This sim times light on a round trip down each of two perpendicular arms, first as the ether theory would have it (Aether mode), then with light at c in every direction (Actual mode). That is the Michelson–Morley experiment, a test of whether light's speed depends on how the apparatus moves.

What's on screen

• Light path: Source, beam splitter, mirrors M₁ (arm A) and M₂ (arm B), telescope detector. The beam takes its colour from λ.
• Red arrows: the ether wind (Aether mode only). At θ = 0° it blows along arm A.
• Table angle θ: the degree scale on the floor and the θ tag at the bottom left.
• Round-trip panel (top right): each arm's round-trip time and A − B, headed by the mode.
• Statistics (foot of the sidebar): the path change Δℓ and the fringe shift ΔN, as numbers. The sim does not draw the fringes.

Press ⌖ on a row to see where that control sits in the sim.

Fixed: the wind speed. It is set to Earth's orbital speed, v ≈ 29.8 km/s, so β = v/c = 9.93×10⁻⁵, and it is not adjustable.

The ether theory says light travels at c relative to a stationary ether. Earth moves through that ether, so the apparatus feels a wind of speed v, with β = v/c. Along arm A, light goes out with the wind at c + v and back against it at c − v.

The two legs do not cancel. The slow leg lasts longer than the fast leg saves, so the round trip is longer than the still-ether time 2L/c. For L = 11 m, 2L/c = 73.4 ns and the extra is 724 as (1 as = 10⁻¹⁸ s).

Arm B lies across the wind. Aimed straight across, a beam would be swept downstream, so it must be aimed upstream. Only √(c² − v²) of its speed is left to cross the arm.

So both arms are slowed. To leading order in β², arm B loses half of what arm A loses: 362 as against 724 as. What the experiment looks for is the difference, A − B = 362 as.

Lecture 7's aeroplane example has the same ordering: 400 km at 100 km/h takes 8 h in still air, 10 h across a 60 km/h wind and 12.5 h along it.

An arm at angle φ to the wind takes:

Arm A sits at θ and arm B at θ + 90°, so turning the table swaps sin² and cos² between them. To leading order, A − B ≈ (Lβ²/c) cos 2θ. For L = 11 m that is +362 as at 0°, zero at 45° and −362 as at 90°.

The table has to turn because the arms of a real apparatus are never exactly equal, and there is no "wind off" setting to compare with. Only the change under rotation can be measured, so the sim's Δℓ and ΔN are referenced to θ = 0°.

A difference of 362 as is 3.6×10⁻¹⁶ s, and no clock reads that. Light does: the two beams recombine, and one fringe is one wavelength of path difference. Multiplying the time difference by c gives the path difference, and dividing by λ gives fringes (t₁ and t₂ are the round trips of arms A and B).

At L = 11 m and λ = 550 nm, c(t₁ − t₂) is +108 nm (0.2 fringe) at 0° and −108 nm at 90°. The sim reports the change from θ = 0°: Δℓ = −217 nm and ΔN = −0.394 at 90°. It never goes positive. The shift grows in proportion to L and shrinks as λ grows.

Michelson and Morley folded their light path with mirrors to an effective arm length near 11 m and turned the apparatus through full revolutions on several days in 1887. At λ = 550 nm the ether prediction was about 0.4 fringe between 0° and 90°. They could resolve about one fortieth of that, 0.01 fringe.

They found no shift at any orientation, within that precision. The sim's Actual mode shows that outcome: in the apparatus's own frame light travels at c in every direction, so both arms take 2L/c at every θ.

The result forces a choice between two things physicists believed: the principle of relativity, and Galilean velocity addition with absolute time. Relativity keeps the first and gives up the second.

• Gravitational-wave detectors. LIGO is a Michelson interferometer with 4 km arms. It reads changes in the difference of the two arm lengths, far smaller than a proton's width.
• Tests of relativity. Modern versions use lasers in rotating optical cavities and limit any direction dependence of the speed of light to about one part in 10¹⁷.
• Spectrometers. A Fourier-transform infrared spectrometer is a Michelson interferometer with one moving mirror. Counting fringes as the mirror moves gives the light's spectrum.

Key points

• In an ether wind the round trips are (2L/c)/(1 − β²) along the wind and (2L/c)/√(1 − β²) across it. Both exceed 2L/c.
• Turning the table swaps the two arms. A − B follows cos 2θ, and only that change can be measured.
• The fringe shift between 0° and 90° is about 2Lβ²/λ: 0.394 at L = 11 m, λ = 550 nm.
• The measured shift was far smaller than predicted, which puts Galilean velocity addition in doubt.

Common mix-ups

• "The out-and-back legs cancel." They do not. The slow leg lasts longer than the fast leg saves.
• "A wind across the arm does nothing." It slows arm B by half as much as arm A.
• "They simply were not sensitive enough." They could resolve about one fortieth of the predicted 0.4 fringe.

Things to try on your own

• In Simplified view, step the table through 0°, 45° and 90° and note the Excess row.
• Set λ = 700 nm, then adjust L until ΔN at 90° is −0.394 again.
• In Aether mode, find the angles where A − B is zero, then compare with Actual mode.