Abstract

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

Lorentz-Type Transformations as Derived from Performable Rod and Clock Operations

Herbert E. Ives
J. Opt. Soc. Am. 39(9) 757-761 (1949)

Theory of the Double Fizeau Toothed Wheel

Herbert E. Ives
J. Opt. Soc. Am. 29(11) 472-478 (1939)

The Measurement of the Velocity of Light by Signals Sent in One Direction

Herbert E. Ives
J. Opt. Soc. Am. 38(10) 879-884 (1948)

Behavior of an Interferometer in a Gravitational Field*

Herbert E. Ives
J. Opt. Soc. Am. 29(5) 183-187 (1939)

On The Relativistic Doppler Effect

R. Clark Jones
J. Opt. Soc. Am. 29(8) 337-339 (1939)