Huh? Their rest mass is 0, but, they have energy, E = h * frequency iirc, so, shouldn't they therefore have a relativistic mass? (if one is going to use the concept relativistic mass at all that is)
It doesn't work for photons, if you want to calculate the momentum (mass) of photons it will be planck's constant / λc.
Going going by the standard relativistic mass calculation of SR alone m = γm0, γ = 1/[square root of (1 − v2/c2)], you get a division by zero which is well a no no, but this is where as you approach the speed of light your mass becomes infinite comes from.
Right. So, if one wants to talk about the "relativistic mass" of a photon, the result is (Energy of the photon)/(c^2) = h/(λc) = h*(frequency)/(c^2) , which is what was implied by what I was originally saying, and which is not 0 .
So, the relativistic mass of a photon (if one wants to use the concept of "the relativistic mass of a photon" at all, which one might quite reasonably not want to, and which yes, does depend on the frame of reference) is not 0, in any frame of reference.
Again that's not relativistic mass, relativistic mass in special relativity is dependant on the velocity, the momentum of a photon is not dependant on the velocity of the photon in vacuum or in any medium. A photon of a given wavelength (energy) has the same momentum regardless of medium it's traveling in, it's also not affected by the center of momentum as in there is never a frame of reference where the rest mass of a photon is equal to its relativistic mass for a given observer.
In general you shouldn't consider relativistic mass to be a "thing" for either massless massive particles, special relativity is useful, but it doesn't attempt to describe the universe as we know it.
As for GR well it's more complicated, GR doesn't give you the ability to calculate the invariant mass of a given system, that's arguably one of its weakest points or at least it's weirder points it's also where people try to poke holes in the theory looking for violations of the equivalence principle.
Is the relativistic mass required to be dependent on the velocity or on the reference frame ? For most massive particles, depending on the one should be equivalent to being dependent on the other, right? Seeing as for massless particles , the velocity is always c and therefore "dependent on the velocity" doesn't really make sense, why isn't "dependent on the reference frame" the appropriate extension of the concept?
The [the quantity I described] definitely depends on the reference frame for which the photon is being described, because the photon's frequency and wavelength depend on ones reference frame.
I don't know why you brought up the photon traveling through different mediums. I've been assuming it was traveling through a vacuum. Bringing in a medium seems like it would just complicate things. Maybe you thought I was thinking of it moving in a medium so that it was sorta moving at less than c, so that there could maybe be reference frame for which it is at rest? This is not what I was thinking of. I mean to address only the case of a photon in a vacuum.
And yes, of course there would be no reference frame in which the photon's [the quantity I'm describing] becomes equal to its rest mass, which is 0. That is implied by what I've said, namely, that the [the quantity I'm describing] is never 0, but changes with the reference frame. There are reference frames in which [the quantity I'm describing] is arbitrarily close to 0, but none in which it is 0.
The footnotes at the bottom of the wikipedia article on "Photon" do describe photons as having non-zero relativistic mass, though also notes that some prefer not to use the concept of relativistic mass.
In any case, at the very least, if one is to speak of the relativistic mass of a photon, it is not 0. If anything it is either "nonsense quantity" or [the quantity I have been describing] . Not 0.
The wikipedia entry is a bit of a hit and miss, but in general "relativistic mass" isn't a concept that is used, in fact many SR courses don't skip it per-say but don't call it that way.
The point is if you apply any of the relativistic momentum formulas to photon you will not get a sensible result, basically you'll either get 0 or 0 over 0, same goes for other mass related things in special relativity such as center of momentum and center of mass also break down.
The "mass" of a photon doesn't come out of special relativity, and trying to calculate it using SR will not work, photons have linear momentum this comes out of Planck's law and the photoelectric effect.
