Yes (some people would say the photon has a "mass equivalence" but that's really just conceptual)! One of the greatest scientific discoveries of all time:
"""Johannes Kepler put forward the concept of radiation pressure in 1619 to explain the observation that a tail of a comet always points away from the Sun.[9]
The assertion that light, as electromagnetic radiation, has the property of momentum and thus exerts a pressure upon any surface that is exposed to it was published by James Clerk Maxwell in 1862, and proven experimentally by Russian physicist Pyotr Lebedev in 1900[10] and by Ernest Fox Nichols and Gordon Ferrie Hull in 1901."""
> [Energy-Momentum relation] is the extension of mass–energy equivalence for bodies or systems with non-zero momentum. It can be written as the following equation:
E^2 = (p^2)(c^2)+(m^2)(c^4)
E^2 = ppcc+(0)(c^4)
E = sqrt(ppcc)
E = sqrt((p^2)(c^2))
c is the speed of light in a vacuum; without superfluidity (which occurs in helium in deep space for example); and without nonlocal entanglement; and without loophole-free solutions to spacetime (quantum teleportation).
Anyways, further from "Energy-Momentum relation":
> The Dirac sea model, which was used to predict the existence of antimatter, is closely related to the energy–momentum relation
> The Dirac sea interpretation and the modern QFT interpretation are related by what may be thought of as a very simple Bogoliubov transformation, an identification between the creation and annihilation operators of two different free field theories.
> [...] Dirac sea theory has been displaced by quantum field theory, though they are mathematically compatible
SQG Superfluid Quantum Gravity says there needn't be antimatter; there is pressure and there are phases of matter in a varyingly Superfluidic cosmos. The Dirac wikipedia article also mentions SQG.
And further from "Energy-Momentum relation":
> The quantities E, p, E′, p′ are all related by a Lorentz transformation. The relation allows one to sidestep Lorentz transformations when determining only the magnitudes of the energy and momenta by equating the relations in the different frames
> But that's for at-rest inertia. Photons are only very rarely if ever "at rest".
Not just rarely; photons are never at rest, period. In circumstances where one might intuitively think they might change speed, instead they change frequency.
That includes that they do not change speed in materials with a different index of refraction than a vacuum, but in that case, they do seem to, so as a shorthand it's often said that the speed of light in e.g. glass is slower than in a vacuum, but that's really just a shorthand -- so that's a can of worms.
Anyway your second equation is the full version of your much more famous first equation precisely because we need the extra term for photons (or any other massless things).
