My Quantum Mechanics' teacher said today on the class that photons don't have mass. I was puzzled because I knew that photons have momentum. If a particle hasn't mass then its momentum sould be $0$ because $p=mv$.
So, how is this possible? Is $p=mv$ only true for Classical Mechanics?
$p=mv$ is true for relativistic mechanics as well. But one should be careful about the definition of $m$. There are two type of masses, rest mass, usually denoted as $m_0$ and the relativistic mass $m=m_0/\sqrt{1-v^2/c^2}$. When physicists say "a particle is massless", this is a jargon which actually means the rest mass $m_0=0$.
Photon has no $m_0$, but it has a nonzero $m$. Roughly speaking, using the equation above you get $m=0/0$, which can be nonzero. BTW, in the famous $E=mc^2$, the $m$ is relativistic mass too, so photons also have nonzero energy.
