What is the rest mass of a photon traveling through water?

Question

Let v be the speed of this photon, and c the speed of light in vacuum. Because v>0, the photon has some energy E>0. But the photon is traveling through water so v<c. From special relativity we know that E=m0*γ*c², with: m0=photon rest mass γ=1/sqrt(1-(v/c)²) Because v<c, γ>0. But E>0, then...

Answer 1

The KE of a particle is k = Mvc; where M = m/sqrt(1 - (v/c)^2). But when m = 0, no matter what the speed there is no KE by this equation. In other words, the physics, that there is no rest mass, disallows us from using the standard KE relationship.

But by experiment we know that E = hF is the total energy of photons with frequency F (h is a constant). And the total energy equation of a particle is E^2 = e^2 + k^2 where e = mc^2 is the mass.energy term.

And here's the deal. When m = 0, like photons, we see that e = 0 so that the particle energy equation collapses to become E = hF = Mvc = Mcc = Pc where P = hF/c is the measurable momentum of photons with frequency F.

In other words, as long as photons are going v = c the speed of light in a vacuum, they'll have no rest mass and their energy (which is all KE) is based on their frequency, not their speed.

And as I think about everyone here has rightly said, photons always travel at light speed c. The reason you hear of slower speeds through media is because that speed is an average speed, not the actual speed when the photons are moving within the media. And on average they move through media slower than through a vacuum because they are delayed a bit each time they collide with the atoms that make up the media.

Bottom line. The photons travelling through water are still rest massless. And just to blow your mind a bit, the photons that exit that glass of water are very likely not the same ones that entered that glass of water.

Answer 2

The equation E = mc^2(sqrt(1-v^2/c^2)) does not apply to photons. It was derived for objects with mass moving at speeds close to the speed of light.

Answer 3

Non Sequitur, Rest Mass has no meaning for photons. Photons exist only at c.

Some physical things do NOT work out by manipulating the equations.

Another example is Newton's Law of Universal Gravity.

The equation for universal gravitation thus takes the form:

F=G * (M1*M2)/r^2

That equation gives reasonable answers only if r is NOT very small. When r approaches 0, FORCE approaches infinity. That is not what happens physically.

Answer 4

In fact the speed of photons in water (and other media) is c. but the delays introduced by the absorption an re-emission of photons as they propagate reduces the observed (average) speed to less than c.

A photon has zero rest mass; the formulae you have used are only for particles with non-zero rest mass.

Answer 5

In mixing up c_vacuum with c_medium. A photon always travels at the speed of light (that's kind of the definition of the speed of light). Those equations you have been using are only valid for massive particles in a vacuum, they're invalid for massless particles (i.e. photons) travelling through a medium.

And btw, those formulae also explode if you set v=c :-)