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Is it possible to experience the same event twice?

  1. Oct 15, 2008 #1


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    This question arose when I read the Rietdijk-Putnam argument or "Andromeda paradox".
    Let's arrange two inertial frames of referance like usually, S being considered stationary (could be you sitting in a chair) and one that moves with a relative velocity v with respect to S, S' (a guy walking past you, passing you at time t=t'=0). Let's suppose that the andromedans in frame S' choose to take off to earth at the time t' = 0, then the time in S can be found using the Lorentz-transformation t = gamma(t' + v*x'/c^2). For simplicy let's assume this velocity between the frames is a walking speed of something like 5 km/h, the gamma factor will be very close to 1 so t is approximately t = v*x'/c^2 which can become quite a significant size because of the distance to the andromeda galaxy (I believe I got something like 4,5 days). Now to the question, let us suppose the guy in S' who saw the event happen at t'=0 at some later time, like t'=0,5day decides to stop (he accelerates so the relative velocity between the frames is zero) since this observer is now in a frame which shares plane of simultaneity with S he must experience the event again at the earlier found time t = v*x'/c^2 and thereby experiencing the same event twice, and actually experiences time "going backwards" in the andromeda galaxy as he decelerates. Is this true? I searched a bit on the subject and found a paper http://arxiv.org/PS_cache/physics/pdf/0411/0411008v1.pdf which comments on a paper by Dolby and Gull. Dolby and Gull wrote

    "If Barbara's hypersurface of simultaneity at a certain time depend so sensitively on her instantaneous velocity as these diagrams suggest, then she would be forced to to conclude that the distant planets swept backwards and forwards in time whenever she went dancing"

    to which is replied "... As far as I can tell, their worry here is that, as Barbara's instantaneous velocity changes from moment to moment, she will be forced to conclude that some events that are in her current subjective future (i.e. that lie within the future light cone of some event on her current hypersurface of simultaneity) were, at some point on her past worldline, judged to be in the past (i.e. lying within the past light cone of some event on her past (then current) hypersurface of simultaneity). Of course, this is no absurdity: it has long been clear that the pretheoretical concepts of "past" and "future" do not mesh perfectly with their relativised versions"

    So is this true? I simply have to ask because I find it to be a quite incredible result that time can be observed to run backwards during acceleration.
  2. jcsd
  3. Oct 15, 2008 #2


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    The issue here is not about what anyone "experiences" in any direct way--the light from the event will only hit your eyes once (edit: aside from mirrors and gravitational lensing and things that allow the light to take multiple paths to reach your eyes, as RandallB points out below)--it's just about what time-coordinates are assigned to events in different inertial coordinate systems. It is true that if you accelerate, then an event on your worldline prior to the acceleration may be simultaneous with some distant event A in the inertial frame where you are at rest before accelerating, and then after the acceleration, in a different inertial frame where you are at rest after accelerating, that event A may have yet to occur immediately after the acceleration, according to this second frame's definition of simultaneity. On their own each frame says the event A happened only once, but they disagree about which event on your worldline happened at the same time-coordinate as A.
    Last edited: Oct 15, 2008
  4. Oct 15, 2008 #3
    NO - There is no form of acceleration, simultaneity or causality that will allow you to directly experience an event twice.

    But you can certainly observer an individual event more than once, you surely have done that many times.
    You recognize hearing an echo because you already heard the sound once and hear it again from the same source reflecting off something. Likewise with seeing the reflection of fireworks in some building just nano-seconds after watching them explode.

    But experiencing observations of the same event more than once is not the same as experiencing the event itself.
  5. Oct 15, 2008 #4


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    The answer depends on what coordinate system(s) Barbara chooses to use.

    A coordinate system is just a function that assigns four numbers (coordinates) to each event. If she chooses to always use the co-moving inertial frame to assign coordinates to events, then the time coordinates of specific distant events will change as she moves. They can go from "earlier" to "later" and then back to "earlier" again. This isn't really strange, since she's using a different coordinate system at each instant.

