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Can time be stopped in special relativity?

  1. May 26, 2013 #1
    By the title of the topic I don't mean stopped in the sense when you're travelling at the speed of light.

    My question is very closely related to the Andromeda paradox and its implications.
    Consider two observers that are both in rest with some state X of the Andromeda galaxy. They have the same plane of simultaneity since they have the same state of motion.

    For instance, in their present they both have 'the decision of the aliens to invade Earth'.
    Now consider the situation in which one observer starts moving away from the Andromeda galaxy and another stays at rest with it. For the observer that is at rest we may say that the 'time on Andromeda passes' and he will have the next situation (the next timelike event) as present, the loading of the aliens in the spaceship.

    Since the plane of simultaneity for the observer who is moving away moves, he will have to have the event that preceded the loading of the aliens in his present frame. That is the event 'the decision of the aliens to invade Earth'.

    Can we say that for the observer who was first at rest, but then started moving away from the galaxy, the time, or the sequence of events stopped? Does this make sense or is there a solution for this derived paradox?

    I look forward to your answers.
     
  2. jcsd
  3. May 26, 2013 #2
    Did you not just get this kind of question answered?

    Of course 'time can't be stopped'.....not by us anyway.

    I see no paradox.
     
  4. May 26, 2013 #3
    Yes, I did, but I think I misunderstood some parts and derived a false assumption about it. So I need an expert to disprove this :D
     
  5. May 26, 2013 #4

    Nugatory

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    Staff: Mentor

    That does not make sense.
    Time certainly has not stopped: all the clocks everywhere in the universe are still ticking, radioactive materials are still decaying, planets are swinging around suns in their orbits, the Cepheid variable stars are still pulsing, ....

    All that's happened is that the moving observer has decided to change the convention he uses to define the bolded words in "What going on in the Andromeda galaxy right now" - and he doesn't even need to be moving himself to do that.

    You might want to search around the internet for "Rindler coordinates" and "Rindler horizon". These describe a very similar situation to what you're describing: A continuously accelerating observer is continuously changing his speed and therefore his planes of simultaneity (assuming he uses a coordinate system in which he is at rest - and remember, that is a choice, he doesn't have to if he doesn't want to!); it turns out that the planes of simultaneity are changing in such a way that there's a point behind him where they intersect. That doesn't mean that time isn't advancing at that point, it just means that the observer is using an unhelpful definition of "at the same time".

    (Note 1: The Rindler horizon does have physical significance in that it describes a point beyond which even a light signal will not be able to reach an accelerating observer. But that has nothing to do with "time stopping" there or any such nonsense. I could do the same calculation using coordinates in which the ship is accelerating past me at rest, and I would get the same predictions for which light beams will or will not reach the ship - even though none of the planes of simultaneity are changing and moving, and the time coordinate is ticking predictably forward at every point in the universe just as your intuition says it should.)

    (Note 2: Someone (DaleSpam?) said in the earlier Andromeda paradox thread not to attach too much meaning to the phrase "right now in another galaxy". That was good advice then, and it's still good advice.)
     
    Last edited: May 26, 2013
  6. May 26, 2013 #5
    Not just stopped, but Andromeda time can also go backwards. If we accept that relative simultaneity is physically real (I don't, but someone might) then it's hard to avoid the conclusion that Andromeda time goes backwards for the observer that accelerates away from Andromeda.

    If we don't take relative simultaneity as physically real, then we have a workaround for this problem. But why even bother to calculate something that we don't believe to be physically real in the first place?

    That is certainly a good advice. And "A long time ago in a galaxy far, far away...." is equally flawed, unless it's really long time ago :wink:
     
  7. May 27, 2013 #6

    It may go backwards relative to the observer who is moving towards the Andromeda, but I don't see how it can go backwards to the observer that is first at rest and then moves away.

    Doesn't it make sense that time passes in the same direction for all reference frames, just that they have the different events in their plane of simultaneity depending on their state of motion?
     
  8. May 27, 2013 #7

    Nugatory

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    Staff: Mentor

    Yes, but in the situation you described, your observer is changing his speed and hence his plane of simultaneity.

    A few posts back in this thread, I suggested that you try searching for "Rindler coordinates". Have you?
     
  9. May 27, 2013 #8
    I did but the only articles I found had little to do with the concrete example I asked about... So time cannot be stopped no matter what the motion of the observer is. Could you please describe what would happen with the planes of simultaneity of the observers that I mentioned in my first post, so I could develop a better understanding of this situation?
     
  10. May 27, 2013 #9
    Hello durant,

    You can see in first image that red events on andromeda occurs for the observer before start travelling. At some point observer start traveling and its seems that the same red events are reoccurring for the obeserver on andromeda. This seems a paradox.
    Image01.jpg


    But, its isn't. Please look at below image.
    Image02.jpg

    It arranges the Lines of simultaneity of observer frame such that red events occurring on andromeda is occurs ones and only one for that observer.
    This solution suggested in this paper http://arxiv.org/abs/gr-qc/0104077

    Before, start travelling LoS of observer frame are horizontal inside light cone. And after start travelling LoS of observer frame are skewed at some degree inside light cone. We can draw a LoS of the combined reference frame which is indicated as blue line. Outside of light cone all the LoS of the combined reference frame are parallel to the blue line.
     
  11. May 27, 2013 #10
    So the events really won't re-occur?
     
  12. May 27, 2013 #11
    Yes,
    Because, that red events occurred at andromeda are outside of the light cone on "travelling start" event on observer's world line. So, that red events cant effect or to be not affected by "travelling start" event. There is no relation between its. So we can arrange LoS of combined frame of observer like this.
     
  13. May 27, 2013 #12
    Could you please refer to the example I gave in my thread with and indication what will each observer have in his present plane of simultaneity (which state of Andromeda). Thank you for the patience. I think I'm slowly understanding this.
     
  14. May 27, 2013 #13

    Dale

    Staff: Mentor

    Time never goes backwards or stops in any valid coordinate system. Part of the definition of a coordinate system is that it is a one-to-one mapping from events in spacetime to points in R4. Time stopping or going backwards implies that the mapping is not one to one since the same event in spacetime would map to multiple coordinates with different values of time.
     
  15. May 28, 2013 #14
    Please, look at below image.

    Image03.jpg

    Red dot show events on andromeda worldline. Observer A's worldline is shown in green color. Observer B's worldline is shown in blue color who is start travelling at some time. A's LoS shown in green color and B's in blue. Before start travelling observer A and B are in same reference frame.

    Now, event A happened in andremeda at time t1 in O's frame. That is actually should happen at t1 for both observer but it is not the case here. Because, B is not all the time in same reference frame. So we need to define combined reference frame for B. Hence, event A in andromeda occurs at t1' for B in B's combined reference frame. Like this event C and E occurs at t2 and t3 for A in A's reference frame and t2' and t3' for B in B's combined reference frame respectively.
     
    Last edited: May 28, 2013
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