Relativity?

* * * [must use a fixed-width font to view diagrams properly] * * *

CONTENTS:

---------------------------------------
Special Relativity
A) Einstein's Two Postulates
B) Understanding the Michelson-Morley Experiment
C) Lorentz Transformation
D) Time Dialation & Length Contraction
E) A Reality Check
F) Simultaneity
G) ..and the Rest

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-A) Einstein's Two Postulates=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Here are Einstein's first two postulates of Special Relativity:

#1) The laws of physics are the same in every inertial frame of
reference. That is, one cannot distinguish one inertial frame from the
others or make one frame somehow more "correct" than another.

#2) The speed of light in a vacuum is the same in all inertial frames
of reference and is independent of the motion of the source.

In the future, when I use the term "frame" I mean it as a short way of
saying
"inertial frame of reference".

Now, for postulate #2 to be true all observers *inside* a frame should
agree with all observers *outside* the frame that the speed of light
coming from a source *inside* the frame is the constant "c".

For convience sake let us make the following defenitions:

* An "Outsider System" is true when all observers *outside* a frame
measure the speed of light which emanates from a source *inside* the
frame to be the constant "c".

* An "Insider System" is true when all observers *inside* a frame
measure the speed of light which emanates from a source *inside* the
frame to be the constant "c".

So, for postulate #2 to be true both the Outsider System and the
Insider System should be true; that is, all observers inside and
outside the frame should agree that the speed of light (which emanates
from a source inside the frame) is the constant "c".

Generally, we will call the person inside the frame (where the light
source is) the "insider" while the person outside the frame will be the
"outsider".

Now, when we measure a length using a ruler or when we measure time
using a clock then we will say that those quanties are "measured". On
the other hand, you could figure out the distance or time of an event
by using the equation "d=v*t" - where "d" is distance, "v" is velocity,
and "t" is time. If we use that equation to determine a length or a
duration of time then we will say that those quantities are "derived".
There are also *many* other ways to derive a duration of time or
quantity of length. For example, another way we can derive a quantity
of length is by taking a picture (using a camera) of the thing we wish
to measure. We assume here that measured quantities are always
correct; whether derived quantities agree with measured quantities is
up for debate (depending on the situation of course).

We will assume in this section that the velocity of Frame A measured
from Frame B is the same as the velocity of Frame B measured from Frame
A. That can be written in math as "v=v'". This seems reasonable to
assume, however, if measured time dialates or measured length contracts
then the assumption could very well be wrong.

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".

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 light-(S)ource to the
light-(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 light-(S)ource to the (M)irror and
back to the light-(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 distance and
the speed of light - derives the time "t" elasped by using the equation
"t=d/c". For this entire section the distance between the
source/detector and the mirror in a light-clock (when observed at rest)
will be "L".

We will be demonstrating later on in this section that Einstein's
thought-experments for Time Dialation and Length Contraction are false.
So, we will assume below that time doesn't dialate and length doesn't
contract. However, you can allow time to dialate and length to
contract and still be led to the same conclusions below so long as you
let the velocity be much less than "c" so that "1/(1-(v/c)²)^½" (a
factor in Einstein's equations) is essentialy equal to "1".

---------------------------------------
Again, we should understand that for postulate #2 to be true then the
Outsider System should be compatible with teh Insider System, that is,
everyone (inside and outside the frame) observes light to travel at
"c".

We will be analyzing two situations. We will first consider both
situations
assuming that the Outsider System is true. Then we will consider both
situations assuming that the Insider System is true. From this we hope
to
determine whether the Outsider System is compatible with the Insider
System, that is, the speed of light is the constant "c" for everyone.

We will call the person outside the frame the "outsider" while the
person inside the frame will be the "insider". The outsider will be
watching the insider who is in a space ship.

Here we go!

---------------------------------------
Situation #1: (assuming Outsider System is correct)

On the space ship is a SD device secured such that the source is at the
back of the space ship and the detector is at the front.

Now, to start off the space ship is at rest with the outsider.

It is the insider's job to start the SD device when we decide to do the
experiment. Let the insider start the experiment.

The outsider will say he saw light traverse a distance "L" in a time
"t". Also, since we are using an Outsider System he will say that the
speed of light is "c". Thus, the outsider will say that:

"L = c*t"

Now, the insider will also say that he saw a flash of light travel a
distance "L" in a time of "t". Thus, the insider will also say that
the light was travelling at a speed of "L/t". From the above equation
we can say that "L/t" equals "c" and so the insider will agree with the
outsider that the speed of light was "c".

Now, let's accelerate this space ship forward so that it ends up with a
speed of "v" relative to the outsider. The velocity "v" is
perpendicular to the line of sight of the outsider. Let's have the
insider do the experment once more.

