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IIT 4/27/2006 SR, Aether, and Experiments 1 Special Relativity, the Lumeniferous Aether, and Experiments. Or: The Importance of Errorbars. Tom Roberts.

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Presentation on theme: "IIT 4/27/2006 SR, Aether, and Experiments 1 Special Relativity, the Lumeniferous Aether, and Experiments. Or: The Importance of Errorbars. Tom Roberts."— Presentation transcript:

1 IIT 4/27/2006 SR, Aether, and Experiments 1 Special Relativity, the Lumeniferous Aether, and Experiments. Or: The Importance of Errorbars. Tom Roberts Muons, Inc. Tom Roberts Muons, Inc.

2 IIT 4/27/2006 SR, Aether, and Experiments 2 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.

3 IIT 4/27/2006 SR, Aether, and Experiments 3 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

4 IIT 4/27/2006 SR, Aether, and Experiments 4 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

5 IIT 4/27/2006 SR, Aether, and Experiments 5 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

6 IIT 4/27/2006 SR, Aether, and Experiments 6 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

7 IIT 4/27/2006 SR, Aether, and Experiments 7 Michelson – Morley Experiment (1887) Finicky experiment: ±0.002 °C, mechanical stability ~nm Result: upper limit of 7.5 km/s (earth relative to aether) * Light Source Mirror Beam Splitter Observer Telescope

8 IIT 4/27/2006 SR, Aether, and Experiments 8 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

9 IIT 4/27/2006 SR, Aether, and Experiments 9 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 ) Result: ∆f/f = (1.5±2.5) ∙ => 0.02 km/s (V earth ) Single-Mode Laser Heterodyne Frequency Counter Single-Mode Laser High-Finesse Fabry-Perot Rotating Table

10 IIT 4/27/2006 SR, Aether, and Experiments 10 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

11 IIT 4/27/2006 SR, Aether, and Experiments 11 Speed of Light Emitted by Moving Sources As a simple test theory, assume the observed speed of light is given by V obs = c + k V source with k to be determined by experiment. A test at CERN using π 0 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

12 IIT 4/27/2006 SR, Aether, and Experiments 12 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

13 IIT 4/27/2006 SR, Aether, and Experiments 13 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

14 IIT 4/27/2006 SR, Aether, and Experiments 14 Visibly Superluminal Astronomical Sources There are numerous astronomical objects observed to have visible speeds greater than c. In 1994 GRS 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%.

15 IIT 4/27/2006 SR, Aether, and Experiments 15 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 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 t0t0 t1t1 Earth distance

16 IIT 4/27/2006 SR, Aether, and Experiments 16 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

17 IIT 4/27/2006 SR, Aether, and Experiments 17 Michelson and Morley’s data 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.

18 IIT 4/27/2006 SR, Aether, and Experiments 18 Michelson and Morley’s data Errorbars are from a histogram of the values that were averaged. They are dominated by the systematic error. Noon P.M.

19 IIT 4/27/2006 SR, Aether, and Experiments 19 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

20 IIT 4/27/2006 SR, Aether, and Experiments 20 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. 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

21 IIT 4/27/2006 SR, Aether, and Experiments 21 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°

22 IIT 4/27/2006 SR, Aether, and Experiments 22 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

23 IIT 4/27/2006 SR, Aether, and Experiments 23 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.

24 IIT 4/27/2006 SR, Aether, and Experiments 24 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…

25 IIT 4/27/2006 SR, Aether, and Experiments 25 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.

26 IIT 4/27/2006 SR, Aether, and Experiments 26 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-point DFT Spectrum 320 points 160 freq. bins

27 IIT 4/27/2006 SR, Aether, and Experiments 27 Miller’s Analysis in the Frequency Domain 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 Analysis StepFrequency Domain This averages 320 readings down to just 8 points. This was quite standard in Miller’s day – they did not realize the implications.

28 IIT 4/27/2006 SR, Aether, and Experiments 28 Miller’s Analysis in the Frequency Domain 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! Period ½ turn 8-point DFT Spectrum

29 IIT 4/27/2006 SR, Aether, and Experiments 29 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.

30 IIT 4/27/2006 SR, Aether, and Experiments 30 A New Analysis of Miller’s Data Remarkably, copies of most of Miller’s original data sheets have survived (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.

31 IIT 4/27/2006 SR, Aether, and Experiments 31 Results of New Analysis of Miller’s Data 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. DFT Amplitude with Period ½ Turn

32 IIT 4/27/2006 SR, Aether, and Experiments 32 Results of New Analysis of Miller’s Data For all of the reasonably stable runs the systematic model exactly reproduces the data. The 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…

33 IIT 4/27/2006 SR, Aether, and Experiments 33 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

34 IIT 4/27/2006 SR, Aether, and Experiments 34 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, without the 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.

35 IIT 4/27/2006 SR, Aether, and Experiments 35 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).

36 IIT 4/27/2006 SR, Aether, and Experiments 36 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

37 IIT 4/27/2006 SR, Aether, and Experiments 37 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.

38 IIT 4/27/2006 SR, Aether, and Experiments 38 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.

39 IIT 4/27/2006 SR, Aether, and Experiments 39 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.

40 IIT 4/27/2006 SR, Aether, and Experiments 40 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

41 IIT 4/27/2006 SR, Aether, and Experiments 41 Summary. And a Glimpse Ahead… Amateurs look for patterns, professionals look at errorbars. Experimenters: Measure your systematic errors!

42 IIT 4/27/2006 SR, Aether, and Experiments 42 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…

43 IIT 4/27/2006 SR, Aether, and Experiments 43 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 E Planck Inherently quantum (e.g. Hopf algebras…)


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