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Is superluminal communication impossible according to STR?

  1. Sep 5, 2012 #1

    Jano L.

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    It is often said that superluminal communication is prohibited by special theory of relativity.

    Do you think this is true? I have doubts about this claim.


    Imagine a communication between two astronauts in two distant inertial frames A,B with any mutual velocity.

    Suppose that both astronauts have one part of a special communication device on their ship. One part is used in the same way as ordinary receiver and transmitter, but when A asks simple question that B can answer, like "What's the time in your ship?", A hears the answer, say "10 a.m." from B immediately, with no delay and with no speech slowing down; the debate goes on as if the two were in the same room. The same happens in B; the whole thing proceeds like subspace call in Star Trek.

    Most of you will probably protest at this point, saying relativity does not allow this because when we look at things from a third moving frame C, everything becomes nonsense.


    Let's see.

    The simplest case to discuss is when A,B are distant but in mutual rest. Judging from this frame, the debate of A,B looks innocent.

    Now imagine observer in frame C moving past both A,B with velocity u, who reconstructs the course of the dialogue in his temporal frame. How does the debate look to him? He will find that in HIS time coordinates the times of questions do not match times of answers, but are systematically shifted by some (perhaps long) time interval. The mutual synchronization will be lost; the events that were almost simultaneous in A, B will become separated by some delay. In particular, the answer "10 a.m." may be spoken BEFORE the corresponding question "what's the time" was asked.

    Does this relativity of ordering look as a contradiction to STR to you? Or is it only contradiction to daily expectation that the answer occurs after the corresponding question?
     
  2. jcsd
  3. Sep 5, 2012 #2
    It's not a big problem when you consider a one-way example from A to B.
    The actual contradictions arise when B sends the signal back to A. Under this circumstance, A will receive the answer before the initial question sent by A to B was even transmitted - and by that you can violate causality.

    http://en.wikipedia.org/wiki/Tachyonic_antitelephone
     
  4. Sep 5, 2012 #3
    @title: yes.
     
  5. Sep 5, 2012 #4

    Jano L.

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    No problem, I do not believe causality has important role in so far developed theories like mechanics or electromagnetic theory anyway. I am curious whether my example violates STR; that is, the two postulates:

    1) Physical laws can be formulated in the same way in any inertial frame
    2) Velocity of pulse of light ray is independent of the velocity of the source.

    or their important consequences, like LT.
     
  6. Sep 5, 2012 #5
    The mathematics of Minkowski space does not impose causality. It is something we put into theory by hand based on observations--namely, we have yet to discover any objects or particles that can have the required spacelike four-velocity to achieve such FTL communication, and we know the properties of such objects or particles to be somewhat exotic. Hence, most often we rule them out.

    Causality plays a role in EM theory. See, for example, retarded Green's functions versus advanced ones.
     
  7. Sep 5, 2012 #6

    Jano L.

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    Exactly what I thought! Yes, it is strange to have this superluminal stuff but the great thing is that relativity does not prohibit such device, in contrast to what most people defend. I think they are in fact just defending causality with false argument that relativity requires it.

    I do not think so, but that would be another discussion. If you like this, I can give you my reasons if we make a new thread somewhere.
     
  8. Sep 5, 2012 #7

    PAllen

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    The assumption of causality (based on experience) preceded SR, and was stated by Newton in Principia. In pre-relativity physics, it prohibited signals or travel to the past. SR carried forward causality as well as most of prior physical laws (EM, modified conservation laws, modified thermodynamics). In SR, the assumption of causality leads to the consequence of no FTL travel or signals. However, just as you can pretend sending signals to the past is possible in Newtonian physics without breaking anything except causality, you can pretend FTL signals or travel in SR without breaking anything except causality.

    I use pretend deliberatly - I think FTL signals being real is exactly as likely as directly sending signals to the past.
     
  9. Sep 5, 2012 #8

    Jano L.

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    Can you explain? There is no causality in current understanding of Newtonian physics. The motions of planets are reversible and require no cause.
     
  10. Sep 5, 2012 #9

    PAllen

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    Reversability and causality are different things. SR laws are also completely reversible irrespective of causality assumption, and irrespective of whether or not you consider FTL impossible.

    Causality in Newtonian physics is the separate assumption that time flows in one direction across the universe. It isn't in Newtonian mechanical laws - it must be added as a separate assumption, and was by Newton and essentially all scientists from way before Einstein. Experience was that nothing traveled back in time, nor could anyone conceive of how one might send signals back in time. This informed the assumption that time flows uniformly in one direction across the universe. This latter assumption was made explicit by Newton in Principia.


    If you take the assumption of causality in SR, just as with conservation laws, it is modified - it precludes FTL as well as direct time travel, because two FTL operations add up to time travel. As with Newtonian physics, it needs to be added as a separate assumption, and always was added as a separate assumption.

    [A secondary point is that the mass of something traveling FTL in SR must be imaginary. To say this is excluded, you have to assume this. You can also treat as an axiom that light cones define the causal structure of spacetime. This is the typical modern, geometric approach. ]
     
    Last edited: Sep 5, 2012
  11. Sep 5, 2012 #10

    Jano L.

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    I always understood causality as referring to the claim that some sequences of events can occur in one order only, not in reverse. The first event is called cause, the subsequent effect. Clearly mechanics does not use this kind of causality.

    But you say
    That is strange definition of the word causality. How time, being real number in mechanics, could "flow in one direction across the universe"? What is direction of time? There is no such thing in mechanics. And how do you compare "directions of time" in two different places of the universe?

    What does that mean? Can you post some reference/link where you read this?

    The problem is clearly in the meaning of words.
     
  12. Sep 5, 2012 #11

    PAllen

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    This is a bogus definition because it is true of no plausible theories (except thermodynamics, which is a theory of macroscopic states). Take any sequence events in Newtonian physics, SR, QFT, whatever, and run them backwards ( in QFT, you may have to reverse CP as well), and the sequence is equally possible. The same is precisely true in GR. This is why it is said that all current theories are time reversible.

    Causality isn't a statement about what could happen. It is a statement about what does happen. Given a sequence of events, we assume (based on experience) that a later one did not influence an earlier one. Independent of this, it is physically allowed for the sequence to occur in revers order - in which case the causality would be reversed.

    For example: billiard ball A hit B and caused B to move. Running this backwards reverses causality. But we never interpret the first sequence as B's later movement caused A to move to hit it.
    Here is the quote from Principia about time flow:

    "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external"

    As for the general claim that classical physicists assumed cause and effect (while being well aware of the mathematical reversibility of laws), I am surprised you find this novel. You can read a discussion of history of this in wikipedia:

    http://en.wikipedia.org/wiki/Causality_(physics)

    in which you find:

    "In classical physics, a cause should always precede its effect. "
     
    Last edited: Sep 5, 2012
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