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Do rotating frames have planes of simultaneity?

  1. Jul 24, 2013 #1
    It's a pretty straight-forward question, and it got me confused since most articles on the internet mention planes of simultaneity in the context of inertial frames. So if rotating frames also have planes of simultaneity, what SR says about it and how does it differ from the planes of simultaneity of inertial frames?

    Regards
     
  2. jcsd
  3. Jul 24, 2013 #2

    Ben Niehoff

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    No, they don't.

    If you take a collection of rotating observers, they are accelerating relative to one another, so the notions of simultaneity between nearby observers do not agree.
     
  4. Jul 24, 2013 #3

    Dale

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    I would say it a little differently. Simultaneity is a convention and non inertial observers (including rotating ones) don not have a standard convention. But you certainly are free to adopt a non-standard convention for rotating observers, you just have to be explicit in what your convention is since nobody will know it.
     
  5. Jul 24, 2013 #4

    WannabeNewton

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  6. Jul 24, 2013 #5
    Interesting. So what would happen in a hypotethical situation where, for instance a ball moves with a constant speed, then starts rotating and then gets back to moving with a constant speed.
    Would the scenario go something like this 'has a plane of simultaneity - doesn't have a plane of simultaneity - has a plane of simultaneity' in each of those 3 states of motion.

    P.S. Thq Wannabe Newton on the link, I'm reading it now!
     
  7. Jul 24, 2013 #6

    WannabeNewton

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    Are you talking about a geometric "time slice" when you say plane of simultaneity? In other words, if I have a family of observers whose worldlines cover all of Minkowski space-time, do these observers define a "time slice" of Minkowski space-time at each instant of time as read by them? Is that what you are asking?
     
  8. Jul 24, 2013 #7
    Yes, exactly that. So I wonder why rotating frames do not have at least some 'point of view' on the events around them, at least some time slice that you refered to. After all, rotating bodies are simultaneous with themselves, as trivial as it sounds, so I wonder from which frame can that fact be deduced since their own frame 'doesn't exist' in this sense.
     
  9. Jul 24, 2013 #8

    Dale

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    The ball is non-inertial so there is no established convention for simultaneity with respect to the ball, but you are free to define one.
     
  10. Jul 25, 2013 #9

    DrGreg

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    It may sound trivial, but it's not true. Or rather, it may or may not be true depending on what simultaneity convention you choose to use.
     
  11. Jul 25, 2013 #10

    WannabeNewton

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    There's a mathematical reason for why a family of observers rotating relative to one another cannot foliate space-time into a family of "time slices" using their worldlines, unlike e.g. a family of inertial observers. This is what Ben was referring to essentially. So yeah if by planes of simultaneity you meant a one-parameter family of "time slices" of space-time orthogonal to the worldlines of the rotating observers in the family then this fails to exist for a mathematical reason (it's easy to see why it fails intuitively and only slightly harder to prove mathematically).
     
  12. Jul 26, 2013 #11
    What exactly do you mean by simultaneity convention? Something like 'whatever you say about this rotating body is true'? After all, isn't being simultaneous with itself necessary so we can speak about the rotating body, or the set of simultaneous points that together rotate? How to explain that?
     
  13. Jul 26, 2013 #12

    WannabeNewton

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  14. Jul 26, 2013 #13
    Thank you for the articles WBN, I've red them but I still don't understand why rotating frames don't at least have a local meaning of simultaneity. By that I mean 'all points taken at once' viewed from their own frame. The previous example you mentioned about the common sense that leads to conclusion that rotating frames don't have simultaneity hyperplanes seems really good and valid, but how can a rotational entity not be simultaneous with itself? I don't understand how this is a matter of conveniton, since we couldn't even define a rotating object without refering to all of its points simultaneously from some frame, in this case its own frame. I hope you see my issue.
     
  15. Jul 26, 2013 #14

    WannabeNewton

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    The Einstein synchronicity convention is an equivalence relation so that in particular any clock is synchronized with itself. This convention is the standard convention for inertial frames; using this convention we can, if we wish to, build global "time slices" (simultaneity slices or planes of simultaneity) of Minkowski space-time using a canonical global time-function. For non-inertial frames you have to define what convention you are using because there is no standard. The reflexivity found in the Einstein convention may or may not carry over, which is what I think DrGreg was referring to.
     
  16. Jul 26, 2013 #15

    Hey, that makes it a little easier to understand. But what would the concrete situation be like in which a rotated object isnt simultaneous with itself? How would we measure it, or even know that's rotating?
     
  17. Jul 26, 2013 #16

    WannabeNewton

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    I'm not sure if it's possible to find a convention in which a clock isn't synchronized with itself (it doesn't make any sense to me physically). I was just trying to interpret what DrGreg meant in his reply to your post #7. It's hard to intepret what you mean by "object isn't simultaneous with itself" because simultaneity involves different events in space-time as represented in a given frame.
     
  18. Jul 26, 2013 #17
    I mean the same as you. By being simultaneous with itself I mean the same as having a clock that is synchronized with itself. So it doesn't make sense to me, since if we had a clock on a rotating object it would measure the duration of the rotation and for that it seems the clock should be in sync with itself. That's my quasi-logical opinion. I hope Dr Greg or DaleSpam could explain this situation.
     
  19. Jul 26, 2013 #18

    Dale

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    I don't know why you think I can explain something you said. I don't think that the phrase "bodies are simultaneous with themselves" has any meaning. Simultaneity is a relationship between events, not bodies.

    My point is and remains that for any non-inertial object there is no standard convention of simultaneity, but you can certainly define one. You just have to tell people explicitly what convention you have chosen because otherwise they won't know.

    You have seemed to completely ignore this point.
     
  20. Jul 26, 2013 #19

    Nugatory

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    "Simultaneous with itself" isn't an especially clear or precise term.. I THINK what you're trying to say is that within a sufficiently small region around the clock and with observers who are at more or less at rest relative to the clock, there's a natural simultaneity convention that we can use. My neighbor and I don't have to employ elaborate relativistic calculations allowing for the rotation and gravitational effects of the earth before saying things like "I'll be done mowing my lawn in an hour".

    However, that local sense of time is just that: local. It cannot be used to define the planes of simultaneity that this thread is about.

    It's not not even all that useful for measuring "the duration of the rotation" as you suggest above: First you have to define the start and the end of a rotation and you can't do that locally. (Consider that the duration, as measured by this clock, of one rotation of the earth about its axis is different in the non-inertial frame in which the sun and the earth are at rest, and the non-inertial frame in which the earth is rotating at the origin while the sun orbits the earth once a year).
     
  21. Jul 26, 2013 #20
    You're close to what I'm trying to say, and thanks for your explanation of some terms. I know simultaneous with itself doesn't have a clear meaning, what I mean was really if we take a non-inertial frame and analyze it, we can measure at least some sort of local time in that frame.. That's the issue. How to define a non-inertial frame if not by taking a set of simultaneous points that are rotating/accelerating?
     
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