Probability in Quantum Physics| Probability in Quantum Physics |
In General > s.a. foundations; interpretations;
hidden variables; many-worlds interpretation;
pilot-wave theory; quantum mechanics.
* Role: Probabilities are
an essential part of the interpretation, obtained from inner products (0
≤ cos2θ ≤ 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; 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.
* QBism:
Quantum Bayesianism or the quantum-Bayesian approach to quantum theory, the personalist
Bayesian view of probability in quantum theory; This view is widely held in general
but not by many physicists; Some physicists who have argued for it are Caves, Fuchs,
Schack, and Mermin (Don Page thinks that there are both frequentist and personalist
probabilities); It has profound implications for the meaning of quantum mechanics.
> Related topics: see
Probability Current; Wigner's Friend.
References
> s.a. measurement in quantum theory; probabilities
in physics [negative probabilities, general probabilistic theories]; QBism.
@ Intros, reviews:
Cufaro Petroni FP(92);
Meyer 95;
Sudarshan qp/01;
Rédei & Summers SHPMP(07)qp/06 [and von Neumann algebras];
Sontz a0902 [simple introduction];
Janotta & Hinrichsen JPA(14)-a1402;
Khrennikov 16 [and classical];
Svozil a1707 [and correlations];
Schleißinger a2001 [simple].
@ General references: Accardi PRP(81);
Accardi & von Waldenfels ed-85;
Van den Berg et al PhSc(90)mar;
Halpin PhSc(91)mar;
Youssef MPLA(91);
Farina AJP(93)may;
Gudder IJTP(93);
Ismael BJPS(96) [conceptual];
Velleman AJP(98)nov;
Noyes & Etter PE(99)qp/98;
Adler qp/00-proc [postulated vs emergent];
Barnum et al PRS(00)qp/99;
Khrennikov qp/01 [context-dependent];
Rylov qp/01 [dynamically based];
Belavkin IDAQP(00)m.PR/05 [history];
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];
Page PLB(09) [insufficiency of quantum state];
Bub a1005-in [and information theory];
Janssens PhD(10)-a1011;
Leifer & Spekkens PRA(13)-a1107 [quantum theory as a causally neutral theory of Bayesian inference];
Blackman & Hsiang PE-a1110 [from large number of degrees of freedom];
Pfister MS-a1203;
Aerts & Sassoli de Bianchi a1401,
a1401;
Hiley LNCS(14)-a1408-conf [structure processes, and non-commutative probability theory];
Yukalov & Sornette PTRS-a1601 [general definition];
Porta Mana a2007 [conditional probabilities];
Niestegge Ent(20)-a2009 [algebraic origin].
@ And quantum foundations: Khrennikov qp/01-conf;
Wilce FP(10);
Holik et al AP(14)-a1211 [origin];
Fröhlich & Schubnel a1310;
de Ronde in-a1506 [probabilities as objective knowledge];
Garola a1806 [epistemic interpretation];
de Ronde et al a1903 [interpretation];
> s.a. origin of quantum theory.
@ From classical probability: Slavnov TMP(06)qp/07;
Grigorescu PhyA(08)-a0711 [classical Fokker-Planck equation and quantum Brownian motion];
Groessing et al a1403.
@ And classical probabilities:
Khrennikov & Loubenets FP(04)qp/02;
Khrennikov JMP(02),
AIP(05)qp/03;
Nyman IJTP(10)-a0906 ["quantum-like representation algorithm"];
Farenick et al JMP(11)-a1110 [classical and non-classical randomness, in terms of operator-valued measures];
Hardy a1303-ch;
Dzhafarov & Kujala FP(14)-a1305,
a1312-PLoS;
Khrennikov a1406-conf;
Hofmann a1606-proc;
Garner & Müller a2004.
@ And decoherence: Bacciagaluppi SHPMP(07)qp [time-directed probability];
Jordan & Chisolm PLA(09)-a0801.
@ Objective vs subjective probabilities: Mohrhoff AJP(01)aug-qp/00;
Saunders ch(05)qp/04;
Srednicki PRA(05)qp;
Huber BJPS(05) [as basis for scientific reasoning];
Ballentine AIP(07)-a0710;
Maudlin SHPMP(07);
Szabó SHPMP(07);
Glynn BJPS(10)#1 [deterministic chances];
> s.a. ψ-Epistemic Theories;
ψ-Ontic Theories.
@ Non-Kolmogorov: Szabó IJTP(94),
IJTP(95)gq/94,
FPL(95)gq/94,
qp/96;
Khrennikov JMP(00)qp,
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 AP(09)-a0710 [quantum vs classical];
Fuchs & Schack RMP(13).
@ Quasi-probability representation: Ferrie RPP(11)-a1001;
Ferrie et al PRA(10) [necessity of negative probabilities];
Ryu et al PRA(13)-a1206 [operationally defined, for qudits].
@ Related topics: Page qp/95,
IJMPD(96)gq/95 ["sensible quantum mechanics", without probabilities];
Shirokov qp/06 [on set of states];
Kupczynski a0810-conf [statistical predictions];
Döring & Isham JMP(12)-a1102 [as truth values in suitable sheaf topoi];
Loeliger & Vontobel a1201-conf [factor-graph representation];
Stairs SHPMP(11);
Henson a1210 [Consistent Exclusivity];
Sokolovski PRD(13)-a1301 [for classes of Feynman paths in spacetime];
Nenashev PS(14)-a1406 [from Zurek's envariance and Gleason's theorem];
> s.a. bell inequalities; Born Rule;
experiments on quantum mechanics; Gleason's Theorem;
histories formulations [including extended probabilities];
measure theory; mixed states;
quantum collapse [GRW]; representations [tomographic].
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