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As I understand, photons are considered mass-less, which is a necessary condition for moving at the speed of light. However, does that mean their density is 0, as they will occupy some volume. If their density is zero, that means there is no matter inside a photon. Thus, shouldn't a photon be able to pass through matter instead of colliding with it? As $E = mc^2$, shouldn't a photon have zero energy, as it has zero mass?

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The complete energy relation is $$E^2 = m^2c^4 + \lvert \vec{p} \rvert^2 c^2$$ The photon has $m=0$, so we are left with $$E = \lvert \vec{p} \rvert c$$ (we don't care about the negative solution here). But according to De Broglie, it is $\vec{p} = \hbar \vec{k}$, so we have $$E = \hbar c \lvert \vec{k} \rvert$$ but $k=\frac{2\pi}{\lambda}$ and $\hbar=\frac{h}{2\pi}$. Therefore $$E=h\frac{c}{2\lambda} = h \nu$$ where $\nu$ is the frequency of the photon.

A photon is not a matter particle (fermion), but a force carrier particle (boson). A boson is not subject to the Pauli exclusion principle. Any number of bosons can occupy the same quantum state. So, if you want to call it like that, one could say the photon does not "occupy some volume". But it still interacts with matter, as it couples to electric charges. The simplest example is Compton scattering.

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  • $\begingroup$ So you can have more than one photon in a single point in space? $\endgroup$ – Gummy bears Jun 19 '14 at 7:16
  • $\begingroup$ A photon is not just a particle, but also a wave. It will therefore occupy not just a single point in space, but yes, any number of photons can occupy the same space. This is not the case for e.g. electrons (since they are fermions). But still: two electrons can occupy the same space, given that one is spin up and one is spin down. Then they don't share the same quantum numbers and are allowed to sit at the same spacetime point. $\endgroup$ – pfnuesel Jun 19 '14 at 7:22
  • $\begingroup$ I understood the part about why they have energy but even if two photons can be at the same point in spacetime, how can they have zero density? There has to be son something. $\endgroup$ – Yashbhatt Jun 19 '14 at 10:31
  • $\begingroup$ What density? Mass density is zero, since there is no mass. Energy density or number density is not zero. $\endgroup$ – pfnuesel Jun 19 '14 at 10:34
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    $\begingroup$ Short answer: because they are fermions. Long answer: physics.stackexchange.com/questions/24389/… $\endgroup$ – M.Herzkamp Jun 19 '14 at 11:25

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