[Coda]

This is relativity because energy-mass equivalence is something that only really matters at relativistic scales.

At normal scales, you can just use p=mv and just ignore the contribution that motion adds to the rest mass. I mean, look at that full equation -- the mass term has c^4, while the momentum term only has c^2. And c is a BIG number. You'd need a momentum in the neighborhood of 10^17 (or a mass on the order of 10^-17 kg) in your equation for those terms to be on the same order of magnitude.

p = mv can be true for massive objects with no velocity. That's why the simplification is used -- it lets you reason about the energy equivalence of the mass itself at scales where the relativistic contribution of its velocity is negligible.

Macroscopic measurements of different types of energy come from the collective behavior of huge numbers of particles. At subatomic scales -- a proton has a mass of less than 10^-30 kg -- many things like "heat" don't have meaning. Temperature, for example, is a measure of the average kinetic energy of the particles in the thing being observed. There are field forces (like gravity and magnetism) that still come into play, so potential energy is a thing that still comes into the picture, but that doesn't participate in energy-mass equivalence as far as I can tell in my research. (I actually had to go look this up because I didn't know.)

Solar sails DO totally seem like sci-fi stuff, don't they?