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The Physical Meaning of the Relatvity of Simultaneity

  1. Dec 21, 2009 #1
    I have recently been reading on the topic of the philosophy of relativity and the nature of spacetime. An interesting example of the difficulty of understanding the physical reality of the relativity of simultaneity has me very much at a loss to explain how the theory of relativity really physically manifests itself in the real world.

    Consider the following scenario:

    An inertial reference frame S' moves with respect to another inertial reference frame S in the positive x direction of S. The clocks in S and S' are synchronized at the instant t = t '= 0 when the coordinate origins O and O' of the two frames coincide. At this instant a light wave is emitted from the point O = O'. After time t it is observed in S that the light wave is spherical with a radius r = ct and is described by the equation r^2 = x^2 + y^2 + z^2 which means that the center of the light sphere as determined in S is at O. Consider now the shape of the light wavefront in S' at time t'. Is it also a sphere whose center is at O'? If so, does this lead to a paradox? If not, does this lead to a contradiction with the principle of relativity?

    The relativity principle requires all physical phenomena to look the same in all inertial reference frames. Therefore an observer in S' should determine that the wavefront of the propagating light signal is also a sphere whose center is at O'. This conclusion is confirmed by the Lorentz transformations. But our everyday experience tells us that there must be something totally wrong here -- the center of the same light wave cannot be at two different places (at O and O' which may be thousands of kilometers apart). A standard explanation of this apparent paradox is the following: the wavefront of the propagating light sphere constitutes a set of simultaneous events and since according to relativity simultaneity is relative, the observers in S and S' have different sets of simultaneous events and consequently different light spheres. This is a correct explanation, but it certainly does not satisfy me.

    The explanation is conceptually incomplete since it merely shifts the paradox from the specific case of light propagation to the relativity of simultaneity itself. What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres (one centered at O and the other at O') given the fact that the two spheres originated from a single light signal. What physical meaning of relativity of simultaneity can be conceptually explained such that this paradox will be explained as well?

    How can we really understand this world we live in?

    Pete B
  2. jcsd
  3. Dec 22, 2009 #2


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    I'm not sure I understand your problem.
    What is there to explain? Just like different observers have different notions of what "at the same place" means, they have different notions of what "at the same time" means. That's only fair.
    I mean, how do you explain that there is a relativity of conlocality?
    (I just made up this word. Is there an official word for "at the same place"?)
  4. Dec 22, 2009 #3


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    How do you 'synchronize' watches without instantaneous communication [which is forbidden]? There is no universal clock. Time is relative throughout this universe.
  5. Dec 22, 2009 #4


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    A thought experiment - moon receeding at superluminal velocity. If the moon suddenly decided to receed from earth at superluminal velocity, what would we see? A moon that redshifts toward infinity, or abruptly winks out of existence?
  6. Dec 22, 2009 #5


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    It is perhaps worth pointing out that, in relativity, the concept of simultaneity is a convention rather than an experimentally meaningful idea. As nothing can be transmitted instantaneously from A to B, nature doesn't care about "simultaneity" at all. It's a man-made concept which eases our mathematical analysis within a frame of reference, but has no real "physical" significance.

    In pre-relativistic physics, all observers agreed on what was simultaneous, which is why we intuitively feel simultaneity is important. In relativity, nobody agrees on simultaneity, but they all agree on the speed of light; it's the notion of being able to send light from event A to event B which is the important relation in connecting events (rather than simultaneity).
  7. Dec 22, 2009 #6


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    I'm not sure what this has to do with this thread but the first, obviously. Even if the moon were moving away faster than the speed of light, at any given instant, it would be a finite distance away from us and we would see the light from it after a finite time.
  8. Dec 22, 2009 #7

    Syncronized clocks still in S cannot be synchronized in S' and vice versa.

    Light sphere is
    S: x^2 + y^2 + z^2 = c^2 t^2
    S':x'^2 + y'^2 + z'^2 = c^2 t'^2
    where γ=1/√(1 - v^2/c^2),
    x'=γ(x - v/c t),
    ct'=γ(ct - v/c x),

    There is no contradiction.

    Last edited: Dec 22, 2009
  9. Dec 22, 2009 #8
    The origin of the light sphere is the origin of O and O' at t=t'=0, which is a single location, not two locations. Where is the paradox?
  10. Dec 22, 2009 #9
    This subject was addressed in the longest ever thread on this forum. It was called the light sphere question.

