Fermilab 12/13/2006 Experimental Tests of SR 1 Experimental Tests of Special Relativity Tom Roberts.

Fermilab 12/13/2006 Experimental Tests of SR 1

ExperimentalTests of

Special Relativity

Tom Roberts


Motivation• It is worthwhile to occasionally check the

basics

• Special Relativity (SR) is part of the foundation of every mainstream theory of physics today.

• The quest for quantum gravity has inspired a search for ways SR might be modified in a consistent manner.

We must know how well it works.


Contents• An overview of experimental tests of SR

– Michelson and Morley– Brillet and Hall– Testing the speed of light emitted from moving sources– Tests of relativistic kinematics– Some recent high-resolution tests of SR

• A deeper look at some experiments that appear to refute SR– Group velocity > c (in anomalously dispersive media)– Visibly superluminal astronomical sources– Michelson and Morley (!)– Dayton Miller’s heroic repetition of the MMX

• Summary, with a very brief glimpse at the future: quantum gravity may well violate SR


Overview: Experimental Tests of SR

• SR makes many predictions, which are well tested:– Isotropy of the speed of light – 42– Isotropy of space – 8– Constancy of the speed of light – 12– Time dilation and Doppler – 16– Length contraction – ZERO– Twin paradox – 5– Relativistic kinematics – 23– Relativistic velocity addition – 5– Variation of c with frequency – 4– g-2 as test of SR – 7– Other – 14

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html


Overview: Experimental Tests of SR

• The isotropy of the speed of light is particularly well tested:– Michelson-Morley (and variations) – 14– Laser/Maser tests – 8– Atomic beams – 2– Frequency-doubling interferometer– Cryogenic optical resonators – 4– One-Way tests

• Two lasers – 6• Two atomic clocks – 3• Rotating Mössbauer absorbers – 4







Michelson – Morley Experiment (1887)

• Finicky experiment: ±0.002 °C, mechanical stability ~nm/m• Result: upper limit of 7.5 km/s (earth relative to aether)

*Light Source

Mirror

Mirror

BeamSplitter

Observer

Telescope

Michelson and Morley, Am. J. Sci. 34, 333 (1887).







Brillet and Hall Experiment (1979)

• Vastly less finicky than Michelson-Morley– Invar components with low thermal expansion– Rotating Fabry-Perot etalon is vacuum– Uses frequency (motion 1 wavelength/sec => 1 Hz, ~1 part in 1015)

• Result: ∆f/f = (1.5±2.5) ∙10-15 => Vearth < 0.02 km/s

Single-Mode Laser HeterodyneFrequency

Counter

Single-ModeLaser

High-FinesseFabry-Perot

Rotating TableBrillet and Hall,

Phys. Rev. Lett. 42, 549 (1979)







Speed of Light Emitted by Moving Sources

As a simple test theory, assume the observed speed of light is given by

Vobs = c + k Vsource

with k to be determined by experiment.

A test at CERN using π0 decay:k < 4∙10-4

Distant supernovas have a velocity spread of the remnants ~10,000 km/s (obtained via Doppler broadening). Observations of supernovas ~5 billion lightyears away show the light reaches us within ~10 days:

k < 10-9







Particle Experiment Tests of SR

• Mostly look at rather old experiments – today particle physicists use SR rather than test it.– Electron kinetic energy as a function of speed agrees with the

prediction of SR to within ~1% (1939)– The Lorentz limiting speed is equal to the speed of light to within

12 parts per million (1972-1991).

• Or one must look at experiments designed to measure something else, but can be interpreted as testing SR.– Super Kamiokande neutrino oscillation observations put a limit of

10-24 on the speed difference between νμ and ντ.

• Two examples below


Elastic Proton-Proton Scattering

Akerlof et al, Phys. Rev. 159, 1138 (1967).

Newtonian mechanics predicts inthe lab frame the scattered

particles will have an angle of 90°.

This experiment verified the kinematics of elastic scattering to about ½%,for incident protons from 5 to 13.4 GeV/c (v/c=0.98 - 0.998).

For high-energy protons that is manifestly not so:


Sidereal Variation in Neutrino Oscillations (LSND)

No significant variation with sidereal time is observed.

The Liquid Scintillator Neutrino Detector at Los Alamos observed an excess of νe events in a beam of νμ

from μ+ decay at rest.







