----------/-----------/
STEP 1:
\-----------\-----------\-----------\-----------\
|
forward -->
|
|
___ The magnet and the cylinder
|
|| move forward...
|
\/
-->
| /-------------
|
| #
X|
| \-------------
|
/\
<--
|
||__ ...as the piston moves backward
|
through the
cylinder
|
|
Now, activate the electromagnet on the
piston. So the piston, which is repelled by the magnet, moves
down the cylinder as the magnet and the cylinder accelerate forward.
/-----------/-----------/-----------/-----------/
STEP 2:
\-----------\-----------\-----------\-----------\
|
forward -->
|
|
|
|
|
/-------------
|
| #
X|
|
\-------------
|
/\
|
||__The piston must be stopped before
|
it hits the back of the cylinder
|
|
In fractions of a second, the piston will have
arrived at the back of the cylinder. The piston must be stopped
before it slams into the back of the cylinder because if it does then
the energy of the piston will cancel out the forward velocity that the
cylinder has gained. So, the energy of the piston must be removed
(by friction, e.g. brakes on the wheels) or harnessed (a method which
converts the "negative" energy of the piston into something
useable).
If friction is used to stop the piston, the
friction must cause the piston to lose velocity in decrements; should
the brake make the piston stop abruptly, then the "negative" momentum
of the piston will be transferred to the cylinder. Consider the
following analogy: If I'm on a bike and I stop abrubtly by
pushing down hard on my brakes, I (my body) will go hurtling forth
until I hit a wall. In the presence of gravity, I might hit the
ground before I hit a wall, but the point remains the same.
However, if I push on my brakes and slowing come to a stop, I can avoid
being thrown forward. And moreover, by coming to a stop slowly,
the momentum of me and the bike is dissipated as heat, and perhaps
sound, by the brakes. Thus, in the "Simple Newton engine" the
"reaction" can be made to be lost due to friction (as heat and possibly
sound) while the "action" is harnessed to propel the cylinder forward.
/-----------/-----------/-----------/-----------/
STEP 3:
\-----------\-----------\-----------\-----------\
|
forward -->
|
|
|
|
|
/-------------
|
|# X|
|
\-------------
|
|
|
|
|
When the piston has reached the end, and has
been brought to a stop, it must then be moved to the front of the
cylinder. Perhaps the piston can slowly move back on its wheels
towards the front of the cylinder. Or, perhaps it can be moved to
the front by hooking it to a chain which is being pulled by a
motor. Or, perhaps the piston can be removed from the cylinder
when it is being transferred to the front, and thus leave the cylinder
free so that another piston can "shoot" through the cylinder.
When you move the piston back to the front of the device you may end up
slowing the device's overall forward velocity but it is possible to
keep that loss to a minimum such that the device is still effective in
creating forward thrust.
/-----------/-----------/-----------/-----------/
Return to STEP 1:
\-----------\-----------\-----------\-----------\
|
forward -->
|
|
|
|
|
/-------------
|
| #X|
|
\-------------
|
|
|
|
|
The piston has been returned to the
front. Overall, the engine has moved and gained velocity.
Now it is ready to restart at "STEP 1".
It should be noted that the "Simple Newton
engine" creates a small amount of force. However, it can maintain
this force for an indefinite duration of time so long that you have
electrical energy. So, this device is ideal for space
transportation because given time (which we have in space) this device
can accomplish a lot of work.
Also, the entire "Simple Newton engine" can
(with an EMF source) be put into a box and the box would move without
interacting with the environment outside the box. Thus, we say it
uses "self-sufficient propulsion".
/-----------/-----------/-----------/-----------/
-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (2) LAW OF CONSERVATION OF ENERGY |-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
The fact that the Law of Conservation of Energy is wrong is perhaps
nature's cruelest trick.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= A) Invention - the Gravitational-Membrane Dynamo -=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
The following is what I call a "Gravitational-membrane dynamo":
_____
| \_____
| _ \_____
| | \_____ \_______
| |
\_____ |
|
|
\___ |
|
|
| |
| |
|
|
|
|
|
|
|
|
|
|
|
------*------ <--\
|
|
| |
|
|
| turbine
|
|
|
Tube B --> |
|
(contains |
|
| |
a fluid |
|
| |
- either |
|
| |
perfluor- |
|
| | <-- Tube A
octane or |
|
| | (contains
salt |
|_________________| |
water)
water)
|
| |
|____________|____________|
/|\
\_ semi-permeable
membrane
A "Gravitational-membrane dynamo" is to be
used to create electricity. It is not necessarily a perpetual
motion dynamo.
Tube A contains 250ml of water. Tube B
contains 750ml of a fluid - either perfluorooctane or salt water.
Tube A and Tube B are connected to each other by a semi-permeable
membrane. Water can permeate through the semi-permeable membrane;
I am assuming here that perfluorooctane and dissolved salt
cannot.
Now, when Tube B is filled with
perfluorooctane, then due to osmotic pressure, the water in Tube A will
pass through the semi-permeable membrane entering Tube B. Since
water is insoluble in perfluorooctane, and since water is less dense
than perfluorooctane, the water will rise to the top of Tube B.
Once enough water has accumulated at the top of Tube B, it will fall,
turning the turbine, and returning back into Tube A.
Now, when Tube B is filled with salt water,
then, again, due to osmotic pressure, the water in Tube A will pass
through the semi-permeable membrane entering Tube B. However,
salt water will accumalate at the top of Tube B and so it will be salt
water that falls, turning the turbine, entering Tube A. Having
salt water in Tube A is obviously undesirable. So, we'd have to
also put a semi-permeable membrane at the top of Tube B (which isn't
shown in the diagram) so that only pure water falls into Tube A.
By putting semi-permeable membranes on both ends of Tube B the salt
will be "trapped" in that tube.
Notice that when we use perfluorooctane the
dynamo relies on the fact that the water will be displaced by the
perfluorooctane due to a density difference. On the other hand,
when we use salt water the dynamo relies on the fact that as water
enters Tube B there is an increase in pressure in that tube causing
water to be expelled from the top of the tube.
Notice that this dynamo didn't require any
input energy, and it will continue to work, creating electricity by
turning the turbine (and generator, which is not shown), so long as the
perfluorooctane or dissolved salt does not seep into Tube A through the
semi-permeable membrane. Eventually, the perfluorooctane or
dissolved salt may seep through the semi-permeable membrane (this is
probably a slow process).
But how can this dynamo generate electricity
without any input energy? First, let's observe that the water at
the top of Tube B has gravitational potential energy. When it
falls, the gravitational potential energy is realized and is converted
into electricity by the turbine (and generator, which is not
shown). But how did the water initially get its gravitational
potential energy? Where is that energy coming from? By the
Law of Conservation of Energy something must lose energy so that
another can gain energy. Since we cannot find anything losing
energy, we must conclude that the Law of Conservation of Energy is
wrong, and that gravity creates forces which then create/destroy
energy; in this case it created energy in the final form of electricity.
As mentioned before, enough perfluorooctane
will probably eventually seep through the semi-permeable membrane
causing the level of the liquid in Tube B to lower such that the water
cannot escape through the top of the tube. And so, the turbine
will stop spinning. At such a point we can easily "unmix" both
liquids by pouring all the liquid into a tall cylinder. If we
leave the two liquids in the tall cylinder for awhile then the water
will accumalate at the top and the perflourooctane will gather at the
bottom. We know that originally there was 250ml of water.
So, we need only take the top 250ml of liquid (water) from the cylinder
and put it into Tube A; the rest of the 750ml of liquid
(perfluorooctane) can be dispensed back into Tube B.
Again, as mentioned before, enough dissolved
salt will probably eventually seep through the semi-permeable membrane
causing the level of the liquid in Tube B to lower such that the water
cannot escape through the top of the tube. And so, the turbine
will stop spinning. At such a point we need not "unmix" both
liquids. Instead, we can simply remove all liquids in both tubes
and put salt water back into Tube B and pure water back into Tube
A.
Notice again that this dynamo creates
electricity without using any input energy! Some may argue that
when we used perfluorooctane then we used energy to "unmix" the two
liquids. That is true *but* even though we used energy to "unmix"
the two liquids we did not *give* the two liquids energy. That
is, two liquids in separate beakers have the same amount of energy as
the same two liquids in the same beaker. And when we used salt
water, then we used energy to put the liquids into both tubes *but* in
that process we did not *give* the two liquids energy.
Of course we can use different liquids in Tube
B; I used perfluorooctane and salt water just as examples.
We can conclude by noting that energy is being
created/destroyed all around us. Gravity and magnetism are prime
examples. Both create forces. The immediate effect of the
forces on the system is nothing (the vectors of the forces cancel each
other out). However, after the immediate effect, and after a
minute amount of real time, the forces will do work on the
system. If "positive work" is done, then the system will gain
energy. If "negative work" is done, then the system will lose
energy. Whether "positive work" or "negative work" is done is
relative to the frame of reference you claim is at rest (we will
discuss this idea later in the section "Relative Views").
This dynamo may be a perpetual motion dynamo
if it creates more energy than is needed to keep the dynamo working,
and if it can sustain itself without using outside resources.
Also, it is possible that the "Gravitational-membrane dynamo" can be
used to create electricity on a large scale. In any case, I am
discussing it here simply to demonstrate that the Law of Conservation
of Energy is wrong and that gravity and magnetism can be used to create
energy.
---------------------------------------
ASIDE:
I define "perpetual motion" as motion that
causes something to continually change inertial frames without any
external forces. But what exactly is an "external force"?
An "external force" is a force that comes from outside a system.
But what exactly is a "system"? A "system" is a space which may
contain objects.
Also, something that is in perpetual motion
should "in theory" (not "in practice") be able to sustain its motion
indefinitally without using outside resources.
A "perpetual motion dynamo" is a machine that
uses perpetual motion to create energy.
Ideally, something in perpetual motion or a
perpetual motion dynamo should be contained in a small system.
But who is to define how "small" a system is? Hence, we can
always argue that any system is small enough.
We've seen above that the
"Gravitational-membrane dynamo" may be a perpetual motion dynamo.
It is possible "in theory" that it should be able to sustain its motion
indefinitally without using outside resources. But of course "in
practice" it cannot sustain its motion indefinitally without using
outside resources; eventually it's parts will wear down and need to be
replaced. The system of a "Gravitational-membrane dynamo" at
first glance seems to be small; but the "Gravitational-membrane dynamo"
requires the gravity of the Earth (or some other planet's gravity) to
keep it working. Hence, the system of a "Gravitational-membrane
dynamo" should encompass the Earth also. We can always *argue*
that this system which encompasses the Earth is small enough, but as
physicists can we all *agree* that it is? Hence, can a
"Gravitational-membrane dynamo" really be a perpetual motion dynamo?
Now, an "ideal planet" in rotation is in
perpetual motion. If you are attached to the planet you will be
constantly changing inertial frames of reference as the planet
rotates. If the planet is "ideal" then the planet will continue
to rotate forever, thus making the motion perpetual. It rotates
forever because the force that causes the rotation is the force that
causes the rotation, which is the force that causes the rotation.. you
get the point. Once a force has been applied to make it rotate,
it will continue to rotate forever - hence it is in perpetual motion.
---------------------------------------
ASIDE:
We have shown above that gravity can create
energy. It is always figured that the universe should collapse
due to gravity. However, gravity doesn't always bring things
together. For example, it is possible to have two stars attract
each other but not collide because of the direction of their initial
velocities. Instead of making a collision they can accelerate
towards each other and then "exit" with a greater speed then what they
"entered" with; I call this a "gravitational dance".
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= B) Potential Energy =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
Suppose we have two magnets with
like-charges.
As the two magnets are moved closer to each
other, potential energy will be gained and kinetic energy will be
lost. As the two magnets move away from each other, potential
energy will be lost and kinetic energy will be gained.
Say, initially, that both magnets are far
apart. Now, let us do work by moving the charges closer
together. When we are done and the magnets are close to each
other, the potential energy will have increased. The increase
will be equivalent to the work we did pushing them together.
Now, let's say that we took two hammers and
pounded both magnets until they lost their magnetism. Then, the
potential energy between the two magnets will dissappear. Thus,
the system has lost energy without any part of the system gaining
energy. We have demonstrated that the Law of Conservation of
Energy is wrong.
Let me recap: First, we did work to move
two repelling magnets together. Thus, we lost kinetic energy
while the magnets gained potential energy. We then destroyed the
magnetism of the magnets, thus losing the potential energy. Thus,
all-in-all, we lost energy.
This idea, which works on magnetism, can also
be applied to gravity, which follows.
---------------------------------------
Consider two stationary gaseous planets, both
made entirely of deutrium.
As the two planets are moved closer to each
other gravitational potential energy will be lost and kinetic energy
will be gained. As the two planets move away from each other
gravitational potential energy will be gained and kinetic energy will
be lost.
Let's do work on the planets, increasing the
gravitational potential energy of the planets, by moving them
apart. The increase in gravitational potential energy will be
equivalent to the amount work we did separating the planets.
Now, let's say that the deutrium of both
planets began to fuse by the following equation:
> deutrium
atom + deutrium atom => helium atom + neutron + 3.27 MeV
(It is true that I didn't include the initial energy to start the
fusion. However, the above equation is properly balanced, so we
do not have to consider the initial energy required. That is, let
us assume the initial energy to start the fusion is supplied.)
Now, it is obvious that mass is being
converted into energy. Since the masses of both planets are
decreasing, the gravitational potential energy between both planets
will also decrease. Thus, the work we did moving the planets
apart (which is now graviational potential energy) will diminish.
We have again demonstrated that the Law of Conservation of Energy is
wrong.
