I think I understand, thank you for your patience. The gravitational red/blue-shift explains it, somehow I had never come across that phenomenon.
I'm still missing something, though:
Photons have zero rest mass, and therefore do not generate any gravitational force, right? If I recall...
Yes, of course. Consider and erg instead of a Joule or perhaps a larger object than a single particle. I was only trying to avoid electromagnetic or other effects that might confuse the issue.
I'm assuming empty space here, so without the intervention of the few atoms of hydrogen that...
Take two uncharged particles (e.g., neutrons) at rest with respect to one another in empty space. Now apply 1 Joule of energy to accelerating them apart. They will eventually come again to rest with 1 Joule of gravitational potential and accelerate back together due to gravity. Their kinetic...