My understanding is that the pillar of SR is not some special property of light but the fact that all inertial frames are equivalent for physics. In the Lorentz Transformations which follow from this fundamental principle you find that there is a speed like parameter (let’s call it K) which must be constant for all inertial observers; the problem is to find the value of that parameter and fix the LT. You know that it can’t be infinite because then you go back to Newton and Galilean transformations. So since it can’t be infinite you set off to find the value of K. By definition and by your fundamental principle (not by causality arguments) this value must be an upper bound for speed and theoretically it could be as close as you like to infinite but not infinite.

Now in order your theory to have a meaning this bound must be reached at least in principle by a physical phenomenon in Nature; such a phenomenon (a phenomenon whose speed in vacuum is constant for all inertial frames) will then fix the K in your LT uniquely, will set a speed limit in Nature and set the boundaries of causality. All inertial observers contacting experiments should in principle be able to measure that speed and agree on its value.

So you have set your prerequisites for the phenomenon and you wait for suggestions. Here comes Maxwell (and experiment) and says I know such a phenomenon, it is the propagation of light in vacuum. Einstein replies ok then, if this is true then my upper bound is reached in Nature by light propagating in vacuum. So I will use the speed of light to fix the K in my LT and I will call it c from now on instead of K since I know that such phenomenon uniquely fixes my LT.

Thus if there is a speed greater than c it could mean two things, either that Maxwell (and experiment) has tricked you and thus your K remains finite but still undetermined (in that case you hope for another physical phenomenon that could fix your K) or that your fundamental principle is wrong and there is a privileged reference frame. In that sense my understanding is that you can’t exceed that bound (the K) if the fundamental principle of SR is right. K (what ever its value might be) fixes the LT, sets the boundaries of causality and automatically constitutes an upper bound for speed. Causality is a prediction bound to SR, you can’t have SR without causality.

@Giotis. I think thats a very good explanation (and much better than the way SR is often taught, except for one thing, where you say “Maxwell has tricked you”. The only trick open to Maxwell is if light does not propagate in the vacuum and/or light is now a wave. It follows immediately from relativity that any wave propagating in the vacuum [ie in the fabric of space time] must lorentz invariant velocity – else there is a preferred reference frame.

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Matt Strassler | September 23, 2011 at 10:40 PM | Reply

Thanks for your comment. Your words sound fancy, but as you know I draw conclusions based on equations. As of yet I don’t know any reason to agree with you, but my mind is open. Could you provide a reference to an article which shows there are no loopholes in your argument?
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Philip Gibbs | September 24, 2011 at 2:30 AM | Reply

Matt (sorry I called your Mark before oops) I think the onus to produce a reference is on the other side. You say that dramatic claims are not justified but I would say that one of four possibilities has to hold.
(1) They made an error. This could mean some embarrassing mistake at one point of the experiment or an unlucky combination of errors over several steps all leading in the same direction
(2) FTL travel and communication with the past is possible. This would be the conclusion if we accept that relativity and the Lorentz transformations are correct at the velocities seen in particle accelerators.
(3) Einstein was wrong. If relativity fails at such velocities then it really is wrong and we have to go back to the drawing board.
(4) We face a major paradism shift. The only other way out is if there is a wrong assumption in the way we think about these things and it is of a nature that we can’t really see it until experiment forces us to rethink our basics. This has happened before but not often.

If you think there is a less radical solution that does not justify at least one of these headlines then I think a reference for that is needed. I know Ellis wrote a nice paper about the scales of violation of Lorentz invariance that led to this measurement but it was a paper that deliberately avoids questions about the details of what kind of theory would be required to provide a result at these scales.

By the way I don’t mean to be confrontational. Your work on this blog has been top class and i have learnt a lot from reading it. I just think this point is an interesting one to argue about :)

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Matt Strassler | September 24, 2011 at 8:37 AM |

Very good. Well, we both made dramatic statements; but I would say they are of slightly different character. You say there is no way out without allowing apparent non-causal behavior, which was a dramatic statement which requires proof that there is no way out; I say only that we don’t know that, which is easier to prove, especially if I simplify it to “I don’t know that”. I know of no evidence yet that Einstein’s theory, which combined with quantum field theory so beautifully describes thousands of experiments, cannot be modified in such a way as to accommodate this result. But I am open to evidence.

I did spend part of yesterday discussing the results with several young scientists from Harvard and MIT, and we noted several technical problems reconciling this result with other experimental results and with existing theory. I’ll summarize those soon.

But it’s quite a jump to saying there’s no universal speed limit, that backward-time-communication is possible, or that the long-cherished causality that is built into that combination of Einstein and quantum field theory must be entirely dropped. Certainly this experiment gives no direct evidence of that; it just measures the speed of one set of particles, at one set of energies. And then there’s the supernova observation, which is pretty clean, in my view. So let’s deal in firm equations and not in wild speculations, and not confuse the public by tossing crazy ideas around.

Papers one should be reading include summary reviews by Alan Kostelecky and his collaborators. There is also some interesting work by Coleman and Glashow from the 90s, though I think in fact it cannot explain the current observation.