Length contraction: Is it permanent?

  • #1
Bertrand Boucquillon
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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.
 

Answers and Replies

  • #2
Dale
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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.
 
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  • #3
phinds
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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.
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?
 
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  • #4
Ibix
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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.
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.
 
  • #5
Bertrand Boucquillon
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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.
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.
 
  • #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.
 
  • #7
Bertrand Boucquillon
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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?
When that particle stops moving, will it's length (relative to mine) be the same as before it started moving?
 
  • #8
phinds
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When that particle stops moving, will it's length (relative to mine) be the same as before it started moving?
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?
 
  • #9
Bertrand Boucquillon
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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?
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
 
  • #10
Bertrand Boucquillon
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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.
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?
 
  • #11
PAllen
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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?
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.
 
  • #12
Orodruin
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once the odometer and clock stop moving?
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).
 
  • #13
Bertrand Boucquillon
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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).
Sorry about that let me rephrase:
Once the odometer and clock are in the same rest frame as the "observer at rest"
 
  • #14
Bertrand Boucquillon
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I already answered that. No, they would not (under idealized assumptions)..
Thanks for your answer, would you be able to explain why? Or provide some proof of that statement?
Thx
 
  • #15
Orodruin
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Sorry about that let me rephrase:
Once the odometer and clock are in the same rest frame as the "observer at rest"
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.
 
  • #16
Bertrand Boucquillon
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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.
Again sorry about not being very clear, I didn't mean objectively at rest, I meant at rest from the observer's perspective.
Thanks
 
  • #17
Laurie K
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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.
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.
 
  • #18
Bertrand Boucquillon
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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.
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?
 
  • #19
Bertrand Boucquillon
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[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
 
  • #20
phinds
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[QUOTE="Laurie K, post: 5351199, member: 578188" the rods will be the same length at points A and B as observed by Bob.
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
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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  • #21
Ibix
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If there were any lasting consequence of length contraction then every particle would carry an imprint of the past history of its motion. Atoms that contain particles that had been through nova explosions would be shortened in one direction (or whatever), while ones that were formed by radioactive decay here on Earth wouldn't. I'm sure this would have interesting (and observable!) consequences for the structure of molecules.
 
  • #22
Bertrand Boucquillon
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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.

Hey phinds thanks for your answer, I completely agree with you, but what if everything in space does fluctuate in size but it would be difficult to observe because every observer and their surroundings within a inertial reference frame would fluctuate in size proportionally with respect to everything else that is within that same reference frame?
Sorry if my questions seem annoying but please bear with me!
Thanks
 
  • #23
phinds
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Hey phinds thanks for your answer, I completely agree with you, but what if everything in space does fluctuate in size but it would be difficult to observe because every observer and their surroundings within a inertial reference frame would fluctuate in size proportionally with respect to everything else that is within that same reference frame?
Sorry if my questions seem annoying but please bear with me!
Thanks
You're still not getting it. They would have to change by differing amounts simultaneously. They would have to BE different lengths simultaneously. Do you really think that's possible?
 
  • #24
Dale
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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"
Yes, I think you are correct. I wouldn't know how to prove that. But if you are given Born rigid motion then the proof is essentially just "by definition"
 
  • #25
Bertrand Boucquillon
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If there were any lasting consequence of length contraction then every particle would carry an imprint of the past history of its motion. Atoms that contain particles that had been through nova explosions would be shortened in one direction (or whatever), while ones that were formed by radioactive decay here on Earth wouldn't. I'm sure this would have interesting (and observable!) consequences for the structure of molecules.

Yes particles would carry an imprint of the past history of their motion, and yes the particles from the exploding nova would be shorter than the ones on earth but how would we know? The only way to observe it would be to go get some of those particles around that exploding nova and come back to earth to compare them to the one formed by radioactive decay here on earth!
 
  • #26
Dale
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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?
Essentially, yes. So since the distance is constant in the proper frame (momentarily co moving inertial frame), once those frames are the same then the distances are the same by definition.
 
