Re: An Analysis of the Resolution of the Michelson-Morley Experiment

From: mountain man (hobbit_at_southern_seaweed.com.op)
Date: 01/27/05 

Date: Thu, 27 Jan 2005 02:41:39 GMT

"Tom Roberts" <tjroberts@lucent.com> wrote in message
news:x1TId.8807$ZV4.7443@newssvr31.news.prodigy.com...
> Title: An Analysis of the Resolution of the Michelson-Morley
> Experiment
> Author: Tom Roberts, tjroberts@lucent.com
> Date: January 23, 2005
>
>
> Introduction
> ------------
>
> There have been several recent attempts to re-analyze the original
> Michelson Morley experiment [1][2]. Cahill[3] has interpreted these
> re-analyses as supporting his theory.

Data from 7 experiments have been re-analysed, not just the MMX.

> Unfortunately, none of these authors understand error analysis, and thus
> do not know how silly their analyses actually are. Their basic problem
> is that they, like the original authors, attempt to interpret this
> experiment as "measuring the velocity of the earth relative to the
> lumeniferous ether". While that was a reasonable approach in 1887, today
> it is completely ludicrous -- not because of the mention of "ether", but
> because today we use experiments like this to _test_theories_, not to
> try to make "measurements" on concepts contained in some particular
> theory.

What was measured was the velocity of the apparatus. It does not follow
and has not been claimed by Cahill, that this was with respect to an aether.
The data from seven experiments is consistent with a speed of some
420 +/-30km/s in a direction RA=5.2hr, Dec=-67deg

> In this case, this change in outlook of the scientific method is clearly
> required because of a simple observation:
> In a hypothetical world in which:
> a) a perfect MMX experiment would yield a truly null result
> and

All gas-mode MMX experiments show rotation-induced fringe shifts.
To talk of a hypothetical world where Roberts knows that these experiments
would be null is not science.

> b) real measurements are subject to measurement errors
> it is statistically highly unlikely that a real MMX measurement will
> yield a null result.

Miller did an MMX experiment with 20,000 rotations with a much larger
apparatus, and in 4 months of the year. That data, in the form of 20
rotations
per A4 page, is now available in 1000 A4 pages. Various people have that
data,
and some have put it into electronic files. The results from that agree
with those from the 1991 coaxial cable experiment by DeWitte. He used
1.5 km of buried coax, and 6 cesium atomic clocks to measure the change in
travel
time of RF signal as the earth rotated. The MMX experiment is being repeated
with high precision resonant cavity techniques,but with a gas in the
cavities.
Vacuum cavity experiments are incapable of detecting absolute motion.

>In such a hypothetical world, of course, the
> non-null result is induced purely by the measurement errors.

How does one know that. Why would two different techniques, namely
M interf and coax cables give the same result?

> But
> with an error analysis of the measurement, it can be determined
> whether or not the measurement is consistent with a theory that
> predicts a null result.
>
> So when Munera[1] repeatedly proclaims "this is a non-null result" for
> various experiments, he is repeating a fundamental error -- sure the
> measurements can be interpreted as a non-null result, but the important
> question is: are they _consistent_ with the predictions of a given
> theory?

Nonsense. Observational data can exist and be reliable.
Of course to interpret that data one needs a theory.

>As we will see below, the actual MMX data are consistent with
> the predictions of SR, and with a wide range of theories in which the
> earth moves relative to the ether.

The postulates of SR, as distinct from the relativistic effects, are in
disagreement with the data. It is now clear that it is the Lorentzian
interpretation that is in agreement with the data.

