"Timo Nieminen" wrote in message
news:Pine.LNX.4.50.0501121223030.9135-100000@localhost...
On Wed, 12 Jan 2005, Androcles wrote:

"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:

"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any transparent
medium
is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a
given
frequency
in diamond, water, air, any stationary medium, is constant
with
respect to
the stationary medium.

Good enough to explain MMX.

So is SR, so is a fully-dragged Galilean ether, so is a Lorentz
ruler-shrinking clock-slowing ether, and so is just about any
emission
theory.

Ordinarily, it would be somewhat pedantic point, but empirical
observations of the speed of light in a moving medium were
historically
important, and continue to be theoretically important, in
chosing
which of
the above explanations of MMX could be correct. In the context
of
using an
emission theory to explain MMX, it's a worthwhile point.

SR isn't good enough, and doesn't.

That's simply wrong.

SR isn't good enough, and doesn't.

Utter nonsense (and repeating it again doesn't add weight to your
argument)!

SR isn't good enough, and doesn't.
Androcles

On Wed, 12 Jan 2005, Androcles wrote:

"Timo Nieminen" wrote:
On Wed, 12 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any transparent
medium
is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a
given
frequency
in diamond, water, air, any stationary medium, is constant
with
respect to
the stationary medium.

Good enough to explain MMX.

So is SR, so is a fully-dragged Galilean ether, so is a Lorentz
ruler-shrinking clock-slowing ether, and so is just about any
emission
theory.

Ordinarily, it would be somewhat pedantic point, but empirical
observations of the speed of light in a moving medium were
historically
important, and continue to be theoretically important, in
chosing
which of
the above explanations of MMX could be correct. In the context
of
using an
emission theory to explain MMX, it's a worthwhile point.

SR isn't good enough, and doesn't.

That's simply wrong.

SR isn't good enough, and doesn't.

Utter nonsense (and repeating it again doesn't add weight to your
argument)!

SR isn't good enough, and doesn't.

Utter nonsense!

Any theory of electromagnetics/optics compatible with the PoR explains it
perfectly well.

I see you are completely unwilling to discuss physics. All the evidence
points to you deliberately lying. Is this the case?

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

"Timo Nieminen" wrote in message
news:Pine.LNX.4.50.0501121240330.9215-100000@localhost...
On Wed, 12 Jan 2005, Androcles wrote:

"Timo Nieminen" wrote:
On Wed, 12 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:
"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any
transparent
medium
is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a
given
frequency
in diamond, water, air, any stationary medium, is constant
with
respect to
the stationary medium.

Good enough to explain MMX.

So is SR, so is a fully-dragged Galilean ether, so is a
Lorentz
ruler-shrinking clock-slowing ether, and so is just about any
emission
theory.

Ordinarily, it would be somewhat pedantic point, but
empirical
observations of the speed of light in a moving medium were
historically
important, and continue to be theoretically important, in
chosing
which of
the above explanations of MMX could be correct. In the
context
of
using an
emission theory to explain MMX, it's a worthwhile point.

SR isn't good enough, and doesn't.

That's simply wrong.

SR isn't good enough, and doesn't.

Utter nonsense (and repeating it again doesn't add weight to your
argument)!

SR isn't good enough, and doesn't.

Utter nonsense!

Any theory of electromagnetics/optics compatible with the PoR explains
it
perfectly well.

I see you are completely unwilling to discuss physics. All the
evidence
points to you deliberately lying. Is this the case?

You saying it doesn't make it so, and since I know you of old as another
big-headed know-it-all, more interested in trolling than recognizing
simple
solutions, I saw fit to simply deny your assertions.

I will now give the proof.
I place two identical evacuated tubes at right angles, with mirrors and
with
sources and detectors of light.
When the light reaches a detector, it turns off the source.
When NO light reaches the detector, it turns the source on.
The path length can be any reasonable one.
I connect the outputs of the detectors to an up/down counter, one for up
and the other for down. I calibrate the tube lengths until there is no
count.
I now have MMX, electronic version and air free.
I rotate the apparatus 90 degrees and what happens? NO count happens.
Acording to SR, and there being velocity as the Earth moves and rotates
x' = (x-vt)/ sqrt(1-v^2/c^2)
y' = y.
So, x' does not equal y'.
The speed of flight in both tubes is c (invariant),
and the tubes are of different lengths.
Therefore a count will occur, the x (up) count exceeding the count of
the
(y) down counter.

It is no good introducing time dilation. It is the same for both tubes,
they are colocated in the same frame of reference.
Unless, of course, you wish to add a time for the x-axis that
differs from the time in the y-axis, but that is not SR.
So I repeat, SR isn't good enough to explain MMX, and it doesn't.

A speed of light that is source dependent will.

Hence YOU are spouting utter nonsense.

Androcles.

Androcles wrote:

You saying it doesn't make it so, and since I know you of old as another
big-headed know-it-all, more interested in trolling than recognizing
simple
solutions, I saw fit to simply deny your assertions.

I will now give the proof.
I place two identical evacuated tubes at right angles, with mirrors and
with
sources and detectors of light.
When the light reaches a detector, it turns off the source.
When NO light reaches the detector, it turns the source on.
The path length can be any reasonable one.
I connect the outputs of the detectors to an up/down counter, one for up
and the other for down. I calibrate the tube lengths until there is no
count.
I now have MMX, electronic version and air free.
I rotate the apparatus 90 degrees and what happens? NO count happens.
Acording to SR, and there being velocity as the Earth moves and rotates
x' = (x-vt)/ sqrt(1-v^2/c^2)
y' = y.
So, x' does not equal y'.
The speed of flight in both tubes is c (invariant),
and the tubes are of different lengths.
Therefore a count will occur, the x (up) count exceeding the count of
the
(y) down counter.

