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| --------------| A COLLECTION OF IDEAS | by Raheman Velji |
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* * * [must use a fixed-width font to view diagrams properly] * * *
CONTENTS:
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(1) Inventions
A) The Seesaw Newton Motor
B) The Simple Newton Engine
Two inventions which will have a lasting effect on transportation,
especially in space exploration.
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(2) Law of Conservation of Energy
A) 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
machine.
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(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.
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(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) INVENTIONS -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
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Inventions:
A) The Seesaw Newton Motor
B) The Simple Newton Engine
Devices that use "self-sufficient propulsion" - like the two
mentioned above - 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 transportation (especially in space exploration).
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
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=3D-=3D-=3D-A) The Seesaw Newton Motor=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
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Top view:
___base
||
\/
_____________
| |
| M1a---M2a | <--front
| | electromagnets
| m1 |
| \ |
| \ | /\
| \ | ||
| o | <--seesaw ||
| \ | ("o" =3D pivot) forward
| \ |
| \ |
| m2 |
| |
| M1b---M2b | <--back
|_____________| electromagnets
Ideally, "M1a", "M1b", "M2a", "M2b", "m1", "m2" are all
electromagnets. (Some of the electromagnets can be changed into
permanent magnets where it is deemed fit.) "M1a", "M1b", "M2a", and
"M2b" are fastened to the base, while "m1" and "m2" are connected to a
"seesaw" whose "pivot" ("o") is connected to the "base". (It is
possible to construct this without the back electromagnets.)
The way this invention works is somewhat hard to explain. Here
is a simplified version:
When "M1a" and "m1" are nearly touching an electric current is
sent through "M1a", "M1b", and "m1". "M1a" should repel "m1" while
"M1b" should attract "m1". Thus, both electromagnets connected to the
base, "M1a" and "M1b", will experience a force in the forward
direction, while the seesaw swings around bringing "m2" close to
"M2a". As "M2a" and "m2" are close now, an electric current will pass
through "M2a", "M2b", and "m2". "M2a" should repel "m2" while "M2b"
should attract "m2". Again, the electromagnets connected to the base,
"M2a" and "M2b", will experience a force in the forward direction
while the seesaw swings back to its starting position to repeat the
cycle. Since all the electromagnets that are connected to the base
experience a force in the forward direction, the entire device will be
propelled forward as the seesaw keeps swinging about. Notice that the
seesaw does *not* rotate, it simply moves back and forth, like a
seesaw.
It should be noted that as the seesaw swings about a bit of the
"backward" energy of the electromagnets on the seesaw will be conveyed
to the base via the pivot, thus slowing down the entire device. That
loss of speed, though, is negligible.
The above explanation of the workings of the "Seesaw Newton
motor" is incomplete. One must understand the following:
Every action has an equal and opposite reaction. The main idea
of the "Seesaw Newton motor" is to harness the "action". When the
front electromagnet, back electromagnet and the electromagnet on the
seesaw are activated, the front and back electromagnets experience a
"positive" force by being forced forward. The electromagnet on the
seesaw, however, experiences a "negative" force as it moves in the
backward direction. One must get rid of the "negative" energy of the
electromagnet on the seesaw. If the "negative" energy is not rid of,
then it will somehow be transferred to the entire device, thus not
allowing the device to gain velocity and move forward.
The "Seesaw Newton motor" does not only get rid of the "negative"
energy, it in fact uses it to propel the device further. Consider the
following scenario: a "Seesaw Newton motor" at rest, and set-up
similar to the diagram above. Now, let us initiate a current through
"M1a", "M1b", and "m1". The electromagnets on the base ("M1a" and
"M1b") will experience a "positive" force by being forced forward.
The electromagnet on the seesaw ("m1"), however, will experience a
"negative" force by being forced backward. However, at the other end
of the seesaw, the electromagnet ("m2") seems to be approaching the
front electromagnet ("M2a") and receding from the back electromagnet
("M2b"). Thus, at the other end of the seesaw, when those
electromagnets are activated, the repulsive force between the
electromagnet on the seesaw and the front electromagnet will be
greater, thus propelling the device further forward. Also, at the
other end of the seesaw, when those electromagnets are activated, the
attractive force between the electromagnet on the seesaw and the back
electromagnet will be greater, again propelling the device further
forward. The fact that both magnets ("M2a" and "M2b") experience a
greater forward force is due to the initial "negative" energy of the
electromagnet ("m1") on the seesaw. Thus, both the "action" and the
"reaction" are harnessed to propel the entire device forward. Thus,
in a sense this invention is more effective than a space shuttle
because it harnesses both the "action" and "reaction", unlike a
shuttle which only uses the "action".