> Michelson and Morley's data are given, in a reduced form, in their 1887
> paper[4]. The above attempts at analysis are based on the data in the
> table on page 340 of [4]. Unfortunately these data are not the original
> readings, but each row is an average over 6 turns of the interferometer
> made over approximately 36 minutes. Note I am discussing only the six
> rows for their six runs, not any of the rows containing means.
>
> In performing an analysis on an experiment performed long ago, with only
> limited access to the data and no access to the apparatus, we are
> limited in our ability to determine the experiment's actual resolution.
> I have identified three approaches:
> 1. Look into a modern Michelson interferometer and estimate the
> measurement resolution.
> 2. Use the original authors' statements to infer their resolution.
> 3. Use the original authors' data in a statistical analysis of the
> resolution displayed by the actual data.
> There are in increasing order of confidence and accuracy.
>
> Note that it is important to refer to the actual measurements, and not
> to averages. Unfortunately, the available data are averages over 6 turns
> of the interferometer, not the original readings. So I will assume that
> the errors in the individual measurements are uncorrelated, and normally
> distributed. While such an assumption is undesirable, the available data
> essentially force it -- a competent modern repetition of this experiment
> would take pains to accurately measure the actual resolutions.
> Fortunately, the presence of a rather large systematic error in the data
> implies that this statistical independence is reasonably likely[#]. In
> keeping with the assumption of normal errors and with modern practice,
> when I discuss "resolution", I mean the sigma of the associated normal
> distribution for the original measurement (in this experiment the
> location of a fringe).
>
> [#] During each rotation the reading changed by 15-30
> divisions. This forces the observer to reposition the
> micrometer for each reading. While statistical independence
> is not assured, it is clearly more likely for a system in
> which the micrometer is repositioned for each reading than
> for a system without the systematic error where the readings
> vary by so little that it would be easy for the observer to
> simply leave the micrometer untouched (thus inducing an
> enormous correlation among readings).
>
>
> When you plot the data given in the table of [4] for each day, it is
> quite apparent that there is a large systematic error that dominates the
> measurements -- the measurements at mark 16 before and after the turn
> are not equal. In fact, for each of the six runs the difference in the
> two marker-16 values is larger than the variations among the other
> readings. The authors [4][1][2] all subtract off an assumed linear
> dependence of this systematic error, and the original authors [4]
> mention a "temperature effect". Given the limited availability of
> original data, this is the best one can do, and I will do likewise.
>
> Note, however, that this analysis technique _forces_ the data to be
> cyclical. That is, the above subtraction ensures that at the beginning
> and end of each turn the value will be exactly zero; any non-zero
> measurement in between will naturally appear to be "cyclical". Given
> non-zero resolution and independent measurements, there will be non-zero
> measurements in between. So claims that somehow the "cyclical nature" of
> the results implies or supports the "motion of the earth relative to the
> ether" are bogus -- _any_ such data will be "cyclical".

Look at the Miller data. There is data from 20,000 rotations.
Work out the speed and direction. Then make a prediction,
based on the Miller data, as to what MM should have seen.

You will find a good agreement, but of course not perfect.
Some of the rotations look very noisy. Others are in remarkable
agreement. So we can see that MM were seeing a real effect.

MM rejected their own data not because it did not produce the
expected form, but because it did not agree with the Newtonian
theory for the interferometer. Based on that theory and the
minimal speed of 30 km/s, from the orbital speed of the earth,
they expected fringe shifts of a certain size.

The actual fringe shifts were much smaller, but were seen.
This is what happens when you judge an experiment by what
you expect to see, and not what is actually seen. The
interpretation that experimentalists put on their data may be
of anecdotal interest, but is certainly not a part of science.

> Lets' look at the above three estimates of Michelson and Morley's actual
> measurement resolution:
>
> 1. Look into a modern Michelson interferometer
> ----------------------------------------------
> I believe that anyone who has ever done so will agree that
> a) it is fairly easy to note the location of a fringe to within
> about 1/5 of a fringe width
> b) it is unlikely to be able to locate fringes to better than
> 1/10 of a fringe width
> Basically the fringes do not have sharp edges, and one must inherently
> guess where the center of a fringe is.

This is nonsense. Read Miller's paper about accuracy.