Let me recap: First, we did work by
moving the two planets apart. Thus, we lost kinetic energy while
the planets gained gravitational potential energy. We then
converted some of the mass of the planets into energy. Thus, we
lost mass and in the process we lost gravitational potential
energy. So, all-in-all, we lost energy.
---------------------------------------
Or, you can consider throwing a ball up.
As the ball is heading upward kinetic energy is being converted into
gravitational potential energy. The ball will reach a maximum
height when it has a velocity of zero and a maximum gravitational
potential energy. When the ball has reached its maximum height
let us convert the mass of the ball into energy. I don't know how
to do this, but nonetheless, it is within the realm of
possibility. By doing that, the mass will disappear and so the
gravitational potential energy will disappear. One might
oversimplify the above to say: "What goes up does not
*necessarily* come down."
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= C) Creating and Destroying Mechanical Energy -=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
"Mechanical energy" is the energy which is
possessed by an object due to its motion and its stored energy of
position. When I use the term "mechanical energy" in this section
I am referring solely to "the energy which is possessed by an object
due to its motion" *not* "its stored energy of position". (I
won't use the term "kinetic energy" because that term is related to the
equation "½mv²", and I do not want to imply that I am using
that equation.)
---------------------------------------
Let's say we have two electromagnets (coils of
wire) with air cores.
Now, let's set them next to each other.
And then, let's send an electrical current through them so that they
repel each other. Because they repel each other they will begin
to move away from each other. The two electromagnets were
stationary and now they are moving - now they have "mechanical
energy". Thus we have created energy (at least it seems that way
since we observed the two electromagnets from this particular frame of
reference).
Now, let's have the two electromagnets move
towards each other. Again, let's send an electrical current
through them so that they repel each other. They will stop
moving. The two electromagnets had "mechanical energy" and then
they stopped. Thus we have destroyed energy (at least it seems
that way since we observed the two electromagnets from this particular
frame of reference).
--> Some may argue that for both scenarios above the total
energy of the system is zero because the momentum of both
electromagnets when taken together is zero. However, the
"mechanical energy" of both electromagnets can be turned into another
form of energy; for example, we can let both electromagnets rub against
a surface like ashphalt. The heat and sound which is produced is
due to friction and it is energy. Thus, we must conclude that the
electromagnets initially also had energy. Thus, the total energy
of the system is not zero! We cannot simply add the "mechanical
energy" of the objects in the system and derive a conclusion from
that. The total "mechanical energy" of a system depends on the
addition of the *individual* "mechanical energies" of the objects in
the system, not just the addition of the "mechanical energies" of the
objects in the system.
--> Some may argue that energy is not created or destroyed but
simply converted from one type of energy into another. For
example, if we were using a battery to power the elecromagnets then
these people would say that the chemical energy of the battery is being
converted into electrical energy which then causes a change in
"mechanical energy" of the electromagnets which we perceive. If
we were plugging the electromagnets into the outlet then these people
would say that "mechanical energy" at the site of the power plant is
being converted into electrical energy which then causes a change in
"mechanical energy" of the electromagnets which we perceive. Now,
if energy is not created or destroyed but simply converted from one
type of energy into another then the amount of electrical energy used
by the electromagnets should *equal* the change in "mechanical energy"
experienced by the electromagnets. Notice that electrical energy
is proportional to current. But what if we inserted iron (a
ferromagnetic material) into the cores of the electromagnets?
Then the repulsive force between the electromagnets will be greater;
thus, the change in "mechanical energy" will be greater. But the
current remains the same!; we used the same amount of electric
energy! Thus, we realize that the amount of electrical energy
used by the electromagnets does not *equal* the change of "mechanical
energy" experienced by the electromagnets because iron cores "amplify"
the magnetic field and cause the change in "mechanical energy" to be
greater than it would be if there were no iron cores! So, we can
conclude that energy is not transformed from one type of energy into
another on a fixed ratio, at least not in this case.
--> Some may argue that "mechanical energy" is being
transformed into potential energy and vice versa. But we know
from the previous section that potential energy can disappear without
being realized.
So we can conclude that the Law of
Conservation of Energy is wrong.
And the fact that ferromagnetic materials
(like iron) amplify magnetic fields means that we should be able to, at
least in theory, hook a battery to a motor which is hooked to a
generator and create more energy (in the form of electricity) than is
used in the battery.
-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (3) WORK AND ENERGY |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
As said before: "Mechanical energy" is
the energy which is possessed by an object due to its motion and its
stored energy of position. When I use the term "mechanical
energy" in this section I am referring solely to "the energy which is
possessed by an object due to its motion" *not* "its stored energy of
position". (I won't use the term "kinetic energy" because that
term is related to the equation "½mv²", and I do not want
to imply that I am using that equation.)
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= A) Defining Force, Work and Mechanical Energy =-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
Before we go on further I need to invent a
word. When I say that A is "generally proportional" to B, I mean
that as A increases so does B.
---------------------------------------
It is worthwhile to define work in physics
similar to how we define work in an intuitive way.
So, how do we define work in an intuitive
way?
Well, as a human, work obviously depends on
the magnitude/difficulty of the task and the duration of the
task. So I propose that in physics work should be generally
proportional to a "magnitude" and a "duration". (The "magnitude"
and "duration" of work will be defined later.)
Also, as a human, we realize that by doing
work we can accomplish some task. Now, that can translate into
physics to mean that work can cause a change in energy of the system.
If all the work causes a change in "mechanical
energy" then we will say that the work is "effective"; if it does not
cause a change in "mechanical energy" then we will say that the work is
"ineffective". If the work causes a change in "mechanical energy"
but is hampered, that is, not all the work causes a change in
"mechanical energy", then we will say the work is
"semi-effective".
Likewise, force and power can also be called
"effective", "ineffective" or "semi-effective".
Notice that given any "unrestrained" object,
any force applied or work done on the object will always be effective.
Now, "effective force" is generally
proportional to mass and acceleration, and, "ineffective force" is
generally proportional to pressure and the area on which the force is
being applied on. Why is this so? Well, we can determine
"why" by doing "simple experiments" on increasing and decreasing a
force. For instance, when we increase "effective force" we find
that either accelertaion will increase or the mass of the object can
increase; if "effective force" decreases then either acceleration or
mass will decrease. We can do "simple experiments" on
"ineffective force" to obtain a similar conclusion.
However, it is best to have "effective force"
be *directly* proportional to mass and acceleration, and to have
"ineffective force" be *directly* proportional to pressure and the area
on which the force is applied. So:
The equation for "effective force" is:
> f_e = ma
• where "f_e" is "effective force"
"m" is mass
"a" is acceleration
The equation for "ineffective force" is:
> f_i = pA
• where "f_i" is "ineffective force"
"p" is pressure
"A" is area
We will define "whole force" as the summation
of all "effective forces" and "ineffective forces".
The equation for "whole force" is:
> f_w = f_e +
f_i
• where "f_w" is "whole force"
It is good to define "effective force" and
"ineffective force" as shown above because now an "effective force"
equals that "effective force" made ineffective and an "ineffective
force" equals that "ineffective force" made effective. Hence,
given any applied force the "whole force" remains constant even if the
applied force is made effective, ineffective or semi-effective.
---------------------------------------
Consider the following scenario: two
classmates, Jack and Jill, who are each going to hold a brick.
The downward force of the brick due to gravity is going to be the same
for either participant. Now, let's say that Jack held his brick
for 20 seconds, and Jill held her brick for 10 seconds. Now,
without using any scientific jargon, who did the most work? Jack
obviously did more work than Jill. Thus, *intuitively*, work
should be generally proportional to force and time. Now work is
already defined. The definition of work as it stands today is
wrong intuitively but it is *very* useful in making calculations.
It calculates work where work is defined as causing an object to be
displaced in a certain direction. So it looks like we have two
different ways of defining work. Let us distinguish between the
two by giving them names. Let the traditional meaning for work -
which is generally proportional to displacement - be called "productive
work" whereas the "new" definition for work - which is generally
proportional to time - be called "general work".
As said above, "productive work" is generally
proportional to force and displacement; we can determine this to be so
by doing "simple experiments". But physicists allow "productive
work" to be *directly* proportional to force and displacement for
simplicity's sake. Thus, we get the following equation for
"productive work":
> W_p = f_e*s
• where "W_p" is "productive work"
"s" is displacement
The force in "productive work" is, by
definition, always effective.
As said above, "general work" is generally
proportional to force and time; again, we can determine this to be so
by doing "simple experiments". It is also sensible to allow
"general work" to be *directly* proportional to force and time, again
for simplicity's sake. Thus, we get the following equation for
"general work":
> W_g = f_w*t
• where "W_g" is "general work"
"t" is a period of time
I propose that the unit for "general work"
should be "P", for Prescott, Joule's middle name. Thus, "one
prescott" equals "one newton second".
(I realize that force multiplied by time is
called an "impulse" or "action". However, the term "general work"
is more fitting because it relates to "productive work". Because
in a sense, "productive work" and "general work" are two sides of the
same coin; hence the reason why both units - joule and prescott - are
two names of the same person.)
---------------------------------------
So, "productive work" depends force and
displacement while "general work" depends on force and time. I
propose that we now define the "magnitude" of work as "force".
And, when we are considering "displacement" and "time" from the point
of view of work we will call them the "duration" of work.
---------------------------------------
When force is effective, "productive work" can
be written in terms of "general work":
> W_p =
W_g²/(2m)
From this we can infer two things: (1) The longer you do
"effective general work" it becomes exponentially rewarding in
productiveness. (2) A given amount of "effective general work"
doesn't always give you the same change in "productive work".
Now, we will call the rate at which "general
work" becomes "productive work" the "conversion rate". Hence,
> CR = W_p/W_g
• where "CR" is the "conversion rate"
Let's consider an object with mass "m" and do
work on it. When force is effective then "f_w = f_e" and so the
"conversion rate" is:
> CR = W_p/W_g
= (f_e*s)/(f_w*t) = s/t
And with a bit of math:
> s/t = v_i +
v_a
• where "v_i" is the initial velocity
• where "v_a" is the average change in velocity
Let us assume that the initial velocity is
zero and so:
> v_i = 0 m/s
and so:
> CR = v_a
So we can now say that the "conversion rate" - when the force is
effective - is the average change in velocity of the object.
Since the average change in velocity (the rate) increases with time, we
can conclude (again) that the productiveness of the "general work"
increases exponentially. Because the productiveness of "general
work" increases with time it is worthwhile to determine what the
productiveness of "general work" is over a small (infinitesmal)
duration of time. Notice that:
> v_a = a*t/2
So, when "t" approaches zero the "conversion rate" is the instantaneous
change in velocity - which is acceleration. Now acceleration can
be written as
> a = f_e/m
So, as mass increases it becomes harder to convert "general work" into
"productive work", that is, the "conversion rate" decreases.
Notice that the greater the initial velocity
the faster "general work" will be made into "productive work", hence,
the "conversion rate" increases.
And when force is effective, we can say that
> effective
power = f_e * s/t = M * CR
• where "M" is the magnitude of work
So, "effective power" is proportional to the magnitude of work and the
"conversion rate".
---------------------------------------
We are now going to consider the energy of a
system which has one particle with a mass of "m" moving at an initial
velocity "v". "Effective work" will be applied on the
particle. We will call the "magnitude" and "duration" of the work
as "M" and "D" respectively.
Notice that the "mechanical energy" of a
particle is generally proportional to its mass and velocity; we can
determine this to be so by doing "simple experiments". We will
"measure" the "mechanical energy" of the particle in two different
ways; we will name them "productive energy" and "general energy".
If we are considering the "productive energy" of the particle, we will
"measure" the energy of the particle using the equation
"½mv²". If we are considering the "general energy" of
the particle, we will "measure" the energy of the particle using the
equation "mv". Both equations - "½mv²" and "mv"
- can be considered to be two different "rulers" used to "measure" the
energy of the particle in the system. Now, notice that the change
in "productive energy" due to "productive work" and the change in
"general energy" due to "general work" is "MD". So, we can create
the following equations to determine the "mechanical energy" and change
in "mechanical energy" of the system:
When we are considering "productive work":
> (M = f_e =
ma) , (D = s)
> E_p =
½mv² + MD
> E_g = mv +
(2mMD)^½
When we are considering "general work":
> (M = f_e =
ma) , (D = t)
> E_g = mv + MD
> E_p =
½mv² + (MD)²/(2m)
• where "E_p" is the equation for "productive energy"
• where "E_g" is the equation for "general energy"
• where "m" is the mass of the particle
• where "v" is the initial velocity of the particle (prior to work)
Now in Newtonian mechanics kinetic energy is
equal to "½mv²" and momuntum is equal to "mv". So the
equation for "productive energy" gauges the Newtonian kinetic energy of
the system while the equation for "general energy" gauges the Newtonian
momentum of the system.
So which "ruler" should we use to "measure"
mechanical energy? Well, it depends on the circumstance. It
is often useful to "measure" mechanical energy using the equation for
kinetic energy because we often find that the kinetic energy of a
system is conserved, even though we know that overall the Law of
Conservation of Energy is wrong.
---------------------------------------
We have two balls; the mass of "Ball A" is "10
kg" while the mass of "Ball B" is "1 kg". Jack will push "Ball A"
and Jill will push "Ball B". Both balls can move without
restraint. Both Jack and Jill will apply the same force on the
balls - "10 Newtons". And they will both apply this force for the
same duration of time - "10 seconds". Hence, both Jack and Jill
will do the same amount of "effective general work" on the balls - "100
prescotts". With a little bit of algebra we can find that Jack's
ball will have been displaced by "50 meters" while Jill's ball will be
displaced by "500 meters". Hence, Jack does "500 joules" of
"productive work" while Jill does "5000 joules" of "productive work".
