How does light have energy? How can light exert force?

Question

Here is what I know:

Photons have no mass.

Force is change in momentum over change in time.

Momentum is mass times velocity.

E=mc²

SO HOW DOES LIGHT HAVE ENERGY AAAA

I also read that massless particles can have momentum and I do not understand that at all.

Please explain how all of this is connected and how light has energy and exerts force. Thank you!

In: 9

Answer 1

The full formula is E^2 = m^2 c^4 + p^2 c^2

E=mc^2 is a simplification for particles with mass at rest.

Photons carry momentum (p) and thus have energy.

Note that force is change in momentum over time, but it doesn’t really apply to individual photons.

A single photon transfers it’s momentum instantaneously. Though if you have a steady stream of photons you can calculate a force based on the average rate of momentum transfer.

Yes it’s weird.