Starting with the Fitzgerald-Larmor-Lorentz contractions of length and frequency the measurements which can be made on a uniformly moving particle from a uniformly moving platform, using clocks and rods moved at observed finite speeds, are determined. A single quantity in the Fitzgerald-Larmor-Lorentz invariant framework is found to be determinable from such measurements. This, the so-called “chronotopic interval” is a length, which is identified with a stationary undistorted dimension of an interferometer, which, experiencing the length and frequency contractions on motion, always gives a “null” result. The complete expression for this quantity in terms of the variant rods and clocks is given by a formula which is not identical with the invariant framework expression, but is a function of all the observed quantities, including the observed velocities of the rods and clocks. Applying the same analysis to observations made in a gravitational field, on certain assumptions, an expression is found for the “chronotopic interval” or interferometer dimension, which is a function of the gravitational constant when expressed in the invariant framework, but is identical with the nongravitational formula when expressed in terms of variant rod and clock measurements.
© 1939 Optical Society of America
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