Why Contraction in Relativity Theory?

[gamb]

I have a very hard question:

why in the Relativity theory the contraction is present always - along the x-axis or a speed v,
instead of an expansion along the other dimensions, transversal to the v?

Is there any mathematical proof, the contraction is the one correct,
and any other possibility is excluded?

 

[Ibix]

Length contraction is a symmetric effect. If I see you length contracted, you see me length contracted. If this happened in the transverse direction, who would be smaller when we collided?

 

[gamb]

Expansion can be a symmetric too: if I see you expanded, then you see me expanded.
And under a collision the both are the same - what's a problem?

After all the contraction can't be observed directy, what Penrose showed already...

I have in the mind the experimental discoveries: Michelson, Kennedy–Thorndike and other of this type, where I can assume the transversal expansion in place of the longitudinal contraction, and all the results will be perfectly the same.

 

[Ibix]

If I see you expanded then you must be bigger than me when we collide. If you see me expanded then I must be bigger than you when we collide. We can't both be right, and there are direct physical consequences to the question. Imagine shooting at a paper target. If the paper expands then the bullet makes a small hole; if the bullet expands it may obliterate the target.

You can't have expansion or contraction perpendicular to the direction of motion without invoking an absolute rest frame (which would let you say in an absolute sense that either the bullet or the target was moving faster). There is plenty of evidence that there is no such thing.

 

[gamb]

I can to say the same:
if I see you contracted then you must be shorter than me when we collide. If you see me shortened then I must be shorter than you when we collide. We can't both be right, and there are direct physical consequences to the question.

Additionaly:
Imagine shooting at a paper target. If the paper expands then the bullet makes a small hole; if the bullet expands it may obliterate the target.

In the reality: the faster, more energetic, particle, then the bigger hole after collision.

And in the reversed case: when the target expands, the holle will be the same, due to the highly energetic debris, which penetrate the neighboring parts...

 

[Ibix]

I can to say the same:
if I see you contracted then you must be shorter than me when we collide. If you see me shortened then I must be shorter than you when we collide. We can't both be right, and there are direct physical consequences to the question.

There are no direct physical consequences to this difference, so yes, we can both be right in this case. Please look up the "rod and barn paradox" (also known as the "ladder and barn paradox" and just the "ladder paradox").

The relevant perspective is that everyone agrees that our front faces collide; exactly how long we both are is irrelevant to this. That is not the case if two observers disagree about how wide we are.

Additionaly:
Imagine shooting at a paper target. If the paper expands then the bullet makes a small hole; if the bullet expands it may obliterate the target.

In the reality: the faster, more energetic, particle, then the bigger hole after collision.

And in the reversed case: when the target expands, the holle will be the same, due to the highly energetic debris, which penetrate the neighboring parts...

You are assuming a physical model of the target that you haven't fully explained, and you are assuming the exact same result regardless of the target material. And in any case, try a different scenario: shoot a bullet through a ring. If the bullet expands it will not pass through the ring. If the ring expands then the bullet will pass through. These results are inconsistent; they cannot both be true.

 

[gamb]

There are no direct physical consequences to this difference, so yes, we can both be right in this case. Please look up the "rod and barn paradox" (also known as the "ladder and barn paradox" and just the "ladder paradox")..

That paradox doesn't exist in the expanding scenario, so the expansion is even better than the contraction in that case.

You are assuming a physical model of the target that you haven't fully explained, and you are assuming the exact same result regardless of the target material. And in any case, try a different scenario: shoot a bullet through a ring. If the bullet expands it will not pass through the ring. If the ring expands then the bullet will pass through. These results are inconsistent; they cannot both be true.

That is just observed in the army:
a very fast projectile, something over 1200m/s, I think, when misses a target, but moves near off only, still destroys it successfully!

 

[Ibix]

That paradox doesn't exist in the expanding scenario, so the expansion is even better than the contraction in that case.

Then your model is different from relativity. Please see the thread FAQ: Experimental basis of special relativity, posted as a sticky at the top of this forum. This has a link to all of the experimental evidence that relativity is correct. If your model is different, it is wrong.

Please also note the Physics Forums policy on the discussion of non-mainstream theories. It says "don't", in short. If you are interested in learning about relativity, we can help with that. If you are trying to put forward some alternative, please take it elsewhere.

That is just observed in the army:
a very fast projectile, something over 1200m/s, I think, when misses a target, but moves near off only, still destroys it successfully!

1200m/s is 0.000004c, nowhere near relativistic speed. Even if your expansion idea were plausible, it would be negligible at this speed. You don't provide a reference, so it is hard to know what you saw - likely damage from shockwaves or explosives. I am not talking about a scenario in air or with explosives, or at such tiny speeds. Please stop going on irrelevant tangents and actually think about what I am saying.