If both "action" and "reaction" are to be harnessed, one must
ensure that the electromagnets on the seesaw should not hit either the
front electromagnets or the back electromagnets. That is because in a
collision the "backward" forces will be conveyed to the base via the
pivot. Thus, input sensors might be needed to calculate the speed of
the seesaw so that the electromagnets can be perfectly timed to avoid
collisions.
Notice that for this invention to actually move the
electromagnets must be very strong and the entire device must be
light. Otherwise, the device will stay in the same spot and the
seesaw will just "wiggle about" instead of moving. Even though when
it is "wiggling about" there still is a forward force; it's just that
the forward force isn't strong enough to overcome static friction.
So, even if on Earth it merely "wiggles about" instead of moving then
it can still be useful in space where there is no static friction.
So, this invention can definetely compete with other devices like ones
that use ion propulsion.
Also, the entire "Seesaw Newton motor" can (with a battery) be
put into a box and the box would move without interacting with the
environment outside the box. Thus, we say it moves using "self-
sufficient propulsion".
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=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-B) The Simple Newton Engine-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D=
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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=2Eg. 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 slowing, 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" is 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 by
hooking it to a chain which is being pulled by a motor. Or perhaps
the piston can slowly move back on its wheels towards the front of the
cylinder. 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.
/-----------/-----------/-----------/-----------/
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 for a relatively minute amount of time.
Nonetheless, I'm sure this invention can be useful in space
exploration.
Also, like the "Seesaw Newton motor", the entire "Simple Newton
engine" can (with a battery) 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".
/-----------/-----------/-----------/-----------/
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-|-|-| (2) LAW OF CONSERVATION OF ENERGY |-|-|-|-|-|-|-|-|-|-|-|-
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The fact that the Law of Conservation of Energy is wrong is perhaps
nature's cruelest trick.
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=3D-=3D-=3D-A) Gravitational-Membrane Dynamo-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
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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 free
energy. It is not necessarily a perpetual motion machine.
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=2E
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 an example.
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 machine if it creates more
energy than is needed to keep the machine 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:
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".
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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 machine" is a machine that uses perpetual
motion to create energy.
Ideally, something in perpetual motion or a perpetual motion
machine 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 machine. 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, is a "Gravitational-membrane dynamo" really a perpetual
motion machine?
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. Now isn't the system which encompasses a whole planet too
big? But notice that we can replace the "ideal planet" with an "ideal
ball". Now an "ideal ball" in rotation is definetely in perpetual
motion. But isn't an "ideal planet" just a really big "ideal ball"?
Hence, an "ideal planet" in rotation is also in perpetual motion.
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=3D-=3D-=3D-B) Potential Energy-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D=
-=3D-=3D-=3D-=3D-=3D
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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 =3D> 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."
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-C) Creating and Destroying Mechanical Energy=3D-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
---------------------------------------
"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 "=BDmv=B2", 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 "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 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.
-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (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
"=BDmv=B2", and I do not want to imply that I am using that equation.)
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-A) Defining Force, Work and Mechanical Energy-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
---------------------------------------
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=2E
---------------------------------------
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".
The equation for "effective force" is:
f_e =3D ma
=B7 where "f_e" is "effective force"
"m" is mass
"a" is acceleration
The equation for "ineffective force" is:
f_i =3D pA
=B7 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 =3D f_e + f_i
=B7 where "f_w" is "whole force"
---------------------------------------
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. 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 =3D f_e*s
=B7 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. It is sensible to also 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 =3D f_w*t
=B7 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.
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.)
---------------------------------------
When force is effective, "productive work" can be written in
terms of "general work":
W_p =3D W_g=B2/(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".
When force is effective then "f_w =3D f_e" and so:
W_p/W_g =3D (f_e*s)/(f_w*t) =3D s/t =3D v_a
=B7 where "v_a" is the average change in velocity
This means that the rate at which "general work" becomes "productive
work" - when the force is effective - is the average change in
velocity of the object. Since average 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. So, when "t" approaches zero the rate at which
"general work" becomes "productive work" is the instantaneous change
in velocity - which is acceleration.
Say that we push a particle with an "effective force" "f_e" over
a displacement of "s". The time it takes for the particle to be
displaced is "(2ms/f_e)^=BD". In such a case the change in velocity is
"(2f_e*s/m)^=BD". Now, if the work becomes semi-effective then that
means that some of the "effective force" has turned into "ineffective
force". So, "f_e" will decrease; thus, the period of time - "(2ms/
f_e)^=BD" - will increase and the change in velocity - "(2f_e*s/m)^=BD" -
will decrease.
