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Simultaneity in Relativity: self-contradictory?

  1. Dec 19, 2007 #1
    Recently I was reading about tunneling experiments showing faster-than-light tunneling effects, and commentary that it should be impossible for them to be FTL, as this would contradict special relativity. In the context of simultaneity being 'relative' in SR, it would cause the paradox of being able to change the past. So I looked in to the "relative" notion of simultaneity, and something looks very odd to me:

    If there is event A at location A, and events B1 and B2 at location B, where B2 occurs after B1 for a stationary observer at location B :

    Now, for observer O1, event A might be simultaneous with event B1, while for observer O2, event A might be simultaneous with event B2.

    The funny thing seems to be, relativity theory doesn't seem to just say that it looks that way, but that it really is that way. But wouldn't that mean that when event A occurs, both events B1 and B2 would have to exist both at the same 'time', so to speak? "Multiple worlds" already in relativity theory?
  2. jcsd
  3. Dec 20, 2007 #2
    Welcome to relativity :smile:
    It's not multiple worlds, it's just that there is no simple distinction between time and space.. so you can consider whether events are "at the same time-and-place", but in general the phrase "at the same place" (or "at the same time") is meaningless.

    I'm not sure that this answer will satisfy you. I guess all I can offer is that, if there seems to be an introductory error in a major branch of knowledge, you must study to deepen your understanding. (Y'know, I can't tell whether there's a mote in your eye if there's a log in mine.) In this case consider an undergraduate textbook.
    Last edited: Dec 20, 2007
  4. Dec 20, 2007 #3
    Well, I had enough physics courses, including about relativity, to know that a) finding such an answer in a book would be pure luck, and b) that working up to that level again would be several months of work. I expect it to be the kind of question that books usually avoid, since it is somewhat a "meta"-theoretical question.

    I'm hoping that one of the experts here finds the question challenging enough to try an answer.
  5. Dec 20, 2007 #4
    Thank you!

    Oh, I now see: that was meant as an answer. But my question is exactly to ask: How does that make sense? You are saying it just is so, but my question goes beyond the plain answer to ask: How does that plain answer make sense from the perspective of the situation illustrated above?
  6. Dec 20, 2007 #5
    Take a look at this page, it explains two of the more famous S.R. paradoxes, the train and tunnel and twins.


    Sorry, to just post a link and leave, but the explaination given there is far better than anything I could give you at the moment.
    Last edited: Dec 20, 2007
  7. Dec 20, 2007 #6


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    Not really, IMO, though you can probably find some philospher somewhere that will argue about it. (Because you've dragged the notion of existence into the picture, the question is not strictly scientific, i.e. the answer to your question cannot be determined by expeiment unless you define your notion of existence so that the question of existence can be determined by experiment.)

    While it is possible to view the situation in terms of "block time", there are other alternatives, of which I will present one.

    I think it is fairly straightforwards to say that if event A causes event B, and event B "has happened", or "exists", we want to say that event A also has happened, or exists.

    So what we need to do is to clarify the notion of causality in SR. Causality can be defined by the notion of the domain of dependency of an event, also known as its light cone.

    If we have an event A, the set of events that can depend on A, or be caused by A, is restricted to events that lie in the light cone of A. This is the "domain of dependency" of event A.

    If we keep things simple by imagining the usual sort of coordinate system (the flat SR coordinate system of SR associated with some observer, possibly moving), then it is necessary but *not* sufficient for B to have a greater time coordinate than A to be in A's domain of dependency.

    So if A has a time coordinate of 0, and B has a time coordinate of 1, B may or may not be in the domain of dependency of A depending on how far away it is in space.

    So the notions of causality and simultaneity are actually separate notions in SR. Simultaneity depends on the observer, but causality does not. Given two events, A and B, all observers will agree about whether or not B is within A's domain of dependncy, i.e. within A's light cone.
  8. Dec 20, 2007 #7


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    I'm not sure if you are using the apparent superluminal tunneling as the impetus or foundation for your question, but you should probably realize that the question on whether the signal actually did go through at superluminal speed isn't a settled issue. In fact, there are several arguments against it as published below:

    H. Winful, PRL v.90, p.023901 (2003)
    M. Buttiker and S. Washburn, Nature v.422, p.271 (2003)
    H. Winful, Phys. Rep. v.436, p.1 (2006).

    This is only a side issue and not central to the rest of your question.

  9. Dec 20, 2007 #8
    I haven't read these specific texts, but I've heard that there are for example doubts about 'group velocity' giving only the impression of apparent FTL in tunneling, and that it isn't real FTL. However, G. Nimtz has replied that the 'group velocity' argument has been answered. But yes, that issue probably still isn't settled yet.

    My question has started that way, but has become a much more general question. For one thing, in quantum entanglement there are said to be superluminal effects as well (even if they can't be used to simply send emails), and these are already proven. But that is a different topic.

    Here my question is to find out what kind of problems there are or would be with FTL in relativity, and what these are based on, and they seem to be related to the relativistic notion of simultaneity. So that's what I'd like to learn and understand here. and also, what the other implications of relativistic simultaneity are. If A can be simultaneous with B1 for one observer, but simultaneous with B2 for a second observer, while B1 and B2 occur for different times for a third observer stationary at location B, then it seems like in some sense B1 and B2 must be indirectly simultaneous and also non-simultaneous.

