system
Given the following post, respond as if you're commenting on Reddit:
human
How can light have momentum if the formula for momentum is p=mv? If light has no mass doesn't that mean it has no momentum?

p=mv where p is momentum, m is mass, and v is velocity.
gpt
The equation p = m v is part of classical mechanics and will hold for particles with non-zero mass at low speeds (compared to the speed of light).

However, in special relativity, things are slightly different. Einstein showed that the following relation between energy, mass and momentum holds:

E^2 = (m c^2 )^2 + p^2 c^2

If the mass of a particle is zero, the first term on the righthand side falls out and you can take the square root to obtain:

E = p c

Which is a relation between the energy and momentum of massless particles, such as photons.

Unrelated to photons, but still interesting is if you consider a particle at rest, so p = 0. The Einstein relation then reduces to:

E = m c^2

which is the equation he is most famous for, the rest energy of particle expressed in terms of its mass and the speed of light.

Obviously there's much more to special relativity than the above relation and its two extreme cases. And an interesting (and necessary!) property is that if you look at the limit case of velocities going to zero (that is, velocities being very small compared to the speed of light), special relativity is reduced to classical Newtonian mechanics.