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SR, LET, FTL & Causality Violation

  1. Nov 28, 2011 #1
    In SR. Anything FTL or superluminal can affect causality because there would be some frame where things move backward in time. Since SR is equivalent to Lorentz Ether Theory. And LET is about additional dynamics that occurs in the backdrop of newtonian absolute space and time. Then how can you model FTL and LET and things moving back in time since the background is supposed to be absolute space and time (where things moving backward is in conflict with its main postulate)? I've been googling this but can't find the information. Thanks.
     
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  3. Nov 28, 2011 #2

    atyy

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    In SR and LET (the form that is equivalent to SR), every inertial frame is a preferred coordinate system, and in that sense physics in an inertial frame is "as good" as Newtonian absolute space and time (Rindler, p43).

    However, what fundamentally distinguishes SR/LET and Newtonian physics, since both have inertial frames or preferred coordinate systems, is the transformation between the inertial frames. In SR/LET, the transformation between inertial frames is given by the Lorentz transforms, whereas in Newtonian physics it is given by the Galilean transform. This is why forms of FTL that violate causality are still forbidden in LET.
     
  4. Nov 28, 2011 #3
    What FTL scenario would break causality? I can understand that FTL would mess up measurements of time/distance for that FoR. You mean "move backward" in propertime, not coordinate time right?.

    So then what does negative propertime mean? Seems meaningless.

    So I think that means FTL breaks the "all physics the same in all FoR", not causality.

    I don't know for sure but isn't a postulate of SR that c is the maximum whatever? Seems like this would have to be assumed for the rest of the theory to "work". Said differently SR doesn't (directly) address FTL. Is that right?

    https://www.physicsforums.com/showthread.php?t=522200

    Picturing the light cone in 3D (as a sphere) was pretty enlighting, including seeing that speed of cause isn't as "important" as it preceeds effect.
     
    Last edited: Nov 28, 2011
  5. Nov 28, 2011 #4

    Fredrik

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    See post #133 here (and post #138 for the correction of a typo).
     
  6. Nov 28, 2011 #5
    Oh cool that's looks quite detailed. I'll read that on my lunch.

    My post above though, is only suggesting that besides the point of whether FTL is possible, it would mean measurements done in that FoR aren't "transferable" / "applicable" to the reality.
     
  7. Nov 28, 2011 #6
    I read that post and I don't understand this part;

    "If she doesn't recieve a message at (0,0), she sends 1 at (8,0). Bob receives that message at (8,10), and replies with 1 at (8,10). So Alice receives 1 at (0,0), and we still have a contradiction."

    That part I don't get. I haven't drawn the diagram (will at home). But Ima guess it's because it's a ST diagram where it's always implied that 1ct = 1x. and that slope seprates timelike from spacelike which also happens to illustrate the line between cause/effect.

    Any cause effect relationship (from a time perspective, I guess the ONLY way causality can appear broken, but is propertime that's "broken" :smile:) that's on the spacelike side means causality isn't illustrated by the photon path anymore. It would be illustrated by the tachyeon things path.

    Said differently a ST diagram where 1ct=1x; 1ct=1x is the speed limit. Seen as the path of a photon (null line) on the diagram. Anything faster and wouldn't ct have to be redefined? I'd say clearly because of cause->effect.

    That's my understanding of FTL and causality.

    With all that being said, I see you qualified the statement with "...the standard argument for why it can't be possible to send instantaneous messages in a special relativistic universe." Which I take as meaning 1ct=1x in this context.
     
    Last edited: Nov 28, 2011
  8. Nov 28, 2011 #7

    Fredrik

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    This short reply is all I have time for today, but I can probably answer follow-up questions tomorrow.

    The contradiction is that she both receives a message at (0,0) and doesn't receive a message at (0,0). I'm just making sure to cover all possibilities about what can happen at (0,0). The possibilities are: a) she receives 1, b) she receives 0, c) she receives nothing. And in all three cases, we end up with a contradiction.

    The most important part of what "special relativistic universe" refers to is that the simultaneity lines of an observer with speed v have slope v in the diagram. (In a Galilean spacetime, the slope would be 0, and that makes it impossible to obtain these paradoxes).
     
  9. Nov 28, 2011 #8
    I know FTL is forbidden in SR.. but we have many examples what would happen if FTL occured... that is.. there would be frames in which it would move backward in time. I just want to know how to model it in LET. If you don't know what I mean. Look at the following web illustration of what would happen if FTL occured in SR.

    http://sheol.org/throopw/tachyon-pistols.html [Broken]

    Now. How do you model the same thing using LET (just for sake of discussion because we knew there was no FTL).
     
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  10. Nov 28, 2011 #9

    Fredrik

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    That's an interesting question that I don't know the answer to, because I've never studied LET or spent any significant time thinking about it. Is there a way to see that my Alice/Bob scenario is logically inconsistent in LET too? If someone who reads this has thought about such things, I wouldn't mind being told the answer so that I don't have to think about it. :smile:
     
  11. Nov 28, 2011 #10

    zonde

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    In LET only one inertial frame is absolute frame. You just don't know which one.
    For that reason Lorentz transform is not symmetric - it only appears symmetric.

