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## Main Question or Discussion Point

It has occured to me that there's a pretty simple thought experiment, and was wondering if any proposed theory of quantum gravity can "handle" it.

Imagine a completely empty universe with just 2 hydrogen atoms. They are set up to orbit the common center of mass, being attracted to each other by gravity.

Is it true that the angular momentum of that system is quantized?

If yes, is there a theory of mass/momentum/gravity that explains how it might work?

Why would the system not radiate gravitational waves (similar to first models of electron orbiting nucleus)?

A side note, I've estimated the distance of the 2 atoms with angular momentum ##\hbar## to be around 2 Mpc and the orbital speed around 55000 Planck lengths per second. I don't think I've seen these numbers before. (probably should have used ##\sqrt 2 \hbar##...)

Imagine a completely empty universe with just 2 hydrogen atoms. They are set up to orbit the common center of mass, being attracted to each other by gravity.

Is it true that the angular momentum of that system is quantized?

If yes, is there a theory of mass/momentum/gravity that explains how it might work?

Why would the system not radiate gravitational waves (similar to first models of electron orbiting nucleus)?

A side note, I've estimated the distance of the 2 atoms with angular momentum ##\hbar## to be around 2 Mpc and the orbital speed around 55000 Planck lengths per second. I don't think I've seen these numbers before. (probably should have used ##\sqrt 2 \hbar##...)