Special relativity the lumeniferous aether and experiments or the importance of errorbars
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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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Special relativity the lumeniferous aether and experiments or the importance of errorbars

Special Relativity,the Lumeniferous Aether,and Experiments.Or: The Importance of Errorbars.

Tom Roberts

Muons, Inc.


Motivation

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.


Contents

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not quite dead, it is just irrelevant

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


Brief overview experimental tests of sr

Brief 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 – 0

    • 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


Brief overview experimental tests of sr1

Brief Overview: Experimental Tests of SR

  • The isotropy of c 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


Contents1

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not quite dead, it is just irrelevant

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


Michelson morley experiment 1887

Mirror

Beam

Splitter

Telescope

Mirror

Observer

*

Light Source

Michelson – Morley Experiment (1887)

  • Finicky experiment: ±0.002 °C, mechanical stability ~nm

  • Result: upper limit of 7.5 km/s (earth relative to aether)


Contents2

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Brillet and hall experiment 1979

Single-Mode

Laser

High-Finesse

Fabry-Perot

Rotating Table

Brillet and Hall Experiment (1979)

Frequency

Counter

  • 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 => 0.02 km/s (Vearth)

Heterodyne

Single-Mode Laser


Contents3

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Speed of light emitted by moving sources

Speed of Light Emitted by Moving Sources

  • As a simple test theory, assume the observed speed of light is given by Vobs = c + k Vsourcewith 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


Contents4

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • A deeper look at some experiments that appear to refute SR

    • Group velocity > c (in anomalously dispersive media)DEMO

    • Visibly superluminal astronomical sources

    • Michelson and Morley (!)

    • Dayton Miller’s heroic repetition of the MMX

  • A surprise: the aether is not dead, it is just irrelevant

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


Contents5

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Visibly superluminal astronomical sources

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%.


Visibly superluminal sources in sr

Visibly Superluminal Sources in SR

  • 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 on earth 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.

t1

Earth

t0

distance


Contents6

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Michelson and morley s data

Michelson and Morley’s data

Noon

P.M.

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.


Michelson and morley s data1

Michelson and Morley’s data

Noon

P.M.

Errorbars are from a histogram of the values that were averaged.

They are dominated by the systematic error.


Contents7

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Dayton miller s heroic repetition of the mmx

Dayton Miller’s Heroic Repetition of the MMX

Miller’s experiment is the most-cited example of

an experiment that is claimed to refute SR.

We’ll examine it in considerable detail.

  • 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

CWRU Archives


Dayton miller s heroic repetition of the mmx1

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.

Miller determined “the absolute motion of the earth”: 10 km/s, R.A. 5h and δ -70°

CWRU Archives


Result from one of dayton miller s runs

Result from one of Dayton Miller’s Runs

Amplitude

~0.06 Fringe

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….


Result from one of dayton miller s runs1

Result from one of Dayton Miller’s Runs

Note change

in 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 error.


Comments on miller s result

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

The Raw Data from That Run

There is a systematic drift ~100 times larger than the above “signal”.

Moreover, that systematic drift is not at all linear.


Miller s analysis in the frequency domain

Miller’s Analysis in the Frequency Domain

320 points

160 freq. bins

320-point DFT Spectrum

Period ½ turn

This spectrum is reasonably close to 1/f noise.

Except, perhaps that one bin.


Miller s analysis in the frequency domain1

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 turns

Miller’s Analysis in the Frequency Domain

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.


Miller s analysis in the frequency domain2

Miller’s Analysis in the Frequency Domain

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!


Comments on miller s analysis

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

A New Analysis of Miller’s Data

  • Remarkably, copies of most of Miller’s original data sheets have survived (available from the CWRU Archives).

  • 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

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

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


Results of new analysis of miller s data

Results of New Analysis of Miller’s Data

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.


Results of new analysis of miller s data1

Results of New Analysis of Miller’s Data

  • For all of the reasonably 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.

