Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times
Bibliographic record
Abstract
A curious feature of quantum tunneling known as the MacColl-Hartman effect results in the numerical observation that particles can traverse a barrier with effective superluminal speed. However, because tunneling is never certain, any attempt to use this effect to send a signal faster than light would require sending many particles. In this work, we consider sending---in parallel, without interactions between particles---sufficiently many particles to ensure at the least one of them tunnels. In this case, in spite of the time advance of the mean time for a single tunneling particle, the mean time to send one bit of information is larger for tunneling particles than for the same number of free photons. This removes any possibility of superluminal signaling. We show that the mean time to send one bit using $N$ particles is determined by the early-time tail of the distribution of tunneling times for one particle and that, when this early-time tail is highly accurately modeled using steepest descent, the MacColl-Hartman effect is seen to fade away.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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 teacher head, 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".