The Special Relativity Discovery MMXI.0

[butchmurray]

The Special Relativity Discovery MMXI.0
Thorntone E. ‘Butch’ Murray
Houston, Texas
June 18, 2011

Problem:
For a body in motion at any relative velocity >0<c the magnitude of a length perpendicular to the direction of motion is not equal to the at rest magnitude of that length as judged from a co-ordinate system moving with the body. This contradicts the Special Relativity tenet: All lengths within a body in motion at any relative velocity will maintain at rest magnitudes as judged from a co-ordinate system moving with the body.

Hypothesis:
The interferometer experiments by Michelson-Morley et al. are accepted as experimental confirmation that all lengths in a body are constant at rest and at any relative velocity as judged from a co-ordinate system moving with the body. Those experiments are also recognized as experimental support for time dilation and length contraction in the direction of but not perpendicular to the direction of relative motion.
For a body at relative rest distance is the product of velocity multiplied by time: d=v*t. For these purposes the terms distance and length (L) are interchangeable. Substitute L for d: L=v*t. Length can be expressed in terms of light speed such as light years, light seconds etc. Light speed (c) can replace velocity. Substitute c for v: L=c*t. For these purposes length perpendicular to the direction of impending motion for the body at relative rest is referred to as Z. Substitute Z for L: Z=c*t. For these purposes Z’ is length perpendicular to the direction of motion for the body in motion. Dilated time within the body in motion is t’. Z’=c*t’. According to Special Relativity Z’=Z. However, Z’=Z if and only if t’=t, which occurs only if the body is at relative rest. For the body in motion t’ does not equal t. And therefore Z’ does not equal Z, which is antithetical to the rule of Special Relativity: All lengths within a body will maintain at rest magnitudes at any relative velocity as judged from a co-ordinate system moving with the body. This oversight, arguably simple math, has apparently gone undetected for more than a century.

Data:
1. For these purposes X is the at rest length of the body in the direction of impending motion.
X=c*t
2. For these purposes X’ is the length of the body in motion in the direction of motion. Length in the direction of motion is contracted per the Lorentz factor for the body in motion as judged from relative rest:
X’=X*sqrt (1-(ve2/ce2))
3. Substitute c*t for X:
X’= c*t*sqrt (1-(ve2/ce2))
4. Time is that of the co-ordinate system from which length is judged. To judge length from the co-ordinate system moving with the body substitute at rest time (t) with dilated time (t’):
X’= c*t’*sqrt (1-(ve2/ce2))
5. Express dilated time in terms of at rest time. Substitute t’ with its at rest time equivalent t’=t/sqrt (1-(ve2/ce2)):
X’= c*t/sqrt (1-(ve2/ce2))*sqrt (1-(ve2/ce2))
Simplify:
X’=c*t
6. Therefore: X’=c*t and X=c*t then X’=X.
In accordance with Special Relativity: length within a body maintains the at rest magnitude at any relative velocity as judged from a co-ordinate system moving with the body.

The same procedure is performed for length perpendicular to the direction of motion:

1. For these purposes Z is the at rest length of the body perpendicular to the direction of impending motion.
Z=c*t
2. For these purposes Z’ is the length of the body in motion perpendicular to the direction of motion. Length perpendicular to the direction of motion is not contracted for the body in motion as observed from relative rest:
Z’=Z
3. Substitute c*t for Z:
Z’= c*t
4. Time is that of the co-ordinate system from which length is judged. To judge length from the co-ordinate system moving with the body substitute at rest time (t) with dilated time (t’):
Z’= c*t’
5. Express dilated time in terms of at rest time. Substitute t’ with its at rest time equivalent t’=t/sqrt (1-(ve2/ce2)):
Z’= c* t/sqrt (1-(ve2/ce2))
6. Therefore: Z’= c* t/sqrt (1-(ve2/ce2)) and Z=c*t.
Z’=Z if and only if v=0. And therefore Z’ does not equal Z for any relative velocity as per the stated Problem. This is also contradictory the null results of the interferometer experiments.

