Gravitational Redshift and Tests of Local Position InvarianceGravitational Redshift and Tests of Local Position InvarianceDavid NorrisApril 26, 2007David NorrisApril 26, 2007Einstein Equivalence PrincipleEinstein Equivalence Principle(1) Trajectories of freely-falling test bodies independent of structure or composition (WEP)(2) Outcome of non-gravitational experiment in local, freely-falling frame independent of frame velocity (LLI)(3) Outcome of non-gravitational experiment in local, freely-falling frame independent of time or place performed (LPI)(1) Trajectories of freely-falling test bodies independent of structure or composition (WEP)(2) Outcome of non-gravitational experiment in local, freely-falling frame independent of frame velocity (LLI)(3) Outcome of non-gravitational experiment in local, freely-falling frame independent of time or place performed (LPI)Gravitational redshiftGravitational redshiftZ =∆νν= −∆λλ=∆Uc2Z =∆νν= −∆λλ=∆Uc2Change in wavelength of light due to difference in gravitational potential energy: Light loses energy when climbing uphill!Einstein (1916): “An atom absorbs or emits light of a frequency which is dependent on the potential of the gravitational field in which it is situated.”How big is the effect?How big is the effect? GPS satellites move at 14,000 km/hr, 20,000 km above the earth  Time dilation effect: 7 µs slow per day Gravitational redshift effect: 45 µs fast per day Net shift: 38 µs fast per day compared to clocks on the ground (error of 10 km per day) GPS satellites move at 14,000 km/hr, 20,000 km above the earth  Time dilation effect: 7 µs slow per day Gravitational redshift effect: 45 µs fast per day Net shift: 38 µs fast per day compared to clocks on the ground (error of 10 km per day)Source: http://www.physicscentral.com/writers/2000/will.htmlWhy is this a test of LPI?Why is this a test of LPI?ν1ν2Identical clocks should have ν1=ν2when measured in their respective local Lorentz frames, independent of location (and gravitational potential.)A comparison of frequencies in one of these frames is a comparison of relative velocities of Lorentz frames, via Doppler shift of light (observed as gravitational redshift), independent of structure of clocks.A deviation from the predicted frequency shift would indicate a dependence of some fundamental constant on position thus a violation of LPI and the EEP.Source: Clifford Will http://relativity.livingreviews.org/Articles/lrr-2006-3/index.htmlThe Pound-Rebka experimentThe Pound-Rebka experimentResultsResults Pound-Rebka measured a net fractional shift of -(5.13±0.51)x10-15over 148 ft. Agrees with GR predicted value of -4.92x10-15to within 10% uncertainty Revised Pound-Snider experiment in 1964 achieved 1% uncertainty Pound-Rebka measured a net fractional shift of -(5.13±0.51)x10-15over 148 ft. Agrees with GR predicted value of -4.92x10-15to within 10% uncertainty Revised Pound-Snider experiment in 1964 achieved 1% uncertaintySpace-Borne hydrogen maser (Gravity Probe-A, 1976)Space-Borne hydrogen maser (Gravity Probe-A, 1976)∆ff0=φs−φec2−r v e−r v s22c2−r r se⋅r a ec2GP-A resultsGP-A results Measured frequency shift consistent with GR (combined effect of gravity and special relativity) to uncertainty of 7x10-5 To date the most precise traditional test of LPI Measured frequency shift consistent with GR (combined effect of gravity and special relativity) to uncertainty of 7x10-5 To date the most precise traditional test of LPINull experimentsNull experiments Since GP-A, improvements in LPI violation have come from null-redshift experiments in which clocks of different composition are compared in a time-modulated gravitational field. 1978 Turneaure & al. (Stanford) used two 1.42 GHz hydrogen masers and three SCSO’s at 8 GHz over 11 days while solar gravity varied (linearly by 3x10-12per day from orbit, sinusoidally by 3x10-13from rotation)Measured no deviation between the clocks, |α|<1.7x10-2 Since GP-A, improvements in LPI violation have come from null-redshift experiments in which clocks of different composition are compared in a time-modulated gravitational field. 1978 Turneaure & al. (Stanford) used two 1.42 GHz hydrogen masers and three SCSO’s at 8 GHz over 11 days while solar gravity varied (linearly by 3x10-12per day from orbit, sinusoidally by 3x10-13from rotation)Measured no deviation between the clocks, |α|<1.7x10-2Null experiments, cont.Null experiments, cont. 1994 (Godone & al.) comparison of cesium and magnesium atomic clocks over 430 days, |α|<7x10-4 2002 (Bauch & al.) comparison of cesium clock with hydrogen maser over one year, |α|<2.1x10-5 2006 (Ashby & al.) comparison of four NIST hydrogen masers with cesium fountain clock standards from NIST, Germany, France, and Italy over 7 years… 1994 (Godone & al.) comparison of cesium and magnesium atomic clocks over 430 days, |α|<7x10-4 2002 (Bauch & al.) comparison of cesium clock with hydrogen maser over one year, |α|<2.1x10-5 2006 (Ashby & al.) comparison of four NIST hydrogen masers with cesium fountain clock standards from NIST, Germany, France, and Italy over 7 years…The current best limitThe current best limit|α|<1.4x10-6|α|<1.4x10-6Additional tests of LPIAdditional tests of LPI Gravitational redshift measured with solar spectra, pulsars, and oscillator clocks on spacecraft Time invariance of fundamental constants (current and past) Gravitational redshift measured with solar spectra, pulsars, and oscillator clocks on spacecraft Time invariance of fundamental constants (current and