- #1
Aziza
- 190
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Let's say something is moving very fast past you. You see the thing to be length contracted. But let's say that thing suddenly slows down very fast and enters your inertial reference frame. Will it suddenly appear to you to have lengthened? My tutor said that this is not the case because of general relativity which I don't yet understand perfectly, but here is my argument as to why he is wrong, using just special relativity:
Suppose something like a stick in the shape of a "T" (such that it has horizontal arms on either sides) falls vertically into a hole (at very high speed) whose rest length is equal to the rest length of the vertical length of the stick. The hole is only wide enough to let the vertical part of the T in. Now if the stick's bottom touches the bottom of the hole, there will be an explosion instantly. If however the arm of the T touches the top of the hole, a signal will be sent such as to deactivate the bomb.
Ok so causality is relative and so according to the T stick, the bottom of the stick will touch the bottom of the hole before the arm of the stick touches the top of the hole, and so there will be explosion.
And according to the hole, the arm of the T will touch the top of the hole before the bottom of the T touches the bottom of the hole. ie, the order of the events is reversed as happens with spacelike separated events.
But if an explosion occurs in one frame it must occur in all others. So here is the meat of my argument: according to the hole's ref frame, the T is length contracted, such that once the arms of the T hit the sides of the hole, the T shouldn't be able to continue falling into the hole such as to touch the bottom...unless the deceleration that the T experiences results in it becoming lengthened. Only then will the bottom of the T be able to touch the bottom of the hole and explode.
(And just to tie loose ends, the fact that according to the hole, the signal to deactivate the bomb was sent before the bottom of the T touched the bottom of the hole doesn't matter because the signal would not have made it in time anyway)
Am i right? does this argument make sense? I want to know before i go yell at my tutor haha:D
Suppose something like a stick in the shape of a "T" (such that it has horizontal arms on either sides) falls vertically into a hole (at very high speed) whose rest length is equal to the rest length of the vertical length of the stick. The hole is only wide enough to let the vertical part of the T in. Now if the stick's bottom touches the bottom of the hole, there will be an explosion instantly. If however the arm of the T touches the top of the hole, a signal will be sent such as to deactivate the bomb.
Ok so causality is relative and so according to the T stick, the bottom of the stick will touch the bottom of the hole before the arm of the stick touches the top of the hole, and so there will be explosion.
And according to the hole, the arm of the T will touch the top of the hole before the bottom of the T touches the bottom of the hole. ie, the order of the events is reversed as happens with spacelike separated events.
But if an explosion occurs in one frame it must occur in all others. So here is the meat of my argument: according to the hole's ref frame, the T is length contracted, such that once the arms of the T hit the sides of the hole, the T shouldn't be able to continue falling into the hole such as to touch the bottom...unless the deceleration that the T experiences results in it becoming lengthened. Only then will the bottom of the T be able to touch the bottom of the hole and explode.
(And just to tie loose ends, the fact that according to the hole, the signal to deactivate the bomb was sent before the bottom of the T touched the bottom of the hole doesn't matter because the signal would not have made it in time anyway)
Am i right? does this argument make sense? I want to know before i go yell at my tutor haha:D