Probability in Physics  

In General > s.a. Determinism; Predictability; random processes; stochastic processes.
* Remark: Physicists' use of probability and statistics is influenced by points of view derived from coin tossing or quantum mechanics, even when these don't apply.
* Role in classical mechanics: Probabilities are used in statistical mechanics, where they are essentially given by fractional phase space volumes.
@ Overviews: Streater JMP(00); Griffiths FP(03)qp/02; Maassen qp/04-ln [and open quantum systems, damped oscillator]; Khrennikov qp/05-in.
@ General references: Feynman in(51); von Weizsäcker BJPS(73); Broyles PRD(82); Accardi & von Waldenfels ed-85; Ballentine AJP(86); Cohen FP(88); Gudder 88; Bitsakis & Nikolaides ed-89; Farhi et al AP(89); Pitowsky 89; Gudder FP(90); Hemion IJTP(90); Squires PLA(90); Halpin PhSc(91); Neapolitan PhSc(92); Ambegaokar 96; Basano & Ottonello AJP(96) [probability paradoxes]; Ismael BJPS(96); Bana & Durt FP(97)qp [Kolmogorov]; Khrennikov JMP(03)ht/01 [and contextuality]; Zurek PRL(03)qp/02 [environment-assisted invariance]; Hardy SHPMP(03) [general and quantum].
@ Objective vs subjective: Saunders qp/04; Srednicki PRA(05)qp; Huber BJPS(05) [as basis for scientific reasoning]; Maudlin SHPMP(07); Szabó SHPMP(07).
@ Interpretation: Saunders Syn(98)qp/01 [geometric]; Loewer SHPMP(01) [paradox of deterministic probabilities]; Bulinski & Khrennikov qp/02 [stochastic]; Anastopoulos AP(04)qp [and event frequencies]; Mardari qp/04 [roulette vs lottery models]; Volchan SHPMP(07)phy/06 [typicality]; Harrigan et al a0709 [ontological models for probabilistic theories].

In Classical Physics > s.a. statistical mechanics; statistics [errors and fluctuations].
@ In classical mechanics: Mayants 84; Ruhla 92; Collins JMP(93); Lasota & Mackey 94.
@ In cosmology: Efstathiou a0802 [limitations of bayesian techniques]; > s.a. acceleration; dark energy types, models; observation.
@ Non-commutative: Khrennikov & Kozyrev qp/02 [examples].

In Quantum Physics > s.a. foundations; interpretations; hidden variables; many worlds; measure theory; pilot wave; quantum mechanics.
* Role: Probabilities are an essential part of the interpretation, obtained from inner products (0 cos2 1).
* Idea: Probabilities do not behave like in classical physics; The basic objects for questions Q are probability amplitudes A(Q), from which the probabilities are calculated as P(Q) = |A(Q)|2; Quantum probability is a variant of contextual probability.
* Calculation: In general, when an event can occur in several different ways, its probability amplitude is the sum of those for the individual ways (interference),

A(Q) = i A(Q, i) .

However, if an experiment is capable of determining which alternative is followed, then interference is lost; For example, if Q is a question whose answer depends on what the system does up to a time t, then

P(Q) = x |A(x at tf, a)|2 = |A(Q)|2 ,    where    tf > t .

* Remark: Independence on t in the above calculation is equivalent to unitarity.
* Remark: One point of view is that probability doesn't change in time; We often ignore the fact that when we talk about time dependence we're talking about different experiments.
@ General references: Accardi PRP(81); Van den Berg et al PhSc(90); Youssef MPLA(91); Cufaro Petroni FP(92) [rev]; Farina AJP(93); Gudder IJTP(93); Ismael BJPS(96) [conceptual]; Velleman AJP(98); Noyes & Etter PE(99)qp/98; Adler qp/00-in [postulated vs emergent]; Barnum et al PRS(00)qp/99; Khrennikov qp/01-in [foundations], qp/01 [context-dependent]; Sudarshan qp/01 [overview]; Rylov qp/01 [dynamically based]; Belavkin m.PR/05 [history]; Rédei & Summers SHPMP(07)qp/06 [rev, ito von Neumann algebras]; Dreyer qp/06 [emergent probabilities]; Lehrer & Shmaya PRS(06) [qualitative approach]; Tipler qp/06; de la Torre EJP(08); Rave a0806 [interpretation with closed loops and phases].
@ From classical probability: Slavnov TMP(06)qp/07; Grigorescu a0711 [classical Fokker-Planck equation and quantum Brownian motion].
@ And decoherence: Bacciagaluppi SHPMP(07)qp [time-directed probability]; Jordan & Chisolm a0801.
@ Objective vs subjective probabilities: Mohrhoff AJP(01)qp/00; Ballentine a0710-in.
@ Non-Kolmogorov: Szabó IJTP(94), FPL(95)gq/94, gq/94, qp/96; Khrennikov qp/00, a0709 [and Bell inequalities].
@ Bayesian approach: Caves et al PRA(02)qp/01; Pitowsky SHPMP(03)qp/02; Schack qp/02 [and Hardy's axioms for quantum mechanics]; Appleby FP(05)qp/04, O&S(05)qp/04; Marlow AP(06)qp/05 [histories], gq/06, JMP(06)qp; Caves et al SHPMP(07)qp/06 [concept of certainty]; Bub SHPMP(07); Rau a0710 [quantum vs classical].
@ Related topics: Page qp/95, IJMPD(96)gq/95 ["sensible quantum mechanics", without probabilities]; Shirokov qp/06 [on set of states]; > s.a. Born Rule, collapse [GRW], Gleason's Theorem, histories formulations [including extended probabilities], representations [tomographic].

Other References > s.a. measurement types; particle statistics; probability theory [including complex]; physical theories.
@ And decision theory: Deutsch PRS(99)qp; Wallace qp/02, SHPMP(03)qp, qp/03 [Deutsch's claim].
@ Propensities: Suárez SHPMP(07) [and quantum mechanics]; Belnap SHPMP(07) [and branching spacetimes].
@ Negative probabilities: Bartlett PCPS(45); Mückenheim PRP(86); Feynman in(87); Scully et al PRA(94).
@ Conceptual: Page gq/94 [real vs mental world]; Arntzenius & Hall BJPS(03); Knuth phy/04-in [as "degrees of implication"]; Lange BJPS(06) [probabilities vs chances]; Martin Ent(07)phy [probability as physical motive]; Dass a0807 ["supmech" unified axiomatization].
@ Related topics: Caticha PLA(98)qp, PRA(98)qp [unitarity and consistency]; Youssef ht/01 [exotic probabilities]; Khrennikov & Loubenets FP(04)qp/02, Khrennikov JMP(02), qp/03-in [and classical probability]; Gyenis & Rédei FP(04) [and causality, common cause]; Marlow qp/05/FPL [and Lorentz invariance].

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