# If photons end up having a tiny mass, say $10^{-54}~\rm kg$, what would be the universal speed of massless particles?

First, I'm no expert so sorry if I get anything confused but I tried to research as much as could before asking this.

So while it is pretty much accepted that photons are massless (Despite this question, I do believe this to be true), we also know that it is possible it could just have a very very very tiny mass. I think $10^{-54}~\rm kg$ is currently the maximum possible limit it could have.

So my question are, if the photon does end up having mass, then what effect would that have on the value of $c$? Is it possible the new $c$ could be infinite or almost infinite? Or is more likely its just slightly faster than a photon.

Second, what implications would this have on the expansion of the universe? We know that universe is expanding faster than light can keep up with it due to what we know of space-time. Would there be any kind of possible correlation between this new $c$ and that expansion?

Edit: And to clarify, when I refer to the new $c$, I mean the speed of a possible massless particle in the case that photons have mass. Not the speed of light in a vacuum.

• "c" is not really the speed of the light, it is much more an universal constant. I.e. it belongs not specifically to the photons, it is a parameter of our universe. If the photons have a minimal rest mass, c wouldn't change, but the speed of the light would be a little bit slower as c. – peterh says reinstate Monica Jul 11 '16 at 19:09

The limit c comes from Maxwell's equations for electromagnetic waves in vacuum. This does not know about photons, is pure mathematics given E and B fields and permittivity and permeability of free space.

$$c= \frac1{\sqrt{\mu_0\varepsilon_0}}= 2.99792458\times 10^8~\mathrm{ms^{-1}}\;.$$

If photons do have a mass within the experimental limit, Quantum electrodynamics will be affected and the way that QED results connect with classical electromagnetic waves, light. The validation of Maxwell's equations is not in doubt, there are innumerable experimental confirmations. So light will be moving with velocity c anyway, regardless of the photon .

One would have to set up a theory that would build up the classical wave with velocity and its limit c from photons with tiny masses. The standard model of particle physics would be much changed.

The standard model fits existing data and predicts new data with great precision. Any drastic modification should predict measurable results in order to consider it as a new model of nature.

That is why the misreading of experimental data on neutrino beams which assigned to neutrinos velocities higher than c ( and neutrinos do have a tiny mass) created such a furor. The whole standard model would have to change. Fortunately it proved to be an experimental error.

• "So light will be moving with velocity c anyway, regardless of the photon ." This cannot be true, can it? – xi45 May 8 '16 at 22:24
• Fortunately it proved to be an experimental error. Or, unfortunately... ;-) – Michael Jul 11 '16 at 4:08
• @xi45 But we know it to be true. We'd just have a hard time figuring out the significance of $c$, now that the photon turned out to have finite mass. – LLlAMnYP Jul 11 '16 at 9:13