Bibliographic record
Abstract
A simple model is provided to obtain the space–time probability-distribution function of a photon emitted without recoil by an excited system (atom, nucleus, …) in one dimension. A three-dimensional formulation is not needed for our discussion. A quantum mechanical calculation, using the Heitler method, is employed to obtain the solution. The space–time probability-distribution function is not the photon wavefunction. In fact, the area under the space–time probability-distribution function is time dependent. It obtains its final value only as t → ∞. The frequency composition of the photon is found and its time dependence determined to be in accord with the time–energy uncertainty principle. In the wave picture, the coherence length of a photon is found to be equal to the distance from the maximum probability-density position in the photon back toward the source to a position where the probability density has decreased to e–1 of its maximum value. The concept of the coherence length is applied to understand the exponential lifetime curve in the wave picture. This latter measurement is usually explained by saying, in the particle picture, that the photon can appear immediately after formation of the excited state or at a variety of later times according to an exponential probability distribution.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".