Histories Formulations of Quantum Theory |
Consistent Histories
* Idea: A closed quantum
system is a Hilbert space, and every statement about it a subspace of
H (no hidden variables); A history is a sequence of subspaces
E1, E2,
..., associated with times t1,
t2, ...; If a history is in a consistent
family, it can be assigned a probability; Within that family, one and only one history
occurs (notion of trajectory); The unitary time evolution generated by the Schrödinger
equation is used to define consistent histories and calculate probabilities; Measurements
play no fundamental role, they influence the history but one can talk of the behavior of
quantum systems in the absence of measurement; In details, consistent historians differ.
* Motivation: Formulate quantum mechanics
in a more covariant way; Find an interpretation that is less instrumentalist than the
Copenhagen one, and more realist.
References
> s.a. formulations of quantum mechanics; path-integral formulation.
@ General: Gell-Mann & Hartle in(90)-a1803;
Hartle ViA(93)gq/92;
Gell-Mann & Hartle PRD(93)gq/92,
gq/94;
Griffiths PRL(93);
Dowker & Kent PRL(95)gq/94;
Omnès 94;
Diósi PLA(95)gq/94;
Schreckenberg JMP(96)gq;
Finkelstein qp/96 [interpretational questions];
McElwaine PhD(96)qp/97 [approximate consistency];
Caticha qp/98 [assumptions];
Kent PRL(98)gq;
Wright CMP(99) [symmetries];
Savvidou PhD(99)gq [continuous time];
Brun qp/03-proc [resolving ambiguities];
Henson JPCS(09)-a0901 [and correspondence principle];
Sorkin a1004-in;
Hohenberg a1101-wd [and interpretation];
Riedel et al PRA(16)-a1312 [and quantum Darwinism, redundant records];
Friedberg & Hohenberg RPP(14)-a1405 [Compatible Quantum Theory];
Hartle a1608 [starting with records of what histories happen].
@ Reviews: Halliwell gq/93-in,
qp/03-proc;
Dowker & Kent JSP(96)gq/94;
Kent PS(98)gq;
Griffiths & Omnès PT(99)aug;
Griffiths 01;
Dass qp/05-ln;
Chisholm JPCS(09)qp/06;
Hohenberg RMP(10)-a0909 [intro];
Griffiths a1105 [and consistent quantum ontology];
Hartle a1901 [cosmology and quantum theory];
Rodrigues Rocha et al a2103-in [history].
@ Choice of consistent set: McElwaine PRA(96)qp/95,
PRA(97)qp/96;
Kent & McElwaine PRA(97)gq/96;
Griffiths PRA(98)qp/97;
Anastopoulos IJTP(98)qp/97;
Losada & Laura AP(14) [generalized contexts].
@ Decoherence functionals: Isham & Linden JMP(94)gq;
Isham et al JMP(94)gq;
Wright CMP(98); Dowker & Wilkes a2011 [strong positivity].
@ Continuous: Isham & Linden JMP(95)gq;
Isham et al JMP(98)qp/97;
Anastopoulos JMP(01)qp/00;
Kouletsis PhD(00)gq/01.
@ Topos theory: Isham IJTP(97)gq/96;
Raptis qp/01;
Flori JMP(10).
@ Other generalized: Isham JMP(94)gq/93,
qp/95-conf;
Pulmannová IJTP(95);
Goldstein & Page PRL(95);
Rudolph IJTP(96)qp/95,
JMP(98);
Kent a1305 [real path quantum theory];
Halliwell PRA(17)-a1704 [incompatible consistent sets of histories].
@ Probabilities: Nisticò CMP(00);
Saunders Syn(98)qp/01,
qp/01-in;
Anastopoulos IJTP(03) [quantum vs stochastic];
Hartle PRA(04)qp [virtual];
Marlow AP(06)qp/05,
IJTP(06) [Bayesian account],
qp/06 [and Gleason's theorem];
Jordan & Chisholm PLA(09)-a0801 [and weak decoherence];
Sudbery a2012.
@ Problems: Peruzzi & Rimini FPL(98)qp/97 [retrodictions];
Bassi & Ghirardi JSP(00)qp/99 [and realism],
reply Griffiths JSP(00)qp;
Nisticò PE(03)qp;
Okon & Sudarsky FP(14)-a1301,
a1504 [interpretational problems, measurement].