Recent High-Resolution Tests of SR

• There has been a mini-Renaissance in testing SR, in part due to the interest in extensions to the Standard Model

• Kostelecky’s Standard Model Extension has dozens of free parameters, requiring many different experiments to put limits on them.

• Recent experiments use clever and elegant techniques to reduce systematic errors and/or increase sensitivity.


Aligned-Spin Torsion PendulumA carefully constructed torsion pendulum of Alnico and SmCo5,

having ~1023 aligned e- spins and zero net magnetization.The entire torsion balance is rotated (permits monitoring systematic

errors), and data were taken over 13 months searching for both sidereal and solar effects.

Sun

Result: energy of spin flip relative to a fixed direction < 10-21 eV.Dimensionless Lorentz-violation parameter < 1.7∙10-36.

Heckel et al, Phys. Rev. Lett. 97 (2006) 021603.

EarthTurntable

Spin


Time Dilation in 7Li+ Ion Storage RingElectron-cooledIon Storage Ring

v/c = 0.064

Fixed laser Detectors

Tunable laser

MirrorHalf-silvered

Mirrors

Freq. Monitor

• Fixed laser is locked to a double resonance of the 7Li+ ions with its parallel and anti-parallel laser beams.

• Parallel alignment of beams to 70 μrad.• 7Li+ linewidth is large, so the fixed laser saturates the

resonance and the tunable laser scans it to achieve resolution comparable to the laser linewidths

• Measurement/SR = 0.9999999995 ± 0.0000000018Saathoff et al, Phys. Rev. Lett. 91, 190403 (2003).


Two-Species Maser Test• 129Xe and 3He in a single maser cavity• Frequency depends on the magnetic field, so 129Xe resonance is

used to stabilize the field• Four data runs spread over 14 months• Frequency variation with orientation < 30 parts in 1012

One Sidereal Day 18 Sidereal Days of One Data Run




• A deeper look at some experiments that appear to refute SR– Group velocity > c (in anomalously dispersive media) DEMO http://gregegan.customer.netspace.net.au/APPLETS/20/20.html– Visibly superluminal astronomical sources– Michelson and Morley (!)– Dayton Miller’s heroic repetition of the MMX








Visibly Superluminal Astronomical Sources• There are numerous astronomical objects observed to have

visible speeds greater than c.

• In 1994 GRS 1915+105 was observed to emit material about the mass of the moon, with an apparent speed of 1.25 c (distance times angular speed). The uncertainty in its distance (40,000 ly) is much less than 25%.


• Looking “top down” on the situation shows how this does not violate SR (drawing grossly not to scale):

• Because the object is moving rapidly toward earth, at later times it takes less time for the light to reach earth. Just multiplying distance times angle and dividing by elapsed time overestimates the actual velocity in the frame of the earth.

• The ejected source of GRS 1915+105 has an actual speed of 0.92 c in the frame of the earth; only the apparent speed is > c.

Visibly Superluminal Sources in SR

t0

t1Earth

distance







Michelson and Morley’s data

Any signal would be a sinusoid with period ½ turn.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.

Noon

P.M.


Michelson and Morley’s data

Errorbars are from a histogram of the values that were averaged.They are completely dominated by a systematic drift.

Noon

P.M.







Dayton Miller’s Heroic Repetition of the MMXMiller’s experiment is the most-cited example of

an experiment that is claimed to refute SR.We’ll examine it in considerable detail.

CWRU Archives

• Improved Michelson- Morley interferometer

• Much Longer arms, using iron girders

• Faster rotation and data taking

• 20-turn runs(instead of 6)

• Used a mechanical harmonic analyzer

(T. J. Roberts, http://arxiv.org/abs/physics/0608238)


Dayton Miller’s Heroic Repetition of the MMX

• He made over 1,000 data runs over more than a decade.• He carried the instrument to the top of Mt. Wilson. Twice.

CWRU Archives

Miller determined “the absolute motion of

the earth”: 10 km/s, R.A. 5h and δ -70°

D.C.Miller, Rev. Mod. Phys. 5, 203 (1933)


Result from one of Dayton Miller’s Runs

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….

Amplitude~0.06 Fringe


Result from one of Dayton Miller’s Runs

Note changein vertical

scale by x10.

Errorbars are from histograms of the 40 readings that were averaged for each point.

They are completely dominated by the systematic drift.


