Could photons have mass?
It could simply mean that neutrinos have less mass than photons, so that the true c should be the speed of neutrinos, not photons.
This was also brought up in the comments section at io9. There’s an element of truth to this observation, since we don’t know for certain that photons have zero mass. From an observational perspective, there’s no functional difference between “zero” and “too tiny to matter.”
But how small could the photon mass be and still be consistent with observations? Short answer: waaaay smaller than is required to explain the neutrino results. Long answer is a bit technical, so if you’re averse to equations, you may want to quit here.
Let’s play along and assume:
- Neutrinos are massless (which they clearly aren’t, since they oscillate) and travel at (which I will cease to call “the speed of light” for this discussion).
- Photons have some (as yet unknown) mass, .
- The disparity between the speed of light and neutrinos is:
where is the speed of the photon. This is the size of the difference we’re talking about, if we take the OPERA result literally.
- For our initial purposes, we’ll suppose that all calibration is done using light at (red).
- Special relativity is correct.
So, under these assumptions, how massive is the photon? Well, we can compute the factor easily enough:
Problem 1: This is not a big factor.
Protons in the LHC have a factor of something like 3500, which means that we would regularly produce particles traveling faster than light. We would notice that.
But, moving on…
Supposing this is the case, we can now compute the mass of the photon. The energy of a relativistic particle can be computed from its wavelength:
we can compute:
I should point out that this wouldn’t account for dark energy or anything like that. The mass-energy for a photon would be only about 0.01 eV, and even in aggregate would constitute less total mass than protons and neutrons.
But even at this tiny mass…
Problem 2: Photons would be non-relativistic, even in the Infrared.
To put things in perspective, thermal emissions given off by people (approximately) are about 0.02eV. If half of that is mass energy, then the photons would move at much less than c. We’d notice. Even worse, photons from the cosmic microwave background (T=3K), are a hundred times smaller. The spectrum wouldn’t even look like what we normally consider thermal, but observationally it does and to insane precision.
But even stranger, photons are the carrier particle for electromagnetism. If you have a massive carrier particle, it drops off after a finite range.
Problem 3: Electromagnetism would be a short-range force.
The range of a force with a mediator particle, is:
where is the Planck length (around ) and is the Planck mass (around ).
You’ll notice that if the mass of the mediator goes to zero, the force becomes universally long range. For the massive photon, this would yield:
Magnets and capacitors and so forth wouldn’t work on even remotely macroscopic scales.
Even worse, we know that magnetic fields operate on the earth (and really, on scales of the solar system and Galaxy, but since your compass works, let’s just focus on the earth), meaning that the maximum possible photon mass consistent with earth-scale magnetic fields is a factor of times smaller than what we’re discussing here.
Finally, there’s the fact that if the photon were massive, different frequencies would travel at different speeds.
Problem 4: Blue light would travel much faster than red.
I’ve done the equations already, but using this mass, we’d find:
But since the uncertainty in the speed of light is much less than 1 m/s (or really, since the uncertainty in the definition of the meter is that small fractionally), we’d notice this effect, even using just visible light.
And remember, all of this is based on assuming the minimum possible photon mass consistent with the explanation provided. If neutrinos also have mass (which they do) photons would have to be even more massive.
In summary: The OPERA results probably don’t tell us anything new about how photons work.