So, Jack does "100 prescotts" of "general
work" while Jill does "100 prescotts" of "general work"; the "general
work" is the *same*. But, Jack does "500 joules" of "productive
work" while Jill does "5000 joules" of "productive work"; the
"productive work" *differs*. Since "100 precotts" equals "100
prescotts" doesn't that imply that "500 joules" equals "5000 joules"?!
At first, that is what I thought; but I was
wrong. You see, Jack and Jill will do the same amount of
"effective general work". However, the rate at which "general
work" becomes "productive work" - the "conversion rate" - is greater
for Jill than for Jack. We know that "effective power" is
proportional to the magnitude of work and the "coversion rate"; the
magnitude of work is the same for both of them and so we see that
Jill's "effective power" is "500 watts", greater than Jack's "effective
power" which is "50 watts". Hence, both Jack and Jill put in the
same *effort* but Jill's work is more productive.
So, suppose you were being hired for a job;
the job requires you to apply a force. You should be concerned
with how much *effort* you'll have to expend applying the force.
That is, you should be asking your employer how much "general work" you
must accomplish to get paid; whether that work is productive or not is
meaningless to you, but perhaps the productiveness of the work is
meaningful to your employer.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= B) Relative Views =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
Now, "mechanical energy" depends on mass and
velocity. But velocity is relative; so, we must conclude that the
"mechanical energy" in a system is also relative! More precisely,
"mechanical energy" depends on what frame of reference you claim is at
rest.
Here's a rule:
• The relative velocity of two objects is constant no matter what
frame of reference you are in (even accelerated frames) so long that
the two objects are not accelerating relative to each other.
For example, consider a skydiver plumetting to
the Earth such that he has reached his terminal velocity. Someone
on the Earth will claim that he is at rest and will observe the
skydiver falling; he will say that the "mechanical energy" of his own
system depends on the mass of the skydiver and the speed at which he is
falling at. On the other hand, the skydiver will claim that he is
at rest and will observe the Earth to be moving towards him; he will
say that the "mechanical energy" of his system depends on the mass of
the Earth and the speed at which the Earth is approaching him. In
both cases the speed of the skydiver and the speed of the Earth are the
same (because velocity is relative). But, the mass of the Earth
is greater than the mass of the skydiver. So, the skydiver will
claim that there is more "mechanical energy" in his frame of reference
than what someone on the ground will claim!
So, the "mechanical energy" of a system
depends on what frame of reference you claim is at rest.
---------------------------------------
The acceleration of the skydiver and the Earth
due to gravity can be determined by tactile observations. That
is, the skydiver and the Earth can *feel* the acceleration. (Now,
it may be difficult to feel the acceleration when you are in free-fall
or when you are on the Earth. But that is just because our
instruments aren't sensitive enough.) If we determine
acceleration by tactile observations then we will say that it is a
"real acceleration"; if we determine force using "real acceleration"
then we will say that it is a "real force". The "real forces" of
gravity on the skydiver and the Earth are equivalent:
> f_s = f_e =
G m_s*m_e / r²
• where "f_s" is the "real force" on the skydiver
"f_e" is the "real force" on
the Earth
"G" is the Gravitational
Constant
"m_s" is the mass of the
skydiver
"m_e" is the mass of the
Earth
"r" is the distance between
the skydiver and the center of the Earth
Work is proportional to force. Now, when
you are *doing* work then the work depends on "real forces".
However, when you are *observing* work then the work depends on
"apparent forces". "Apparent force" is determined by "apparent
acceleration"; and "apparent acceleration" is determined by visual
observations of acceleration, not by tactile observations like "real
acceleration". When we are *doing* work we will call the work
"real work" while when we are *observing* work we will call the work
"apparent work".
The "total acceleration" is the sum of the
"apparent acceleration" of the skydiver and the "apparent acceleration"
of the Earth:
> a_t = a_s +
a_e
• where "a_t" is the "total acceleration"
"a_s" is the "apparent
acceleration" of the skydiver
"a_e" is the "apparent
acceleration" of the Earth
Notice that the "total acceleration" is constant no matter what frame
of reference you are in (even an accelerated frame!):
> a_t = G
(m_s+m_e) / r²
Here's a rule:
• The relative "apparent acceleration" of two objects (which is
the "total acceleration") is constant no matter what frame of reference
you are in (even accelerated frames) so long that the relative
"apparent acceleration" of the two objects is not increasing/decreasing
(that is, the "apparent acceleration" isn't itself "accelerating").
If someone on Earth were to assume that he is
at rest then he will say that an "apparent force" is being applied on
the skydiver; if the skydiver were to say that he is at rest then he
will say that an "apparent force" is being applied on the Earth.
Now, "apparent force" is proportional to mass and "apparent
acceleration". In both cases the "apparent acceleration" of the
skydiver and the "apparent acceleration" of the Earth are the same
(because "apparent acceleration" is relative). But, the mass of
the Earth is greater than the mass of the skydiver. So, the
skydiver will claim that a greater "apparent force" is being applied on
the Earth and so, more "apparent work" is being done from his frame of
reference than what someone on the ground will claim! And so, a
greater change in "mechanical energy" will be witnessed by the skydiver.
Of course, we can always claim that a certain
frame is at rest such that an "apparent force" is being applied on the
skydiver *and* an "apparent force" is being applied on the Earth.
For instance, there is a frame which is at rest such that "apparent
forces" equal "real forces". Also, it is worth noting that an
"apparent force" that isn't a "real force" is usually called a
"fictitious force".
So, we saw above that the "mechanical energy"
of a system depends on what frame of reference you claim is at
rest. Likewise, we can now say that "apparent acceleration",
"apparent force", "apparent work" and change in "mechancal energy" also
depend on what frame of reference you claim is at rest.
-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (4) SPECIAL RELATIVITY -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= A) Preliminary -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
Here are Einstein's two postulates of Special
Relativity:
--> (1) The laws of physics take the same form in all
inertial frames.
That is, one cannot distinguish one inertial frame from the others or
make one frame somehow more "correct" than another.
(Often referred to as the "relativity postulate".)
--> (2) In any inertial frame, the velocity of light "c"
is the same whether the light is emitted by a body at rest or by a body
in uniform motion.
That is, the speed of light will always be measured to be "c" when the
light-source is in an inertial frame.
---------------------------------------
When you *measure* a quantity using an
instrument we will say that that quantity is "measured". On the
other hand, if you *just* use an equation to determine a quantity we
will say that the quantity is "derived". It is often hard to
determine whether a quantity is "measured" or "derived" because in
certain cases we can either use an instrument to determine the unknown
or use an equation to determine the unknown. I make a distinction
between the two here: a "measured quantity" is always made by using an
instrument (and perhaps an equation), and we assume here that "measured
quantities" are always correct; "derived quantities" are made *solely*
by using equations and they may or may not agree with "measured
quantities". Notice that there may be more than one way to
determine a "derived quantity", but there is usually only one way to
determine a "measured quantity".
Why should we use the terms "measured" and
"derived" to differentiate between quantities? - Because "derived
quantities" don't always match "measured quantities" (as we will see in
the section "The Constancy of the Speed of Light"). So it is
useful to distinguish between quantities which we believe to be more
"correct" than other quantities - and so, we make the assumption that
"measured quantities" are always correct, and "derived quantities" may
or may not agree with the "measured quantities". Now how do we
determine which quantity is more "correct"? - Subjectively, of course,
but there is reasoning behind the choice. For instance, what if I
were to use a clock and an equation to determine a duration of time?;
say that the duration of time derived by the equation differs from the
duration of time measured by the clock. Which is right? - So long
that the clock isn't faulty, I'd vouch for the clock. I say this
because I believe that time is a property of the universe which should
be *measured* by using an instrument - a clock; if we use an equation
to determine a duration of time then I'd say that the equation works
only when it agrees with a clock.
(Side-tracking a bit: how do you measure a
length? If the endpoints of the thing you wish to measure are at
rest with your own frame then you can measure the thing using a ruler;
otherwise, the endpoints of the thing you wish to measure are moving
relative to you and so you need to measure the thing by perhaps using
visual observations (which may include the use of something like a
ruler, or other instrument).)
Now, a "measured length" is determined by
using a ruler or by using visual observations. A "measured time"
is determined by using a clock. On the other hand, you could
figure out displacement (a length) by using the equation "d=vt" or a
duration of time by using the equation "t=d/v" - where "d" is distance,
"v" is velocity, and "t" is time; by using those equations we can
determine "derived length" and "derived time".
Now, we can determine velocity using the
Doppler effect. If we use an instrument to determine the
frequency then by the equation for Doppler's effect we will find
"measured velocity". On the other hand, if we determine the
frequency by other means then by the equation for Doppler's effect we
will find "derived velocity". Of course, we can also find
"derived velocity" by using the equation "v=d/t".
Also, a "measured mass" is determined by using
a scale. Of course, to use a scale you need to know the strength
of the gravitational field you are emmersed in, and if there is no
gravitation field then the scale will fail. "Derived mass" is
figured out by using the equation for kinetic energy or the equation
for momentum or some other equation. "Measured mass" is usually
called "rest mass"; "derived mass" is often called "relativistic
mass". However, I prefer to use the terms "heavy mass" in place
of "measured mass" and "inert mass" in place of "derived mass" because
they are more descriptive terms and because they are the terms Einstein
himself uses in his essay "E=MC²". Notice that "inert mass"
need not equal "heavy mass"; in Newtonian mechanics it does, but in
Special Relativity it doesn't.
Now, there may be other ways to determine
derived length, time, velocity and mass. I wonder how they should
be added to the mix..
I said above that "we assume here that
"measured quantities" are always correct". If "derived
quantities" do not correlate with "measured quantities" then it is - to
put it bluntly - the "derived quantities" fault. It should be
physic's goal in general to have all "derived quantities" equal
"measured quantities" for this is not so in present day physics as we
will see in what follows. If a "derived quantity" does not equal
a "measured quantity" then that "derived quantity" is *wrong* and its
use should be discontinued, unless its use is somehow otherwise
justified. (Consider the term "derived mass"; it does not
necessarily equal "measured mass" but its use *is* nevertheless
justified because it has the redeeming feature that it contrasts (can
be compared) with "measured mass". That is, it can be useful to
compare "inert mass" with "heavy mass", especially if they
differ.) And when all "derived quantities" match "measured
quantities" then we can drop the qualifiers "measured" and "derived"
because both quantities will always "agree" with each other. That
day is not here yet, at least not for Special Relativity.
---------------------------------------
I am now going to invent two "thought
devices"; "ideal emitters" and "ideal receivers". Ideal emitters
are used to send signals to ideal receivers. The signal goes from
the emitter to the receiver *instantaneously*. So, there is
absolutely no time lag; that's why they're called "ideal".
In practice there is always some delay in our
signalling devices; there is always some error. "That there is a
lower limit to this error merely asserts that our intellects are more
delicate than our physical apparatus."
---------------------------------------
Also, we will be using three different
devices; what I call "SD devices" and "SMD devices", and
"light-clocks". All three aparatus have a light-source and a
light-detector, and perhaps a clock and a mirror. To simplify
verbiage, the "light-source" will be called the "source" and the
"light-detector" will be called the "detector".
In any thought-experiments, all devices are
equipped with ideal emitters at the source and the detector.
Anyone can get an ideal receiver and thus determine *exactly* when the
source emits the light and when the light gets received by the detector.
A "SD device" is an apparatus consisting of a
clock, a source and a detector. The apparatus is set up such that
the clock starts when the source emits a flash of light. The
light then gets registered by the detector which causes the clock to
stop. The device is called an "SD" device because light goes from
the (S)ource to the (D)etector.
A "SMD device" is very similar to a "SD
device" except that it has a mirror. The apparatus is set up such
that the clock starts when the source emits a flash of light. The
light is then reflected off the mirror. The light returns to the
source where it is registered by the detector which causes the clock to
stop. The device is called an "SMD" device because light goes
from the (S)ource to the (M)irror and back to the (D)etector.
It should be noted that "light-clocks" differ
from SMD devices. Einstein used light-clocks in his famous
thought-experiments. A light-clock is an apparatus set up like a
SMD device but without the clock. The crucial difference between
the two is that a SMD device *measures* an amount of time while a
light-clock *derives* an amount of time. How does a light-clock
derive time? Well, when you look at a light-clock in action you
will see the light traverse a certain distance "d". A user using
a light-clock assumes that the speed of light is the constant
"c". Thus, the light clock - using displacement "d" and the speed
of light "c" - derives the time "t" elasped by using the equation
"t=d/c".
---------------------------------------
I will refer to a velocity measured relative
to the "absolute frame" as an "absolute velocity".
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= B) A Reality Check -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Now, when I looked at the moon a while ago it
was a full circle. Today I look at the moon and it is half a
circle. I can look at this from two angles. I can say that
my observations are accurate and the moon is now half of what it used
to be. Or, I can say that my observations are flawed and I can
only see half the moon. Which is true? From the Earth, from
my particular observations, I cannot say one is more right than the
other. But, it is much better to believe that I am only seeing
half the moon because it is hard to explain where half the moon
suddenly disappeared to. Thus, when we examine a situation we
must decide what is reality in such a way that we can easily describe
the Universe.
For each individual case we must ask ourselves
are our observations an accurate description of reality or are our
observations flawed? It is fundamentally impossible to prove one
over the other; that is because our perception of reality is through
our observations, and one cannot know whether to trust the observations
or assume that there is a reality outside of our observations.
These questions must be asked when we consider
simultaneity, which follows in the next section.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= C) Simultaneity =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Einstein and relativity are wrong in their
treatment of simultaneity. The failure of relativity's treatment
of simultaneous events is best described by Professor W. D. MacMillan
in "A Debate on the Theory of Relativity":
"The notion of simultaneity in two distant
places according to Newtonian mechanics is not ambiguous, as is so
frequently asserted by the relativists. We can set two distant
clocks to indicate the same time with a certain margin of error.
