Could somebody explain to me why we're able to calculate the mass of a Photon (theoretically) from the Planck Relation by substitution in mc^2 for E in the lefthand side of the equation, when a Photon doesn't have any mass? I constantly hear that Photons are massless, so is this just incongruous for some reason I don't know?

Question

mendicant_bias · Answer

I.E., Planck Relation: $$E = hv ||| E _{photon} = \frac{ hc }{ \lambda } $$
The second part is arrived at by substituting in the relation between frequency and wavelength for electromagnetic radiation,$$c = \lambda \nu $$
Then to what I'm talking about, substituting in mc^2 for E in the Photon variant of the Planck Relation:

$$E = mc ^{2}$$$$mc ^{2} = \frac{ hc }{ \lambda }|||m = \frac{ h }{ \lambda c }$$
How does this make any sense if Photons are supposed to be massless?

mendicant_bias · Answer

@jim_thompson5910 @ganeshie8 @dmezzullo Anybody here understand/know this?

anonymous · Answer

I think that the rest mass is zero, the mass we get must be the mass when travelling at the speed of light.

mendicant_bias · Answer

But photons are never still. They don't have a real rest mass. All electromagnetic radiation, far as i'm aware, travels exactly at the speed of light, despite their frequency and wavelength varying.

anonymous · Answer

Hi @Mendicant_Bias My (albeit shoddy) understanding of the matter (pun intended!) is that this "mass" one calculates from your two relations is referred to as relativistic mass, which is not very highly regarded ;) (see here: http://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass) For an explanation why: "The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature."