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Proper accelerations and rigid bodies.

  1. Feb 7, 2007 #1
    "Proper" accelerations and rigid bodies.

    In Special Relativity, the term "proper" in front of a property means, as I understand it, the value of that property as measured by an observer with test equipment at rest relative to the object being measured. Thus "proper length" is the length determined by an observer in the same frame as the object and the "proper time" is the time according to a clock that is carried with the observer throughout the relevant period.

    However, in textbooks, articles and research papers in SR, I frequently come across the statement that "the "proper acceleration" of the rear end of an accelerated rigid rod must be greater than that of the front end." This is often illustrated by a Minkowski diagram showing two differently curved hyperbolae for the trajectories of the ends.

    This is very strange since it is clearly the accelerations of the rod ends estimated by an un-accelerated, inertial observer that are being represented - quite contrary to the established meaning of the term "proper". From consistency of meaning "proper acceleration" should refer to accelerations measured by co-moving observers.

    Since co-moving observers verify a constant "proper" length for the rod, and an observer at each end will record the same "proper" time, then by definition the "proper" acceleration must surely in fact be identical at each end of the rod, whether they are measured by inertial accelerometers or by reference to the background inertial frame.
     
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  3. Feb 7, 2007 #2

    ZapperZ

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    To make sure that this thread doesn't end up in a never-ending loop, please make exact citation to such sources so that others can check up and see if what you understood here is identical to what is claimed in these sources.

    Since this thread is in the same vein as a previously-closed thread, I will right out front tell everyone that wants to be involved in this that the Moderators will give it a very short leash. If we intend to repeat the same mess in that previous thread, this thread will be shut down and this topic will be banned for good.

    Zz.
     
  4. Feb 7, 2007 #3

    Ich

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    The meaning of "proper" in physics is the same as the german prefix "eigen-", meaning "belonging to". It is always an invariant quantity, belonging to the object in question independently of coordinate transforms. Thus proper acceleration of an observer means the Lorentz-Invariant acceleration that this observer actually measures locally, e.g. using a customary accelerometer. It never refers to coordinate accelerations in some specific system, "comoving" or not.
     
  5. Feb 7, 2007 #4
    Exactly my point : that that is how it's being mis-used !
     
  6. Feb 7, 2007 #5

    Meir Achuz

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    When there is acceleration, the rest systems of the two ends will not be the same. "Proper" does mean in the rest frame, but that will be at different times for the two ends if the time is the same in the system in which both are moving.
     
  7. Feb 7, 2007 #6
    I'm afraid it won't - the proper times will be the same unless by "if the time is the same" you mean clocks have been re-synchronised and therefore no longer carry proper time.
    Synchronisation and simultaneity are not the same thing. Simultaneity shifts "by itself" as a result of the motion, but synchronisation requires manual intervention. Proper time is defined by clock readings.
    So the proper time at one end is not what observer at the other end perceives, but what is actually elapsed on an in situ un-adjusted clock. It is that the clocks are unaffected by acceleration and maintain the same rate that causes each observer to claim a differing "simultaneous" time as the simultaneity shifts with acceleration, and thus arises the necessity for re-synchronising.
     
    Last edited: Feb 7, 2007
  8. Feb 7, 2007 #7

    pervect

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    If the four peer-reviewed papers by five authors cited in the last thread haven't convinced B. that he's wrong, what will? If showing B. the evidence, in the literature, that he's wrong doesn't convince him, I don't see what else we can reasonably do.

    Is there any particular person (preferably on this board) that B would listen to or is interested in hearing from? He's already blown off one professional in the field, one with many published papers.

    [add]
    For another citation, see for instance, Misner, Thorne, Wheeler, "Gravitation", pg 165 I've posted this before on another forum

    "At distances l away from his world line, strange things of dimensionless magnitude gl happen to his (ed: the accelerated observer's) lattice - e.g, the acceleration measured by accelerometers differs from g by a fractioanal amount gl (exercise. 6.7); also, clocks intially synchronized with the clock on his world line get out of step (tick at different rates) by a fractional amount ~gl (exercise 6.6).
     
    Last edited: Feb 7, 2007
  9. Feb 7, 2007 #8

    ZapperZ

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    To add to what pervect has mentioned, *I* am still waiting for the citations that I've asked for earlier. Please do not ignore this request.

