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

From: greywolf42 (mingstb_at_marssim-ss.com)
Date: 01/24/05 

Date: Mon, 24 Jan 2005 21:08:39 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.
>
> 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.

LOL! Well, Tom just trashed all statistical analysis courses. Measurement
theory is designed to measure *values* of observables. Not to test other
theories.

> In this case, this change in outlook of the scientific method is clearly
> required because of a simple observation:

LOL! Tom is requiring abandonment of the scientific method!

> In a hypothetical world in which:
> a) a perfect MMX experiment would yield a truly null result

Tom retreats immediately into a gedanken. Or is it simply allegory?

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

This is simply setting up a straw man. Null result has a definite meaning.
Tom is trying to redefine it.

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

That is simply because Tom first assumed that there was nothing to measure.
And because Tom has now attempted to mislead the audience, by claiming that
statistical fluctuations below the resolution of the instrument are claimed
to be "non-null." This is simply begging the question.

> 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.

And error analysis can also determine whether or not the measurement is
consistent with a theory that predicts a *non-null* result.

But in the experiment, we don't really care what various theories claim.
The observations (data) stand on their own.

> 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?

That is important only to fixated priests, like Tom. If there is a 'signal'
that shows above pure noise or the physical resolution of the instrument, it
exists. Even if we don't (yet) have a theory that predicts that
experimental result.

> 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.

So, get to it, already, Tom! Enough of the preaching and hypotheticals!

> 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.

Yet this is still far more 'data' than modern papers typically include (i.e.
Krisher).

> 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.

Tom, why don't you simply once again admit that you've merely
"guessed" about the physical resolution all these years in the FAQ?

> I have identified three approaches:
> 1. Look into a modern Michelson interferometer and estimate the
> measurement resolution.

What about duplicating the MMX interferometer. Why make this a *different*
interferometer?

> 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.

#3 has nothing to do with the physical resolution of the instrument -- which
doesn't change regardless of how many readings we take. Resolution is not
precision (sigma).

> There are in increasing order of confidence and accuracy.

You've got it backwards, Tom. The best way is to recreate the MMX apparatus
and directly measure the physical resolution. The worst way is to play with
statistics.

> 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.

At the moment, we are discussing how to determine the physical resolution of
the apparatus. But Tom is here simply presupposing that he's going to use
#3. (The first two were provided only as a diversion.) Tom never even
considered looking at the actual apparatus, or at the statements made by
Michelson and Morely.

> 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.

Tom is calling Michelson incompetent! And more modern efforts *did* take
great pains to measure the actual physical resolution. (Miller. But Tom
doesn't like that one, either.)

> Fortunately, the presence of a rather large systematic error in the data
> implies that this statistical independence is reasonably likely[#].

I am presuming that Tom is referring to the apparent drift in the readings
(2 to 5 divisions per minute) as a "large systematic error".

> 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).

Ah, but sigma is not "resolution!" That is the statistical "precision".
The
resolution of the instrument is the minimum values detectable by the device.
It is completely independent of the number of measurements made *with* the
device.

For example, a series of measurements made with a meter stick may reveal an
average with a "sigma" of 5 cm. But the resolution of the meter stick will
still be about 1-2 mm. Tom has simply attempted to define his way out of the
problem.

> [#] During each rotation the reading changed by 15-30 divisions.

At a rotational speed of one turn each 6 minutes (page 339), that is a
change of 2 to 5 divisions per minute. Since "one division means 0.02
wave-length", that is a change of 0.04 to 0.10 wavelength per minute. Or a
total of 0.3 to 0.6 wavelength per rotation.

> This forces the observer to reposition the
> micrometer for each reading.

That *is* the method for taking the reading ... the change in the screw
position for the micrometer.

> 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).

A completely unsupported, and fallacious statement. Correlations are no
more likely if the micrometer is left untouched (because the system is more
stable).

> 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.

Michelson and Morely mention a temperature effect as follows:

"It was found that by keeping the apparatus in slow uniform motion, the
results were much more uniform and consistent than when the stone was
brought to rest, and during this time effects of change of temperature came
into action."

But Tom is correct that M&M aren't very clear what they mean.

> 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".

A linear assumption in no way forces a cyclical variation onto data. What
Tom is alluding to here, is that point 16 is both the start and end location
of each turn of the apparatus -- and is zeroed. However, *true* noise would
have no correlation with position of the apparatus. There would be no
reason for the "noise" to correlate to specific orientations of the table.

And the correct way of addressing the issue is to do a chi squared fit on a
sinusoidal pattern.

> 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".

A complete falsehood by Tom.

> 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.
>
> So this approach yields an estimate of resolution between 0.1 and 0.2
> fringe widths.

Tom in earlier posts claimed 0.1 fringe. But that was before it was pointed
out to him that Miller's results were 0.2 fringe. (So Tom has changed his
standards to try to exclude Miller.) Tom has also championed 0.01 fringe
for Cahill -- simply because Tom "likes" Cahill's conclusion.

But let's stick with Tom's estimate for physical resolution of the
apparatus -- for the purposes of this post. The physical resolution of the
MMX -- according to Tom -- is 0.1 to 0.2 fringes. This is equivalent to 5
to 10 divisions.

