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Speed of light

  1. Jun 11, 2007 #1
    2nd postulate of SR says that speed of light is constant in all inertial frames. And it exlains all SR. but How to prove this? I have seen that michelson-morley experiment can be explained by this. Is this exp is only reason?:confused:
     
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  3. Jun 11, 2007 #2

    Ich

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  4. Jun 11, 2007 #3
    Why is it difficult to test length contraction in SR?
    I don't see any experiements on that.
     
  5. Jun 11, 2007 #4

    rbj

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    i seem to remember a mu-meson decay experiment that can be viewed as two ways. either (from our perspective) the clocks of the mu-mesons have been slowed down due to time dilation or (from the mu-meson's perspective) the distance between the earth's surface and the bottom of the mineshaft has been decreased due to length contraction.
     
  6. Jun 14, 2007 #5

    Aether

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    The michelson-morley experiment proves that the two-way (round-trip) speed of light is the same for every direction, but there is no experiment that can prove this for the one-way speed of light. The standard formulation of SR comprises this "2nd postulate of SR" only because it makes practical calculations very simple; and not because there is any empirical basis for it at all. The empirical content of SR is not dependent on this postulate at all.
     
  7. Jun 14, 2007 #6
    What do you mean by "prove"? If you start with some EM equations, Maxwell's, you find the wave equation which gives you the EM wavespeed as a constant (with respect to frames).
     
  8. Jun 14, 2007 #7
    The magnetic field of a wire, acting on a charge moving parallel to the wire, seems like a simple demonstration of length contraction.

    Herein lies the OP's problem: it is difficult to move so fast as to transparently verify specific simple aspects of relativity; the reason physicists believe relativity is that it perfectly explains "countless" phenomena which each might not seem like "obviously" proof of anything if taken individually.
     
  9. Jun 14, 2007 #8

    Office_Shredder

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    I think it was them entering the atmosphere... some scientists were measuring the density of mu-meson particles at different altitudes, and found that they were decaying much deeper into the atmosphere than they expected, then realized it would be explained by relativity's length contraction

    Ah, this seems to explain it
    http://www.egglescliffe.org.uk/physics/relativity/muons1_.html
     
  10. Jun 15, 2007 #9
    The invariance of the speed of light is taken as an axiom in SR, which means that we don't know why this is so and we are therefore unable to prove it. However if you, instead, posulate that the proper mass of the photon is zero then it can be proved by using Maxwell's equations. I placed the derivation of the wave equation from Maxwell's equation on my web site at

    http://www.geocities.com/physics_world/em/maxwells_equations.htm

    Notice that the speed of light is derived from two constants which are also invariant according to SR. If a photon had mass then there would be a photon proper mass term in the result which would mean that the resulting equations would predict waves traveling at speeds less that the value of c that we obtain from measurements.

    Pete
     
  11. Jun 15, 2007 #10

    Aether

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    There is not one shred of physical evidence that the one-way speed of light is invariant, much less explaining "why this is so". The standard formulation of SR is simply designed to simplify calculations by exploiting the fact that there is no evidence to contrary either.

    The standard formulation of SR is a mixture of conventional and non-conventional concepts. Only the non-conventional concepts of SR have any empirical basis at all. The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.
     
  12. Jun 15, 2007 #11

    Aether

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    Wrong.

    I have neither asserted an aether, nor have I denied SR.

    How familiar are you with GR?
     
  13. Jun 15, 2007 #12

    jambaugh

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    [edit] I've deleted the original post where I "put my foot in it".

    Hmmm.... I seem to have put my foot in it.

    As I understand it this ambiguity is simply a matter of choice of gauge. I see your point now. Both the one-way-speed convention and the convention of assuming slow clocks remain synchronized in the limit are the same assertion and untestable. It is precisely a gauge condition.

    It reminds me that you can actually "do" GR by taking the speed of light in various directions as your variable instead of (in part a definition of) the metric and/or connection. A point I had to make once to someone with his pet alternative to GR theory. It seems I'm getting forgetful in my old age.

    Pardon, though I did speak hypothetically, I implied facts not in evidence. I was biased in part by your choice of user name and in part by my memory of past arguments with various "aetherists". My most humble apologies, I consume crow with relish. I should have read more carefully.
    Pretty familiar. I've worked a few problems and contributed to a paper or two, e.g. :http://arxiv.org/abs/gr-qc/0009099

    Again my apologies. You are quite quite right and I quite wrong! (And rude about it too!)

    Regards,
    James Baugh
     
    Last edited: Jun 16, 2007
  14. Jun 15, 2007 #13

    Aether

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    Thank-you, but no apologies are necessary. My user name is designed to throw you off balance at first, and you righted yourself well. :approve:

    Cool! I will look at this paper.
     
    Last edited: Jun 15, 2007
  15. Jun 15, 2007 #14

    rbj

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    how would you ever know any variation in c? the speed of light is always 1 Planck Length per Planck Time. always. if you think it has varied (because of a change in the number of meter sticks per clock tick), it's because of a more fundamental dimensionless value (the number of Planck Lengths per meter stick and/or the number of Planck Times per clock tick) that has changed. those are the salient quantities that, if changed by different degrees, might be perceived as a change in c.