    Zz.
     
  10. Feb 8, 2007 #9

    Ich

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    Well, I think that misuse is exactly what you do. I'll try to give a line of reasoning why the proper accelerations have to be different:
    In the t-x-diagram of an inertial observer A, the worldline of a particle with constant proper acceleration follows a defined hyberbola.
    It would follow the same (but translated) hyperbola if it started from a different point.
    So in A's frame, front and rear end are always at a constant distance.
    Inevitably, in every other frame, including a comoving one, the distance must be greater.
    Thus, in a comoving frame, the rocket appears longer.
    When the acceleration ceases, this distance can be identified with the proper length of the rocket.
    So the rocket actually grew longer. It cannot be 'rigid'.
     
  11. Feb 8, 2007 #10
    Correct, force does not propagate instantaneously in a solid, it propagates at the speed of sound. This reality has an effect on how different parts of a body are accelerated differently. For example, a rocket experiences different speeds during launch, with the rear (where the engine is) having a higher speed than the tip.

    "Unsubstantiated": ZZ asked you to produce proof that this is the interpretation as published in the references. Yo can scan the pages you are refering to and attach them to your next post in a JPEG form.
     
  12. Feb 8, 2007 #11
    Proof that what I am saying follows standard SR detail

    Just a few typical examples of the point I made in the #1st post about regarding the accelerations measured from a different inertial frame as "proper" accelerations of the moving system - in reversal of the accepted meaning of the term "proper"
    www.csupomona.edu/~ajm/professional/talks/relacc.ppt
    http://www.mathpages.com/home/kmath422/kmath422.htm
    http://arxiv.org/PS_cache/gr-qc/pdf/0301/0301050.pdf
    I can't however find the "four peer-reviewed papers" Pervect refers to - I can only find the Nicolic one which I wholeheartedly disagree with simply because it's faulty.


    The narrow point at issue here, following Meir Achuz's comment, concerns "proper time" and is easily clarified by paying attention to the following absolutely stock-standard features of Special Relativity.

    For inertial systems in constant relative v motion, each with lines of synchronised clocks laid out along the direction of motion, they each find that comparison shows that the clocks in the other relatively moving system are set out-of-synch but run at the same rate as each other.
    To be more specific using the train+platform for illustration, the platform observer regards the clocks toward the front of the train as increasingly set behind (in time) those at the back. Or in other words, the rear train clocks appear set ahead (in time) of the forward clocks.
    Reciprocally, the train rider sees the platform clocks out of synch in the same way - that is, the platform clocks at the far end as he approaches appear to be set ahead (in time) of the clocks at the "near" end that he would pass first.
    Neither observer claims that the other's clocks are running at different rates - merely that they have been set "out-of-synch".

    This is understood in SR as due to each observer's "lines of simultaneity" having become tilted with respect to the other at a specific angle for any given velocity.
    So although the platform clocks are perfectly synchronised to the guy on the platform, the train rider's judgement of "simultaneity" has tilted "upward" or forward in time ahead of him while dipping backward in time behind, so that "now" ahead of him is later in time than for the platform in that direction, and he therefore regards the clocks as set forward in time.

    Now what happens as the train accelerates from rest ? The "lines of simultaneity" at every point of the train start parallel and smoothly rotate so as to increasingly tilt forward in time towards the front and backwards in time towards the rear.
    Note especially that nothing physical happens at any given point - all that happens is that the simultaneity of other places has changed with respect to the given point.
    So nothing changes at the rear of the train except that events "later" in time at the front of the train have become simultaneous, whereas nothing has happened at the front of the train except that rear-train events "earlier" in time have become simultaneous.
    Since this is progressive during acceleration, it's as if the rear train rider sees time passing faster at the front and the front rider sees time passing slower at the rear.

    The train clocks themselves of course, have not changed and continue to show the same (proper) time as each other, as the "stationary" platform observer will verify.
    The rear train rider will, however, see as simultaneous with his clock "now", the reading of the front clock a bit later in time. The front rider perceives as simultaneous the rear clock as it was a bit earlier.

    It is thus quite incorrect to claim that the front clock "speeds up" or "goes faster" than the rear clock during acceleration.

