Miller had done a reanalysis of the original MMX and he which he
claimed that the 360 degrees result is in perfect agreement with his
findings.

Intrigued by that I tried the opposite approach:
I think, in principle not only the 180 degree results may be averaged,
but even the 90 degrees results may be averaged, by adding them
inversely from the opposite ends and dividing by two. It's similar to
a quarter standing wave counting from the boundary. I don't remember
to have seen that done before.

This is what I got (check it for yourself if you want to be sure *):

All-average quarter periods effect of original MMX

degree 1/1000 fringe
0 0.0
22.5 4.9
45 9.3
67.5 5.6
90 0.0

I plotted it and with a smooth spline through it, it looks really
neat!

Coincidence? Temperature? (unlikely, similar in eveing as at noon).
Observer bias again? Or maybe there is something after all?
Your comments will be highly appreciated!

By the way, just for reality check, I exchanged two data of the total
average of 180 degrees to see the effect: big mess, not at all like a
quarter wave.

Harald

* Original unstraightened averages for 180 degrees (measured in
opposite directions):

Point Noon Evening
0 0.784 1.047
1 0.762 1.062
2 0.755 1.063
3 0.738 1.081
4 0.721 1.088
5 0.720 1.109
6 0.715 1.115
7 0.692 1.114
8 0.661 1.120

Harry:
Miller had done a reanalysis of the original MMX and he which he
claimed that the 360 degrees result is in perfect agreement with his
findings.

Intrigued by that I tried the opposite approach:
I think, in principle not only the 180 degree results may be averaged,
but even the 90 degrees results may be averaged, by adding them
inversely from the opposite ends and dividing by two. It's similar to
a quarter standing wave counting from the boundary. I don't remember
to have seen that done before.

This is what I got (check it for yourself if you want to be sure *):

All-average quarter periods effect of original MMX

degree 1/1000 fringe
0 0.0
22.5 4.9
45 9.3
67.5 5.6
90 0.0

I plotted it and with a smooth spline through it, it looks really
neat!

You can't fit to a spline. All that does is smooth your data and
introduce artifacts. (This also goes to my point about a null hypothesis).
In order to fit the data to a theory, you need to use a fitting function
derived from the theory, where the variables in the theory constitute
the parameter space of the fitting function. In this case, the parameters
to be fit are the velocity and direction of the so-called "ether wind".

Also, what errors are on those measurements? In principle, you should
have multiple measurements of each angle, so that you you have the
amplitude of the fringe shift +/- the error in the amplitude of the
fringe shift (assuming the angle itself is reproducible much better
than the matters).

Now, to address the question of a null hypothesis, all you need to
do is ask what hypothesis you know that can give you the parameters
for a fitting function?

Coincidence? Temperature? (unlikely, similar in eveing as at noon).
Observer bias again? Or maybe there is something after all?
Your comments will be highly appreciated!

Without all of the raw data, it would be impossible to say much.
The reason no one really cares about the michelson morely experiment
for more than historical reasons is that modern experiments are
much more precise.

(Bilge) wrote in message ...
Harry:
Miller had done a reanalysis of the original MMX and he which he
claimed that the 360 degrees result is in perfect agreement with his
findings.

Intrigued by that I tried the opposite approach:
I think, in principle not only the 180 degree results may be averaged,
but even the 90 degrees results may be averaged, by adding them
inversely from the opposite ends and dividing by two. It's similar to
a quarter standing wave counting from the boundary. I don't remember
to have seen that done before.

This is what I got (check it for yourself if you want to be sure *):

All-average quarter periods [I meant halve period] effect of original MMX

degree fringe [1/1000]
0 0.0
22.5 4.9
45 9.3
67.5 5.6
90 0.0

I plotted it and with a smooth spline through it, it looks really
neat!

You can't fit to a spline. All that does is smooth your data and
introduce artifacts. (This also goes to my point about a null hypothesis).
In order to fit the data to a theory, you need to use a fitting function
derived from the theory, where the variables in the theory constitute
the parameter space of the fitting function. In this case, the parameters
to be fit are the velocity and direction of the so-called "ether wind".

