You're correct that the classical definition of momentum, p = mv, does not directly apply to massless particles such as light. However, in the realm of modern physics, momentum is still defined and understood for massless particles using the principles of special relativity.
In special relativity, the momentum of a particle is related to its energy and momentum 4-vector, which combines spatial momentum and energy into a single mathematical object. For a massless particle, like a photon, the energy-momentum relation is given by:
E^2 = (pc)^2
Here, E represents the energy of the particle, p represents its momentum, and c is the speed of light in vacuum. Notice that there is no factor of mass (m) in this equation because massless particles have zero rest mass.
To find the momentum (p) of a massless particle, we rearrange the energy-momentum relation:
p = E/c
This equation shows that the momentum of a massless particle is proportional to its energy and inversely proportional to the speed of light.
It's important to note that this definition of momentum for massless particles arises from the principles of special relativity and is consistent with experimental observations. In the quantum realm, photons and other massless particles can indeed carry momentum despite having no mass.