Tests of General Relativity – Redshift and Signal Retardation| 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.
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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