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Originally Posted by Celestial Mechanic
The Sagnac effect requires that two beams of light travel the complete circuit so that their phases may be compared. Since your circle has radius one billion light-years, that means that at least 6.28 billion years must pass before the "Sagnac observer" can detect anything.
Also, nothing in your gedankenexperiment says anything about light being constrained to travel in a circle. Back to the drawing board!  |
Time is not important here, if it takes 6.28 billion years, so be it. Also light doesn’t have to travel in a circle, it can be reflected of 4 mirrors - forming a square pattern. And the sagnac observer’s circle touches it tangentially at four points.