Cleveland, July 1887. Six turns at every mark.
The Fringe That Would Not Move
Rotate Michelson and Morley's interferometer and calculate the 0.4-fringe shift a stationary aether predicted. Then lay their 1887 readings over it, test the null honestly, and make Dayton Miller's later signal survive the checks it must.
Centered fringe position
+0.200000
The 90 degree change is twice this centered amplitude.
Layer 1: the rotation
A change, not a line at 0.4
The paper's 0.4 fringe is the change between two orientations 90 degrees apart. On a centered half-turn curve, the rigid stationary-aether prediction therefore runs from +0.2 to -0.2 fringe. The live exact calculation uses Galilean round-trip times. Its second-order approximation is 2(D/lambda)(v/c)^2.
The teal trace is not zero. It is the published noon mean after one named drift correction. What is absent is a repeatable curve at the predicted size and phase. The two models that give zero here, FitzGerald contraction and special relativity, cannot be told apart by this experiment alone.
Layer 2A: the raw-ledger lab
Seventeen marks, then decide what drift means
These are the paper's reported screw readings. Each cell is already the mean of six revolutions. The repeated mark at the end is the closure reading.
Drift rule, chosen before the harmonic fit
Joining the repeated mark assumes the drift accumulated linearly during one turn. That is a free analysis choice, not an observation.
| mark | angle | screw divisions | adjusted fringe | fit |
|---|
Layer 2B: the later claim
Four seasons are not four blank cheques
Dayton Miller later claimed a positive result. His 1933 paper compressed 316 observation sets into four seasonal rows. Those rows are numerical and can be operated. They are not his surviving data sheets, and they do not carry an uncertainty for each derived direction.
A separate direction for every epoch always lands exactly on every row. That perfect fit cannot fail. The locked screen below spends two parameters on one common direction instead of eight on four independent directions. Its verdict changes when you change the assumed directional scatter, because that scatter is unknown here.
The aggregate-coherence bench
How much scatter do four directions permit?
South-apex directions, apparent velocities, and displacements are transcribed from Miller's 1933 Tables I to III. This is a limited common-direction screen, not a reconstruction of his celestial solution.
This is a free scale, not an error bar published by Miller.
BIC comparison, lower is better
locked direction
locked 6.75, free 16.64
The ranking flips below 4.56 deg assumed scatter.
The free model uses eight direction coordinates for eight coordinate observations. Its exact fit is saturated, so it is not evidence of coherence.
| epoch | south RA | south declination | apparent speed | displacement | locked residual |
|---|
A drift can wear a half-turn mask
This is synthetic. It shows only why a freely chosen amplitude and phase per session can turn smooth instrumental drift into a fitted second harmonic. It does not establish what caused Miller's historical readings.
computing
The check
The numbers below are recomputed in this browser from the transcribed source inputs. The independent Node verifier begins from its own transcription, reproduces the published table means, and then checks the browser results and deliberate wrong turns.
Uncertainties and free choices
- Rounded historical inputs. About 11 m, nearly 20 million wavelengths, and v/c near 0.0001 are published rounded inputs. No exact yellow-light wavelength is invented here. The preset displays them, it does not derive them.
- Qualitative bounds. The authors' "certainly" below 0.02 fringe and "probably" below 0.01 fringe are historical judgments. They are not standard errors, confidence intervals, or modern detection limits.
- Screw conversion. One division is treated as 0.02 wavelength because the paper says the fringe width varied from 40 to 60 divisions, with a mean near 50. That spread is not propagated into a modern error bar.
- Detrending is chosen. No correction, joining the repeated endpoint, and removing a least-squares line give different half-turn amplitudes. The control exposes the choice. None is silently privileged as the one true reduction.
- The ledger is already averaged. The 102 cells shown are published means of six revolutions at each marked position, not the individual visual readings.
- Miller is aggregate-only here. The four rows are Miller's numerical Tables I to III, not raw sheets. His paper does not give a per-row uncertainty for the derived directions. The scatter slider is a free choice. The common-direction screen omits the full orbital projection and cannot reproduce his complete celestial solution.
- The score has a model. The BIC screen treats the two direction coordinates per epoch as independent, equally scattered Gaussian observations. It counts two parameters for the common direction and eight for the saturated fit. That likelihood and parameter count are declared analysis choices, not facts printed by Miller.
- The drift model is a toy. Its drift size, curvature, and ripple are chosen. It demonstrates a failure mode only. Shankland and colleagues' attribution to statistics and local temperature comes from their reanalysis, not from this simulator.
- Unmodelled apparatus effects. Air and optical dispersion, mechanical strain, thermal gradients, fringe-width variation, and manual visual readings remain in the error ledger.
- Models tied here. FitzGerald contraction and special relativity both give a null in this instrument. This experiment alone does not choose between them, exclude every possible aether model, prove Earth stationary, or establish a simple causal story about Einstein.
Settings that cannot teach you anything
Setting D/lambda = 0 or v/c = 0 forces zero by definition. Comparing an angle with itself plus 180 degrees is also identically zero because cos(2 theta) repeats. Fitting a separate direction to each Miller epoch is saturated. Subtracting the fitted second harmonic before checking for it would guarantee a null. The controls avoid the first setting, name the others, and keep the informative rotation at 90 degrees.
Run the independent check: node research/michelson-morley/verify-michelson-morley.mjs
What, narrowly, ended
The 1887 object rules out the large 0.4-fringe orientation change predicted by the specific rigid, undragged stationary-aether calculation with the assumed orbital component. It does not turn every reading into zero, and it does not settle every theory that once used the word aether. FitzGerald's 1889 contraction proposal is one historical demonstration of that remaining logical room.
The later argument and the publication record
Miller's 1933 article claimed a positive absolute-motion solution. Shankland, McCuskey, Leone, and Kuerti reanalysed Miller's original sheets in 1955 and reported that small periodic displacements were partly statistical fluctuations, with the remainder associated with local temperature conditions. Thomas Roberts later derived a 6 km/s upper limit, but that number belongs to a three-version, non-peer-reviewed 2006 arXiv preprint. It is a published analysis result shown for provenance, not a live computation or an accepted precision bound.