---> WHAT THE OUTSIDER SEES:
|
| c*t
| |--------------------------|
| forward -->
|...|··················|·······|
|
| |------------------|-------|
| L v*t
\_________________________________

Notice that this round it will take more time than "t" for the light to
be detected. This is because the ship is moving forward, and so, the
front of the ship will have moved forward by a factor of "vt" before
the flash of light could reach the detector. So this time the outsider
will say that he saw a flash of light travelling at a speed of "c"
traverse a distance "L+vt" in a time of "t". Thus, we arrive at the
following equation:

"L + v*t = c*t"

Again, the insider (who is inside the ship) will say that he saw a
flash of light travel a distance "L" in a time of "t". Thus, the
insider will say that the light was travelling at a speed of "L/t".
From the above equation we can say that "L/t" equals "c-v" and so the
insider will not agree with the outsider that the speed of light was
"c"; he will say that the speed of the flash of light was "c-v". Thus,
when we use an Outsider System somebody inside the frame where the
source of the light is will not agree with someone outside the frame
that the speed of light is the constant "c".

But notice that the above equation can be solved for "v"!:

"v = c - L/t"

So far we have said that "v" is the relative velocity of the outsider
and the space ship. But we have a little problem. The insider will
measure the time elasped during the experiment to be some "fixed
value". This fixed value has nothing to do with the relative velocity
of the outsider and the space ship! Even though the above equation is
what the outsider observes, the insider can conduct the experiment on
his own and thus get a value for "v" without any aid or reference to
the outsider! Now, what exactly is this velocity relative to? It must
be a velocity that is measured relative to some "absolute frame of
reference"! Put another way: If the time (in the above equation) is
some fixed value then we find that the velocity must be some fixed
value! Now what exactly does a "fixed value" for the velocity mean?
Again, a "fixed value" for velocity must mean that the velocity is
relative to some "absolute frame of reference". And since we said
above that "v" is the relative velocity of the outsider and the space
ship then we must notice that we have inadvertently put the outsider at
rest with the "absolute frame of reference". (From now on I will refer
to the "absolute frame of reference" as the "absolute frame". Also, a
velocity measured relative to the absolute frame will be called an
"absolute velocity".)

And so we have just proved that the first postulate is wrong! Look!
We have distinguished one inertial frame from the others! We've
derived an equation that determines the velocity of the ship relative
to an absolute frame.

Now let's consider an outsider that is travelling at a speed of "u"
relative to the absolute frame. If the outsider's velocity is in the
same direction as the space ship then the outsider will see the light
traverse a distance "L+(v-u)t" in a time "t". Using the above equation
we can say that the outsider will say the light travelled at a speed of
"c-u". Now, if the outsider's velocity is in the opposite direction of
the space ship then he will see the light traverse a distance
"L+(v+u)t" in a time "t". Thus, he will then say he saw light travel
at the speed of "c+u". Thus, only the outsider at rest with the
absolute frame will measure the speed of light to be the constant "c".

---------------------------------------
Now, we need to add to the definition above of the "Outsider System"
and the "Insider System" because they are incomplete. We avoided
mentioning this before to avoid confusion: Sometimes light will appear
to move from the source in a straight line only from one particular
frame; all other frames will see the light "bend".

Einstein claims that the speed of light is constant. However, he never
decided from which frame does the light always seem to leave the source
in a straight line. Big error. I claim here - without any
justification - that the observer who sees light travel from the source
in a straight line is also the observer who witnesses light travel at
the constant speed "c". I claim this because my intuition tells me so
and I will only be validated or discredited by physical experiments.

If we are using an "Outsider System" then the direction of the light
follows the direction the source is pointing in as seen by an outsider
(someone outside the frame). Now, all the outsiders are in different
frames so that they will all (usually) disagree as to what the actual
direction of the light is. Because only one outsider can be "right" as
to what the actual direction of the light is, then we are led to the
conclusion that only one frame of reference is "right". This leads us
directly back to the idea and necessity to create an absolute frame.
This means that (usually) only one outsider in a unique frame will see
light follow from the source in a "straight" line. Everyone else will
(usually) see light "bend", that is, the light will not follow from the
source in a straight line.

On the other hand, if we are using an "Insider System" then the
direction of the light follows the direction the source is pointing in
as seen by an insider. Now, since all insiders are in the same frame
then they will all agree as to what the actual direction the light is
moving in. So, we have no need in this case to create an absolute
frame. This means that only the insiders will always see light follow
from the source in a "straight" line. Everyone else will (usually) see
light "bend", that is, the light will not follow from the source in a
straight line.

The reason why we could leave these points out of the definitions
before is because in Situation #1 all outsiders and all insiders will
agree as to what the direction the light is heading in; this is not
always the case as Situation #2 will demonstrate.

