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Light Speed Travel and Causality

  1. Mar 24, 2008 #1
    This is my first post, so if I am in any way out of line for the the norm on this site please forgive and instruct me. That said, I found this site while trying to comprehend a physics issue I just cannot seem to get my head around. That would be the claim that faster than light travel woudl violate causality. I understand the concept that if one were able to go back in time, one could theoretically do things which placed the effect before the cause. What I am having trouble understanding is why going faster than light would allow one to travel backwards in time. I have read several articles on the subject, and do not feel I am any closer to a solution. I would be most thankful if someone could help to clear up this tricky concept for me.
    Last edited: Mar 24, 2008
  2. jcsd
  3. Mar 24, 2008 #2
    If thats breaking causality then we're doing it every day when flying faster than speed.
  4. Mar 24, 2008 #3


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    Welcome to PF!

    Hi Violator! Welcome to PF! :smile:

    Yes, faster than light travel would violate causality.

    No, going faster than light would not allow one to travel backwards in time.

    If you could go to alpha centauri, four light years away, at twice the speed of light, and I stayed on Earth and waited for you, then I would say that it took you two years to get there and two years to get back. You would return to Earth 4 years later, not earlier!

    Would you be younger or older? Well, if you travelled at almost the speed of light, then you would be only a few days older (instead of 4 years). You can't go faster than light, of course … but if you could, the equations say that your age would be imaginary (a complex number). :smile:
  5. Mar 24, 2008 #4


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    If SR is correct and the laws of physics work the same way in every inertial frame, it would, because the relativity of simultaneity means that if the event of the signal being received lies outside the future light cone of the event of the signal being sent, then there will be some frames where the event of it being received happened before the event of it being sent. And if it's possible to have the signal arrive before it was sent in some frames, then if the laws of physics are the same in every frame, this must be possible in any frame, which allows you to use a pair of signals to make it so that an observer will receive the reply-signal before he sends the original signal, a definite violation of causality in every frame. Here's something I posted on this thread which dealt with the same issue:
    Last edited: Mar 24, 2008
  6. Mar 24, 2008 #5
    I guess this is what I am not understanding then. What is it that allows the signal to go backwards in time? It seems as if any negative time component would merely be an illusion created by the event happening faster than the image of the event. I feel as if I am missing some large piece of the puzzle that everyone else has. Is there perhaps some theory or concept I need to be familiar with in order to understand this issue?
  7. Mar 24, 2008 #6


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    Are you familiar with the relativity of simultaneity? That events at different locations in space which are judged to happen at the same time in one frame will be judged to happen at different frames in another? The way the math works out is that if you have two events A and B, then if there is a "timelike separation" between them (meaning a signal traveling slower than light could go from A to B) or a "lightlike separation" (meaning a signal traveling at exactly the speed of light could go from A to B), then all frames will agree on the order of the two events, and there is no frame where they are simultaneous. But if there is a "spacelike separation" between them, meaning that no signal traveling at the speed of light or slower could be emitted from A and make it to B, then that means it will always be possible to find a frame where the events are simultaneous, it will always be possible to find a frame where A happened before B, and it will always be possible to find a frame where B happened before A. Since there would automatically be a spacelike separation between an FTL signal being sent and it being received, this means you can always find a frame where it was received before it was emitted.

    See here for some more on the relativity of simultaneity, and here for some more on the timelike/lightlike/spacelike distinction.
  8. Mar 24, 2008 #7


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    … violation of causality …

    Hi Violator! :smile:

    I think you know that two events, A and B, which are simultaneous for you will not be simultaneous for someone with a different velocity.

    Observer X may say that A happened before B.
    Observer Y may say that B happened before A.

    I assume you're happy with that.

    Now suppose a signal goes infinitely fast between A and B.

    X will say that A caused it to go to B.
    Y will say that B caused it to go to A.

    But they can't both be right, can they?

    This is what we mean by violation of causality.

    (And it applies to any faster-than-light speed - think about it! :smile:)
  9. Mar 24, 2008 #8
    I am familiar with the concept of the realitivity of simultanity, but its seems wong to me. I am not saying that it is wrong, I am not so arrogant to think I can rewrite physics. But, for example, in the train experiment referenced in the link, only one of the people involved can be right, and this could be objectively measured. Either the light arrives at the same time or it doesn't. If both can be right, from there point of view, isn't faster than light speed just a difference of degree?

