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Contradiction in special relativity?

  1. Nov 24, 2008 #1
    ok so according to special relativity, light moves at a fixed speed C in every frame of reference. Special relativity also makes clear that any two things moving at a constant velocity along side each other, will perceive each other to be motionless. In other words, in any specific frame of reference, there is absolutely no difference between constant velocity motion and no motion at all, according to that frame of reference. So my question is as follows:

    If two photons are traveling along side each other, what do they perceive the other photon to be doing? One would intuitively think that the answer is that they would appear motionless, as special relativity states. Yet it also statest that light moves at C according to ANY reference frame. The reference frame of a photon should be as justified as every other reference frame. So whats going on here?

    People have answered this question by stating that photons cannot "perceive" and the question is meaningless. But this misses the point. Surely there reference frame is as valid as any other, even tho they can't technically "perceive."

    To take this one step further, lets assume, as I've been told before, that light cannot evade itself at speed C because it's already moving at speed C. So the answer is that the two photons would indeed "perceive" each other as motionless. Well...ok, but now that raises another question. As special relativity states, an object (lets call it Object A) is traveling at .9999......%C will still perceive light to evade it at speed C. Thats fine, but then lets say that Object A could reach speed C and become a photon. Now it perceives light to evade it at speed zero (motionless). So doesn't that mean that special relativity should state that light moves at a fixed speed C in every reference frame EXCEPT the small fraction between .9999...%C and C?

    My apologies for the length of the question. Also, I've heard over and over to watch the terms i use, such as "perceive." But clearly you understand the overall point to my argument. I also understand that an everyday object, such as Object A, would never be able to reach speed C and become a photon because it would require an infinite amount of energy. But surely there must still exist a gradual succession of speeds between .999999999....%C and C. Please help me out! Thanks
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  3. Nov 24, 2008 #2

    Doc Al

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    Sorry, but photons do not have a reference frame in relativity. Treating them as if they do will lead to all sorts of nonsense.
  4. Nov 24, 2008 #3
    hey doc thanks. this seems to me to be the only logical answer to my question. but it is really not a satisfying answer at all. I thought one of the fundamental postulates of special relativity was that ALL frames of reference are equally valid. The fact that we could say "yes all of them are valid EXCEPT the reference frame of a photon" seems to be an answer that is simply there to make the theory work. do u agree?
  5. Nov 24, 2008 #4


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    That should be "in every inertial frame".

    There are coordinate systems in which the photon is stationary, but none of them is an inertial frame.

    Yes, it is.

    That's impossible. If it moved at a speed <c before, it had a positive mass. If it did, it can't ever move at the speed of light (which requires it to be massless).

    If you understand that, I don't see why you assumed it to be false in your argument above.

    The speed is ≥0 and <c, but there are no other restrictions on it.

    You may find the velocity addition law useful, if you don't know it already. In 1+1 dimensions:

    [tex]u\oplus v=\frac{u+v}{1+\frac{uv}{c^2}}[/tex]
  6. Nov 24, 2008 #5

    Doc Al

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    No, I don't agree. One of the postulates of relativity is that light travels at speed c with respect to every inertial frame. That means there is no inertial frame in which a photon is at rest.
  7. Nov 24, 2008 #6


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    They are. Even the non-inertial ones. (But the postulate I think you have in mind only mentions the inertial frames). However, the speed of light is only c in the inertial frames. We can make the speed of light whatever we want it to be by choosing the appropriate (non-inertial) coordinate system.

    There is no such thing as a "reference frame of a photon". There's a natural way to associate an inertial frame with a massive object moving at constant velocity. You define the time axis to be the object's world line. You choose the scale on the time axis that agrees with the proper time along the world line. Then you choose the spatial axes so that the speed of light is 1 (or c). (This specifies the frame up to a rotation in space).

    There's no way to do this to a photon. If you let the world line of a photon be the time axis of a coordinate system, you'd have to use something other than proper time to set the scale on that axis, since proper time is zero along a null line. There's also no way to choose the spatial axes so that the speed of light is 1.
  8. Nov 24, 2008 #7
    thanks fredrik, i see your points.

    I've asked the question many times and i understand why people respond the way they do. The answers you give are correct, according to the theory. But the reason i say things like "an object A becoming a photon" even though i know it can't, is because i am trying to think without the restrictions of the theory.

    By no means am i putting down special relativity. i understand its precise predictions. But it always seems like the question can't be answered because of the restricitons of the theory. is it wrong to ask a question based on special relativity that doesn't require an answer that special relativity gives?

