Is Gravitational Quantization Supported by the Stability of Orbital Electrons?

[Cato]

Does the fact that orbital electrons are stable suggest that gravitation is quantized, analagous to the observation that the stability of orbital electrons suggested that electromagnetic energy was quantized?

 

[Drakkith]

I don't believe so. I know for a fact that we don't have a working theory of quantized gravity and I don't think we have any evidence suggesting that gravitation is quantized at this time either.

 

[Cato]

Thanks, Drakkith. I may be missing something obvious here, but I do not see why orbital electrons do not lose energy by emitting gravitational waves.

 

[Jilang]

Perhaps for the same reason they cannot lose energy by electromagnetic means (except in jumps)?

 

[HallsofIvy]

What makes you think the fact that "orbital electrons are stable" has anything to do with gravitation being quantized?

 

[dextercioby]

The question which started this thread (rephrased in post# 3) is a very good one. Currently, the stability of almost elementary matter such as H-atoms and more complicated atomic/molecular structures is only the consequence of the classical/quantized electromagnetic interactions between the various elementary (or not) particles. There's little that we know about gravity at particle physics level. But what we know is that the gravitational interaction (modeled for simplicity through Newton's gravity) is extremely tiny with respect to the electromagnetic one, thus its possible predictions at atomic level are totally negligible.

 

[jtbell]

It might make an interesting exercise, although highly hypothetical, to imagine a hydrogen-like atom containing two electrically neutral particles with the masses of the proton and electron, bound only by (classical) gravity, and calculate the "Bohr radius" and energy levels predicted by the Schrödinger equation for this system.

 

[secur]

Einstein had this to say in June 1916, discussing gravitational waves: (according to A. Pais, "Subtle is the Lord", p.278)

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He [Einstein] also pointed out that the existence of radiationless stable interatomic orbits is equally mysterious from the electromagnetic as from the gravitational point of view. "It seems that the quantum theory will have to modify not only Maxwell's electrodynamics but also the new gravitational theory". [meaning GR].

Note, however, "at that time he mistakenly believed that a permanently spherically symmetric mechanical system can emit gravitational radiation". [It wasn't until 1918 that he presented the quadrupole formula].
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Now it seems to me (this is secur speaking) that after this comment was made, it was decided that the atomic system should be viewed as an essentially static configuration of proton / electron "standing waves", NOT a dynamical system where the one whirls around the other like a planet. Obviously we can't currently deal with gravitation of a quantum field (or, wave function) since there's no theory of Quantum Gravity. But intuitively, from a classical view, if the atom system is "static", it should emit no gravitational (or EM) waves.

Another way of looking at it: doesn't the normal explanation work for gravitational waves also? The electron has no lower energy level to fall down to, so it can't lose energy.

At any rate, it's interesting that Einstein asked essentially the same question as you, Cato - you're in good company!

 

[Drakkith]

But intuitively, from a classical view, the atom system is "static", therefore no gravitational (or EM) waves.

Classically the atomic system isn't stable, as it presents electrons as circling about like planets orbiting a star. This would indeed radiate EM radiation if it were the case.

 

[secur]

Thanks Drakkith, let me clarify. Quantum Mechanically (not classically) the system can be considered stable. Applying this view to gravity is not possible since we have no quantum gravity theory. But applying it intuitively, we might say that it makes sense the static system emits no gravitational waves. Admittedly that's speculative but given the circumstances - we have no accepted theory to deal with the situation - it seems justified.

BTW prior to your comment I edited my wording a little - changed the part you quoted - precisely to avoid the interpretation you gave it. Unfortunately you responded too quickly!

 

[Drakkith]

. But applying it intuitively, we might say that it makes sense the static system emits no gravitational waves. Admittedly that's speculative but given the circumstances - we have no accepted theory to deal with the situation - it seems justified.

I agree. Given what quantum theory tells us, it makes sense that no gravitational radiation would be emitted since the electrons are not like little planets orbiting a star.

BTW prior to your comment I edited my wording a little - changed the part you quoted - precisely to avoid the interpretation you gave it. Unfortunately you responded too quickly!

 

[Demystifier]

I don't think we have any evidence suggesting that gravitation is quantized at this time either.

How about http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.979 ?

 

[Drakkith]

How about http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.979 ?

Maybe. This is the first time I've seen anything like this.

 

[secur]

I can't find that paper to read, but I did find references. Stanford Encyclopedia article on Quantum Gravity was the most informative. This "indirect evidence" is NOT experimental. It's only a gedanken, meant to prove (or suggest) gravity can't be quantized. Page and Geilker suppose that the stress-energy tensor in the Einstein field equation would be a quantized matter field. Then they try to derive a contradiction. If, upon measurement, it collapses, you'd get non-conservation of energy; if not, violate uncertainty principle, or get FTL communication. A number of theoreticians are involved, it's not entirely clear what this particular paper says, but the bottom line is: no consensus. After all it was published in 1981, if it actually proved Quantum Gravity was logically impossible we'd know it by now! Anyway, there are no experiments that indicate gravity is quantized, according to this article - as Drakkith says.

By the way - to avoid potential confusion - there was an experiment ballyhooed in the popular press as "detecting gravitons", not too long ago. Since it's really not relevant I didn't bother to look it up; but if you google you'll find it. Using very cold neutrons, it demonstrated their wave function, in Earth's gravity field, had quantized energy levels. But the levels arose from absolutely standard QM particle-in-a-box, not gravitons! Don't misunderstand, it was an impressive bit of work; but had nothing to do with quantized gravity, contra USA Today.

 

[Cato]

Thank you all for all of your comments. I have been out of electronic touch for more than a week and have just this discussion. Fascinating stuff. thanks again.

 

[Davephaelon]

In this 2012 paper (https://publications.ias.edu/sites/default/files/poincare2012.pdf) by Freeman Dyson, it's indicated, in equation 14, page 8, that the average cross section of absorption of a graviton, by an electron or nucleon (neutron, proton) is the same. This conclusion is based on Quantum Mechanical arguments.

However, this is at variance with the classical picture, where the gravitational coupling is proportional to the masses involved. I must be overlooking something.

 

[Jilang]

Emission?

 

[Davephaelon]

I started to reread the fascinating paper by Freeman Dyson, mentioned above, at a coffee shop where it was air conditioned, but at home now it's hard to think at 91 degrees and high humidity. The overall assessment of the paper is rather discouraging as far as detecting individual gravitons.

One thing I like to do is follow the theory argument of the author and do the calculations myself. I started doing that at the coffee shop, but didn't come out with the right result for equation 3. I know I made some simple mistake, and am going over it again. It's fun to do the calculations as it gives you a much better 'feel' for the physics.