    And as there is only one "real" simultaneity in LET there is no paradox with FTL particles.
     
  12. Nov 29, 2011 #11

    Fredrik

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    That was my initial reaction, but than I thought "that would mean that the two theories aren't equivalent". Aren't they supposed to be?
     
  13. Nov 29, 2011 #12

    atyy

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    In https://www.physicsforums.com/showpost.php?p=2588832&postcount=133 & https://www.physicsforums.com/showthread.php?p=2588832#post2588832 you already give the coordinates in Alice's frame. Since you only use one inertial frame for the coordinates, it is already in LET form. It looks like Bob is able to send signals back in time from (8,10) to (0,0).
     
  14. Nov 29, 2011 #13

    Fredrik

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    OK, but is there something in the theory that suggests that if Bob uses the same kind of device as Alice to send messages, his answer will go back in time?
     
  15. Nov 29, 2011 #14

    zonde

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    Ah, but you have to have meaningful description for FTL particle in SR to say that they are not equivalent.

    Wordline of FTL particle propagating at constant speed is spacelike. That means that we can find inertial reference frame where it propagates from A to B, another inertial reference frame where it propagates from B to A and another one where it "happens" all at once along the path from A to B.
    Now to send some information you have to perform some modulation of FTL signal and you have to be able to "read" that modulation of signal. Now the question is in what direction this modulation will propagate? Form A to B or from B to A? I would say that SR does not give you answer about that.
     
  16. Nov 29, 2011 #15

    Dale

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    Yes. The Lorentz transform still applies between two arbitrary frames in LET. So use the Lorentz transform to generate a causality violation as normal. Now, the speed of the aether is unknown, so boost your solution by an unknown v. You will see that causality is violated in the aether frame regardless of the value of v.

    Any scenario which violates causality in SR violates causality in LET. The only way around it is to have the aether measurably violate the principle of relativity (eg tachyonic signals go at 2c, but only in the aether frame)
     
  17. Nov 29, 2011 #16
    They are not equivalent. There is no spacetime in LET, so in LET the Lorentz transform is something that applies to objects with respect to a single arbitrary reference frame. So time dilation and length contraction are properties of an object based on relative motion with respect that frame. Thus, this means that all particles subject to relativistic speeds must also have internal degrees of freedom (if they length contract), contrary to the view of "indivisible" particles. The is no speed limit in LET if we assume that this length contraction is a weaker or non-existent effect for some particles, such as neutrinos. The forces we know about travel up to a limit, perceived locally as c. So LET combined with the facts concerning the gravitional delay (c.f. Shapiro Delay) of light would require that the speed of light be variable even in the vacuum of space from the point of view of the single preferred frame of LET.
     
    Last edited: Nov 29, 2011
  18. Nov 29, 2011 #17
    In other words. Anything FTL in LET would have objects that have negative contraction and negative time dilation? Is this what you mean that objects can still go back in time in LET?

    Anyway. You said there was no spacetime in LET. Are you saying the length contraction or time dilation are properties of objects that occur in newtonian absolute space and time? But PeterDonis wrote the following:

    "I'm not familiar enough with Lorentz's papers to know whether he thought at first that his results could be explained by just adding on length contraction to Newtonian space and time. But I don't think it really matters, because Einstein's 1905 relativity papers did make it clear that that wasn't possible; that to make kinematics consistent with the speed of light being constant for all observers, you *had* to give up Newtonian space and time."

    What do you think?
     
  19. Nov 29, 2011 #18

    atyy

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    I can't think of any reason why this should be. So perhaps SR and LET are not equivalent in the realm of FTL. My inclination to try to formulate a LET tachyon was to set up a tachyonic version of Maxwell-like wave equations. Unfortunately, they don't seem to have the properties of particle tachyons in SR, at least judging by http://www.desy.de/user/projects/Physics/ParticleAndNuclear/tachyons.html. OTOH, do tachyonic waves automatically enforce FTL without paradoxes, since wave FTL requires nonlocality?
     
    Last edited: Nov 29, 2011
  20. Nov 29, 2011 #19
    I'm saying, "[L]ength contraction [and] time dilation are properties of objects that occur in [N]ewtonian absolute space and time."

    http://en.wikipedia.org/wiki/Relativity_of_simultaneity

    I would drop the first assumption immediately and say that the second is also questionable. Dropping the first assumption is sufficient to reject PeterDonis' argument. As for the second one, I do think that anytime that light changes speed due to the nature of the medium, it must refract one way or another. Light travels slower in highly refractive media, and faster in relatively non-refractive media. Our time keeping devices are not altered by such media in the same way that light is. This might also be true in the space between stars, but in the opposite way.
     

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    Last edited: Nov 30, 2011
  21. Nov 29, 2011 #20

    zonde

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    Instead or reading what PeterDonis wrote you might want to read this Lorentz ether theory
    and Einsteins 1905 relativity paper - On the Electrodynamics of Moving Bodies

    I we look at this quote from Einsteins 1905 paper:
    "The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."
    it says "superfluous" not "contradictory".

    And in 1920 Einstein wrote in some letter that:
    "More careful reflection teaches us, however, that the Special Theory of Relativity does not compel us to deny the Aether."

    So I would like to encourage you to take "more careful reflection".
     
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