How can photon have energy, but no mass if “m=E/c^2” (E= mc^2)
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E = mc^2 is the simple version of the equation that relates energy to relativistic mass. And yes, light does have relativistic mass (which is equivalent to gravitational mass). In fact Einstein came up with this equation to show that light had mass, which it does, if by mass you mean specifically relativistic or gravitational mass, or mass-energy content.
What we are all used to is that light is massless, by which we mean light has no rest mass (which is more like the amount of “stuff” in something). You get that from the more useful equation that combines rest mass with kinetic energy via:
E^2 = m^2 c^4 + p^2 c^2.
Here, the m is rest mass and the p is momentum. For light, 100% of its energy (or mass) comes from it’s momentum, and none of it comes from rest mass – it has no rest mass. This is true for anything travelling at the speed of light.
You can use these equations to show that for objects with mass, travelling at low speeds, we observe kinetic energy to be roughly 1/2 mv^2 = 1/2 p^2 / m (when kinetic energy makes up a small fraction of the total mass-energy). But for light, this approximation is completely irrelevant, and momentum doesn’t mean the same thing we are used to (in how it’s related to velocity).
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