    Why can't i say ..."Hypotheticaly, if object A could reach speed c, then doesn't there have to be a small fraction where light does not escape that object at speed c, during the period between 99.9999c and c?" .....maybe it is just meaningless because the only way to answer it is through relativity and that in itself makes the question lose validity.

    I do strongly feel that there is a reason to speak of a photons reference frame, even though it is not an inertial one. This is why i am looking for an answer beyond SR, which is obviously one hard to come by.
  9. Nov 24, 2008 #8


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    I am sorry that you consider a logical answer to be unsatisfying, but what can you possibly expect anyone else to be able to do about that?

    When you deliberately go outside a theory then you cannot reasonably ask what the theory predicts. You would have to develop a whole new theory on your own.

    It seems to me that you know the theory well enough to understand that it is logically consistent and experimentally valid, but you just don't "like" it. Somehow it feels aestetically unpleasing for no logical reason, and even though you know it intellectually it is strange enough to bother you anyway. If this is the case, I truly understand. I don't think there is anyone here who didn't grapple at some point with the wierdness of it all.
  10. Nov 24, 2008 #9


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    If you make assumptions that contradict the theory, then your conclusions won't be about SR. They will be conclusions about a theory in which your assumptions are true. (Unless your argument is of the reductio ad absurdum type).

    In this case, it can't even be asked in the framework of SR.

    If you ask a question based on SR and get an answer that contradicts SR, then there's a problem with the logic somewhere.

    If it could reach c, then it's either massless or we're not using Minkowski space as a model of space and time. I don't understand the rest of your question. You'd probably have to specify what specific model of space and time I'm supposed to use before I can even attempt to answer it.

    You'd have to define what "a photon's reference frame" means before you can really speak of it. Finding a frame in which it's stationary is no problem. Pick any inertial frame and make the coordinate change t'=x-ct, x'=x+ct. (Note that this turns the world line of a photon moving to the right into the new time axis, and the world line of a photon moving to the left into the new spatial axis).
  11. Nov 24, 2008 #10
    hey dalespam,

    Well yes, this is pretty much the case for me. i'm not a physics student or a teacher. I've just read a whole bunch of books on it. I feel like i have a good grasp on it and understand it pretty well considering.

    "When you deliberately go outside a theory then you cannot reasonably ask what the theory predicts. You would have to develop a whole new theory."

    ...this is sort of what i'm getting at. I'm not trying to develop a new theory, or ask anyone else to in order to answer my question. I understand the question becomes meaningless (according to relativity) for reasons we've mentioned. You say i "cannot reasonably ask what the theory predicts".....you're right, i cant for this question, but that doesn't mean that the question can't be pondered and thought about.

    I just feel like even though (accroding to SR) nothing with any rest mass can ever reach light speed, this doesn't mean that we can't talk of something that does. It's more of a thought provoking question than a practical one, and i just find it unsettling that the theory can't answer it because it doesn't allow it.
  12. Nov 24, 2008 #11
    "If you ask a question based on SR and get an answer that contradicts SR, then there's a problem with the logic somewhere."

    ......maybe there is a problem with the logic of SR. But like i said before, i'm not trying to hate on the theory, which is why i've read so much about it. but it seems to me like there IS something wrong there. but what do i know im just an animator lol.
  13. Nov 24, 2008 #12


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    Unfortunately, yes you are.

    Anyway, I understand your discomfort. It is not rational, but you already knew that. You really should be no more upset by this than by the fact that division by zero is undefined, and once you see the connection it may be less uncomfortable.
  14. Nov 24, 2008 #13
    Does this not also imply that photons are not inertial?

    I guess that opens up questions about what is meant by inertial, but let me try to cut off one discussion ... while inertia usually implies mass, I don't believe that "inertial frame" as used in SR implies mass.

    According to http://en.wikipedia.org/wiki/Inertial_frame" [Broken]:

    Inertia itself, again according to http://en.wikipedia.org/wiki/Inertia" [Broken]:

    Photons certainly seem have that (or the splitting of white light into a spectrum would not happen). The inertia of photons is just related to the frequency (a measure of energy) rather than mass (another measure of energy). So, at least in one sense, photons are inertial.

    Is there a sense in which they are not?


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  15. Nov 24, 2008 #14
    thanks for the responses
  16. Nov 24, 2008 #15


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    There is a gradual succession of speeds between 0.99999999999c and c. A massive object can reach any speed between 0.99999999999c and c, but it cannot reach c itself. If a massive object is travelling at constant velocity 0.999999999999999999999c, it is just as good as stationary. So the speed of light is very special sort of boundary. It reminds me of Escher's "Angels and Devils" http://www.artprints.com/-ap/Angels-and-Devils-Posters_p78503_.htm [Broken]. Between some point in the disc and the edge, there are an infinite number of angels and devils. According to Thurston, someone on the disc trying to get to the edge would never get there because the edge is "at infinity" http://books.google.com/books?id=9kkuP3lsEFQC&printsec=frontcover#PPA56,M1.