    Instead of using lots of different inertial frames, she could use one non-inertial coordinate system. She could e.g. define one like this: The time axis is her world line. The time coordinate is the proper time (what her own clock displays). The hypersurfaces of constant time coordinate, and the distance to each point on them, are defined by "radar". (It would take a separate post to explain what that means).

    This "coordinate system" would also assign time coordinates in a way that has distant events "jumping" back and forth between the past and the future when she goes dancing, but only if we extend the hypersurfaces of simultaneity far enough to let them intersect, and if we do, the "coordinate system" isn't really a coordinate system. It assigns two sets of coordinates to each point where the hypersurfaces intersect, so it isn't even a function.

    If we really want to define a coordinate system this way, we have to cut those hypersurfaces off before they intersect. The coordinate system's domain of definition is then some open set containing the world line. That makes it a local coordinate system, unlike the (global) inertial frames that are defined on all of Minkowski space. This coordinate system doesn't assign any coordinates at all to events in the Andromeda galaxy, because it isn't defined that far from her world line. (The size of the region of spacetime where the coordinate system is defined depends on how straight the world line is).
  6. Oct 15, 2008 #5


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    I thought this was obvious from context :) but when I say experience I mean in a spacetime-sort of way, I just don't know what word to use. When I say experience an event, I mean coordinatesystem-experience or let's say that a specific (one) plane of simultaneity represents the present, when I say experience an event, I mean that the event lies within this plane. So what I'm asking is if an event in S' lies below this plane and S' then accelerates and then continues to move inertially, can this event lie above this "plane of the present".
  7. Oct 15, 2008 #6


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    OK, that terminology isn't something I would recommend. I wouldn't say that I "experience" any events that aren't on my world line. To "experience the same event twice" means (to me) that the world line intersects itself. That isn't possible in special relativity.

    (My reply in my previous post doesn't depend on any interpretation of what you asked in the subject line, so it's still my answer).
  8. Oct 16, 2008 #7
    We could say that the event can be "observed" twice (or any number of times). This is interestingly related to causality and pre-destination.

    The trick is of course that "observing" is quite loosely defined in Relativity: it can be direct observing or merely calculating under some assumptions. "Observing" something isn't much real.
  9. Oct 16, 2008 #8
    I embarrassed myself with a bad interpretation of the Rietdijk-Putnam argument. I did interpret it to mean it was "possible to experience the same event twice" and took exception to that. In fact the Rietdijk-Putnam argument does not claim this with respect to anything you can actually observe. All that you would be able to observe is distant events speeding up or slowing down via standard time dilation. If you calculate backwards to the time of the event in question then yes, based on your frame dependent notion of simultaneity the calculation makes it look as if the event itself causally reversed direction at times. The reason for this is that your notion of simultaneity is frame dependent and you changed frames during the observation. Yet when you calculated backwards to see when the events occurred you assumed your changing notion of simultaneity remained consistent. It didn't due to your changing frames of reference and the Relativity of Simultaneity.
  10. Oct 16, 2008 #9
    Is observing/detecting entanglement between two particles "experiencing the same same event twice"?
  11. Oct 16, 2008 #10


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    I don't think you embarrassed yourself. I'm always happy when someone else asks my stupid question! Victor Weisskopf said about Pauli "There was no worry that he would think a particular question stupid, since he thought all questions were stupid". http://books.google.com/books?id=dl...=X&oi=book_result&resnum=8&ct=result#PPA74,M1

    I read the end of Eagle's paper about Dolby and Gull's paper, and he says: "Dolby and Gull have given an elegant and precise example of how to apply the standard Einsteinian convention on assignments of distant simultaneity in the twin paradox case. ...... Firstly because there was no intuitive paradox or problem with the standard textbook presentations ...... Secondly, many people regard the definition of simultaneity as a conventional matter in any case ......"

    Anyone want to comment on whether it's possible to construct hypersurfaces of simultaneity in the circular twin paradox?
    Two Examples of Circular Motion for Introductory Courses in Relativity.
    Stephanie Wortel, Shimon Malin, Mark Semon
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