That there is a lower limit to this error merely asserts that our
intellects are more delicate than our physical apparatus. However
fast or slow light may go, we can imagine a speed a million times as
great, or any other ratio that may be desired, and there is no lower
limit, save zero itself, to the determination of simultaneous events so
far as the mind is concerned. To say that simultaneity does not
exist because it is unattainable in practice is like saying that a
straight line does not exist because it, too, physically is
unattainable. Shall we then put geometry into the discard because
it is ambiguous and without meaning? If we do the matter is
ended, for there is nothing left for us to talk about."
Different observers measure different events
to be simultaneous. Is each observer correct in his own
frame? Or is there an underlying reality unseen because our
observations are faulty? What is reality? Relativity claims
the former idea.
Einstein claims that events which are
simultaneous with reference to one frame are not simultaneous with
respect to another frame.
So, is simultaneity absolute or
relative? Is only half the moon showing or has half the moon
disappeared?
The fact that we do observe events out of
order is because our observations are faulty. If we had a way to
transmit information instantaneously (like by using ideal emitters and
ideal receivers) then our observations would correlate with reality and
simultaneity would not seem to be ambiguous. The fact that we
don't have such devices merely implies "that our intellects are more
delicate than our physical apparatus".
So, simultaneity is absolute. That is,
two events are either simultaneous or not; it does not matter what
frame you are in. Now, if you were to see two events occur at the
same time then we will say that the events "appear to be simultaneous";
if you don't see two events occur at the same time then we will say
that the events "do not appear to be simultaneous". If we had the
use of ideal devices then all simultaneous events would appear to be
simultaneous and all "non-simultaneous" events would not appear to be
simultaneous; this is not always so when we do not use ideal devices.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= D) The Constancy of the Speed of Light -=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
INTRODUCTION:
We will see in what follows that to maintain
the constancy of the speed of light we need to have time dialate and/or
length contract. We will examine the thought-experiments used to
derive Special Relativity's equations for time dialation and length
contraction.
Both thought-experiments are set-up the
simalarily:
There are two people, an "insider" and an
"outsider". The "outsider" is standing on the Earth while the
"insider" is sitting on a train. The train is travelling forward
at a velocity "v" relative to the Earth.
---------------------------------------
DEFINING VARIABLES:
There is a light-clock and a ruler on the
train. We must define some variables on observations made on that
light-clock and ruler.
----------------
Observations made by the "insider":
• "tI" is the time it takes for the light to go
from the source to the
detector
• "dI" is the distance the light traverses going
from the source to the
detector
• "tI1" is the time it takes for the light to go
from the source to the
mirror
• "tI2" is the time it takes for the light to go
from the mirror to the
detector
• "dI1" is the distance the light traverses going
from the source to the
mirror
• "dI2" is the distance the light traverses going
from the mirror to the
source
• "lI" is the length of the ruler inside the train
as measured by the "insider"
----------------
----------------
Observations made by the "outsider":
• "tO" is the time it takes for the light to go
from the source to the
detector
• "dO" is the distance the light traverses going
from the source to the
detector
• "tO1" is the time it takes for the light to go
from the source to the
mirror
• "tO2" is the time it takes for the light to go
from the mirror to the
detector
• "dO1" is the distance the light traverses going
from the source to the
mirror
• "dO2" is the distance the light traverses going
from the mirror to the
source
• "lO" is the length of the ruler inside the train
as measured by the "outsider"
----------------
Hence:
> tI = tI1 +
tI2
> dI = dI1 +
dI2
> tO = tO1 +
tO2
> dO = dO1 +
dO2
---------------------------------------
This is how the "Time Dialation"
thought-experiment is set up:
The light-clock on the train is orientated
such that the source/detector is secured on the floor of the train
while the mirror is fastened above the source such that it will
(hopefully) reflect the light from the source directly back down to the
detector. The ruler fits snuggly between the source/detector and
the mirror.
---------------------------------------
Einstein claims that the speed of light is
always a constant. However, he never said from which frame does
light always leave the source in a straight line. We will observe
below that when light appears to travel from the source in a straight
line as observed by an "outsider" then the "Time Dialation"
thought-experiment fails.
---------------------------------------
"TIME DIALATION" THOUGHT-EXPERIMENT:
(assuming light leaves the source in a straight line as observed by an
"outsider")
As assumed, the flash of light will leave the
source in a straight line as observed by an "outsider". While the
flash of light is heading upwards towards the mirror the train has
moved forward. Thus, if the train is fast enough then it may have
moved forward enough such that the flash of light might not even hit
the mirror at all! The light may not hit the mirror because the
light is travelling upwards as seen from outside the frame, not
inside. The "insider" will see light "bend" [See Diagram A].
(A) ---> WHAT THE INSIDER SEES:
|
| ______
| • |
| • |
| • |
lI forward -->
| • |
| • |
| •|
\_________________________________
The experiment as stated by Special Relativity
requires that the light gets reflected back to the detector on the
floor of the train and so, this "Time Dialation" thought-experiment
does not produce proper results when we assume that light leaves the
source in a straight line as observed by an "outsider".
---------------------------------------
So, we will now assume that light appears to
travel from the source in a straight line as observed by the "insider".
---------------------------------------
"TIME DIALATION" THOUGHT-EXPERIMENT:
(assuming light leaves the source in a straight line as observed by an
"insider")
The "insider" is at rest with the light-clock
so:
> dI1 = dI2 =
lI
Meanwhile, the "outsider" sees the light
travel a greater distance [See Diagram B]. So:
> dO1 = dO2 =
[(vtO/2)²+lO²]^½
(B) ---> WHAT THE OUTSIDER SEES:
|
| ___
|
| •
|
| •|•
|
| • | •
| lO | • |
• forward -->
| |
• | •
| |
• | •
| _|_ •_____|_____•
|
|
|-----------|
|
vtO
\_________________________________
And we assumed that both the "insider" and the
"outsider" see light travel at the constant "c". Now, we will use
the equation "t=d/c", where "t" is an amount of "derived time", "d" is
the "measured distance" the light traverses, and "c" is the speed at
which light (supposedly) travels at. So:
> tI = dI/c =
2lI/c
and
> tO = dO/c =
2[{(vtO/2)²+lO²}^½]/c
And in this case, both insider and outsider
will agree that
> lI = lO
Using the above three equations, the "Time
Dialation" thought-experiment goes on to derive the following general
equation:
>(1a) tO = ytI
• where "y" equals "1/[1-(v/c)²]^½"
---------------------------------------
The above thought-experiment shows that if we
want to maintain the speed of light as a constant then we need for time
to dialate in a particular way. If time doesn't dialate, that is,
if time is constant for the "insider" and "outsider", then the two will
not agree that the speed of light is "c".
---------------------------------------
This is how the "Length Contraction"
thought-experiment is set up:
The light-clock on the train is orientated
such that the source/detector is secured at the back of the train while
the mirror is fastened at the front of the train such that it will
(hopefully) reflect the light from the source directly back to the
detector. Again, the ruler fits snuggly between the
source/detector and the mirror.
---------------------------------------
As said above, Einstein claims that the speed
of light is always a constant. However, he never said from which
frame does light always leave the source in a straight line. But
in the "Length Contraction" thought-experiment below both the "insider"
and the "outsider" will see light travel from the source in a straight
line, and so we have no problem like we did for the "Time Dialation"
thought-experiment.
---------------------------------------
"LENGTH CONTRACTION" THOUGHT-EXPERIMENT:
The "insider" is at rest with the light-clock
so:
> dI1 = dI2 =
lI
Meanwhile, the "outsider" sees things
differently.
When the light is travelling to the mirror the
light traverses a greater distance than "lO" because the front of the
ship has moved forward by a factor of "vtO1" [See Diagram C]. So:
> dO1 = lO +
vtO1
(C) ---> WHAT THE OUTSIDER SEES:
|
|
dO1
| |--------------------------|
|
| |••••••••••••••••••|•••••••|
forward -->
|
| |------------------|-------|
|
lO vt01
\_________________________________
When the light is travelling to the detector
the light traverses a smaller distance than "lO" because the back of
the ship has moved forward by a factor of "vtO2" [See Diagram D].
So:
> dO2 = lO -
vtO2
(D) ---> WHAT THE OUTSIDER SEES:
|
|
dO2
|
|----------|
|
|
|••••••••••| forward -->
|
| |-------|
|
vt02
|
|------------------|
|
lO
\_________________________________
Since the speed of light is constant:
> dO1 = ctO1
and
> dO2 = ctO2
Using the above four equations, we get the
following two equations:
> tO1 =
lO/(c-v)
and
> tO2 =
lO/(c+v)
Combining the above two equations with this
equation
> tO = tO1 +
tO2
we get:
> tO = 2
y² lO / c
• where "y" equals "1/[1-(v/c)²]^½"
Now, from the "Time Dialation" thought-experiment:
> tO = ytI
and we know that:
> tI = dI/c =
2lI/c
Using the above three equations, the "Length
Contraction" thought-experiment goes on to derive the following general
equation:
>(2a) lO = lI/y
---------------------------------------
The above thought-experiment shows that if we
want to maintain the speed of light as a constant then we need for
length to contract in a particular way. If length doesn't
contract, that is, if length is constant for the "insider" and
"outsider", then the two will not agree that the speed of light is "c".
---------------------------------------
For us to maintain that the speed of light is
constant for everyone we need for time to dialate and/or length to
contract in a particular way. Essen describes this perfectly in
his book "The Special Theory of Relativity":
"A critical examination of Einstein's papers
reveals that in the course of thought-experiments he makes implicit
assumptions that are additional and contrary to his two initial
principles. The initial postulates of relativity and the
constancy of the velocity of light lead directly to length contraction
and time dialation simply as new units of measurements, and in several
places Einstein gives support to this view by making his observers
adjust their clocks. More usually, and this constitutes the
second set of assumptions, he regards the changes as being observed
effects, even when the units are not deliberately changed. This
implies that there is some physical effect even if it is not understood
or described. The results are symmetrical to observers in
relative motion; and as such can only be an effect in the process of
the transmission of the signals. The third assumption is that the
clocks and lengths actually change. In this case the relativity
postulate can no longer hold.
"The first approach, in which the units of
measurement are changed, is not a physical theory, and the question of
experimental evidence does not arise. There is no evidence for
the second approach because no symmetrical experiment has ever been
made. There is no direct experimental evidence of the third
statement of the theory because no experiments have been made in an
inertial system. There are experimental results that support the
idea of an observed time dialation, but accelerations are always
involved, and there is some indication that they are responsible for
the observed effects."
(This book was written a while ago and so
things may have changed experimentally in the second paragraph above.)
Essen discussed three cases; they all attempt
to maintain the speed of light as a constant for everyone by claiming
that time dialates and/or length contracts in a particular way.
In this case, why does time dialate and/or length contract? In
short, either because..
• CASE #1: .."the clocks and lengths actually change".
(meaning that "measured quantities" change depending on your frame)
OR
• CASE #2: ..we adjust our clocks and rulers (and our equations).
(meaning that *only* "derived quantities" change depending on your
frame)
OR
• CASE #3: ..it is a result of an intrinsic property of our
observations.
(meaning that quantities change "when observations are made on a moving
body")
I will now discuss the above three cases in
detail.
---------------------------------------
CASE #1 - INTRODUCTION:
Here we will consider that time dialates and
length contracts because "the clocks and lengths actually change"; that
is, "measured quantities" change depending on your frame.
We will split this discussion into two parts;
one dealing solely with the "Time Dialation" thought-experiment, one
dealing with both thought-experiments together.
----------------
CASE #1 - DISCUSSION OF THE "TIME DIALATION" THOUGHT-EXPERIMENT:
Now, since the "outsider" sees the light
travel a greater distance than the "insider" Einstein and his friends
then use the equation "t=d/c" to claim that the "outsider" will measure
a greater amount of time to elapse than the "insider". The fact
that the "outsider" sees the flash of light travel a greater distance
than the "insider" is *directly* responsible for the fact that we then
get an equation which demonstrates that time dialates. The time
dialation equation means that since the "measured quantity" of distance
the light traverses differs depending on your frame then "derived time"
has dialated; this does not neccesarily mean that "measured time" has
dialated. Einstein and his friends often make the mistake of
saying "measured time" has to dialate because "derived time" dialates;
this is wrong.
As said above, the fact that "derived time"
dialates does not necessarily mean that "measured time" dialates.
Consider the outsider; "measured time" for him will pass at a certain
rate. In fact, "measured time" will *always* pass for him at a
certain rate whether there is a train in front of him or not.
Now, the distance the light traverses (in the light-clock on the train)
as observed by the outsider depends on the velocity of the train.
So, using the equation "t=d/c" we find that "derived time" dialates
according to the velocity of the train. This does not necessarily
mean that "measured time" dialates because "measured time" will
*always* pass for the outsider at a certain rate whether there is a
train in front of him or not!
Because "derived time" does not always equal
"measured time" when we assume that the speed of light is constant we
find that the equation "t=d/c" works only to find "derived time".
But shouldn't "derived time" match "measured time"?? So, if we
assume that the speed of light is constant then isn't the equation
"t=d/c", which is used to determine "derived time", wrong? Now,
on the other hand, if the speed of light is not constant and if light
acted "normally" then "derived time" would always equal "measured time"
when "derived time" is determined by using the following equation:
"t=d/z", where "z" is the speed of the flash of light which depends on
the frame you are in.
Let me clarify things: Einstein and I
both agree that during the "Time Dialation" thought-experiment the
"outsider" and "insider" will measure the distance travelled by the
light to be different. Einstein then says that the speed of light
is constant so time *has* to dialate. I say that time is a
constant and so the speed of light is what "dialates"; that is, it is
speed of light as observed by the "insider" and "outsider" which
differs, not time.