Are you saying SR predicts the time light takes to travel down each tube
will depend on how the tubes are oriented, or on the velocity of the
tubes in your reference frame? If so, you are badly misunderstanding how
the Lorentz transformations work. I can calculate explicitly what the
Lorentz transformations would predict about the speed of light down
perpendicular tubes in two different reference frames, if you like--I
promise they will predict it is c in all cases.


It is no good introducing time dilation. It is the same for both tubes,
they are colocated in the same frame of reference.
Unless, of course, you wish to add a time for the x-axis that
differs from the time in the y-axis, but that is not SR.
So I repeat, SR isn't good enough to explain MMX, and it doesn't.

A speed of light that is source dependent will.


But of course, saying the speed of light is source dependent means
throwing out Maxwell's laws, and scientists have no reason to do that
unless someone can come up with a new theory that both predicts the
speed of light is source dependent *and* that can replicate all the
experimentally-verified predictions of Maxwell's laws about the way
charged objects interact with each other and with the electromagnetic field.

Jesse

On Wed, 12 Jan 2005, Androcles wrote:

I will now give the proof.
I place two identical evacuated tubes at right angles, with mirrors and
with
sources and detectors of light.
When the light reaches a detector, it turns off the source.
When NO light reaches the detector, it turns the source on.
The path length can be any reasonable one.
I connect the outputs of the detectors to an up/down counter, one for up
and the other for down. I calibrate the tube lengths until there is no
count.
I now have MMX, electronic version and air free.

What's wrong with an actual Michelson interferometer where one looks for
fringe shifts as the optical path length changes?

Since your original assertion was specific to MMX, I'll first deal with
the actual MMX. Then your modified experiment.

I rotate the apparatus 90 degrees and what happens? NO count happens.
Acording to SR, and there being velocity as the Earth moves and rotates
x' = (x-vt)/ sqrt(1-v^2/c^2)
y' = y.
So, x' does not equal y'.

Why would you want to analyse the experiment using a reference frame
moving wrt the Earth? An analysis using any theory that is compatible with
the PoR allows us to use any reference frame. The frame in which the
apparatus is stationary allows the simplest analysis, so why not use it?
Are you trying to deliberately obfuscate the problem?

In a reference frame in which the apparatus is stationary, x and y don't
change as the apparatus is rotated (assuming x and y are the
arm-lengths). No frequency shifts, since there is no relative motion, no
wavelengths shifts, so no change after rotation.

Do you dispute this?

The speed of flight in both tubes is c (invariant),
and the tubes are of different lengths.
Therefore a count will occur, the x (up) count exceeding the count of
the
(y) down counter.

In a reference frame in which the MMX apparatus is moving, yes, according
to SR, there is a length contraction. The length contraction applies
equally to the wavelength in the contracted arm, so the length as measured
in wavelengths along the arm remains exactly the same.

Note that the wavelengths for the incoming and the reflected wave are
different in the arm along the direction of motion. This means that the
points where the two waves destuctively interfere in the arm move. If you
bother to do the maths, you will see that those points move at the same
speed as the whole apparatus, so in the moving frame one sees a moving
"standing" wave pattern. Measure the length of the arm in terms of this
pattern.

Therefore, no change, even in the moving frame.

Remember, an interferometer like this does not measure physical lengths,
it measures optical path length, in wavelengths. In the moving frame, the
wavelength is different in the two arms.

The above is the simple, algebra-free explanation. What follows is a
simple, algebra-based analysis of the experiment you described:

In the frame where the tubes are stationary, the rotation makes no
difference.

In the moving frame, the arm along the motion is contracted
by 1/gamma, so we have x' = y'/gamma. The mirror moves at v, so the light,
moving at c in the moving frame, moves at c-v towards the mirror, as
measured in the moving frame, and takes y'/(gamma (c-v)) to get there. The
return journey is at c+v relative to the detector, as measured in the
moving frame, so the return journey takes y'/(gamma (c+v)). Therefore the
total time along that arm for the round trip is

y'/gamma * (2c/(c^2 - v^2)).

Don't forget that the mirror (and detector) in the other frame is also
moving. In time t1 that the light takes to go from the source to the
mirror, the mirror moves v t1. The distance the light needs to travel is
then sqrt(y'^2 + v^2 t1^2), which must be equal to c t1. So,

t1 = y' / sqrt( c^2 - v^2 ) = y' c / (gamma * (c^2 - v^2)).

For the return trip, t2 = t1, so the total time for the round trips in
each arm is exactly the same.

No change is seen. Null result.

It is no good introducing time dilation. It is the same for both tubes,
they are colocated in the same frame of reference.

Not needed at all.

So I repeat, SR isn't good enough to explain MMX, and it doesn't.

Not even algebra is needed to show that SR explains it perfectly well. If
you want to use algebra, well, that also shows that SR explains MMX
perfectly well.

A speed of light that is source dependent will.

Any theory of optics satisfying the PoR explains it perfectly well, so of
course emission theories explain it perfectly well.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

Androcles wrote:

"Jesse Mazer" wrote in message
...


Androcles wrote:



"Jesse Mazer" wrote in message
...



Androcles wrote:




"Jesse Mazer" wrote in message
...





Of course, before Einstein physicists didn't think Maxwell's laws
would be correct in every observer's reference frame--they thought
they would only hold exactly in the rest frame of the aether. They
would have believed that to state the laws of electromagnetism in a
way that would hold in all frames, you'd have to replace every x in
Maxwell's laws with (x - v*t), where v represents the observer's
velocity relative to the rest frame of the aether...any derivatives
of x would have to be replaced in the same way, like replacing
dx/dt with (dx/dt - v). This would give a new set of
electromagnetic laws which would be Galilei-invariant, and which
would reduce to Maxwell's laws in the case where v=0.

But a prediction of this Galilei-invariant analogue of Maxwell's
laws would be that for an observer in motion relative to the
aether, light will be observed to move at different speeds in
different directions, relative to himself. Unfortunately this was
not supported by the Michelson-Morley experiment.