Conclusion:
The Lorentz Transformations contradict the null results of the interferometer experiments. As judged from a co-ordinate system moving with the interferometers the aggregate influences applied to each of the equal arms must be equal for the arms to remain equal. The formulation applies two complementary influences - length contraction and time dilation - to one of two equal lengths, arm length in the direction of motion. And only one of the two influences - time dilation - to the other of the two equal lengths, arm length perpendicular to the direction of motion. The outcome is inequality of the two originally equal lengths, clearly in contradiction to the null results of the experiments.
Additionally, the recorded fringe shifts disproved the existence of the luminiferous aether. Therefore, “failure” of the experiments was declared. However, it was assumed that the earth’s orbital velocity around the sun should affect the speed of light in a manner detectable by the interferometers. That not being the case, it was further assumed that there could be only one reason for the non-detection so the Lorentz Transformations were formulated. The trouble is that those assumptions have no basis in fact and are primarily validated by Special Relativity, of which, those assumptions are a key component.

Predictions:
Relative velocity greater than the speed of light will be proven theoretically possible.


Thorntone E. ‘Butch’ Murray

[caveman1917]

For a body at relative rest distance is the product of velocity multiplied by time: d=v*t.

This is the mistake that leads you to faulty conclusions.
First, if the body is at "relative rest", velocity is 0 so you'd get a length of 0.
Secondly, from the rest frame of the body, the length is seen by making the endpoints simultaneous. Thus, also the time difference is zero, making length again 0.

What is the proper length of a body?

[Tensor]

This is just the same misunderstanding of Special Relativity you promoted in this thread or in this thread The only differences between the three are the scenarios. Nothing new here.

[korjik]

The Special Relativity Discovery MMXI.0
Thorntone E. ‘Butch’ Murray
Houston, Texas
June 18, 2011

Problem:
For a body in motion at any relative velocity >0<c the magnitude of a length perpendicular to the direction of motion is not equal to the at rest magnitude of that length as judged from a co-ordinate system moving with the body. This contradicts the Special Relativity tenet: All lengths within a body in motion at any relative velocity will maintain at rest magnitudes as judged from a co-ordinate system moving with the body.

Thorntone E. ‘Butch’ Murray

Most of this snipped by me, as it isnt all that important.

To a coordinate system moving with a body, the velocity of the body is zero. Therefore, the amount of length contraction is zero, and all the lengths of the body are what they are.

Your problem is solved trivially by realizing that coordinates moving with the body are moving with the body, and that means that the relative velocity is zero

[Swift]

This is just the same misunderstanding of Special Relativity you promoted in this thread or in this thread The only differences between the three are the scenarios. Nothing new here.

I'll make that official.

butchmurray - In your very next post in this thread, you will explain completely and succinctly exactly how this thread is substantially different from your previous threads on this topic. If it is not substantially different, the thread will be close - our rules allow only one 30 day period for each ATM idea. If you ignore my instructions you will be infracted.

[butchmurray]

Caveman1917:

The statement you cite is the first step is used to draw the connection between distance and length emphasizing the time component. The progression is: d=v*t – length (L) can replace distance L=v*t – length can be expressed as light seconds etc, L=c*t – then for these purposes the lengths of the body will be defined as stated in the first and second numbers 1 and 2 under Data:

1. For these purposes X is the at rest length of the body in the direction of impending motion.
X=c*t.;
2. For these purposes X’ is the length of the body in motion in the direction of motion;
and The same procedure…
1.For these purposes Z is the at rest length of the body perpendicular to the direction of impending motion.
2. For these purposes Z’ is the length of the body in motion perpendicular to the direction of motion.

The first sentence states:
For a body in motion at any relative velocity >0<c the magnitude of a length perpendicular to the direction of motion is not equal to the at rest magnitude of that length as judged from a co-ordinate system moving with the body.

The objective is to prove that even though length perpendicular to the direction of motion is not dilated for a body in relative motion it is affected in the same way that the contracted length is in that body.

The usage of “as judged from a co-ordinate system moving with the body” - that is the circumstance in which the effects of both length contraction and time dilation can be observed. From relative rest only the effect of length contraction can be observed,

Korjik:

An observer at relative rest will judge length in the direction of motion to be contracted for the body in motion. However, from the co-ordinate system moving with the body that contracted length is observed from dilated time and not judged as contracted.

Swift:

This thread is different in that the others were observational and presented anecdotal evidence. If this post is really read and not given the brush off you will see that the hard facts and math backup is there. What’s ironic is I have learned from you guys that my posts must be bullet proof. But, that was at the expense of my credibility and greatly reduced chances of anyone wanting to really read and try to understand what I am attempting to convey.

Oh well, live and learn.

