Equivalence Principle and Gravitational Redshift

Abstract

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter wave, microwave, optical, and Mössbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the 10 −6 level.Gravity makes time flow differently in different places. This effect, known as the gravitational redshift, is the original test of the Einstein equivalence principle (EEP) [1] that underlies all of general relativity; its experimental verification [2-6] is fundamental to our confidence in the theory. Atom interferometer (AI) tests of the gravitational redshift [4,6] have a precision 10 000 times better than tests based on traditional clocks [3], but their status as redshift tests has been controversial [7]. Here, we show that the phase accumulated between two atomic wave packets in any interferometer equals the phase between any two clocks running at the atom's Compton frequency following the same paths, proving that atoms are clocks. For a quantitative comparison between different redshift tests, we use the standard model extension (SME) [8][9][10][11], which provides the most general way to describe potential low energy Lorentz symmetry-violating (thus EEP-violating) signatures of new physics at high energy scales. We show that all EEP tests are sensitive to the same five terms in the minimal gravitational SME [9][10][11] and, for the first time, comprehensively rule out EEP violation in redshift tests greater than a few parts per million for neutral matter.If two clocks are located at different points in spacetime, they can appear to tick at different frequencies, despite having the same proper frequency ω 0 in their local Lorentz frames. For clocks moving with nonrelativistic velocities v 1 and v 2 in a weak gravitational potentialThe first term is the gravitational redshift, originally measured [2] by Pound and Rebka in 1960, while the second term is the time dilation due to the clocks' relative motion. The redshift term can be isolated from the time dilation if the clocks' trajectories are known.The state of each clock can be described by a timevarying phase. If two clocks 1 and 2 are synchronized to have identical phase ϕ 0 = 0 at time t = 0, then theirMach-Zehnder clock or atom interferometer. Two otherwise freely falling clocks (or halves of an atomic wavepacket) receive momentum impulses that change their velocity by ±vr. The dashed lines indicate trajectories without gravity.specializing to a homogenous gravitational field so that φ 1 −φ 2 = g· r 12 , with r 12 being the clocks' distance vector and g the local acceleration of free fall. If the clocks are freely falling, then their motion is an extremum of their respective actions [12]Thus δϕ f is proportional to the difference S 1 − S 2 in the...

High-Resolution Atom Interferometers with Suppressed Diffraction Phases

“…We decrease the influence of diffraction phases by an amount that is considerably larger than the increase in sensitivity and are in fact able to null them by feedback to the laser pulse intensity. With this increase in signal and suppression of diffraction phase systematics, we expect to see improvements in many applications of atom interferometry, such as measuring gravity and inertial effects [10][11][12][13], measuring Newton's gravitational constant G [14,15], testing the equivalence principle [16][17][18][19][20][21][22], CPT and Lorentz symmetry [23] and perhaps even antimatter physics [24] and detecting gravitational waves [25]. Diffraction phases occur between the waves reflected and transmitted by a beam splitter and cause an unwanted (usually) shift of the interference pattern in an interferometer.…”

Clocks in Space for Tests of Fundamental Physics

“…Let us mention that in this framework, atomic clocks have been successfully used (see e.g. Wolf et al, 2006, Reinhardt et al, 2007, Hohensee et al 2011.…”

Observational Constraints on Local Lorentz Invariance

“…•Gravity Tests [156,157,158,159,160,161,162,163]: Lorentz violation in the gravity sector stems from both matter-gravity couplings and pure-gravity couplings. In some cases, the matter-gravity couplings can lead to sensitivity to forms of Lorentz violation that would otherwise go undetected in the absence of gravity.…”