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The Trouble with Tachyons

  1. Jan 17, 2009 #1
    I have been thinking about the hypothetical situation of actually measuring a FTL signal and problems that this might entail. SOme questions have come from this which I dont have any answers for.
    PREMISES

    1) SR is totally valid with regard to all known physics
    2) The invariance of the omnidirectional measurement of the speed of light c ,in any inertial frame, is only possible due to the desynchronization of clocks within those relative frames.
    3) The method of synchronization utilizing light, automatically produces the exact degree of desynchronization necessary to insure that invariance.
    4) When dealing with light and sub c phenomena this desynchronization is completely undetectable by any physical means.
    5) The hypothetical actuality of FTL including EPR tangled photon instantaneous transmission.

    Inertial frames-------------
    The fundamental implicit Postulate of SR is:
    NO inertial frame can EVER be assumed to be ACTUALLY at REST
    The power of the system is such that in practical application the exact opposite assumption is routinely applied:
    ANY inertial frame can always be considered to be at REST.
    As this was the essential purpose of the system it is not surprising that this assumption works without any problems whatsoever. This allows jumping back and forth between frames , assigning velocities and times ,analyzing phenomena etc with accuracy and agreement between frames.

    A question arises: Is it reasonable to expect that this would still hold true with regard to Faster Than Light phenomena?

    The hypothetical measurement of the speed of FTL
    GIVEN: An inertial frame S ,, 20 light seconds long traveling at 0.8c in the +x' direction wrt an Earth frame E.
    Synchronous clocks located at the middle M ( x=0) , the rear R ( x=-10) and front F (x=10) with M (t=0x=,0) coincident with E (t'=0,x'=0)
    An EPR FTL transmitter at M and receivers at R and F that are set up to emit light flashes upon reception..
    Given instantaeous transmission: Considering S at rest it is easy. Transmission at M t=0 would mean reception at R t=0 and F t=0 This assumption is not very satisfactory for a couple of reasons.
    1) It would seem to indicate absolutely synchronized clocks.
    2) The same assumption as applied in frames of different relative velocities would obviouly produce identical results which would imply the impossibe state of all frames having actually synchronous clocks

    If we look at it from the perspective of E frame at rest we get: At x'=0 t'=0 we would expect the clock R (x=-10)in A to read t=8
    and the clock at F(x=10) to read t=-8.
    This seems at least nominally more likely, considering we can reasonably expect some degree of desynchronization to be present in S. If we tentatively adopt this premise there are two obvious inferences :
    1) The signal to the rear travelled forward in time 8 sec. , while the signal to the front travelled backward in time 8sec.
    This would require an assumption of actual temporality attached to observed clock readings within a system and would open up a whole other can of questions

    2) That FTL would simply make apparent the inherant desynchronization that was totally undetectable when dealing with light..
    If this was the case then we could surmise that:

    a) These clock readings would provide no directly meaningful information regarding either elapsed time or any derivation of velocity from that time.
    b) It seems not unreasonable to assume that some degree of this effect would take place on an increasing scale for any velocity between c and instantaneous.
    c) The only circumstance in which it would be exected to observe equal bi-directional measurements or actually, any meaningful measurements of any kind, would be a system that had a system of clocks synchronized by the usual method but utilizing tachyons instead of light.

    A simple quantitative experiment: If a light signal was sent from M to R (in S frame), it is obvious that it would arrive at t=10

    As viewed from E frame it would be seen that the clock at R would be moving toward the signal and that the lights path was 3.34 light sec.,,the time for this transit translated into the S frame would be 2 sec. on the clock at R added to the 8 sec already on the clock at the time of transmission, would give the observed time of t=10

    On this basis it would seem that a 2c FTL particle would take between 1 and 2 secs transit time as the decreased time would result in a longer path, because the clock would have moved a shorter distance during transit. This time added to 8sec would give an onserved time of between 9 and 10 sec. While this makes some kind of sense it still provides no real information regarding time or a derived velocity.and no way to arrive at this time within S frame itself.