    Additional Reason:
    For example, if the de-synchronisation was caused by, say, the front clock going faster, then when it is turned back during re-synchronisation at the end of acceleration period, the effect would be to restore agreement between the train clocks and the platform clocks - exactly contrary to accepted constant velocity SR.

    However, if as I am pointing out, the clocks continue to read the same (proper) time during acceleration, then when say, the front clock is turned back during re-synchronisation at the end of the acceleration period, it will become de-synchronised with the rear from the point of view of the platform observers, who will find it set behind (in time) the rear train clocks ---- exactly as constant velocity SR says it should be.
     
    Last edited: Feb 8, 2007
  13. Feb 8, 2007 #12

    Doc Al

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    That last statement is hardly consistent with "absolutely stock-standard" Special Relativity. To be clear: Track-frame observers make measurements that allow them to conclude that (1) the train clocks are out of synch, and that (2) the train clocks run slowly compared to their track-frame clocks. Of course, these effects are perfectly symmetric so the Train-frame observers draw the same conclusions about the track-frame clocks.

    This is standard relativity.
     
  14. Feb 9, 2007 #13

    Jorrie

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    Just to clarify what you are not agreeing to: is it this? (from slide 12 of the referenced presentation by Mallinckrodt, dealing with 'rigid rod' acceleration):
    I read it that the first item refers to coordinate accelerations, which differs from each other and also from the proper accelerations (the second item).
     
  15. Feb 9, 2007 #14
    To pick up on Doc Al's comment - It is actually stock-standard SR. Although I was trying hard to be as unambiguous as possible without long-windedness, I could have been more precise by including ".....running at different rates from each other - merely that they.....", which is what I meant. That is, all the train clocks run at the same rate but appear set progressively out-of-synch.

    Jorrie - I think it's clear that both refer to what he means by proper accelerations as depicted by differently shaped hyperbolae in the diagram (eg. see 9). I agree with you they are actually coordinate accelerations perceived from an inertial frame and the way he elides from just "acceleration" to "proper acceleration" in referring to the same thing is just what one has to watch out for.
     
    Last edited: Feb 9, 2007
  16. Feb 9, 2007 #15

    ZapperZ

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    Remember what you said:

    I would loosely accept those as "articles" (I would prefer something more valid than those that are used commonly in physics). However, they are certainly not textbooks and research papers, unless you think anything appearing in ArXiv are automatically "research papers". Please cite actual physics textbooks and actual peer-reviewed physics papers to back up your claim before you proceed any further.

    Remember the short leash that I'm giving this thread.

    Zz.
     
  17. Feb 11, 2007 #16

    pervect

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    Well, google scholar finds:
    http://www.iop.org/EJ/article/0143-0807/24/2/361/ej3261.pdf

    with the same title and by the same authors. (And I've seen the name Tartaglia before, he's done some papers that I like on the rotating disk).

    so it would seem that this preprint was actually published, in the European Journal of physics.

    As far as I know, this is a reputable peer-reviewed journal. I'm afraid I can't confirm that the arxiv paper is the same as the published paper, though I see no reason to expect any differences.

    Oddly enough, (or perhaps not so oddly), this paper comes to the same conclusion that Nikolic's paper,

    http://arxiv.org/abs/physics/9810017

    also published in a peer reviewed journal (Am. J of physics)
    http://scitation.aip.org/getabs/ser...00067000011001007000001&idtype=cvips&gifs=yes

    and to the same conclusion that MTW does in "Gravitation", namely that the proper acceleration is different at two ends of a "long" rod, and that two observers, who acclerate with the same proper acceleration, will increase the distance between them, so that a string connecting them will break.

    There were a couple of more papers cited in Nikolic's paper as well, which also came to similar conclusions.

    Having seen the number of papers which say that the string does break in the Bell spaceship paradox, perhaps we should now ask for papers similarly published in peer reviewed journals that show that the string does not break?
     
  18. Feb 11, 2007 #17
    Well that is obvious, since that is a characteristic of a Minkowski space-time. Except, of course, for the trivial case where the observers start from the same space-time location. Note that it is not just the distance that gets affected also the times go out of phase.

    In a way one you could argue, but obviously not prove, that the origin of inertia is exactly the change in distance and the shift in times inside any non-zero length object when it undergoes acceleration.

