Propagation of light in non-inertial reference frames

TL;DR

This paper explores how light propagates in non-inertial and gravitational fields, emphasizing the importance of average coordinate and proper velocities, and discusses effects like the Sagnac effect and variations in the Shapiro delay.

Contribution

It introduces the concept of average coordinate and proper velocities of light in non-inertial frames and derives new expressions for light propagation and time delay effects.

Findings

Average coordinate velocity of light is necessary in non-inertial frames.

Shapiro time delay depends on measurement point and gravitational field configuration.

Derived expression explains the Sagnac effect in rotating frames.

Abstract

It is shown that the complete description of the propagation of light in a gravitational field and in non-inertial reference frames in general requires an average coordinate and an average proper velocity of light. The need for an average coordinate velocity of light in non-inertial frames is demonstrated by considering the propagation of two vertical light rays in the Einstein elevator (in addition to the horizontal ray originally discussed by Einstein). As an average proper velocity of light is implicitly used in the Shapiro time delay (as shown in the Appendix) it is explicitly derived and it is shown that for a round trip of a light signal between two points in a gravitational field the Shapiro time delay not only depends on which point it is measured at, but in the case of a parallel gravitational field it is not always a delay effect. The propagation of light in rotating frames (the Sagnac effect) is also discussed and an expression for the coordinate velocity of light is derived. The use of this coordinate velocity naturally explains why an observer on a rotating disk finds that two light signals emitted from a point on the rim of the disk and propagating in opposite directions along the rim do not arrive simultaneously at the same point.