---------------------------------------
Situation #2: (assuming Outsider System is correct)

On the space ship is another SD device such that the source is secured
on the floor of the space ship and the detector is fastened above so
that it will (hopefully) register the light from the source.

(The beginning of Situation #2 is similar to Situation #1.)

To start off the space ship is at rest with the outsider.

It is the insider's job to start the SD device when we decide to do the
experiment. Let the insider start the experiment.

The outsider will say he saw light traverse a distance "L" in a time
"t". Also, since we are using an Outsider System he will say that the
speed of light is "c". Thus, the outsider will say that:

"L = c*t"

Now, the insider will also say that he saw a flash of light travel a
distance "L" in a time of "t". Thus, the insider will also say that
the light was travelling at a speed of "L/t". From the above equation
we can say that "L/t" equals "c" and so the insider will agree with the
outsider that the speed of light was "c".

Now, let's accelerate this space ship forward so that it ends up with a
speed of "v" relative to the outsider. The velocity "v" is
perpendicular to the line of sight of the outsider. Let's have the
insider do the experment once more.

Now, the outsider will see exactly what he saw before. That is, he
will see the light emanate from the source an move upward.

However, while the flash of light is heading upwards towards the
detector, the space ship has moved forward by a factor of "vt". Thus,
if the space ship is fast enough then it may have moved forward enough
such that the flash of light might not even hit the detector! The
light may not hit the detector because the light is travelling upwards
as seen from outside the frame, not inside.

---> WHAT THE INSIDER SEES:
|
| vt
| ______
| · |
| · |
| · | ct forward -->
| c*(1+(v/c)²)^½ * t · |
| · |
| ·|
\_________________________________

The insider will say he saw light travel a distance
"((vt)²+(ct)²)^½" in a time "t". Thus, he will say he saw light
travel at the speed of "c*(1+(v/c)²)^½". So, the insider will
measure the speed of light to be greater than or equal to the constant
"c", but never less.

Now we can measure the length "vt" using a ruler. Let that length be
"Z". Then we can create an equation that solves for v:

"v = Z/t"

Again, since we are using an Outsider System we can solve for "v" which
is the velocity relative to the absolute frame. Also, above we have
inadvertently put the outsider at rest with the absolute frame.

Also, notice that during Situation #2 the insider will see light bend!
The light is travelling upwards as seen from outside the frame so
inside the frame the light will appear to bend, that is, it will not
follow from the source in a straight line!

---------------------------------------
Before we move on, it should be noted that above in Situation #1 and
Situation #2 we only examined the velocity in one dimension. So, if we
are to try to actually implement the thought-experiments in real life
then one would have to consider the other dimensions of the velocities
of the spaceship and the flash of light.

---------------------------------------
CONCLUSIONS: From the above, if we are to say that the Outsider System
is true then we are led to three inevitable conclusions:

--> (1) Postulate #1 is wrong! There must be some absolute frame for
"v" to be relative to, and so, we have distinguished one frame from the
others.

--> (2) Postulate #2 has errors! We've used the Outsider System and
we've found that the original definition of the Outsider System is
wrong! The speed of light is only the constant "c" when it is measured
from the absolute frame.

--> (3) When observed from inside the frame where the light source
is, the flash of light may seem to "bend", that is, it may not follow
from the source in a straight line.

We have seen above that the Outsider System is ridden with pitfalls.
Now, many experiments have been done where the light source and the
experimenter are inside the frame. In such experiments the speed of
light has never deviated from "c" and light has never appeared to
"bend". So with these problems it is likely that we started with the
wrong assumption.

So instead let us now assume that the Insider System is right.

---------------------------------------
Situation #1: (assuming Insider System is correct)

On the space ship is a SD device secured such that the source is at the
back of the space ship and the detector is at the front.

Now, to start off the space ship is at rest with the outsider.

It is the insider's job to start the SD device when we decide to do the
experiment. Let the insider start the experiment.

The insider will see the light traverse a distance "L" in a time "t".
Also, since we are using an Insider System the insider will say the
light travelled at the speed of "c". So,

"L = c*t"

Now let's consider an outsider that is travelling at a speed of "v"
relative to the space ship. The velocity "v" is perpendicular to the
line of sight of the outsider. Let the insider do the experiment once
more.

The insider will again see light traverse a distance "L" in a time "t".
In fact, the insider will *always* observe this same thing because we
are using an Insider System, which means that the speed of light is
always constant within the frame.

