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),
in(94)gq/93,
96,
phy/04-proc;
Mackey 92;
Zeh 07,
a1012-ch;
Kuzemsky RNC(18),
FS(20) [interdisciplinary].

@ __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];
Ellis & Drossel FP(20)-a1911
[the evolving block universe and the different local arrows of time].

@ __Fundamentally irreversible theory__:
Cortês & Smolin PRD(18)-a1703;
Diósi Ent(18)-a1806;
Gallego Torromé a2007 [and emergent quantum theory];
> s.a. Dynamics.

@ __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];
Chen a2001 [and *de se* probabilities];
te Vrugt SHPMP(21)-a2004 [five sub-problems].

> __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.

* __Past Hypothesis__: The assumption, commonly
used to explain the arrow of time, that the universe started in a low-entropy state.

@ __The Past Hypothesis__:
Earman SHPMP(06) [critique and alternative];
Wallace in(17);
Lazarovici & Reichert a1809 [without];
Gryb a2006 [difficulties];
Chen a2006 [and quantum entanglement, Humean solution];
Keming Chen a2008 [as a candidate fundamental law].

@ __And causality__: Rohrlich SHPMP(00) [causality and self-interaction];
Nikolić FPL(06) [and causal paradoxes];
Coecke & Lal PRL(12)-a1108 [vs causal structure];
Donoghue & Menezes PPNP(20)-a2003
[the arrow of time follows from the causal structure of quantum physics].

@ __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;
Hoover & Hoover a2010 [in Hamiltonian mechanics];
> s.a. Coarse-Graining.

@ __Numerical experiments__: Fowles AJP(94)apr;
Georgeot & Shepelyansky EPJD(02)qp/01 [and quantum computers];
Seif et al a1909 [machine learning algorithm].

@ __Reversal__: news cosmos(19)mar [superconducting qubits in a quantum computer];
Xian & Zhao PRR(20)-a1911 [wormholes and entangled states].

> __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 29 apr 2021