[Coda]

Now we're getting into relativity. Fun stuff!

E=mc^2 is actually a simplification of the full formula, which is E^2 = p^2*c^2 + (m*c^2)^2, where p is momentum and m is rest mass, by setting momentum equal to zero (that is, considering an object at rest). If you instead set mass to zero, like for a photon, then you get E = p*c, which is to say, the momentum of a photon times its speed (obviously, the speed of light) equals its total energy. Mass-energy equivalence means that a particle's mass while in motion is greater than its mass when at rest.

When it comes down to it, energy is energy, and energy is the thing that actually does stuff. So it doesn't matter if the energy comes from rest mass or momentum; you can combine the two into into a single measurement and treat them as interchangeable.

It should be noted that a photon's relativistic mass is very very small. It's possible to set up an experiment to observe the effect of photon momentum on Earth, but it requires sensitive tools, because friction (including drag from the air) will easily overwhelm it. However, a spacecraft was launched in 2010 that uses a solar sail for propulsion -- the only thing making it move is the light from the sun pushing on its sail like wind in a kite. And it's still accelerating today!

To give you an idea of just how small the forces involved are: A solar sail 800m x 800m square can catch enough sunlight to exhibit a force of only around 5 newtons.