Fire a bullet at a significant fraction of the speed of light in a vacuum at a ring that it can just pas through at very low speed. In your symmetric expansion scenario the bullet passes through the ring (from the point of view where the ring is moving and therefore expanded) and strikes it (from the point of view where the bullet is moving and therefore expanded). You can replace the ring with a grid of laser beams if you wish, so nothing fatal happens to the bullet or target. In one frame many beams in the grid are broken by the expanded bullet; in the other very few beams are broken because the grid is expanded and the bullet may even pass through the gaps between beams.

 

[Nugatory]

Is there any mathematical proof, the contraction is the one correct,
and any other possibility is excluded?

We start with Einstein's two postulates (the laws of physics are the same in all inertial frames; and the speed of light is the same in all inertial frames). There is an ironclad mathematical derivation of the Lorentz transformations from these postulates, and there is an ironclad mathematical derivation of length contraction from the Lorentz transformations.

Therefore, EITHER:
1) Einstein's postulates are wrong and possibilities other than length contraction are not excluded; OR
2) Einstein's postulates are correct and any possibility except length contraction is excluded.

There is no mathematical proof that Einstein's postulates are correct (of course not - they're postulates!), but there is an enormous amount of very convincing experimental evidence that they are correct descriptions of the universe we live in.

 

[gamb]

I simply asked for the reason of the contraction... its very special role, preference (postulate?) in the relativity.
I see a rational reason of this.. assumption(?) doesn't exist at all, in the strong mathematical sense at least, therefore I get what I want.
Thanks.

 

[Ibix]

You asked why contraction was preferred over expansion, which was the question I answered.

If you want to know where length contraction comes from, look up the light clock thought experiment. No maths more complex than Pythagoras' Theorem is needed to understand it.

 

[gamb]

If your model is different, it is wrong.

BTW.
Sorry, but I can't omit the very nice fallacy in education practice.
Nobel for... Nobel. :)

 

[mfb]

I simply asked for the reason of the contraction... its very special role, preference (postulate?) in the relativity.

It is a direct consequence of finding a set of laws which satisfy two conditions:
(a) the laws of physics are the same for every observer
(b) there is a universal speed limit. This speed limit is commonly called "speed of light" because according to our observations light travels at this speed limit.

Both (a) and (b) have been tested with incredible accuracy. You can show mathematically that length contraction is a consequence of it, and that no expansion is possible without violating (a) or (b). There are tons of books and websites proving it, I won't repeat the proof here.

 

[Nugatory]

I simply asked for the reason of the contraction... its very special role, preference (postulate?) in the relativity.
I see a rational reason of this.. assumption(?) doesn't exist at all, in the strong mathematical sense at least, therefore I get what I want.

It's not an assumption, it's a conclusion mathematically derived from Einstein's postulates. If that's not a "strong mathematical" reason, I don't know what would be.

 

[PeterDonis]

Sorry, but I can't omit the very nice fallacy in education practice.

It's not a fallacy: he's making a quite valid point, that the standard SR model is supported by a very large amount of experimental evidence within its domain of validity, so adopting a model that gives different answers within that same domain is, indeed, wrong.

 

[weirdoguy]

I see a rational reason of this.. assumption(?) doesn't exist at all, in the strong mathematical sense at least

Oh please, Lorentz contraction is derived (mathematically) in almost every book or script about SR... If haven't seen it, what sources do you use to get your knowledge?

 

[Chestermiller]

I simply asked for the reason of the contraction... its very special role, preference (postulate?) in the relativity.
I see a rational reason of this.. assumption(?) doesn't exist at all, in the strong mathematical sense at least, therefore I get what I want.
Thanks.

If you are looking for the reason for the observed contraction, it is a direct consequence of the unique 4D non-Euclidean geometry of space-time. This geometric framework was deduced by Hermann Minkowski (Einstein's former undergraduate math professor) after studying the geometric consequences of the Lorentz transformation.

 

[gamb]

I'm still not convinced of the superiority of the contraction over the expansion.
Maybe a derivation of some consequences of the expansion helps.

If I simply assume the expansion then the Lorentz transformation looks like this:
x' = x-vt and y' = y/gamma.

I don't know what is now the time transformation: t' = ?
But I think it can be derived...

 

[Dale]

I have in the mind the experimental discoveries: Michelson, Kennedy–Thorndike and other of this type, where I can assume the transversal expansion in place of the longitudinal contraction, and all the results will be perfectly the same.

Do you have a source for this claim?

If I simply assume the expansion then the Lorentz transformation looks like this:
x' = x-vt and y' = y/gamma.

This transformation does not follow the principle of relativity. Do you have a source for it?

PF is not for personal theory development. This thread is closed.