    "why this is so" means the burden of proof is on the other side. why should a vacuum whizzing past me be meaningfully differentiated from a "stationary" vacuum? if you cannot tell the difference, if there is, in fact, no meaningful difference between a moving vacuum and a stationary vacuum, then the burden of proof is on the person who claims that the speed of light (or the speed of any ostensibly instantaneous action) is different for any inertial observer, unless you have some reason to declare that this one inertial observer is at rest in an absolute sense and this other inertial observer (moving relative to the first) is in motion. if you cannot do that, there is no reason to think that the laws of physics (including the quantitative value for c) is different for the two.

    so the burden of proof lies the other way: there is not one shred of physical evidence that the speed of light in vacuo varies, much less explaining why such variance could even be observationally meaningful. the variation of dimensionful constants is not only non-existant, such variation is operationally meaningless[\b]. you couldn't tell if such changed, even if it somehow did (while all dimensionless constants associated with it remaining constant). it's only the dimensionless values that count. a variation in [itex]\alpha[/itex] matters, while a variation in c or G or [itex]\hbar[/itex] or [itex]\epsilon_0[/itex] is meaningless. such a purportedly perceived variation is more meaningfully attributed to a dimensionless quantity varying.

    it cannot be demonstrated empirically at all (or falsified). that's because it's not a dimensionless quantity and every meaningful physical measurement we make, with a numerical value, is fundamentally dimensionless.
     
    Last edited: Jun 16, 2007
  16. Jun 15, 2007 #15

    Aether

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    I am looking at this paper, but it will be next week before I can get a copy of ref. 2; do you have a link to that paper anywhere online?

    In view of the Beckenstein bound where the information entropy of any black hole is proportional to the area of the event horizon, and not the volume it encloses, have you considered that (in the case of a black hole at least) the modulus may be proportional to the area of the event horizon rather than the volume enclosed?
     
    Last edited: Jun 16, 2007
  17. Jun 15, 2007 #16

    Aether

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    [add]
    In this case pmb_phy said that "we don't know why this is so and we are therefore unable to prove it" which is wrong; we do know why this is so, it is so because we defined it so.

    It seems clear that pmb_phy thinks that he is talking about an empirically established fact, e.g. that the one-way speed of light is invariant, and that we don't know why nature is this way. Therefore, the burden of proof is on him. My objection is to his implicit assumption that the invariance of the speed of light is an empirically established fact; it is not, it is a postulate.
    [/add]

    I don't necessarily disagree with you. Remember, I also said this:
    We are on the same page here.

    Measurements of the (an)isotropy of the speed of light are always dimensionless quantities. For example, the Michelson-Morley experiment compares the travel times of two light rays and yields a dimensionless (typically null) result.
     
    Last edited: Jun 15, 2007
  18. Jun 15, 2007 #17
    At the last conference I went to, I saw several talks reporting on tests of the one-way speed of light; why the scaremongering ("not one shred")?
     
  19. Jun 15, 2007 #18

    Aether

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    Please cite those papers. There are papers out there claiming to have made measurements of the one-way speed of light, but these can all be shown to be either outright wrong, or meaningless coordinate-system dependent measurements.
    Because there really is not one shred...it is not possible to measure the one-way speed of light in a coordinate-system independent way without contradicting the non-conventional content of SR, not even in principle. Any vaild claim to the contrary would amount to an empirical disproof of SR.
     
    Last edited: Jun 15, 2007
  20. Jun 16, 2007 #19

    rbj

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    yeah, but there could be an issue of whether we can simply define it so, by fiat. (i agree that we can, though.)

    i think that the, given a symmetry regarding the two opposite directions that light moves back and forth on the M-M inferometer, that if the two-way speed of light is invariant, there is no apparent reason for such speed to be different in one direction vs. its opposite and you are measuring the change of the means of two different speeds.

    it is empirically inferred from M-M that there is no measurable consequence of any notion of aether, because you would expect the Earth to be passing though it at a speed roughly that of its orbital speed, at least during some season of the year. so with that expectation, then there is empirical support, if not decisive proof that there is no aether that serves as the medium for which light (and other EM) propagates in. but, as Einstein has been heard to say (or write), it's not as if God had any choice in the matter (paraphrased from memory). Eistein knew of M-M, but i think he would have been greatly disconcerted if M-M had turned out the other way (a noticable fringe shift when turned 90 degrees at some season of the year.)

    yeah, i figgered that out, now. sorry for thinking otherwize.
     
  21. Jun 16, 2007 #20

    pervect

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    This is rather misleading, at minimum. There exist some unusual and non-standard defintions of speed which make the one-way speed of light different in differing directions. (Technically, this would be a non-isotropic speed of light).


    These unusual definitions of "speed" amount to using non-standard (i.e non-isotropic) clock synchronizations.

    However, these sorts of definitions aren't actually useful. For instance, these definitions are incompatible with the common sense requirement that two objects of equal mass moving in opposite directions "at the same speed" must have zero total momentum. These definitions are rather like saying that an airplane that leaves chicago at 6am and arrives at Los Angeles at 8am has a "speed" of 820 miles/hour. (Check out united 101 for example). If one uses a "fair" (aka isotropic) clock synchronization (rather than pst and cst), or uses a rapidity measurement (time elapsed on the airplane) rather than a speed measurement, , the actual trip time is 4 hours, and not 2, and the speed is half the above value. The "speed" computed in this non-standard manner is very non-physical, it for instance has no particular relationship to momentum.

    Besides not being very useful, these unusual definitions aren't standard. For instance, Will talks about one-way speed tests of light http://prola.aps.org/abstract/PRD/v45/i2/p403_1, as some posters have mentioned. (Will uses "slow clock transport" as a non-light based means of clock synchronization).
     
    Last edited: Jun 16, 2007
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