When "general work" is fully productive (due to "effective
force") the rate at which it becomes "productive work" is the
acceleration, which can be written as "f_e/m". So, as mass increases
it becomes harder to convert "general work" into "productive work".
As the "general work" becomes less productive (less displacement due
to "semi-effective force") the average change in velocity is less, and
so the rate at which "general work" becomes "productive work" is less
than the acceleration. As the "productive work" nears zero (no
displacement due to "ineffective force") then the average change in
velocity nears zero and so the work is almost entirely general.
When force is effective, power equals "f_e*v_a". So, "effective
power" is proportional to the rate at which "general work" becomes
"productive work".
---------------------------------------
Above, we observed that "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.
---------------------------------------
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 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 "=BDmv=B2". If we are
considering the "general energy" of the particle, we will "measure"
the energy of the particle using the equation "mv". Both equations -
"=BDmv=B2" 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 =3D f_e =3D ma) , (D =3D s)
E_p =3D =BDmv=B2 + MD
E_g =3D mv + (2mMD)^=BD
When we are considering "general work":
(M =3D f_e =3D ma) , (D =3D t)
E_g =3D mv + MD
E_p =3D =BDmv=B2 + (MD)=B2/(2m)
=B7 where "E_p" is the equation for "productive energy"
=B7 where "E_g" is the equation for "general energy"
=B7 where "m" is the mass of the particle
=B7 where "v" is the initial velocity of the particle (prior to work)
Now in Newtonian mechanics kinetic energy is equal to "=BDmv=B2" 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.
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-B) Relative Views-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
---------------------------------------
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:
=B7 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 =3D f_e =3D G m_s*m_e / r=B2
=B7 where "f_s" is the "real force" on the skydiver
"f_e" 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 =3D a_s + a_e
=B7 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 =3D G (m_s+m_e) / r=B2
Here's a rule:
=B7 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".
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 -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-A) Preliminary=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
---------------------------------------
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".
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=3Dvt" or a duration of time by using
the equation "t=3Dd/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=3Dd/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. "Measured mass" is usually called "rest mass"; "derived
mass" is usually called "inertial mass".
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). And when the day comes 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.
For this entire section the distance between the source and the
detector in a SD device will be "L".
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. For this entire section the distance between
the source/detector and the mirror in a SMD device will be "L".
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=3Dd/c". For this entire section the distance between the
source/detector and the mirror in a light-clock will be "L". The
distance between the source/detector and the mirror in a light-clock
is always "L"; this is true no matter what frame you are looking at
the light-clock from. The displacement of light, "d", is what differs
depending on your frame.
---------------------------------------
I will refer to a velocity measured relative to the "absolute
frame" as an "absolute velocity".
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-B) A Reality Check=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
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.
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-C) Simultaneity-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D=
-=3D-=3D-=3D-=3D-=3D-=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
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.
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-D) The Constancy of the Speed of Light=3D-=3D-=3D-=3D-=3D-=3D-=
=3D
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
---------------------------------------
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.
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":
=B7 "tI" is the time it takes for the light to go
from the source to the detector
=B7 "dI" is the distance the light traverses going
from the source to the detector
=B7 "tI1" is the time it takes for the light to go
from the source to the mirror
=B7 "tI2" is the time it takes for the light to go
from the mirror to the detector
=B7 "dI1" is the distance the light traverses going
from the source to the mirror
=B7 "dI1" is the distance the light traverses going
from the mirror to the source
=B7 "lI" is the length of the ruler inside the train
as measured by the "insider"
----------------
----------------
Observations made by the "outsider":
=B7 "tO" is the time it takes for the light to go
from the source to the detector
=B7 "dO" is the distance the light traverses going
from the source to the detector
=B7 "tO1" is the time it takes for the light to go
from the source to the mirror
=B7 "tO2" is the time it takes for the light to go
from the mirror to the detector
=B7 "dO1" is the distance the light traverses going
from the source to the mirror
=B7 "dO1" is the distance the light traverses going
from the mirror to the source
=B7 "lO" is the length of the ruler inside the train
as measured by the "outsider"
----------------
Hence:
tI =3D tI1 + tI2
dI =3D dI1 + dI2
tO =3D tO1 + tO2
dO =3D 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.