The speed of light in diamond, water, air, any transparent medium is
constant with respect to the medium. MMX fails to support aether.
In MMX, the medium is air. It is as simple as that.




What do you mean "the medium is air"?



I mean that air was used as a medium for light,
by Michelson, in his interferometer, of course.
He did not perform the experiment in an evacuated chamber, on the
surface
of the moon, or aboard the ISS.






My point was that when waves are considered as a vibration in a
medium, like sound waves, the speed of any wave will be constant with
respect to the rest frame of the medium.



Your points are invariance, x-vt, Maxwell's laws, derivatives, aether
and
anything else you can mention hoping to cover the issue, but you
omitted
to say anything about the physical medium used and asked me what I
meant by it, so clearly it was NOT your point, it is MY point.

Recall that Einstein's second postulate is
"light is always propagated in empty space with a definite velocity c
which is independent of the state of motion of the emitting body".



Maxwell's laws also say that light's velocity is independent of the
state of motion of the emitting body,



For light in a medium. Maxwell believed in aether.


Who cares what Maxwell believed? Maxwell's laws are just a set of
equations telling you how charged objects interact with the
electromagnetic field, and how the electromagnetic field in turn affects
the movements of charged objects. You don't have to believe in aether to
make use of the equations, and by pure mathematics it is possible to
show that these equations imply that charges create waves in the
electromagnetic field when they accelerate (light is a form of
electromagnetic wave), and that the velocity of these waves is c in
empty space regardless of the source velocity. This would be true
whether you believed that empty space is really filled with an invisible
"aether" or if you think that electromagnetic waves can travel through a
vacuum (as modern physicists do).

This is a pure mathematical consequence of the equations of Maxwell's
laws. And these equations can make predictions about any distribution of
charges you like, predictions which have been verified by experiments.
From my old E&M textbook, here are some random examples of the types of
problems which can be solved using Maxwell's laws (or rules that can be
derived mathematically from Maxwell's laws, such as 'Gauss's law'):

-find the electric field inside and outside a spherical shell of radius
R, which carries a uniform surface charge of density d.

-suppose we place a point charge q at the center of a neutral spherical
conducting shell with inner radius a and outer radius b. It will attract
negative charge to the inner surface of the conductor. How much induced
charge will accumulate there?

-find the capaciance of a "parallel-plate capacitor" consisting of two
metal surfaces of area A held a distance d apart.

-Find the magnetic field on the axis of a tightly wound solenoid
(helical coil) consisting of N turns per unit length wrapped around a
cylindrical tube of radius R and carrying current I. Consider the turns
to be essentially circular.

-Find the exact magnetic field a distance z above the center of a square
loop of side s, carrying a current I.

For reference, Maxwell's equations themselves can be found he

http://hyperphysics.phy-astr.gsu.edu...ric/maxeq.html

You can see that "the speed of light is c" is not a
tacked-on-assumption, the basic equations say nothing about the speed of
electromagnetic waves caused by accelerating charges, that's something
that has to be derived from them. And the answer to any question
involving classical electromagnetism, like the ones I provided above,
can also be derived from them. So if you want to say the speed of light
is source-dependent, you need to come up with a new set of equations
that can replicate all the predictions of Maxwell's equations which have
been confirmed experimentally, yet do not have the consequence that the
speed of light is independent of source velocity.





regardless of whether you have the relativistic understanding of
these laws (that they hold in all reference frames)



Michelson was intending to use doppler shift to measure the
the speed of light in the aether as the Earth flew through it. He was
certainly NOT claiming the speed of light was invariant. Neither was
Maxwell. Both believed time and distance are invariant, as indeed
they are.


Yes, they believed that Maxwell's laws only worked in a single preferred
reference frame. But in relativity, which neither Michelson nor Maxwell
believed in (because it hadn't been invented yet), if Maxwell's laws are
true in one reference frame they must be true in all of them (because
they have the mathematical property of Lorentz-invariance).





or the pre-relativistic understanding of them (that they only hold in
one preferred frame, and in other frames the velocity of light would
be c+v in one direction and c-v in the other).



Both are wrong. The speed of light is source dependent in a vacuum,
and medium dependent when passing though a medium. The medium
becomes the new source, of course.


So you assert. But this does not fit with the predictions of classical
electromagnetism, and you don't have an alternate theory that can
replicate all of the successful predictions of classical electromagnetism.








All speeds are relative to something.
When requesting a drink on a plane, my speed relative to the flight
attendant is also zero, even though travelling at 500 mph ground speed
and 250 mph by the air speed indicator.
The speed of light inside a plane, as with the speed of sound, is
relative.



That's because the plane carries its own little pocket of air with it,



So does MMX, so we can put that one to bed. MMX has nothing
whatever to do with Einstein's relativity. Have it struck from the
FAQ's, which are a biased and prejudiced sham, a disgrace to science.


Should the theory of electromagnetism (the non-quantum version, ie
Maxwell's equations) also be struck from the FAQ's? It seems that it
conflicts just as badly with your ideas.








so inside the plane you are at rest relative the local medium. If you
were skydiving and you tried to yell out to a fellow skydiver below
you, if you were both moving down at velocity v relative to the rest
frame of the atmosphere, then you would observe the soundwaves to be
going at s-v downward and s+v upwards, in your reference frame (s is
the speed of sound in the air's rest frame).

There were some attempts to explain the MMX by suggesting the earth
dragged a pocket of aether along with it as it orbited, just like a
plane carries a pocket of air, so people on earth were always at rest
in relation to the local aether.



There is no doppler shift to observe for either sound or light, nor do
I expect there to be.
MMX is an attempt to measure doppler shift. It failed.



No it isn't.


Yes it is.
The anticipated fringes are a beat frequency between the light doppler-
shifted in the direction of motion through the aether and light that is
transverse to it.


