Equivalence Principle  

In General, Versions > s.a. affine connections; mass; Reference Frames [acceleration and gravity]; quantum equivalence principle.
* Idea: All bodies fall with the same acceleration in a gravitational field; The force of gravity can be made to disappear locally by going to a suitable reference frame; It motivated the development of general relativity and is naturally implemented in geometrical theories of gravity, although alternatives are possible.
* History: The heuristic principle was introduced by Einstein in 1907 as a primary motivation for general relativity, and formulated more precisely during his time in Prague in 1911-1912.
$ Weak (Galileo): All (pointlike, neutral) test bodies fall in the same way in a (possibly strong) gravitational field; Gravity is like an inertial force.
$ Weak (Newton): For (possibly extended) slowly-moving bodies in weak fields, inertial and gravitational masses are proportional, independently of composition/form.
$ Weak Equivalence Principle II: All small bodies, including rotating ones, fall in the same way in a (possibly strong) gravitational field.
* Relationships: When all assumptions are satisfied, the two above versions are equivalent.
$ Modern versions: The only long-range field with gravitational-strength couplings to matter is a massless spin-2 field, the graviton; The PPN γ parameter is the same for all types of matter.
$ Einstein equivalence principle: In a freely falling reference frame, gravity disappears locally.
* Remark: This principle concerns the passive gravitational mass \(m_{\rm pass}^~\), but \(m_{\rm act}^~\) must be equal to \(m_{\rm pass}^~\) in order for momentum to be conserved and Newton's third law to be valid, so an exterior gravitational field is independent of what type of matter produces it; This is more than just a statement on the gravitational effects felt by matter.
* Strong (idea): All (small) objects are equally affected by gravity in every respect; A stationary observer in a gravitational potential V is indistinguishable from one moving with acceleration −∇V and no gravitational field; All gravitational effects can be locally transformed away and no local measurement can detect a gravitational field; Requires that matter be coupled to gravity only through gab and Γabc, not the curvature.
* And general relativity: The weak equivalence principle is built into the theory (in fact, it is one of the three pillars that support all metric theories of gravity), as one can see using differential geometry and the connection to relate local Minkowski spaces; In fact, a number of features of general relativity such as gravitational redshift, light deflection and the fact that space must be curved (and thus the tensorial nature of the gravitational field) can be deduced from it; The strong equivalence principle is not built in, and there are situations where it is not satisfied.
@ Strong version: Bertotti & Grishchuk CQG(90); in Ohanian & Ruffini 94 [good]; Aldrovandi et al FP(03)gq/02 [with torsion].

Violations > s.a. geodesics [quantum corrections]; tests of the equivalence principle; modified lorentz symmetry.
* Of wep: May occur if there are s = 0 and 1 particles with gravitational strength couplings [@ Maddox Nat(91)mar], such as those predicted by some unified theories like string theory; The best known consequences are variation of "constants'', non-universality of free fall, and relative drift of atomic clocks; May also induce neutrino oscillations without the need for a neutrino mass (& P Halprin).
* Of sep: There are at least two local effects (using infinitesimal-size objects) that can detect gravitational fields, the tidal distorsion of an object, and the precession of a spinning non-spherical gyroscope; A gravitational field implies an unambiguous, non-zero \(R^a_{\,\,bcd}\); The strong equivalence principle fails even in Newtonian gravity; It is violated in QED in curved spacetime, with "faster than light" photons (> see causality violations), and by metric-affine theories that predict vacuum birefringence (> see phenomenology).
@ Of wep: Will PRL(89) [in non-symmetric gravity]; Göklü & Lämmerzahl CQG(08)-a0801 [from metric fluctuations]; Gasperini a2101-ch [gravity at finite temperature].
@ From string dilaton: Damour gq/97-proc, gq/97-proc; [Landau et al ap/03-wd].
@ Classical charged particles: Goto et al CQG(10)-a1007 [and radiation reaction]; Toth a1404.
@ And cosmology: Hui et al PRD(09)-a0905 [from modified gravity]; Hees et al a1504-proc [some cosmological consequences].
@ Other situations: Ellis gq/03 [leptons]; Ellis et al IJMPA(04)gq/03 [from spacetime foam]; Barrow & Scherrer PRD(04)ap [fermions vs bosons]; Hehl & Obukhov GRG(08)-a0705 [and electromagnetic coupling, axion and dilaton]; Bertolami et al PLB(07), Le Delliou et al AIP(07)-a0709 [dark energy–dark matter interaction in A586]; Carroll et al PRL(09)-a0807 [dark-matter-induced]; Damour & Donoghue PRD(10)-a1007 [through dilaton-like scalar field]; Minazzoli PRD(18)-a1811 [matter with unconventional coupling to geometry]; Blasone et al a1812 [scalar-tensor gravity at finite temperature]; > s.a. Chameleon Field; fifth force; scalar-tensor gravity.

