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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

Thank you

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

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?

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

Thank you