How does relativistic momentum work for photons with no rest mass?

[JerryL]

I’ve been trying to wrap my head around the concept of a photon having momentum despite having no rest mass. In my classical mechanics class, momentum was always mass times velocity, so this seems like a direct contradiction. I don’t understand how the relativistic momentum equation resolves this, especially when considering something like radiation pressure.

[EllaW]

Think of it this way: for light the relation between energy and the quantity that mediates push is E = p c when the rest mass is zero. So if a photon has energy hf, then p = hf / c. That means it carries a small amount of the quantity that mediates push. The classical mv picture doesn't apply to light because its rest mass is zero; in relativity you use E^2 = (pc)^2 + (m c^2)^2, which reduces to E = p c for m=0. So light can push on surfaces. If a beam is absorbed, the surface gets a kick equal to p, and if it's reflected it gets about twice that kick because the photon reverses direction. This is what creates radiation pressure.

[LukeIM]

From a hands on angle, I tried a small solar sail project. The sunbeam carries energy, and when it lands on a thin reflective sheet you feel a tiny push on the sheet. It’s not dramatic, but with a very sensitive scale you can see the force change when you angle the sail or switch from absorbing to reflecting. The practical rule I remember is that absorption gives F roughly equal to energy flux divided by c, and reflection doubles it.

[IsabellaG]

Another way that clicks for some people is the four momentum idea. For a massless particle the relation E = p c holds, so along its path there is a quantity p that acts as the carrier of impulse. The math isn't complicated here, but it shifts the intuition from mass to energy flow. It still lets the beam transfer a kick to a surface when the energy is absorbed or reflected.

[AlexanderMM]

Do you think the real snag is thinking in terms of rest mass, or is there another piece about how energy flow and direction play into the effect you’re seeing in radiation pressure experiments?