# Space contraction and stress.

1. Nov 16, 2009

### matheinste

The following is from Accelerating spaceships paradox and physical meaning of length contraction by Vesselin Petkov. Quite a well known paper I think. Speaking of Bell's Spaceship Paradox he says

----This paradox still appears to be regarded by some physicists as proof that (i) only physical bodies, but not space, undergo relativistic length contraction and (ii) a relativistically contracted body experiences a stress.-----

I assume from the context that he is talking about standard SR formulation rather than Lorentz formulation. If my assumption is incorrect then my questions are irrelevant so please ignore them.

The first part seems to be disputed.

What are the arguments for space not contracting in standard SR as opposed to Lorentz Ether Theory? I have seen the question about space contraction asked before on the forum but no one seems to have given a yes or no answer to the question.

As to the second, it seems so obvious to me (not always a good sign) that it it cannot be true that relativistically contracted bodies, as opposed to Lorentz contracted bodies, experience stress. What are the arguments for such stresses ocurring?

Matheinste.

2. Nov 16, 2009

### Al68

It seems nothing more than semantics to me. Clearly, if you have two objects at rest a distance apart, and a "measuring rod" (at rest) with ends local to each object, any reference frame that agrees that the measuring rod ends are local to the separated objects must also agree that the distance between the objects is equal to the length of the measuring rod.

It seems to me that length contraction is space contraction by definition, since at least in principle, we can always have a "measuring rod" at rest spanning the distance between any two objects.

In Bell's paradox, the distance between the ships is contracted as well as the string in the launch frame, but the proper distance between the ships is increasing with time while the proper length of the string remains constant, so it breaks. The "contracted" distance between the ships is made to stay constant in the launch frame by stipulation. The distance between the ships is still shorter in the launch frame than in a co-moving reference frame.

Last edited by a moderator: Nov 16, 2009
3. Nov 16, 2009

### matheinste

My thoughts entirely. After all Lorentz transformations are just coordinate transfiorms. But what are the arguments, which are supposed to exist, against this?

Matheinste

4. Nov 16, 2009

### Al68

My only guess is that some may be confused about Bell's paradox and not realize that the distance between the ships is also contracted in the launch frame, and by the same factor as the string.