Those who have already gone over this mathematically correct derivation
of Fizeau's experimental results are free to drop to the bottom of the
page where an additional essay on the philisophical nature of
measurement based theory has been included.

Fizeau's results are correctly accounted for as such:

Attachment 1: Fizeau: Table of Comparisons

In reference to Fizeau's experimental results of the speed of light
in moving media:

Following is a table of results obtained from three various equations
using a detector at rest wrt the Earth, speed of water measured wrt
Earth, and sodium light.

n = 1.332 c = 3e8 w = c/n = 225225225.225

Light and media moving in the same direction wrt detector.

Fizeau W = w + v(1 - 1/n^2)

Galilean W = v + w(c^2 - vc)/(vw + c^2 - vc)
= v + c(c - v)/(v + n(c - v))

Relativistic W = (v + w)/(1 + vw/c^2)
= (v + c/n)/(1 + v/nc)

All speeds below are in m/s
_______________________________________________

Water W-Fizeau W-Galilean W-Relativistic

1m/s 225225225.6616m/s 225225225.6616m/s 225225225.6616m/s

2 225225226.098 225225226.098 225225226.098

3 225225226.5343 225225226.5343 225225226.5343

4 225225226.9707 225225226.9707 225225226.9707

5 225225227.4071 225225227.4071 225225227.4071

6 225225227.8435 225225227.8435 225225227.8435

7 225225228.2798 225225228.2798 225225228.2798

8 225225228.7162 225225228.7162 225225228.7162

9 225225229.1526 225225229.1526 225225229.1526

10 225225229.589 225225229.589 225225229.589

Interesting outcome, to say the least.

The three equations diverge at very high values of v, but the
Galilean and Relativistic equations both give W = c when v = c.
OTOH wrt these two, ironically, only the Galilean derivation holds
the speed of light constant at c wrt the 'medium' space (vacuum).
______________________________________________


Attachment 2: Fizeau: The Galilean Derivation

A necessary introduction:

It should be kept in mind that the semantic interpretation of the
following mathematical arguments is that light propagates through the
local medium at c wrt the medium, and that the Earth is relatively at
rest wrt that medium, or at least enough so that any variations in
light speed have no measurable effect on the derived outcomes in the
table above in the preceding attachment. The physical media (in this
case water) is not the medium, it's particles simply interfere with
the light in its translation through the actual medium, which is the
vacuum itself (it should also be clarified that the vacuum is just
the extension of all surrounding matter, so in effect the surrounding
matter is collectively the medium).

The observed refractive index is simply another form of stating the
observed speed of light through the media, and it is therefore a
redundant inclusion into the theory, and in fact harmful in that it
lends to the illusion that n is constant irrespective of motion of the
media wrt the medium. It is not. Although if arbitrarily defined as
constant, then it follows deductively that an adjustment factor is
required to compensate for this incorrect definition. That factor is
provided in the final conclusion. What we will find is that w in the
equations below is not the speed of light wrt the moving media, but
rather it is the speed only wrt the stationary media, hence if we
substitute the variable s for the defined-as-constant w, we get

W = v + s as a correct statement.

's' is the speed of light wrt the 'moving' media, and is not constant
through changes in v, in contrast to Einstein's assumption that it is.

The light, in its propagation from source to detector, is periodically
absorbed by the material media, and subsequently re-emitted. During
the intervals when the light energy is contained as PE within the
media, it necessarily propagates at the same speed as the media over
that interval, thus we obtain the reduced 'effective' speed of light
through the media. IOW for a portion of the total time interval the
light is not propagating at all, in fact for that portion of the total
time interval there is no light. We can form an analogy to a jet that
periodically lands on moving ships for refueling; it's effective speed
is less than its propagational speed, and moreover, the propagational
speed wrt the ship will depend entirely upon the speed of the ship
wrt the medium, in this case air.

This addendum (this entire introduction) was added to clarify the
argument; it consists of definitions, and thus it is inarguable, so
please reserve your arguments for the math that follows.

