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| Bruce Richmond... |
 Posted: Sun Oct 04, 2009 3:22 pm |
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Hi Tom,
When discussing Miller's experiments you said that one of his problems
involved averaging. Averaging does not increase the accuracy of a
measurement. I was just wondering how that applies to something like
the satellite measurement of sea level.
http://sealevel.jpl.nasa.gov/technology/technology.html
The two parts of the measurement are to measure the height of the
satellite above the earth's surface (accurate to 2-3 centimeters) and
the measurement of the distance from the satellite to the surface of
the sea directly below it (accurate to 3-4 centimeters). By
subtraction they claim to have a measurement that is accurate to
within 4-5 centimeters.
Seems to me that the errors could combine so it is in fact only
accurate to within 5-7 centimeters. Also they claim, "By averaging
the few-hundred thousand measurements collected by the satellite in
the time it takes to cover the global oceans (10 days), global mean
sea level can be determined with a precision of several millimeters."
How does this work if we apply error bars to the original data? Would
the measurement of a 2mm rise in sea level a year later be considered
significant?
Thanks, Bruce |
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| Tom Roberts... |
| Posted: Tue Oct 06, 2009 3:08 pm |
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Bruce Richmond wrote:
[quote:d8bdf22a03]When discussing Miller's experiments you said that one of his problems
involved averaging.
[/quote:d8bdf22a03]
The problem is not averaging per se, but rather in assuming that averaging does
things that averaging cannot do. In particular, averaging does NOT project out
the signal he wanted.
[quote:d8bdf22a03]Averaging does not increase the accuracy of a
measurement.
[/quote:d8bdf22a03]
No. But in many common cases where one can make multiple STATISTICALLY
INDEPENDENT measurements of a SINGLE quantity, then the average of those
measurements gives a better estimate of the quantity's true value than does any
individual measurement. Moreover, the variance of the measurements gives
information about how accurately that average is determined. This is the
underlying basis for error analysis.
[quote:d8bdf22a03]I was just wondering how that applies to something like
the satellite measurement of sea level.
http://sealevel.jpl.nasa.gov/technology/technology.html
The two parts of the measurement are to measure the height of the
satellite above the earth's surface (accurate to 2-3 centimeters) and
the measurement of the distance from the satellite to the surface of
the sea directly below it (accurate to 3-4 centimeters). By
subtraction they claim to have a measurement that is accurate to
within 4-5 centimeters.
[/quote:d8bdf22a03]
Those appear to me to be statistically independent measurements, because they
are based on completely different technologies. I'll assume that, and also that
the quoted accuracies are the sigmas of the underlying distributions of the
individual measurements (probably a good assumption, as this is standard practice).
[I'm ignoring the obvious problem of resolving individual
waves; I assume they handled it in a reasonable manner.]
Given two measurements: a +- sigma_a, and b +- sigma_b, with statistically
independent normally distributed errors, their difference is:
(a-b) +- sqrt(sigma_a^2+sigma_b^2)
which is consistent with the statements on that website. In short, when the
conditions are satisfied, the errorbars add in quadrature. As those guys
presumably are competent, they surely know this and also know that the
conditions are satisfied.
One can understand this, remembering that the statistical
model is that a and b are individually sampled from random
values normally distributed around their true values. For
the measurement in which a happens to be at the top of its
range, b is not likely to also be at the top of its range.
Work it out for all combinations, and one gets the above
formula. Note that for this to be valid a and b MUST be
normally distributed, and they MUST be statistically
independent.
BTW the sigma of (a+b) is the same as that of (a-b).
Here's how errorbars work for the mean of multiple measurements:
Given a set of N measurements {m_i} of a SINGLE quantity, with the measurements
being STATISTICALLY INDEPENDENT, one can compute their mean and sigma:
mean = (1/N) sum_i{ m_i }
sigma = sqrt( (1/N) sum_i{ (m_i - mean)^2 } )
When one considers the mean to be the best estimate of the true value, one
assigns an errorbar:
mean +- sigma/sqrt(N-1)
Exercise for the reader: derive this from the above formula
for the sigma of the sum of a and b. You'll also need the fact
that given a +- sigma_a, multiplying by a constant K gives
K*a +- K*sigma_a. Hint: the hard part is the "-1", so first
do without it. You'll need to look more deeply into this in
order to understand the "-1".