    It would seem to me that this is possible only if the past and future are cast in stone, and completely deterministic. If that is indeed an implication of relativity, I'd like to find out and know, in fact I would think that this would be of general interest.
  10. Dec 20, 2007 #9
    Thanks for this link! I will read it completely tomorrow, but I've already read the part about simultaneity. After the train example, it seems to change the topic again quickly, and that is quite typical for such learning material, in that it doesn't give enough background information to answer such a question as the one I have here.

    The text doesn't seem to answer the difference between something looking a certain way, and something being that way. As it is argued that with faster-than-light or instantaneous movement, things would not only look "as-if" they caused a paradox, but would actually allow changing the past and therefore be impossible.

    So this question is not only about what things visually looks like, but more so about whether relativity implies a "real" contradiction.

    And with above example, it would seem to me that even without FTL (faster-than-light), there are already problems, at least for me in understanding how that can be possible.

    It would seem to me that B1 and B2 would have to be "real" simultaneously, even if indirectly, and in spite of occurring at a different time for an observer at location B.

    This is like the world would have to be "real" in different time-slices at the same time, these time-slices being diagonal to each other, and therefore requiring all time to "be real" in a fixed way, cast in stone. As if time were just like space, which also exists at the same "time" so to speak. And actually relativity seems to say that c*t is very much like a space dimension.
    Last edited: Dec 20, 2007
  11. Dec 20, 2007 #10
    I have a bit of a pedantic, philosophical leaning, so my first question would be "what do you mean by 'simultaneity'?" I do think that observers can work out whether two events are simultaneous if they know the separations between the events and each observer when the events were observed, the relative positions of the observers at the times of the observations and the relative velocity of the observers - simultaneous here meaning "if the two events were collocated, they would have happened at the same time".

    You can certainly have collocated events which simultaneous (irrespective of the relative velocity maintained by any observers - the disagreement will only come later when you try to work out how long ago the simultaneous event happened). This is because events are points in space and time, events themselves do not have velocities - unlike observers of those events.

    To work out whether two spacially separate events were simultaneous, observers would have to use Lorentz transforms to ensure that they compare apples with apples. You could say that the Lorentz transforms can restore simultaneity of distant events relative to observers in different inertial frames.


    Last edited: Dec 20, 2007
  12. Dec 20, 2007 #11
    Well, actually my question is more: "What does relativity theory mean by simultaneity?"

    As far as I understand, for different observers, at different speeds and/or at different locations, different things may appear and/or "really" be simultaneous. Therefore my question about "Do different times have to be 'real', so to speak, at the same time?"

    How can one remove the "at-the-same-time" part in the last question, without casting all time in stone?

    Thanks, yes, so how does one correctly apply Lorentz transformations, speaking in general, to situations like the above? What kind of result does one get? Does one need to use time as if it existed in a fixed way, like it does on paper if you use a coordinate system with time as one axis?

    On paper, with a coordinate system and a 'time' axis, all 'time' is 'real' at the same time.
  13. Dec 20, 2007 #12
    No time used by any one observer is more real than any time used by any other observer.

    This means you can work out whether two events were simultaneous, but you can't determine when exactly the happened without arbitrarily determining one point of view to be privileged. The best you can do is to say that my time is right for me, your time is right for you but until we share the same inertial frame we will never agree on precisely when events happened nor where.

    Try to think of "when" in a way similar to the way we think of "big". It's a relative thing, a little elephant will always be bigger than a big frog, but that doesn't mean we are wrong to consider the frog big or the elephant little since we are using the term relatively.

    We might have different ideas of "when" but neither of them is wrong, relative to our own frames of reference.


  14. Dec 20, 2007 #13


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    Your understanding is correct. Simultaneity in relativity means nothing more than assigning the same time coordinate to different events. It is observer dependent.

    As far as philosophy goes, I find it convenient to distinguish between quantities that are observer dependent and observer independent.

    Now, if one makes the assumption that observer-independent quantities are "real", then one finds that none of the concepts of distance, simultaneity, time, or space is "real" in relativity, as all of them depend on the observer.

    What is "real" in the sense of being observer independent in relativity? The Lorentz interval is "real" in this sense.

    This point of view takes a bit of getting used to, but you can view the Lorentz interval as being "more fundamental" than the traditional concepts of time or space. This is closely related to the way that space-time is regarded as a unified entity, rather than two separate ones.
  15. Dec 20, 2007 #14


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    Here is my two cents about why the relativity of simultaneity is something reasonable:

    The universe doesn't care about simultaneity, it cares about cause and effect. Two events that are simultaneous, by definition, cannot be causally related. If two events are not causally related then it really doesn't matter which came first. On the other hand, if one event causes another event then the cause must always preceed the effect, in that case it does matter.

    In the universe, as described by SR, things happen exactly as you would expect: causes come before effects in any frame, and for the rest the order doesn't matter.
  16. Dec 20, 2007 #15
    Thanks for the responses already! I'm still at work, but will catch up soon.
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