Tests of the Equivalence Principle  

In General > s.a. eötvös experiment and fifth force; quantum equivalence principle.
* Idea: Possible consequences of a small violation of the equivalence principle include small differences in the free-fall acceleration of different materials, and a rotation of the plane of polarization for linearly polarized radiation propagating over cosmological distances.
* History: The earliest recorded test was by Galileo; The best experimental test is to compare the free-fall acceleration of different materials; Late 1800s, validated to one part in 108 by the Eötvös experiment; 2001, Eöt-Wash experiments on the weak principle, the best tests so far, confirm it up to corrections of order 10−13 and have reached their thermal limit; 2004, The most accurate experiment with atoms shows no departure [@ news pw(04)nov]; 2016, MICROSCOPE launched.
* Of the strong equivalence principle: 2003, The only technique available to test it is Lunar Laser Ranging (> see tests of general relativity); 2004, results give \(\Delta(m_{\rm g}/m_{\rm i})_{\rm SEP}\) = \((-2.0 \pm 2.0) \times 10^{-13}\), and \(\eta:= 4\beta-\gamma-3 = (4.4 \pm 4.5) \times 10^{-4}\).
* Results from the Nordtvedt effect: Experiments give \(m_{\rm g}/m_{\rm i}\) = 1 + \(\eta(U_{\rm G} / mc^2)\), with \(\eta < 10^{-12}\) so far.
* Results with self-energy: Satisfied up to 10−3 [@ Baeßler et al PRL(99), news PT(99)nov].
* Plans: 2004, NASA-ESA STEP (Satellite Test of the Equivalence Principle) to be put in orbit in 2005, aims at \(10^{-18}\) accuracy; SEE (Satellite Energy Exchange); GReAT experiment, involving a free fall by 4 km in the stratosphere, will test the wep to 1 part in \(5 \times 10^{15}\) at 95% cl, 100 times better than ground-based; 2005, MICROSCOPE (MICRO-Satellite à trainée Compensée pour l'Observation du Principe d'Équivalence) scheduled for 2008, will measure differential acceleration of test masses in a rotating spacecraft to better than 1 part in \(10^{15}\); 2010, MICROSCOPE now scheduled for 2012 launch; 2012, MICROSCOPE now scheduled for 2016 launch, Galileo Galilei (GG) mission planned, with accuracy of 1 part in \(10^{17}\), and STEP is still only a design concept; 2014, STE-QUEST (as opposed to MICROSCOPE and STEP) will use fundamentally quantum-mechanical systems.
@ Status, reviews: Damour CQG(96)gq, gq/97-proc; news pw(05)jan; news NASA(07)may; issue CQG(12)#18; news Sci(15)mar; Schlippert et al a1507-proc [Earth-based tests]; Tino et al PPNP(20)-a2002 [and precision gravity tests].
@ General references: Gabriel & Haugan PRD(90); Klein & Mittelstaedt AJP(97)apr [demo]; CPLEAR collaboration PLB(99) [K0s]; Haugan & Lämmerzahl LNP(01)gq; Luo et al PRD(02)gq/01 [rotation]; Gundlach NJP(05) [lab tests]; Newburgh EJP(08) [simple demonstration]; Hohensee et al PRL(11)-a1102 [matter-wave redshift experiments and clock comparisons]; Hohensee & Müller JMO(11)-a1106 [with matter waves]; Unnikrishnan & Gillies CQG(12); Hohensee & Müller proc(14)-a1307 [differences between spaceborne and quantum mechanical tests, and conventional tests]; Nobili PRD(16)-a1608 [smallness of general relativistic effects on experiments].

Specific Systems and Experiments > s.a. fine-structure constant; neutrino experiments; neutrino oscillations; tests of general relativity with light.
* Cosmology: A field non-minimally coupled to the electromagnetic Lagrangian can induce a violation of the Einstein equivalence principle, which in a cosmological context would break the validity of the cosmic distance duality relation and cause a time variation of the fine structure constant.
