# Lorentz-Fitzgerald contraction hypothesis

The Lorentz-Fitzgerald contraction hypothesis was proposed by Fitzgerald and independently proposed and extended by Lorentz to explain the negative result of the Michelson-Morley experiment, which attempted to detect Earth's motion relative to the luminiferous aether.

Fitzgerald suggested that when a body moves through space it experiences a compression in the direction of the motion. Lorentz showed how such an effect might be expected based on electromagnetic theory and the electrical constitution of matter, that is, when a body moves through space its dimension parallel to the line of motion might become less by an amount dependent on its speed. If the speed of the body is v and the speed of light is c, then the contraction is in the ratio

[itex]\sqrt{1 - \frac{v^2}{c^2}} : 1[itex]

For Earth moving in its orbit at about 18.5 mile/s (30 km/s), the contraction would amount to about one part in 200,000,000, which would be about 2.5 inches (64 mm) on the diameter of Earth. This small change accounts (by design!) exactly for Michelson and Morely's negative result by making the source of light and the mirror draw closer together when the system is moving lengthwise.

Interestingly, from the formula itself, it is impossible for velocity (v) to surpass the speed of light. Doing so results in a fraction larger than 1; thus a square root of a negative number.

Lorentz was not particularly satisfied with his hypothesis because he realized that it was ad hoc and not testable by experiment.

To quote Henri Poincaré (Science and Hypothesis):

"Then more exact experiments were made, which were also negative; neither could this be the result of chance. An explanation was necessary, and was forthcoming; they always are; hypothesis are what we lack the least"

The theory of the luminiferous aether and the necessity for the Lorentz-Fitzgerald contraction hypothesis to 'save' it were ultimately supplanted by Albert Einstein's theory of relativity.

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