> So this approach yields an estimate of resolution between 0.1 and 0.2
> fringe widths.
>
>
> 2. Use the original author's statements to infer their resolution
> -----------------------------------------------------------------
> Michelson and Morley[4] state "The width of the fringes varied between
> 40 to 60 divisions, the mean value being near 50[...]". In keeping with
> the assumption that the measurement errors are normally distributed,
> I'll assume that this means that 95% of measurements of fringe widths
> were contained in the interval from 40 to 60 divisions of their
> micrometer. That means their resolution for measuring fringe width is 5
> divisions, or 0.1 fringe. As the measurement of a fringe width requires
> two measurements of the location of a fringe, their base resolution is
> sqrt(2) time this.
>
> So this approach yields an estimate of resolution of 0.14 fringe widths.
>
>
> 3. A statistical analysis of the resolution displayed in the data
> -----------------------------------------------------------------
> The key to doing this is to find instances in the data where they
> measured the same value multiple times; then a histogram of the multiple
> measurements will give a distribution of the errors, and the resolution
> can be obtained from the distribution.
>
> In an idealized Michelson interferometer, the interfering light rays
> travel both directions along each path, so there is exact 180 degree
> symmetry. In the actual apparatus, the ray paths are indeed
> out-and-back, so this symmetry should apply to the measurements. The
> original authors applied this symmetry in their analysis. Here we will
> use it to estimate their resolution.
>
> [In fact for perpendicular arms there is an additional
> 90-degree symmetry, unexploited by all authors including
> me.]
>
> The idea is to first subtract the linear systematic from each of the six
> rows of data, thus forcing the two measurements at mark 16 to be equal
> for each run. Then histogram the eight differences for measurements 180
> degrees apart, for all six rows, and determine the resolution of the
> measurement from the histogram. This was done in an Excel spread***,
> but it is not feasible to display the details in this ASCII medium. The
> histogram does not look very Gaussian, but is rather flat between -5 and
> +7 divisions. The likely source of this non-Gaussian behavior is the
> systematic error that was _assumed_ to be linear, and nonlinearities due
> to either non-uniform behavior or non-uniform spacing of the
> measurements could cause this. The sigma of the histogram is 3.0
> divisions, corresponding to 0.060 fringe widths; as each point is an
> average of 6 turns, the resolution of the original measurements is
> sqrt(6) times this value.
>
> So this approach yields an estimate of resolution of 0.15 fringe widths.
>
>
> Discussion
> ----------
> None of the above estimates are particularly compelling, mainly because
> the histogram of method 3 is not really Gaussian; this does not destroy
> that approach, but makes it less compelling that it would be with
> Gausssian errors. But their agreement indicates they are not crazy.
> Certainly there is no support for any resolution estimate much lower
> than 0.14-0.15 fringe width.
>
> To compare to the original authors' data table, each row is an average
> of 6 turns, and so should have a resolution of 0.14/sqrt(6) = 0.057
> fringe width. After subtracting the assumed-linear systematic from the 6
> rows, the largest deviation from zero is 0.132 fringe widths, or 2.3
> sigma; of the 96 data points, only 1 point exceeds 2 sigma, and 11
> exceed 1 sigma. Clearly the readings are not Gaussian distributed. But
> equally clearly they are consistent with a null result, and provide only
> equivocal support for the notion that there is a non-null result.
>
> Interestingly, when one histograms the data with the assumed-linear
> systematic subtracted, the deviations from zero are roughly Gaussian
> distributed with a mean of -0.01 fringe and a sigma for individual
> measurements of 0.1 fringe. While this is _not_ an error plot, when
> compared to the above resolution estimates it solidly demonstrates that
> the measurements are consistent with the hypothesis of a truly null
> result.
>
>
> When Consoli and Costanzo [2] display a graph of the July 9 PM data,
> they drew error bars approximately 0.005 fringe -- more than a factor of
> ten too small. They give no indication whatsoever how they arrived at
> this value; certainly the original authors gave no error bars. The above
> estimate of 0.057 fringe is larger than their entire plot, and indicates
> their fit is meaningless. Their fit has 10 parameters for 16 data
> points, so it is not surprising that they can draw a line through most
> of the points, even with tiny error bars. They do not mention any
> chi-squared tests for goodness of fit, and without that and realistic
> error bars their estimates on the errors in their parameters are
> completely bogus. It is clear that with the above error estimate a
> zero-parameter flat line fits the data as well as their 10-parameter
> Fourier decomposition.
>
> Munera[1] correctly points out that for a velocity relative to the ether
> the MMX only displays the projection of the velocity vector onto the
> plane of the interferometer, and this implies that it is unlikely that
> such a signal will be a pure cosine. He goes on to claim that even the
> intra-session average of 6 turns is invalid as during 36 minutes there
> is a change in this projection. While true, that is not important,
> as his values show it changes by at most ten percent -- this is wildly
> exceeded by the resolution of the measurement.
>
> Cahill[3] has interpreted this as a positive observation of motion
> relative to his ether, with a value consistent with the CMBR dipole=0
> frame. As mentioned above, he is performing an invalid comparison, and