Nope, you're wrong. The anticipated fringes are due to the expectation
that the peaks of the light waves would have different velocities down
the two arms of the interferometer, not that the frequency would be
different as in a doppler shift. It's a phase shift, not a frequency
shift. See the diagrams and explanation on this page, for example:

http://www.glafreniere.com/sa_Michelson.htm






Doppler shift is only about change in frequency--you tried to prove
otherwise with an equation, but you didn't answer where you got the
equation when I asked (it was not the same as the doppler shift
equation I found when I looked it up), and I also didn't understand
how you were trying to use it to prove that the frequency wouldn't
change.

Would you agree that if I hear the whistle of a train coming towards
me, the pitch will be changed but the speed of the sound wave will not
be an different than the speed of a sound wave from a train standing
still?



Would you agree that if I hear the whistle of a stationary train
I'm driving toward, the pitch will be changed and the speed of the sound
wave will be very different than the speed of a sound wave from a train
standing still in my frame of reference?


Yes. But in this case, you are not in the rest frame of the air.

Doppler's equation is
c+u
f' = f -------------
c+v
u the speed of my car, v the speed of the train, c the speed of sound in
the
medium.


OK, that's correct (assuming the speed of the car and the speed of the
train are measured relative to the rest frame of the air). But this
confirms what I said earlier, that Doppler's equation is just about a
change in frequency, not a change in the velocity of the sound waves (or
light waves).


There is no aether.
Shall I then say, the speed of sound is invariant because there is no
doppler shift aboard a plane?



Again, the explanation for that is just that the plane carries its own
pocket of air along with it, so you are still at rest relative to the
medium of soundwaves inside the plane.



There is no doppler shift for the light, either. Same reason.
Hence the speed of light is not invariant.


OK, ignoring for the moment that you are incorrectly using "no doppler
shift" to mean "no change in the speed of light relative to the air",
it's not true that Maxwell's equations would predict the speed of light
in the air has anything to do with whether you're in the air's rest
frame or not. So again, if you're claiming that it does, then you had
better be able to come up with a whole new theory of electromagnetism
that can replicate the successful predictions of Maxwell's laws.











In any case, if you're just saying MMX is consistent with your idea
that the speed of light depends on the source velocity, I wouldn't
disagree,



Good. So why complicate matters?
"Everything should be made as simple as possible, but not
simpler." -Einstein.
Pity he didn't take his own advice.




but the point is that Maxwell's laws are *not* consistent with that
idea,



"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.

"It is known that Einstein's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena" - Androcles.

So, something is wrong with Maxwell's equations that Einstein attempts
to fix, but in doing so introduces absurdities that are obvious to the
meanest intelligence, but accepted by "theoretical" physicists. Wrong
fix.
Maxwell was an aetherialist, and there is no aether.



Maxwell's laws are just equations for predicting the dynamical
behavior of a system of charges.



I have no objection to dB/dt = E or dE/dt = B.
The solutions are E.sin(omega t) and B.cos(omega t)


Those are not Maxwell's laws. Again, see this page for the equations:

http://hyperphysics.phy-astr.gsu.edu...ric/maxeq.html


Once it is realized that an electric field can exist in a vacuum, a
magnetic
field can exist in a vacuum,


"Once it is realized"? All modern physicists already believe that
electromagnetic fields can exist in a vacuum.

and that sin^2 + cos^2 = 1, that being
constant energy and conserved, there is no requirement for c at all.


Again, it can be derived mathematically as a consequence of Maxwell's
laws that charges create electromagnetic waves when they accelerate, and
these waves always travel at c. There is a derivation on this page, for
example:

http://www.vttoth.com/LIGHT/light.htm



The photon exists and propagates with whatever velocity was imparted
to it.



It is totally irrelevant whether you interpret them in terms of aether
or not.



We don't need any aether.


Yes, I agree, as do pretty much all modern physicists who make use of
Maxwell's equations.





Again, when Einstein said "as usually understood at the present time",
he was referring to the idea that Maxwell's laws would only hold in a
single preferred reference frame (which most physicists imagined to be
the rest frame of the aether, but again, this is irrelevant) and in
other frames they'd have to be modified using the Galilei
transformation (substituting x + vt for x in the equations).






whether you assume Maxwell's laws hold in all frames (as in
relativity) or you assume they only hold in a particular frame, and
you have to do a Galilei transform on them to describe E&M in other
frames (as physicists assumed would be true before relativity).
Maxwell's laws are very successful at predicting all sorts of
electromagnetic behavior, so if you want to throw them out, you'd
better have a good alternative which can make most of the same
predictions.



I do.



OK, present the complete equations of your theory,



I don't have a theory. All theories are the work of others.
I have good alternatives which make the same predictions


But I think you mean "make the same predictions" in a few isolated
cases, not in any problem which can be solved using Maxwell's equations,
like the ones from my textbook above.




but this would be false according to both Maxwell's laws *and* the
modified Galilei-invariant analogue of Maxwell's laws (which says
that light waves, like sound waves, always travel at the same speed
in the rest frame of the aether/air,




Forget aether, it doesn't exist. Air does, though. So does water.
A stick passing through the air-water interface appears bent.
That is empirical evidence that the speed of light is medium
dependent.




I don't think aether exists either, I was just describing what would
be predicted by the modified Galilei-invariant analogue of Maxwell's
laws which physicists believed in before relativity.




What Galilean invariance are you talking about?
Time, length and mass are invariant. length/time is not, time/mass is
not,
mass/length is not.



I already explained Galilean invariance in a previous post. Here's the
definition of a Galilei transformation again, followed by an
explanation of what it means for a set of laws to be
Galilei-invariant:



x'=x - vt
y'=y
z'=z
t'=t



Yes, ok, t is invariant, distance is invariant. You missed out mass,
though.


