Lorentz Contraction Physical Reality

[curiousphoton]

Simple thought experiment I read and would like to hear what others think will the result will be:

Let two spaceships A and B accelerate along a straight line. Observer C does not accelerate. The accelerations, as judged by C, are constant for both ships. Each ship is equipped with a yard-arm, and a thread is tied between the two arms. Does the thread break, due to Lorentz contraction? (Assume that the acceleration is gentle enough that the thread does not break simply because of its own inertia).

 

[soothsayer]

Nope. For one, there is no length contraction in the accelerating frame, and two, according to observer C, everything in the system is contracting, including the distance between the two spaceships, so the perceived "tension", if you will, on the string according to observer C doesn't even change, since the length of the string and the distance the string spans changes at the same rate.

 

[Samshorn]

Let two spaceships A and B accelerate along a straight line. Observer C does not accelerate. The accelerations, as judged by C, are constant for both ships. Each ship is equipped with a yard-arm, and a thread is tied between the two arms. Does the thread break, due to Lorentz contraction?

Your paraphrase of Bell's spaceship scenario is a bit imprecise. You need to assert not that the accelerations of A and B (per the rest frame coordinates of C) are constant, but rather that they are equal. Given this clarification, the answer is obviously yes, the thread will break. John Bell famously used this scenario to argue that many people who think they understand special relativity actually don't, because of how many people confidently give the wrong answer.

 

[curiousphoton]

Nope. For one, there is no length contraction in the accelerating frame, and two, according to observer C, everything in the system is contracting, including the distance between the two spaceships, so the perceived "tension", if you will, on the string according to observer C doesn't even change, since the length of the string and the distance the string spans changes at the same rate.

See below

Your paraphrase of Bell's spaceship scenario is a bit imprecise. You need to assert not that the accelerations of A and B (per the rest frame coordinates of C) are constant, but rather that they are equal. Given this clarification, the answer is obviously yes, the thread will break. John Bell famously used this scenario to argue that many people who think they understand special relativity actually don't, because of how many people confidently give the wrong answer.

You spoiled the fun

And I should have said equal AND constant, correct. Thanks.

 

[cephron]

Ah, so it was a setup from the beginning, was it? xD

Well here's a chance for me to understand SR a little bit better - could you explain why the thread breaks?

For the thread to break, the ships must contract, but the space between them doesn't...or, from the ship's frame of reference: they do not perceive themselves to be contracting, but the space between them expands as they accelerate.

Is this the case specifically because we're dealing with an accelerating frame of reference?

 

[Fewmet]

Ah, so it was a setup from the beginning, was it? xD

Well here's a chance for me to understand SR a little bit better - could you explain why the thread breaks?

For the thread to break, the ships must contract, but the space between them doesn't...or, from the ship's frame of reference: they do not perceive themselves to be contracting, but the space between them expands as they accelerate.

Is this the case specifically because we're dealing with an accelerating frame of reference?

Is it really true that accelerating observers would not report a length contraction? They see other effects of acceleration (like the bandanna hanging from the rear view mirror swinging backwards). As I understand it the equivalence principle says they cannot whether the effect if from increasing velocity one direction or being subject to a stronger gravitational field in the opposite direction...

 

[soothsayer]

Does it have to do with perceived length contraction according to the ships since they are moving relativistically? If the length between the ships contracts, what is the implication of this for the string spanning this distance? And I guess from an outside perspective, the rockets are contracting, expanding the space between the connecting points of the string?

 

[bcrowell]

Curiousphoton, when you quote someone (in this case me), always make sure to use quotation marks and credit the source properly: http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.3

This is a famous relativity paradox called Bell's spaceship paradox. Anyone who wants to see my own explanation of how the paradox is resolved can read it in the link above.

 

[bcrowell]

Your paraphrase of Bell's spaceship scenario is a bit imprecise. You need to assert not that the accelerations of A and B (per the rest frame coordinates of C) are constant, but rather that they are equal.

Thanks for pointing that out. I didn't state that clearly.

 

[bcrowell]

And I should have said equal AND constant, correct. Thanks.

Er, you mean *I* should have said that...?

 

[Samshorn]

You spoiled the fun

I believe it's called trolling.

And I should have said equal AND constant, correct. Thanks.

No, just equal. Constancy has nothing to do with it.