Arrow of Time and Irreversibility |

**In General** > s.a. computation; electromagnetism;
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 entropy production and the tendency of potential energy
to decrease, particle decay, and radiation); Quantum measurement (may not really exist);
Cosmological (expansion); Gravitational (clumping); Psychological (memory of the past).

* __Relationships__:
T Gold proposed that the thermodynamical and cosmological ones are related;
The psychological one seemed to be independent, because the entropy of the brain
does not increase; 2013, Landauer's principle used to explain the relationship
between psychological and thermodynamic arrows of time.

* __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); 1927, 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? It could be related to the Big Bang or black holes
close to the Planck 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), related to measurement devices and quantum state reductions, or the
Weyl curvature hypothesis (Penrose); The problem is, Show how.

@ __I__: Rothman ThSc(97)jul [Brussels school];
Magnon 97; Dodd SA(08)jan.

@ __Reviews, books__: Davies 74;
Price BJPS(91) [review],
in(94)gq/93,
96, phy/04-proc;
Mackey 92;
Zeh 07, a1012-ch [rev].

@ __General references__: Margenau PhSc(54)apr;
Popper Nat(57)jun;
Gold in(58), AJP(62)jun;
Coveney Rech(89)feb;
Page in(91); Lebowitz PT(93)sep;
Savitt ed-94, BJPS(96) [rev];
Nikolić phy/98;
Rohrlich FP(98) [point particle approximation];
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];
Ćirković & Milošević-Zdjelar FS(04)phy [three];
Rovelli SHPMP(04) [refute Rohrlich];
Castagnino & Lombardi JPA(04) [non-entropic];
Aiello et al FP(08) [local from global];
Feng & Crooks PRL(08) [length of time arrow];
Zeh a0908-ch [conceptual];
Ellis SHPMP(13)-a1302 [top-down causation];
Barbour et al a1310,
PRL(14)-a1409
+ Carlip Phy(14)
+ news wired(14)nov [gravitational origin];
Rovelli a1407,
a1505 [time-oriented coarse-graining];
Barbour a1602-proc,
et al a1604 [in unconfined systems].

@ __Fundamentally irreversible theory__: Cortês & Smolin a1703;
Diósi a1806.

@ __Psychological arrow of time__: Wolpert IJTP(92),
Maroney FP(10)-a0709 [and computers];
Mlodinow & Brun PRE(14)-a1310 [and the thermodynamic one].

@ __Conceptual__: Reichenbach 56;
Rakić BJPS(97) [open future and special relativity];
Dorato SHPMP(06) [becoming];
Torretti SHPMP(07) [reexamination];
van Strien SHPMP(13) [mechanism and the reversibility objection];
Neri a1309 [meta-theoretical approach].

> __Online resources__:
see Wikipedia page;
2015 video with interviews.

__Related subjects__: see arrow of time in various physical theories.

**Related Topics** > s.a. CPT symmetry [time reversal];
hilbert space; measurement in quantum mechanics;
time in quantum gravity.

@ __And causality__: Rohrlich SHPMP(00) [causality and self-interaction];
Nikolić FPL(06) [and causal paradoxes];
Coecke & Lal PRL(12)-a1108 [vs causal structure].

@ __And information__: Hitchcock qp/00;
Diósi LNP(04)qp/03;
Schlesinger a1404 [and Gödel incompleteness].

@ __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];
Kupervasser et al FP(12)-a1011, Kupervasser EJTP-a1106 [instability and universal arrow of time].

@ __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);
Kupervasser EJTP-a1107;
> s.a. Coarse-Graining.

@ __Numerical experiments__: Fowles AJP(94)apr;
Georgeot & Shepelyansky EPJD(02)qp/01 [and quantum computers].

> __Related topics__: see CPT [*T*-reversal];
entropy; Evolution; Landauer's Principle;
Recurrence; thermodynamic concepts [reversible process].

"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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send feedback and suggestions to bombelli at olemiss.edu – modified 24 jun 2018