References > s.a. Internal Relativity; variation of constants.
@ General: in Dicke 64; Klein Sci(71)jan; Hughes CP(93) [experimental basis and consequences]; Iliev JGP(98)gq; Camacho MPLA(99)gq [continuous quantum measurement]; Rohrlich FP(00) [critique]; Damour CRAS-gq/01 [rev]; Ghins & Budden SHPMP(01) [conceptual]; Nordtvedt gq/02 [consequences of incorporating special relativity]; Drake AJP(06)jan [and special / general relativity transition]; Fabbri in(12)-a0905 [and the geometrization of gravity]; Damour CQG(12)-a1202 [theoretical aspects]; Nobili et al AJP(13)jul [universality of free fall and gravitational redshift]; Di Casola et al AJP(15)jan-a1310 [precise formulation of the various versions, and relationships]; Brown & Read AJP(16)feb-a1512 [misconceptions]; Kapotis & Kalkanis TPT(16)oct [in class].
@ History: Rabinowitz IEEE(90)phy/07 [falling bodies]; Schücking & Surowitz gq/07, Weinstein a1208 [Einstein 1907]; Janssen SHPMP(12); > s.a. history of relativistic gravity.
@ Geometric formulation: Coleman & Schmidt JMP(95); Iliev JPA(96)gq, JPA(97)gq; Wesson GRG(03) [5D, weak]; Iliev gq/06-proc [and geodesic deviation].
@ Criticisms: Logunov et al SPU(96); Ginzburg & Froshenko SPU(95), SPU(96) [reply].
@ In deformed theories: Tkachuk PRA(12)-a1301 [and GUP, minimal length, deformed Poisson brackets]; Ghosh CQG(14)-a1303 [and GUP]; Gnatenko & Tkachuk PLA(17)-a1701 [non-commutative theories].
@ In other theories: Olmo PRL(07)gq/06 [in f(R) gravity theories]; Kraiselburd & Vucetich IJMPE(11)-a0902 [Bekenstein's theory]; Deruelle GRG(11)-a1104 [Nordström's scalar theory]; Sheikh-Jabbari IJMPD(11) [Lovelock and other higher-order theories]; Puetzfeld & Obukhov PRD(15)-a1505 [scalar-tensor gravity]; > s.a. gravitational energy-momentum; kaluza-klein phenomenology; modified gravity ["ultra-strong" version].
@ For Casimir energy: Fulling et al PRD(07)ht; Milton et al JPA(07)-a0705, JPA(08)-a0710-proc, a0810-conf; Shajesh et al JPA(08)-a0711-proc; Milton et al PRD(14)-a1401.
@ And electromagnetism: Özer gq/99; Trzetrzelewski EPL(18)-a1504 [Lorentz force and geodesics]; Ni IJMPD(16) [and phenomenology, cosmology]; > s.a. electromagnetism in curved spacetime.
@ Generalized: Lyre IJMPD(00)gq [for gauge charges]; Chiao gq/02/PRL [extended, and Kramers-Kronig relations]; Mensky PLA(04) [from energy-momentum conservation]; Wiltshire PRD(08)-a0809 [cosmological]; Kopeikin a1311 [in FLRW cosmology]; Di Casola et al PRD(14)-a1401 [for self-gravitating bodies, and purely metric theories of gravity]; Hetzroni FP(20)-a2001 [in abstract spaces]; > s.a. cosmological constant problem; physical constants ["c equivalence principle"].
@ Related topics: 't Hooft JGP(84) [and black-hole radiation]; Kreinovich & Zapatrin gq/97 [operational]; Carlip AJP(98)may-gq/99 [and kinetic energy]; Rohrlich PRD(01) [despite self-interaction]; Rodrigues & Sharif FP(01)mp/03 [and local Lorentz invariance]; Maluf et al CQG(07)-a0704 [tetrads and energy in freely falling frames]; Hui & Nicolis PRL(11)-a1009 [for scalar forces]; Hohensee et al PRL(13)-a1308 [for bound kinetic energy].

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