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I Length contraction: Is it permanent?

  1. Jan 20, 2016 #1
    • This is not a homework problem, just a technical question organized in a similar fashion
    Lorentz contraction problem:
    By Bertrand Boucquillon

    Components of the problem:
    - Bob (observer)
    - 2 identical rods that both measure 1 meter. Let's call them rod X and rod Y
    - Point A
    - Point B

    Scenario (step by step):
    1) Bob is at point A, and is at rest with both rods in his hands
    2) Bob throws rod X at 87% of the speed of light (.87c) at a target located at point B
    3) rod X hits the target and is now at rest
    4) Bob travels over to point B at walking speed, still holding rod Y in his hand
    5) Bob is now at point B, at rest again, and grabs rod X from the target
    6) Bob compares the length of rod X and rod Y

    Question:
    Is the length of rod X still the same as the length of rod Y? Please provide a detailed explanation of your answer and/or a source where the answer is explained properly.
     
  2. jcsd
  3. Jan 20, 2016 #2

    Dale

    Staff: Mentor

    Assuming that all rods are accelerated Born-rigidly, then the lengths will be the same. If the rods are not accelerated Born-rigidly then you would need some material modeling.

    I know that isn't a detailed answer.
     
    Last edited: Jan 20, 2016
  4. Jan 20, 2016 #3

    phinds

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    Well, how about this: you, right now as you read this, are massively length contracted according to a particle at CERN. Are you the same size as when that particle wasn't moving relative to the CERN accelerator?
     
  5. Jan 20, 2016 #4

    Ibix

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    Is Born rigidity necessary? Don't you just need a material that behaves elastically under the forces used? I'd think that as long as it doesn't deform plastically (like a perfectly ordinary non-relativistic bullet hitting a target does in practice) the answer is "the same length". I agree that we need more detail on the properties of the rod and target, and the acceleration method used, before a detailed description is possible.

    The easiest would be shooting the rod out of a bow. Then the acceleration and deceleration phases are mirror images, at least qualitatively.
     
  6. Jan 20, 2016 #5
    Thanks for your answer Dale, I'm not familiar with the term Born-rigidly, I will do some research on it and get back to you.
     
  7. Jan 20, 2016 #6

    PAllen

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    A ruler measures spatial interval. A tick on a metronome measures an interval of time. Replace rulers with metronomes and you get the same result - both ruler and metronome (under idealized assumptions) are the same when both mutually at rest, irrespective of their history.

    If you replace your rulers with clocks, one of which travels .87c to destination, then waits, versus one walked over, the former will show an earlier time when they are compared. The spatial analog of the clock is an odometer. An odometer attached to the clock that was thrown would permanently show that it traveled less distance as well as less time.
     
  8. Jan 20, 2016 #7
    When that particle stops moving, will it's length (relative to mine) be the same as before it started moving?
     
  9. Jan 20, 2016 #8

    phinds

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    You should be asking if YOUR length will be the same when YOU stop moving. What makes you think that your belief that it is moving is any more valid than its belief that you are moving?
     
  10. Jan 20, 2016 #9
    I guess it doesn't really matter who's perpective we take, the particle or myself, is our length proportionally equal before and after that particle moved in CERN?
    Thanks
     
  11. Jan 20, 2016 #10
    Thanks for your answer, I understand that the recorded traveled distance would permanently show less distance traveled, but would the length of the clock and odometer themselves be contracted permanently from the perpective of an observer at rest, after the event once the odometer and clock stop moving?
     
  12. Jan 20, 2016 #11

    PAllen

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    I already answered that. No, they would not (under idealized assumptions). However, neither would the tick on the clock or a metronome interval be altered once they were mutually at rest again. The behavior to time and space is completely symmetric as long as you compare like with like.
     
  13. Jan 20, 2016 #12

    Orodruin

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    There is no such thing as "stop moving". This would imply that there is an objective absolute rest frame, which there is not. Lorentz contraction is not about something which physically happens to an object (the amount of contraction depends on the observer).
     
  14. Jan 20, 2016 #13
    Sorry about that let me rephrase:
    Once the odometer and clock are in the same rest frame as the "observer at rest"
     
  15. Jan 20, 2016 #14
    Thanks for your answer, would you be able to explain why? Or provide some proof of that statement?
    Thx
     
  16. Jan 21, 2016 #15

    Orodruin

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    But again this is the point - there is no observer who is objectively at rest, so you cannot use it as a qualifier. Two observers moving at different velocities will find an object to have different lengths. This is not about something which happens to the object, it is a result of how different observers percieve space and time.
     
  17. Jan 21, 2016 #16
    Again sorry about not being very clear, I didn't mean objectively at rest, I meant at rest from the observer's perspective.
    Thanks
     
  18. Jan 21, 2016 #17
    With respect to Bertrand's OP the rest frame referred to is more like the observers frame or Bobs frame.

    The process starts with Bob standing and holding rods X and Y at point A then he throws rod X at a relativistic velocity towards B where it hits a target and stops. Bob then walks from point A to point B, picks up rod X and once again stands with both rods in his hands. If we can stop the relativistic rod X at point B in a Born rigid manner without destroying point B and rod X we don't have to worry about how far point A is away from point B (and whether point A, Bob and rod Y get destroyed as well), the rods will be the same length at points A and B as observed by Bob.
     
  19. Jan 21, 2016 #18
    Hey Dale,
    After doing some research on born-rigid motion, this is what I understand it asks, correct me if I'm wrong :
    What acceleration profile is required by the far end of rod X (the end closer to point B) so that the distance between both ends of rod X remain constant in their proper frame?
     
  20. Jan 21, 2016 #19
    [QUOTE="Laurie K, post: 5351199, member: 578188" the rods will be the same length at points A and B as observed by Bob.[/QUOTE]

    Hi Laurie and thanks for your answer,
    I understand that this is what is believed to be true by most, however my real question is:
    Is there any explanation and/or proof of this statement?
    Thx
     
  21. Jan 21, 2016 #20

    phinds

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    You really need to let go of this. If length contraction were "real" or permanent, then everything in the universe would fluctuate wildly in size every instant because everything in the universe is constantly undergoing length contraction of differing amounts SIMULTANEOUSLY and for differing lengths of time. That's what I was trying to get you to see when I asked about your length.
     
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