Quantum Probability as an Application of Data Compression Principles
Bibliographic record
Abstract
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be norm-squared (due to the Gleason-Busch Theorem) this fact conflicts with various popular, non-wavefunction-based phenomenological measures - such as observer, outcome or world counting - that are frequently demanded of Everettians. These alternatives conflict, however, with the wavefunction realism upon which Everett's approach rests, which seems to call for an objective, basis-independent measure based only on wavefunction amplitudes. The ability of quantum probabilities to destructively interfere with each other, however, makes it difficult to see how probabilities can be derived solely from amplitudes in an intuitively appealing way. I argue that the use of algorithmic probability can solve this problem, since the objective, single-case probability measure that wavefunction realism demands is exactly what algorithmic information theory was designed to provide. The result is an intuitive account of complex-valued amplitudes, as coefficients in an optimal lossy data compression, such that changes in algorithmic information content (entropy deltas) are associated with phenomenal transitions.
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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 | 0.003 | 0.013 |
| 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 | 0.008 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| 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".