Can corner-cube absolute gravimeters sense the effects of Special Relativity?

Abstract

Relativistic treatment of the finite speed of light correction in absolute gravimeters, as evolved by Rothleitner and Francis in Metrologia 2011, 48 442-445, following the initial publication in Metrologia 2011, 48 187-195, leads to spurious conclusions. The double Doppler shift implemented in the gravimeters obliterates the difference between its relativistic and non-relativistic formulation. Optical heterodyning used in Michelson-type interferometers makes the quadratic Lorenz-like term of the double Doppler shift discernable against the linear term, while in relativistic experiments the quadratic term has to be detected against the unit. The disturbance of the registered trajectory caused by the finite speed of light includes tracking signal delay as intrinsic part not reducible to the Doppler shifts.

Experimental assessment of the speed of light perturbation in free-fall absolute gravimeters

“…As mentioned above, one also realizes that by timing and counting the occurrence of the interference fringes, the position of the moving prism at the time when the reflection happens, as seen by the detector, can be determined as a function of time. We also want to remind that the previous formula is just based on the constant speed of light c and is not testing any other aspect of special relativity [14].…”

“…This is the idea behind the present work. We present here the analysis of new sets of data from different gravimeters and find experimental 1 As described in [14], these perturbations do not test the foundations of special relativity, and are just related to the finite speed of propagation of light. agreement with the classical result given in [12,[3][4][5][6][7][8][9][10][11].…”

Enabling a linear model for the IMGC-02 absolute gravimeter

“…When calculati ng g using the formulas (22,23) or (10,11) the time shift can be ignored, because the estimates for the quadratic coefficient of the simple parabola (1) are not sensitive to the time shift, so that…”

“…+ In the IMGC-02 instrument the speed-of-light disturbance is also contra-directed to the velocity, due to the upper position of the interferometer * Some researchers believe that the coefficient in the formula (51) has to be 2 rather than 3. Interested readers can follow the discussion of the subject in publications [19], [20], [21], [22]…”

“…7.) We compared the results obtained by processing the data by both linear and non-linear models with no harmonics included to the results obtained by including one harmonic with known frequency and varying the frequency in the range of (16)(17)(18)(19)(20)(21)(22)(23)(24) Hz with 1 Hz increment in every processing run.…”