Butch

[Shaula]

Physics is not just about blindly substituting into equations. You are making the classic mistake of applying equations without properly working out what is happening in your scenario. I think your big issue is with the notions of simultaneity and how you actually measure the width of a body with light. I did an example like this a long time ago at uni - am going to sit back and wait for someone to give the correct explanation rather than fluff it myself! SR is not just about the Lorentz contractions - it is about the consequences of light having a finite speed and what that means for two or more people taking measurements.

[macaw]

This thread is different in that the others were observational and presented anecdotal evidence. If this post is really read and not given the brush off you will see that the hard facts and math backup is there.

No, it isn't different, it contains the same basic errors in understanding the MM experiment.

What’s ironic is I have learned from you guys that my posts must be bullet proof.

Yet, your posts are riddled with the same basic mistakes. This thread is IDENTINTICAL to your previously closed ones.

[korjik]

Caveman1917:
Korjik:

An observer at relative rest will judge length in the direction of motion to be contracted for the body in motion. However, from the co-ordinate system moving with the body that contracted length is observed from dilated time and not judged as contracted.

Butch

So what exactly is the problem? All measurements are local, and different frames are not required to make any of the same measurements other than the speed of light. As a matter of fact, with the requirement that the speed of light be constant, then length measurements must be different in different frames.

[butchmurray]

Shaula:

This has nothing to do with simultaneity. It IS about the consequences of light having a finite speed and what that means for two or more people taking measurements.

I did not blindly substitute into equations. Under the DATA heading (I should have created a better system to reference specific points) for the first numbers 1 through 6:

1. The definition I use for “at rest” length of the body in the direction of motion.
2. The definition I use for length in the direction of motion for the body in motion, which is contracted per the Lorentz factor as observed from relative rest.
3. I substitute the “at rest” length in the direction of motion with its previously assigned definition.
4. I substitute time that is used to judge length in the body in motion from relative rest with dilated time that is used to judge length in the body in motion “from within the body in motion” that is referred to in the literature as and is tantamount to “ from the co-ordinate system moving with the body”
5. I substitute dilated time with its “proper time” equivalent which facilitates the comparison of “at rest” length with length as judged from within the body in motion where time is dilated.
I then simplify the equation.
6. The result proves that the mathematical definition of “at rest” length in the direction of motion and the mathematical definition of time dilated and contracted length in the direction of motion as observed from within the body in motion are identical. So, in accordance with Special Relativity, length within a body maintains the at rest magnitude at any relative velocity as judged from a co-ordinate system moving with the body (another way of saying as judged from within the body in motion).

But that is just the SET UP. The PAYOFF is:

Next EXACTLY THE SAME PROCEEDURE done for length perpendicular to the direction of motion proves that the mathematical definition of “at rest” length perpendicular to the direction of motion and the mathematical definition of time dilated length perpendicular to the direction of motion as observed from within the body in motion are NOT the same. That CONTRADICTS the Special Relativity tenet that all lengths within a body maintain the “at rest” magnitudes at any relative velocity as judged from within the moving with the body.


Macaw:

Identify the “same basic errors” and the “same basic mistakes” that this post is “riddled with”.


Korjik:

The problem is that all lengths within a body DO NOT maintain the “at rest” magnitudes at any relative velocity as judged from within the moving with the body as stipulated in Special Relativity.


All:

This is precisely why I made the post here. It’s kinda like New York. If you can make it here, you can make it anywhere.


Butch

[macaw]

Macaw:

Identify the “same basic errors” and the “same basic mistakes” that this post is “riddled with”.

1. Inability to understand frames of reference
2.Inability to understand Lorentz transforms
3.Inability to understand the consequences of the Lorentz transforms (i.e. time dilation, length contraction)
4.Inability to understand MMX as judged from the proper frame of the lab.
5. Inability to understand MMX as judged from a frame external to the lab.
6. Free mixing of frames (frame jumping)
7. Inability to understand even the most basic aspects of relativity.

There is more....

[korjik]

Korjik:

The problem is that all lengths within a body DO NOT maintain the “at rest” magnitudes at any relative velocity as judged from within the moving with the body as stipulated in Special Relativity.

Butch

How do you figure that? The relative velocity of the moving object to the moving frame is zero. That gives zero length contraction. An object at rest in a frame at rest has a zero relative velocity and zero length contraction. If you measure from a moving frame to a stationary object, or a stationary object to a moving frame, then you get contraction.

[Shaula]

This has nothing to do with simultaneity.

