The Rotating Frame Fights Back: Sagnac Phase Corrections for Transit on Earth

Rotation writes itself into any phase measured around a loop, and transit paths on a rotating planet are loops whether their designers draw them that way or not. This paper computes the Sagnac-type timing and phase offsets for transit paths on Earth. A path enclosing one square metre accrues 1.623e-21 s; a city-scale path enclosing one square kilometre accrues 1.623e-15 s, which at a 1 MHz drive frequency is a phase offset of 0.0000 rad, comparable to the 0.0667 rad phase budget; a continental path enclosing 1e12 m^2 accrues 1.623e-09 s and 0.0 rad, many full turns of phase. Eastward and westward transits of the same route differ by twice these offsets. Rotation is therefore a negligible correction in the laboratory, a budget-level correction at city scale, and the dominant phase term at continental scale. Computed; not measured. SIMULATED, NOT MEASURED.