The Galilei transforms are just about translating between different
coordinate systems, they're not saying anything is "invariant". For
example, if in my coordinate system a ball hits the ground at position x
= 3 meters, y = 2 meters and z = 8 meters, and at time t = 12 seconds,
then if another observer is flying along my x-axis at 4 meters/second,
then assuming our three spatial axes are parallel and that the origins
of our coordinate systems coincided at t = 0 seconds, then in his
coordinate system the ball hit the ground at x' = 3 - 4*12 = -45 meters,
y' = 2 meters and z' = 8 meters, and at time t = 12 seconds, according
to the Galilei transformations.




x=x' + vt'
y=y'
z=z'
t=t'

To say a certain physical equation is "Galilei-invariant" just means
the
form of the equation is unchanged if you make these substitutions.
For
example, suppose at time t you have a mass m1 at position (x1, y1,
z1)
and another mass m2 at position (x2, y2, z2) in your reference frame.
Then the Newtonian equation for the gravitational force between them
would be:

F = Gm1m2/[(x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2]

Now, suppose we want to transform into a new coordinate system moving
at
velocity v with respect to the first one. In this coordinate system,
at
time t' the mass m1 has coordinates (x1', y1', z1') and the mass m2
has
coordinates (x2', y2', z2'). Using the Galilei transformations, we
can
figure how the force would look in this new coordinate system, by
substituting in x1 = x1' + vt', x2 = x2' + vt', y1 = y1', y2 = y2',
and
so forth. With these substitutions, the above equation becomes:

F = Gm1m2/[(x1' + vt' - (x2' + vt'))2 + (y1' - y2')2 + (z1' - z2')2]

and you can see that this simplifies to:

F = Gm1m2/[(x1' - x2')2 + (y1' - y2')2 + (z1' - z2')2]

In other words, the equation has exactly the same form in both
coordinate systems. This is what it means to be "Galilei invariant".
More generally, if you have *any* physical equation which computes
some
quantity (say, force) as a function of various space and time
coordinates, like f(x,y,z,t) [of course it may have more than one of
each coordinate, like the x1 and x2 above, and it may be a function
of
additional variables as well, like m1 and m2 above] then for this
equation to be "Galilei invariant", it must satisfy:
f(x'+vt',y',z',t') = f(x',y',z',t')


And to clear up a point you misunderstood earlier, the statement "f(x'
+ vt',y',z',t') = f(x',y',z',t')" must hold true for *all* values of v
in order for a given physics equation to have the property of "Galilei
invariance".



I have no idea what your function f is, but the arguments (x' + vt') and
(x') do not appear to be relevant. The remaining arguments being
identical,
I expect equality.


The function f is any law of physics that depends on the position and/or
time-coordinates of certain objects. For example, in Newtonian gravity
the gravitational force between two masses depends on their respective
positions. I provided the actual equation for Newtonian gravity in the
quote above, and I did a calculation to verify that this law has the
property of f(x' + vt', y', z', t') = f(x', y', z', t'). You could check
if any other equation involving positions and/or times had this
property, and some would, while others wouldn't. Maxwell's laws do not,
for example.




Maxwell's laws are not Galilei-invariant, but if you take the
equations of Maxwell's laws and replace x with x + vt, and dx/dt with
dx/dt + v (I got the sign wrong in the other post), then this modified
version of Maxwell's laws should have the property of
Galilei-invariance (for example, since the ordinary version of
Maxwell's laws predicts that dx/dt = c for an electromagnetic wave,
these modified laws would say that dx/dt + v = c, which means that the
velocity of the wave will be dx/dt = c - v, if you are in a frame
moving at v with respect to the preferred frame where Maxwell's laws
hold exactly). As I said before, the common belief about Maxwell's
laws before Einstein was that they would only hold in a preferred
frame, so if you jumped to a different frame which was related to the
preferred frame by a certain Galilei transformation, you'd have to use
these modified Maxwell's equations to make predictions about
electromagnetic behavior in your frame.



The common belief before Einstein was correct, then, although I fail
to see how dB/dt = E is frame dependent.

dB/dt = E is not a law of electromagnetism.








regardless of the velocity of their source).




Source dependency only applies in the absence of a medium. There is
no aether.




Both Maxwell's laws and the Galilei-invariant analogue of Maxwell's
laws predict that the velocity of a light wave is independent of the
velocity of the source.



You have yet to show what you mean by "Galilei-invariant analogue "



I have explained several times that if you substitute x + vt for x in
Maxwell's equations, and dx/dt + v for dx/dt (I actually said x - vt
and dx/dt - v earlier, but that was a sign mistake), you should get an
analogue of Maxwell's laws that is Galilei-invariant.



Here' a little something to think on.
Imagine a standing wave in a long tank of water.
\/\/\/\/\/\/\/\/\/\/\ t=0
/\/\/\/\/\/\/\/\/\/\/ t=1

It has a frequency 1 Hz and wavelength 1 metre, but it is a
standing wave.
Now imagine you are alongside a crest at t0 and intend to
walk the length of the tank to count crests and divide the
tank length (10 metres) by the count to get the wavelength.
/\ /\
/ \ / \
/ x \ / y \
/ \/ \

You walk to the next crest at y, but guess what? It isn't there.
It became a trough while you moved.
\ /\ /\
\ x / \ y / \
\ / \ / \
\/ \/ \

So you don't count it. When you get to the end of the tank
your wavelength will be 10 metres /5(counts) = 2 metres.
You check your watch and find that 10 seconds have elapsed.
So the frequency is 5/10 = 0.5 Hz.
Ok, so c = wf = 2 * 0.5 = 1.


Your example has nothing to do with how the speed of waves is calculated
in physics. You don't count crests one by one in order to find the
frequency, we assume you can measure the amplitude of the wave at
multiple points in space at the same time (for a water wave, you could
just take a photo).

Do you agree that Maxwell's laws predict, rightly or wrongly, that the
velocity of an electromagnetic wave such as light is always
independent of the velocity of the source, regardless of whether you
take the relativistic view that Maxwell's laws work in every frame, or
the pre-relativistic view that they only hold exactly in a certain
preferred frame, and that in other frames the velocity of light would
be c+v in one direction and c-v in the other?



