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Consistency of the speed of light

  1. Apr 9, 2008 #1
    Einstein's second postulate states that the speed of light is constant as viewed from any frame of reference. Most of the books on relativity that I have been reading usually ask the reader to accept that fact because proving it is behind the scope of the book. Can anyone help me understand the actual reason behind the second postulate?
    thanks...
     
  2. jcsd
  3. Apr 9, 2008 #2
    (if I may Ill add one more question here so I dont flood the forums)
    Based on that assumption, isnt the speed of light defying the laws of relativity? Everything is relative BUT the speed of light, so shouldnt we be able to measure how fast we move no matter what frame of reference are we in beacause the speed of light is the same for all of us?
     
  4. Apr 10, 2008 #3
    Actually it is the opposite, if the speed of light would not be equal for all intertial observers we could deduce a form of absolute motion with respect to light. :smile:
     
  5. Apr 10, 2008 #4
    >> Based on that assumption, isnt the speed of light defying the laws of relativity? Everything is relative BUT the speed of light

    Wrong statement - "Everything is relative". The real thing is
    1. All laws of nature are absolute - they are not relative to the speed of the observer.
    2. observable quantities like mass, lenngth, time, etc are relative to the speed of the observer.

    if there exists a law, which becomes relative to the speed of the observer - the law is wrong. it needs correction. When relativity was introduced, all the existing laws of physics needed a review in the light of relativity. In that sense relativity is a 'law of laws'. All theories of physics when through a change after relativity was taken into account - except maxwell's EM theory.
    In 1905, the following theories existed in phusics
    1. Newton's laws of motion F = m.a
    2. Newotn's law of gravity.
    3. Maxwell's EM theory

    QM was not known in 1905, in the present form today. Statistical laws of nature were known - like thermodynamcs, but they didn't require a review.

    1. Newtons' laws of motion was modified by the following replacements
    m = m0 sqrt ( 1/ C^2 - v^2 ), similarly for time and lenght.

    2. Newton's law of gravity was scrutinized in the light of relativity and it gave berth to General realtivity in 1915 or so
    3. Maxwell's EM theory remained unaffected.

    Motion of light doen't happen due to kinetic inertia, unlike a football. Motion of ligght if due to fluctuations in EM field and the formula for the same is C = sqrt ( 1/ Mu. Epsilon), derivable for EM theory.

    Motion of light is a fundamental law of nature. More accurate answers can be given with higher dimensions, but those are not experimentally tested yet and of course, controversial.
     
  6. Apr 10, 2008 #5

    jtbell

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    We could say that it's because space-time apparently posseses Lorentz symmetry, but then that would lead to the question, "why does space-time possess Lorentz symmetry?", wouldn't it? :smile:
     
  7. Apr 10, 2008 #6

    HallsofIvy

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    The most fundamental "reason behind" the invariance of ligh speed is "that's what the experimental evidence shows"!
     
  8. Apr 10, 2008 #7

    DrGreg

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    The reasoning behind this has some subtle complexity that is not always appreciated. The short answer is that the speed of light is constant because we define distance and time in such a way that it is automatically true.

    If you are a beginner in relativity, it might help to just accept the short answer and come back to this later when you have learnt more.

    Now for the longer answer.

    To measure the speed of something, you need to measure the distance it travels from A to B, the time when it passes A and the time when it passes B. To measure times we need two clocks that are stationary in the frame of reference, one at A and one at B. The reason we can't use a single clock that moves from A to B is that we already know, from the twin paradox, that motion affects clocks (or to be more precise, relative motion between clocks affects their synchronisation).

    The problem arises, how do you synchronise the two clocks at A and B? You can't do it by transporting a clock from A to B, as already mentioned. The convention is, we use light signals sent from A to B and reflected back to A. Assuming the speed of light is the same in both directions, we can set the time at B to be half-way between the transmission and reception times at A.

    However, as we have now used the constancy of the speed of light to sync the two clocks, if we now use those two clocks to measure the speed of light, it is inevitable that they will measure the same speed in both directions.

    If we then combine this fact with the experimentally-verified fact of the constancy of the so-called "two-way speed of light" (its average speed when reflected A-B-A as above, and timed using a single clock at A) then we must conclude that the "one-way" (A-B) speed of light is constant in all reference frames.

    Note that all of this depends on our choice of clock-synchronisation convention. In special relativity it is assumed that the "Einstein synchronisation convention", which I described above, is always used. It is possible to use other methods of synchronisation, and then the speed of light wouldn't be constant measured in those non-standard coordinates.

    I have already said you can't sync two clocks by transporting a clock from A to B. But in fact, you can consider what happens as the transported clock moves slower and slower. If you extrapolate the results as the speed of the clock tends to zero (relative to our frame of reference), it can be proved that this "ultra slow clock transport" sync gives exactly the same result (in the limit) as the "Einstein sync" I described above. This lends credence to the proposition that "Einstein sync" is the natural way to sync, and thus that the speed of light should be constant.
     
  9. Apr 11, 2008 #8
    I dont think this is true.. Your basically suggesting SR is false and is simply a result of the fact that we cant properly synchronize clocks. If we were to synchronize clocks using sound rather than light (which has a constant speed in the rest frame of the earth), we would still find SR to be true...
     
  10. Apr 11, 2008 #9

    DrGreg

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    No, I'm saying we can sync clocks to make the one-way speed of light constant and so SR is true.

    And you can sync clocks other ways, and then under those weird coords, the coord speed of light is no longer constant, but that doesn't mean SR is false, it just means you're using a weird coord system.

    By the way, the problem of syncing with sound is that the "two way speed of sound" is not constant as can be proved by experiment. But there are weird ways of syncing where the "2-way speed of light" is constant but the "1-way speed" is not. See the very end of this very recent post for an example!
     
  11. Apr 11, 2008 #10
    Viewed from any inertial reference frame.

    Much of learning relativity involves "retraining" your physical intuition. For this reason it is often best to ask many facts to be accepted outright at first, let the students play with the math and consequences, and then after they are able to form a better intuition it is possible to go back and relearn the foundations with much more precision.

    There is an equivalent formulation of relativity (I saw it in Landau and Lif****z mechanics book if you happen to have that) which is basically just taking classical mechanics and adding the condition that there is a finite propagation speed of interactions.

    In some sense, it is merely a coincidence that the speed of light is equal to this propagation speed limit (due to photons having zero invariant mass). It is not necessary for relativity to refer directly to light at all.

    Some people find it much more "intuitive" that interactions between spatially separated objects are not 'instantaneous'. So some find the rephrasing of the postulate as something like "there is a finite propagation speed of interaction", to be more intuitive.

    Does that help any?
    I'm not entirely sure what you are looking for.


    EDIT: Hahaha.. are you serious? Lifsh_itz is a censored word?
     
    Last edited: Apr 11, 2008
  12. Apr 11, 2008 #11
    Einstein based his 2nd postulate on the results of the Michelson-Morley experiment. He did not attempt to explain it, but used it as a foundational element.

    It's geometrical, and is explained in 'velocity measurement' here.
     
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