    Also, and please don't pereceive this as challenging or argumentative, it is not intended that way, but it seems like a lot of times, the articles demonstrating that faster than light speeds violate causality, seem to depend on the assumption this is true to prove it is true. Maybe I am wrong here, or maybe just out of my depth.
  10. Mar 24, 2008 #9


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    Are you talking about the classic train thought-experiment given by Einstein where lightning strikes to ends of a moving train and the light converges towards an observer at the center of the train, while an observer on the tracks analyzes the whole thing in his frame as well? The point here is that both do agree that the light arrives at the center at the same time (all frames agree on local facts like that), but this gives different conclusions about whether the strikes that created the flashes happened at the same time. In the frame of the observer on the track, the observer in the center of the train is constantly moving in the direction of the front of the train, so naturally if light travels at the same speed in both directions in this frame, it will take less time for light from a flash at the front to reach the train-observer than for light at the back to reach the train-observer (since the train-observer moving towards the position of a flash at the front and away from the position of a flash at the back). So, the only way the light from both flashes could reach the train-observer at the same moment is if the flash at the back happened before the flash at the front, so that even though the light takes longer to get from the back to the train-observer than it does to get from the front to the train-observer, because the light coming from the back had a "head start" it can reach him at the same time as the light coming from the front.

    On the other hand, the wikipedia link featured a different thought-experiment where light is emitted from the center of the train, and different frames disagree about whether it reaches the front end and the back end at the same time or different times. But how do you propose we could settle which is "really" true? Normally in relativity it's assumed that each observer has a network of synchronized clocks at rest relative to themselves which they use to assign time coordinates to different events using local readings on the clock right next to the event as it happened, but the point is that different observers use light signals to "synchronize" their own clocks, so different observers will see each other's clocks as being out-of-sync. Given that the laws of physics work exactly the same in every observer's own frame, how would you propose to settle who is "really' correct?
    It's true that if you accept the relativity of simultaneity, then that automatically implies that any FTL signal can also be seen as going backwards in time in another frame. But I would actually disagree a little with tiny-tim when he says that a signal moving backwards in time in some frame is itself a violation of "causality". If FTL signals were possible, but they violated the postulate of SR that says all the laws of physics work the same way in every inertial frame, so that there was some preferred frame where FTL signals could go arbitrarily fast in any direction but they could not go back in time in that frame, then even though there would be other frames where they do go back in time, I'd say this isn't a true violation of causality because no observer can send a message to his own past. It's only when you assume that "backwards in time signals are possible in some frames" implies "backwards in time signals are possible in every frame" that you can prove that, by sending a message to another observer who's moving relative to me and having him bounce the message back to me, I can actually receive the reply before I sent the original message, a clear physical causality violation no matter which frame you use to analyze it (the key is that the original signal moves FTL in my frame but backwards in time in the other observer's frame, and he sends the reply so that it moves FTL in his frame but backwards in time in my own).
    Last edited: Mar 25, 2008
  11. Mar 24, 2008 #10
    I was referring to the experiment in the wikipedia article. It seems as if the light has no frame of reference in the article. But in reality, doesn't the light source have to either be stationary, like the platform observer, or in motion, like the train observer? And that being the case, isn't the frame of refrence from which the light originates going to be the "correct" interpretation, and the other merely an optical illusion?

    Also, a point I am unclear on is this. If we are willing to accept that simultanity is relative, doesn't that imply causality is an illusion? It seems that if two events that happen at once from one point of view can be said to happen at differing times from differing points of view, then violations of causality are implicit in the concept of varying references, so long as you can generate enough speed. However, everything I read seems to go in a circle which says you can't go faster than light because it would violate causality, and causality isn't compromised because you cannot go faster than light.
  12. Mar 25, 2008 #11


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    No, in classical electromagnetism (Maxwell's laws) the speed of a light wave has nothing to do with the motion of an emitter. This is also true of sound waves, which always travel at the speed of sound relative to the rest frame of the air, regardless of how fast the source of the sound is moving relative to the air; so before relativity it was imagined that light was a kind of sound wave in a medium filling space called the "aether", and that Maxwell's laws would only work precisely in the rest frame of the aether. Relativity showed that it is actually possible for Maxwell's laws to hold in every inertial frame. But either way, there is no way that the speed of light can be dependent on the speed of the emitter in a frame where Maxwell's laws hold.
    No, not as long as all causal influences are limited to the speed of light or slower. As I said, as long as the separation between events is timelike or lightlike--meaning that one event lies on or in in the "future light cone" of the other--then all frames agree on their order. It is only for events with a spacelike separation that there can be disagreements about their order, but in relativistic theories events can only have causal relationships with other events lying on or in their past or future light cones.
    The statement "FTL would violate causality in relativity" can be proved fairly easily from the Lorentz transformation which relates the coordinate systems of different inertial observers (which includes the relativity of simultaneity), and the assumption of relativity (which all the experimental evidence seems to confirm) that all the laws of physics have the mathematical property of being invariant under the Lorentz transform (so if you write down the equations for the laws of physics in one frame and then use the Lorentz transform to see how the same laws would be written in the coordinates of a different frame, you get back exactly the same equations). Likewise, the statement "as long as there are no FTL causal influences, all frames will agree on the order of causally-related events" can also be proved from the Lorentz transform. No one claims these facts as definitive proof that FTL doesn't exist in nature, since after all it is possible that either the assumption of no causality violations or the assumption that all laws of physics are Lorentz-invariant might be incorrect, but given that all the evidence so far favors the second assumption, and that violations of causality seem so outlandish and there is no evidence to suggest FTL, it does give people reason to think it is unlikely that FTL exists in nature.
  13. Mar 25, 2008 #12
    Just a side point, and a hypothetical but the speed of light at least in speculatory physics is both and upper limit for particles travelling at or slower than light and for particles travelling faster than light. If for example tachyons actually exist, then causality is only violated if they travel slower than light. I found that a rather interesting if completely hypothetical consequence of the maths and theory.
  14. Mar 25, 2008 #13


