Arrow of Time and Irreversibility  

In General > s.a. computation; cpt symmetry [time reversal]; thermodyamics; time [culturally].
* Idea: Although the fundamental laws are (apparently) time-reversible, real world processes don't seem to be; Formally described by using semigroups rather than groups of time-evolution operators in physical theories.
* Versions: Thermodynamical, including the tendency of (potential) energy to decrease, particle decay, and radiation; Quantum measurement (may not really exist); Cosmological (expansion); Gravitational (clumping); Psychological (consciousness); T Gold proposed that the thermodynamical one and the cosmological one are related.
* History: 1872, Boltzmann argues that irreversibility can be derived from a time-reversible microphysics using statistical mechanics and entropy (there are logical gaps, but it has become the majority view); Eddington introduces the expression "arrow of time"; Supporters of the opinion that irreversibility is fundamental include Planck, Poincaré (statistical mechanics is primary, cannot be derived from Newtonian physics), Prigogine (the connection goes through unstable systems); 1999, Schulman's simulations, two opposite ones can coexist.
* Open future view: The common-sense view that there is an ontological difference between the past, the present, and the future; The past and the present are real, whereas the future is not yet a part of reality.
* Points of view: Irreversibility is at least partly a question of initial conditions [Boltzmann, Reichenbach, Grünbaum], but many hope there is more):
- Not fundamental: It comes from coarse-graining, disordered states being by far more numerous than ordered ones; the problem is, At what scale?
- Intermediate: Rohrlich argues that the arrow of time is not built into the fundamental equations of motion for a point particle (e.g., Lorentz-Abraham-Dirac equation), but appears in every finite-size version.
- Fundamental: Emergent structures in non-equilibrium processes, rigged Hilbert spaces (Prigogine and Brussels school), or Weyl curvature hypothesis (Penrose); The problem is, Show how.
@ References: Reichenbach 56; Rakic BJPS(97) [open future and special relativity]; Dorato SHPMP(06) [becoming]; Torretti SHPMP(07) [reexamination].
> Related topics: see CPT [T-reversal]; entropy; Evolution; Recurrence; thermodynamic concepts [reversible process].

In Quantum Theory > s.a. causality; quantum statistical mechanics; quantum systems; resonance; time in quantum theory.
* Idea: The standard formalism rules out the existence of an arrow of time because it is based on conserved probabilities; The Brussels school proposed formalism based on the presence of resonances and the use of rigged Hilbert space and time-evolution semigroups; Or one can try quantum field theory.
@ General references: Fargue & Fer AFLB(76); Toyozawa JPSJ(89); Lenz & Zyczkowski JPA(92); Gell-Mann & Hartle gq/93-in [and quantum cosmology]; Page PRL(93)gq; Bohm & Kielanowski APPB(96)qp/95 [different types]; Kadomtsev SPU(95); Fain 00; D'Ariano et al PLA(00)qp [and phase squeezing]; Bishop qp/02-in; de la Madrid qp/03-in [and boundary conditions]; Bohm IJTP(03) [resonances and decay]; Bishop IJTP(05)qp-in [and mental systems]; Castagnino et al FP(06); Pérez-Madrid PhyA(07); Holster NJP(03) [time asymmetry]; Polonyi a0801 [semiclassical Coulomb field and decoherence]; Strauss et al a0802, comment Hall a0802 [arrow-of-time operator]; Bohm et al a0803-in.
@ Quantum measurement: Aharonov et al PR(64); Zeh FP(79)qp/03; Baaquie IJMPA(94) [decoherence and Friedrichs model]; Schulman 97; Bohm et al IJTP(99); Srivastava et al IJMPB(99)qp/98 [information and entropy].
@ Rigged Hilbert space: Schulte et al qp/95; Bishop IJTP(04), IJTP(05) [Bohm vs Brussels-Austin], qp/05; > s.a. hilbert space.
@ Brussels school: Prigogine & Petrosky PhyA(87); Hasegawa et al FP(91); Antoniou & Prigogine PhyA(93); Bohm IJTP(97)ht [K decay]; Ordóñez PhyA(98)mp/00; Bostroem qp/00; Castagnino & Gunzig IJTP(99)qp/00 [axiomatic], qp/00 [comparison]; Bishop SHPMP(04) [overview]; Bohm et al qp/07 [framework].
@ Brussels school, critiques: Batterman PhSc(91); Verstraeten PhSc(91); Karakostas PhSc(96).
@ In quantum field theory: Vitiello ht/01-in; Buchholz CMP(03); Atkinson SHPMP(06) [QED].
@ And observation: Bohm et al qp/07 [with single ion]; > s.a. quantum effects [reversal of evolution].