Comments on Miller’s Result

• Miller thought he was “measuring the absolute motion of the earth”.

• The modern attitude is to use such experiments to test theories.

• In Miller’s context, one would test the class of theories:“The earth is moving with speed X in direction Y”with X and Y determined by fitting to the data.

• Given the large errorbars of his results, the errorbars on X and Y are enormous. His result is not statistically significant.

• Let’s look at where those enormous errorbars came from, and why the above result looks so much like a real signal,but isn’t…


The Raw Data from That Run

Remember the above “signal” is ~0.06 fringe in amplitude.There is clearly a systematic drift ~100 times larger.

Moreover, that systematic drift is not at all linear.


Miller’s Analysis in the Frequency Domain

Period ½ turn

This spectrum is reasonably close to 1/f noise.Except, perhaps that one bin.

320-

poin

t DFT

Spe

ctru

m

320 data points160 freq. bins



• 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 just 3 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 turns

Analysis Step 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.



The final result is an 8-point signal with just 3 nonzero frequency bins.The lowest nonzero frequency bin has period ½ turn.

One frequency dominates, so the signal looks roughly sinusoidal. Any noise with a falling spectrum would look quite similar.

No wonder Miller was fooled!

Period ½ turn

8-po

int D

FT S

pect

rum

8 data points4 freq. bins


Comments on Miller’s Analysis• Clearly this analysis is seriously flawed:

– Averaging simply does not do what is desired.– Assuming the systematic is linear is very bad.– There is no quantitative error analysis.

• These flaws apply to Michelson and Morley, and all other experiments analyzed with this algorithm.

• Even understanding the frequency domain does not tell us if that ½-turn amplitude is a real signal or not.

• Fortunately, Miller took enough data so a new analysis can quantitatively model the systematic error in each run.


A New Analysis of Miller’s Data• Recently, copies of many of Miller’s original data sheets

have been found (available from the CWRU Archives).

1. Model the systematic error– Any real signal depends only on orientation modulo 180°– Readings at a given orientation for successive turns differ only

by the systematic error– Readings at different orientations are interleaved by the rotation– Fit the differences for each orientation to a single function of

time that is as continuous as possible

2. Subtract the systematic, compute the ½-turn DFT amplitude; determine errorbar from the fit.

3. Analyze 67 of Miller’s runs, omitting unstable ones.


Results of New Analysis of Miller’s Data

The 14 runs with open circles (20%) do not meet stability criteria.The lack of variance around zero is due to the quantization of the data.

|DFT

Am

plitu

de| w

ith P

erio

d ½

Tur

n


Results of New Analysis of Miller’s Data• For all of the stable runs the systematic model

exactly reproduces the data.

• The 0.015 Fringe errorbar is smaller than the false signal in the run above. It gives an upper bound on “absolute motion” of 6 km/sec (90% confidence).

• Miller was unknowingly looking at insignificant patterns in his systematic error that precisely mimicked the appearance of a real signal. No wonder he was fooled!No wonder his results were anomalous!He could not have known this…







Summary

Amateurs look for patterns,professionals look at errorbars.

Experimenters:Measure your systematic errors!

Perform a comprehensive error analysis!

You don’t want someone like me coming along 80 yearslater and explaining why your results are insignificant!


Summary

• Today SR stands unrefuted experimentally(within its domain of applicability)

• Experiments that some people claim refute SR, such as Miller’s, do not do so when carefully scrutinized.

• Experiments should be interpreted as testing theories, not as “measuring this or that”.

– let engineers measure things

• SR and its Lorentz invariance have been instrumental in the search for new fundamental theories of physics:GR, QED, Electro-weak, QCD, the Standard Model.

• But there are tantalizing indications this may not be true in the future…


Quantum Gravity May Well Violate SR

• Quantum gravity might have detailed structure at the Planck scale.– Strings ?– Topological “defects” ?– “Loops” ?– The whole notion of “differentiable manifold” may break down…– Non-commutative geometry?– Etc. ?

• Such real structure might well be an “Absolute Frame” – but why don’t we see it today?

• Perhaps, like the QED vacuum, it is “Lorentz invariant”...– Doubly Special Relativity

• Two invariant scales: c and EPlanck

• Inherently quantum (e.g. Hopf algebras…)

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Fermilab 12/13/2006 Experimental Tests of SR 1 Experimental Tests of Special Relativity Tom Roberts.

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