Other people might assume a better physical resolution -- or actually
measure it (i.e. like Miller). The results of Tom's analysis are completely
dependent upon his starting assumption (which is different than Tom's
earlier assumptions).

> 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.

That is between 0.1 and 0.2 fringe, so I won't belabor this one.

> 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.

The physical resolution has already been obtained, above. 0.14 fringe
(according to Tom). Variations in actual measurements are merely
statistical error. Better known as 'precision' or 'sigma.'

> 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.

Sic, precision (sigma).

> [In fact for perpendicular arms there is an additional
> 90-degree symmetry, unexploited by all authors including
> me.]

Symmetry is irrelevant in determining statistical variations (precision).

> 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.

I'll take your word for it for the 3.0 division value, below for the moment.

> 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.

Or, the data may simply be sinusoidal on top of random error. :)

> 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

Sic, precision or experimental error.

> of the original measurements is
> sqrt(6) times this value.

Nice try, but no. You cannot determine the variation in the orginal data
from the average value. {You cancel this error, later.}

> So this approach yields an estimate of resolution of 0.15 fringe widths.

This is within the physical resolution range already mentioned. Thus
obviating any of the above manipulations.

> 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

sic, precision (sigma).

> estimate much lower
> than 0.14-0.15 fringe width.

0.06 fringe width, according to your own spread***.

> To compare to the original authors' data table, each row is an average
> of 6 turns,

Clarification: Each value on the table is an average of indifidual readings
made during six separate turns.

> and so should have a resolution

sic, precision (or sigma)

> of 0.14/sqrt(6) = 0.057 fringe width.

You can't determine the precision of the average measurement from the
absolute value of the measurement! However, in this case, your prior error
cancels your former error. And you return yourself to the 0.06 fringe width
given by your spread ***. (Hint: Tom, you are trying too hard.)

> 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.

As would be expected if there were an underlying sinusoidal pattern. ;)

> 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.

How would you know, Tom? You haven't attempted an analysis for a sinusoidal
pattern. You've only done your analysis for an SR zero prediction.

As I noted in the other thread, Tom assumed a zero result, and calcuated the
"sigmas" from zero. But he did not determine a chi-squared fit to a
sinusoidal curve, and then compare the two -- to see which theory was the
'better' fit.

Tom is now claiming that the MMX is both "consistent" with SR (null result)
and "equivocal" with a non-null result. But it can't be both. If it is
"equivocal" for non-null, then it is "equivocal" for SR.

> 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.

The same would be true of a pure sine wave, Tom.

> 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.

No, they simply started with a value that was a factor of 10 smaller than
you started with, Tom.

> They give no indication whatsoever how they arrived at
> this value;

In this, they are no different than you were, Tom. You simply started with
a bald assertion that the physcial resolution *was* between 0.1 and 0.2
fringe.

> certainly the original authors gave no error bars.

In this, they are no different than you were, Tom, in the claims you have
made in the FAQ and many posts on this newsgroup -- where you have admitted
that you simply "guessed" what the resolutions were.

> The above
> estimate of 0.057 fringe is larger than their entire plot, and indicates
> their fit is meaningless.

No, it simply means that Tom's intial estimate of error is different than
C&C's intial estimate of error.

> 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,

But then, neither does Tom, here. Or anywhere else. :)

Tom is afraid to do the chi squared fit for a sinusoid versus a straight
line. Because he can see the wave just as well as anyone else. (Tom, if
you'll send me a copy of your spread***, I'll be happy to do the chi
squared fits for you.)

> and without that and realistic error bars
> their estimates on the errors in their parameters are
> completely bogus.

And so, without a chi-squared test, Tom's estimate on the errors is
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.

But then, there is no reason for them to use Tom's estimate of error. For
Tom used his own (quite arbitrary) values at the beginning of his effort.
We'll need to see C&C's criteria to see what support they have. (Tom has in
the past supported a 0.01 fringe physical resolution for Cahill.)

> 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.

Projection will change only the zero point and the magnitude of the signal.
Not the fundmental shape.

> 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.

Only by Tom's estimate, of course. Tom doesn't mention what Munera claims
for a physical resolution.

> 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
> is basically imposing his hopes and dreams onto the data.

Well, Tom mentioned this in his prosyletising intro, but he's never
supported the claim. He's not even looked at Cahill's data -- at least in
this post.

> 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.

Tom, if you don't *know* the speed and direction of the motion relative to
the aether, then you can't predict anything! Except a sinusoidal shape with
table orientation.

> 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.

Only because Tom assumes a null result. But runs away from doing a chi
squared fit on a sinusoid.

> Conclusion
> ----------
> The recent attempts to "re-analyze" the Michelson Morley
> experiment[1][2] are woefully incomplete, and do not include an accurate
> consideration of the experiment's actual resolution.

Translation: They disagree with Tom.

> 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.

Yes. Lorentz would have a different answer.

> For the ether theory used by the original authors,

Michelson and Morely didn't use an aether theory. They used an absolute
space.

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

Only if you first fudge the numbers, then avoid doing any chi squared
fits -- or actually reading (or addressing) Cahill's paper.

> [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 

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}
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