Yes it does. It really does. By shifting from a length to a velocity time product you are implicitly changing what you mean by length. A speed time product is not the same as an instantaneous length measurement based on a standard ruler - hence your subbing in time primed is blindly substituting. You implicitly shift from one to the other by making this substitution and by missing this point betray that you have not set up your thought experiment fully. Your point 4 sums your misunderstanding up well. You have gone from measuring length to time speed product and not taken that into account.

[butchmurray]

Tensor is always at relative rest.
The rest dimensions of the body are 1cs in the direction of motion and 1cs perpendicular to the direction of motion.
Macaw is in the two dimensional body. The body has the constant relative velocity of .866c.
The Lorentz factor, sqrt (1-(ve2/ce2)) for that velocity is .5.
Dilated time for that velocity is t/sqrt (1-(ve2/ce2))=1s/.5=2
The steps are the same as in the post.

For length in the direction of motion:

1. This the “at rest” length of the body in the direction of impending motion from Macaw’s and Tensor’s perspectives:
1c*1s =1cs
2. Length in the direction of motion is contracted per the Lorentz factor (.5) for the body in motion. As judged from Tensor’s perspective this is the length of the body in motion in the direction of motion:
1cs*(.5)=.5cs
3. Substitute 1c*1s for 1cs:
1c*1s*(.5)=.5cs
4. Time is that of the co-ordinate system from which length is judged. To judge length in the direction of motion from Macaw’s point of view substitute “at rest” time (1s) with Macaw’s dilated time (1s/.5):
1c*(1s/.5)*(.5)=1cs
5. Express Macaw’s dilated time (1s/.5) in terms of at rest time. Substitute dilated time with its at rest time equivalent (2s).
1c*(2s)*(.5)=1cs
Simplify:
1c*1s =1cs
Therefore: The “at rest” length of the body in the direction of motion from Macaw’s perspective is 1cs.
At the constant relative velocity of .866c length of the body in the direction of motion from Macaw’s perspective is 1cs.
In accordance with Special Relativity: in constant relative motion length within a body maintains the at rest magnitude as judged from Macaw’s point of view.

THIS IS WHAT, APPARENTLY, NO ONE HAS DONE FOR OVER A HUNDRED YEARS:
For length perpendicular to the direction of motion:
1. This the “at rest” length of the body perpendicular to the direction of impending motion from Macaw’s and Tensor’s perspectives:
1c*1s =1cs
2. Length perpendicular to the direction of motion is not contracted. As judged from Tensor’s perspective this is the length of the body in motion perpendicular to the direction of motion:
1cs
3. Substitute 1c*1s for 1cs:
1c*1s =1cs
4. Time is that of the co-ordinate system from which length is judged. To judge length perpendicular to the direction of motion from Macaw’s point of view substitute “at rest” time (1s) with Macaw’s dilated time (1s/.5):
1c*(1s/.5) =2cs
5. Express Macaw’s dilated time (1s/.5) in terms of at rest time. Substitute dilated time with its at rest time equivalent (2s).
1c*(2s)=2cs
Simplify:
1c*2s=2cs
Therefore: The “at rest” length of the body perpendicular to the direction of motion from Macaw’s perspective is 1cs.
At the constant relative velocity of .866c length of the body perpendicular to the direction of motion from Macaw’s perspective is 2cs.

IN CONTRADICTION TO SPECIAL RELATIVITY length within a body at a constant relative velocity DID NOT maintain the at rest magnitude as judged from Macaw’s point of view. The interferometer experiments by Michelson-Morley et al. are accepted as experimental confirmation that all lengths in a body maintain the at rest magnitude as judged from the equivalent of Macaw’s point of view.

All of the steps from the post were included here though not necessary when using real values and have no material effect.

[butchmurray]

Macaw:

You have a right to your opinions but the “same basic errors” and “same basic mistakes” refer to actual items. You have not specifically identified a single item in the post.


Korjik:

Hopefully, the post I just made addresses your point.


Shaula:

But length is a velocity time product. For instance: if a car travels on a road at 60 miles per hour (velocity) for 1 hour (time) the LENGTH of highway that it covered is 60 miles. The DISTANCE between the start point and the end point is 60 miles. Length and distance are the same thing.
The length of something is the same as the distance from one end of it to the other end of it.