---------------------------------------
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. So, 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". (Diagram A)
(A) ---> WHAT THE INSIDER SEES:
|
| ______
| =B7 |
| =B7 |
| =B7 | L forward -->
| =B7 |
| =B7 |
| =B7|
\_________________________________
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:
dI =3D 2L
Meanwhile, the "outsider" sees the light travel a greater
distance as shown in Diagram B:
dO =3D 2[(vtO/2)=B2+L=B2]^=BD
(B) ---> WHAT THE OUTSIDER SEES:
|
| ___
| | =B7
| | =B7|=B7
| | =B7 | =B7
| L | =B7 | =B7 forward -->
| | =B7 | =B7
| | =B7 | =B7
| _|_ =B7_____|_____=B7
|
| |-----------|
| 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=3Dd/
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 =3D 2L/c
and
tO =3D 2[{(vtO/2)=B2+L=B2}^=BD]/c
Using the above two equations, the "Time Dialation" thought-
experiment goes on to derive the following general equation:
(1a) tO =3D ytI
=B7 where "y" equals "1/[1-(v/c)=B2]^=BD"
---------------------------------------
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. The ruler fits snuggly between
the source/detector and the mirror.
---------------------------------------
"LENGTH CONTRACTION" THOUGHT-EXPERIMENT:
The "insider" is at rest with the light-clock so:
dI1 =3D dI2 =3D lI
Meanwhile, the "outsider" sees things differently.
When the light is travelling to the mirror the light traverses a
distance "dO1" as shown in Diagram C. So:
dO1 =3D lO + vtO1
(C) ---> WHAT THE OUTSIDER SEES:
|
| dO1
| |--------------------------|
|
| |=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7|=B7=B7=B7=B7=B7=
=B7=B7| forward -->
|
| |------------------|-------|
| lO vt01
\_________________________________
When the light is travelling to the detector the light traverses
a distance "dO2" as shown in Diagram D. So:
dO2 =3D lO - vtO2
(D) ---> WHAT THE OUTSIDER SEES:
|
| dO2
| |----------|
|
| |=B7=B7=B7=B7=B7=B7=B7=B7=B7=B7| forward -->
|
| |-------|
| vt02
| |------------------|
| lO
\_________________________________
Since the speed of light is constant:
dO1 =3D ctO1
and
dO2 =3D ctO2
Using the above four equations, we get:
tO1 =3D lO/(c-v)
and
tO2 =3D lO/(c+v)
Using the above two equations, we get:
tO =3D 2 y=B2 lO / c
=B7 where "y" equals "1/[1-(v/c)=B2]^=BD"
Now, from the "Time Dialation" thought-experiment:
tO =3D ytI
and we know that:
tI =3D dI/c =3D 2lI/c
Using the above three equations, the "Length Contraction" thought-
experiment goes on to derive the following general equation:
(2a) lO =3D 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..
=B7 CASE #1: .."the clocks and lengths actually change".
(meaning that "measured quantities" change depending on your frame)
OR
=B7 CASE #2: ..we adjust our clocks and rulers (and our equations).
(meaning that *only* "derived quantities" change depending on your
frame)
OR
=B7 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 you 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=3Dd/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=3Dd/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=3Dd/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=3Dd/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=3Dd/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. 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 =3D ytO
And if you repeat the "Length Contraction" thought-experiment you will
derive the following contradictory equation:
(2b) lI =3D 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; 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=3Dd/z" and for displacement (a length) that
equation is "d=3Dzt", 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?:
=B7 Perhaps our experiments are wrong and "measured time" actually
doesn't dialate!
=B7 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. In this
case we do not need to invent an "absolute frame".
=B7 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 means, as we explain in an aside in
the section "Outsider System vs. Insider System", that there must be
an ether; and so, this explanation is unlikely to be true because we
get a null result in the Michelson-Morley experiment.
=B7 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 wierd
"quantum effect". In this case we do not need to invent an "absolute
frame". (I realize that this idea seems a bit over-the-top..)
Physical experiments need to be done to know why "measured time"
appears to dialate.
---------------------------------------
"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. 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
strike the tracks, one at the front of the train, the other at the
back of the train.
---> DIAGRAM OF "TRAIN" THOUGHT-EXPERIMENT
|
|
| train __
| ||
| \/
| _______________________
| * | I | *
| FL * ------------------------- * FL --> forward
| * =D8 =D8 =D8 =D8 =D8 =D8 *
|---------------------------------------------
| O
| /\
| embankment __||
|
|
| =B7 where "I" is the "insider"
| "O" is the "outsider"
| "FL" is a flash 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 issue 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
"sets up" the "Train" thought-experiment: 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 in 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.
I strongly suggest reading "The Special Theory of Relativity" by
L=2E 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 not treated in this paper. Read
the book; it's transcendental.
-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=
=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-=3D-
=3D-=3D-=3D-E) Outsider System vs. Insider System-= |
