The Maraner effect as a particular case of the quadratic Sagnac effect

Abstract

The quadratic Sagnac effect consists in a Michelson interferometer (MI) being located on a rotating base with a phase difference in its arms arising, the value of which depends on the orientation of the MI arms relative to the rotating base and on the angle of its rotation. This phase difference is caused by different values of the Newtonian (nonrelativistic) scalar gravitational potential of Coriolis forces acting on different MI arms, which leads to time dilation and varies with change in the angle of MI rotation. Distributions of the scalar gravitational potential of Coriolis forces over different parts of MI arms are considered. Allowance for this distribution makes it possible to calculate a value of the certain effect that is a higher approximation of the quadratic Sagnac effect. This effect is shown to be the Maraner effect known earlier, which also leads to a change in the phase difference of MI arms, but differs in value from the quadratic Sagnac effect. Consequently, the Maraner effect is a particular case of the quadratic Sagnac effect. Numerical estimations are performed.