  11. Dec 22, 2009 #10


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  12. Dec 22, 2009 #11
    Thanks for all the comments. Let me clarify something: this is not a thought experiment that I made up, this is taken verbatim freom a university textbook written by a Professor who studies and teaches the Philosophy of Physics. So the question does have meaning, it is not trivial or meaningless as someone implied. The comments and questions in my post were a blend of my own thoughts and (mostly) those of the author who provided it as an illustration of the difficulty of conceptualizing the physical reality of the principles of relativity.

    I mention this because there appears to be some misunderstanding, for example one poster claims it is not possible to synchronize two clocks, one in each of two different frames of reference, to set each clock to zero at the same instant. This is indeed entirely possible and is furthermore mentioned in almost every book on the physics of relativity, usually in terms of two vehicles or trains passing each other or whatever, or as a spaceship that starts off from earth with a clock synchronized with a clock on earth. In fact, if such were not possible, we could kiss GPS devices and satellite navigation systems goodbye.

    To further clarify my discussion, as I see it, the heart of the problem is the issue presented by relativity dealing with the one flash of light generated and perceived as originating at the same physical point, physically coincident in the two frames at time t = t'= 0 at the **same** coincident physical location/origin in the two frames O = O'. When considered at a later time in the two different different inertial frames, the single, unique wavefront generated at the origin location must be treated as though each reference frame had originated its own individual unique spherical wavefront, specific only to that frame, that is identical to the spherical wavefront observed in the other frame of reference. The paradox occurs because the two different wavefronts **physically measured** in the two separated frames were generated by the same one flash of light and thus **in physical reality** shoild be ONE and the SAME wavefront. But that would cause a paradox because the physically same original wavefront should not physically appear identical in the two frames because the frames have moved thousands of kilometers apart since the wavefront was generated.

    The observer in each inertial reference frame sees a perfect spherical wavefront in his reference frame, with dimensions as stated in my post, centered at the origin, O or O', of that observer's inertial frame. Yet the time lapsed since the generation of the wavefront means that the two origins, O and O', will be thousands or more kilometers apart from each other because the two frames of reference are in motion relative to each other. So relativity demands that each independent frame of reference will see that wavefront as a sphere generated at its own origin, which means the one unique flash of light is now somehow physically observed as two separate independent spherical wavefronts. one for the observer in each of the two independent inertial frames. How can one sphere morph into two separate spheres yet still physically be the one unique original sphere? We started with one sphere at the instant of generation, as the two frames moved relative to each other, the one sphere became two separate independent spheres as proven by the Lorentz transformations.

    The question is, how is this **physically** possible? What does it mean in terms of what we perceive of our physical world? Two observers, moving independently relative to each other, see a spherical wavefront centered at one and the same unique physical location, but no matter how the two observers have moved apart, each observer sees identically the same spherical wavefront centered on that observer's own origin.

    Logic would say that the observers will each see a different perspective of that wavefront if they have moved away from each other, and neither will see a sphere, rather they will see the sphere from two different locations and thus it will not appear the same to the two observers. Yet we know from relativity that such is noit the case.

    So in my mind the question boils down to, is this a real physical phenomenon in the universe, or is it simply a mathematical calculation that has no real foundation in the physical world we perceive. IOW if it wre physically possible to actually conduct this exercise, would the results be as discussed her and specified by relativity, or would they physically be something else?

    Somebody mentioned that this problem has been covered before in an earlier thread. If so, I do not want to rehash old material, can someone point me to that thread if it is still around? Or at least tell me what the final conclusion was in that discussion?

    One last thing: I am not a physicist. I am a retired EE who has had a lifelong interest in physics, but I am not an expert. If I made mistakes here, please be gentle with me in correcting my errors. I am just insatiably curious about these things.

    Pete B
  13. Dec 22, 2009 #12


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    Follow the link in my post which immediately precedes yours.

    Several of the regular posters here posted various examples showing how relativity of simultaneity works in the "light sphere" situation, in a futile attempt to convince one person who kept insisting that we had to be wrong.
  14. Dec 22, 2009 #13


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    That's how it is.
    What do you exactly mean by "should not physically appear identical"? That the center of the light sphere coincides with different physical locations, in different frames?

    That is not paradoxical, because unlike the wavefront itself, the light sphere center is not a physical object. It is just an abstract coordinate, calculated from those coordinates which are hit by the wavefront simultaneously, according to some arbitrary simultaneity convention.

