Simple thought experiment merging GR and QT

[SlowThinker]

It has occurred 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 $\sqrt 2 \hbar$...)

 

[Haelfix]

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 $\sqrt 2 \hbar$...)

Depending on the initial velocities of the atoms, you will find different orbital characteristics (eccentricity, semi major axis etc). The problem is you aren't testing quantum gravity, but rather Newtonian physics. So you might arrange the initial conditions to be a little different, so that the atoms get much closer to each other. But then you are no longer testing Newtonian gravity, but rather classical Atomic physics. Closer still and you start probing quantum mechanics (and so on, you get the point).. At some point you might realize that it might not be a good idea to use Hydrogen atoms for this little test.

Anyway, quantum gravity will be an immensely tiny effect relative to everything else, and yes in principle you might expect gravitational radiation when you start probing relativistic regimes.

 

[SlowThinker]

The problem is you aren't testing quantum gravity, but rather Newtonian physics.

It is true that I used Newtonian physics to arrive at these values, but technically quantized momentum & Newton's gravity is an illegal combination. There should be 1 equation that gives me the orbital parameters.

So you might arrange the initial conditions to be a little different, so that the atoms get much closer to each other.
...
Anyway, quantum gravity will be an immensely tiny effect relative to everything else, and yes in principle you might expect gravitational radiation when you start probing relativistic regimes.

Actually I've convinced myself that this is the closest the 2 atoms can miss each other, unless they collide head-on - the angular momentum can be $0\hbar$ or $1\hbar$ but nothing between.
That also means no waves unless they stop the atoms on the spot.

At some point you might realize that it might not be a good idea to use Hydrogen atoms for this little test.

I was wondering is second-order EM effects could be stronger than the gravity but didn't want to use neutrinos for the experiment since I don't know their rest mass. But perhaps you have somethng else in mind?

 

[romsofia]

Why do you think you'd need a theory of quantum gravity for this? All you have is 2 atoms barely moving on a flat spacetime! However, i'll put a little thinking into this problem, but after 3 minutes of thinking, it gets tough pretty fast.

So even if you propose that the atoms don't move, just by existing, the worldlines of the electrons/protons will create currents! So now we have unlocked all of E+M just by simply existing, and that will be more powerful than anything gravity could say with the two atoms. Also, because of this, we will have to consider self-force effects... and my thinking is done. I see no situation in where this will lead to anything fruitful for trying to understand gravity at a fundamental level!

 

[SlowThinker]

Why do you think you'd need a theory of quantum gravity for this? All you have is 2 atoms barely moving on a flat spacetime!

Because, again, the angular momentum of the system needs to be quantized. You can stitch together quantization and Newton's gravity or GR, but it's not really a single consistent theory.

So even if you propose that the atoms don't move, just by existing, the worldlines of the electrons/protons will create currents!

It wasn't my intent to bring EM into this. If you feel it's impossible to neglect these, I guess we're stuck with neutrinos.

 

[Vanadium 50]

You do know that quantum effects of objects in classical gravitational potentials have been measured, don't you? And that no quantum gravity is needed?

 

[SlowThinker]

You do know that quantum effects of objects in classical gravitational potentials have been measured, don't you? And that no quantum gravity is needed?

You can use Newton's mechanics to describe motion of planets, and you can use Maxwell equations to describe movement of light. You could say we don't need "Newtonian electrodynamics" until we try to describe fast moving charges, but even before that it's pretty obvious that both Newtonian mechanics and Maxwell equations can't be The Unified Theory, simply because they are different.
You can use General relativity to describe most of gravity, and use quantum theory to describe microscopic particles. You could say we don't need "quantum gravity" until we try to describe heavy particles on microscopic scales, but even before that it's pretty obvious that both GR and QT can't be The Unified Theory, simply because they're different.

Unless there is a formulation of GR in the language of QT or vice versa, you're really just using 2 incompatible theories. You might get some results, like the existence of black holes in Newtonian gravity, but really that's not "unifying" them.

 

[Vanadium 50]

You might get some results, like the existence of black holes in Newtonian gravity, but really that's not "unifying" them.

Just like your thought experiment.

 

[SlowThinker]

Just like your thought experiment.

Exactly. That's why I asked if there is already any theory that could be used to describe this experiment, even if we don't have the means to verify the theory (yet).
If neither String theory nor LQG can describe two neutral particles in an empty universe, someone really should be working harder...
I'm even willing to accept that such an empty universe with no edges or CMB is not possible, or any other backdoor.
I'm not asking for the actual equations or simulations, just wondering if we have something.

