How Can Photons Be Massless Yet Have Energy According to Einstein's Equations?

[ginevradabenci]

TL;DR

How can photons be massless if they have energy?

Since E = mc^2, how can photons be massless? If a photon has no mass, then, according to Einstein's formula, its energy is given by E = 0 x c^2, which is 0. Yet, photons do have energy. This seems to be a complete contradiction. Please explain! Thank you.

 

[Ibix]

Since E = mc^2, how can photons be massless?

That formula is only correct for stationary massive objects. The general formula is $m^2c^4=E^2-p^2c^2$, from which you can see that you can have zero mass objects with non-zero energy as long as their momentum, $p$, satisfies $E=|p|c$.

 

[PeroK]

TL;DR Summary: How can photons be massless if they have energy?

Since E = mc^2, how can photons be massless? If a photon has no mass, then, according to Einstein's formula, its energy is given by E = 0 x c^2, which is 0. Yet, photons do have energy. This seems to be a complete contradiction. Please explain! Thank you.

The equation $E = mc^2$ only applies to a particle with mass. And, indeed, that's its energy only when it is at rest. The full equation is:
$$ E^2 = p^2c^2 + m^2c^4$$Where $p$ is the magnitide of the particle's momentum. This equation applies to all particles, whether they have mass or not, and whether they have kinetic energy or not. For a photon with zero mass, the equation reduces to $E = pc$.

 

[Herman Trivilino]

Since E = mc^2, how can photons be massless?

Because the correct equation is $E_o=mc^2$ where $E_o$ is the so-called rest energy. Rest energy is one of Einstein's greatest discoveries.