The space inside an atom is taken to be flat a priori. If this were not the case, we should consider the effect of curvature on the atomic phenomena. How much one would expect to get if such an effect is taken into consideration?
i do not know the answer. But apparently, this question makes sense.
Gravity is too much weaker than electromagnetic force. Quantum electrodynamics agrees with theory upto 11 decimal places. There is no use of correction at 42nd decimal places.
I am against the way in which the theoricients resonates today. I think that we must distinguish between the very useful mathematical description to study the natural phenomena and the physical reality sometimes hide behind this description .
In my opinion the adoption of the mathematical description as a physical reality takes us further away from the truth. Although this description is required to predict the effects of the cause.
The question relevant to the possibility of including curved space inside the atoms does not make too much sense for the following reasons
a) there is no way of introducing gravity effects because amazingly small
b) If the curvature effects are induced by the electromagnetic field (in a way which should be specified) there is no possibility of detecting them experimentally and, even if, any deviation from the ordinary quantum theory (in e. g. the atomic spectra ) could be confused with higher-higher...higher order quantum corrections
c) I cannot image any charge distribution producing distortion of the space time and even no electromagnetic wave intensity, but, if so, the radiative effects would be dominant (and probably catastrophic) over any other observable phenomenon
d) a nice exercise could be the evaluation of the electromagnetic wave intensity to produce any space time distortion (in the sense of general relativity) on a moving charge
d) On the top of everything, a very sophisticated theory including the quantization of pace time and the reformulation of gauge theories is necessary just to start thinking about these problems.
Frankly speaking for at least the next 500 years this kind of problems will not attract too much attention.
@Arbab I. Arbab:
Answer to your question is Yes. But the treatment cannot include any gravitational effect because the range of gravitational and electromagnetic effects are far removed from each other as discussed in following article. Following theory reveal that as the result of curvature of space time the electron velocity is about 30% less than the Bohr atomic model. This theory replaces Schwarzschild metric with a new metric which can explain the rotation curves of galaxies as well as the Hydrogen spectra. The curvature of the space time is taken into account as deviation to flat Minkowski metric in the form of ratio of Coulomb acceleration to the actually occuring centrifugal acceleration.
Article Hydrogen spectra using Einstein's field equations
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