Michelson-Morley Experiment Simulator

What the Michelson-Morley experiment was

In the 19th century light was known to be a wave, and waves were thought to need a medium. The proposed medium was a luminiferous aether filling space. If the Sun sat still in it, the Earth would move through it at about 30 km/s as it orbits, and an observer on Earth would feel an “aether wind”, just as a cyclist feels a wind on a still day. Albert Michelson (alone in Potsdam in 1881, then with Edward Morley in Cleveland in 1887) built an interferometer to detect it: a lamp, a half-silvered mirror that splits the light into two beams, two mirrors at the ends of perpendicular arms, and an eyepiece where the recombined beams make fringes. Mounted on a heavy stone that floated in a trough of mercury, the instrument could be turned smoothly through every direction.

The arithmetic

A beam sent along the wind and back takes 2L/c ÷ (1 − v²/c²). A beam sent across the wind and back takes 2L/c ÷ √(1 − v²/c²). They differ by roughly (L/c)(v²/c²). With L = 11 m and v/c = 10⁻⁴ that is 3.7 × 10⁻¹⁶ s, a path difference of 110 nm, about a fifth of a wavelength. Turning the instrument through 90° swaps the roles of the arms, doubling the change, so the fringes should slide by N = 2Lv²/(λc²) ≈ 0.4 of a fringe. Michelson and Morley could see a hundredth of a fringe. They saw no shift of the expected size.

What the null result meant

The numbers are not in dispute; the interpretation is where the choices lie, and the Theory menu above lets you switch between them:

• The aether is dragged along with the Earth. Use the “Wind that reaches the lab” slider. Complete dragging is hard to square with the aberration of starlight, and Michelson himself pursued it.
• Lorentz–FitzGerald contraction. Arms shrink along the direction of motion by exactly the factor that cancels the delay (try it on the “Why the times differ” tab). The aether then exists but cannot be detected this way.
• Special relativity. There is no preferred frame; light moves at c for every inertial observer, and the null result is expected. Einstein's 1905 paper does not rely on the experiment, but it explains it.
• Emission theories. Light travels at c relative to its source. It also gives a null result here, but is contradicted by other observations, such as the light of double stars.

Whichever you favour, the simulation shows the same thing: if the Earth moved through a still aether and nothing compensated, a 11 m instrument would have shown 0.4 fringe, and the reported shifts were many times smaller.

Later experiments

Morley and Miller built a longer instrument in 1902–04. Dayton Miller ran one on Mount Wilson in the 1920s and reported a small signal of about 10 km/s; later analysis (Shankland and colleagues, 1955) found it consistent with temperature effects on the apparatus. Georg Joos in 1930 used a sealed, temperature-controlled instrument and set a limit of about 1.5 km/s. In 1932 Kennedy and Thorndike used arms of unequal length to test whether the result depends on the Earth's speed at different times of year. Modern versions use rotating cryogenic optical resonators and limit any directional difference in the speed of light to a few parts in 10¹⁷ or better. This page covers only the classic fringe-counting version.

What the page simulates, and what it does not

The arm times are the exact formulas, computed in the frame of the aether, not the small-speed approximation (the two agree to better than one part in 10⁸ at 30 km/s). Fringes are drawn from the exact phase difference with an idealised monochromatic source. The turntable run adds Gaussian reading noise and fits cos 2θ and sin 2θ by least squares. Not modelled: the real instrument's flexing, temperature drift, the tilt of the fringe field, and the Earth's changing wind direction over a day and a year. It is a teaching model, not an analysis tool.

Things people ask

• Why is the effect second order? Going out and back along the wind, the first-order gain and loss cancel. What is left is proportional to (v/c)², about 10⁻⁸, which is why it needed a precise interferometer.
• Why turn the instrument? The wind direction was unknown, and the sign of the effect changes every 90°, so the signature is a wobble that repeats twice per turn. A fixed offset in the fringes (from imperfect mirror alignment) does not matter.
• Why not just compare the two arms at rest? You cannot tell the arms' lengths apart to a fraction of a wavelength, so only the change on rotation is meaningful.
• Did Michelson get a Nobel Prize for it? He won the 1907 Physics Nobel “for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid”.

Everything runs on your device; nothing is uploaded. MES Math Q/A 57: the Michelson-Morley experiment · All the Aether Q/As · Atomic clock simulator · Photoelectric effect simulator · Earth curvature calculator · More MES tools