---> WHAT THE OUTSIDER SEES:
|
| (c-v)*t
| |----------|
|
| |··········| forward -->
|
| |-------|
| v*t
| |------------------|
| L
\_________________________________

If the outsider's velocity is in the forward direction of the space
ship, the outsider will see the light traverse a distance "L-vt" in a
time "t". Using the above equation we can say that the outsider will
see the light travel at a speed of "c-v".

---> WHAT THE OUTSIDER SEES:
|
| (c+v)*t
| |--------------------------|
| forward -->
|...|··················|·······|
|
| |------------------|-------|
| L v*t
\_________________________________


Now, if the outsider's velocity is in the opposite direction of the
forward direction of the space ship, then he will see the light
traverse a distance "L+vt" in a time "t". Thus, he will then say he
saw light travel at the speed of "c+v". This means that someone
outside the frame will not agree with the insider that the speed of
light is the constant "c"!

---------------------------------------
Situation #2: (assuming Insider System is correct)

On the space ship is another SD device such that the source is secured
on the floor of the space ship and the detector is fastened above so
that it will (hopefully) register the light from the source.

(The beginning of Situation #2 is similar to Situation #1.)

Now, to start off the space ship is at rest with the outsider.

It is the insider's job to start the SD device when we decide to do the
experiment. Let the insider start the experiment.

The insider will see the light traverse a distance "L" in a time "t".
Also, since we are using an Insider System the insider will say the
light travelled at the speed of "c". So,

"L = c*t"

Now let's consider an outsider that is travelling at a speed of "v"
relative to the space ship. The velocity "v" is perpendicular to the
line of sight of the outsider. Let the insider do the experiment once
more.

The insider will again see light traverse a distance "L" in a time "t".
In fact, the insider will *always* observe this same thing because we
are using an Insider System, which means that the speed of light is
always constant within the frame.

---> WHAT THE OUTSIDER SEES:
|
| v*t
| ______
| · |
| · |
| · | L forward -->
| (c²+v²)^½ * t · |
| · |
| ·|
\_________________________________

If the outsider's velocity is in the forward direction of the space
ship, the outsider will see the light traverse a distance
"(L²+(v*t)²)^½" in a time "t".

---> WHAT THE OUTSIDER SEES:
|
| ·|
| · |
| (c²+v²)^½ * t · | L forward -->
| · |
| · |
| ·_____|
| v*t
\_________________________________

If the outsider's velocity is in the opposite direction of the forward
direction of the space ship, the outsider will see the light traverse a
distance "(L²+(v*t)²)^½" in a time "t".

Both observations above are symetrical. Thus, we find that the
outsider will measure the speed of light to be "c*{1+(v/c)²}^½"

---------------------------------------
CONCLUSIONS: From the above, if we are to say that the Insider System
is true then we are led to two conclusions:

--> (1) Postulate #1 is right! We have no need to create an absolute
frame and so postulate #1 is liberated.

--> (2) Postulate #2 has errors! We've used the Insider System and
we've found that the speed of light is the constant "c" only when
measured from inside the frame where the light source is.

---------------------------------------
So, when we use the Outsider System then light travels at the constant
"c" from the absolute frame but not "c" from all other frames. When we
use the Insider System then light travels at the constant "c" from
inside the frame but not "c" from all other frames. Thus, we can
conclude that the Outsider System is incompatible with the Insider
System. Postulate #2 is wrong no matter which way you look at it!
Either the Outsider System is right or the Insider System is right, not
both! The Outsider System means that the speed of light does not
depend on the motion of the source of light while the Insider System
means that the speed of light does depend on the motion of the source
of light; contradiction ensues.

---------------------------------------
We can create a simple experiment to determine (at last!) if light
always travels at the constant speed "c".

We start with two sources, Source A and Source B, and two detectors,
Detector A and Detector B. Source A is pointing at Detector A and
Source B is pointing at Detector B. Both detectors are side-by-side.
Source A is on the ground a fair distance away from Detector A. Source
B is on a train, a fair distance behind Source A.

The idea of the experiment is to let the train (which has Source B)
accelerate towards Detector B. When Source B reaches Source A (which
is on the ground) both sources emit a flash of light. Both flashes of
light will traverse the same distance to reach the detectors. We just
have to see which flash of light gets recorded by the detectors first
and draw our conclusions from there! I assume that Detector B will
register the light first, and so the Insider System will be validated.

Very simple idea. I wonder why I have never heard of such an
experiment being performed..

---------------------------------------
ASIDE:

Sound propagates through air using an Outsider System.

Consider two people, a pilot and a co-pilot, both sitting in the
cockpit of a plane. The co-pilot is behind the pilot. The plane is
travelling faster than the speed of sound relative to the ground and
atmosphere.

Now, if the cockpit is closed then when the co-pilot says something the
sound of his voice will travel forward to the pilot. The speed of the
sound of his voice will be travelling at the speed of sound relative to
the air in the cockpit.

