Tests of General Relativity – Redshift and Signal Retardation  

Gravitational Redshift / Time Dilation > s.a. doppler effect [redshift]; Gravity Probe A.
* Idea: A photon's energy/frequency decreases as it climbs out of a gravitational potential well.
* Calculation: One can calculate it as the amount of proper time elapsed at a point x2 per unit proper time at x1, which is closely related to mass in 4D; In a static spacetime, where we know how to relate t at different points, it is \(z = [g^{~}_{00}(x^{~}_2)/g^{~}_{00}(x^{~}_1)]^{1/2} - 1\); Without a preferred time foliation it is more arbitrary, but the condition \(g^{~}_{00} = 0\) still defines the infinite-redshift set.
* History and tests: 1907, Predicted by Einstein using just the equivalence principle; 1959, Demonstrated experimentally by R Pound and G Rebka in a tower at Harvard University using the Mössbauer effect, to within 1% (> Wikipedia page); 1967, Test carried out with the atomic clock aboard Gravity Probe A during a 2-hour mission; The effect has to be taken into account by the GPS; 2010, Controversy over whether atom interferometry can be used to detect gravitational redshift [@ news iop(11)jun]; 2015, (Atom interferometry controversy not settled) Two Galileo satellites accidentally launched into wrong, elliptical orbits will be used to measure gravitational redshift with higher precision (below 0.004%); ESA's Atomic Clock Ensemble in Space (ACES) is scheduled to fly in 2017 on the ISS; 2018, Results from Galileo satellites improve on previous bounds.
* Plan: Put a stable clock around the Sun, to give \(\sigma(\beta) = 10^{-6}\), \(\sigma(\gamma) = 10^{-7}\).
@ General references: Pound & Rebka PRL(60); Vessot & Levine GRG(79); Vessot et al PRL(80); Okun et al AJP(00)feb [pedagogical]; Okun MPLA(00), MPLA(00)hp [thought experiment]; Malec CQG(02)gq/01 [exact treatment in Schwarzschild spacetime]; Teyssandier et al ASS(07)-a0711-in [using Synge's world function]; Hohensee et al JPCS(11)-a1009; Li CQG(14) [interpretation as Doppler shift]; Brown & Read AJP(16)feb-a1512 [misconceptions]; Li et al a1802 [underlying mechanism]; news sn(18)jul [observation, star near galacic center]; Herrmann et al PRL(18)-a1812 + news sn(18)dec [observation by Galileo satellites]; Okolow EJP(20)-a1906 [pedagogical introduction and examples]; news pt(20)may [best transportable clocks].
@ In the Solar System: Briatore & Leschiutta NCB(77) [on Earth]; Kopeikin et al PLA(07)gq/06 [Cassini and radio waves near the Sun]; Wolf & Blanchet CQG(16)-a1509 [in the field of the Sun and the Moon]; Uggerhøj et al EJP(16)-a1604 [the center of the Earth is younger than the surface]; Litvinov et al PLA(18)-a1710 [with an Earth-orbiting satellite]; Nunes et al ASR(19)-a1904 [up to 350,000 km from Earth]; González Hernández et al a2009 [around the Sun].
@ Other situations: Desloge AJP(90)sep [in a uniform field]; Manly & Page PRD(01) [light dispersion in the lab]; DeDeo & Psaltis PRL(03)ap [atomic lines from neutron stars]; Müller AN(07)ap/06 [from disk around black hole]; Wojtak et al Nat(11)sep-a1109 [galaxies in custers]; Delva et al CQG(15)-a1508 [with stable clocks in eccentric orbits]; Burns et al AJP(17)oct [undergraduate research project]; Dai et al ApJ-a1812 [main-sequence stars and red giants]; Nucamendi et al a2012 [NGC 4258 nucleus].
@ In other theories: Florides a1310 [vs general relativity]; Arms & Serna a1610-conf [special-relativity analog]; Buoninfante et al EPJC(20)-a1907.
@ And matter interferometry: Müller et al Nat(10)feb + a1008-conf, criticism Wolf et al Nat(10)sep-a1009 + CQG(11)-a1012 + a1106-proc [test]; Chou et al Sci(10)sep + news pw(10)sep [meter-scale observations]; Hohensee et al JPCS(11)-a1009 [tests]; Sinha & Samuel CQG(11)-a1102; Hohensee et al PRL(11)-a1102; Unnikrishnan & Gillies a1106; Hohensee et al CQG(11)-a1112; Wolf et al CQG(12)-a1201; Ufrecht et al a2001 [and universality of free fall]; Roura PRX(20) [quantum clock interferometry]; Di Pumpo et al a2104.
blue bullet Related topics: see gravitational phenomenology; light bending.

Signal Retardation (Shapiro time delay) > s.a. gamma-ray astronomy; neutron stars; photon phenomenology [light travel time].
* Idea: The light travel time between planets is longer than the corresponding flat spacetime value.
* Remark: It is always a delay, not an advance, as follows from the energy conditions [@ Visser et al NPPS(00)gq/98].
* Results: Measurements of the time delay lead to estimates of the PPN parameter γ, and so far (2020) are consistent with γ = 1; Planetary echoes (with Mercury) had an uncertainty of 0.02 in γ, the Viking landers relativity experiment 0.002, Jupiter and quasar signals \(2\times10^{-4}\); 2003, 1.5 order of magnitude improvement with Cassini, to \(2\times10^{-5}\); A gravitational wave detector approach has been proposed, but it will be less precise.
@ General references: Shapiro PRL(64); Reasenberg et al ApJL(79); Richter & Matzner PRD(83); in Wald 84, 146-148; Bruckman & Esteban AJP(93)aug; Teyssandier et al ASS(07)-a0711-in [using Synge's world function]; Ashby & Bertotti CQG(10)-a0912 [accurate higher-order terms].
@ In binary systems: Laguna & Wolszczan ApJ(97)ap [pulsar-black hole]; van Straten et al Nat(01)jul [pulsar-black hole]; Tartaglia et al PRD(05)gq.
@ Related topics: Kopeikin ApJL(01)gq [quasars, extra term from speed of gravity]; Iorio NCB(03)gq/02 [in Kerr spacetime]; Ciufolini et al PLA(03)gq/02 [rotating masses]; Ruggiero & Tartaglia PRD(05)gq [binary pulsars, gravitomagnetic corrections]; Bertotti et al CQG(08)-a0709, comment Kopeikin PLA(09)-a0901 [effect of Sun's motion]; Kutschera & Zajiczek APPB-a0906 [for relativistic particles]; Ballmer et al CQG(10)-a0905 [on Advanced LIGO laboratory distance scales]; Boudjemaa et al GRG(11)-a1006 [in the Einstein-Straus solution]; Ashby & Bender a1106-conf [proposed space mission]; Jia & Liu PRD(19)-a1906 [in gravitational lensing of Schwarzschild spacetime].
@ Measurements: Bertotti et al Nat(03)sep + pw(03)sep [Cassini]; Sullivan et al a2005 [using next-generation gravitational wave detectors].
@ In other theories: Asada PLB(08)-a0710; Schucker & Zaimen A&A(08)-a0801 [effect of cosmological constant]; Bailey PRD(09)-a0906 [Lorentz-violating SME]; Magueijo & Mozaffari CQG(13)-a1212 [infrared modifications and time delays across saddles]; > s.a. brans-dicke theory; Non-Symmetric Gravity.

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