[Shaula]

No. This is the root of your misconception - as I have pointed out. You have failed to understand this which is one of the reasons you insist that no one has done your substitution in 100 years. They have, and then their physics lecturer has carefully explained how they should have done it. And then cautioned them about the dangers of blind substitution.

Think about what appears to happen when you fire a light beam from one side of an object to the other to measure its width (which is what you are doing in the case of subbing in ct). You will realise that you are invoking an implicit simultaneity that is not valid in both frames. If you do not then you need to do a relativity 101 to learn how to think about these things.

[Garrison]

But length is a velocity time product. For instance: if a car travels on a road at 60 miles per hour (velocity) for 1 hour (time) the LENGTH of highway that it covered is 60 miles. The DISTANCE between the start point and the end point is 60 miles. Length and distance are the same thing.
The length of something is the same as the distance from one end of it to the other end of it.

You realize your analogy is hopelessly flawed because it ignores time dilation don't you? Yes you can do that at 60 mph but not when discussing travelling at fractions of c. And time dilation have been measured and verified experimentally so you can't just wave it away whatever your take on relativity.

[butchmurray]

Shaula and Garrison:

Let’s try this:

From where the tail originates at the comet to the end of the tail is a distance of 1 light second.

The comet’s tail is, therefore, 1 light second long. Its length is 1 light second.

The length and the distance are the same.

Right?

[Garrison]

Shaula and Garrison:

Let’s try this:

From where the tail originates at the comet to the end of the tail is a distance of 1 light second.

The comet’s tail is, therefore, 1 light second long. Its length is 1 light second.

The length and the distance are the same.

Right?

And what velocity is the comet moving at?

[AstroRockHunter]

Shaula and Garrison:

Let’s try this:

From where the tail originates at the comet to the end of the tail is a distance of 1 light second.

The comet’s tail is, therefore, 1 light second long. Its length is 1 light second.

The length and the distance are the same.

Right?

According to who?

1. A person riding on the comet?
2. A person in a rocket that is traveling at exactly the same velocity as the comet?
3. A person in a rocket traveling at the same speed as the comet but perpendicular to the comets path?
4. A person on the Moon, observing the comet?
5. A person on Earth observing the comet?
6. All of the above?
7. None of the above?

[butchmurray]

Garrison and AstroRockHunter:


OK, how about this:

The observer is looking at a huge flat object.
The observer is stationary with respect to the object.
The observer and the object are at relative rest with respect to each other.
There are 2 marks on the object.
The observer judges the distance between the two marks to be 1 light second.
The observer physically scribes a line from one mark to the other mark.
The length of the line between the two marks is one light second.
The distance between the two marks is one light second.

The distance and the length are the same.
Right?

[Strange]

If we carry on like this, we might actually get somewhere...

[butchmurray]

AstroRockHunter:

Just read the very bottom of your post.
Very,very COOL!

Butch

[Garrison]

Garrison and AstroRockHunter:


OK, how about this:

The observer is looking at a huge flat object.
The observer is stationary with respect to the object.
The observer and the object are at relative rest with respect to each other.
There are 2 marks on the object.
The observer judges the distance between the two marks to be 1 light second.
The observer physically scribes a line from one mark to the other mark.
The length of the line between the two marks is one light second.
The distance between the two marks is one light second.

The distance and the length are the same.
Right?

Actually to put this back on a proper ATM footing why don't you explain what you think would happen if the observer and the object aren't at rest relative to one another?

[butchmurray]

Strange:

Thanks, I needed that.

Butch

[butchmurray]

Garrison:

Already did at the beginning of the thread.

Do you agree in the case of the two marks that length and distance are the same?

Butch

[Garrison]

Garrison:

Already did at the beginning of the thread.

Do you agree in the case of the two marks that length and distance are the same?

Butch

And it was wrong, again please describe what you expect to happen in the case where the two are not at relative rest?

[Shaula]

Do you agree in the case of the two marks that length and distance are the same?

You are still missing the point. How do you MEASURE these quantities? You are applying time dilation effects to your lengths. In order to do that and be correct you have to fulfil some very specific criteria. Just arguing that because in the specific case of a rest frame the length and distance are the same thing in no way helps you flawed set of substitutions. Let's not go down the "Well if A = B then ..." route while you are ignoring the basic assumptions implicit in the formulation of A = B. Your steps 3-6 are plain wrong and an entry level course on SR would have shown you why. I am trying to find a good online resource to explain it better than I can. If I find it I will post it.