The following is the correct Galilean derivation of Fizeau's
empirical results, which were obtained from his measurements of the
'speed of light in moving media' (water).


x = length of column of water between the source and detector.
x'= segment of column of water traversed by the source photons.
t_o = total duration of the event
(emission of photon by source - detection at the detector).
td= time delay of light incurred within a stationary volume of water
introduced into, and at rest wrt, the medium of propagation, i.e.
into the space through which the photon propagates.
td'= time delay of light incurred within a moving volume of water
introduced into, and in motion wrt, the medium of propagation,
i.e. into the space through which the photon propagates.
w = net speed of propagation through 'stationary' column of water
wrt the water, as derived from n, water at rest wrt Earth.
W = net speed of propagation through column of water that is
in motion wrt Earth, as measured in the Earth frame.
s = net speed of propagation relative to the 'moving' column of water,
as measured in Earth frame.
n = c/w = index of refraction of media (water).
c = speed of light in a vacuum at rest wrt Earth.
v = speed of water column wrt Earth.


We begin with a source of light and a detector located at each end
respectively of a pipe through which water flows. The direction of
water flow will be from source to detector. The object is to derive
an equation based upon the following premises, that will accurately
provide for Fizeau's empirical data, and this will be accomplished
without reference to any experimental data, or to any other
formulations pertaining to this effect that have been thus far
derived, with the exception of the obvious data, e.g. index of
refraction of the media, the speed of light in a vacuum wrt Earth,
and premise 1 below.

Premises:
1) Light moving through a homogenous material medium, which is in
uniform motion at a constant velocity, has a speed wrt that medium
that is independent of the length of the path through that medium.
From this follows that any time delay associated with the speed of
propagation through a given volume of space, that is altered by
the presence of a homogenous material media within that volume, is
proportional to the path length through that media. Viz.

td/x = td'/x'

2) The medium of propagation is vacuum itself, and is considered to
be 'at rest' wrt Earth when located within an Earth environment.
I.e. An observer in motion wrt Earth is moving equally wrt the local
'space' medium.

3) The Galilean transformation is valid for the description
of all natural phenomena.

A photon is emitted from the source and propagates through the space
between the source and the detector, (both of which are at rest wrt
the vacuum) and the photon is absorbed at the detector. Its time of
flight is recorded. The tube length is immaterial to the following
argument, per Premise 1 above.

The path length traversed by the photon, through a stream of water
moving from source to detector at a speed v, is given by the
Galilean transform as:

x - vt_o = x'

The time delay experienced by the photon during its flight per above
is:

td x'/x = td'

td, over the length x, is in turn given by

x/w - x/c = td = x(1/w - 1/c)

Thus td/x = (1/w - 1/c) = td'/x'

That is, td is the difference in the actual time of flight through
water that is at rest wrt the vacuum, source, and detector, as
compared to the time of flight when the space between the source
and detector is evacuated.

From the frame of reference of the water, the water itself is
motionless, i.e. it is at rest. However, from this frame of reference
the medium of propagation is in motion, i.e. the vacuum, source, and
detector are moving wrt the observer at v, and any light
propagating through the vacuum is, according to the Galilean
transform, moving relative to our observer at c-v.

From the frame of reference of the water we have:

t_o = x'/(c-v) + td'

t_o = (x'/(c-v)) + td x'/x

t_o = x'((1/(c-v)) + td/x)

t_o = x'((1/(c-v)) + (1/w - 1/c))

s = x'/t_o

Therefo

s = x'/ x'((1/(c-v)) + (1/w - 1/c))

s = 1/((1/(c-v)) + (1/w - 1/c))

s = 1/(1/(c-v) + 1/w - 1/c))

s = 1/(1/(c-v) - 1/c + 1/w))

s = 1/(v/(c^2-vc) + 1/w))

s = 1/(vw +(c^2-vc)/(wc^2-wvc))

s = w(c^2 - vc)/(vw + c^2 - vc)

The Galilean transform gives:

s = W - v

Hence

W = v + w(c^2 - vc)/(vw + c^2 - vc)

Or just

W = v + s (see above definition of s in the intro)

And thus the results are perfectly consistent with normal velocity
addition, and with the Galilean transform. Moreover the corrections of
SR to this solution will provide a doubling of the predicted shift in
W, and thus SR has been proved by the experiment to be false, in
contrast to the unsubstantiated claims quite to the contrary.

As already shown, the above equation agrees immaculately with the
results of Fizeau's experiments, to several decimal places when v
is small, as was the case in all of those experiments.

______________
The correct relativistic treatment of electromagnetic forces is
derived he

http://www.cswnet.com/~rper/Electromagnetism.html

There is simply no need for a change in relativistic framework in
order to clarify what are ambiguities only wrt those who failed to
reason the problems through correctly.