This all comes from the central limit theorem of statistics, and REQUIRES that
the measurements be statistically independent, and that N be large enough so the
mean is normally distributed. In practice, it is often the case that N as low as
5 works well.
Note I have not discussed systematic errors, which behave
in a VERY different manner, and there is no general theory
to apply to them; that's why each experiment or measurement
needs its own error analysis.
For Miller's data, surfer keeps attempting to apply these formulas in situations
where the conditions for their validity are not satisfied. In particular, after
a DSP filter the data points are NOT statistically independent, their errors are
NOT normally distributed, and the errorbars surfer claims are wrong. By HUGE
factors.
Tom Roberts |
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| Bruce Richmond... |
| Posted: Tue Oct 06, 2009 3:35 pm |
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On Oct 6, 5:08 pm, Tom Roberts <tjrob... at (no spam) sbcglobal.net> wrote:
[quote:1313f4c3c8]Bruce Richmond wrote:
When discussing Miller's experiments you said that one of his problems
involved averaging.
The problem is not averaging per se, but rather in assuming that averaging does
things that averaging cannot do. In particular, averaging does NOT project out
the signal he wanted.
Averaging does not increase the accuracy of a
measurement.
No. But in many common cases where one can make multiple STATISTICALLY
INDEPENDENT measurements of a SINGLE quantity, then the average of those
measurements gives a better estimate of the quantity's true value than does any
individual measurement. Moreover, the variance of the measurements gives
information about how accurately that average is determined. This is the
underlying basis for error analysis.
I was just wondering how that applies to something like
the satellite measurement of sea level.
http://sealevel.jpl.nasa.gov/technology/technology.html
The two parts of the measurement are to measure the height of the
satellite above the earth's surface (accurate to 2-3 centimeters) and
the measurement of the distance from the satellite to the surface of
the sea directly below it (accurate to 3-4 centimeters). By
subtraction they claim to have a measurement that is accurate to
within 4-5 centimeters.
Those appear to me to be statistically independent measurements, because they
are based on completely different technologies. I'll assume that, and also that
the quoted accuracies are the sigmas of the underlying distributions of the
individual measurements (probably a good assumption, as this is standard practice).
[I'm ignoring the obvious problem of resolving individual
waves; I assume they handled it in a reasonable manner..]
Given two measurements: a +- sigma_a, and b +- sigma_b, with statistically
independent normally distributed errors, their difference is:
(a-b) +- sqrt(sigma_a^2+sigma_b^2)
which is consistent with the statements on that website. In short, when the
conditions are satisfied, the errorbars add in quadrature. As those guys
presumably are competent, they surely know this and also know that the
conditions are satisfied.
One can understand this, remembering that the statistical
model is that a and b are individually sampled from random
values normally distributed around their true values. For
the measurement in which a happens to be at the top of its
range, b is not likely to also be at the top of its range..
Work it out for all combinations, and one gets the above
formula. Note that for this to be valid a and b MUST be
normally distributed, and they MUST be statistically
independent.
BTW the sigma of (a+b) is the same as that of (a-b).
Here's how errorbars work for the mean of multiple measurements:
Given a set of N measurements {m_i} of a SINGLE quantity, with the measurements
being STATISTICALLY INDEPENDENT, one can compute their mean and sigma:
mean = (1/N) sum_i{ m_i }
sigma = sqrt( (1/N) sum_i{ (m_i - mean)^2 } )
When one considers the mean to be the best estimate of the true value, one
assigns an errorbar:
mean +- sigma/sqrt(N-1)
Exercise for the reader: derive this from the above formula
for the sigma of the sum of a and b. You'll also need the fact
that given a +- sigma_a, multiplying by a constant K gives
K*a +- K*sigma_a. Hint: the hard part is the "-1", so first
do without it. You'll need to look more deeply into this in
order to understand the "-1".
