The aether hypothesis and Michelson-Morley

Why physicists imagined an aether

Mechanical waves require media. Sound travels through air, water waves travel through water, and waves on a string travel through the string. Since light was understood as a wave, many nineteenth-century physicists assumed it must also travel through a medium. This hypothetical medium was called the luminiferous aether.

The aether was thought to fill space, be extremely rigid to support fast light waves, yet offer almost no resistance to planets moving through it. These requirements were physically awkward, but the aether seemed natural to people used to mechanical waves.

A preferred frame

If the aether existed, it would define a preferred rest frame: the frame in which light travels at speed $c$ equally in all directions. Earth moves around the Sun, so Earth should move through the aether. This motion would create an apparent aether wind.

By analogy, a boat moving through still water experiences different travel times upstream and downstream. Light traveling parallel and perpendicular to Earth's aether wind should take slightly different times.

The Michelson interferometer

Albert Michelson and Edward Morley designed a sensitive interferometer to detect this effect. A beam of light was split into two perpendicular arms, reflected by mirrors, and recombined. If the two beams took different times, their phase difference would change, shifting interference fringes.

The expected phase shift depended on Earth's speed through the aether and the orientation of the apparatus. Rotating the interferometer should change which arm was parallel to the aether wind, causing a measurable fringe shift.

Expected time difference

If the apparatus arm length is $L$ and Earth moves at speed $v$ through the aether, classical reasoning predicts a tiny time difference of order

Delta tsim rac{Lv^2}{c^3}

The effect is second order in $v/c$, which is small but within the sensitivity of the experiment as designed.

The relevant small parameter is

rac{v^2}{c^2}

Earth's orbital speed is about $3.0 imes10^4 m/s$, while light speed is about $3.0 imes10^8 m/s$, so $v/csim10^{-4}$ and $v^2/c^2sim10^{-8}$.

The null result

Michelson and Morley did not observe the expected fringe shift. The result was essentially null: there was no detectable evidence of motion through the aether.

This was shocking because the experiment did not merely fail casually; it was designed precisely to detect the expected effect. Improved experiments continued to support the null result.

Possible explanations

Several explanations were proposed. One was that Earth somehow dragged the aether along with it, but this conflicted with other optical observations. Another was length contraction: objects moving through the aether might physically contract in the direction of motion by just the amount needed to hide the effect.

The Lorentz-FitzGerald contraction idea was mathematically suggestive, but without Einstein's reinterpretation, it seemed like an ad hoc fix.

Einstein's shift

Einstein removed the need for aether by proposing that the laws of physics are the same in all inertial frames and that light speed in vacuum is the same for all inertial observers. The Michelson-Morley result becomes natural: there is no aether wind to detect.

The big idea

The aether hypothesis tried to preserve a mechanical medium for light and a preferred rest frame. The Michelson-Morley experiment searched for Earth's motion through that medium and found no expected effect. Its null result helped motivate the abandonment of the aether and the development of special relativity.