@ In quantum cosmology:
Hartle in(93)gq/92,
in(93)gq,
in(95)gq/93,
in(94)gq [and closed systems];
Kessari CQG(07)gq/06;
Halliwell IJTP(06);
Craig & Singh FP(11)-a1001,
AIP(10);
Kent a1204-proc
[conditioning on the occurrence of a fixed sequence of cosmological events];
Craig & Singh CQG(13)-a1306 [in lqc + scalar],
a1603-MG14 [probability of a non-singular bounce];
Craig IJMPD-a1604 [rev];
Lloyd a1608 [and the cosmological measure problem].
@ Other systems and topics: Griffiths qp/95,
PRA(96)qp [quantum reasoning];
Kent LNP(00)gq/96 [subspace implications].
> Specific types of systems: see
parametrized systems; QED; quantum
field theory in curved spacetime; quantum constrained systems.
Related Topics
> s.a. causality; entanglement and spacetime [entangled-history
states]; locality in quantum theory; logic [anhomomorphic logic].
@ And contrary inferences: Kent PRL(97)gq/96,
comment Griffiths & Hartle PRL(98)gq/97;
Kent PRL(98)gq.
@ And Bohmian mechanics:
Kent in(96)qp/95;
Griffiths PLA(99)qp;
Hiley & Maroney qp/00;
Hartle PRA(04)qp/02.
@ And no-hidden-variables: Bassi & Ghirardi PLA(99)gq/98 [problem];
Griffiths PLA(00)qp/99 [no problem].
@ And measurement: d'Espagnat PLA(87);
Brun PRA(00)qp/97 [continuous];
Sokolovski & Liu PLA(01);
Lloyd qp/05 [generalized];
Seidewitz FP(11) [measurements in spacetime];
Griffiths PRA(13)-a1308 [restrictions on what an observer can know about a quantum system];
Okon & Sudarsky SHPMP-a1309;
Griffiths a1501
[comparison with alternative approaches];
Ghazi-Tabatabai a1610 [observer dependence];
> s.a. zeno effect.
@ And decoherence: Paz & Zurek PRD(93)gq [environment-induced];
Halliwell PRD(01)qp/00 [approximate].
@ Geometry and structures:
Craig qp/97 [geometry];
Dass & Joglekar AP(01) [symmetries];
Blute et al gq/01 [on graphs].
@ Phase space representation: Anastopoulos JMP(01)qp/00,
AP(03)qp/02 [in phase space];
Larsson ht/04 [histories phase space, harmonic oscillator and free scalar];
Burch JMP(07)qp [perturbation theory, oscillator].
@ Other approaches: Raptis et al IJTP(07) [tomographic histories representation];
Leffler a1302 [different approach];
Cotler & Wilczek PS(16)-a1502 [quantum history states];
Castellani a1810 [history operator];
Diaz et al PRD(19)-a1910 [history state formalism];
> s.a. Trajectories [quantum states as ensembles of trajectories].
@ Other topics: Halliwell PRD(93)qp,
PRD(93)qp [and the uncertainty principle];
Diósi et al PRL(95) [and quantum state diffusion];
Omnès FP(95) [epistemology];
Savvidou JMP(99)gq/98 [action operator];
Clarke qp/00;
Halliwell qp/01-in [and spacetime conditions];
Griffiths PRA(02)qp [relativistic, and paradoxes];
Bosse & Hartle PRA(05)qp [spacetime alternatives for operators];
Hartle PRA(08)-a0801 [and extended probabilities];
> s.a. generalized bell inequalities; quantum
effects [time of arrival]; wave function collapse.
Decoherent Histories > s.a. decoherence;
entropy; relationship classical-quantum mechanics.
* Idea: Environmental noise
furnishes the inevitable dephasing that collapses the wave function.
@ General references:
Halliwell NYAS(95)gq/94,
PRD(98)qp [hydrodynamic-type variables],
PRD(01)qp/00;
Hartle et al PRD(95)gq/94 [closed systems, conservation laws];
Halliwell QIP-a0904;
Gell-Mann & Hartle PRA(12)-a1106 [with one "real" fine-grained history].
@ Decoherence conditions: Scherer et al PLA(04)qp [arbitrarily long histories];
Wallden IJTP(08)gq/06 [spacetime coarse-grainings].
@ Types of theories: Halliwell & Wallden PRD(06)gq/05 [reparametrization-invariant];
> s.a. parametrized theories.
> Gravity-related theories:
see FLRW quantum cosmology; minisuperspace quantum cosmology;
spin networks; time in quantum gravity.
Coevent Formulation > s.a. measure theory [quantum measures].
@ References: Wallden JPCS(13)-a1301;
Ghazi-Tabatabai a1303 [coevents as beables, and topos theory];
Ghazi-Tabatabai a1306 [in terms of truth valuations].
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