Tests of General Relativity – Redshift and Signal Retardation  

Gravitational Redshift > 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 = [g00(x2)/g00(x1)]1/2 – 1; Without a preferred time foliation it is more arbitrary, but the condition g00 = 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.
* Plan: Put a stable clock around the Sun, to give σ(β) = 10–6, σ(γ) = 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].
@ Specific situations: Briatore & Leschiutta NCB(77) [on Earth]; Desloge AJP(90)sep [in a uniform field]; DeDeo & Psaltis PRL(03)ap [atomic lines from neutron stars]; Kopeikin et al PLA(07)gq/06 [Cassini and radio waves near the Sun]; Müller AN(07)ap/06 [from disk around black hole]; Wojtak et al Nat(11)sep-a1109 [galaxies in custers].
@ In other theories: Florides a1310 [vs general relativity]; Arms & Serna a1610 [special-relativity analog].
@ 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.
@ Other tests: Manly & Page PRD(01) [light dispersion in the lab]; Delva et al CQG-a1508 [with stable clocks in eccentric orbits]; Wolf & Blanchet a1509 [in the field of the Sun and the Moon].
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: Consistent with γ = 1, with σ(γ) = 0.002, from Viking landers; 2003, 1.5 order of magnitude improvement with Cassini.
@ 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]; Bertotti et al Nat(03)sep + pw(03)sep [Cassini]; 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].
@ 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.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 oct 2016