    As for what light "perceives", my favourite crackpot says "a photon would not 'experience' any passage of time at all!" http://books.google.com/books?id=oI0grArWHUMC&printsec=frontcover#PPA255,M1.
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  17. Nov 25, 2008 #16


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    That's not what I meant. I meant that a person who finds an internal contradiction in SR has made a mistake. It's very obvious that there are no internal inconsistencies in SR. The mathematical model it uses consists of the set [itex]\mathbb R^4[/itex] and some functions. There's no way that it could contain a contradiction that isn't already present in the axioms of set theory. If SR contains a contradiction, then all of mathematics would fall with it.
  18. Nov 25, 2008 #17
    I'm not saying that there's any mathematical inconsistencies in SR, but that doesn't make it perfect. Just because a theory is mathematically consistent and proven to high degrees of accuracy, doesn't mean it describes the full picture. Quite like Newtons laws weren't wrong at all, they just required a deeper understanding such as that of SR.

    I think that to simply say something can reach every speed before C, but never in fact reach C itself, is sort of like sweeping the problem under the table. For me, its the same issue i have when physicists or mathematicians consider a problem meaningless or undefined when the answer turns out to be infinity. Maybe there's nothing wrong with the question, but theres something wrong with the answer.

    By giving such answers to my question like "it's a strange feature of the universe" or "anything with a rest mass can NEVER reach C" is, in my opinion, missing the point. It's the same as if one were to ask Newton HOW gravity transmits its effects and him replying "it just does." I feel like those are the type of answers I am getting on this question and thats what is a little frustrating. If SR wants to claim that we can reach every single speed except C itself, thats fine for theory. But for reality, I think when we come across things like infinity or "a boundary that can never be reached (such as C)," I think it's much more likely that it is the restrictions of the math that lead to such vague answers, rather than the true nature of how the universe works.

    I don't want to come across as attacking SR by any means and I'm certainly in no position to do so. As i said before, I'm no physicist. But just as the concept of infinity is hard to swallow because we don't have a complete understanding of it, I feel like the unreachable boundary of C is hard to swallow for the same reason. Just because the math in the theory says it can't be reached, doesn't mean that it truly can't. It means that up until this point, we have no other way of describing why something can't ever reach C other than saying that it's because that "something" would require an infinite amount of energy. But since the concept of infinity is so hard for mathematicians to cope with, we answer the question by saying that it simply CAN'T. This is the essence of the question I was asking.
  19. Nov 25, 2008 #18


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    curiosBos. I understand the desire to set up thought experiments, such as 'what would a photon experience'?

    But if you do so, you cannot pick and choose the implications of that what-if. Buy into it all the way.

    Consider: whether it started off life moving at c because its a photon, or whether it started off at less than c and was (somehow, say, by becoming massless) accelerated to c, there is a consequence upon the object that you haven't factored in:

    It ceases to experience time.

    And that's why its frame of reference makes no sense.

    Two photons travelling next to each other, are, in fact, not travelling at all. They are simply two static lines.

    Reformulate your initial questions removing all references to time (and this must therefore include all references to movement and speed - which are merely distances per unit time) and you will see that the paradox falls away.
  20. Nov 25, 2008 #19


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    Maybe SR tells us that we cannot observe any mass travelling at c or greater. This makes sense because the object in question would go behind a horizon, wherefrom no signal could reach us. For example a test particle travelling from rest at infinity(!) towards a Schwarzschild BH would not reach c ( wrt a distant observer) until the very moment it reaches the event horizon.

    Also in the FLRW expanding universe model, there is a horizon at a certain distance in every direction, caused by bodies exceeding c wrt to the observer.

    So nature appears to be censoring this from us. But what do we know ? Experiment and/or observation is the only actual truth we can rely on.
  21. Nov 25, 2008 #20
    I am well aware that a photon does not experience the flow of time. But that is not the issue at hand. The only point i'm trying to make is that there must exist some speed at which light does not evade something at light speed. And that speed must be some extremely small fraction between 99.999...c and C itself. The only reason there is no answer is because currently we know of nothing that can surpass this boundary. It's either a photon or it's not. But like i have said multiple times, i'm asking a thought provoking question about reality, not about practicality. Just because our math gives us a boundary to get extremely close to C but never quite reach it, does not mean its the true nature of how the universe works.
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