Also, what errors are on those measurements? In principle, you should
have multiple measurements of each angle, so that you you have the
amplitude of the fringe shift +/- the error in the amplitude of the
fringe shift (assuming the angle itself is reproducible much better
than the matters).

Now, to address the question of a null hypothesis, all you need to
do is ask what hypothesis you know that can give you the parameters
for a fitting function?

Coincidence? Temperature? (unlikely, similar in eveing as at noon).
Observer bias again? Or maybe there is something after all?
Your comments will be highly appreciated!

Without all of the raw data, it would be impossible to say much.
The reason no one really cares about the michelson morely experiment
for more than historical reasons is that modern experiments are
much more precise.

Bilge I largely agree, except that few of those repeats were
undisputibly the same experiment. in fact I only provided this as
illustration for my question about this group's reanalysis of MMX.
I suspected, and suspect more now, that such reanalysis for
"relativity" has not been done at all, and that the likely available
analysis is unknown (except Miller's) and undiscussed (incl. Miller's
reanalysis of MMX which is known but neglected).

I worked from a bad copy of the original MMX results; after I've been
back in the office I'll try to reanalyze and present it in a
statistical way, if no one else does (or did).
I think it's literally a shame that few experiments nowadays provide
the data, as M&M did.

Harald

PS:

"Bilge" wrote in message
...
Harry:
SNIP
Without all of the raw data, it would be impossible to say much.
The reason no one really cares about the michelson morely experiment
for more than historical reasons is that modern experiments are
much more precise.

I found it back, the data are accessible for all on:
http://www.aip.org/history/gap/PDF/michelson.pdf

Harald

Here is a first refinement.

I put the data in a spreadsheet, but could not destill more info out
of it.
The errors are rather high indeed, and it looks pretty random until
the last rounds of averaging.

from my own intuition, I did the following simple analysis for a
non-zero periodic signal: I would expect some correlation with a sinus
when averaging to halve and quarter periods.

1. 2.
sin(2alpha) halve periods quarter periods
0 0.00 0.00 lin.regr. 1= 0.978
0.71 4.88 5.26 lin.regr. 2= 0.987
1 9.25 9.25
0.71 5.63

What could cause this correlation?

Meanwhile I ordered the paper that Miller referred to:
- W.M.Hicks, Phil.Mag. [6] 3, 9, 256, 555 (1902).
As I don't know what the 555 stands for ("also from p." is strange and
"until p." is enormous) it may take a few times asking...

Below you can find all the raw data belonging to the M-M experiment (
http://www.aip.org/history/gap/PDF/michelson.pdf ), ready to copy in
your spreadsheet.

Harald


Position Day
8.5 8.75 9.5 9.75 11.5 11.75

0 44.7 61.2 57.4 26.0 27.3 51.3
1 44.0 63.3 57.3 26.0 23.5 51.9
2 43.5 63.3 58.2 28.2 22.0 52.5
3 39.7 68.2 59.2 29.2 19.3 53.9
4 35.2 67.7 58.7 31.5 19.2 53.8
5 34.7 69.3 60.2 32.0 19.3 54.1
6 34.3 70.3 60.8 31.3 18.7 54.3
7 32.5 69.8 62.0 31.7 18.8 53.7
8 28.2 69.0 61.5 33.0 16.2 53.4
9 26.2 71.3 63.3 35.8 14.3 54.3
10 23.8 71.3 65.8 36.5 13.3 53.8
11 23.2 70.5 67.3 37.3 12.8 54.2
12 20.3 71.2 69.7 38.8 13.3 55.0
13 18.7 71.2 70.7 41.0 12.3 56.8
14 17.5 70.5 73.0 42.7 10.2 57.2
15 16.8 72.5 70.2 43.7 7.3 57.7
16 13.7 75.7 72.2 44.0 6.5 58.6