[butchmurray]

Shaula:

In the scenario with Macaw and Tensor with the body at relative rest the both made the measurements with a light pulse generator/timer and a mirror. With the light pulse generator/timer at one surface and the mirror at the opposite surface a light pulse was emitted in the direction of impending motion. The timer indicated 2 seconds, which was divided by 2 because of the round trip. The one-way time was 1 second, thus the length of 1 light second. The measurement of length perpendicular to the direction of impending motion was done in the same manner with an identical result.

With the body in motion at .866c tensor at relative rest could not make direct physical measurements. He calculated the dimensions per SR. He determined that length in the direction of motion was contracted to .5 light seconds and length perpendicular to the direction of motion was not contracted and remained 1 light second in length as judged from his perspective at relative rest.

Within the body at the relative velocity of .866c in relation to Tensor at relative rest, Macaw again made the measurements with a light pulse generator/timer and a mirror. At this relative velocity time is dilated to 2 times the proper time of Tensor at rest. Macaw emitted the light pulse in the direction of motion. Even though this length in the direction of motion is contracted to .5 light seconds the round trip time for the pulse is 2 seconds. Divided by 2 yields the one-way time of 1 second for the length of 1 light second.
So the contracted length of .5 light seconds within a body with time dilated by a factor of 2 results in length in the direction of motion as judged by Macaw to be 1 light second (2*.5=1)

Macaw performs the same procedure for length perpendicular to the direction of motion. Remember, this length was not contracted. PLEASE DON’T EXPLODE WHEN YOU READ WHAT IS NEXT. READ TO THE END THEN EXPLODE IF YOU MUST. The round trip time for the pulse is 4 seconds. Divided by 2 yields the one-way time of 2 second for the length of 2 light seconds. So the non-contracted length of 1 light second within a body with time dilated by a factor of 2 results in length perpendicular to the direction of motion as judged by Macaw to be 2 light second (2*1=2)


Remember that time dilation, for the relative velocity of .866, is 2. Within the body length in the direction of motion is double the length as judged from relative rest. Within the body length perpendicular to the direction of motion must also be double the length as judged from relative rest. You can’t just pick and choose which lengths are affected by time dilation and which lengths are not. Either they all are or they all are not, unless you have a real good reason.

I think I’m ready for the onslaught. Just don’t get personal.

[macaw]

With the body in motion at .866c tensor at relative rest could not make direct physical measurements.

Nonsense, you just claimed that Tensor is at rest wrt the object he's measuring.

He calculated the dimensions per SR. He determined that length in the direction of motion was contracted to .5 light seconds

Nope. Tensor is at rest wrt the object, so there is no length contraction. If you are going to try to disprove relativity, you will need to learn it first.

Within the body at the relative velocity of .866c in relation to Tensor at relative rest, Macaw again made the measurements with a light pulse generator/timer and a mirror. At this relative velocity time is dilated to 2 times the proper time of Tensor at rest. Macaw emitted the light pulse in the direction of motion. Even though this length in the direction of motion is contracted to .5 light seconds the round trip time for the pulse is 2 seconds. Divided by 2 yields the one-way time of 1 second for the length of 1 light second.
So the contracted length of .5 light seconds within a body with time dilated by a factor of 2 results in length in the direction of motion as judged by Macaw to be 1 light second (2*.5=1)

Your "intuition" is leading you astray. In a different thread I showed the correct calculation and you will need to know that it is more complicated than what you wrote above. The reason is that the light wave "chases" after the mirror.

Macaw performs the same procedure for length perpendicular to the direction of motion. Remember, this length was not contracted. PLEASE DON’T EXPLODE WHEN YOU READ WHAT IS NEXT. READ TO THE END THEN EXPLODE IF YOU MUST. The round trip time for the pulse is 4 seconds.

Wrong. From macaw's perspective light travels a different path than what you think. You will need to figure out that path on your own. Suffice to say that it isn't what your "intuition" is telling you. Again, you will need to think about the fact that the mirror moves while the light wave "chases" after it.

Within the body length perpendicular to the direction of motion must also be double the length as judged from relative rest.

Wrong again.

You can’t just pick and choose which lengths are affected by time dilation and which lengths are not.

Time dilation is isotropic, does not depend on direction, so you are striking out again.

I think I’m ready for the onslaught. Just don’t get personal.

Not at all. Just remember, you will never manage to disprove relativity if you don't understand it and if you refuse to learn it. All you will manage is to post your mistakes .