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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?

Qmechanic
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Élio Pereira
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    Just in case one of the answers does not contain this trivial piece of truth: we do not know if photons have rest mass, or not. We do know that, it they do, it has to be extremely small, so small, indeed, that we can neglect it for all known purposes. – CuriousOne Sep 16 '15 at 19:24

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$p=mv$ 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.

pathintegral
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    There is only rest mass and other concepts of mass are unenlightening. – Robin Ekman Sep 16 '15 at 14:59
  • Yeah, sure. But it is important for newcomers to know this distinction. I've heard physicists talking with general audience about all kinds of massless particles and on the other hand the most famous equation says $E=mc^2$. – pathintegral Sep 16 '15 at 15:10
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    I think it is better to let this outdated concept die and explain that the correct relation is $E^2 = m^2 + p^2$. – Robin Ekman Sep 16 '15 at 15:44
  • Einstein would be mad at you :) – pathintegral Sep 16 '15 at 15:54
  • I'm doing a PhD in physics and I have no idea about the meaning of "relativistic mass", if you study some QFT it can be really misleading. $E=m c^2$ when the particle is at rest. – Karozo Sep 16 '15 at 23:36