# One has to wonder about photon interaction, and when to think of them

by Science>All
Tags: e=mc^2, einstien, light, mass, photons
 P: 906 One has to wonder about photon interaction, and when to think of them Photons have a mass identically equal to zero. The equation E mc^2 cannot be applied to massless particles such as photons. The short explanation is that photons have momentum, but no mass. The longer explanation has to come with the derivation of E = mc^2. As Cragar said, the actual equation for a massive particle is, $$E =\sqrt{p^2c^2 + m^2c^4}$$ This can be rewritten as, $$E = mc^2\sqrt{1+\dfrac{p^2}{m^2c^2}}$$ We can Taylor expand this in terms of p^2/m^2c^2, $$E = mc^2(1+ \dfrac{1}{2}\dfrac{p^2}{m^2c^2}-\dfrac{1}{8}(\dfrac{p^2}{m^2c^2})^2+...)$$ When we assume a small momentum (in nonrelativistic cases the momentum is always much smaller than the mass times c), we can just take the first two terms, $$E = mc^2+ \dfrac{p^2}{2m}$$ One can recognize the second term as the formula for kinetic energy. However, in the nonrelativistic limit we recover the peculiar mc^2 term, which seems to be momentum-independent. This is why we say tha E = mc^2. Note also that in the derivation, we must assume that p << m, and this certainly isn't true for a massless particle. E = mc^2 only works when you understand that a particle can have momentum but no mass. Hope this helps!