4/3 problem, Poynting theorem, and electromagnetic energy–momentum tensor
Why this work is in the frame
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Bibliographic record
Abstract
We show that the familiar 4/3 problem originates from the incorrect determination of the momentum of the electromagnetic field generated by an isolated charged particle, which results from an incorrect application of the Poynting theorem to the field. To demonstrate this, we consider a macroscopic problem: splitting a charged oil droplet into two identical smaller droplets in the rest frame K of the original droplet, and in another inertial frame [Formula: see text] moving with respect to K with some constant velocity, and arrive at a physically senseless solution in the framework of the standard approach. To solve this problem in a correct way, we suggest a modified Poynting theorem for an isolated charge and recalculate the momentum of the electromagnetic field of this charge, which yields the usual relativistic relationship between the field energy and momentum. Our approach is not at odds with the idea about “Poincaré stresses”; however, in contrast to the standard method, it provides a usual relationship between the “Poincaré stress–energy” and the associated momentum stress component. Finally, the continuity equation in four-dimensional form for the case of isolated moving charge is also proposed, which completely resolves the 4/3 problem.
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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