Precision test for the new Michelson-Morley experiments with rotating cryogenic cavities

A new ether-drift experiment in Düsseldorf is currently measuring the relative frequency shift of two cryogenic optical resonators upon active rotations of the apparatus. I point out that the observed fractional amplitude of the sidereal variations of the signal in February, Csid ∼ (11 ± 2) · 10, is entirely consistent with the expectations based on Miller’s observations in the same epoch of the year. This leads to predict that, with future data collected in August-September, the observed sidereal variations should increase by ∼ +70%, i.e. up to Csid ∼ (19 ± 2) · 10 −16 retaining the present normalization. This would represent clean experimental evidence for the existence of a preferred frame. PACS: 03.30.+p, 01.55.+b 1. Modern ether-drift experiments look for a preferred frame by measuring the relative frequency shift δν between two cavity-stabilized lasers upon local rotations [1] or under the Earth’s rotation [2]. Today, by combining the possibility of active rotations of the apparatus with the use of cryogenic optical resonators, a new experiment [3] is currently trying to push the relative accuracy of the measurements to the level O(10). It is generally believed that such an extremely high precision, that strongly constrains the anisotropy of the speed of light, can also rule out the idea of a preferred frame. However, as discussed in Refs.[4, 5] (see also [6]), vanishingly small values of δν, by themselves, cannot rule out the old Lorentzian formulation of Relativity. In fact, if light propagates isotropically in a preferred frame Σ, the relative frequency shift observed on the Earth is given by δν ν ∼ (Nmedium − 1) v earth c2 (1) where Nmedium ∼ 1 is the refractive index of the medium where light propagation takes place and vearth denotes the Earth’s velocity with respect to Σ (value projected in the plane of the interferometer). This frequency shift vanishes identically when the speed of light coincides with the same parameter ”c” entering Lorentz transformations, i.e. in an ideal vacuum where Nvacuum = 1. Starting from this observation, one can re-read [4, 5] the classical and modern etherdrift experiments in a consistent framework where there is a preferred frame relatively to which the Earth is moving with a velocity ∼ 200 km/s (value projected in the plane of the interferometer). This velocity is consistent with the values deduced by Miller (see Table V of Ref.[7]) on the base of the sidereal variations of the ether-drift effect in different periods of the year. The aim of this Letter is to show that the sidereal variations observed in February by the authors of Ref.[3] are completely consistent with Miller’s observations in the same epoch of the year. This also suggests a precise prediction to be tested with future data collected in the period of August-September. A confirmation of this prediction would represent clean experimental evidence for the existence of a preferred frame. 2. The basic ingredient for our analysis is the relation [4] for the frequency shift of two orthogonal optical resonators to O( v 2 earth c ) δν(θ) ν = ū(π/2 + θ)− ū(θ) u ∼ |Bmedium| v earth c2 cos(2θ) (2)