| > in some reference frames where an object would be observed as at rest, is it still "using" energy There are numerous ways to measure relativistic mass (total energy) of a system from outside of it. As long as there is a measured energy, it is still using energy. Observation tricks usually just juggle energy from potential to kinetic, they don't change the total energy, so they don't change the usage. > I don't really understand what "use" means here. Energy causes change. The total amount of energy of a system measures the total number of changes happening every second, essentially actions per second.
Action = Energy x Time = (Action / Seconds) * Seconds = Action Energy is really only transformed, it is never created nor destroyed, you probably already know this basic tenet that Einstein espoused. The energy of mass is commonly thought to be "at rest" but in actuality, mass is just the phenomena of localizing the changes that the energy must cause. When this localization is upset, you get a nuclear explosion, a lot of change that once was concealed. We might want to know how many changes per second a single Joule of energy causes. We can calculate this by taking the inverse of the Planck constant. Since Planck constant, h = Joule / Hz [1], the inverse would give us Hz / Joule. Which yields a value of about 10^34 Hz per Joule of energy. I wish I knew all of this earlier in my life, as a lot of my _energy_ was spent on trying to do Cellular Automata simulations of our universe. Knowing how fast our universe computes, makes any simulation attempts with our current computers seem quite foolish if magnitude matters at all. Some might still argue the rules are more important, but sometimes, as you see in strength sports, even a 50% difference in strength beats any technique advantage a fighter can muster. [1] https://en.wikipedia.org/wiki/Planck_constant#Value |