The principle behind the Uncertainty Principle
Bibliographic record
Abstract
Department of Mathematics and Statistics and Institute for Quantum Science and Technology,University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4(Dated: May 12, 2015)Whilst physicists have long been aware of the existence of a fundamental uncertainty princi-ple in quantum mechanics, an explicit understanding of this principle has remained an enigma,our grasp limited to speci c \uncertainty relations. In this work we overcome these limitationsby clarifying the concept of uncertainty, based on minimalistic axioms. Applying this notion toquantum-mechanical measurements, we arrive at a general, overarching framework for character-izing all quantum-mechanical uncertainty relations, which we unify into our proposed UncertaintyPrinciple. Along the way, we nd that the variance is an uncertainty measure only in a restrictedsense.
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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 | 0.007 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.016 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 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".