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Proper time of a 'half-moving object'

  1. Jun 3, 2013 #1
    As I've red, we can measure the proper time of an object with a clock that is at rest with respect to the object. So, how would we measure the proper time of an object that is partially moving and partiall at rest. For instance if I'm moving my head and the rest of my body is at rest, how would this situation be measured? Or how would the rest frame of me in that 'situation' be defined?
     
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  3. Jun 3, 2013 #2

    PeterDonis

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    You wouldn't, because there is no such thing as "the" proper time of such an object. Different parts of the object that are in relative motion will have different proper times.

    It wouldn't, because there would be no such thing as a single "rest frame" that is yours. Your head would have one rest frame, and the rest of your body would have another.
     
  4. Jun 3, 2013 #3
    But shouldn't my body, as a whole, have its unique worldine/worldtube?
     
  5. Jun 3, 2013 #4

    Nugatory

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    Worldtube, yes. Worldline, no. Points have worldlines, objects have worldtubes.

    The worldtube is the collection of all the worldlines, one for each point of your body. Trace the path of a single point on your body through spacetime, and you'll have a single worldline; put all of these worldlines together like fibers in a bundle and you'll have a world tube.
     
  6. Jun 3, 2013 #5
    Yes, I got that. And thank you for the explanation. What I was referring to is the possible implication of the things DaleSpam mentioned. My opinion is that my body, and any other body that is 'partiall-moving' should have its rest frame because that 'allows' the sequence of timelike-events of that body. It sounds absurd to say that my body as a whole doesn't follow the transition from 'state A' to 'state B', which are timelike events.
     
  7. Jun 3, 2013 #6

    Dale

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    As was already mentioned it is an extended object so it has a worldtube, not a worldline. In this case the worldtube would look somewhat like a trumpet. There is no inertial coordinate system where a trumpet-shaped worldtube is entirely parallel to the time axis.
     
  8. Jun 3, 2013 #7

    Dale

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    Your opinion is incorrect.

    Draw a trumpet on a piece of paper. Then try to rotate the piece of paper such that each part of the trumpet is vertical.
     
  9. Jun 3, 2013 #8

    And yours is, of course, correct, because you are the omnipotent relativity expert.

    Why are you so hard on me, first closing the thread, and then brutally discrimnating what I just wrote. Can you rather explain how is this possible, since all I read is that we define proper time with the events on the worldtube, and we define it as the one measured from the rest frame..

    So in one sense you're saying that there exists a worldtube, but no rest frame. How would we know what's happening with the worldtube? And I don't mean any childish 'challenges' to you by this question, cause I'm aware and respect your knowledge, I just want the appropiate answer that makes sense.
     
  10. Jun 3, 2013 #9

    PAllen

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    To understand physics beyond simple classical physics, you need to expand your sense of what makes sense. Both relativity and quantum theory radically diverge from everyday physical intuition.

    Specifics:

    For a body, if the constituent parts are in relative motion (turning your head), then there is no rest frame for the object as a whole. Period. There are different frames in which different parts of your body are at rest. Each part of your body will have its own proper time. FYI, your head is older than your feet unless you've spend most of your life sleeping like a bat.
     
  11. Jun 3, 2013 #10
    On what basis would my head be older than my feet?
     
  12. Jun 3, 2013 #11

    Dale

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    Why? Because you ask a question, and get the same perfectly correct answer from multiple sources, and then insist on arguing about it based on nothing other than your preconceptions about how the universe should work. Why bother asking the question if you don't want the answer? It is obnoxious.

    The fact is that the universe doesn't conform to your preconceptions. The sooner you recognize that (as we all have had to do) the sooner you can make some actual progress.
     
  13. Jun 3, 2013 #12

    Dale

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    Yes. In order for there to be a single rest frame there must be a frame where all of the worldlines composing the worldtube are parallel to the time axis. Since the worldlines are not parallel to each other it is not possible for them to all be parallel to another line. This is straightforward geometry.

    We don't need a rest frame to know what is happening with the worldtube. We can calculate anything that we would like to calculate about the worldtube from any frame at all. That is the whole point of the first postulate of relativity.

    The answers you have received to your questions here on this forum are universally correct and make sense. They may not conform to your preconceptions, but they are correct.
     
  14. Jun 3, 2013 #13

    You're wrong, I'm open to make adjustments on the stuff you guys state, and I respect it. Maybe the problem is my lack of understanding, or mabye the problems is your definition about some things. When you're answering me, you simply state a number of definitions that you probably have in your head without thinking that I'm not in the same knowledge positon as you are. You're attitude is like everybody who's not familiar with relativity is inferior. Secondly, I'm from Croatia, so I put a lot of effort in using english to describe some complicated terms, or to understand some phrases that you guys use when typing on the forum. Again, I'm not some ignorant person who comes here to disrespect your words and knowledge, I want to learn about it, and if you're a polite forum member you will have the patience for me to get through this and understand it.

    So, back to the basic question, the object that I described has a worldtube, that's beyond doubt, right? How could we know what's happening inside it? Does the entity that we speak of have stages of its existence which are timelike events? Basically, what I've been searching for is the answers about the properties of that kind of object.
     
  15. Jun 3, 2013 #14

    PAllen

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    Mostly because it is at higher average elevation than your feet. Thus if there were a particle of uranium lodged in your head, and another in your foot, the one in your head would have emitted more alpha particles over your life (a direct measure of age). This is due to what is called gravitational time dilation. Sticking to special relativity, if you were in deep space and did a lot of activity with your hands, then your hands would be younger than your torso.
     
  16. Jun 3, 2013 #15
    So, all observers will agree about the sequence of events and properties of the worldtube?
     
  17. Jun 3, 2013 #16
    Oh, that's a relief. I thought you meant something else rather than the time dilation. I understand why the effect occurs then.
     
  18. Jun 3, 2013 #17

    Nugatory

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    If you remember that a rest frame is defined as a frame in which a point is at rest (when you hear someone speaking of "the rest frame of an object" they are using a convenient shortcut for the more precise "a frame in which every point of that object is at rest") it's clear that there is no such thing as "the rest frame of a partially moving object".

    However, that doesn't affect the time-like ordering of events in any meaningful way. Let's go back to your extended cat. It catches its tail in a door, a nerve impulse travels from its tail to its brain, and it yowls. Look at the world-line of the tip of the tail and of the point in the brain where the signal arrives; draw a slanting line between those two world lines to track the path of the nerve impulse to its brain. Every observer, regardless of their speed and reference frame or anything else, will agree that the tail-in-door event happened before the signal-reached-brain event. No observer will believe that these two events were simultaneous (that is, no observer will believe that the nerve impulse took no time to travel from tail to brain).
     
    Last edited: Jun 3, 2013
  19. Jun 3, 2013 #18

    Dale

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    All observers will agree about the properties of the worldtube because anything that can be termed a property of the worldtube is an invariant.

    Things that are not invariant are not properties of the worldtube but rather relationships between the worldtube and the reference frame. The sequence of causally disconnected events is one such thing. The sequence of causally disconnected events is not a property of the worldtube but a relationship between the worldtube and the observer's reference frame. Thus different observers will disagree about that.
     
  20. Jun 3, 2013 #19
    What would happen if the cat was, hypotethically, moving its tail (while the other parts are at relative rest), and changing color as a whole? Would all observers agree on that?
     
  21. Jun 3, 2013 #20
    Ok, that's one of the things that I've been seekin' clarification for... Good to know that we're on the same page.
     
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