----------------
CASE #1 - DISCUSSION OF BOTH THOUGHT-EXPERIMENTS:
Most physics textbooks leave the subject of
both thought-experiments as they are above. However, what if we
moved the light-clock from the train down to Earth beside the
"outsider"? Then, in a sense, the "outsider" will become the
"insider" and the "insider" will become the "outsider". So, if
you repeat the "Time Dialation" thought-experiment you will derive the
following contradictory equation:
>(1b) tI = ytO
And if you repeat the "Length Contraction" thought-experiment you will
derive the following contradictory equation:
>(2b) lI = lO/y
Now both sets of equations - (1) and (2) -
demonstrate that time dialates and length contracts! If we are to
say that "derived quantities" change then there doesn't seem to be much
of a problem. But if we mean that "measured quantities" change
then we have the following problem: which equation is true and which is
false? Both the "insider" and the "outsider" have equal rights to
have their "measured time" dialate with respect to the other or have
their "measured length" contract with respect to the other. In
essence both time-equations together mean that "My time is faster than
your time which is faster than my time which is faster than your time
which is, etc..." A similar statement can be made for the
length-equations. Now, physics books and thought-experiments
often allow one of the equations to be true while the other equation is
dismissed (e.g. the famous "Twin Paradox" thought-experiment); such
action is unjustified.
Now, for both sets of equations, only one of
the two equations can be true. Again, if we are to say that
"derived quantities" has changed then we seem to have no
problems. However, if we are to say that "measured quantities"
change then only *one* observer - in a unique frame - will not have
time dialate; everyone else will. Also, only *one* observer - in
a unique frame - will not have length contract; everyone else
will. This leads us to the idea and necessity of creating an
"absolute frame" if "measured quantities" change because we must create
a "unique frame"; this invalidates Postulate #1, the relativity
postulate, which Essen rightly points out.
Einstein's equations hinge on the fact that
velocity is relative. In the "Length Contraction"
thought-experiment we find that the length of the ruler has contracted
(as observed by the "outsider"); but shouldn't that also mean that the
distance "vt01" and "vt02" (as observed by the "outsider") should also
contract? Let me explain: If length contracts then that
means that a certain axis of our coordinate system contracts; hence,
since "vtO1" and "vt02" are parts of that coordinate system in the same
direction in which the contraction is happening both quantities should
also contract. The same can be said for the distance "vtO" in the
"Time Dialation" thought-experiment. If these distances contract
then I doubt that velocity will remain relative.
Now, even if "measured quantities" change then
this actually does not save Special Relativity's second
postulate! Let us assume here that the "insider" is in the
"absolute frame". So, only such "outsiders" looking at the
light-clock with "insider" (who's in the "absolute frame") will observe
"measured quantities" to equal "derived quantities". And so it is
only these "outsiders" who will have "measured quantities" change
properly such that the speed of light remains a constant. If the
"outsiders" are looking at a light-clock that is *not* at rest with the
"insider" (who's in the "absolute frame") then the equations for time
dialation and length contraction cannot be properly used to maintain
the speed of light as a constant; this is because "measured quantities"
will no longer equal "derived quantities".
And what if we move the light-clock around
(change its orientation)?!? Special Relativity does not consider
that scenario!!! Now, on the other hand, if the speed of light is
not constant and if light acted "normally" then changing the
orientation of the light-clock would no longer be problematic.
Now, if "measured quantities" don't dialate
and contract then Einstein's thought-experiments demonstrate that
"derived time" dialates and "derived length" contracts. We are
saying here that "derived quantities" do not correlate with "measured
quantities". So, in this case the fact that "derived time"
dialates and "derived length" contracts is due to our equations, not
due to reality. But shouldn't our equations describe reality?! -
shouldn't our equations describe "measured quantities"?!
Nonetheless, in this case if "derived time" dialates and "derived
length" contracts such that the speed of light is maintained a constant
then we have essentially described "CASE #2", which is discussed next.
---------------------------------------
CASE #2:
Let us now consider the idea of creating "new
units of measurements" "by making observers adjust their clocks" and
rulers so that the speed of light *appears* to maintain the constant
speed "c". By adjusting our instruments (clocks and rulers) we
are essentially adjusting our equations. So, we are saying here
that "derived time" dialates and/or "derived length" contracts, not
that "measured time" dialates and/or "measured length" contracts.
This method of maintaining that the speed of
light is constant in all frames is the most seductive because we need
not abandon any "pre-relativity" physics! So, we can say that the
speed of light is not constant, and light acts "normally", and
"measured time" does not dialate and "measured length" does not
contract. But, if we let "derived time" to dialate and we let
"derived length" to contract then we hope to find that the speed of
light *appears* to be travelling at the constant speed "c" from any
frame. We can let "derived time" dialate and "derived length"
contract by adjusting our equations.
As Essen puts it: "..making the velocity of
light have the constant value "c" even to observers in relative motion
is comparable to making it a unit of measurement." "[And so] the
contraction of length and the dialation of time can now be understood
as representing the changes that have to be made to make the results of
measurement consistent [so that the speed of light *appears* to
maintain a constant speed]. There is no question here of a
physical theory but simply of a new system of units in which "c" is
constant, and [derived] length and [derived] time do not have constant
units but have units that vary.."
So we are proposing here that there are two
ways to determine "derived time" and "derived length". One way is
by using equations that match "measured time" and "measured length";
for a duration of time that equation is "t=d/z" and for displacement (a
length) that equation is "d=zt", where "z" is the speed of the flash of
light which depends on the frame you are in. The second way is to
use equations which allow "derived time" to dialate and/or "derived
length" to contract such that the speed of light *appears* to maintain
the constant speed "c". In that case, those "derived quantities"
will not match "measured quantities" and so the "derived quantities"
are *wrong*. These wrong "derived quantities" should be used only
in so much that it allows the speed of light to *appear* to remain
constant; otherwise its use should be discontinued.
Now, certainly the equations (1a) and (1b) in
"CASE #1" dialate "derived time" such that the speed of light is
maintained a constant; right? And certainly the equations (2a)
and (2b) in "CASE #1" contract "derived length" such that the speed of
light is maintained a constant; right? But what happens if we
move the light-clock around (change its orientation)?!? In such
cases "derived time" will dialate by a different factor and so the
time-dialation equations - (1a) and (1b) - will no longer be able to be
used to allow the speed of light in the light-clock to be maintained
the constant "c". "Derived length" will also contract by a
different factor making the length-contraction equations - (2a) and
(2b) - useless. Now, on the other hand, if the speed of light is
not constant and if light acted "normally" then changing the
orientation of the light-clock would no longer be problematic.
Of course we could always have time
dialate by a "unique factor" and/or length contract by a "unique
factor" such that the speed of light remains constant in a light-clock
no matter how it is orientated. But why? In that case, time
and length would always dialate and/or contract by a *unique* factor
depending on the orientation of the light-clock. So, we would not
really be able to create a consistent "new system of units" because
time and/or length will vary depending on the object (light-clock) you
are looking at; hence, if you are looking at more that one object
(light-clock) then you may find that time and/or length are not
constant in your frame!; this seems ridiculous. So, what's the
use?
The "Length Contraction"
thought-experiment shows that length contracts only in the direction of
the velocity. As said in "CASE #1", "if length [whether it be
"measured length" or "derived length"] contracts then that means that a
certain axis of our coordinate system contracts". Now, what if
you were looking at two different objects (light-clocks) that are in
different frames? So, the direction of the velocity of both
objects (light-clocks) could be askew. If these directions are
askew then two axis of our coordinate system that are askew would
contract. Hence, it would be unlikely for us to maintain a "new
system of units" consistent.
It seems that having time and length change by
"unique factors" is useless. It seems that the only way to make
having the speed of light a constant desirable is if we have time and
length change by "general factors", that is, factors that allow one to
maintain a system of units always consistent. But I do not know
of a way how we can have "derived time" dialate and/or "derived length"
contract by "general factors" such that the speed of light is *always*
maintained a constant. And even if we could, would it be
useful? In this case if we allow "derived time" to dialate and
"derived length" to contract they will not match "measured time" and
"measured length", and so the dialated "derived time" and the
contracted "derived length" are *wrong*. So, what's the use?
In any case, this method of maintaining the
speed of light as a constant does not in any way clash with other
theories, for as Essen correctly points out, it is not a "physical
theory". And so, we can actually say without doubt in this case
that the speed of light is *not* constant.
---------------------------------------
CASE #3:
If time dialates and/or length contracts
because it is an intrinsic property of our observations then we must
ask "why is this so?". Somehow, "the clock rates [and lengths]
are changed when observations are made on a moving body"! But how
can that be? In this case we are saying that the dialation of
time and the contraction of length are similar to an illusion.
That is, time and space are conspiring together to make the speed of
light always seem to be the constant "c". However, what if you
are looking at two objects (light-clocks) that are in different
frames?; then, time and space will have to conspire in two different
ways to keep the speed of light constant for both objects
(light-clocks). It is then unlikely that we can maintain a
consistent system of units; we came to similar conclusions in "CASE #2".
Now we have not explained "why is this so?",
just that somewhere along the line time dialates and/or length
contracts. So, this "explanation" does not really explain
anything afterall. Moreover, this "effect" is "not understood or
described" by *any* physics theories; without an explanation of what
the effect is or how it's derived it is likely - by Occam's razor -
that there actually isn't an effect to begin with.
---------------------------------------
CONCLUSIONS:
Above, we tried to maintain the speed of light
as a constant by having time dialate and length contract in a
particular way. However, in our attempts we found that when we
had time dialate and length contract we ran into problems and
contradictions and so, it is likely that the speed of light is not
constant.
---------------------------------------
SO WHY DOES TIME APPEAR TO DIALATE?:
We have seen above that time cannot dialate
and length cannot contract in a particular way such that the speed of
light can be maintained a constant. Now, I have never seen a
physical experiment that shows that "measured length" contracts.
However, there have been physical experiments that demonstrate that
"measured time" dialates. But notice that the fact that "measured
time" dialates does *not* in this case maintain the speed of light as a
constant. For example, it has been shown that muons created in
the atmosphere are observed to have the time of their half-lives
dialated. Why?:
• Perhaps our experiments are wrong and "measured time" actually
doesn't dialate! (This option seems the most simple.)
• Perhaps the "real acceleration" of the muon as it approaches
the Earth causes time to dialate. This means that anything
experiencing a "real acceleration" will have their "measured time"
dialate. (This option seems the most likely. As Essen put
it: "There are experimental results that support the idea of an
observed time dialation, but accelerations are always involved, and
there is some indication that they are responsible for the observed
effects.")
• Perhaps the "measured time" of the muon will dialate according
to the velocity of the muon measured from the "absolute frame".
This means that anything will have their "measured time" dialate
according to its "absolute velocity". (This option is very
unlikely to be true because the Michelson-Morley experiment failed to
detect an ether, and the "ether" is really just an "absolute frame".)
• Perhaps our observation of the muon *causes* time to
dialate. The fact that the halflife dialates is directly because
we made the *measurement* of the muon's velocity. It is the *act*
of making the measurement which causes time to dialate. This
means that if we *measure* the velocity of any particle then the time
for that particle will dialate according to the observed
velocity. Now, we've never observed that measuring the velocity
of a train causes time to dialate for the humans on the train;
afterall, the velocity of the train can be anything depending on your
frame and so that means that time can dialate by any factor. So,
why doesn't this work with humans and trains which are, afterall, just
large conglomerates of particles? Now, quantum mechanics
describes the "small world" (things like muons) but has trouble
describing the "big world" (things like humans and trains). So,
perhaps the dialation of time is like some kind of weird "quantum
effect". (I realize that this option seems a bit
over-the-top.. I'm not quite sure what it means now that I look
at it..)
Physical experiments need to be done to know
why "measured time" appears to dialate.
---------------------------------------
SPEED OF MATTER:
If light can travel faster than "c" depending
on your frame of reference then we certainly can expect to find that
matter can travel faster that "c" depending on your frame of
reference. However, in experiments we find that matter seems not
to be able to go at or faster than "c". Hence, it is likely that
given an inertial frame of reference we cannot do work (apply force) on
matter to accelerate it at or past the speed "c" as measured from the
inertial frame. So, it is likely that Special Relativity is right
in that "inert mass" of matter increases relative to your inertial
frame as the velocity of that matter increases relative to your
inertial frame such that the speed "c" is unattainable.
---------------------------------------
"TRAIN" THOUGHT-EXPERIMENT:
We will now discuss the famous "Train"
thought-experiment Einstein used to show that events which are
simultaneous with reference to one frame are not simultaneous with
respect to another frame.
Einstein says that events which are
simultaneous with reference to one frame are not simultaneous with
respect to another frame; this allows him to maintain that the speed of
light is constant. But we know from above (in the section on
"Simultaneity") "that two events are either simultaneous or not; it
does not matter what frame you are in". So, we are discussing the
"Train" thought-experiment here as a method to determine whether the
speed of light is constant for everyone.
We know from physical experiments that
"measured time" does dialate. At this point we do not know why;
more physical experiments need to be done. Now, in this section
we will say that "measured time" doesn't dialate; by the nature of this
experiment you will find that this premise should not appreciably
affect our conclusions because we can make the dicussed velocity
miniscule in comparison with "c". And when we determine why
"measured time" appears to dialate we should update this discussion of
the thought-experiment.
There is a train passing by an
embankment. The length of the train is "2L". There is
someone standing in the middle of the train; let that person be called
the "insider". There is also someone standing on the embankment
across the "insider"; let that person be called the "outsider".
The train is moving forward with a velocity relative to the embankment.