You are referring to the Cahill and Kitto paper.
There the speed was noted to be comparable to
the CMB speed, but the direction was not indicated.

Subsequently, in numerous papers by Cahill, it
became clear that the direction was almost
perpendicular to the CMB direction.

Also, get it right please Roberts, Cahill has never
referred to prefered frame as the aether.

> is basically imposing his hopes and dreams onto the data. A proper
> analysis would take his formulas with an unknown speed and direction of
> motion relative to the ether, and _predict_ the results of the
> measurement.

This has been done in great detail in Cahill, Apeiron 11,
No. 1, 2004, pp.53-111, for the Miller data. One can
then determine a best speed and direction from a least
squares fit.

The speed then comes out to be 420+/-30 km/s.

> Presumably this could then determine the speed and
> direction of that motion. Had he done so, it is clear that with the
> above resolution estimate his formula would fit the data for any speed
> between zero and several thousand km/s and any direction whatsoever.
>
>
> Conclusion
> ----------
> The recent attempts to "re-analyze" the Michelson Morley
> experiment[1][2] are woefully incomplete, and do not include an accurate

The main data on absolute motion is Miller.
Would Roberts please analyse that data
and report back.

> consideration of the experiment's actual resolution. If considered as a
> measurement of the motion of the earth relative to some ether, the value
> depends upon the details of the theory used to model such motion. For
> the ether theory used by the original authors, an upper limit of 5 km/s
> is appropriate, but might be reduced by a careful modern analysis. For
> Cahill's theory an upper limit of several thousand km/s is appropriate.

This is incorrect. See above results from analysis of Miller data.
The results of all seven experiments were never null.

The small value from MMX was because they used an invalid
theory. Why does Roberts use the Newtonian theory to get a
speed of 5km/s?, and then claims that this supports his case for
SR. In analysing an experiment one must use one theory
throughout the analysis., and not swap back and forwards to
suit the desired outcome.

The relativistic effects must be used in the theory for the
apparatus, in particular the Fitzgerald-Lorentz contraction effect.
As well the gas has an important role. Without that the other
effects cancel. The relativistic effects are real.

The spacetime ontology is invalidated by experiment. What needs
to be done is to reassess all the data in respect of the Lorentzian
interpretation of these relativistic effects.

It looks like Lorentz got it right long ago.

> In any case, the experiment is indeed solidly consistent with the
> prediction of SR -- a null result.

To summarise by repetition ... the postulates of SR, as distinct
from the relativistic effects, are in disagreement with the data.

It is now clear that it is the Lorentzian interpretation that is in
agreement with the data.

> [1] H.Munera, APEIRON _5_ (1998), p37.
> [2] Consoli and Costanzo, http://arxiv.org/abs/astro-ph/0311576
> [3] Cahill, http://arxiv.org/abs/physics/0501051
> Cahill and Kitto, http://arxiv.org/abs/physics/0205070
> [4] Michelson and Morley, Am. J. Sci., _XXXIV_ (1887), p333.
> http://www.aip.org/history/gap/PDF/michelson.pdf

Have a nice day, 

-- 
Pete Brown
Falls Creek
OZ
www.mountainman.com.au/process_physics
Quantcast