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    … a tachyon-producing banana …

    (Oh good … a short post … I'll read the others later … !)

    Hi Schrodinger's Dog :smile:

    I disagree.

    Consider A sends 200 tachyons to C, one at a time.

    Halfway through, we insert a banana, B, in between.

    So the first 100 go from A to C, and the next 100 go from A to B, where they are absorbed.

    An observer with a different velocity will say that 100 tachyons went from C to A, and 100 went from B to A.

    So he regards the banana as emitting the tachyons!

    Isn't that a breach of causality … what caused the tachyons? smile:
  15. Mar 25, 2008 #14
    Only if you assume certain things. If for example time is bi-direcitonal and can run forwards and backwards, you could avoid this. A more standard explanation is:


    This all of course completely hypothetical.
    Last edited: Mar 25, 2008
  16. Mar 25, 2008 #15
    OK. This is actually starting to make sense for the first time ever, so for that I am much obliged. I think I have just one question left, and this one is more of a tangential question. Earlier JesseM referred to spacelike separatation. From what I read it seemed as if the breaking the light barrier would imply a signal could transmit from A to B across a spacelike separation without moving forward in time. My question is, even at FTL speeds, wouldn't it still take some time, no matter how diminuitive to transmit the information? Thank you again to everyone who has answered.
  17. Mar 25, 2008 #16
    Yes, in the frame in which you measure the signal's speed as FTL, it clearly takes some time, just less that it would for a light signal. This means that if you calculate the space-time interval between the events of sending and receiving of the signal, it will be space-like. This in turn means that there is a another frame of reference in which these two events are simultaneous, as well as an infinite number where their order is reversed.
  18. Mar 25, 2008 #17
    Oh, and one more point - any observed velocity (except that of light) is always frame-dependent, of course, so while the signal is FTL but finite in one frame, it will be infinite in the frame where the sending and receiving events are simultaneous, and have the opposite sign in any frame where the order of the events is reversed.
  19. Mar 25, 2008 #18


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    Different frames disagree about the amount of time between event A (the signal being sent) and event B (the signal being received). In a frame where B happens t seconds after A, then yes, it takes t seconds to transmit the information. In a frame where A and B happen simultaneously (which, again, is only possible if there is a spacelike separation between them), then it takes 0 seconds to transmit the information. In a frame where B happens t seconds before A, then in some sense it takes -t seconds to transmit the information, since the message is received before it was sent.
  20. Mar 25, 2008 #19


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    See my discussion of Feinberg's idea starting in post #11 of this thread--basically, my point was that if tachyons can be used to transmit information FTL, then it will be possible to transmit information backwards in time--for example, after seeing the lottery drawing I could immediately send an FTL message with the winning numbers to my friend moving away from Earth at relativistic speed, then he could send a reply with the winning numbers which moved FTL in his frame, and I could receive the reply before sending the original message, learning the winning numbers before they are drawn. Even if you reinterpret the tachyon "emission" and "reception" events in my frame so that emissions always happen before receptions, it seems to me that receiving information about the future should qualify as a violation of causality.
  21. Mar 25, 2008 #20
    Signals can go faster than light without violating causality depending on the relative speed of the sender and receiver. As long as the signal is travelling slower than c^2/v, where v is the velocity between sender and receiver, then the signal would be received by the receiver in his frame after it was sent. If the two talkers are not moving wrt one another, the signal can be infinitely fast without violating causality.

    Of course, since there's no obvious reason nature would limit the speed of communication to c^2/v, there's no reason to believe this is possible at all. Not to mention the possibility of another party, who was moving fast wrt the sender, intercepting the communication and causing causality problems. But it's still a curious fact nonetheless.
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