Now, two events happen simultaneously; two
flashes of light - "A" and "B" - strike the tracks, one - "B" - at the
front of the train, the other - "A" - at the back of the train.
---> DIAGRAM OF "TRAIN" THOUGHT-EXPERIMENT
|
|
| train __
|
||
|
\/
|
_______________________
| *
|
I | *
| A * ------------------------- *
B --> forward
| *
Ø Ø Ø
Ø Ø Ø *
|---------------------------------------------
|
O
|
/\
| embankment __||
|
|
| • where "I" is the "insider"
| "O" is the "outsider"
| "A" and "B" are
flashes of light
\_________________________________
Both the "outsider" and the "insider" will see
both flashes of light traverse the *same* distance "L".
If the events appear to be simultaneous then
it takes *equivalent* times for both flashes to cover the *same*
distance "L"; this can only happen when the speed of light is
*constant*.
We can also reverse that fact: if the events
do not appear to be simultaneous then it takes *different* times for
both flashes to traverse the *same* distance "L"; and this can only
happen when the speed of light is *different*.
So, if light travels at a constant speed for
all frames then the "outsider" and "insider" should *both* observe the
events to appear to be simultaneous! If the "outsider" or
"insider" do not see the events to appear to be simulataneous then we
can conclude that the speed of light is not constant for everyone!
I will now discuss how Einstein treats this
"Train" thought-experiment in his book "Relativity: The Special and
General Theory".
I want you to notice that when Einstein
conducts this "Train" thought-experiment he finds that the speed of the
flashes of light reaches the "insider" and "outsider" at *different*
times. This should imply to any rational person that the speed of
light is not always constant. However, Einstein circumvents this
answer by saying that both events are simultaneous for one observer,
and *not* simultaneous for the other observer!!! It is this con
which allows him to maintain that the speed of light is
constant!!! This is quite ridiculous, because "two events are
either simultaneous or not; it does not matter what frame you are
in".
Let me explain the above paragraph
clearly. This is how Einstein *himself* analyzes the "Train"
thought-experiment in his book: "When we say that the lightning
strokes A and B are simultaneous with respect to the embankment, we
mean: the rays of light emitted at the places A and B, where the
lightning occurs, meet each other at the midpoint M [the point where
the outsider "O" is] of the length A -> B of the embankment.
But the events A and B also correspond to positions A and B on the
train. Let M' [the point where the insider "I" is] be the
mid-point of the distance A -> B on the travelling train. Just
when the flashes (as judged from the embankment) of lightning occur,
this point M' naturally coincides with the point M, but it moves
towards the right in the diagram with velocity v of the train. If
an observer sitting in the position M' in the train did not possess
this velocity, then he would remain permanently at M, and the light
rays emitted by the flashes of lightning A and B would reach him
simultaneously, i.e. they would meet just where he is situated.
Now in reality (considered with reference to the railway embankment) he
is hastening towards the beam of light coming from B, whilst he is
riding on ahead of the beam of light coming from A. Hence the
observer will see the beam of light emitted from B earlier than he will
see that emitted from A. Observers who take the railway train as
their reference-body must therefore come to the conclusion that the
lightning flash B took place earlier than the lightning flash A."
In essence, this is what he is saying: Let us
say that the flashes of light are simultaneous for the
"outsider". In that case, the "insider" will not see the two
flashes to appear to be simultaneous; the "insider" will see the flash
from the front before the flash from the back. Now, the "insider"
can explain this situation in two ways:
--> (1) The speed of the flash of light from the front
is faster than the speed of the flash of light from the back and so the
speed of light is not constant, as observed by the insider.
OR
--> (2) The flash of the light from the front occured
earlier than the flash of the light from the back and so the events are
not simultaneous, as observed by the insider.
Both options explain why the front flash is
seen before the back flash. Now, Einstein vouches for option
(2). But if the event is simultaneous for the outsider then it
must also be simultaneous for the insider because "two events are
either simultaneous or not; it does not matter what frame you are
in". If we had the use of ideal devices then the insider would
*certainly* agree that the events are simultaneous! So, option
(2) goes to the garbage! And we are left with option (1).
As Essen puts it: "Einstein then considers the
question of simultaneity and shows that events that are simultaneous
for one observer are not simultaneous for an observer moving relative
to the first. This is, however, a consequence of Einstein's
assumption that the measured velocity of light is the same for both of
them - that is, of the adoption of the constant value of "c" as a unit
of measurement. There is no such difficulty if this assumption is
not made."
So, there is no reason to believe that the
speed of light is constant! The only way that the speed of light
can remain a constant now is if we conduct this experiment and both the
"outsider" and "insider" observe the events to *appear* to be
simultaneous. This is unlikely to happen.
So, we should conduct the above
thought-experiment in reality to determine whether the speed of light
is constant.
(ASIDE: To conduct this experiment we'd
have to consider at least three cases; one, when the source of flashes
are at rest with the "outsider", the second, when the source of flashes
are at rest with the "insider", the third, when the source of flashes
are not at rest with the "insider" nor the "outsider". Why do we
have to consider (at least) three cases? Because, as we see in
the section "Outsider System vs. Insider System", it is possible (and
likely) that the speed of light depends on the motion of the source.)
---------------------------------------
REMARKS:
Now, Einstein claimed many many years ago that
the speed of light is a constant in all frames. Why hasn't
anybody checked this?!?! We should do many experiments, some on
Earth, some in space, some in inertial frames, some in accelerated
frames. We should observe the distance the light traverses and
the time elasped from many different frames, and see if the speed of
light is constant for everyone!!!
And we should not be satisfied with
thought-experiments; we must conduct real physical experiments to
verify the *integrity* of thought-experiements! As Essen puts it:
"Perhaps the strangest feature of all [pertaining to relativity], and
the most unfortunate to the development of science, is the use of the
thought-experiment. The expression itself is a contradiction in
terms, since an experiment is a search for *new* knowledge that cannot
be confirmed, although it might be predicted, by a process of logical
thought." And so a thought-experiment should be used only to
create hypotheses, not as proof.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= E) Outsider System vs. Insider System =-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
INTRODUCTION:
For convience sake let us make the following
definitions:
• An "Outsider System" is true when all observers *outside* a
frame measure the speed of light which emanates from a source *inside*
the frame to be the constant "c".
• An "Insider System" is true when all observers *inside* a frame
measure the speed of light which emanates from a source *inside* the
frame to be the constant "c".
Now, for Postulate #2 to be true all observers
*inside* a frame should agree with all observers *outside* the frame
that the speed of light coming from a source *inside* the frame is the
constant "c"; that is, the "Outsider System" and the "Insider System"
should be compatible.
We will be analyzing two situations. We
will first consider both situations assuming that the "Outsider System"
is true. Then we will consider both situations assuming that the
"Insider System" is true. From this we hope to determine whether
the "Outsider System" and the "Insider System" are compatible, that is,
the speed of light is the constant "c" for everyone.
These situations we will be analyzing are
thought-experiments. They should be tested out in reality by
physical experiments to verify their integrity. A reasonable
physical experiment to determine which of these thought-experiments are
correct will be outlined at the end of this section ("'Outsider System
vs. Insider System' Experiment").
We saw above that time cannot dialate and
length cannot contract such that the speed of light is maintained a
constant. So, we will use Galilean transformations here instead
of Lorentz transformations. Nonetheless, we know from physical
experiments that "measured time" does dialate. At this point we
do not know why; more physical experiments need to be done. Now,
in this section we will say that "measured time" doesn't dialate; by
the nature of these thought-experiements you will find that this
premise should not appreciably affect our conclusions. And when
we determine why "measured time" appears to dialate we should update
these thought-experiments.
We will call the person outside the frame the
"outsider" while the person inside the frame, on the space ship, will
be the "insider".
Let us now assume that the "Outsider System"
is right. Here we go!
---------------------------------------
SITUATION #1: (assuming "Outsider System" is correct)
On the space ship is a SD device secured such
that the source is at the back of the space ship and the detector is at
the front so that the detector will (hopefully) register the light from
the source. The distance between the source and the detector is
"L".
Now, to start off the space ship is at rest
with the "outsider".
It is the "insider's" job to start the SD
device when we decide to do the experiment. Let the "insider"
start the experiment.
The "outsider" and the "insider" are both in
the same frame. Hence, they will both agree that the light
traverses a distance "L" in a time "t" travelling at a speed "c".
So:
> L = ct
---------------------------------------
Now, let's accelerate this space ship forward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experment once more
[See Diagrams A1 & A2].
(A1) ---> WHAT THE INSIDER SEES:
|
|
(c-v)t
| |------------------|
|
| |••••••••••••••••••| forward
-->
|
| |------------------|
| L
\_________________________________
(A2) ---> WHAT THE OUTSIDER SEES:
|
|
ct
| |--------------------------|
|
| |••••••••••••••••••|•••••••|
forward -->
|
| |------------------|-------|
|
L vt
\_________________________________
Notice that this round it will take more time
for the light to be detected. This is because the ship is moving
forward, and so, the front of the ship will have moved forward by a
factor of "vt" before the flash of light could reach the
detector. So this time the "outsider" will say that he saw a
flash of light traverse a distance "L+vt" in a time of "t" at a speed
of "c". Thus, we arrive at the following equation:
> L + vt = ct
Again, the "insider" will say that he saw a
flash of light travel a distance "L" in a time of "t". Thus,
using the equation "L+vt=ct" he will say he saw light travel at the
speed "c-v". This means that someone inside the frame may not
agree with the "outsider" that the speed of light is the constant "c".
But notice that the above equation can be
solved for "v"!:
> v = c - L/t
So far we have said that "v" is the relative
velocity of the "outsider" and the space ship. But we have a
little problem. The "insider" will measure the time elasped
during the experiment to be some "fixed value". This "fixed
value" has nothing to do with the relative velocity of the "outsider"
and the space ship! Even though the above equation is what the
"outsider" observes, the "insider" can conduct the experiment on his
own and thus get a value for "t" without any aid or reference to the
"outsider"! Thus, using that value of "t" the "insider" can
figure out the value of "v" using the above equation! Now, what
exactly is this velocity relative to? It must be a velocity that
is measured relative to some "absolute frame of reference"!
Put another way: You can be alone on the
space ship and conduct this experiment and get a unique value for the
change in time. Now, "L" and "c" are constants, so we must
conclude that "v" is also unique. That is, a unique value of "t"
corresponds to a unique value of "v". Now, what is a "unique"
velocity? It must be a velocity measured from some "absolute
frame".
And since we said above that "v" is the
relative velocity of the "outsider" and the space ship then we must
notice that we have inadvertently put the "outsider" at rest with the
"absolute frame of reference". If the "outsider" is not at rest
with the "absolute frame" then he will see the speed of light to be
some constant, but that constant will not be "c".
---------------------------------------
Now, let's accelerate this space ship backward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams B1 & B2].
(B1) ---> WHAT THE INSIDER SEES:
|
|
(c+v)t
| |------------------|
|
| |••••••••••••••••••| forward
-->
|
| |------------------|
| L
\_________________________________
(B2) ---> WHAT THE OUTSIDER SEES:
|
| ct
| |----------|
|
|
|••••••••••|
forward -->
|
|
|-------|
|
vt
| |------------------|
|
L
\_________________________________
Notice that this round it will take less time
for the light to be detected. This is because the ship is moving
backward, and so, the front of the ship will have moved backward by a
factor of "vt" before the flash of light could reach the
detector. So this time the "outsider" will say that he saw a
flash of light traverse a distance "L-vt" in a time of "t" at a speed
of "c". Thus, we arrive at the following equation:
> L - vt = ct
Again, the "insider" will say that he saw a
flash of light travel a distance "L" in a time of "t". Thus,
using the equation "L-vt=ct" he will say he saw light travel at the
speed "c+v". This means that someone inside the frame may not
agree with the "outsider" that the speed of light is the constant "c".
Again, we can determine the "absolute
velocity" of the ship:
> v = L/t - c
Again, we have inadvertently put the
"outsider" at rest with the "absolute frame". If the "outsider"
is not at rest with the "absolute frame" then he will see the speed of
light to be some constant, but that constant will not be "c".
---------------------------------------
ADDING TO DEFINITIONS:
Now, we need to add to the definition above of
the "Outsider System" and the "Insider System" because they are
incomplete. We avoided mentioning this before to avoid confusion:
sometimes light will appear to move from the source in a straight line
only from one particular frame; all other frames will see the light
"bend".
Einstein claims that the speed of light is
constant. However, he never decided from which frame does the
light always seem to leave the source in a straight line. Big
error. I claim here - without any justification - that the
observer who always witnesses light travel at the constant speed "c" is
also the observer who always sees light travel from the source in a
straight line. I claim this because my intuition tells me so and
I will only be validated or discredited by physical experiments.
If we are using an "Outsider System" then the
direction of the light follows the direction the source is pointing in
as seen by an "outsider". Now, all the "outsiders" are in
different frames so that they will all (usually) disagree as to what
the actual direction of the light is. Because only one "outsider"
can be "right" as to what the actual direction of the light is, we are
led to the conclusion that only one frame of reference is
"right". This leads us directly back to the idea and necessity to
create an "absolute frame". This means that (usually) only one
"outsider" in a unique frame will see light follow from the source in a
"straight" line. Everyone else will (usually) see light "bend",
that is, the light will not follow from the source in a straight line.
On the other hand, if we are using an "Insider
System" then the direction of the light follows the direction the
source is pointing in as seen by an "insider". Now, since all
"insiders" are in the same frame then they will all agree as to what
the actual direction the light is moving in. So, we have no need
in this case to create an "absolute frame". This means that only
the "insiders" will always see light follow from the source in a
"straight" line. Everyone else ("outsiders") will (usually) see
light "bend", that is, the light will not follow from the source in a
straight line.
