On a possible quantum manifestation of the perihelion advance in a hydrogen-like atom
Bibliographic record
Abstract
In a static and spherically symmetric case, by following an analog procedure for obtaining a Reissner–Nordstrom solution, thanks to the use of both the Einstein-type equation for an electromagnetic field as well as the Maxwell equation in curved space–time, we managed to find the Schwarzschild-like solution outside a charged sphere Q in interaction with a test charged particle q at an atomic scale where the gravitational force is negligibly small compared to the electrostatic force. Then, in the context of an extension of the equivalence principle to the electromagnetic interaction, we have studied the hydrogen atom. At the atomic scale, where quantum effects can no longer be ignored and the concept of trajectory is abandoned, the corrective terms derived from the geodesic equation for the electron are used within a perturbation theory. At the first order, these radial corrections of the Hamiltonian can partially remove the degeneracy of Bohr’s levels through a Lamb-like shift of the energy levels (2s) and (2p), estimated to E(2s) – E(2p) = 2.4595087102 × 10−4 eV. To match the experimental value of the Lamb shift, 4.372 × 10−6 eV, we have postulated the existence of an electromagnetic background that would describe statistically the vacuum energy by the introduction of a “cosmological”-like constant in the Einstein-like equation for electromagnetism. We have pointed out a divergence when n → +∞ in energy corrections due to a “cosmological” constant that technically could be overcome by the use of a cutoff as well as the renormalization of the electron’s mass.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".