Hidden Momentum and the Absence of the Gravitational Spin Hall Effect in a Uniform Field
Bibliographic record
Abstract
We re-examine the recent claim that a Dirac particle freely falling in a uniform gravitational field exhibits a spin-dependent transverse deflection (gravitational spin Hall effect). Using a circulating mass model, we show that hidden momentum arises in uniform fields when an object carries angular momentum. On the quantum side, we analyze the Dirac Hamiltonian in a uniform potential, construct its Foldy–Wouthuysen form, and evaluate the Heisenberg evolution of spin-polarized Gaussian packets. The state used previously, with ⟨p⟩=0, is not at rest: because canonical and kinetic momenta differ, the packet carries a spin-dependent hidden momentum from t=0. Imposing ⟨x(0)⟩=⟨v(0)⟩=0 requires a compensating spin-dependent ⟨p(0)⟩; with this preparation ⟨x(t)⟩=0 to leading order in the gravitational acceleration g. Generalizing, an exact Foldy–Wouthuysen transformation (linear in g but to all orders in 1/c) shows that spin-dependent transverse motion begins no earlier than at O(g2) for a broad class of wave packets. We conclude that a uniform field does not produce a gravitational spin Hall effect at linear order; the previously reported drift stems from inconsistent initial states and misinterpreting canonical momentum.
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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 | 0.002 |
| 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 | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".