I understand that when the electron and proton are arranged to form a hydrogen atom, the potential energy of the system is lower than when separated. As a result, according to mass-energy equivalence, the mass of the hydrogen atom is lower. However, my question is about the physical process through which the mass or "inertia" is lowered. How does the arrangement of the proton and electron reduce the force needed to accelerate the system?
If what I am asking is not clear enough, consider the following example I borrowed from a PBS space-time video. Imagine a massless box with a perfectly reflective interior containing photons. The photons have energy and are contained in the box; Therefore, the box must have mass. This mass or "inertia" is felt when accelerating the box since more photons bounce off the backside of the box than the front, creating resistance.
Similarly, I am asking for the process behind the lower inertia of the hydrogen atom.
Also, if every system has a different "process" for why energy causes mass, it seems like too much of a coincidence. Is there a common process for why the mass is increased or decreased?
Edit: If it is not clear what I mean by physical process, I mean the kind of reasoning Matt – the guy in the video – gives for the 2 examples (one of the photon box and the other of a compressed spring) in the video at 1:32.
link to video: https://www.youtube.com/watch?v=gSKzgpt4HBU&vl=en
Best Answer
Mass in special relativity is just energy, as measured in the center of momentum frame. So to determine how massive something is relative to something else, you can just consider how much work it takes to go from one arrangement to another.
If you have a large box with photons in it, it takes energy to make it smaller, since the photons exert pressure on the walls of the box as you push them in. Hence, a small box with photons in it has more energy and thus is more massive than a larger box with the same photon content.
On the other hand, protons and electrons are attracted to one another, so it takes energy to separate them. Thus, a system with a proton and electron separated has more energy and thus more mass than a hydrogen atom.