__________________________________________________ _____________________
*New

Invariance is a matter of simply removing observers from the equations
of physics.
This is accomplished by simply framing the laws of physics
around the relative velocities of the elements in the system, i.e.
by incorporating their velocities wrt each other rather than their
velocities wrt some arbitrary observer. Reference frame transformations
thus no longer apply to the description of nature. All laws will in this
way be rendered frame invariant. On the other hand, it is possible
to describe the relative velocity of the particles in terms of their
velocities wrt an arbitrary observer, but then reliability of
measurement
becomes an issue, and a major source of controversy.

While the valid laws of physics must be independent of measurement, we
are nevertheless constrained in our verification of those laws to the
errors
inherent in measurement processes, since we must conduct measurements in
order to provide data to plug into the equations. These measurements
must of necessity involve some frame outside of the system under study.
In most cases the
measurement error will not cause a significant difference in the
measured
vs. predicted results, and as it stands we have no choice but to
tolerate
the difference.

No theory will agree perfectly with observation because of this
uncertainty in measurement. Again, this issue of measurement
disagreements and errors is completely independent of the form
that valid laws of physics must take, thus the relativity debate has
less to do with the structure of space-time, and more to do with the way
in which space-time presents itself to us.

For the time being it must be noted that either Lorentzian or Galilean
space-time can be assumed as premises, the equations of motion will
simply differ in the respective systems, though providing for the very
same outcomes. The difference is one of measurements and of the
standards of measurement employed, whilst reality is oblivious to either
system, simply trudging along according to its own logic, in spite of
our attempts at simulation. OTOH, the true laws of the universe are
those that are valid independently of imagined protocols.

Richard Perry

Richard:


All speeds below are in m/s
_______________________________________________

Water W-Fizeau W-Galilean W-Relativistic

1m/s 225225225.6616m/s 225225225.6616m/s 225225225.6616m/s

Surely you jest. Where exacly did you get 13 significant figures
as your precision? Sheeesh....

Richard wrote:

Those who have already gone over this mathematically correct derivation
of Fizeau's experimental results are free to drop to the bottom of the
page where an additional essay on the philisophical nature of
measurement based theory has been included.


Fizeau
http://scienceworld.wolfram.com/biography/Fizeau.html
http://www.google.com/search?q=Fizea...ld.wolfram.com

Speed of Light
http://scienceworld.wolfram.com/phys...edofLight.html

Crank Information
http://www.google.com/search?q=perry...ers.pandora.be

Bilge wrote:

Richard:


All speeds below are in m/s
_______________________________________________

Water W-Fizeau W-Galilean W-Relativistic

1m/s 225225225.6616m/s 225225225.6616m/s 225225225.6616m/s

Surely you jest. Where exacly did you get 13 significant figures
as your precision? Sheeesh....

Just a comparison between the various equations Bilge. I do believe that
the snipped text explains this thoroughly. The actual data was less
precise, and thus none of the equations can be preferred as the correct
solution, they all agree to many more than 13 significant figures at
these low media velocities. Hope this answers your question. Moreover,
note that I rounded off light speed. It doesn't matter, had I used an
exact value the table would still show a very near agreement at low
media speeds. But thank you for your question, I'll probably go back and
add this explanation to the draft.

Richard Perry


Richard Perry

Sam Wormley wrote:

Richard wrote:

Those who have already gone over this mathematically correct derivation
of Fizeau's experimental results are free to drop to the bottom of the
page where an additional essay on the philisophical nature of
measurement based theory has been included.


Fizeau
http://scienceworld.wolfram.com/biography/Fizeau.html
http://www.google.com/search?q=Fizea...ld.wolfram.com

Speed of Light
http://scienceworld.wolfram.com/phys...edofLight.html

Crank Information
http://www.google.com/search?q=perry...ers.pandora.be

Reference:

http://www.cswnet.com/~rper/Electromagnetism.pdf

Crank information:

Fizeau
http://scienceworld.wolfram.com/biography/Fizeau.html
http://www.google.com/search?q=Fizea...ld.wolfram.com

Speed of Light
http://scienceworld.wolfram.com/phys...edofLight.html

Richard:


Bilge wrote:

Richard:


All speeds below are in m/s
_______________________________________________

Water W-Fizeau W-Galilean W-Relativistic

200000000
1m/s 225225225.6616m/s 225225225.6616m/s 225225225.6616m/s

Surely you jest. Where exacly did you get 13 significant figures
as your precision? Sheeesh....

