Reconstructing simultaneity using Doppler-based inference: A frame-specific convention within special relativity
Bibliographic record
Abstract
Simultaneity of spatially separated events in special relativity is not directly observed but inferred through synchronization conventions. Einstein’s method assumes light travels at the same speed in all directions, while alternative conventions—such as Selleri’s—allow for anisotropic light speeds. This paper presents a complementary approach: a Doppler-based method in which an observer—such as one aboard a moving train in the classic lightning strike scenario—uses known rest-frame emission frequencies and measured Doppler shifts to back-calculate the emission times of signals and determine whether events were simultaneous in their own frame. This method applies in scenarios—such as the one presented here—where the rest-frame frequency of the source is known (for example, if the light source—envisioned as a light bulb—was marked by the manufacturer while at rest in its own frame). Although this rest frame corresponds to the ground frame in our scenario, the train observer’s analysis remains entirely within their own frame. This approach does not assert that all observers agree on a single time of occurrence; rather, it respects that simultaneity is frame-dependent and that observers in relative motion are subject to time dilation. The method highlights that conclusions about simultaneity depend on the chosen synchronization framework—even when all frames apply consistent physical reasoning. This demonstrates that simultaneity is a frame-dependent reconstruction, consistent with Einstein’s acknowledgment that simultaneity rests on a chosen stipulation, leaving room for alternative conventions.
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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 | 0.008 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".