    Also consider the situation where all objects in a Minkowski space-time are at relative rest with each other. If all objects accelerate at the same time (Einstein synchronized) then distances do increase and clocks will become desynchronized.
    A kind of expansion of the universe. :wink:

    Isn't relativity a wonderful thing? :smile:
     
    Last edited: Feb 11, 2007
  19. Feb 11, 2007 #18


    If you read between the lines, it appears that Boustrophedon believes that force propagates instantaneously (with infinite speed), which is the only way to explain why both ends of the rod would have the same acceleration profile as outlined in the OP. Of course, the exact opposite is the truth.
     
    Last edited: Feb 11, 2007
  20. Feb 12, 2007 #19

    Jorrie

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    Does this mean that you still hold the opinion that the overriding reason why the two ends of a length-wise accelerated rod have different proper accelerations is caused by the finite speed of sound in the rod (or the finite speed of propagation of the force applied at one end)?

    My understanding is that the mainstream literature (as adequately quoted by Pervect and others) disagrees with your view (if it is in fact how you see it) and that the difference in proper acceleration at the two ends is a purely relativistic effect, valid even if the rod would be "perfectly rigid" (or accelerated as Born-rigid for that matter).

    I am asking this because I think it is quite important to clear this one, perhaps by an answer from a science advisor. Robust debate on it is fine, but so far it has been difficult to find the real answer.
     
    Last edited: Feb 12, 2007
  21. Feb 12, 2007 #20
    In addition to Pervect's helpful tracing of the Euro.J.of Phys. reference, I could also refer to Wolfgang Rindler's "Essential Relativity" section 3.8 or A.P.French & E.F.Taylor "Limitation on proper length in SR" Am.J.Phys. 51 p.890 (1983) or J.E.Romain "A Geometrical Approach to Relativistic Paradoxes" Am.J.Phys. 31 p.580 (1963).

    However, Pervect's assertion :
    - is factually incorrect. The quote he used earlier supports no such particular construction, since it does not even involve a second observer, let alone any connecting string. The quote is in fact highly ambiguous and almost certainly wrong if taken literally. The comments refer to the observer's "lattice" when of course no such lattice ( of rods & synchronised clocks etc.) is feasible during acceleration.

    Since Pervect has introduced the so-called "Bell spaceship problem" I should point out that the falsity of Bell's claim follows inevitably from the demonstration that both time dilation and length "contraction" effects follow in a elementary way from the divergence in simultaneity without any "extra" assumptions that a moving rod or clock is any different from a "stationary" one.
    It is easy to see that the observers disagree about the length of a rod simply and solely because they disagree about whether each other recorded the ends simultaneously. This is a non-physical, purely kinematical effect and cannot possibly give rise to any "stresses", "forces", "tensions" or "string-breaking". The same causes ( differing simultaneity ) would give the same effects ( differing length estimates ) if the ends of the rod were not even connected.

    As I showed earlier, the shift in simultaneity that accompanies acceleration cannot affect the clocks themselves ( as otherwise the same clock would be read as two different times by the two momentarily adjacent observers ). It is after acceleration ceases that, for instance, the forward obs. turns his clock back to synchronise with his "tilted" perspective of the rear clock ( and rear obs.'s similar but contrary shift in perspective of the front clock ) thus de-synchronising them from POV of obs. who had remained unaccelerated. The differently synchronised clocks now conform to the different simultaneity in each frame and observers in either frame will measure lengths in the other frame to be shorter.
    In SR the diminishing measurements of the length of an accelerated rod are not due to any change in rod length but actually due to a growing disparity between the simultaneity of each frame.

    Once it is realised that "constant to&fro speed of light" >>> "shifted or non-parallel simultaneity between relatively moving inertial frames" >>> "each frame sees the other's 'synchronised' clocks as desynchronised >>> "moving clocks appear to run at a retarded rate" + "moving lengths appear shorter".....SR is seen as elegant and obvious as Einstein is justly famous for making it.

    Addendum:
    Nakrusil seems to be bogged down in consideration of inertial forces, which are not relevant. It is invariably implicit in such thought experiments that accelerations are sufficiently gentle and/or evenly distributed that they can be rendered negligable and disregarded.
    It might help to read the lines themselves instead of looking for messages between them !

    Jorrie - Why do you ask if I "still" hold an opinion that I have never held, nor would ever give
    the slightest consideration to.
     
    Last edited: Feb 12, 2007
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