Electromagnetic energy of electric and magnetic dipoles
Why this work is in the frame
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Bibliographic record
Abstract
We derive a novel expression for the relativistic energy of electric and magnetic dipoles in an external electromagnetic field and discuss its implications. In particular, we find the relativistic dependence of the energy of a dipole on its velocity, v, and show that in the most convenient presentation of the energy (when the proper electric (p 0 ) and magnetic (m 0 ) dipole moments are involved, whereas the electric (E) and magnetic (B) fields are defined in the laboratory frame), its value essentially depends on the orientation of the velocity, v, with respect to vectors p 0 , E, and m 0 , B. To better understand the relativistic behavior of the energy of electric and magnetic dipoles, we introduce the notion of “latent” momentum of an electric dipole, in addition to the known concept of “hidden” momentum of a magnetic dipole. We finally show that the contribution of energy terms related to “hidden” and “latent” momenta of an electric or magnetic dipole is important in the relativistic case.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it