The effect of the fitzgerald-lorentz contraction on the frequency of longitudinal vibration of a rod

Abstract

The failure of the Michelson-Morley experiment to detect ether-drift led Fitzgerald in 1892 to suggest that the framework which supported the interferometer mirrors was distorted by its motion through the ether in such a way that the expected ether-drift effect was exactly neutralized. Later experiments by Morley and Miller, in 1903, using different materials for the framework led substantially to the same result. Fitzgerald’s hypothesis received the support of Lorentz in 1895, and as recently as 1921 the latter remarks “ There can be no question about the reality of this change of length Lorentz considered that the change of length produced by motion was just as real as that produced by change of temperature. * According to the Fitzgerald-Lorentz theory, a moving body contracts in the direction of motion in the ratio 1 to(1- v 2 / c 2 ) 1/2 , where v is the velocity of translation of the body and c is the velocity of light. The velocity of the earth’s orbital motion is approximately 30 km./sec., and the velocity of light is 300,000 km./sec. A body carried by the earth is therefore subject to a contraction of 5 parts in 109 of its length as it is oriented from a direction at right angles to a direction along the line of the earth’s orbital motion.