This all comes from the central limit theorem of statistics, and REQUIRES that
the measurements be statistically independent, and that N be large enough so the
mean is normally distributed. In practice, it is often the case that N as low as
5 works well.
Note I have not discussed systematic errors, which behave
in a VERY different manner, and there is no general theory
to apply to them; that's why each experiment or measurement
needs its own error analysis.
For Miller's data, surfer keeps attempting to apply these formulas in situations
where the conditions for their validity are not satisfied. In particular, after
a DSP filter the data points are NOT statistically independent, their errors are
NOT normally distributed, and the errorbars surfer claims are wrong. By HUGE
factors.
Tom Roberts
[/quote:1313f4c3c8]
Thank you for the thorough answer.
Bruce |
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| Surfer... |
| Posted: Wed Oct 07, 2009 9:24 am |
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On Tue, 06 Oct 2009 16:08:01 -0500, Tom Roberts
<tjrob137 at (no spam) sbcglobal.net> wrote:
[quote:a8c0404bed]
For Miller's data, surfer keeps attempting to apply these formulas in situations
where the conditions for their validity are not satisfied.
I disagree.[/quote:a8c0404bed]
As Miller's data is periodic, passing it through a DSP filter is
similar to passing signals from an antenna through a tuning circuit
(which these days could very well be a DSP filter).
Tuning circuits and DSP filters are very effective at removing noise
OUTSIDE the band of frequencies used to pass the selected signal.
They don't adversely affect the selected signal, provided the
bandwidth is sufficient to contain all the signal components.
For Miller's signal that would be the case because his signal is only
modulated by very low frequencies (such as the earth rotation effect).
That allows us two choices.
1) We can calculate errorbars from the raw data containing signal,
plus noise components of a FULL RANGE of frequencies, or,
2) We can calculate errorbars from the filtered data containing
signal, plus noise components of only a NARROW RANGE of frequencies
passed by the filter.
You prefer the former and get error bars that are larger than the
signal.
I prefer the latter and get error bars that are smaller than the
signal.
Surfer |
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| Surfer... |
| Posted: Wed Oct 07, 2009 10:30 am |
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On Thu, 08 Oct 2009 01:42:56 +1030, Surfer <no at (no spam) spam.net> wrote:
[quote:d95c20d34f]
As Miller's data is periodic,
That should of course be "As the signal in Miller's data is[/quote:d95c20d34f]
periodic...."
Surfer |
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| Tom Roberts... |
| Posted: Thu Oct 08, 2009 8:21 pm |
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Surfer wrote:
[quote:965b1b8bae]On Tue, 06 Oct 2009 16:08:01 -0500, Tom Roberts
tjrob137 at (no spam) sbcglobal.net> wrote:
For Miller's data, surfer keeps attempting to apply these formulas in situations
where the conditions for their validity are not satisfied.
As Miller's data is periodic, passing it through a DSP filter is
similar to passing signals from an antenna through a tuning circuit
(which these days could very well be a DSP filter).
[/quote:965b1b8bae]
But you don't account for the effect on the errorbars of such a filter.
[quote:965b1b8bae]They don't adversely affect the selected signal, provided the
bandwidth is sufficient to contain all the signal components.
[/quote:965b1b8bae]
If you understood error analysis, you would know that the errorbars can
be affected differently from the "signal".
Another aspect you don't understand is that while you can indeed find a
non-zero amplitude for a period 1/2-turn sinusoid, you have no way to
demonstrate that it is of cosmic origin, and is not simply an aspect of
the ENORMOUS background.
My analysis, on the other hand, shows that the orientation-dependent
component of Miller's data is zero, with an errorbar SMALLER than the
false "signal" that Miller found.
[quote:965b1b8bae]You prefer [...]
I prefer [...]
[/quote:965b1b8bae]
This is not about "preferences", this is about what an accurate and
comprehensive error analysis _IS_. You simply do not understand the
subject, and your opinions and "preferences" are useless.