  • #27
Ibix
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Yes particles would carry an imprint of the past history of their motion, and yes the particles from the exploding nova would be shorter than the ones on earth but how would we know? The only way to observe it would be to go get some of those particles around that exploding nova and come back to earth to compare them to the one formed by radioactive decay here on earth!
The Sun, of course, is not a first generation star. Much of the solar system is reconstituted from bits that were parts of other stars that exploded. Wikipedia, for example, says "a high abundance of heavy elements in the Solar System, such as gold and uranium...could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive second-generation star." [my bold]. In other words, we'd see particles bearing the imprint of previous high speed movement right here on Earth. I'm not aware of us ever having done so (probably because the concept makes no sense, as phinds points out).

Length contraction is closely related to the observation that the cross-section of a cylinder looks like a circle when it is end-on to you and elliptical when it is off at an angle to you. It'll look like a circle again if you look at it end-on again. Expecting there to be after-effects from not looking at it end-on (unless you squashed it when you were rotating it - hence my first post) would be daft.
 
  • #28
Orodruin
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Yes particles would carry an imprint of the past history of their motion, and yes the particles from the exploding nova would be shorter than the ones on earth but how would we know? The only way to observe it would be to go get some of those particles around that exploding nova and come back to earth to compare them to the one formed by radioactive decay here on earth!
This really does not make any sense. Where do you think the heavier elements in the solar system have originated. And as I have told you repeatedly in this thread, length contraction is not about an object changing its physical properties, it is about how the object is perceived by different observers who are in relative motion.
 
  • #29
phinds
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... as I have told you repeatedly in this thread, length contraction is not about an object changing its physical properties, it is about how the object is perceived by different observers who are in relative motion.
I have also pointed this out several times. This thread is getting tedious.
 
  • #30
Bertrand Boucquillon
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This really does not make any sense. Where do you think the heavier elements in the solar system have originated. And as I have told you repeatedly in this thread, length contraction is not about an object changing its physical properties, it is about how the object is perceived by different observers who are in relative motion.

Hey thanks for your answer.
I'm not looking to argue what the sun is made of, and trust me I'm not trying to prove that you guys or physicists in general are wrong. Please be patient with me because I take this thread very seriously(I've been ignoring my customers for the past couple days just to focus on my research), I do hope you guys can keep an open mind about things and not get upset just because I'm questioning what is believed by the community.
Like I said repeatedly before I understand that everybody believes that length contraction doesn't change the physical properties and that it is about perception, but did you guys just accept it because it's what has been said by scientists 50 years ago or did you research the proof? And please don't dodge the question with a vague answer about what we would observe because what humans can observe is limited.
As far as I know the physicists that asked the question about length contraction are Dewan, Beran and Bell in the Bell's spaceship paradox and it looks like they only arrived to their conclusions through deductions that don't cover all the angles.
Like I said before please don't feed me some generic answer or some previously said statement because that is irrelevant to me, if you can't give me a proof it's all good but just let me know so I don't keep looking for an answer that can't be verified.

Like Einstein said: "Common sense is what tells us the earth is flat"
 
  • #31
Ibix
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I'm not looking to argue what the sun is made of
Neither are we. We are just pointing out that everything around you is made up of a mix of matter that has travelled at relativistic speeds relative to its current state and matter that has not. Your idea would have physical consequences that we don't see. It's a non-starter I'm afraid.

Edit: not to mention, what does an observer co-moving with the moving rod see? According to Bob the rod accelerated from rest. According to this new observer the rod decelerated to rest. Should it be showing these after-effects of length contraction (because it has decelerated according to the new observer) or not (because it hasn't yet decelerated according to Bob)?

Like I said repeatedly before I understand that everybody believes that length contraction doesn't change the physical properties and that it is about perception, but did you guys just accept it because it's what has been said by scientists 50 years ago or did you research the proof?
Please see my previous paragraph. And my previous post. And the post by Orodruin that you quoted...
 
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  • #32
Orodruin
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Please be patient with me because I take this thread very seriously(I've been ignoring my customers for the past couple days just to focus on my research), I do hope you guys can keep an open mind about things and not get upset just because I'm questioning what is believed by the community.
There is an overwhelming amount of experimental evidence for the consequences of SR and GR. So much in fact that any description even attempting to build further must include them. This quoted text rings large warning bells to me as it seems to suggest you do not "believe" in the effects of relativity and therefore has started to work on your own theory. This is doomed to fail. The effects are well established experimental facts. Also note that Physics Forums, while encouraging asking questions to learn and understand, forbids the discussion of personal theories and speculation.

The original question has been answered several times over. I am therefore closing this thread.
 

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