Evidence of violation of quantum mechanics due to gravity?

[kochanskij]

Quantum mechanics does not take gravity into account at all. So when the energy levels of the hydrogen atom are calculated, the results should be exact only in flat spacetime (no gravitational fields). Energy levels of an H atom in a gravitational field should require a quantum gravity theory.

Has any experiment ever shown a difference between energy levels of an atom on Earth (or on the sun) and that which standard quantum mechanics predicts? (I am not referring to a gravitational redshift of the light emitted. I mean an actual violation of standard QM inside the atom.) The difference would be very tiny but it would give an experimental test of any new quantum gravity theory.

Jeff

 

[tom.stoer]

Do you expect that gravity will change numerical results, or the formalism of standard quantum mechanics?

I do not see any reason why we need quantum gravity to calculate corrections of the energy levels; quantum gravity will become relevant only in extemly strong fields.

Why not try the following: let H° be the Hamiltonian of the hydrogen atom (w/ or w/o corrections like spin-orbit coupling), and let h = -mgz be the correction due to the gravitational field of the Earth (with the z-coordinate and the electron mass m). Then you can calculate the shift of the energy levels by standard perturbation theory methods. Due to the structure of the correction (z) you can use the same matrix elements as for corrections from a constant electric field. Then you can compare the effects of the gravitational and of the electric field.

 

[torquil]

Note that there is a difference between describing a quantum system in a curved geometry (gravity), and describing the interaction between a quantum system and quantum gravity.

The former is possible to do, by treating gravity as a classical field. The latter is beyond the current state of physics.

So it would be possible to calculate the change in energy levels of the hydrogen atom because of tidal forces from it being in a curved spacetime. And that would not require a quantum gravity.

In both these cases, the difference would be tiny, as you say. In fact, I don't thing the word "tiny" is strong enough to encapsulate the smallness of this effect... I don't believe us humans will ever be able to measure it. But I may be wrong, of course.

If you put your hydrogen near a black hole, on the other hand, you would be able to calculate an appreciable difference because of the tidal forces. I'm still talking about a hydrogen in an external classical field, here. Not quantum gravity.

It does not "invalidate" quantum physics. Quantum physics in a curved background is perfectly OK.

Torquil

 

[kochanskij]

I agree with both the responses above. I know that gravity can be treated as a classical field in the Newtonian sense and thus as a perturbation to standard QM. But I am asking about the shift in energy levels on an atom in a relativlistic gravitational field (like an H atom near a black hole).
I was wondering if an experiment could show a difference in energy levels due to quantum gravity theory modifying QM? If so, this could be an experimental guide to help develop the quantum gravity theory.
Treating gravity as a Newtonian field perturbation to QM will not work near a black hole. So it should work only approximately in the Earth's or sun's gravity. Since we can not get near a black hole, can an experiment be done that is precise enough to measure the violation of QM due to gravity here on earth? How tiny of a QM violation would this amount to?

 

[tom.stoer]

Treating gravity as a Newtonian field perturbation to QM will not work near a black hole. So it should work only approximately in the Earth's or sun's gravity.

I do not agree; the gravitational force near the horizon of a giant black hole is rather weak, so Newtonian approximation is not as bad as it seems. I guess that the order of magnitude can be safely estimated by Newtonian gravity.

The next step would be to couple the hydrogen atom to curvature; this is possible via the Dirac equation in a classically curved spacetime manifold - still no need for quantum gravity.

The final step is to set up a theoretical framework for quantum gravity coupled to "ordinary (quantized) electromagnetic interaction" and to calculate something like the "gravitational lamb shift"; as far as I can see this is far beyond the current status of research programs like LQG or ST.

 

[atyy]

http://arxiv.org/abs/0810.5333
Universality of Quantum Gravity Corrections
Saurya Das, Elias C. Vagenas
"... Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb Shift ..."

 

[tom.stoer]

I tried g=9.81 m/sec² for the electron and an electric field with 10⁵ V/m. Then I get E_grav / E_el = 5.6 10^-16 for the ratio of the shifts coming froma linear Stark effect and a "gravitational Stark effect"

 

[gccphys]

Has anyone checked out this paper?

http://arxiv.org/abs/1002.2962

This came after the original post, I think.

 

[ZapperZ]

Quantum mechanics does not take gravity into account at all. So when the energy levels of the hydrogen atom are calculated, the results should be exact only in flat spacetime (no gravitational fields). Energy levels of an H atom in a gravitational field should require a quantum gravity theory.

Has any experiment ever shown a difference between energy levels of an atom on Earth (or on the sun) and that which standard quantum mechanics predicts? (I am not referring to a gravitational redshift of the light emitted. I mean an actual violation of standard QM inside the atom.) The difference would be very tiny but it would give an experimental test of any new quantum gravity theory.

Jeff

This is rather puzzling. Haven't you heard about the http://physicsworld.com/cws/article/news/3525" done years ago?

There is nothing to prevent you, or anyone else, from including the gravitational potential into the hydrogen atom Hamiltonian. The question is, would THAT make any measurable difference in the result? You have made claims, with no quantitative evidence to back up such claims.

Zz.

 

[tom.stoer]

see my post #2 where I tried to provide a quantitative result

 

[muppet]

Thanks for the link, ZZ; I actually hadn't heard of that!
There's also an experiment done using neutron interferometry that's described in chapter 2 of Sakurai, in which the interferometer was tilted; the ensuing difference in gravitational potential energies induced the interference pattern you'd predict from plugging the Newtonian potential into the Schroedinger equation.