Tom Roberts |
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| Surfer... |
| Posted: Fri Oct 09, 2009 11:58 am |
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On Thu, 08 Oct 2009 21:21:03 -0500, Tom Roberts
<tjroberts137 at (no spam) sbcglobal.net> wrote:
[quote:3375f188cf]
But you don't account for the effect on the errorbars of such a filter.
Yes I do. The filter removes noise OUTSIDE the band of frequencies[/quote:3375f188cf]
used to pass the signal. The errorbars are therefore greatly reduced
by the filter, as calculated here:
http://miller.0catch.com/DSP/
[quote:3375f188cf]
If you understood error analysis, you would know that the errorbars can
be affected differently from the "signal".
Of course they are affected differently. The signal is PASSED[/quote:3375f188cf]
approximately as is and the errorbars are greatly REDUCED !
(IOW signal to noise ratio is greatly increased !)
[quote:3375f188cf]
Another aspect you don't understand is that while you can indeed find a
non-zero amplitude for a period 1/2-turn sinusoid, you have no way to
demonstrate that it is of cosmic origin, and is not simply an aspect of
the ENORMOUS background.
That can be demonstrated by confirming that the signal is[/quote:3375f188cf]
appropriately modulated by earth rotation and earth orbit effects.
Miller showed that was the case in his 1933 paper:
The Ether-Drift Experiment and the Determination of the Absolute
Motion of the Earth
http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf
[quote:3375f188cf]
My analysis, on the other hand, shows that the orientation-dependent
component of Miller's data is zero, with an errorbar SMALLER than the
false "signal" that Miller found.
Your analysis is essentially a straw man argument in that your error[/quote:3375f188cf]
bars are calculated from raw data and so include noise OUTSIDE the
band of frequencies that are passed by Miller's algorithm.
Miller's algorthm produces essentially the SAME output as the DSP
filter, as shown here.
http://miller.0catch.com/DSP/HTMLFiles/index_32.gif
Surfer |
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| Dirk Van de moortel... |
| Posted: Fri Oct 09, 2009 4:10 pm |
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Surfer <no at (no spam) spam.net> wrote in message
9htuc55927mvuja3delqs24ojobt2p0mur at (no spam) 4ax.com
[quote:ce5b15a7b2]On Thu, 08 Oct 2009 21:21:03 -0500, Tom Roberts
tjroberts137 at (no spam) sbcglobal.net> wrote:
[/quote:ce5b15a7b2]
[snip the usual]
[quote:ce5b15a7b2]My analysis, on the other hand, shows that the orientation-dependent
component of Miller's data is zero, with an errorbar SMALLER than the
false "signal" that Miller found.
Your analysis is essentially a straw man argument
[/quote:ce5b15a7b2]
Cahill, to a crow, *everyone* looks like a straw man.
Dirk Vdm |
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| Tom Roberts... |
| Posted: Fri Oct 09, 2009 8:34 pm |
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Surfer wrote:
[quote:6ad748a45f]On Thu, 08 Oct 2009 21:21:03 -0500, Tom Roberts
tjroberts137 at (no spam) sbcglobal.net> wrote:
But you don't account for the effect on the errorbars of such a filter.
Yes I do. The filter removes noise OUTSIDE the band of frequencies
used to pass the signal.
[/quote:6ad748a45f]
The errorbars indicate how well the "signal" is measured. No matter what
you do, you must come to grips with the FACT that for that 0.062 fringe
"signal" the original measurements varied by almost 6.000 fringes at
EACH ORIENTATION. So the ORIENTATION-DEPENDENT part must be 100 times
smaller than the variation in the measurements. THAT is what errorbars
represent, not how well any particular filter can discard unwanted
frequency bands.
[quote:6ad748a45f]The errorbars are therefore greatly reduced
by the filter, as calculated here:
http://miller.0catch.com/DSP/
[/quote:6ad748a45f]
No, they are not. You are wrong. That is NOT what errorbars represent.
