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Typical = Random.
- Source :
-
Axioms (2075-1680) . Aug2023, Vol. 12 Issue 8, p727. 27p. - Publication Year :
- 2023
-
Abstract
- This expository paper advocates an approach to physics in which "typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions state that some property Φ (x) holds for P-almost all x ∈ X , where P is a probability measure on some space X. Their more refined (and typically more recent) formulations show that Φ (x) holds for all P-random x ∈ X . The computational notion of P-randomness used here generalizes the one introduced by Martin-Löf in 1966 in a way now standard in algorithmic randomness. Examples come from probability theory, analysis, dynamical systems/ergodic theory, statistical mechanics, and quantum mechanics (especially hidden variable theories). An underlying philosophical theme, inherited from von Mises and Kolmogorov, is the interplay between probability and randomness, especially: which comes first? [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 170711623
- Full Text :
- https://doi.org/10.3390/axioms12080727