@ Spin-gravity coupling: Silenko & Teryaev PRD(07)gq/06; Tarallo et al PRL(14)-a1403 + Phys(14)jul [search for effects on different falling Sr isotopes]; Hojman & Asenjo a1610 [testing the universality of free fall as opposed to spin-gravity coupling].
@ Neutrino oscillations: Halprin et al PRD(96); Fogli et al PRD(99)hp; Datta PLB(01).
@ STEP mission: Sumner GRG(04); Overduin et al ASR(09)-a0902; Overduin et al CQG(12)-a1401; Pereira et al PRL(16)-a1607 [as a test of MOND].
@ MICROSCOPE experiment: Touboul et al CQG(12); Bergé et al JPCS(15)-a1501 [status]; Pihan-Le Bars et al a1705; Hardy et al SSR(17)-a1707 [signal processing]; Touboul et al PRL(17) + news sn(17)dec, Touboul et al CQG(19)-a1909 [first results]; > s.a. MICROSCOPE site.
@ Other Earth satellites: CQG(01)#13 issue; Moffat & Gillies NJP(02)gq [wep]; Nobili et al PLA(03), CQG(12) [GG proposal]; Iorio GRG(04)gq/03 [wep]; Nobili et al GRG(08) [LAGEOS and LAGEOS II, limitations]; Ni PRL(11)-a1105 [Gravity Probe B and wep II]; Aguilera et al CQG(14)-a1312, Altschul et al ASR(15)-a1404 [STE-QUEST proposed satellite mission, using cold-atom interferometry]; Williams et al NJP(16)-a1510 [QTEST, on the ISS]; Nobili & Anselmi PLA(18)-a1709 [expected improvements]; Nobili & Anselmi PRD(18)-a1803 [after MICROSCOPE]; Ciufolini et al a1907.
@ Solar system: Anderson et al ap/95-conf, ApJ(96)ap/95 [Earth-Mars ranging]; Overduin PRD(00)gq [and higher-dimensional gravity]; Shiomi PRD(06)-a0811 [geophysical]; Rubincam PRD(11) [Mars seasonal polar caps]; Williams et al CQG(12), Murphy et al CQG(12) [lunar laser ranging]; Overduin et al CQG(14)-a1307; De Marchi & Congedo IJMPD(17)-a1702 [experiment to measure η on the future mission BepiColombo]; > s.a. gravitational redshift.
@ Of the strong equivalence principle: Congedo & De Marchi PRD(16)-a1602 [spacecraft near Lagrangian points]; news sn(18)jan [triple star system].
@ Binary pulsars: Wex A&A-gq/95 [proposal]; Arzoumanian ap/02-proc.
@ Extragalactic transient sources: Wei et al PRL(15)-a1512, Tingay & Kaplan ApJL(16)-a1602 [fast radio bursts]; Nusser ApJL(16)-a1601 [tighter constraints]; Wang et al PRL(16)-a1602 [PeV neutrinos from blazar flares]; Sang et al MNRAS(16)-a1605 [short GRBs and the PPN parameter γ]; Yang et al MNRAS(17)-a1706 [polarized GRBs]; Yu et al ApJ(18)-a1708 [robust method using time delays]; Tangmatitham & Nemiroff a1903 [cosmological GRBs]; Wei & Wu PRD(19)-a1905 [GRB polarization].
@ Gravitational waves: Yao et al a1909 [binary neutron star merger GW170817]; Yang et al a1912 [LIGO-Virgo catalog GWTC-1]; Unnikrishnan & Gillies a2007.
