Do photons have mass?

Question

As a student in a highschool physics class, my teacher has repeatedly told me that photons are massless. Yet, I have also heard from other sources that photons have momentum. If photons were to have momementum, that would mean that they have mass as according to p = mv.

Do photons really have mass?

Also, how would this mass be calculated?

Answer 1

Photons do not have mass, and they do have momentum. The issue is that $p = mv$ is only an approximation. A more accurate equation for the momentum of a relativistic particle like a photon is $pc = \sqrt{E^{2}-m^{2}c^{4}}$. Plugging in 0 for the mass and rearranging, we can see that a photon's momentum is its energy is divided by the speed of light.

Answer 2

1. Your teacher is right that photons have no rest mass.
2. You are right that photons have momentum.
3. The equation $p = m v$ is only valid for objects moving much more slowly than the speed of light, and therefore it is not valid for photons, which move at the speed of light. Therefore (1) and (2) do not conflict
4. The momentum of a photon can be found from its energy $E$ by $p=E/c$. The momentum can also be found for the frequency $\nu$ of the photon by $p=h \nu /c$ where $h$ is Planck's constant. The momentum can be found from the wavelength $\lambda$ of the photon by $p=h/\lambda$.