How can a photon have momentum without mass?

[Nora3]

I’ve been trying to wrap my head around why the concept of a photon having momentum despite having no mass doesn’t click for me. I get the equation p = h/λ, but my intuition keeps pulling me back to classical momentum as mass times velocity, and I can’t seem to reconcile the two frameworks properly.

[Kevin.L]

I remember staring at p = h/λ and trying to fit it into mv intuition. In a lab thought experiment, when light hits a tiny mirror the mirror gets a real push. That made momentum feel tangible even without mass, but the mv picture kept tugging at me.

[PatrickT]

For a photon the energy is hf and p = E/c, so p = hf / c. Since λ = c/f, you get p = h/λ. The click comes from treating momentum as a property of the wavefront rather than mass.

[PenelopeJ]

I ran a quick, tiny experiment in my head: a laser pulse imparting a hairline impulse to a foil. The impulse is real but minuscule; it matches p = h/λ only as a statistical sense, which is maddeningly abstract when you look for a clean picture.

[RileyA]

I keep thinking maybe the problem is that I’m forcing a single classical story onto something that isn’t classical at all. Momentum in relativity isn’t mv when you’re massless, and maybe I’m chasing the wrong kind of intuition. Is this really the core issue, that I expect momentum to behave like mv even for light?