Annus Mirabilis · Interactive critical edition in preparation
Optical arm times with and without contraction
Compare two hypotheses for the same equal-arm apparatus.
Modern SI calibration and illustrative settings. This is not a verified historical dataset or a strict 1904-mode instrument. No FrankenSim WASM execution is claimed.
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.
The explanation
Full explanation
Keep the arm length, wavelength, and wind speed fixed while changing the contraction hypothesis. The fringe prediction is a model consequence, not an observed experimental bound.
Show every step of the investigation
Inspect both round-trip times, their difference, and the predicted change after a right-angle rotation. Compare the exact model with the leading low-speed approximation. The supplied calibration is modern and illustrative, not a strict 1904 dataset.
An explanatory model, not an observation of nature. This embed starts from the laboratory’s worked defaults, not a saved run. Presentation options change the surrounding guide, never the numerical inputs.