Just a comparison between the various equations Bilge. I do believe that
the snipped text explains this thoroughly.

I did snip the explaination of the precision: you had a value
for `c' listed as 3 x 10^8, which has exactly 1 significant figure.
So, every number in your table should be 20000000 (with no decimal
point either).

The actual data was less
precise, and thus none of the equations can be preferred as the correct
solution, they all agree to many more than 13 significant figures at
these low media velocities.

The precision of a calculated value cannot be any better than the
precision of the number in the calculation which has the _least_
number of significant digits.

Hope this answers your question. Moreover, note that I rounded off
light speed.

Suppose you have two numbers, quoted as A = 1 and B = 3 (no decimal
point). What is the value of A/B. How about if they are quoted
A = 1.0 and B = 3.0? Here's one that's trickier: A = 1 and B = 3.005
and finally what if A = 1.0 and B = 3.00529675678906762 ?

The answers a 0, 0.3, 0, 0.3

Bilge wrote:

Richard:


Bilge wrote:

Richard:


All speeds below are in m/s
_______________________________________________

Water W-Fizeau W-Galilean W-Relativistic

200000000
1m/s 225225225.6616m/s 225225225.6616m/s 225225225.6616m/s

Surely you jest. Where exacly did you get 13 significant figures
as your precision? Sheeesh....

Just a comparison between the various equations Bilge. I do believe that
the snipped text explains this thoroughly.

I did snip the explaination of the precision: you had a value
for `c' listed as 3 x 10^8, which has exactly 1 significant figure.
So, every number in your table should be 20000000 (with no decimal
point either).

The actual data was less
precise, and thus none of the equations can be preferred as the correct
solution, they all agree to many more than 13 significant figures at
these low media velocities.

The precision of a calculated value cannot be any better than the
precision of the number in the calculation which has the _least_
number of significant digits.

Hope this answers your question. Moreover, note that I rounded off
light speed.

Suppose you have two numbers, quoted as A = 1 and B = 3 (no decimal
point). What is the value of A/B. How about if they are quoted
A = 1.0 and B = 3.0? Here's one that's trickier: A = 1 and B = 3.005
and finally what if A = 1.0 and B = 3.00529675678906762 ?

The answers a 0, 0.3, 0, 0.3

I simply defined lightspeed to be 3e8 m/s, to an infinite number of
significant digits, for the purpose of showing that the equations were
in agreement to a good number of significant digits. Maybe I should have
written
3.000... e8,
but I thought that I had explained it clearly enough. If you object to
such a practice as leaving off the 0's, then simply plug in the
currently accepted value of c to as many significant digits as are
available.
You will find that all three equations are still in agreement to many
more significant digits than Fizeau's experimental data has. Once again,
I was only showing that none of the equations can be preferred, because
they all agree to more significant digits than even the data provides.
Ok? Ok.

Furthermore don't ever say something stupid like, there are 2 people in
a room, according to you this is incorrect unless it is specified that
there are
2.000.... people.

Richard Perry

Richard:


Furthermore don't ever say something stupid like,

You apparently have no understanding of data analysis and/or think
textbooks on data reduction are stuppid. If you don't like the response,
then either don't post the kind of junk that draws one or find an article
on data analysis that disagrees with what I said.

there are 2 people in
a room, according to you this is incorrect unless it is specified that
there are
2.000.... people.
_
Which would be specified as: 2.0 or 2 (exact). If you say 2 people
without specdifying an uncertainty, then your results are restricted
to 1 significant digit.

Bilge wrote:

Richard:


Furthermore don't ever say something stupid like,

You apparently have no understanding of data analysis and/or think
textbooks on data reduction are stuppid. If you don't like the response,
then either don't post the kind of junk that draws one or find an article
on data analysis that disagrees with what I said.

there are 2 people in
a room, according to you this is incorrect unless it is specified that
there are
2.000.... people.
_
Which would be specified as: 2.0 or 2 (exact). If you say 2 people
without specdifying an uncertainty, then your results are restricted
to 1 significant digit.

What a crock. You couldn't find an error in the math or the argument so
you manufactured one. There is a time and place for specifying margins
of error, namely when you need to know. The table in question isn't one
of those occasions. If you plug in the values listed givens into a
calculator, the results you will get go to as many significant digits as
the calculator supports. If you had the perfect calculator the answer
would be exact, I simply rounded to enough significant digits to surpass
the experimental margin of error. This was the purpose of the table, and
it serves that purpose well.

Richard Perry