It wouldn't break current theory, it would just mean that photons travel slower than "speed of light" and have non-zero rest mass. Constant c in relativity instead of speed of photons would just mean fastest speed possible.
For example, there is a certain speed where if you exceed it you are able to violate causal time relationships. I can't think of any experiments that would validate this. However, there is also the fact that theoretically, if you attempt to accelerate matter to the speed of light it's mass will increase infinitely. So if you accelerate it a little bit it's mass should increase a little bit, and you should be able to confirm the speed of light through an experiment where you measure infinitesimal increases in mass during large acceleration.
So my comment is that if he just broke the speed at which light travels, then everything is fine. But if he broke the speed at which you are able to violate causality, or the speed at which the mass of an object is infinite, then our entire understanding of physics is likely to be invalid.
Related reading - tachyon pistols
So you can't just use c for "the highest speed any particle can have in vacuum".
Non-zero rest mass photons will break a lot of theories.
Plus, the "speed of light" is not merely an experimental result coming out of an interferometer. It's also a theoretical result, e.g. from Maxwell's equations - that's the one referred to by special relativity.
I think this is wrong. Regardless of the medium the speed of light is always constant. It seems to slow down because the photons are getting absorbed and re-transmited by atoms. But the speed of light is always the same regardless.
Here is a relevant piece:
When light enters a material, photons are absorbed by the atoms in that material, increasing the energy of the atom. The atom will then lose energy after some tiny fraction of time, emitting a photon in the process. This photon, which is identical to the first, travels at the speed of light until it is absorbed by another atom and the process repeats. The delay between the time that the atom absorbs the photon and the excited atom releases as photon causes it to appear that light is slowing down.
If the photon is traveling less D over the same amount of T, I am ok with saying the velocity is lower, and it has slowed down.
Nobody would say that they slowed down if they increased their speed as they went through a turn.
"Light traveling within a medium is no longer a disturbance solely of the electromagnetic field, but rather a disturbance of the field and the positions and velocities of the charged particles (electrons) within the material. The motion of the electrons is determined by the field (due to the Lorentz force) but the field is determined by the positions and velocities of the electrons (due to Gauss' law and Ampere's law). The behavior of a disturbance of this combined electromagnetic-charge density field (i.e. light) is still determined by Maxwell's equations, but the solutions are complicated due to the intimate link between the medium and the field. Understanding the behavior of light in a material is simplified by limiting the types of disturbances studied to sinusoidal functions of time. For these types of disturbances Maxwell's equations transform into algebraic equations and are easily solved. These special disturbances propagate through a material at a speed slower than c called the phase velocity."
As another commented pointed out, you're splitting hairs. The "speed" of light and how fast it is "moving" depends on how you define those terms. The second paragraph of the wikipedia speed of light article has it right "The speed at which light propagates through transparent materials" - which does change.
There is a good description of what is going on in this Stack Exchange post:
http://physics.stackexchange.com/questions/13738/propagation...
It explains why saying "c is the speed of light" makes sense, because when we say light is traveling more "slowly" through a material, we are including the time spent interacting with the material, being absorbed and re-emitted.
I'm bristling a little at your statement that "the speed of light is not constant". Imagine two men walking at the same speed from A to B. But one of them is walking in a straight line, while the other is zig zagging. It would be fair to say that the one walking in a straight line is travelling from A to B faster, even though they are both moving at the same speed. The speed of light is a constant, it is just that light travelling through a medium doesn't necessarily spend all of its time travelling in one direction.
And as for the "c" in e=mc^2, doesn't this suddenly make "c" an unknown constant? Doesn't the fact that "c" changes suddenly change the values of the other variables in that equation as well? That seems pretty fundamental to me...
So if there's something faster, it changes our understanding of photons but not the existence of this fundamental maximum speed.
As you note, our efforts to measure c may have been off due to measuring the wrong thing, but I don't know the ramifications of a small % change in c.
(I'm not a physicist)
(Another basic assumption, this time for general relativity, is the equality of inertial and gravitational mass, which is not a self-evident thing. However, so far no difference has been found. (see http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_experiment)
Photons speed up and slow down routinely, depending on what medium they're traveling through. c, as it is used in the equations of relativity, is currently believed to be equal to the speed of light in a vacuum. But, with my limited knowledge of GR, my understanding is that gaika is correct and that the rest of the theory can still stand if this equality is broken.
A photon's instantaneous speed is always the speed of light.
Do they really? As far as I know their speed is always constant in any medium. They just seem to slow down because they get absorbed and re-transmited. That is where the lost of velocity comes from. When traveling between one atom and another, which is a vacuum, they are always traveling at the speed of light.
I don't know whether changing c by this amount would break many experimental results. Adding a rest mass to photos sounds potentially revolutionary.