# LorentzFitzGerald contraction hypothesis

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

After reading a paper by Heaviside in which was shown that electric and magnetic fields are deformed by motion, FitzGerald inferred that similarly, when a body moves through space it experiences a deformation due to motion, and that this may explain the "null result". Lorentz showed independently 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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{1 - \frac{v^2}{c^2}} : 1}**

For Earth moving in its orbit at about 30 km/s (18.5 mile/s), the contraction would amount to about one part in 200,000,000, which would be about 6 cm (2.5 inches) on the diameter of Earth. This small change accounts for Michelson and Morley'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 of objects (v) to surpass the speed of light. Doing so results in a fraction larger than 1; thus a square root of a negative number.

Henri Poincaré was not particularly satisfied with that hypothesis. In *Science and Hypothesis* he commented on the Lorentz contraction:

- "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; hypotheses are what we lack the least"

The Lorentz-FitzGerald contraction hypothesis was reinterpreted by Albert Einstein as a consequence of the Principle of relativity (see Special relativity). According to him, early explanation attempts including the Lorentz-Fitzgerald contraction hypothesis had been "ad-hoc".

Lorentz did not agree as can be seen from his draft letter of 1915 to Einstein:

- "I felt the need for a more
*general theory*, as I tried to develop later, and as has actually been developed by you (and to a lesser extent by Poincaré). However, my approach was not so terribly unsatisfactory. [...] And the interpretation given by me and FitzGerald was not artificial. It was more so that it was the only possible one, and I added the comment that one arrives at the hypothesis if one extends to other forces what one could already say about the influence of a translation on electrostatic forces. Had I emphasized this more, the hypothesis would have created less of an impression of being invented*ad hoc*."