I'm an amateur physics enthusiast with no formal university education in Physics. So my question might sound very naive, so forgive me.

I had this question in the back of my mind since the wrong discovery of neutrinos travelling faster than light.

My understanding of special relativity is as following. You can measure the physical parameters like length, time, mass of objects in a frame of reference (A) from another frame of reference (B) having a constant relative velocity with A by only looking into the information signals coming from A to B. Since the light(electromagnetic radiation) is the fastest known carrier of information between two frames and since light has a constant relative velocity with any moving inertial frame, the length/time measurements between moving inertial frames are formulated based on its velocity.

Back in 2011 when the 'faster than light' neutrinos were reported one point I heard in popular science reports was that it will invalidate the special theory of relativity. But why is it so? Any particle faster than light would simply interchange the constant $c$ in the special relativity with some new constant(provided this particle also has a constant relative velocity with inertial frame). Doesn't the special relativity theory still holds with the information being exchanged with this new fast particle instead of light? As long as these particles don't travel with infinite velocity all measurements from moving frames will have the time dilation and length contraction. Is my understanding right?

Edit 1: I see another question here and the answer to that seems like my understanding is right. Special relativity theory can be derived from any particle travelling with a constant speed.

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    $\begingroup$ possible duplicate of What is so special about speed of light? $\endgroup$ – John Rennie Aug 22 '14 at 10:31
  • $\begingroup$ @John Rennie, I had already seen that answer before posting this question, but that doesn't answer my question. $\endgroup$ – PermanentGuest Aug 22 '14 at 10:33
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    $\begingroup$ $c$ is special because it's the only speed a massless particle (like a photon) can travel at, and any massive particle must travel slower. Whether a neutrino is massless or massive, if it travelled at $> c$ that would break special relativity. $\endgroup$ – John Rennie Aug 22 '14 at 10:53

Your understanding is right, but you have to also realize that there is a rich variety of experimentally verified relativistic effects where the constant $c$ is occurring and this constant would suddenly have to be changed. Namely all the particles suffice the relation $$E = mc^2 = \sqrt{m_0 c^4 + p^2 c^2}$$ This relation is used e.g. to compute the mass defect of the nucleus relating precisely the "missing mass" and released energy. Were a different constant $c'$ the "speed limit", we would get it also in this relation. Another limit for large velocities of the $E = mc^2$ is $$E = pc$$ Used every day thousands of times in particle accelerators for understanding collisions. They also feel the "speed limit" very well when accelerating the particles. So, experimental particle physicists would notice very soon if $c$ were a different constant. This is not going to be a complete list, but another effect quantitatively connected with $c$ are the prolonged life-times of particles. For a mean particle life-time at rest $\tau$ we get through time-dilation it's lifetime $\tau'$ when moving with a velocity $v$: $$\tau' = \gamma \tau = \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$$ So e.g. a particle such as a muon with a lifetime a few microseconds can be observed to have a life-time of a few seconds.

All these effects have been observed and tested so many times, it is more or less impossible that a different constant than $c$ would occur in them. So it has to be understood that when we say "the speed of light" we do not mean the speed of one particle but this constant springing up basically everywhere in high energy physics and quantitatively determining phenomena.

It would be inconsistent to observe all these effects with a precise $c$ and find a particle moving at a speed $c + \epsilon$. Thus, relativity would be falsified and a different framework would have to be found. (probably a very very ugly one)

  • $\begingroup$ Thank you for the answer, Void. If the new particle is the medium of information exchange, then the 'signals' will be 'observed' with different relative velocity (c') within the absorbing frames, right? In this case, wouldn't all these formulas remain the same? $\endgroup$ – PermanentGuest Aug 22 '14 at 15:59
  • $\begingroup$ The only reason for often taking light as "the" medium of signals is because it is the fastest one. Anything can be a carrier of signals. You can see e.g. in this derivation of time dilation that the constancy of $c$ is essential for all the effects. But one of the consequences of such considerations is that no massive particle (such as a neutrino) can reach (or be at) the speed of light. But relativity allows for massive particles to be always above the speed of light. $\endgroup$ – Void Aug 23 '14 at 7:11
  • $\begingroup$ Ok, so $c'$ would then not be constant in all frames of reference and larger than $c$, we can work with that. However, you can see e.g. in this answer that could violate causality. E.g. you could get a message about what the results of the lottery would be tonight before sending them afterwards to an accomplice. Physicists hate gambling, so this is not allowed. (Yeah, and it also violates the fundamentals of science unless some complicated modifications are made to stop this.) $\endgroup$ – Void Aug 23 '14 at 7:15

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