The momentum of electromagnetic waves in dielectric materials<sup>*</sup>
Bibliographic record
Abstract
Abstract Variation of the generally covariant version of Minkowski's Lagrangian of macroscopic Maxwell theory with respect to the metric yields a symmetric tensor T μν which reproduces the Poynting vector 𝒮 i = cT 0i , and therefore would seem to favor Abraham's proposal 𝒫 A i = 𝒮 i /c 2 for the momentum density in a macroscopic electromagnetic wave. However, the T 00 component does not reproduce the standard energy density in the rest frame in the flat limit. The difference between the energy density and T 00 has the same structure as the difference between the Minkowski momentum density 𝒫 M i = n 2 𝒮 i /c 2 and the Abraham momentum density. The result therefore adds further credibility to Minkowski's original energy‐momentum tensor and his proposal for the total momentum density of electromagnetic waves in dielectric materials. We draw attention to the facts that the covariant formulation of macroscopic Maxwell theory of dielectric materials requires a field strength‐velocity coupling term which could only be inferred in a long wavelength limit from quantum electrodynamics, and that the theory is clearly limited to interactions of sub‐UV photons with matter. Therefore, in spite of the fact that macroscopic Maxwell theory can formally be written in generally covariant terms, the theory for n ≠ 1 should be considered as inherently non‐relativistic, with non‐relativistic corrections of order n ‐ 1. The difference 𝒫 M ‐ c ‐2 𝒮 between Minkowski's momentum density and the rescaled Poynting vector is an example of an order n ‐ 1 correction.
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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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".