  • 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…


Contents8

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Aether theories

Aether Theories

  • The classical aether theory underlying Maxwell’s equations has the aether at rest in some (unknown) inertial frame throughout space.

    (We still teach and use Maxwell’s equations, withoutthe underlying aether. How that happened is an interesting story beyond the scope of this presentation.)

  • Light propagates as a disturbance in the aether, isotropically with speed c relative to the aether frame.

  • As in Newtonian mechanics, Galilean relativity applies.

  • This theory has several fatal problems:

    • Maxwell’s equations are not valid on earth, even though they were discovered here.

    • By ~1900 about a dozen experiments failed to see effects related to the motion of the earth through the aether.


Early attempts to fix up aether theories

Early Attempts to “Fix up” Aether Theories

  • Around 1890 both Fitzgerald and Lorentz started guessing that rulers were physically shortened when they moved relative to the aether.(They were guessing that EM forces held matter together; remember atomic theory as we know it was not at all solidly established back then.)

  • In 1904 Lorentz (and Poincaré in 1906) showed how to make Maxwell’s equations valid on earth:

    • There is a unique aether frame

    • Clocks and rulers moving relative to the aether frame behave as described by the Lorentz transform.

      (This is why we call them “Lorentz transforms”)

  • This “Lorentz Ether Theory” is the first of a class of aether theories that remain valid today (except for quantum phenomena).


Other attempts to fix up aether theories

Other Attempts to “Fix up” Aether Theories

  • Attempts were made to construct theories in which the aether is “dragged” by the earth.

    • Trouble with stellar aberration

    • Trouble with Newton’s third law

    • Trouble with Fizeau’s experiment and general optical and electrical phenomena in media

  • And there were theories in which the aether is not continuous, but is particulate

    • Light propagates similar to sound in air (transverse waves ?!)

    • Aether particles must be “dragged”, so this has the same troubles


Ad hoc aether theories i

Ad Hoc Aether Theories - I

  • From the test theories of SR, one can construct a class of theories specifically crafted to be experimentally indistinguishable from SR.

  • Physical justification is lacking, which is why they are called “ad hoc”.

  • They have two basic properties:

    • There is a unique aether frame in which the one-way speed of light is isotropically c.

    • In any inertial frame, the round-trip speed of light is isotropically c (one-way speed need not be isotropic).

  • Those properties imply the only difference between any of these theories and SR is the way coordinate clocks are synchronized. Clock synchronization is conventional, and cannot possibly affect physical phenomena.


Ad hoc aether theories ii

Ad Hoc Aether Theories - II

  • Within the domain of SR, these ad hoc theories are every bit as valid as is SR.

  • None are refuted experimentally.

  • ALL of the experiments mentioned earlier support these theories just as much as they support SR.

  • In all of these theories, slow clock transport yields Einstein synchronization, not their coordinate synchronization.

  • They make no new predictions, and provide no explanations, so they are irrelevant to modern physics.


General problems aether theories face

General Problems Aether Theories Face

  • There are still the quantum problems that all aether theories face:

    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?

  • To date, no aether theory has seriously addressed these issues. All aether theories are well outside today’s mainstream of physics.


Contents9

Contents

  • A brief overview of experimental tests of SR

    • Michelson and Morley

    • Brillet and Hall

    • Testing the speed of light emitted from moving sources

  • 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

  • A surprise: the aether is not dead, it is just irrelevant

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


Summary and a glimpse ahead

Summary. And a Glimpse Ahead…

Amateurs look for patterns, professionals look at errorbars.

Experimenters:

Measure your systematic errors!


Summary and a glimpse ahead1

Summary. And a Glimpse Ahead…

  • Today SR stands unrefuted experimentally.

  • 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 May Well Violate SR

  • Quantum gravity probably has detailed structure at the Planck scale.

    • Strings ?

    • Topological “defects” ?

    • “Loops” ?

    • Etc. ?

  • Such real structure might 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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