Arrow
of Time and Irreversibility| Arrow
of Time and Irreversibility |
In General > s.a. computation;
CPT symmetry [time reversal]; statistical
mechanics; 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
(the approach to equilibrium, 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 and
violations; 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 PRD(08)-a0801 [semiclassical
Coulomb field and decoherence]; Strauss et al a0802,
comment Hall a0802 [arrow-of-time
operator]; Bohm et al JPA(08)-a0803-in;
Maccone PRL(09),
comment Jennings & Rudolph a0909 [resolution based on information].
@ 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]; Halabi a0908.
@ 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)jun;
Verstraeten PhSc(91)dec;
Karakostas PhSc(96)sep.
@ In quantum field theory: Vitiello ht/01-in;
Buchholz CMP(03);
Atkinson SHPMP(06)
[QED]; Morgan a0810.
@ 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)apr;
Popper Nat(57)jun;
Gold in(58), AJP(62)jun;
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]; Feng & Crooks PRL(08)
[length of time arrow]; Zeh a0908-in [conceptual].
@ 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)dec
[Albert's proposal vs Reichenbach]; Tian JHEP(05)gq [thermal
time, in de Sitter]; Hagar PhSc(05)jul;
Maroney SHPMP(05),
Gallavotti Chaos(06)
[irreversibility time scale]; Ladyman et al SHPMP(07)
[logical vs thermodynamical arrow of time]; Partovi PRE(08)-a0708 [violation
in high-correlation environment]; Lucia PRS(08)
[and ergodicity]; Swendsen AJP(08)jul
[model, qualitative understanding]; Drory SHPMP(08)
[no paradox]; Schulman a0811-in
[role of cosmology]; > s.a. entropy [production]; 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 BJP-gq/05-in,
a0910-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; Bojowald a0910-in
[lqc].
@ 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)aug
[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)apr;
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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nov
2009