Special Relativity , the Lumeniferous Aether, and Experiments. Or: The Importance of Errorbars. Tom Roberts Muons, Inc. Motivation. It is worthwhile to occasionally check the basics Special Relativity (SR) is part of the foundation of every mainstream theory of physics today.
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Light SourceMichelson – Morley Experiment (1887)
Rotating TableBrillet and Hall Experiment (1979)
The 30 km/s orbital speed of the earth corresponds to 0.4 fringe.
These data are averages of 3 runs collected over 4 days.
Errorbars are from a histogram of the values that were averaged.
They are dominated by the systematic error.
Miller’s experiment is the most-cited example of
an experiment that is claimed to refute SR.
We’ll examine it in considerable detail.
Miller determined “the absolute motion of the earth”: 10 km/s, R.A. 5h and δ -70°
Wow! That sure looks like a sinusoid with period ½ turn!
(Any real signal is a sinusoid with period of ½ turn.)
We’ll see where it came from shortly, but first things first….
scale by x10.
Errorbars are from histograms of the 40 readings that were averaged for each point.
They are completely dominated by the systematic error.
There is a systematic drift ~100 times larger than the above “signal”.
Moreover, that systematic drift is not at all linear.
160 freq. bins
320-point DFT Spectrum
Period ½ turn
This spectrum is reasonably close to 1/f noise.
Except, perhaps that one bin.
A comb filter that keeps integral harmonics of 1 turn(including dc)
Reduces the remaining Fourier amplitudes by about half
Zeroes the dc frequency bin
A comb filter that keeps integral harmonics of ½ turn
Average the 20 turns
Subtract the linear systematic(even though it clearly is not very linear)
Subtract the mean
Average the first and second ½ turnsMiller’s Analysis in the Frequency Domain
This averages 320 readings down to just 8 points.
This was quite standard in Miller’s day – they did not realize the implications.
Period ½ turn
8-point DFT Spectrum
The final result is an 8-point signal with 3 nonzero frequency bins.
The lowest nonzero frequency bin has period ½ turn.
Any noise with a falling spectrum would look quite similar.
One bin dominates, so the signal looks roughly sinusoidal.
No wonder Miller was fooled!
DFT Amplitude with Period ½ Turn
The 14 runs with open circles have ≤5 stable turns (out of 20).
The lack of variance around zero is due to the quantization of the data.
(We still teach and use Maxwell’s equations, withoutthe underlying aether. How that happened is an interesting story beyond the scope of this presentation.)
(This is why we call them “Lorentz transforms”)
1. If light propagates as a wave in the aether, how does the quantization of light arise?
2. If light propagates as a wave in the aether, how do absorption spectra arise?
3. Why are some materials opaque and some trans-parent? Why do some reflect almost perfectly?
Amateurs look for patterns, professionals look at errorbars.
Measure your systematic errors!
– let engineers measure things.