I don't know what you mean by laws.


These equations right he

http://hyperphysics.phy-astr.gsu.edu...ric/maxeq.html

And again, here's a derivation which shows that these equations
necessarily imply that the speed of all electromagnetic waves is c:

http://www.vttoth.com/LIGHT/light.htm



The speed of light in a medium
is medium dependent and that takes care of MMX.


Again, although Maxwell's laws do say that a medium like air or water
slows down electromagnetic waves, they *don't* say that the speed of
electromagnetic waves through such a medium has anything to do with the
rest frame of the medium (but sound waves in air or water do--they
always travel at the same speed in the rest frame of the medium).




So unless he can find a theory that gives correct predictions for
all the various experiments in classical electromagnetism, and yet
does not have the feature that the velocity of light is independent
of the source velocity, then his ideas wouldn't even have seemed
plausible to a physicist in a time before the theory of relativity
had been published (but after the Michelson-Morley experiment had
been done).




Nobody has a computer then. Today we can calculate what the result
would be if a bullet stream from a moving machine gun moving in an
elliptical
orbit that obeyed Kepler's laws were to arrive at any distance.
The intensity of arriving bullets (grey line) looks like this.


http://www.androc1es.pwp.blueyonder....r/V1493Aql.JPG

If you examine the image closely, you'll see a crossover where the
faster bullets
has caught up with and passed the slower bullets.
That is a simple distance / time plot, distance vertical and time
horizontal.
What you would see is a sudden increase in the rate of arrival of
bullets,
then a second maximum, eventually tailing off.
A star in elliptical orbit would do the same thing.
Androcles.







What does this have to do with the comment you were responding to?
Either you have a complete theory of electromagnetism, which can make
correct predictions about all the experiments in classical
electromagnetism that have been done to date (which Maxwell's laws
can do), or you don't. And I'm pretty sure you don't.



Guessing again, are you not?



Sure, but I'd bet $100 that you don't have a complete set of equations
for predicting the dynamics of an arbitrary system of charges, with
the theory making the same predictions as Maxwell's laws for every
experimental setup which has been tested and found to agree with these
predictions. Will I have to pay up?



No. I do not have all the answers and never claimed to. I certainly do
not
have a complete set of equations, it took me ages to understand
Kepler's
equation M = E-e.sin(E).


Fair enough, but then why should you expect any physicists to believe
you when you say Maxwell's equations are wrong in the prediction that
the velocity of electromagnetic waves is independent of the velocity of
the source, yet they have been extremely successful at predicting the
behavior of systems of charges in all sorts of cases, and you don't have
any equally successful theory to replace them with?


However, I do claim that Einstein's equation,
½[tau0+tau2] = tau1
is fallacious and nonsensical. The ½ is meaningless drivel.

Which section of Einstein's paper is this one from?

Jesse

"Timo Nieminen" wrote in message
news:Pine.LNX.4.50.0501121351240.9519-100000@localhost...
On Wed, 12 Jan 2005, Androcles wrote:

I will now give the proof.
I place two identical evacuated tubes at right angles, with mirrors
and
with
sources and detectors of light.
When the light reaches a detector, it turns off the source.
When NO light reaches the detector, it turns the source on.
The path length can be any reasonable one.
I connect the outputs of the detectors to an up/down counter, one for
up
and the other for down. I calibrate the tube lengths until there is
no
count.
I now have MMX, electronic version and air free.

What's wrong with an actual Michelson interferometer where one looks
for
fringe shifts as the optical path length changes?

Nothing really, except it failed to prove to you that SR doesn't resolve
the null result. I'm pulsing the light to make its natural wavelength
irrelevant.


Since your original assertion was specific to MMX, I'll first deal
with
the actual MMX. Then your modified experiment.

I rotate the apparatus 90 degrees and what happens? NO count happens.
Acording to SR, and there being velocity as the Earth moves and
rotates
x' = (x-vt)/ sqrt(1-v^2/c^2)
y' = y.
So, x' does not equal y'.

Why would you want to analyse the experiment using a reference frame
moving wrt the Earth?

Simple, really.
If you analyse it from a frame that is at rest, you prove nothing at
all.
Hence we analyze from a relatively moving frame. Get your telescope
out and watch the fringe shifts from a plane if you like. As you look
at Michelson's light, you'll notice it is doppler-shifted. Stay at rest
and
you won't.

An analysis using any theory that is compatible with
the PoR allows us to use any reference frame.

There you are, then. You've answered your own question.

The frame in which the
apparatus is stationary allows the simplest analysis, so why not use
it?

Because It doesn't prove anything.

Are you trying to deliberately obfuscate the problem?

No, but you are by deliberately taking out v.



In a reference frame in which the apparatus is stationary, x and y
don't
change as the apparatus is rotated (assuming x and y are the
arm-lengths).

Exactly. So you prove nothing. However, Einstein's postulate is
"light is always propagated in empty space with a definite velocity
c which is independent of the state of motion of the emitting body"
Reference :
http://www.fourmilab.ch/etexts/einstein/specrel/www/

The Earth is moving in the empty space, which is the reference frame.
Are you trying to deliberately obfuscate the problem?

No frequency shifts, since there is no relative motion, no
wavelengths shifts, so no change after rotation.

Do you dispute this?

Yes. Michelson and Maxwell thought there was aether and that
was indeed the rest frame. It is also Einstein's rest frame, he is
saying so by his second postulate and modifying the PoR so that
c = (c+v)/(1-v/c)
You want to obfuscate the problem by declaring v = 0, satisfying
c+v = c+0 = c. If you declare that, then the problem is solved and
SR is irrelevant. The speed of Michelson's light is source dependent.
Without a |v| 0, SR vanishes without a trace.