However, if the cockpit is open and the co-pilot says something the
sound of his voice will *not* travel forward to the pilot. The speed
of the sound of his voice will be travelling at the speed of sound
relative to the air of the atmosphere. But since the plane is
travelling faster than the speed of sound relative to the atmosphere,
the co-pilot's voice will not be heard by the pilot.

*(I am interested in knowing how open the cockpit can be such that the
pilot still hears the co-pilot's voice.)*

Notice that if the cockpit is open then we can determine the velocity
of the plane relative to the atmosphere as we did above with light.
The velocity is zero when the plane is stationary with the atmosphere,
the atmosphere being the medium through which sound propagates through.


Thus, if we are to assume that the Outsider System for light is true,
then we can say that when the space ship's absolute velocity is zero
then it is stationary with the "ether", the medium through which light
(supposedly) propagates through.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-B) Understanding the Michelson-Morley Experiment=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Now, the Michelson-Morley experiment attempts to find the Earth's speed
relative to the ether. The experiment has its errors. I will now
point out those errors and explain why we get a "null result" when we
perform the experiment. My experiment is different from
Michelson-Morley's setup but it essentially demonstrates the same
thing.

I will be assuming that light propagates through space using the
Insider System.

We will have two SMD devices and we will do this experiment on the
equator of the Earth. One SMD device is set up perpendicular to the
equator while the other SMD device is set up parallel to the equator.
The SMD device perpendicular to the equator has the source/detector
south and the mirror north, while the SMD device parallel to the
equator has the source/detector west and the mirror east.

And there are two people, an insider and an outsider. The insider is
on the ground next to the two SMD devices. The outsider is in a space
ship above the Earth such that he observes the SMD devices to be
directly below him every 24 hours. (This last bit of information is
unneccesary but I include it so that you can visualize the situation
better; that is, the time "24 hours" can really be anything..)

Now, when we are doing experiments on Earth we are not in a inertial
frame of reference because we are accelerating due to gravity. But,
for an experiment that lasts a brief period of time - like this one -
we can assume that the Earth is not changing inertial frames of
reference. So we can assume that the insider and the SMD devices
remain in the same inertial frame of reference.

Now, let's do the experiment; let's activate the SMD devices.

---------------------------------------
Since we are using an Insider System we can say that the insider will
see the light in both SMD devices to be travelling at a constant speed
"c". For both the SMD devices the insider will say he saw the light
traverse a distance "L" twice. Since the speed is constant and the
distance traversed is constant we can say that for both SMD devices it
takes the same amount of time for the light to go from the source to
the mirror as it does for the light to go from the mirror to the
detector. We will call that time "t". So, "t" is the time it takes
for a one way trip from the source/detector to the mirror. We get the
following equation:

"t = L/c"

The outsider, on the other hand sees the experiment differently. The
Michelson-Morley experiment has its errors here. The equations I get
for the observations of the outsider differs from what Michelson-Morley
use in their experiment.

Before we go on, it should be noted that the outsider sees the Earth to
be rotating at a speed of "v". (If the time for one complete orbit is
"24 hours" as said above, then "v" equals approximatly "3*10^4" meters
per second. Again, this information is unnecessary and I include it
only so that you may visualize the situation better.) The velocity "v"
is perpendicular to the line of sight of the insider.

Now, for the apparatus perpendicular to the equator:

---> WHAT THE OUTSIDER SEES:
|
| ·|
| · |
| c*{1+(v/c)²}^½ * t · | L forward -->
| · |
| · |
| ·_____|
| v*t
\_________________________________

When the light is travelling towards the mirror the outsider sees the
light travel at a speed of "c*{1+(v/c)²}^½" traversing a distance
"(L²+(v*t)²)^½" in a time "t".

---> WHAT THE OUTSIDER SEES:
|
| |·
| | ·
| | · c*{1+(v/c)²}^½ * t forward -->
| L | ·
| | ·
| |_____·
| v*t
\_________________________________

When the light is returning back to the detector he sees light travel
at a speed of "c*{1+(v/c)²}^½" traversing a distance
"(L²+(v*t)²)^½" in a time "t".

Now, the above two situations are symetrical. Thus we only derive one
equation which works for both situations:

(1) "c*{1+(v/c)²}^½ * t = (L² + (v*t)²)^½"

For the apparatus parallel to the equator:

---> WHAT THE OUTSIDER SEES:
|
| (c+v)*t
| |--------------------------|
| forward -->
|...|··················|·······|
|
| |------------------|-------|
| L v*t
\_________________________________

When the light is travelling towards the mirror the outsider sees light
travel at a speed of "c+v" traversing a distance "L+v*t" in a time "t".