@ Other astrophysics: Guzzo et al APP(02) [supernova neutrinos]; Freire et al CQG(12)-a1205 [for strongly self-gravitating bodies]; Asvathaman et al MNRAS(16)-a1506 + news pt(17)jan [supermassive black holes]; Wei et al ApJL(16)-a1601 [using TeV blazars]; Yang & Zhang PRD(16)-a1608, Zhang & Gong ApJ(17)-a1612 [Crab pulsar and γ]; Wu et al PRD(17)-a1703 [polarized light from astrophysical events]; Wei et al JCAP(17)-a1710 [multimessenger, GW170817 and its electromagnetic counterparts]; Xie PRD(18)-a1807 [astrometry of quasars]; Amorim et al, GRAVITY Collaboration PRL(19)-a1902 [near Sgr A*]; Li et al PRR(20)-a1912 [black-hole shadows]; Li et al a2102 [photon ring].
@ Dark sector: Kesden & Kamionkowski PRD(06)ap [galaxy tidal tails]; Mohapi et al JCAP(16)-a1510, Bahrami JCAP(19)-a1810 [constraints].
@ CMB: Boucher et al PRD(04)ap [constraints]; Arai et al PRD(16)-a1605 [spectral distortions]; > s.a. cmb.
@ Other cosmology: Amendola & Quercellini PRL(04)ap [large-scale structure]; Bertolami et al GRG(09) [Abell cluster A586]; Hees et al PRD(14)-a1406 [electromagnetic sector]; Creminelli et al JCAP(14)-a1312 [consistency relations for Large Scale Structure]; di Serego Alighieri IJMPD(15)-a1501 [cosmic polarization rotation]; Martins et al JCAP(15)-a1508 [and the stability of the fine-structure constant]; Luo et al JHEA-a1604 [with supercluster Laniakea]; Holanda & Barros PRD(16)-a1606; Holanda et al CQG(17)-a1705; Bonvin & Fleury JCAP(18)-a1803; Bonvin et al a2004 [proposed null test based on galaxy surveys]; Giani & Frion a2005 [lensing time delays].
@ Torsion-balance tests: Schlamminger et al PRL(08) [rotating]; Wagner et al CQG(12)-a1207; Cowsik et al a1808 [long-period].
@ Atom interferometry: Fray et al PRL(04); Dimopoulos et al PRL(07)gq/06; Giulini a1105-conf [rev]; Wolf et al a1109-proc; Herrmann et al CQG(12) [rev]; Schlippert et al PRL(14)-a1406 + news db(14)jun [using Rb and K atoms (different elements), no effect up to 10−7]; Zhou et al PRL(15)-a1503; Hartwig et al NJP(15)-a1503; Roura PRL(17)-a1509 [circumventing Heisenberg's uncertainty principle]; Lefèvre et al a1705-proc; Asenbaum et al a2005 [\(10^{-12}\) level].
@ Other atomic systems: Peters et al Nat(99)aug [cooled Cs atoms]; Duan et al PRL(16) [Rb atoms of opposite spin orientation fall at the same rate]; Rosi et al nComm(17)-a1704 + news sn(17)apr [atoms in superpositions of internal energy eigenstates]; Zhou et al a1904 [Rb atoms].
@ Anti-hydrogen: Holzscheiter et al PRP(04); Perez & Sacquin CQG(12) [GBAR experiment]; Doser et al CQG(12) [AEGIS experiment, pulsed cold beam of antihydrogen]; news pw(13)apr [ALPHA experiment at CERN]; Scampoli & Storey MPLA(14) [AEGIS experiment at CERN].
@ Other proposals: Álvarez & Mann PRD(97)gq/96 [lepton and meson sectors]; Wesson IJMPD(05)gq/06 [and higher-dimensional gravity]; Kirch phy/07 [muonium]; Reasenberg & Phillips CQG(10) + news po(10)may, Reasenberg et al CQG(12) [wep, suborbital rocket]; Saha PRD(14)-a1306 [COW test of the weak equivalence principle and spacetime non-commutativity]; Bonder et al PRD(13)-a1305 [with unstable particles]; Hohensee et al PRL(13)-a1303 [radio-frequency spectroscopy]; Kalaydzhyan a1608-conf [relativistic matter in accelerators]; Terno et al a1811 [optical interferometric test proposal].
> Related topics: see Nordtvedt Effect; radiation [accelerated charge]; self-force [radiation reaction].

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