Length Contraction in Accelerated Frame

[sqljunkey]

I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis.

I was looking a this paper for clarification.

 

[PeterDonis]

would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis.

Special relativity can handle acceleration just fine (what it can't handle is curved spacetime). So if by "length contraction" you just mean the measured dimensions of the object along the z and y-axis in a fixed inertial frame, the answer is no regardless of whether the object is accelerating along the x-axis or not.

I was looking a this paper for clarification.

This paper does not appear to be peer-reviewed, and is discussing a fairly advanced subject. So it's probably not a good source for someone without a fairly advanced background in relativity.

Also, it's not clear that the paper is talking about the simple question you pose, which I answered above. It appears to be talking about more complicated questions. (I haven't read it all yet, only skimmed, but that's my initial impression.)

 

[sqljunkey]

If an object is accelerating in special relativity isn't it creating a curved coordinate system against with time and position? If I was switching between my flat spacetime to the accelerating spacetime wouldn't I have to undergo some curved coordinate transformations?

 

[sqljunkey]

I don't understand how special relativity can handle acceleration, if I had an elevator with someone in it, and it was accelerating this person would feel a force, which means there is curved spacetime activity going on.

 

[PeterDonis]

If an object is accelerating in special relativity isn't it creating a curved coordinate system against with time and position?

Coordinate systems are not physical things. They're abstract human conventions. You can describe the motion of an accelerating object perfectly well in standard inertial coordinates.

If I was switching between my flat spacetime to the accelerating spacetime

There is no such thing as an "accelerating spacetime". An accelerating object doesn't change the spacetime geometry it's moving in.

I don't understand how special relativity can handle acceleration

Then you need to spend some time learning SR.

if I had an elevator with someone in it, and it was accelerating this person would feel a force, which means there is curved spacetime activity going on

Curved spacetime is not the same as acceleration or feeling a force.

 

[sqljunkey]

what about equating an accelerating elevator with an elevator sitting on Earth ? Where the person sitting inside the elevator wouldn't feel a difference.

 

[PeterDonis]

what about equating an accelerating elevator with an elevator sitting on Earth ?

That's an example of the equivalence principle. But the equivalence is only local; what it's telling you is that the spacetime around the Earth is locally flat, just like the spacetime of the accelerating elevator. The difference in the Earth case is that the spacetime is not globally flat, only locally flat. In the case of the accelerating elevator, the spacetime is globally flat (at least, it is for the scenario we are discussing in this thread). But you can't tell the difference from inside the elevator, i.e., from local measurements. You can only tell by making measurements over a wide enough region of the spacetime to determine whether it is curved or flat globally.

 

[sqljunkey]

I still don't understand how special relativity would describe length contraction. Suppose I put an apple down in a rocket and accelerate with so much force that I explode the apple into a million pieces, how is special relativity going to explain that transformation? If this was all special relativity I could plot the trajectory of the atoms and molecules of this apple I guess.

 

[PeterDonis]

I still don't understand how special relativity would describe length contraction.

Using the Lorentz transformation.

Suppose I put an apple down in a rocket and accelerate with so much force that I explode the apple into a million pieces, how is special relativity going to explain that transformation?

It doesn't by itself; you need a theory of the material of the apple and how it responds to stress. But that transformation is not length contraction and has nothing to do with length contraction, so you should not expect SR to explain it.

If this was all special relativity

What do you mean by "all special relativity"? Again, if you're expecting SR, all by itself, to give you a complete theory of materials and how they respond to stress, you're expecting too much.

I could plot the trajectory of the atoms and molecules of this apple I guess.

Yes, you could do that. But SR by itself won't tell you what those trajectories are. Again, you would need a theory of the material of the apple and how it responds to stress. Any such theory must be consistent with relativity, but that doesn't mean relativity by itself tells you what it is.

 

[sqljunkey]

well that is why I was asking, is there going to be some kind of deformation in the apple's y and z axis' if the rocket with the apple inside were to accelerate violently in the x direction. and I think you would agree that if the apple exploded into 1 million pieces y and z would be covered in apple.

and I think even with an infinite rigid body there would be distortions in both axis's.

I jst would say SR fails to explain all the nuanced interactions that would happen to a body as a result of acceleration.

 

[PeterDonis]

that is why I was asking, is there going to be some kind of deformation in the apple's y and z axis' if the rocket with the apple inside were to accelerate violently in the x direction

And the answer to that question is no, as I've already said.

I think you would agree that if the apple exploded into 1 million pieces y and z would be covered in apple.

And this is a different question, which, as I've already said, has nothing to do with special relativity. It has to do with the physics of materials and stresses. Trying to view it as a relativity problem is only going to confuse you.

even with an infinite rigid body

There is no such thing in relativity; relativity places finite limits on the rigidity of materials.

there would be distortions in both axis's

Not if the body is intact and only moving along the x axis. If the body is not intact, if it explodes or otherwise comes apart, then, once more, its behavior is not a matter of relativity; it's a matter of the physics of materials and stresses.

I jst would say SR fails to explain all the nuanced interactions that would happen to a body as a result of acceleration.

As a result of acceleration just by itself, it does. As a result of acceleration that results in explosions or other such things, no, of course it doesn't. See above.

 

[PeterDonis]

The OP question has been answered and the thread is degenerating into topics irrelevant to the OP. Thread closed.