Thus we get the following equation:

(2) "(c+v) * t = L + v*t"

---> WHAT THE OUTSIDER SEES:
|
| (c-v)*t
| |----------|
|
| |··········| forward -->
|
| |-------|
| v*t
| |------------------|
| L
\_________________________________

When the light is returning back to the detector he sees the light
travel at a speed of "c-u" traversing a distance "L-v*t" in a time "t".

Thus we get the following equation:

(3) "(c-v) * t = L - v*t"

---------------------------------------
Now, I will leave it to you to simplify the above three equations.
They all simplify to the following equation:

"L = c*t"

Thus, the equations of the outsider agree with the insider! The
insider and the outsider will agree with each other that "L=c*t" is
true.

Since they agree we can see why we get a null result when we do the
Michelson-Morley experiment: We chose the outsider arbitrarily. The
outsider could have been in any inertial frame of reference. Thus,
from the above we can say that *any* outsider in *any* inertial frame
will agree with the insider that "L=c*t". That is why we get a "null"
result from the Michelson-Morley experiment because everybody who looks
at the experiment simply observes that the following equation is true:
"L=c*t".

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-C) Lorentz Transformation-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Lorentz transformations are used to convert coordinates from one frame
of reference to another. Let "x", "y", "z" and "t" be the space-time
coordinates in frame "S" and let "x'", "y'", "z'" and "t'" be the
space-time coordiantes in frame "S'".

Converting from frame S' to frame S we use the following equations:

x = y(x'+vt')
y = y'
z = z'
t = y(t'+vx'/c²)

Converting from frame S to frame S' we use the following equations:

x' = y(x-vt)
y' = y
z' = z
t' = y(t-vx/c²)

Notice that we are using different equations to transform between
frames!; when we are converting from frame S' to frame S we add the
value "vt'" to "x'" and we add the value "vx'/c²" to "t'" but when we
are converting from frame S to frame S' we subtract the value "vt" from
"x" and we subtract the value "vx/c²" from "t".

Now, you should be able to move from one frame to another using the
*same* transformation! The fact that we can't means that Einstein's
first postulate is wrong. His first postulate claims that "one cannot
distinguish one inertial frame from the others or make one frame
somehow more "correct" than another". But above we have made the
distinction between two frames! In one frame we add the factors and in
the other we subtract the factors. How do we decide which frame should
add the factors and which should subtract the factors? To answer that
we must distinguish between inertial frames and so that's why postulate
#1 is violated.

Perhaps there is an "absolute frame" and that frame is represented in
Lorentz transformations as either S or S'. Physical experiments need
to be done to determine that.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-D) Time Dialation & Length Contraction=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Now we will discuss Einstein's thought-experiments which are used to
derive the equation for Special Relativity's Time Dialation and Length
Contraction. The experiments assume that postulate #2 is correct, that
is, they assume that both the Outsider System and the Insider System
are true and compatible. We know better though, that the two frames
are incompatible.

So:

(1>) First, it will be shown that when the Outsider System is used the
Time Dialation thought-experiment fails.

(2>) Secondly, it will be shown that even if postulate #2 is right
(that is, the Outsider System and the Insider System are compatible)
then the thought-experiment for both Time Dialation and Length
Contraction fail.

(3>) Thirdly, it will be shown that when we are using the Insider
System the Time Dialation thought-experiment fails.

---------------------------------------
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.
The velocity "v" is perpendicular to the line of sight of the outsider.

There is a SMD device on the train 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. This Time Dialation
thought-experiment is similar to the thought-experiment described in
Situation #2.

---------------------------------------
(1>) Now, if we are to use an Outsider System the outsider will see
the flash of light emanate from the source and move upward. While the
flash of light is heading upwards towards the mirror, the train has
moved forward a bit. 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 experiment as stated by Special Relativity requires that the light
gets reflected back to the ground, and so, this experment does not
produce proper results when we use the Outsider System.

For the moment let us assume that the experiment was simply to have the
source send a flash of light upward (i.e. it didn't need to get
reflected downward by the mirror). In this case, the outsider will say
he saw light travel a distance "L" in a time "t". And since we are
using an Outsider System he will say that he saw light travel at the
speed of "c".

---> WHAT THE INSIDER SEES:
|
| "vt"
| ______
| · |
| · |
| · | "ct" forward -->
| "c*(1+(v/c)²)^½ * t" · |
| · |
| ·|
\_________________________________

On the other hand, the insider will say he saw light travel a distance
"((vt)²+(ct)²)^½" in a time "t". Thus, he will say he saw light
travel at the speed of "c*(1+(v/c)²)^½". So, the insider will
measure the speed of light to be greater than or equal to the constant
"c", but never less. (Again, notice that since we are using an
Outsider System we can solve for "v" which is the velocity relative to
the absolute frame. Also, above we have inadvertently put the outsider
at rest with the absolute frame.)