The reason why we could leave these points out
of the definitions before is because in "Situation #1" all "outsiders"
and all "insiders" will agree as to what the direction the light is
heading in; this is not always the case as the next situation will
demonstrate.
---------------------------------------
SITUATION #2: (assuming "Outsider System" is correct)
On the space ship is another SD device such
that the source is secured on the floor of the space ship and the
detector is fastened above so that the detector will (hopefully)
register the light from the source. The distance between the
source and the detector is "L".
To start off the space ship is at rest with
the "outsider".
It is the "insider's" job to start the SD
device when we decide to do the experiment. Let the "insider"
start the experiment.
The "outsider" and the "insider" are both in
the same frame. Hence, they will both agree that the light
traverses a distance "L" in a time "t" travelling at a speed "c".
So:
> L = ct
---------------------------------------
Now, let's accelerate this space ship forward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams C1 & C2].
(C1) ---> WHAT THE INSIDER SEES:
|
|
vt
|
______
|
• |
|
• |
|
• | L forward -->
| c[1+(v/c)²]^½ * t • |
|
• |
|
•|
\_________________________________
(C2) ---> WHAT THE OUTSIDER SEES:
|
| ___
| •
| •
| ct • L forward -->
| •
| •
| _•_
|
\_________________________________
Now, let's accelerate this space ship backward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams D1 & D2].
(D1) ---> WHAT THE INSIDER SEES:
|
| vt
| ______
| |
•
| | •
| L |
•
forward -->
| | •
c[1+(v/c)²]^½ * t
| | •
| |•
\_________________________________
(D2) ---> WHAT THE OUTSIDER SEES:
|
| ___
| •
| •
| ct • L forward -->
| •
| •
| _•_
|
\_________________________________
In both cases above, the "outsider" will see
the same thing. That is, he will see the light emanate from the
source and move upward, traversing a distance "L" in a time "t" at a
speed "c". But while the flash of light is heading upwards
towards the detector, the space ship has moved forward or backward by a
factor of "vt". Thus, if the space ship is fast enough then it
may have moved forward or backward enough such that the flash of light
might not even hit the detector! The light may not hit the
detector because the light is travelling upwards as seen from outside
the frame, not inside. So, the "insider" will see light "bend".
Now "t" should be the time it takes for the
light to go from the source to the detector. But in this case, if
the velocity of the space ship is sufficient then the light may not get
registered by the detector. So for this particular situation "t"
is the time it takes for the light to go from the source to the ceiling
(not to the detector).
In both cases, the "insider" will say he saw
light travel a distance "((vt)²+(ct)²)^½" in a time
"t". Thus, using the equation "L=ct" he will say he saw light
travel at the speed of "c[1+(v/c)²]^½". So, the
"insider" will measure the speed of light to be greater than or equal
to the constant "c", but never less. This means that someone
inside the frame may not agree with the "outsider" that the speed of
light is the constant "c".
Now, the light will hit the ceiling of the
space ship at a certain point. So, we can measure the length "vt"
using a ruler; let that length be "Z". We can also determine "t"
using a clock. Then we can create an equation that solves for the
"absolute velocity", "v":
> v = Z/t
Again, we have inadvertently put the
"outsider" at rest with the "absolute frame". If the "outsider"
is not at rest with the "absolute frame" then he will see the speed of
light to be some constant, but that constant will not be "c".
---------------------------------------
CONCLUSIONS: (assuming "Outsider System" is correct)
From the above, if we are to say that the
"Outsider System" is true then we are led to three inevitable negative
conclusions:
--> (1) Postulate #1 is wrong! There must be some
"absolute frame" for "v" to be relative to, and so, we have
distinguished one frame from the others.
--> (2) Postulate #2 has errors! The speed of
light is the constant "c" only when it is measured from the "absolute
frame", otherwise it isn't.
--> (3) When observed from inside the frame where the
light source is, the flash of light may seem to "bend", that is, it may
not follow from the source in a straight line.
We have seen above that the "Outsider System"
is ridden with pitfalls. Now, many experiments have been done
where the light source and the experimenter are inside the same
frame. In such experiments the speed of light has never deviated
from "c" and light has never appeared to "bend". So with these
problems it is likely that we started with the wrong assumption.
So instead let us now assume that the "Insider
System" is right and redo the thought-experiments.
---------------------------------------
SITUATION #1: (assuming "Insider System" is correct)
On the space ship is a SD device secured such
that the source is at the back of the space ship and the detector is at
the front so that the detector will (hopefully) register the light from
the source. The distance between the source and the detector is
"L".
Now, to start off the space ship is at rest
with the "outsider".
It is the "insider's" job to start the SD
device when we decide to do the experiment. Let the "insider"
start the experiment.
The "outsider" and the "insider" are both in
the same frame. Hence, they will both agree that the light
traverses a distance "L" in a time "t" travelling at a speed "c".
So:
> L = ct
---------------------------------------
Now, let's accelerate this space ship forward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams E1 & E2].
(E1) ---> WHAT THE INSIDER SEES:
|
|
ct
| |------------------|
|
| |••••••••••••••••••| forward
-->
|
| |------------------|
| L
\_________________________________
(E2) ---> WHAT THE OUTSIDER SEES:
|
|
(c+v)t
| |--------------------------|
|
| |••••••••••••••••••|•••••••|
forward -->
|
| |------------------|-------|
|
L vt
\_________________________________
Again, the "insider" will see the same
thing. In fact, the "insider" will *always* observe the light to
traverse a distance "L" (towards the detector) in a time "t" at a speed
"c". Also, the light will *always* reach the detector because the
"insider" will never see light "bend".
According to the "outsider", the front of the
ship will have seemed to move forward by a factor of "vt" before the
flash of light could reach the detector. So, the "outsider" will
see the light traverse a distance "L+vt" in a time "t". Using the
fact that "L=ct" we can say that the "outsider" will see the light
travel at a speed of "c+v". This means that someone outside the
frame may not agree with the "insider" that the speed of light is the
constant "c".
---------------------------------------
Now, let's accelerate this space ship backward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams F1 & F2].
(F1) ---> WHAT THE INSIDER SEES:
|
|
ct
| |------------------|
|
| |••••••••••••••••••| forward
-->
|
| |------------------|
| L
\_________________________________
(F2) ---> WHAT THE OUTSIDER SEES:
|
| (c-v)t
| |----------|
|
|
|••••••••••|
forward -->
|
|
|-------|
|
vt
| |------------------|
|
L
\_________________________________
Again, the "insider" will see the same
thing. In fact, the "insider" will *always* observe the light to
traverse a distance "L" (towards the detector) in a time "t" at a speed
"c". Also, the light will *always* reach the detector because the
"insider" will never see light "bend".
According to the "outsider", the front of the
ship will have seemed to move backward by a factor of "vt" before the
flash of light could reach the detector. So, the "outsider" will
see the light traverse a distance "L-vt" in a time "t". Using the
fact that "L=ct" we can say that the "outsider" will see the light
travel at a speed of "c-v". This means that someone outside the
frame may not agree with the "insider" that the speed of light is the
constant "c".
---------------------------------------
SITUATION #2: (assuming "Insider System" is correct)
On the space ship is another SD device such
that the source is secured on the floor of the space ship and the
detector is fastened above so that the detector will (hopefully)
register the light from the source. The distance between the
source and the detector is "L".
To start off the space ship is at rest with
the "outsider".
It is the "insider's" job to start the SD
device when we decide to do the experiment. Let the "insider"
start the experiment.
The "outsider" and the "insider" are both in
the same frame. Hence, they will both agree that the light
traverses a distance "L" in a time "t" travelling at a speed "c".
So:
> L = ct
---------------------------------------
Now, let's accelerate this space ship forward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams G1 & G2].
(G1) ---> WHAT THE INSIDER SEES:
|
| ___
| •
| •
| ct • L forward -->
| •
| •
| _•_
|
\_________________________________
(G2) ---> WHAT THE OUTSIDER SEES:
|
|
•|
|
• |
| c[1+(v/c)²]^½ * t •
| forward -->
|
• | L
|
• |
|
•_____|
|
vt
\_________________________________
Now, let's accelerate this space ship backward
so that it ends up with a speed of "v" relative to the
"outsider". Let's have the "insider" do the experiment once more
[See Diagrams H1 & H2].
(H1) ---> WHAT THE INSIDER SEES:
|
| ___
| •
| •
| ct • L forward -->
| •
| •
| _•_
|
\_________________________________
(H2) ---> WHAT THE OUTSIDER SEES:
|
|
vt
|
______
|
• |
|
• |
|
• | L forward -->
| c[1+(v/c)²]^½ * t • |
|
• |
|
•|
\_________________________________
Again, the "insider" will see the same
thing. In fact, the "insider" will *always* observe the light to
traverse a distance "L" (towards the detector) in a time "t" at a speed
"c". Also, the light will *always* reach the detector because the
"insider" will never see light "bend".
But while the flash of light is heading
upwards towards the detector, the space ship has moved forward or
backward by a factor of "vt". Thus, the "outsider" will see light
"bend". So, the "outsider" will see the light traverse a distance
"(L²+(vt)²)^½" in a time "t". Using the fact
that "L=ct" we can say that the "outsider" will see the light travel at
a speed of "c[1+(v/c)²]^½". So, the "outsider" will
measure the speed of light to be greater than or equal to the constant
"c", but never less. This means that someone outside the frame
may not agree with the "insider" that the speed of light is the
constant "c".
---------------------------------------
CONCLUSIONS: (assuming "Insider System" is correct)
From the above, if we are to say that the
"Insider System" is true then we are led to one inevitable negative
conclusion:
--> (1) Postulate #2 has errors! The speed of
light is the constant "c" only when measured from inside the frame
where the light source is, otherwise it isn't.
Notice that two negative conclusions from when
we considered the "Outsider System" have gone!: (1) We no longer need
to "create" an "absolute frame" and (2) light does not seem to "bend"
when the source and the observer are in the same frame.
So, comparing the conclusions we find that it
is likely that the "Insider System" is correct, not the "Outsider
System".
To recap, when we use the "Outsider System"
then light travels at the constant "c" from the "absolute frame" but
not "c" from all other frames. When we use the "Insider System"
then light travels at the constant "c" from inside the frame (where the
source is) but not "c" from all other frames. Thus, we can
conclude that the "Outsider System" and the "Insider System" are
incompatible. Postulate #2 is wrong no matter which way you look
at it! Either the "Outsider System" is right or the "Insider
System" is right, not both! The "Outsider System" means that the
speed of light does not depend on the motion of the source while the
"Insider System" means that the speed of light does depend on the
motion of the source; contradiction ensues.
---------------------------------------
REMARKS:
It should be noted that in the above
thought-experiments we only examined the velocity in *one*
dimension. So, if we are to try to actually implement the
thought-experiments in real life then we may have to consider the other
dimensions of the velocities of the spaceship and of the flash of light
in the SD device.
---------------------------------------
ASIDE:
It should be noted that in Eintein's treatment
of the "Train" thought-experiment he implicitly assumes that the
"Outsider System" is correct. This assumption is
unjustified. Only physical experiments can determine whether
light behaves by an "Outsider System" or by an "Insider System".
Such an experiment is described below.
---------------------------------------
"OUTSIDER SYSTEM VS. INSIDER SYSTEM" EXPERIMENT:
We can create a simple experiment to determine
(at last!) if light travels using an "Outsider System" or an "Insider
System".
We start with two sources, "Source A" and
"Source B", and two detectors, "Detector A" and "Detector B".
"Source A" is pointing at "Detector A" and "Source B" is pointing at
"Detector B". Both detectors are side-by-side. "Source A"
is on the ground a fair distance away from "Detector A". "Source
B" is on a train quite far behind "Source A".
The idea of the experiment is to let the train
(which has "Source B") accelerate towards "Detector B". When
"Source B" reaches "Source A" (which is on the ground) both sources
emit a flash of light. Both flashes of light will traverse the
same distance to reach the detectors. We just have to see which
flash of light gets recorded by the detectors first and draw our
conclusions from there! I predict that "Detector B" will register
the light first, and so the "Insider System" will be validated.
If "Detector A" and "Detector B" register the light from the sources at
the same time then the "Outsider System" is validated.
Very simple idea. I wonder why I have
never heard of such an experiment being performed..
If the "Outsider System" is validated then we
run into difficulties. For instance, we can put "Source B" at the
back of the train and "Detector B" at the front of the train. Let
"L" be the distance between the source and the detector. Then we
can redo the experiment and measure the time "t" (using a clock) it
takes for the light to go from "Source B" to "Detector B".
Now, if you were a person on the train you'd
expect that "t" would be a constant; this is not so. When the
train is stationary then the light traverses a distance "L" with a
speed "c"; when the train is moving (with velocity "v") then the light
traverses a distance "L+vt" with a speed "c". Thus, when the
train is stationary the time it takes to conduct the experiment is
"L/c" while when the train is moving it takes "L/(c-v)". Now, you
can be alone on the train and conduct this experiment and get a unique
value for the change in time. "L" and "c" are constants, so we
must conclude that "v" is also unique. That is, a unique value of
"t" corresponds to a unique value of "v". Now, what is a "unique"
velocity? It must be a velocity measured from some "absolute
frame"..
(Again, we have inadvertently put ourselves at
rest with the "absolute frame" making the speed of light "c"; this
assumption may very well be wrong. If we are not at rest with the
"absolute frame" then we will see the speed of light to be some
constant, but that constant will not be "c".)
With these difficulties when we use the
"Outsider System" it is likely that light travels instead by the
"Insider System", which is why I predict it to be so above.
