If moving object decelerated into your frame, will it lengthen?

[harrylin]

This is essentially the same as the bug-rivet paradox, which is one of my favorites.
[..] http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/bugrivet.html

That's a very nice variant.

A bit shocking though, is the last sentence: after at a first glance nicely explaining the paradox, the author states: "The paradox is not resolved." Perhaps the author did not read recent publications...

Aziza, I give you an "A" for this (although that won't count for your uni) if you now explain what hyperphysics overlooks.

 

[Dale]

A bit shocking though, is the last sentence: after at a first glance nicely explaining the paradox, the author states: "The paradox is not resolved." Perhaps the author did not read recent publications...

Oh, I am so embarassed to have posted the link! Oops.

I guess I should work it out completely, but I am not sure if I will have time today.

 

[harrylin]

Oh, I am so embarassed to have posted the link! Oops.

I guess I should work it out completely, but I am not sure if I will have time today.

I hope that you won't, for it would be great to leave the opportunity to Aziza!

 

[arindamsinha]

GR is irrelevant. Gravity is not significant in this problem, so it is SR only. Please stop confusing students with unnecessary and irrelevant complications.

Yes DaleSpam, I see what you mean. My mistake.

 

[PAllen]

So I assume everyone here is agreed the explosion does happen for the written problem, and we would very much like to here how the professor could possibly argue otherwise. I will give a brief recap using the wording and hints in the problem. Then I will answer one of loose end mysteries on this thread.

1) The special reference frame is obviously the one where T and the hole are moving towards each other at the same speed. In this frame, event 1 (AB collision), and event 2 (CD collision) are simultaneous. The invariant fact is that no matter what is assumed about material behavior, events 1 and 2 are causally disconnected (spacelike separation) in every frame, even though their order must change for different frames. However, the wording of the problem requires that to avoid an explosion, event 1 must have a point on worldline of D before event 2 in its future light cone. However, since 1 and 2 are causally disconnected, all points on D's world line that are in the future light cone of event 1 are in the future of event 2 on D's world line. Thus explosion must occur.

2) One loose end that I don't see picked up is how to understand the breaking of the T (C leg pulling away (towards C) from the A bar of the T, in the reference frame of the T. I presume it is clear why the T breaks in the hole reference frame, and also pretty clear why it happens in the reference frame I describe in (1) - T leg doesn't know yet about the CD collision and moves away from the A bar that has hit at B. So on to the T reference frame. It is best to think of a piece of the hole near B. When CD collision occurs (first event in this frame), matter at B can't be influenced by it, so it continues to move left at near c. Because of the head start along T leg that B has, even assuming matter influence could travel at c, the influence of the CD collision cannot catch up to B before B hits A and breaks the T.

 

[harrylin]

[..] One loose end that I don't see picked up is how to understand the breaking of the T (C leg pulling away (towards C) from the A bar of the T, in the reference frame of the T. [..]

I discussed that in my post #34, but it's always useful to have it presented in different ways. As you made use of the picture, your explanation is likely easier to understand.

Note however that your discussion suffers from the same non-generality as my remark in post #12: it's not true that a T of any material that hits such a hole at any speed, will break.

 

[Demystifier]

Aziza, I would suggest you to show your tutor this paper
http://xxx.lanl.gov/abs/physics/9810017
Relativistic contraction of an accelerated rod, Am. J. Phys. 67 (1999) 1007.

 

[Fredrik]

...i guess the T should get torn apart because the bottom doesn't know that the top stopped moving, but are you saying that the T gets torn apart in the hole's reference frame?

I don't have time to think this through and write a good answer right now. I will return to this later today.

Sorry about not getting back to this the same day. I have thought about it now. I was a bit confused at first, because it seemed to me that in the T's frame, the T will be crushed from the front, and in the hole's frame, it will be pulled apart from behind. This would have been a contradiction. After some thought, I think all frames will agree that the front will be crushed from the front by the collision with the bottom of the hole, and that the top of the T will be torn off from the rest of it by the collision with the top of the hole. There's no contradiction here, since these two statements are referring to different parts of the T.

 

[A.T.]

I think all frames will agree that the front will be crushed from the front by the collision with the bottom of the hole, and that the top of the T will be torn off from the rest of it by the collision with the top of the hole. There's no contradiction here, since these two statements are referring to different parts of the T.

That's why it is confusing to speak about "T's frame". There is no frame where the whole T will remain at rest, during the entire scenario.

In the rest frame of the T-bottom, the T-bottom hits the bottom of the hole. Then the frame becomes non-inertial: The rest of the T suddenly accelerates down and contracts, while the previously contracted hole expands, hitting the T-top with the edges and tearing it off.

In the rest frame of the T-top, the T-bottom hits the bottom of the hole. The frame is still inertial here. The rest of the T suddenly accelerates up and contracts, while the hole depth remains constant. At some point the rest of the T has contracted below the constant hole depth, and the T-top hits the hole edges.

 

[PAllen]

I discussed that in my post #34, but it's always useful to have it presented in different ways. As you made use of the picture, your explanation is likely easier to understand.

Note however that your discussion suffers from the same non-generality as my remark in post #12: it's not true that a T of any material that hits such a hole at any speed, will break.

I allowed for speed of sound up to c. Really, I assume only that 'all causal influence is limited by c'. Then, if speed and material are such that breakage occurs in any frame, my discussion shows why it would happen in the T frame. It is obviously true that if all components are made of idealized chewing gum (for example) no breakage will occur in any frame at any speed.

 

[harrylin]

I allowed for speed of sound up to c. Really, I assume only that 'all causal influence is limited by c'. Then, if speed and material are such that breakage occurs in any frame, my discussion shows why it would happen in the T frame. [..]

Yes the speed is not given in the problem as presented in the OP. However, I still think that it's reasonable practical assumption that it will break, the way it is presented.

It is obviously true that if all components are made of idealized chewing gum (for example) no breakage will occur in any frame at any speed.

That's a guess, and your guess differs from mine (perhaps because I don't consider anything "idealized"). However, with that the discussion is drifting off-topic, and I don't want to spend time now on such theoretical material research.