Tom Roberts |
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| Surfer... |
| Posted: Sat Oct 10, 2009 10:12 am |
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On Fri, 09 Oct 2009 21:34:26 -0500, Tom Roberts
<tjroberts137 at (no spam) sbcglobal.net> wrote:
[quote:563b7d00e0]
The errorbars indicate how well the "signal" is measured. No matter what
you do, you must come to grips with the FACT that for that 0.062 fringe
"signal" the original measurements varied by almost 6.000 fringes at
EACH ORIENTATION.
Provided the variations lie outside the filter frequency band used to[/quote:563b7d00e0]
pass the signal, it doesn't really matter how large they are.
What is more important is whether or not the final signal is
appropriately modulated by earth rotation and orbit effects.
To determine that, Miller only needed to know how signal amplitude and
phase varied with time. He did not need to know the fringe shifts at
each orientation.
Surfer |
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| eric gisse... |
| Posted: Sun Oct 11, 2009 12:50 am |
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Surfer wrote:
[quote:4537dba700]On Fri, 09 Oct 2009 21:34:26 -0500, Tom Roberts
tjroberts137 at (no spam) sbcglobal.net> wrote:
The errorbars indicate how well the "signal" is measured. No matter what
you do, you must come to grips with the FACT that for that 0.062 fringe
"signal" the original measurements varied by almost 6.000 fringes at
EACH ORIENTATION.
Provided the variations lie outside the filter frequency band used to
pass the signal, it doesn't really matter how large they are.
What is more important is whether or not the final signal is
appropriately modulated by earth rotation and orbit effects.
To determine that, Miller only needed to know how signal amplitude and
phase varied with time. He did not need to know the fringe shifts at
each orientation.
[/quote:4537dba700]
NOBODY - LEAST OF ALL MILLER OR YOU - KNOWS HOW THE TRANSIENT TEMPERATURE
EFFECTS BEHAVED AS A FUNCTION OF TIME. FUCK.
Same stupid fucking argument over and over.
[quote:4537dba700]
Surfer[/quote:4537dba700] |
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| Tom Roberts... |
| Posted: Sun Oct 11, 2009 10:22 am |
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eric gisse wrote:
[quote:6004ac3e74]NOBODY - LEAST OF ALL MILLER OR YOU - KNOWS HOW THE TRANSIENT TEMPERATURE
EFFECTS BEHAVED AS A FUNCTION OF TIME.
[/quote:6004ac3e74]
Actually, I do -- Miller measured it (without realizing it). Look in
section IV of my paper where I remove any orientation-dependent
component from one of Miller's runs and display the pure time
dependence: Fig. 10 shows the time-dependent variations for each
orientation of his apparatus, using the run in Fig. 1. So this plot
includes not just temperature effects, it has all
non-orientation-dependent effects. That is, ALL backgrounds.
I did this for 67 of Miller's runs. Of those, the 53 which are stable
enough so my background model is valid give the same answer: the
time-dependent component is equal to the original data. So there is no
orientation-dependent signal at all. The errorbar on any
orientation-dependent signal with period 1/2-turn is smaller than the
false "signal" that Miller found.
Unlike surfer's erroneous computation of errorbars
after a DSP filter, my analysis uses such a filter
in a VALID way to obtain the desired errorbar. In
particular the errorbar is determined in the usual
way by an increase of 1 in the chisq of the fit.
Read the paper for how that is projected onto the
period 1/2-turn signal bin.
Also unlike surfer's nonsense, this approach EXPLICITLY computes the
value and errorbar of the ORIENTATION-DEPENDENT signal. There's no need
to ask whether the result is due to a time-dependent background that
happens to have the right period. Surfer has no way to distinguish
between orientation dependence and time dependence (other than hopes,
dreams, and personal prejudices).
Tom Roberts |
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| Surfer... |
| Posted: Sun Oct 11, 2009 12:37 pm |
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On Sun, 11 Oct 2009 11:22:06 -0500, Tom Roberts
<tjroberts137 at (no spam) sbcglobal.net> wrote:
[quote:8717247ae9]Surfer has no way to distinguish
between orientation dependence and time dependence (other than hopes,
dreams, and personal prejudices).