---------------------------------------
ASIDE:
If we are to assume that light travels abiding
by an "Insider System" then that means that the speed of light depends
on the motion of the source. This means that if two objects are
heading *away* from each other such that the relative velocity of two
objects is greater than "c" then the light from one object will never
reach the other. Also, by the Doppler effect the frequency of the
light would be an imaginary number. Now, we know that the
universe is expanding so it is likely that our planet Earth has a
relative velocity greater than "c" with many of the objects in the
universe. Perhaps that is why we cannot see dark matter..
And what happens when the relative velocity is greater than "c" when
the two objects are heading *towards* each other? Again, the
frequency of the light will be an imaginary number. Again, is
that why we cannot see dark matter?.. So, is the equation we use
for the Doppler effect for light correct?..
---------------------------------------
ASIDE:
Sound propagates through air using an
"Outsider System".
Consider two people, a pilot and a co-pilot,
both sitting in the cockpit of a plane. The co-pilot is behind
the pilot. The plane is travelling faster than the speed of sound
relative to the ground and atmosphere.
Now, if the cockpit is closed then when the
co-pilot says something the sound of his voice will travel forward to
the pilot. The speed of the sound of his voice will be travelling
at the speed of sound relative to the air in the cockpit.
However, if the cockpit is open and the
co-pilot says something the sound of his voice will *not* travel
forward to the pilot. The speed of the sound of his voice will be
travelling at the speed of sound relative to the air of the
atmosphere. But since the plane is travelling faster than the
speed of sound relative to the atmosphere, the co-pilot's voice will
not be heard by the pilot.
*(I am interested in knowing how open the
cockpit can be such that the pilot still hears the co-pilot's voice.)*
Notice that if the cockpit is open then we can
determine the velocity of the plane relative to the atmosphere as we
did above with light. The velocity is zero when the plane is
stationary with the atmosphere, the atmosphere being the medium through
which sound propagates through.
Thus, if we are to say that the "Outsider
System" for light is true, then we can say that when the space ship's
"absolute velocity" is zero then it is stationary with the "ether", the
medium through which light (supposedly) propagates through. If
the "Insider System" for light is true then we don't need to introduce
an "ether".
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= F) Understanding the Michelson-Morley Experiment -=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
INTRODUCTION:
We saw above that time cannot dialate and
length cannot contract such that the speed of light is maintained a
constant. So, we will use Galilean transformations here instead
of Lorentz transformations. Nonetheless, we know from physical
experiments that "measured time" does dialate. At this point we
do not know why; more physical experiments need to be done. Now,
in this section we will say that "measured time" doesn't dialate; by
the nature of this experiment you will find that this premise should
not appreciably affect our conclusions. And when we determine why
"measured time" appears to dialate we should update this discussion of
the experiment.
My experiment is different from
Michelson-Morley's setup but it essentially demonstrates the same thing.
We will have two SMD devices, "SMD X" and "SMD
Y", and we will do this experiment on the equator of the Earth.
"SMD X" is set up parallel to the equator while "SMD Y" is set up
perpendicular to the equator. "SMD X" has the source/detector
west and the mirror east while "SMD Y" has the source/detector south
and the mirror north. The distance between the source and the
detector in both SMD devices is "L".
In the experiment done by Michelson and
Morley, they themselves were the "insiders", and there was no
"outsider".
In our experiment, there are two people, an
"insider" and an "outsider". The "insider" is on the ground next
to the two SMD devices. The "outsider" is in a space ship above
the Earth such that he observes the SMD devices to be directly below
him every 24 hours; so, the "outsider" will see the Earth rotating at a
velocity of "3*10^4" meters per second.
We assume here that the "insider" and the SMD
devices are at rest; this is not so. The Earth, or rather, the
*crust* of the Earth, is constantly accelerating (and changing inertial
frames of reference) because the entire Earth is rotating. But,
if we conduct the experiment quickly then we can dismiss this
acceleration.
The Michelson-Morley experiment attempts to
find the Earth's speed relative to the ether by observing a fringe
shift in the interference pattern of two beams of light. The fact
that the experiment fails is because there is no ether.
In this experiment we are not finding "fringe
shifts"; we are looking for a "time discreptancy" in the times of both
SMD devices. But if there is a time discreptancy then that
implies that in a Michelson Interferometer we should expect to see a
fringe shift.
In the Michelson-Morley experiment the
"insiders" (themselves) witnessed light travel at the constant speed
"c". Now, if the "outsider" also sees light travel at the
constant speed "c" then he needs for length to contract so that he can
agree with the "insiders" that there is no time discreptancy and hence,
no fringe shift. However, we have found above, in the section
"The Constancy of the Speed of Light", that length cannot contract (and
time cannot dialate) in any way to *always* maintain the speed of light
constant. But fortuanately, it turns out that if we assume that
light abides by an "Insider System" then the null result in the
Michelson-Morley experiment is no longer problematic for the "outsider"
to explain. We will demonstrate this below.
Let's now activate the SMD devices in our
minds and see what we should expect to happen in this experiment when
we assume that light abides by the "Insider System".
---------------------------------------
FOR "SMD X" and "SMD Y": (for the "insider")
Now the speed of light from the "insider's"
view is "c" because we are using an "Insider System". For both
SMD devices the "insider" will say he saw the light traverse a distance
"L" twice. So, if "t" is the total time it takes for the light in
both SMD devices to go from the source, to the mirror, and back to the
detector, then:
> t = 2L/c
So, the "insider" will not observe a time
discreptancy. And so, when using a Michelson Interferometer the
"insider" should expect not to see a fringe shift because the time
elasped for both SMD devices is equal.
---------------------------------------
DEFINING VARIABLES:
The "outsider" on the other hand sees the
experiment differently.
Observations made by the "outsider":
----------------
In "SMD X":
• "tX" is the time it takes for the light to go
from the source to the
detector
• "tX1" is the time it takes for the light to go
from the source to the
mirror
• "tX2" is the time it takes for the light to go
from the mirror to the
detector
----------------
----------------
In "SMD Y":
• "tY" is the time it takes for the light to go
from the source to the
detector
• "tY1" is the time it takes for the light to go
from the source to the
mirror
• "tY2" is the time it takes for the light to go
from the mirror to the
detector
----------------
Hence:
> tX = tX1 +
tX2
> tY = tY1 +
tY2
When we are deriving the time variables for
the "Insider System" we need to know the velocity of the light; but
we've already computed them! One needs only refer to the two
situations in the section "Outsider System vs. Insider System" where we
assumed that the "Insider System" is right.
---------------------------------------
FOR "SMD X": (for the "outsider")
When the light is travelling towards the
mirror the "outsider" sees the light traversing a distance "L+vtX1" in
a time "tX1" [See Diagram A1].
(A1) ---> WHAT THE OUTSIDER SEES:
|
|
(c+v)tX1
| |--------------------------|
|
| |••••••••••••••••••|•••••••| East
-->
|
| |------------------|-------|
|
L vtX1
\_________________________________
As shown in the section "Outsider System vs.
Insider System" where we assumed that the "Insider System" is right we
find the speed of light as observed by the "outsider" in this case is
"c+v". Hence:
> (c+v)tX1 = L
+ vtX1
And so:
> tX1 = L/c
When the light is returning back to the
detector the "outsider" sees the light traversing a distance "L-vtX2"
in a time "tX2" [See Diagram A2].
(A2) ---> WHAT THE OUTSIDER SEES:
|
|
(c-v)tX2
|
|----------|
|
|
|••••••••••| East -->
|
| |-------|
|
vtX2
|
|------------------|
|
L
\_________________________________
As shown in the section "Outsider System vs.
Insider System" where we assumed that the "Insider System" is right we
find the speed of light as observed by the "outsider" in this case is
"c-v". Hence:
> (c-v)tX2 = L
- vtX2
And so:
> tX2 = L/c
---------------------------------------
FOR "SMD Y": (for the "outsider")
When the light is travelling towards the
mirror the "outsider" sees the light traversing a distance
"[L²+(vtY1)²]^½" in a time "tY1" [See Diagram B1].
(B1) ---> WHAT THE OUTSIDER SEES:
|
|
•|
|
• |
| c[1+(v/c)²]^½ • |
L East -->
| * tY1
• |
|
• |
|
•_____|
|
vtY1
\_________________________________
When the light is returning back to the
detector the "outsider" sees the light traversing a distance
"[L²+(vtY2)²]^½" (again) in a time "tY2" [See Diagram
B2].
(B2) ---> WHAT THE OUTSIDER SEES:
|
|
|•
|
| •
|
| • c[1+(v/c)²]^½ East
-->
|
L | • * tY2
|
| •
|
|_____•
|
vtY2
\_________________________________
So, for both cases above:
As shown in the section "Outsider System vs.
Insider System" where we assumed that the "Insider System" is right the
speed of light as observed by the "outsider" in this case is
"c[1+(v/c)²]^½".
Hence, by Pythagoras' theorem:
> L² +
(vtY1)² = c²[1+(v/c)²] * tY1²
> L² +
(vtY2)² = c²[1+(v/c)²] * tY2²
And so:
> tY1 = tY2 =
L/c
---------------------------------------
TALLYING THE TIMES:
> tX = tX1 +
tX2 = L/c + L/c
>
= 2L/c
> tY = tY1 +
tY2 = L/c + L/c
= 2L/c
> tX-tY = 2L/c
- 2L/c
>
= 0
When we assume that the "Insider System" is
right the "outsider" does not find a time discreptancy. This
means that in a Michelson Interferometer, if we abide by an "Insider
System", the "outsider" will not expect to see a fringe shift.
---------------------------------------
CONCLUSIONS:
The truth is that the fringe shift doesn't
exist as demonstrated by physical experiments. And so, we can
conclude that there is no ether.
Einstein's Special Relativity claimed to have
solved the mystery of why we get a null result from the
Michelson-Morley experiment. Special Relativity claims that "the
speed of light will always be measured to be "c" when the light-source
is in an inertial frame", and so, in the experiment both the "insider"
and the "outsider" should see light travel at the constant speed
"c". However, when Michelson and Morley conducted the experiment
they were the "insiders" and there were no "outsiders"! So, the
fact that we get a null result means that we can say that the speed of
light in the experiment for the "insider" is the constant "c".
However, assuming that the speed of light for the "outsider" is also
"c" is *unjustified*; the experiment didn't have an "outsider"!
We've seen above that we cannot maintain the constancy of the speed of
light no matter how we have time dialate and length contract. So
instead, it is likely that light abides by the "Insider System".
And when we assume that light abides by the "Insider System" then we
find (as shown above) that the "outsider" no longer sees light travel
at the constant speed "c" and yet, he agrees with the "insider" that
there is no fringe shift! Hence, the null result is explained and
should be expected when we assume that light abides by the "Insider
System"!
This thought-experiment should be conducted in
reality (with an "insider" *and* an "outsider") to ascertain whether
the above conclusions are correct.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-= G) The Finale =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
---------------------------------------
Until more experiments are performed this
paper leaves physics in a puddle of mud. In getting out of this
puddle we have to check many things like the following:
• why time seems to dialate
• whether there is an "absolute frame"
• whether velocity and acceleration are relative
• does light propogate using an "Insider System" or an "Outsider
System"
• the Doppler effect for light
---------------------------------------
When you discount all the major pitfalls of
Special Relativity - and there are many - it turns out to be a very
beautiful theory. I believe that that is the main reason why the
average physicist believes that Special Relativity is a coherent
theory. But watching someone who is explaining Special Relativity
is like watching a good salesman try to sell a bad vacuum.
Or, as Essen says in an article "Relativity
and Time Signals" published in "Wireless World":
• "Students are told that the theory must be accepted although
they cannot expect to understand it. They are encouraged right at
the beginning of their careers to forsake science in favour of
dogma. The general public are misled into believing that science
is a mysterious subject which can be understood by only a few
exceptionally gifted mathematicians. Since the time of Einstein
and of one of his most ardent supporters Eddington there has been a
great increase in anti-rational thought and mysticism. The theory
is so rigidly held that young scientists who have any regard for their
careers dare not openly express their doubts."
Thank god I haven't got a career to regard!
Or, put more bluntly as a certain "Mike" put
it on the usenet newsgroup "sci.physics.relativity":
• "Relativists are cranks because they deny the immediately
given. they are also ad hominen animals, just watch how many of
them will turn ad hominen because of this post. they are so ad hominen,
they do not even get a job at MacDonalds and lurk in the usenet
24/7."
Hahahaha...
---------------------------------------
I have quoted these sources:
(1) "A Debate on the Theory of Relativity" by Professor W. D. MacMillan.
(2) "The Special Theory of Relativity" by L. Essen.
(3) "Relativity: the Special and General Theory" by A. Einstein.
(4) "Relativity and Time Signals" published in "Wireless World" by L.
Essen.
---------------------------------------
I strongly suggest reading "The Special Theory
of Relativity" by L. Essen. All the ideas in this section are
essentially drawn from that book; I have just explained them from a
different perspective. And Essen discusses other subjects (e.g.
General Relativity) not treated in this paper. Read the book;
it's transcendental.
Essen also does a good job explaining the
problems of Special Relativity in "Einstein's Special Theory of
Relativity" published in the "Proceedings of the Royal Institution of
Great Britain, Volume 45".
There must be many other people who have come
to the same conclusions I have here; the faults of Special Relativity
are too obvious. I introduce you to two people:
(1) Ardeshir Mehta has come up with many clever thought-experiments
which debunk Special Relativity:
• http://homepage.mac.com/ardeshir/Relativity.html
(2) Richard Moody Jr. has written an article worth reading:
• http://www.aulis.com/albert_einstein.htm
-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| THE END! -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
by Raheman Velji
email blochee@yahoo.ca
you can also view this paper (and updated versions) at...
...https://www.angelfire.com/un/rv
...https://www.angelfire.com/rebellion2/rahemanvelji
! ! ! BEWARE OF THE ILLUMINATI ! ! !
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