Laboratory · Historical model comparison · Explanatory preview
Michelson–Morley: what does a null result decide?
Hold the apparatus fixed and compare the predicted rotation shift with and without longitudinal contraction.
Change one setting and compare the consequences
Static worked exampleBar range: −0.4 to +0.4 fringes. The center line is zero. The scale is recalculated after Apply.
Accepted calculation 0. Every model row shares these inputs.
Inputs used for these results
- Equal one-way arm length
- 11 m
- Vacuum wavelength
- 5.5 × 10⁻⁷ m
- Signed ether-wind speed divided by c
- 0.0001
| Observable | Ether without contraction | Ether with longitudinal contraction |
|---|---|---|
| 90° rotation shift (fringes) | 0.4 | 0 |
| Leading order in β² (fringes) | 0.4 | 0 |
| Parallel round-trip time (s) | 7.338 × 10⁻⁸ | 7.338 × 10⁻⁸ |
| Perpendicular round-trip time (s) | 7.338 × 10⁻⁸ | 7.338 × 10⁻⁸ |
| Arm-time difference before rotation (s) | 3.669 × 10⁻¹⁶ | 0 |
For these equal arms, the contraction hypothesis cancels the rotation signal. A null result therefore does not by itself distinguish this contracted-ether model from every other null-predicting account. The arm-time difference at one orientation is not the full 90° rotation fringe shift. The β² expression is a low-speed approximation, not the exact high-speed curve.
An instrument splits a beam of light along two arms at right angles, sends each out and back, and compares the returns. If the Earth moved through a fixed medium for light, turning the instrument should shift the pattern measurably; the shift found was far smaller, and this lab shows what that null result does and does not decide.
In an ether at rest, light out and back along an arm of length L parallel to the ether wind takes 2L/(c(1 − β2)), and across it 2L/(c√(1 − β2)), where β = v/c. Turning the apparatus through 90 degrees swaps the arms, and the fringe pattern should shift by about 2Lβ2/λ. With arms of 11 m, light of 550 nm and β = 10−4, about the Earth's orbital speed, the ether without contraction predicts 0.4 fringes. If the arm along the motion is shortened by √(1 − β2), the two times become equal and the prediction is 0. A null result therefore rules out the resting ether without contraction, but it cannot choose between contraction in an ether and Einstein's kinematics, which both predict zero. The relativity paper mentions only unsuccessful attempts to detect the Earth's motion relative to the light medium, and names no experiment.
Along the wind, light goes out against it at c − v and back with it at c + v, so the round trip takes L/(c − v) + L/(c + v) = 2Lc/(c2 − v2) = (2L/c)/(1 − β2). Across the wind, the light must aim upstream to reach the mirror at all; its speed across is √(c2 − v2), and the round trip takes 2L/√(c2 − v2) = (2L/c)/√(1 − β2). For small β the first is about (2L/c)(1 + β2) and the second about (2L/c)(1 + β2/2), so they differ by (L/c)β2. Rotating by 90 degrees swaps the roles, which doubles the difference to (2L/c)β2, and counted in wavelengths of the light that is 2Lβ2/λ fringes. With L = 11 m, β = 10−4 and λ = 5.5 × 10−7 m, that is 2 × 11 × 10−8/(5.5 × 10−7) = 0.4 fringes. Now shorten the arm along the wind to L√(1 − β2): its round trip becomes (2L/c)√(1 − β2)/(1 − β2) = (2L/c)/√(1 − β2), exactly the time across, so the shift is 0 at every speed. The contracted ether and relativity both give 0, so the null result cannot tell them apart.
Michelson ran the experiment in 1881 and, with Morley, much more precisely in 1887, finding a shift well under the 0.4 fringes expected. FitzGerald in 1889 and Lorentz in 1892 proposed the contraction that removes it. How much the experiment weighed with Einstein in 1905 is a matter of historical debate; the paper names no experiment. The instrument's settings are illustrative rather than the historical apparatus, and no measured shift is plotted.
These are host reference calculations with modern SI calibration and illustrative settings. They are not historical measurements, a reviewed historical dataset, or publication of the strict 1904 shelf. No FrankenSim WASM calculation is claimed.
What is being calculated?
The apparatus has equal one-way arm lengths before any hypothesized contraction. The wind is aligned with one arm, and the displayed fringe prediction is the change after a 90° rotation. Unequal arms, angular sweeps, source coherence and an empirical upper bound are not modeled here.
These formulas describe the uncontracted case. For the contracted case the longitudinal arm is shortened by √(1 − β²), which equalizes the two round-trip times for equal rest lengths. The numerical owner evaluates the small difference in a cancellation-resistant form.
Try doubling the arm length, then doubling the wavelength, then reversing the wind. Finally choose a much larger speed ratio and inspect where the leading β² approximation departs from the exact model expression. Large ratios are mathematical stress tests, not claims about terrestrial wind speeds.
Prediction is not a measurement
No observed points, digitized fringe shifts or experimental confidence bounds have been added to these plots. A reviewed source-specific dataset, with its geometry, wavelength, protocol and uncertainty, is still needed before making a numerical comparison with a historical experiment.
The reference implementation is src/physics/reference/shelfOptics.ts. Its functions own the arm times, fringe shifts, drag speeds and wave residuals; the interface only projects their results. Numerical precision in a table does not imply measurement accuracy.
This comparison belongs to the special-relativity discovery route.