 

[PAllen]

Somewhat related, I know of one paper proposing the possibility of testing whether gravity must be quantized:

https://arxiv.org/abs/0803.3456

 

[romsofia]

If neither String theory nor LQG can describe two neutral particles in an empty universe, someone really should be working harder...

I'm just going to be blunt: Study more. Your thought experiment isn't interesting, and it has nothing to do with quantum gravity. Second off, you start of with atoms in OP, now you're talking about particles. Which one is it? Either way, you don't need string theory, or LQG to describe particles in an empty universe.

Finally, you're stuck in the 1920s. We have quantum general relativity, we have quantum field theory in curved spacetimes. You need to do literature review before you make statements such as "someone really should be working harder..." when you haven't put in any work. There are papers dating back to the 50s on what happens to charged particles in an empty universe. It is disrespectful to think that someone needs to "work harder" when you haven't done any work yourself!

Now, if you're truly interested in these types of issues, here is a paper to start: https://link.springer.com/article/10.12942/lrr-2011-7

 

[SlowThinker]

I'm just going to be blunt: Study more. Your thought experiment isn't interesting, and it has nothing to do with quantum gravity.

It can't be fully described using Quantum Theory, and it can't be fully described using General Relativity. Therefore it is my understanding that it requires a theory that combines the two.

Second off, you start of with atoms in OP, now you're talking about particles. Which one is it?

As explained above, I want to make the situation as simple as possible, but I didn't want to use "massive points" because these are unphysical and I'm asking for a physical theory.
I'm still convinced that a hydrogen atom at these distances is a reasonably accurate approximation to a massive point, but if you don't agree, we can switch to neutrinos.

Either way, you don't need string theory, or LQG to describe particles in an empty universe.

Are you suggesting to use quantization with Newtonian gravity and Newtonian mechanics the way I did in OP, or something different?

Finally, you're stuck in the 1920s. We have quantum general relativity, we have quantum field theory in curved spacetimes.

There is a lot of literature but I was wondering if any of it is ready for actual calculations.
Quantum general relativity is a very broad term that includes both String theory and LQG. I'm aware of the existence of the two.
QFT in fixed static curved background does not apply here.

Now, if you're truly interested in these types of issues, here is a paper to start: https://link.springer.com/article/10.12942/lrr-2011-7

This seems to use GR only, and in a sense, it solves the issues it raises.

 

[ohwilleke]

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

This is the least of the issues and efforts to determine the gravitational form factors of some common hadrons address this issue to a great extent from a practical perspective.

I can't imagine any practical way to every measure this (which, of course, isn't strictly a requirement for a thought experiment), or any obvious macro-level effects of quantized angular momentum in quantum gravity relative to classical GR, but maybe I'm just not that creative today.

Some of the bigger quantum gravity v. general relativity issues include (1) the fact that gravitational energy is localized in quantum gravity but not in GR, (2) the fact that mass-energy is conserved locally but not global in GR, but would have to be conserved globally in quantum gravity, (3) the existence of quantum tunneling giving rise to Hawking radiation in quantum gravity but not in GR (which is particularly relevant for "primordial black holes"), (4) reconciling deterministic GR with stochastic quantum gravity, (5) figuring out how to secure dark energy effects represented by the cosmological constant in GR in quantum gravity where this would seem to require a new scalar field of some kind, (6) the very different treatment from a computational perspective at a minimum of gravitational field self-interaction in GR (where it is implicit but normal naively visible on the face of the equations) and in quantum gravity where it would have to be a coupling, (7) the impact of an additional graviton boson on the beta functions of the Standard Model physical constants, and (8) figuring out why gravity is relatively "well behaved" in reality despite having a non-renormalizable quantum formulation in the naive quantum gravity case, which suggests that we are missing systemic cancellations or symmetries that make quantum gravity much more mathematically behaved that it appears in the usual current formulation.

 

[ohwilleke]

Another big issue for quantum gravity is whether and in what fashion the gravitational coupling constant runs with energy/momentum level.

 

[SlowThinker]

Another big issue for quantum gravity is whether and in what fashion the gravitational coupling constant runs with energy/momentum level.

Good question but I wouldn't expect theoretical advancements on this front until experiments show something.
It can go many ways without breaking existing results.

 

[Vanadium 50]

someone really should be working harder...

That someone is you.

You don't understand either QM nor GR, and yet you blame others for not working hard enough. That, my friend, is not where the problem lies. As pointed out to you at least twice, your thought experiment has nothing to do with quantum gravity.

 

[Nugatory]

This thread has reached the point of diminishing returns and has been closed.

As always, you can PM any mentor if you need it reopened o add something to the discussion.