---------------------------------------
(2>) Now, the way this Time Dialation experiment goes is that the
Outsider System and the Insider System are assumed to be compatible;
that is, both the insider and the outsider measure the speed of light
to be "c". Also, it assumes that the light from the source does infact
hit the mirror and get reflected downward back to the detector. We
know that these assumptions are wrong and contradictory, but let us go
forward anyway. Also, instead of using a SMD device, the Time
Dialation experiment uses a light-clock.

When the two observe the light-clock let the insider derive a time of
"tI" to elaspe while the outsider derives a time of "tO" to have
elasped.

The insider sees the light travel a distance "2L".

---> WHAT THE OUTSIDER SEES:
| ___
| | ·|·
| | · | ·
| L | · | · forward -->
| | · | ·
| | · | ·
| _|_ ·_____|_____·
|
| |-----------|
| "vtO"
\_________________________________

Meanwhile the outsider sees the light travel a distance
"2*[{(vtO/2)²+L²}^½]".

And we assumed that both the insider and the outsider see light travel
at the constant "c". Now, we will use the equation "t=d/c", where "t"
is an amount of derived time, "d" is an amount of derived distance, and
"c" is the speed at which light (supposedly) travels at. So the
insider derives a time

"tI = 2L/c"

while the outsider derives a time

"tO = 2*[{(vtO/2)²+L²}^½]/c"

Since the outsider sees the light travel a greater distance than the
insider, Einstein (and his friends) then use the equation "t=d/c" to
claim that the outsider will measure a greater amount of time to elapse
than the insider.

Using the two equations, the Time Dialation experiment goes on to
derive the following equation:

(1) "tO = y*tI"

* where "y" equals "1/(1-(v/c)²)^½"

Now, this equation is supposed to demonstrate that time "dialates".
Notice that the outsider sees the flash of light travel a greater
distance than the insider. This is *directly* responsible for the fact
that we then get an equation which demonstrates that time dialates.
This is wrong! All this says is that the light *seemed* to travel a
greater distance as seen by the outsider. The time dialation equation
means that since the *derived* quantity of distance has dialated then
the *derived* quantity for time has then also dialated; this does not
imply that the *measured* quantity of time has dialated. Einstein (and
his friends) often make the mistake of saying *measured* time dialates
because *derived* time dialates; this is wrong. In fact, I have no
qualms of saying that *derived* time dialates; the problems arise when
we say that *measured* time dialates.

Let me put it another way: What if I were with the insider on the
train and I was looking at the light-clock's reflection in a concave
mirror. Because the mirror is concave I would not see the light-clock
properly; the light-clock would appear to be larger. Thus, it would
seem to me that the light in the light-clock travels a greater
distance. Can I then conclude that measured time has dialated because
it seems that the light has travelled a greater distance for me? Of
course not! Measured time does not depend on how I *look* at the
light!

Let me clarify things: Einstein and I both agree that during the above
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.

In any case, this is how most physics textbooks leave the subject.
However, what if we moved the light-clock down to Earth beside the
outsider? Then the outsider will become the insider and the insider
will become the outsider. Then, if you repeat the Time Dialation
thought-experiment one will derive the following equation:

(2) "tI = y*tO"

Now both equations - (1) and (2) - demonstrate that time dialates! If
we are to say that derived time dialates then there is no problem. But
if we mean that measured time dialates 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 there measured time dialate
with respect to the other. In essence both 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..." 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"
experiment); such action is unjustified.

Also, above we assumed that the velocity "v" of the insider is
perpendicular to the line of sight of the outsider. Thus, the equation
for time dialation is subject to that restricting rule. So, what
happens if the velocity "v" is not perpendicular to the line of sight
of the outsider? In that case the outsider will see the light in the
light-clock traverse a different distance than what he found above.
Since the light traversed a different distance he will then use the
equation "t=d/c" to say that a different amount of time has elapsed,
that is, time has dialated by a different factor. All observers in the
frame with the light-clock measure the derived time to be a certain
figure. However, each observer outside the frame sees the light
traverse a unique distance and so he derives a unique amount of time to
have elapsed. Again, if we are to say that derived time has dialated
then we have no problems. However, if we are to say that measured time
dialates then only one observer - in a unique frame - can be right.
This again leads us to the idea and necessity of creating an absolute
frame if measured time dialates.

