Test of the Isotropy of the Speed of Light Using a Continuously Rotating Optical Resonator

Abstract

We report on a test of Lorentz invariance performed by comparing the resonance frequencies of one stationary optical resonator and one continuously rotating on a precision air bearing turntable. Special attention is paid to the control of rotation induced systematic effects. Within the photon sector of the Standard Model Extension, we obtain improved limits on combinations of 8 parameters at a level of a few parts in 10 −16 . For the previously least well known parameter we findκ ZZ e− = (−1.9 ± 5.2) × 10 −15 . Within the Robertson-Mansouri-Sexl test theory, our measurement restricts the isotropy violation parameter β − δ − 1 2 to (−2.1 ± 1.9) × 10 −10 , corresponding to an eightfold improvement with respect to previous non-rotating measurements. Local Lorentz invariance (LLI) is an essential ingredient of both the standard model of particle physics and the theory of general relativity. It states that locally physical laws are identical in all inertial reference frames i.e. independent of velocity and orientation. However, several attempts to formulate a unifying theory of quantum gravity discuss tiny violations of LLI. Modern high precision test experiments for LLI are considered as important contributions to these attempts, as they might either rule out or possibly reveal the presence of such effects at some level of measurement precision. An experiment of particular sensitivity to LLI-violation is the Michelson-Morley (MM) experiment [1] testing the isotropy of the speed of light. Modern versions employ high finesse electromagnetic resonators, whose eigenfrequencies depend on the speed of light c in a geometry dependent way (ν ∼ c/L for a linear optical Fabry-Perot cavity of length L). Thus a measurement of the eigenfrequency of a resonator as its orientation is varied, should reveal an anisotropy of c/L. Recently, such an anisotropy of c has been described as a consequence of broken Lorentz symmetry within a test model called Standard Model Extension (SME) [2]. This model adds all LLI violating terms that can be formed from the known fields and Lorentz tensors to the Lagrangian of each sector of the standard model of particle physics. It thus allows a consistent and comparative analysis of various experimental tests, including the MM experiment. The latter however, is also often interpreted according to a kinematical test theory, formulated by Robertson [3] and Mansouri and Sexl [4] (RMS). This test theory assumes a preferred frame, commonly adopted to be the cosmic microwave background (CMB). Combinations of three test parameters (α, β, δ) then model an anisotropy as well as a boost dependence of c within a frame moving at velocity v relative to the CMB. In view of the substantial impact that LLI-violation would have all over physics, the new approach of the SME has triggered a new generation of improved MMtype experiments [5,6,7,8]. So far all of these recent measurements relied solely on Earth's rotation for varying resonator orientation, which was made possible by the low drift properties of cryogenical...

Tests of Relativity by Complementary Rotating Michelson-Morley Experiments

“…Data has been collected for 396 d, totalling to 62 d of useful data in 27 sets (118,000 turntable rotations), beyond the data already reported in [14]. To analyze the data, we first break it down into i = 1....N subsets of 10 table rotations each.…”

“…L and n are properties of macroscopic matter and thus sensitive to Lorentz violation in the Maxwell and Dirac equations that govern its constituents. However, each of the simple MM-experiments performed so far (recently, [9,10,11,12,13,14,15,16,17]) does not by itself provide enough information to distinguish between the different influences and thus can only bound combinations of them. To remove these restrictions, experiments featuring dissimilar cavities that have a different depen- * Electronic address: holgerm@stanford.edu…”

Bounds on spin-dependent Lorentz violation from inverse Compton observations

“…Bounds on the Lorentz-violating coefficients for electrons come from clock comparison experiments [4,5], experiments with spin-polarized matter [6,7], Michelson-Morley experiments with cryogenic resonators [8,10,9,11], and Doppler effect measurements [12,13]. Finally, some of the best bounds come from high-energy astrophysics [14,15,16,17,18].…”

“…These are the absolute maximum values that each |d νµ | may take when the components are subject to all eleven of the inequalities (10). The second set of bounds were calculated using the same method, but this time the linear program also incorporated priors from the clock comparison data.…”

Lorentz violation andαdecay

“…Sensitive searches for Lorentz violation have included studies of matter-antimatter asymmetries for trapped charged particles [13,14,15] and bound state systems [16,17], determinations of muon properties [18,19], analyses of the behavior of spin-polarized matter [20,21], frequency standard comparisons [22,23,24,25], Michelson-Morley experiments with cryogenic resonators [26,27,28], Doppler effect measurements [29,30], measurements of neutral mesons [31,32,33,34,35,36], polarization measurements on the light from distant galaxies [37,38,39,40], high-energy astrophysical tests [41,42,43,44] and others. The results of these experiments set bounds on various SME coefficients.…”