The output from the DSP filter is a signal with a period of half a[/quote:8717247ae9]
turn. The phase of the signal is orientation dependent wrt the
interferometer.
The amplitude of the signal is modulated by the earth rotation effect.
The envelope of the waveform for that has a period of one sideral day,
and the phase of the envelope is orientation dependent wrt to the
celestial sphere.
The amplitude is also modulated by the earth orbit effect.
The envelope of the waveform for that has a period of one year.
Such different periods allow the effects to be readily distinguished,
allowing Miller to quite accurately calculate speed and direction for
absolute motion.
Figure 23 in his paper
http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf
shows he was able to calculate the direction in two different ways,
namely,
- Apex from magnitude, and,
- Apex from azimuth
and that the two ways gave consistent results.
Surfer |
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| eric gisse... |
| Posted: Sun Oct 11, 2009 12:52 pm |
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Tom Roberts wrote:
[...]
[quote:a68811420e]Unlike surfer's erroneous computation of errorbars
after a DSP filter, my analysis uses such a filter
in a VALID way to obtain the desired errorbar. In
particular the errorbar is determined in the usual
way by an increase of 1 in the chisq of the fit.
Read the paper for how that is projected onto the
period 1/2-turn signal bin.
[/quote:a68811420e]
This is the part of the process that I find exceptionally dishonest on
Surfer's part.
He makes assumptions about the noise background, and then thinks he can use
signal processing tricks to find a "signal". When cornered, he brings out
the "lock in amplifier" non-sequitur response. I haven't seen his reply to
your message yet but I figure there's a 50% shot that it is in there.
[quote:a68811420e]
Also unlike surfer's nonsense, this approach EXPLICITLY computes the
value and errorbar of the ORIENTATION-DEPENDENT signal. There's no need
to ask whether the result is due to a time-dependent background that
happens to have the right period. Surfer has no way to distinguish
between orientation dependence and time dependence (other than hopes,
dreams, and personal prejudices).
[/quote:a68811420e]
That's basically it. I'm personally tired of watching him repeat the same
failed arguments and am waiting for a coherent re-run of Miller's experiment
since he is so "sure" a signal was detected.
Signal processing has never been an especially strong tool in my bag of
tricks, but I believe I know enough to know how stupid it is for this
argument to continue. I can't wait for the next repetition of the "n^2-1"
argument for using a gas-mode interferometer design that ignores other
experiments that contradict him which use gas, or other experiments using a
*solid* which contradict him even more strongly.
*shrug, he belongs on this newsgroup.
[quote:a68811420e]
Tom Roberts[/quote:a68811420e] |
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| eric gisse... |
| Posted: Sun Oct 11, 2009 12:54 pm |
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Surfer wrote:
[quote:bf25e9107b]On Sun, 11 Oct 2009 11:22:06 -0500, Tom Roberts
tjroberts137 at (no spam) sbcglobal.net> wrote:
Surfer has no way to distinguish
between orientation dependence and time dependence (other than hopes,
dreams, and personal prejudices).
The output from the DSP filter is a signal with a period of half a
turn. The phase of the signal is orientation dependent wrt the
interferometer.
The amplitude of the signal is modulated by the earth rotation effect.
The envelope of the waveform for that has a period of one sideral day,
and the phase of the envelope is orientation dependent wrt to the
celestial sphere.
The amplitude is also modulated by the earth orbit effect.
The envelope of the waveform for that has a period of one year.
Such different periods allow the effects to be readily distinguished,
allowing Miller to quite accurately calculate speed and direction for
absolute motion.
Figure 23 in his paper
http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf
shows he was able to calculate the direction in two different ways,
namely,
- Apex from magnitude, and,
- Apex from azimuth
and that the two ways gave consistent results.
[/quote:bf25e9107b]
Just not consistent with modern error analysis, or other experiments.
[quote:bf25e9107b]
Surfer[/quote:bf25e9107b] |
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