The speed of flight in both tubes is c (invariant),
and the tubes are of different lengths.
Therefore a count will occur, the x (up) count exceeding the count of
the
(y) down counter.

In a reference frame in which the MMX apparatus is moving, yes,
according
to SR, there is a length contraction. The length contraction applies
equally to the wavelength in the contracted arm, so the length as
measured
in wavelengths along the arm remains exactly the same.

That has nothing to do with the *speed* of light. Speed is defined as
distance/time. The distance along the contracted arm is less that
the distance along the transverse arm. How much you contract the
wavelength of the light to cram in the same count of wavelenghts along
the contracted arm is completely irrelevant. Time is the same in both
arms.
The distances are different. You've change the *speed* of light.
SR says that is illegal. This is why the electronic MMX has an advantage
over the original. It doesn't care about the wavelength, the light is
pulsed
and only pulses are counted.



Note that the wavelengths for the incoming and the reflected wave are
different in the arm along the direction of motion.
This means that the
points where the two waves destuctively interfere in the arm move. If
you
bother to do the maths, you will see that those points move at the
same
speed as the whole apparatus, so in the moving frame one sees a moving
"standing" wave pattern. Measure the length of the arm in terms of
this
pattern.

Therefore, no change, even in the moving frame.


Damnly, my frank, I don't give a dear about the wavelength. I'm using
pulses. You are deliberately obfuscating. The solution you've just
given is for the speed of light being source dependent. I could make
my light tubes become sound tubes and still get a null result. I'm
applying
a velocity of the earth through the empty space from a moving source
and supposing that the speed of the light is independent of the source.


Remember, an interferometer like this does not measure physical
lengths,
it measures optical path length, in wavelengths. In the moving frame,
the
wavelength is different in the two arms.

That's why I'm using pulses (remember?)


The above is the simple, algebra-free explanation.

You mean algebra free obfuscation. Actually, all you have done is
given the classical mechanics explanation, you haven't use SR at all.


What follows is a
simple, algebra-based analysis of the experiment you described:

In the frame where the tubes are stationary, the rotation makes no
difference.

In other words, you are not using SR.


In the moving frame,

MOVING WITH RESPECT TO WHAT?
You can't have a moving frame unless you define what the rest frame is.


the arm along the motion is contracted
by 1/gamma, so we have x' = y'/gamma. The mirror moves at v, so the
light,
moving at c in the moving frame, moves at c-v towards the mirror, as
measured in the moving frame, and takes y'/(gamma (c-v)) to get there.
The
return journey is at c+v relative to the detector, as measured in the
moving frame, so the return journey takes y'/(gamma (c+v)). Therefore
the
total time along that arm for the round trip is

y'/gamma * (2c/(c^2 - v^2)).

There ya go.
You've just contradicted the invariance of the speed of light.
I'm done.
Androcles.



Don't forget that the mirror (and detector) in the other frame is also
moving. In time t1 that the light takes to go from the source to the
mirror, the mirror moves v t1. The distance the light needs to travel
is
then sqrt(y'^2 + v^2 t1^2), which must be equal to c t1. So,

t1 = y' / sqrt( c^2 - v^2 ) = y' c / (gamma * (c^2 - v^2)).

For the return trip, t2 = t1, so the total time for the round trips in
each arm is exactly the same.

No change is seen. Null result.

It is no good introducing time dilation. It is the same for both
tubes,
they are colocated in the same frame of reference.

Not needed at all.

So I repeat, SR isn't good enough to explain MMX, and it doesn't.

Not even algebra is needed to show that SR explains it perfectly well.
If
you want to use algebra, well, that also shows that SR explains MMX
perfectly well.

A speed of light that is source dependent will.

Any theory of optics satisfying the PoR explains it perfectly well, so
of
course emission theories explain it perfectly well.

--
Timo Nieminen - Home page:
http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits:
http://www.users.bigpond.com/timo_nieminen/spirits.html

"Jesse Mazer" wrote in message
...


Androcles wrote:

You saying it doesn't make it so, and since I know you of old as
another
big-headed know-it-all, more interested in trolling than recognizing
simple
solutions, I saw fit to simply deny your assertions.

I will now give the proof.
I place two identical evacuated tubes at right angles, with mirrors
and with
sources and detectors of light.
When the light reaches a detector, it turns off the source.
When NO light reaches the detector, it turns the source on.
The path length can be any reasonable one.
I connect the outputs of the detectors to an up/down counter, one for
up
and the other for down. I calibrate the tube lengths until there is no
count.
I now have MMX, electronic version and air free.
I rotate the apparatus 90 degrees and what happens? NO count happens.
Acording to SR, and there being velocity as the Earth moves and
rotates
x' = (x-vt)/ sqrt(1-v^2/c^2)
y' = y.
So, x' does not equal y'.
The speed of flight in both tubes is c (invariant),
and the tubes are of different lengths.
Therefore a count will occur, the x (up) count exceeding the count of
the
(y) down counter.

Are you saying SR predicts the time light takes to travel down each
tube will depend on how the tubes are oriented, or on the velocity of
the tubes in your reference frame?
No.

If so,

It isn't so, therefore [snip unread]

It is no good introducing time dilation. It is the same for both
tubes, they are colocated in the same frame of reference.
Unless, of course, you wish to add a time for the x-axis that
differs from the time in the y-axis, but that is not SR.
So I repeat, SR isn't good enough to explain MMX, and it doesn't.

A speed of light that is source dependent will.


But of course, saying the speed of light is source dependent means
throwing out Maxwell's laws, and scientists have no reason to do that
unless someone can come up with a new theory that both predicts the
speed of light is source dependent *and* that can replicate all the
experimentally-verified predictions of Maxwell's laws about the way
charged objects interact with each other and with the electromagnetic
field.

Jesse
Oh, shut up about Maxwell's laws. I've proven SR doesn't solve the
null result of MMX.
Androcles.

