Relativistic Analysis of Sagnac Effect in the Reference Frame of the Accelerating Observer

We present a simple, clean relativistic derivation of the Sagnac effect from the perspective of the rotating observer/detector. The well-known Sagnac formula just emerged right on the first run of the calculation, without any tweaking of arguments to get the desired result. The key, novel idea introduced in this paper is that two observers moving with the same velocity at the same point of space simultaneously at a given instant of time will observe the same, identical phenomenon ( for example, interference fringe position) at that point, regardless of their motion history before that instant of time. Therefore, we introduce an imaginary inertial observer who is moving with the same instantaneous velocity at the point of light detection as the accelerating observer. The two observers (the real accelerating observer and the imaginary inertial observer) will observe identical phenomena at that point of space and time. Thus, acceleration of the detector/observer is irrelevant and the known non-relativistic Sagnac effect can be fully understood within the framework of special relativity theory.