Michelson–Gale–Pearson experiment

The Michelson–Gale–Pearson experiment (1925) is a modified version of the Michelson–Morley experiment and the Sagnac-Interferometer. It measured the Sagnac effect due to Earth's rotation, and thus tests the theories of special relativity and luminiferous ether along the rotating frame of Earth.

Experiment

The aim, as it was first proposed by Albert A. Michelson in 1904 and then executed in 1925 by Michelson and Henry G. Gale, was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth.

The Michelson-Gale experiment was a very large ring interferometer, (a perimeter of 1.9 kilometers), large enough to detect the angular velocity of the Earth. Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source (carbon arc) after travelling in two directions. The major change was to replace the two "arms" of the original MM version with two rectangles, one much larger than the other. Light was sent into the rectangles, reflecting off mirrors at the corners, and returned to the starting point. Light exiting the two rectangles was compared on a screen just as the light returning from the two arms would be in a standard MM experiment. The expected fringe shift in accordance with the stationary aether and special relativity was given by Michelson as:

Δ

=

4

A

ω

sin

⁡

ϕ

λ

c

{\displaystyle \Delta ={\frac {4A\omega \sin \phi }{\lambda c}}}

where

Δ

{\displaystyle \Delta }

is the displacement in fringes,

A

{\displaystyle A}

the area of the ring,

ϕ

{\displaystyle \phi }

the latitude of the experiment site in Clearing, Illinois (41° 46'),

c

{\displaystyle c}

the speed of light,

ω

{\displaystyle \omega }

the angular velocity of Earth,

λ

{\displaystyle \lambda }

the effective wavelength used. In other words, this experiment was aimed to detect the Sagnac effect due to Earth's rotation.