Quadratic Sagnac Effect Recorded by an Observer in the Laboratory Frame
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ICAL OPTICS
Quadratic Sagnac Effect Recorded by an Observer in the Laboratory Frame G. B. Malykina, * and V. I. Pozdnyakovab a Federal b The
Research Center Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, 603155 Russia Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia * e-mail: [email protected] Received February 20, 2020; revised May 28, 2020; accepted June 16, 2020
Abstract—The quadratic Sagnac effect, recorded by an observer in the laboratory frame of reference (inertial frame), relative to which the Michelson interferometer moves, has been considered. The quadratic Sagnac effect was previously calculated in a rotating frame of reference, where it occurs as a consequence of the influence of the gravitational potential of the Coriolis force in the rotating frame of reference and leads to a phase difference in the rotating Michelson interferometer. It has been shown that the quadratic Sagnac effect values calculated in the inertial frame and rotating frame of reference are practically the same. It has also been shown that, in various cases, the calculation of the quadratic Sagnac effect is most rational to carry out either in the inertial frame or in the rotating frame of reference. The numerical estimates performed have shown that the experiments on recording the quadratic Sagnac effect are quite possible. The concept of effective lengths of the arms of a Michelson interferometer moving relative to a stationary observer: the light paths lengths during its propagation in the forward and backward directions, has been introduced. These effective arm lengths coincide with neither Michelson interferometer proper arm length L nor its relativistic length L /γ . The introduction of this concept is due to the fact that the moving Michelson interferometer mirrors move during the light propagation. In some calculations, it is advisable to take into account the Michelson interferometer effective arm lengths. Keywords: quadratic Sagnac effect, Michelson interferometer, Michelson–Morley experiment DOI: 10.1134/S0030400X20100197
1. INTRODUCTION In our work [1], we considered the quadratic Sagnac effect, which occurs because of the influence of the gravitational potential of the Coriolis force, recorded by an observer who is in the reference system moving with the rotation of the Michelson interferometer or, in other words, in the rotating frame of reference. The quadratic Sagnac effect results in a phase difference in the arms of the rotating Michelson interferometer. As shown in [1], in the case when the platform in the plane of which the Michelson interferometer is located is oriented orthogonally to the plane of rotation and one of the Michelson interferometer arms is rotated by a ψ angle relative to some straight line lying in the plane of rotation, the optical phase difference in the Michelson interferometer arms is (1) ΔΦ(ψ) = − L Ω R cos 2ψ. λ c2 Therefore, the value of the quadratic Sagnac effect is proportional to the length L o
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