Exploring the Relationship Between Gravity and Bound States in Hydrogen Atom

[qsa]

In hydrogen atom the electron and the proton come very close to each other statistically(their wavefunctions even merge), so why we do not see the effect of gravity which should be on the order of other forces at Planck distance. Otherwise, compton to compton wavelength distance is too high for QG.

 

[Salman2]

If the gravity effect is predicted by theory at Planck scale, and we do not see it, and assuming the effect it is at a level that can be measured, then our model of the interaction between electron and proton is incorrect--would this not be correct ?

 

[qsa]

If the gravity effect is predicted by theory at Planck scale, and we do not see it, and assuming the effect it is at a level that can be measured, then our model of the interaction between electron and proton is incorrect--would this not be correct ?

It seems that p-e model is correct since QED has been confirmed experimentally. but I have my doubts about gravity theories at short distances because their effect should be noticable. searching the net I have not found anything about this question. Although a related minimum length/dimention has been investigated.


http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.4227v1.pdf

as an example

 

[negru]

The gravitational effects are very many orders of magnitude lower than the interaction between an electron and a proton. Why do you think we need huge accelerators to probe just QCD (still orders below QG) while electron-proton stuff is done in table-top experiments. Heck even chemists can do electron-proton stuff !

The electron and proton do come close but no where near the Planck scale
compare atom size of 10^-10m to Planck length 10^-35m

 

[qsa]

The gravitational effects are very many orders of magnitude lower than the interaction between an electron and a proton. Why do you think we need huge accelerators to probe just QCD (still orders below QG) while electron-proton stuff is done in table-top experiments. Heck even chemists can do electron-proton stuff !

The electron and proton do come close but no where near the Planck scale
compare atom size of 10^-10m to Planck length 10^-35m

while it is true that electrons spend mostly (statistic) at bohr radius(more like expectation value), but as a wave and a probabilty of location they can practically be on top of each other. Doesn't that count for anything.

 

[qsa]

here is a paper that sheds some light on the subject, it was listed by MTd2

This paper will be published on Nature!

http://arxiv.org/abs/1010.0793

Quantum gravitational contributions to quantum electrodynamics

David J. Toms
(Submitted on 5 Oct 2010)
Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. But that claim has been very controversial with the situation inconclusive. Here I report an analysis (free from earlier controversies) demonstrating that that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the reduction of the electric charge at high energies, a result known as asymptotic freedom.

 

[atyy]

http://arxiv.org/abs/0810.5333

 

[qsa]

here is one more possibility

http://arxiv.org/abs/1010.2784

Surprising Connections Between General Relativity and Condensed Matter
Gary T. Horowitz
14 pages; based on talk given at GR19
(Submitted on 13 Oct 2010)
"This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity."

 

[atyy]

here is one more possibility

http://arxiv.org/abs/1010.2784

Surprising Connections Between General Relativity and Condensed Matter
Gary T. Horowitz
14 pages; based on talk given at GR19
(Submitted on 13 Oct 2010)
"This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity."

That's a very exciting line of work, but I don't think it is what you were asking about - ie. gravity interacting with matter in our spacetime. That work is about matter in our spacetime being describable as gravity in another spacetime.

 

[qsa]

That's a very exciting line of work, but I don't think it is what you were asking about - ie. gravity interacting with matter in our spacetime. That work is about matter in our spacetime being describable as gravity in another spacetime.

Thanks for the clarification.But I guess I was more thinking about this sort of line


http://www.fqxi.org/data/essay-contest-files/Jannes_janneslimits.pdf

"
First, the fundamental `quantum gravity' theory is generally assumed to have the Planck level as its characteristic scale. Expressed as a temperature, this Planck level lies at approximately 10^32 K. On the other hand, almost all of the observable universe has temperatures that barely exceed the cosmic background radiation temperature of a few Kelvins. Even the interior of a star such as the sun is more than 20 orders of magnitude colder than the Planck temperature, while the highest energies that are planned to be produced at the Large Hadron Collider are still roughly 15 orders of magnitude lower than the Planck scale. So the degrees of freedom of quantum gravity, independently of their fundamental structure, are probably effectively frozen out in most of our universe, just like in a condensed matter system in a low-temperature laboratory.

"

 

[qsa]

I reitrate my question, why is it that when two particles waves overlap no gravitational interaction is expected. yet the particles could be sitting on top of each other statistically. I assume running coupling G is almost 1 near the particle.

 

[negru]

Like it's been said, there will be gravitational effects, just very small. Even if you take the classical force laws, and compare gravity to coulomb force, for eg two electrons you'll get that gravity is like 10^-40 weaker than coulomb force. Eg zero for all purposes, and unmeasurable.

 

[qsa]

Like it's been said, there will be gravitational effects, just very small. Even if you take the classical force laws, and compare gravity to coulomb force, for eg two electrons you'll get that gravity is like 10^-40 weaker than coulomb force. Eg zero for all purposes, and unmeasurable.

Thank you for your response. the classical calculation is well known to me, but I guess I am not clear in my question. Since I am trying to get some connection between wavefunction(QM) and gravity I am more asking about the nature of QG. So when two waves overlap that is equivalent (or is it) to two particles sitting on top of each other, then shouldn't the particles gravities affect each other since their potential is of 1/r and r is going to zero (or maybe G going to 1). Or I guess the whole wavefunction must be taken into account. In this case you should see some effect if both are delta function sitting near each other. but the wave function must carry G somewhere (probably involving all constants but changing with distance). Any other ideas!

 

[qsa]

a follow up idea is that the two delta functions (at or near Lp) represent particles with huge masses, which I guess no amount of gravity force can make them budge. hence f=ma breaks down since a=0, what do you think.