    If we consider an arrival time of t=5 for a moment:
    a) It would appear to travel back in time as considered from E frame
    b) It would raise the question of what physical principle would dictate a particle to arrive at this particular point of space-time , which is actually completely arbitrary considering the clock situation unless the system was actually at rest with absolutely synchronous clocks ,which we know we cant assume.
    c) On this assumption we would then assign equal bi-directional measurements in this and all other relative frames at the same value . In spite of the fact that we have reason to assume a range of degrees of desynchronization in those systems.

    System Motion
    In any moving system it is clear that path length of a particle moving toward the back of the system [which is moving towards it] will be shorter than the path of a particle moving in the direction of the front [which is moving away from it.]
    With light this is of course not detectable and equal bi-directional measurements can be expected and asigned because the clocks assure this.
    It seems to me that this could not be expected to apply to FTL unless the clocks were synchronized with FTL or the system by, some cosmic fluke, was actually at rest.
    SO it seems reasonable to assume that any measurements would reflect system motion to some degree and bi directional times would be asymetrical . Creating the same problem for relevant temporal intervals or velocities derived from them.

    As I am sure many have noted , all of the above is basically arrived at by assuming E frame as a preferred reference frame. SO it may or may not be interesting, in a general principle way, but is useless in any quantitaive sense and suggests no method for actually attacking the problem.
    I have kept things as simple as possible and so have not considered length contraction or time dilation directly as they might be relevant but would complicate rather than simplify.

    So , does anyone have any ideas why these problems would not occur ???
    Any ideas for a rational basis for assigning times to FTL phenomena that would be expected to apply to an actual situation [ in the unlikely event that FTL should prove a reality]???
    Anything obvious I have missed???.

    Any ideas? Thanks
     
  2. jcsd
  3. Jan 17, 2009 #2

    Dale

    Staff: Mentor

    You can have at most two of FTL, relativity, and causality. So from your premises it looks like you want to keep FTL and relativity. This means that you discard causality, i.e. you can send information from the future to the past and therefore an effect can preceed its cause.

    Other than that, no problems.
     
  4. Jan 17, 2009 #3

    Fredrik

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    Staff Emeritus
    Science Advisor
    Gold Member

    Austin, you should really try to make your arguments shorter. There's just too much to read in a post like that. It's not just that it's too long, it's also that it's often hard to understand what you're talking about and why. When you write posts like this, you're asking other people to make more of an effort to decode what your point is than you made trying to make your point clear.
     
    Last edited: Jan 18, 2009
  5. Jan 18, 2009 #4

    JesseM

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    Science Advisor

    Do you understand that the first postulate of relativity explicitly says that all laws of physics (not just the ones that were known in Einstein's time) should work exactly the same in all inertial frames, so there can be no physical phenomenon that picks out a preferred frame? If there was something about tachyons that prevented us from treating all inertial frames as equivalent, or stopped us from "jumping back and forth between frames", then this would be a violation of the first postulate and thus we'd be dealing with a universe in which SR doesn't hold.
     
  6. Jan 18, 2009 #5
    Causality would be violated by FTL Tachyons, which is probably why they are completely hypothetical, that and the answers given above.
     
  7. Jan 19, 2009 #6
    Given a preference I would definitely keep SR. As for FTL I try to keep an open mind but do not actually consider it very likely as a physical possibility.
    That is not the question of this post.
    Simply put: Given the unlikely actuallity of FTL and the ability to travel at significant velocites do you consider it likely or in fact possible that FTL signals could be measured as having equal bi-directional dt/dt in both directions???
    That any measurements would be directly meaningful as velocities???

    If you do think this is likely, do you have any theoretical concept of why clock desynchronization would not be a factor???

    Why it would be undetectable as it is with light???

    Any idea why system motion would not effect measurements???

    Thanks
     
  8. Jan 19, 2009 #7

    Dale

    Staff: Mentor

    You lost me here. Obviously dt/dt=1 so it is equal in "both directions", but I am pretty sure that is not what you wanted to ask. Could you try to restate your question more concisely (1-2 sentencec). I will try to answer based on the presumption of FTL and relativity, but not causality.
     
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