This idea and necessity of creating an absolute frame also appears in
Einstein's thought-experiment for length contraction. He introduced an
equation for length contraction which is similar to his equation for
time dialtion. It too can be written in two ways; here they are:

"LO = 1/y*tI"

and

"LI = 1/y*tO"

* where "LO" is the length measure by the outsider
* where "LI" is the length measure by the insider

So, when you say that measured time dialates or measured length
contracts then only one of the equations can be used. And when you use
only one equation you are choosing a particular frame from which to
observe velocity. Thus we see the need to create an absolute frame of
reference (a *unique* frame) if measured time dialates or measured
length contracts; this invalidates postulate #1.

Now, Einstein's thought experiments demonstrate that derived time and
derived length dialate and contract. Only physical experiments will
determine if measured time and measured length dialate and contract.
If measured time or measured length is found to dialate or contract
then Einstein's thought experiments must be altered to accomodate those
facts.

---------------------------------------
(3>) Now, if we are to use an Insider System then the insider will
observe that a flash of light emanates from the source and moves upward
such that it hits the mirror affixed above, and gets reflected back
down to the detector. We can be assured that the light hits the mirror
because the light is travelling upwards as seen from inside the frame.

In this case, the insider will say he saw light travel a distance "2L"
in a time "t". And since we are using an Insider System he will say
that he saw light travel at the speed of "c". So: "2L=c*t".

---> WHAT THE OUTSIDER SEES:
| ___
| | ·|·
| | · | ·
| L | · | · forward -->
| | · | ·
| | · | ·
| _|_ ·_____|_____·
|
| |-----------|
| "vt"
\_________________________________

On the other hand, the outsider will say he saw light travel a distance
"2*((vt/2)²+L²)^½" in a time "t". Thus, he will say he saw light
travel at the speed of "c*(1+(v/c)²)^½. So, the outsider will
measure the speed of light to be greater than or equal to the constant
"c", but never less.

Notice that if we take the three observations made by the outsider -
(1) the distance the light traversed, (2) the time it took, and (3) the
speed of the light - and make an equation out of them then the equation
will simplify to become "2L=c*t".

In any case, when we are using an Insider System for light we no longer
find that time dialates.

---------------------------------------
Now, finally, does measured time really dialate? Some experiments
demonstrate that it does. Does measured length really contract? I
have never heard of an experiment that supports this claim. In any
case, more physical experiments need to be done to get the big picture
in focus. Thought-experiments like the ones generated by Einstein are
riddled with pitfalls, and should not *define* physics, but rather be
used to *explain* physics.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-E) A Reality Check=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Now, when I looked at the moon two weeks 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.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-F) Simultaneity-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

I have said nothing about how relativity treats simultaneity of events.
Again, Einstein and relativity are wrong. The failure of relativity
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 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. This is wrong. The fact that we
can (and do) observe events out of order is because our observations
are faulty. If we had a way to transmit information instantaneously
then our observations would correlate with reality and simultaneity
would obviously be an absolute concept.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-G) ..and the Rest-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

We have seen above that the only way to know if measured time dialates
or if measured length contracts is by physical experiments. Until
those experiemnts are performed this leaves physics in a puddle of mud.
In getting out of this puddle we may have to check the validity of
many things like the following:

(1) whether the velocity of Frame B measured from Frame A is the same
as the velocity of Frame A measured from Frame B (that is, "v=v'" ?)
(2) the way velocities add under Special Relativity
(3) the Doppler effect for light
(4) the way masses "alter" under Special Relativity
(5) whether mass can travel faster than the speed of light

Many of the above are true only if we invent some sort of absolute
frame.

I cannot say more about these topics because of my lack of knowledge,
and my lack of emperical data which can only be determined by physical
experments.

---------------------------------------
When you discount all the major pitfalls of Special Relativity - and
there are many - it turns out to be a very beautiful theory. I believe
that that is the main reason why the average physician believes that
Special Relativity is a coherent theory. But watching or reading
someone who is explaining Special Relativity is like watching a good
salesman try to sell a bad vacuum.

---------------------------------------
There must be many other people who have come to the same conclusions I
have here. The faults of Special Relativity are too obvious.

A great but short book, which I have often consulted, identifies the
various failures of Special Relativity:

"The Special Theory of Relativity" by Essen, L.

Above, in the section for "Simultaneity" I have quoted this book:

"A Debate on the Theory of Relativity" by Professor W. D.
MacMillan.

Also, Ardeshir Mehta has come up with many thought-experiments which
debunk Special Relativity:

http://homepage.mac.com/ardeshir/Relativity.html

-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| THE END! -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

by Raheman Velji
rahemanvelji@xxxxxxxx

August 18, 2006


you can also view this paper (and updated versions) at...
...http://www.angelfire.com/un/rv

or a less updated copy can be found at...
...http://www.angelfire.com/rebellion2/rahemanvelji


! ! ! BEWARE OF THE ILLUMINATI ! ! !

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