Strain Energy Density in the Elastodynamics of the Spacetime Continuum and the Electromagnetic Field
Bibliographic record
Abstract
We investigate the strain energy density of the spacetime continuum in the Elastodynamics of the Spacetime Continuum by applying continuum mechanical results to strained spacetime. The strain energy density is a scalar. We find that it is separated into two terms: the first one expresses the dilatation energy density (the “mass” longitudinal term) while the second one expresses the distortion energy density (the “massless” transverse term). The quadratic structure of the energy rel ation of Special Relativity is found to be present in the theory. In addition, we find that the kinetic energy pc is carried by the distortion part of the deformation, while the dil atation part carries only the rest-mass energy. The strain energy density of the electromagnetic energy-momentum stress tensor is calculated. The dilatation energy density (the rest-mass energy density of the photon) is found to be 0 as expected. The transverse distortion energy density is found to include a longitudinal electromagnetic energy fl ux term, from the Poynting vector, that is massless as it is due to distortion, not dilat ation, of the spacetime continuum. However, because this energy flux is along the direct ion of propagation (i.e. longitudinal), it gives rise to the particle aspect of the el ectromagnetic field, the photon. The Elastodynamics of the Spacetime Continuum (STCED) is based on the application of a continuum mechanical approach to the analysis of the spacetime continuum [1‐3]. The applied stresses from the energy-momentum stress tensor result in strains in, and the deformation of, the spacetime continu um (STC). In this paper, we explore the resulting strain energy per unit volume, that is the strain energy density, resulting fr om the Elastodynamics of the Spacetime Continuum. We then calculate the strain energy density of the electromagnetic field from the electromagnetic energy-momentum stress tensor. 2 Strain energy density of the spacetime continuum The strain energy density of the spacetime continuum is a scalar given by [4, see p. 51]
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".