Reference Frames |

**In General** > s.a. coordinate systems; Covariance; Frame [more
mathematical]; Observer; Relativity; tetrads.

* __Idea__: A smooth atlas
on the spacetime manifold; In classical non-relativistic mechanics, a reference
frame
can be seen as a connection
on
a configuration space fibered over the time axis.

* __Inertial__: One in which
the components of the spacetime metric are constants, usually taken to be an
orthonormal set of coordinates, for which the metric is diag(–1, 1, ...,
1); The cornerstone of Newtonian mechanics;
Transformations between inertial frames form the Poincaré group; > s.a. inertia; mach's
principle.

* __Rest frame__: The reference frame in which the center of mass for a system is at rest; > s.a. Wikipedia page.

* __Accelerated__: In an
accelerated frame Newton's first law does not hold, so fictitious inertial
forces appear; In special relativity (Minkowski space) an observer in such
a frame sees a causal horizon, and the inertial quantum vacuum is seen as a
thermal state (this is known as the Unruh effect); > s.a. rindler
space.

@ __General references__: Arminjon & Reifler IJGMP(11)-a1003 [formal definition].

@ __Rest frame for a system__: Arnold et al JHEP(14)-a1408 [absence in far-from-equilibrium quantum matter].

@ __Inertial frames__: Stephens FPL(96)
[in quantum field theory]; Rodrigues & Sharif FP(01)
[in general relativity, and local Lorentz invariance]; Smolin a1007 [limitations
of the concept in non-commutative spacetime]; Baccetti et al a1302-MG13 [with Lorentz-symmetry breaking]; Saunders PhSc(13) [role in Newton's theory of motion]; Shojai & Shojai AJP(15)-a1505 [in general relativity, and the equivalence principle].

@ __Related topics__: Meli HSPS(93) [history];
Bel gq/00 [rotation
along a world-line]; Dickson SHPMP(04)
[and uncertainty relations]; Llosa & Soler CQG(04)
[geometric structure,
and rigid motion]; Rosinger qp/05 [covariance
of physical laws, general relativity and unification];
Marmo & Preziosi IJGMP(06) [coordinate-free formulation];
Jennings PRA(11)-a1011 [optimal primitive reference frames and quantum information];
> s.a. Aberration; locality.

@ __In Newtonian spacetime__: Coll et al a0707 → FP(09),
PRD(09) [four
causal classes]; > s.a. (post-)newtonian gravity.

@ __Practical realizations__: Malkin IAU(12)-a1311 [relating the international celestial and terrestrial reference frames]; Berceau et al a1512 [high-performance space-time reference with an orbiting clock].

@ __Preferred reference frames__: Perez a1405-FQXi;
> s.a. standard cosmological model;
violations of lorentz symmetry.

> __In other mechanical theories__:
see astronomy; kinematics
of special relativity; relativistic
quantum mechanics.

> __In specific field theories__:
see canonical general relativity [material
reference systems]; electromagnetism; types
of field theories [non-local].

**Accelerated / Non-Inertial Frames** > s.a. lorentz group [representations]; poincaré group; unruh effect.

@ __General references__: Padmanabhan ASS(82)
[definition of particle]; Mashhoon PRA(93)
[general theory]; Marzlin PLA(96);
Chicone & Mashhoon AdP(02)gq/01 [kinetic
and dynamic memory]; Mashhoon in(03)gq, IJMPD(05)
[non-locality]; Semay EJP(06)
[constant proper acceleration]; Sardanashvily a0708 [non-relativistic
mechanics in arbitrary frames, inertial forces, etc]; Mashhoon AdP(08)-a0805 [non-local]; Semon et al AJP(09)may
[and the transition from special to general relativity]; Boyer FP(13)-a1204 [contrasting classical and quantum vacuum states]; Martin-Martinez et al PRA(12)-a1204 [fundamental limitations to information transfer].

@ __Uniformly accelerated__: Desloge AJP(89)dec
[non-equivalent to uniform gravitational field]; Muñoz & Jones AJP(10)-a1003 [equivalent
even in a relativistic context]; Friedman & Scarr PS(13)-a1404 [spacetime transformations]; Llosa a1507 [coordinate transformation laws and infinitesimal generators]; > s.a. non-commutative
geometry.

@ __Relativistic__: Mitskevich 05 [relativistic physics in arbitrary frames]; Turyshev et al JMP(12)-a1109 [relativistic, in Minkowski space]; Lusanna LNP-a1310 [in special and general relativity]; > s.a. special-relativistic kinematics.

@ __Rotating frames__: Strauss IJTP(74); Grøn IJTP(77);
Strauss IJTP(79);
McFarlane IJTP(81) [appearance of a corotating disk]; Weber AJP(97)jun,
Tartaglia FPL(99)phy/98 [rotating
disk and Ehrenfest
paradox]; Bashkov & Malakhaltsev gq/01;
Klauber gq/01 [frequency
and wavelength of light];
Rodrigues & Sharif FP(01)
[and the
Sagnac
effect]; Peres gq/04|AJP
[Ehrenfest paradox]; Dieks in(04)-a1001 [coordinates
and spacetime measurements]; Mashhoon PRA(09)-a0903 [electromagnetic
waves]; Kassner AJP(12)sep-a1109; Bel a1112 [uniformly rotating]; Kassner AJP(12)dec-a1302 [anisotropic one-way speeds of light, resolving Selleri's paradox]; Manjarres et al AJP(13)aug [work and energy]; > s.a. Mössbauer Effect; rotation; Sagnac Effect.

@ __In quantum mechanics__:
Mensky TMP(98)gq/97 [thermal particles and Unruh effect]; Angelo & Ribeiro JPA(12); Klink & Wickramasekara AP(14) [violations of the non-relativistic equivalence principle]; > s.a. entanglement phenomenology [frame dependence].

@ __In field theories__: Lynden-Bell et al AP(99)
[gravity and electromagnetism]; Lusanna a0707-conf
[in general relativity, observables and constraints]; Lenz a0808 [gauge
fields]; Maluf & Ulhoa AdP(10)-a1009 [electrodynamics]; Banks & Fischler a1301 [in the formalism of holographic spacetime, and effective field theory]; Boyer FP(13) [stochastic electrodynamics vs QED]; Lynch a1504-GRF [acceleration-induced particle physics processes]; Dasgupta a1508 [quantum field theory].

> __Related topics__:
see newton-cartan theory; quantum field theory effects [negative energies]; Saha Equation; thermal radiation.

**Related Concepts**

* __Quasilocal frame__: A choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume.

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