Time in Physical Theories |

**In General** > s.a. time [different views, general aspects].

* __Two-time physics__:
The theory proposed by Itzhak Bars and collaborators has one extra timelike
and one extra spacelike dimension (4+2); Claimed to be free of problems with
unitarity and causality, and to explain CP conservation in QCD
without the need for the axion, among other things.

@ __Parametrized theories__:
Hartle & Kuchař in(84);
Magnon NCB(96), NCB(98) [relational];
Albrecht & Iglesias PRD(08)-a0708 [emergent];
Rañada & Tiemblo FP(08);
Gryb & Thébault FP(12)-a1110 [relational];
Höhn JPCS(12)-a1110 [effective approach, semiclassical regime];
Anderson CQG(14)-a1305;
Gueorguiev a1903-conf
[Lagrangian and extended Hamiltonian formalism];
> s.a. Relationalism; time in gravity.

@ __Two-time physics__: Bars PRD(00)ht,
PRD(00)ht [in field theory],
CQG(01)ht/00 [survey];
Bars & Deliduman PRD(01)ht [particle + gauge field];
Bars PRD(06)ht,
AIP(07)ht/06 [and standard model];
Chagas ht/06 [with minimum length];
news pn(07)jun;
Bars & Kuo PRL(07) [with *N* = 1 Supersymmetry];
Chagas a0802 [in quantum mechanics];
Craig & Weinstein PRS(09) [initial-value problem];
Foster & Müller a1001 [general properties];
Frederico & Rivelles PRD(10) [transition amplitudes];
Caruso a1405 [on proving the one-dimensionality of time];
> s.a. black holes in modified theories; brane world;
higher-dimensional gravity; kaluza-klein theory;
time in gravity and quantum gravity.

@ __Multi-time physics__: (one for each particle)
Petrat & Tumulka PRS(14) [classical and quantum];
> s.a. Pair Creation.

@ __Complex time__: Mejías et al CSF(04);
Fujii qp/07-conf [comment on a paper by Rajeev].

@ __Different views__:
Oleinik et al qp/00-conf [dynamical inhomogeneity];
Lynds FPL(03);
Sadatian ILCPA-a1404 [inhomogeneous time?].

> __Other theories__:
see time in gravitational theory; time
in quantum theory; time in quantum gravity.

**In Classical Mechanics**

* __Idea__: In its usual presentation, classical
mechanics appears to give time a very special role, but it is well known that it can be
formulated so as to treat time on the same footing as the other variables in the extended
configuration space.

@ __General references__: Muñoz-Díaz & Alonso-Blanco a1707 [and quantum mechanics].

@ __As a dynamical variable__: Grigorescu CJP(00)mp [canonical];
Bhamathi & Sudarshan PLA(03);
Rañada & Tiemblo CJP(12)-a1106 [parameter time vs physical time].

@ __In thermodynamics__: da Costa & Sant'Anna FPL(01)gq,
mp/01,
FP(02) [thermodynamics without *t*].

@ __Discrete time__:
Jaroszkiewicz & Norton JPA(97);
Jaroszkiewicz 14 [and in quantum mechanics, field theory].

@ __Related topics__: Wetterich FP(12)-a1002 [probabilistic];
Thébault BJPS(12) [and symplectic reduction].

**In Special Relativity** > s.a. special relativity.

* __Idea__: Time loses the uniqueness
it had in classical mechanics; It is no longer a specific function, but just a measure
of timelike distance along some worldline; The direction of time is now defined up to
a Lorentz transformation.

* __Clock hypothesis__: The assumption
that the time read by an accelerated clock is given by the elapsed Minkowski proper time,
i.e., the length of the timelike curve.

@ __General references__:
Rodrigues & Rosa FP(89);
Kobe AJP(93)nov [parametrizations];
Selleri FP(97);
Lindesay & Gill FP(04) [proper *τ*];
Ya'acov JPA(06) [internal time];
Boyarsky & Gora a0705
[time measurement definition using fundamental scale];
Paiva & Teixeira a1107 [and general relativity; in Esperanto/English];
Chappell et al a1205
[time identified with the three rotational degrees of freedom of space, and Clifford's geometric algebra];
Bacelar a1302,
Fletcher FP(13) [time for accelerated observers and the clock hypothesis];
Bacelar a1312 [flow of time];
Brunet a1609 [geometric time and causal time];
Bacelar a1610 [inertial time, light clocks].

@ __Effects__: Goy & Selleri FPL(97)gq [rotation];
Bahder gq/98 [rotating clock];
Leffert ap/02/MNRAS [running backwards??].

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