    If you are interested in physical reality, then you have to realize that the light sphere center has no physical relevance at all.
  15. Dec 22, 2009 #14
    In relativity, there is only one spherical wavefront, not two. In O, the center of the wavefront remains at the origin of O, while the origin of O' is in motion relative to the light sphere's center. At any given time t > 0, in O, the origin of O' is no longer at the center of the light sphere because the origin of O' moved.

    The reason that in O', the origin of O' remains at the center of the light sphere is because the sphere itself is defined by clocks, and two clocks in O' on either side (equal distance) of its origin will have the same reading when the light reaches them. In O, the light reaches those clocks at two different times, because in O, the origin and clocks of O' are in motion relative to the center of the sphere.
  16. Dec 22, 2009 #15
    OK I admit I just quickly browsed the beginning of that other thread, whch did indeed discuss the same problem, but it seemed concerned with the mathematical proof or demonstration of the scenario. My concern is with the implications in physical reality of the scenario. What are the physical phenomena that occur in the real physical world as a result of this phenomenon? The math is rather simple and IMO is indisputable, I am concerned with how this outcome is physically perceived in our real universe.

    The most recent reply about the paradox seems to indicate it is not a paradox because the whole thing is just an arbitrary mathematical abstraction rather than a physically real phenomenon. That is what I am seeking to find out, whether this is just an abstract mathematical concept, or is it an actual physically perceivable, theoretically observable phenomenon we can observe and measure in our universe.

    Pete B
  17. Dec 22, 2009 #16
    It's physically real, and not a paradox. The wavefront of a single light sphere must be spherical in every inertial frame as a consequence of the constant speed of light postulate.

    The fact that this presented a paradox in Newtonian physics is what motivated SR, since SR was created specifically to resolve this apparent paradox, and successfully does so.

    In SR, the single wavefront is spherical in each frame, since synchronized clocks in each frame show the light to travel at c isotropically in each respective frame. Those same clocks are out of synch in other frames, since in other frames the clocks are in motion relative to the origin of the light.
  18. Dec 22, 2009 #17
    Please pay a little bit attention on the difference of adjustment and synchronization.

    There are many clocks everywhere and stay still in S.
     here ______________________ somewhere

    S clock0:00 →synchronized1← clock0:00

    adjustment when passing by

    S' clock0:00

    There are many clocks everywhere and stay still in S'.
     here ______________________ somewhere

    S clock0:00


    S' clock0:00 →synchronized2← clock0:00

    However,in integration,

     here ______________________ somewheres

    S clock0:00 →synchronized1← clock0:00 "We are synchronized. Their way of synchronization2 is wrong."


    S' clock0:00 →synchronized2← clock0:00 "We are synchronized. Their way of synchronization1 is wrong."

    As an example, In another passing-by at not "here",

    S clock0:00 "We are now in adjustment by passing at "here". Your clock is ten minutes forward in synchronization"
    S' clock0:10 "We have finished adjustment by passing by at "here" ten minutes ago. Your clock is ten minutes behind in synchronization"

    Last edited: Dec 22, 2009
  19. Dec 22, 2009 #18
    Yes, it is of course possible to synchronize two passing clocks, moving with respect to each other at the event of their meeting, in the sense that they can be set to show the same time.

    Clocks at rest with respect to one another in an inertial frame are usually synchronized using the Einstein synchronization procedure and will remain in synchronization with each other to an observer in that frame. If this is done seperately in the two reference frames concerned, two clocks meeting at the same point, which we can designate as the origin, can be set to the same time (synchronized) for all observers for that moment. However, thereafter, clocks in one reference frame, although synchronous with other clocks in the same frame when observed by an observer in that frame, will not show the same time as passing clocks in the other frame. That is, clocks in one frame will not remain synchronized to an observer in the other frame.

  20. Dec 23, 2009 #19
    take a photo at the nigth sky and date it.
    we have captured light from events that we call simultaneous, even if they happened/originated at diferent moments by some hypotetical 'master' clock. it is the observer that determines what is simultaneous, by convention. this way, observer rules,causality is preserved.
  21. Dec 23, 2009 #20
    'Reality itself' is not observer dependent because one 'object' ,say, has to have multiple objective realities, one for each observer candidate.
    then the 'reality we see' is dependent on 'reality itself' and also observer dependent (motion, field, mass distribution, and more, yet to be told ).
    this calls for a 'modification' on the observer. But this is hard to directly measure because as we change, as observer, also our rulers change, and we get a null result on such a direct test.
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