References > s.a. hilbert space; measurement in quantum mechanics; time in quantum gravity.
@ I: Rothman ThSc(97)jul [Brussels school]; Magnon 97; Dodd SA(08)jan.
@ General: Margenau PhSc(54); Popper Nat(57); Gold in(58), AJP(62); Davies 74; Coveney Rech(89)feb; Page in(91); Price BJPS(91) [review], in(94)gq/93, 96, phy/04-in; Mackey 92; Lebowitz PT(93)sep; Savitt ed-94, BJPS(96) [rev]; Nikolic phy/98; Rohrlich FP(98) [point particle approximation], SHPMP(00) [causality and self-interaction]; Bernstein & Erber JPA(99) [local vs global]; Costa de Beauregard IJTP(99); Castagnino qp/00 [global nature]; Price BJPS(02), North BJPS(02) [two conceptions]; Cirkovic & Milosevic-Zdjelar FS(04)phy [three]; Rovelli SHPMP(04) [refute Rohrlich]; Castagnino & Lombardi JPA(04) [non-entropic]; Nikolic FPL(06) [and causal paradoxes]; Zeh 07; Aiello et al FP(08) [local from global].
@ Radiation: Frisch BJPS(00) [dissolution of puzzle]; Price SHPMP(06); Frisch SHPMP(06); Boozer EJP(07) [and retarded potentials].
@ In classical mechanics / thermodynamics: Hutchison BJPS(93); Savitt BJPS(94); Hutchison BJPS(95) [friction implies irreversibility in practice], comment Callender BJPS(95); Zak IJTP(96); Busch CMC(00)mp/99; Zeh FPL(99)phy; Brown & Uffink SHPMP(01) [source]; Callender in(01); Muratov JPA(01) [classical statistical mechanics]; Castagnino & Laciana CQG(02); Yukalov PLA(03) [quasi-isolated systems]; Cirkovic FP(03) [Boltzmann-Schütz argument and multiverse approach]; Winsberg PhSc(04) [Albert's proposal vs Reichenbach]; Tian JHEP(05)gq [thermal time, in dS]; Hagar PhSc(05); Maroney SHPMP(05), Gallavotti Chaos(06) [irreversibility time scale]; Ladyman et al SHPMP(07) [logical vs thermodynamical aot]; Partovi a0708 [violation in high-correlation environment]; Lucia PRS(08) [and ergodicity]; Swendsen AJP(08) [model, qualitative understanding]; > s.a. modified thermodynamics.
@ In (quantum) cosmology: Page IJTP(84) [inflation]; Hawking PRD(85); Hawking et al PRD(93)gq [from boundary conditions]; Hu in(94)gq/93 [fluctuation-dissipation relation]; Kiefer & Zeh PRD(95)gq/94 [reversal in recollapse]; Rothman & Anninos PRD(97) [clumping and phase space volume]; Dastidar MPLA(99)qp-in [and cmb]; Allahverdyan & Gurzadyan JPA(02) [relation with thermodynamics, and cmb]; Albrecht ap/02-in [inflation]; Castagnino et al CQG(03)qp/02, FP(03) [and other arrows]; Carroll & Chen ht/04 [spontaneous inflation]; Kiefer gq/05-in [origin is in quantum cosmology]; Wald SHPMP(06)gq/05-in, Earman SHPMP(06) [and initial conditions]; McInnes NPB(07) [strings]; Carroll SA(08)may.
@ And information: Hitchcock qp/00; Diósi qp/03-in.
@ And determinism: Elitzur & Dolev FPL(99)qp/00 [black hole evaporation], PLA(99); Dolev et al qp/01/SHPMP.
@ And chaos: Roberts & Quispel PRP(92); Calzetta JMP(91); Lee PRL(07) [irreversibility not sufficient for chaos]; > s a. quantum chaos.
@ Opposing arrows of time: Schulman PRL(99)cm + pn(99)dec, PRL(00)cm, PLA(01)cm [causality paradoxes], comment Zeh Ent(06); Goldtein & Tumulka CQG(03) [and non-locality].
@ Versions, examples: Baker AJP(86) [simple model]; Géhéniau & Prigogine FP(86); Bonnor PLA(85), PLA(87) [gravitational]; Brout FP(87); Brout et al PLB(87); Fukuyama & Morikawa PRD(89); Maroney a0709 [psychological, and computers].
@ Numerical experiments: Fowles AJP(94); Georgeot & Shepelyansky EPJD(02)qp/01 [and quantum computers].

"Then go and invert them" - Boltzmann to Loschmidt, who had asked him what
happens to his statistical theory if one inverts the velocities of all particles.


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