special relativity - Where does all the mass created from energy go?

So mass can be created from energy when small protons speed up, 430 times bigger to be exact. I don't know if this is a stupid question, but I'm in middle school so cut me some slack. Where does all that mass go? Is it converted to thermal energy? Say we covered the earth with solar panels, that would produce a lot of energy, also producing a lot of mass. I don't know if that's the right wording, I don't want to sound like I don't know energy can't be created or destroyed but if anyone could answer these questions for me that'd be great.

Answer

The notion of "mass" is probably less deeply meaningful as you might think. Science has come a long way since the days when mass was thought to have such deep significance. Nowadays, energy is the primary concept, because there is a law of conservation of energy, and energy is linearly additive: that means that the sum of energies for two separate systems equals the total energy for the system as a whole. These two properties - conservation and linear additivity make energy a useful notion in physics.

Mass has neither of these properties. It is not conserved, and it is not additive. The rest mass of a system two photons moving in opposite directions is nonzero, whereas the rest mass of each is nought.

In particular, since mass is not conserved, it doesn't have to "go anywhere", unlike energy. It can simply disappear or appear, as in the photon example. So nowadays mass is less useful as a concept in physics.

Modern physics simply thinks of the notion of rest mass of a system, and this is a shorthand for the total energy of a system as measured from a reference frame at rest relative to the system (in SI units, we multiply by $c^2$ in the rest frame to get from mass to energy). But the notion is still all about energy. The rest mass $m_0$ can be used in the relativistic version $\mathbf{F}=\frac{\mathrm{d}}{\mathrm{d}\tau}(m_0\,\mathbf{u})$ of Newton's second law, where $\mathbf{F}$ is the Four Force and $\mathbf{u}$ the four velocity. As such, rest mass can also be thought of as measuring a system's inertia. Rest masses are important identifying data for fundamental particles, because the total energy of these particles is always the same when measured from a frame at rest relative to them. This last statement holds for massive particles: massless particles like the photon have no rest frame.

Incidentally, though, if you want to express the solar energy incident on Earth as a mass, then it works out to be roughly a kilogram each second. Of course, long term, all of that is radiated back into space. Human energy usage is about five tonnes per year, or about 0.2 grams per second.