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Clock postulate and differential aging

  1. Jan 20, 2010 #1
    In a recent thread about differential aging in the archetypal twin scenario, I suggested that the periods of oscillators are affected by accelerations, or in other words that a clock's tick rate is affected by changes in its speed.

    This statement was disagreed with by some, who said that it was contradicted by the clock hypothesis or postulate.

    However, the clock postulate just says that the rate of the earthbound clock is always related to the rate of the travelling clock by (1-v2)-1/2 .

    From the above mentioned thread, when asked for an equation relating tick rate and acceleration, I replied:

    To which DaleSpam replied:

    Note that v is speed.

    Are we in agreement then? Has it been straightened out?
     
  2. jcsd
  3. Jan 20, 2010 #2
    No.

    I had already provided an example:
    2 twin scenatio with identical acceleration, with the same distance where second twin is accelerated, but with 2 different "arms" - total travel distance where the accelerated twin is moving without acceleration

    Based on your hypotesis, age difference will be the same in both cases (as acceleration is identical), while it is not (in a case with a longer arm there is more difference)
     
  4. Jan 20, 2010 #3

    Dale

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    I believe so, yes. We use the same formula for making predictions about clock rates and elapsed time. Everything else is either a philosophical argument about alternative interpretations of the same equations or a semantic argument about the best way to translate the math into English.
     
  5. Jan 20, 2010 #4
    "To translate the math into English..." Let me finish that for yah... "Which is basically impossible, and totally impossible right now for SQM."

    :)

    It's true, but it does make life a little difficult sometimes.
     
  6. Jan 20, 2010 #5

    bcrowell

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    For a couple of good discussions of this, see p. 9 of Dieks http://www.phys.uu.nl/igg/dieks/rotation.pdf [Broken] and this page by Baez http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html . I find Dieks' argument very persuasive and physically enlightening; you don't need a separate postulate, because it follows directly from SR. Both Baez and Dieks agree that this statement of clocks holds iff the clocks are small enough (infinitesimally small).
     
    Last edited by a moderator: May 4, 2017
  7. Jan 20, 2010 #6
    I have seen in many places and accept that the travelling twin clock slows with respect to the earth clock caused by relativity.
    Can anyone explain or point to an explanation for how this mechanism works.
     
  8. Jan 20, 2010 #7
    Thanks DaleSpam. I thought that my original statement that precipitated the confusion was really pretty innocuous and not very informative -- and, I'm glad you've helped confirm that. :smile:

    And I remain absolutely amazed and fascinated by the physical phenomenon of differential aging.
     
  9. Jan 20, 2010 #8
    I agree that if you run one clock longer at the higher speed, even though the acceleration histories are otherwise identical, then that clock will accumulate less time.

    Neither your scenario nor the clock postulate-hypothesis contradict the statement that changes in speed (accelerations) affect the periods of oscillators (the tick rates of clocks).
     
  10. Jan 20, 2010 #9

    Dale

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    I think part of the original problem is the wording of statements like this. All changes in speed involve acceleration, but not all accelerations involve changes in speed. They are not always equivalent.

    I think Baez said it well in the link bcrowell provided above, and I would highly recommend a careful reading of it. But in the end, if we use the same equation then in my book we agree on everything important.
     
  11. Jan 20, 2010 #10

    Dale

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  12. Jan 20, 2010 #11

    bcrowell

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    The only thing that makes me want to point people to Dieks in addition to Baez is that Dieks explains how it's not necessary to make it a separate postulate. It follows logically from the usual postulates of SR.
     
  13. Jan 20, 2010 #12

    Dale

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    I am still reading that one, but it looks good so far.
     
  14. Jan 21, 2010 #13

    russ_watters

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    If the clocks accumulate less time for longer periods at high speed, then the acceleration has to cause a permanent change in speed, not just a change in speed while the clock is accelerating. Is that what you mean, because your wording doesn't imply that to me.
     
  15. Jan 21, 2010 #14
    Sure that's a true statement, but incomplete, since the following statement is just as true:

    When the velocity (relative to the observer) of the travelling clock changes (when the clock is not accelerated), then its tick rate (wrt the observer) changes.

    So while your statement is perfectly true, it would be just as true if the clock doesn't accelerate, and for the same reason.

    So a more precise statement would be: If the relative velocity of a clock changes (whether it accelerates or not), then its tick rate (wrt the observer) changes.

    As an example, in the start of the twins paradox, the ship accelerates away from earth. The tick rate of earth's clock (the periods of oscillations of earth's clock) changed relative to the ship observer due to the change in the relative velocity of earth's clock relative to the ship. Would you say that the tick rate of earth's clock was affected by the ship's acceleration?
     
    Last edited by a moderator: Jan 21, 2010
  16. Jan 21, 2010 #15
    Hmmm... I suppose that would depend on which frame of reference you looked at. If you were born on that ship during its accelerating period you'd percieve the tr on earth to be faster relative to your own clock. From the point of view of a third observer at rest relative to the ship and Earth, what would they percieve? Wouldn't the change in tick rate be purely a matter of which Intertial Frame you happen to be in? A third observer is still going to agree on the order of events and the way they unfold will be consistant, regardless of which tr you decide is valid. They are, after all... relative, aren't they?
     
  17. Jan 21, 2010 #16
    Hi DaleSpam,
    Good reference. I am quite familiar with the different versions of the diagram shown in that reference.

    But I have a problem.
    When the earthbound twin is the observer (presumably inertial) I plot events for the earthbound twin using the orthagonal axes and for the astrounat twin plot events using rotated axes. That's what I see shown in the diagram.

    So far so good.

    But the skeptic wants to see corroboration. The skeptic asks "What about when the astronaut is the observer?" So I draw the diagram with the astonaut as the observer. So then the astronaut gets events ploted using the orthagonal axes and the earthbound twin gets events ploted using the rotated axes. The diagram looks the same but the people and agings are reversed.

    I get a parodox.
     
  18. Jan 21, 2010 #17

    atyy

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    But the time read by an ideal accelerated clock surely it requires an additional definition, as Dieks's limit, ie. the proper time. As I understand it, the clock hypothesis is a definition of an ideal clock.
     
  19. Jan 21, 2010 #18
    You're missing something. In the case of the astronaut both observers on earth and "the rocket ship" agree that the rocket is accellerating in relation to a (relatively) stationary Earth. If you're going to invert the experiment the way you did, then you have to take into account that both Earthbound observers and the Astronaut need to "agree" that the EARTH to be accelerating away from the astronaut. It's one of those "lost in translation" issues between the math and the thought experiment.

    What matters is what is under acceleration relative to the Intertial Frames you're comparing it to (returning to in the case of the astronaut, to Earth). The body under acceleration experiences the effect, and in this thought experiment we can't equivocate "velocity and acceleration", because an astronaut MUST undergo a period of acceleration and then braking in relation to his initial Frame.
     
  20. Jan 21, 2010 #19
    Thanks for your reply Frame Dragger. I am familiar with the arguments you present. But I was talking about using a Minkowski Diagram to describe the the action when the astronaut is the observer. What do your arguments have to do with that? I'm asking how one draws a Minkowski Diagram for the Twins problem when the astronaut is the observer.
     
  21. Jan 21, 2010 #20
    That's easy... http://en.wikipedia.org/wiki/Twin_paradox Halfway down this issue is addressed. Here is the relevant portion...

    Check the page for the equations, I can't copy-paste them, and I'm not writing them out here when I can link lol.
     
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