"Androcles" wrote in message
k...

[snip]

You can assume I'm not a fool. That's about all you can assume abut
me.

There is no evidence to support that assertion. There is, on the
contrary, vast quantities of evidence tosupport the opposite. Reread
all the garbage Androclown has spouted about simple non-relativistic
position-time calculations.

[snip]

Both Maxwell's laws and the Galilei-invariant analogue of
Maxwell's
laws predict that the velocity of a light wave is independent of
the
velocity of the source.

You have yet to show what you mean by "Galilei-invariant analogue "

I gave Androclown a references for that calculation about four times
now. You have failed to follow it up.
Here it is again:

Turner "Relativity Physics"Section 2.4 Page 26.

It is an introductory undergrad text and the algebra involved ia quite
simple, but in all probability not simple enough for Androclown to
follow, judging by past performance.

[snip]

Franz

"Jesse Mazer" wrote in message
...


Androcles wrote:

"Jesse Mazer" wrote in message
...

Androcles wrote:


"Jesse Mazer" wrote in message
...


Androcles wrote:



"Jesse Mazer" wrote in message
...




Of course, before Einstein physicists didn't think Maxwell's laws
would be correct in every observer's reference frame--they
thought they would only hold exactly in the rest frame of the
aether. They would have believed that to state the laws of
electromagnetism in a way that would hold in all frames, you'd
have to replace every x in Maxwell's laws with (x - v*t), where v
represents the observer's velocity relative to the rest frame of
the aether...any derivatives of x would have to be replaced in
the same way, like replacing dx/dt with (dx/dt - v). This would
give a new set of electromagnetic laws which would be
Galilei-invariant, and which would reduce to Maxwell's laws in
the case where v=0.

But a prediction of this Galilei-invariant analogue of Maxwell's
laws would be that for an observer in motion relative to the
aether, light will be observed to move at different speeds in
different directions, relative to himself. Unfortunately this was
not supported by the Michelson-Morley experiment.



The speed of light in diamond, water, air, any transparent medium
is
constant with respect to the medium. MMX fails to support aether.
In MMX, the medium is air. It is as simple as that.



What do you mean "the medium is air"?


I mean that air was used as a medium for light,
by Michelson, in his interferometer, of course.
He did not perform the experiment in an evacuated chamber, on the
surface
of the moon, or aboard the ISS.





My point was that when waves are considered as a vibration in a
medium, like sound waves, the speed of any wave will be constant
with respect to the rest frame of the medium.


Your points are invariance, x-vt, Maxwell's laws, derivatives,
aether and
anything else you can mention hoping to cover the issue, but you
omitted
to say anything about the physical medium used and asked me what I
meant by it, so clearly it was NOT your point, it is MY point.

Recall that Einstein's second postulate is
"light is always propagated in empty space with a definite velocity
c which is independent of the state of motion of the emitting body".


Maxwell's laws also say that light's velocity is independent of the
state of motion of the emitting body,


For light in a medium. Maxwell believed in aether.


Who cares what Maxwell believed? Maxwell's laws are just a set of
equations telling you how charged objects interact with the
electromagnetic field, and how the electromagnetic field in turn
affects the movements of charged objects. You don't have to believe in
aether

I do not, but Maxwell did. OK? So whatever Maxwell's "laws" may be,
they are premised on aether. There is no aether, so Maxwell has no law.
If you wish to discuss Maxwell's equations, we can do that. I refuse
to discuss Maxwell's "laws".
[snip]


This is a pure mathematical consequence of the equations of Maxwell's
laws.
[snip]

For reference, Maxwell's equations themselves can be found he

http://hyperphysics.phy-astr.gsu.edu...ric/maxeq.html

I see Gauss, Faraday and Ampere.


You can see that "the speed of light is c" is not a
tacked-on-assumption,

Ampere uses it. It IS a tacked on assumption.

I also see mu0 and epsilon0, properties of aether.
That is the tacked on assumption.



regardless of whether you have the relativistic understanding of
these laws (that they hold in all reference frames)


Michelson was intending to use doppler shift to measure the
the speed of light in the aether as the Earth flew through it. He was
certainly NOT claiming the speed of light was invariant. Neither was
Maxwell. Both believed time and distance are invariant, as indeed
they are.


Yes, they believed that Maxwell's laws only worked in a single
preferred reference frame. But in relativity, which neither Michelson
nor Maxwell believed in (because it hadn't been invented yet), if
Maxwell's laws are true in one reference frame they must be true in
all of them (because they have the mathematical property of
Lorentz-invariance).

Mathematical properties of aether. There is no aether. yawn



or the pre-relativistic understanding of them (that they only hold in
one preferred frame, and in other frames the velocity of light would
be c+v in one direction and c-v in the other).


Both are wrong. The speed of light is source dependent in a vacuum,
and medium dependent when passing though a medium. The medium
becomes the new source, of course.


So you assert.

So the stars assert, but you'd have them blowing themselves to
smithereens,
settling back to normal and blowing themselves to smithereens again.
You'd have them puffing up and down like blowfish. You'd have them
throwing out flares a 1000 times brighter than the star itself. You'd
have
a different model for every single phenomenon, and I have one model
for all of them. I don't think your many models are plausible, whatever
Maxwell's so-called "laws" may say.



But this does not fit with the predictions of classical
electromagnetism,

Of course it doesn't! Classical electrodynamics uses aether. THERE
IS NO AETHER.

and you don't have an alternate theory that can replicate all of the
successful predictions of classical electromagnetism.

I've told you. I do not have a theory at all. All theories are the work
of others. What I have is a discovery. I'm telling you about the
discovery.
The speed of light, in a vacuum, is source dependent, just like a
bullet from a gun. YOU figure out the theory.


All speeds are relative to something.
When requesting a drink on a plane, my speed relative to the flight
attendant is also zero, even though travelling at 500 mph ground
speed
and 250 mph by the air speed indicat