Androcles wrote:
"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
...
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]
No, you're wrong. Maxwell's equations are premised on empirical
observations.
(Sigh).
Here's an empirical observation.
http://www.androc1es.pwp.blueyonder....r/00918-ck.gif
Maxwell's "laws" are NOT based on that empirical observation
I don't know what that graph represents. Anyway, no, Maxwell's laws are
not based on *that* empirical observation, they are based on *other*
empirical observations involving electricity and magnets. Unless you
disagree with that, then you must agree that Maxwell's laws are based on
empirical observations, not on theories about "aether".
I really don't care if you use air as a medium for light's speed
I don't, because the idea is meaningless. When we say that air is the
medium for the propogation of soundwaves, we mean that soundwaves are
nothing more than *moving variations in the density of the air*--the
"peaks" of the wave are regions where the air is denser, the "valleys"
are where it's less dense. See the illustration of "Longitudinal waves"
on this page:
http://www.gmi.edu/~drussell/Demos/w...avemotion.html
The fact that soundwaves are variations in the density of the medium is
the basis for the idea that soundwaves travel at a constant speed in the
medium's rest frame. Even when light travels through a medium like air,
the peaks and valleys are still assumed to be variations in the
electromagnetic field, not in the density of the air. So there is no
reason whatsoever that *anyone* would think the rest frame of the air
has anything whatsoever to do with the speed of light--this is based
only on your own misunderstanding of what people mean when they say "X
is the medium for a certain type of wave" (they don't just mean that the
wave is travelling through that medium--even when electromagnetic waves
travel through air, air is not the medium for the propogation of these
electromagnetic waves).
because
I agree that the speed of light is medium dependent. I'm sure of it.
Maxwell can base his "laws" on observations made in a medium
until the cows come home
Nonsense, for a couple of reasons. First of all, Maxwell's laws do *not*
predict that the the speed of light has anything to do with the rest
frame of the air. Second of all, all the experiments that form the basis
for Maxwell's laws can easily be done in a vacuum. For example,
Faraday's law is one of the Maxwell equations, and it concerns the fact
that if a conductor (like a copper wire) is placed in a varying magnetic
field, a current will be induced in the conductor. This law can easily
be tested in a vacuum-sealed chamber, for example. The other experiments
which form the basis for Maxwell's laws are equally easy to perform in a
vacuum.
Physicists don't believe in aether anymore, but they still use
Maxwell's equations to make predictions about electromagnetic fields,
because the predictions of these equations STILL AGREE WITH
EXPERIMENTS. Are you disagreeing with this?
I'm predicting V1493 Aql will provide another outburst in about 200
years.
Are you disagreeing with me?
I have no idea what that claim is based on, or what V1493 Aql even is,
since you haven't explained it. But please answer my question--do you
agree or disagree that Maxwell's equations lead to correct predictions
for the thousands of experiments involving electricity and magnetism and
electromagnetic fields that have been done to date?
Yes, many of the set of equations known as "Maxwell's laws" had
already been discovered before Maxwell. But Maxwell was the first to
write down the complete set of equations for the electromagnetic
field, hence this collection of equations is known as "Maxwell's
laws". If you don't like this terminology, feel free to come up with
some other name for this set of six equations, and we can use that
name for the rest of our discussion; the equations will be the same
either way.
Here's another site which also refers to these equations as "Maxwell's
equations", so you can verify that I'm using the standard terminology:
http://en.wikipedia.org/wiki/Maxwell's_equations
Understand this: Mathematics can only DESCRIBE physics. It cannot
BE physics.
All modern physicists would disagree with you. In any case, if you have
a set of equations that have been extremely successful at making
predictions, then even if you say this is only a "description" of
physics, isn't it reasonable to think that any prediction which is in
contradiction with what the equations predict is more likely than not
incorrect?
If Einstein wants to play games pretending that time is
not invariant by claiming the time for light to get to a distant point
is 1/2 the time it takes to make the round trip, just because he can't
figure it out any other way, he's
1) wrong.
2) dead wrong.
3) an idiot savant.
I thought we were talking about electromagnetism, and the prediction
that the speed of light doesn't depend on the velocity of the source.
Anyway, it's not that Einstein couldn't figure it out any other way,
it's that he realized if different observers choose to synchronize
clocks by *assuming* light travels the same speed in both directions,
and if their rulers shrink and their clocks slow down in the manner
suggested by Lorentz, then if Maxwell's laws hold in one observer's
coordinate system they will hold in all observer's coordinate systems.
This is because Maxwell's laws have that mathematical property of
"Lorentz-invariance" which I mentioned earlier. And if all the
fundamental laws of physics are Lorentz-invariant, you can use this to
prove that rulers *must* shrink and clocks *must* slow down in just this
manner. And all the most fundamental laws that have been discovered so
far are, in fact, Lorentz-invariant; time dilation has also been
observed directly in a large number of experiments.
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.
Ampere's law does not say anything about the speed of light.
I give up.
There is quite clearly a c^2 in the middle box on the page
you referred to.
That's just the modern form, since now we know that light is an
electromagnetic wave. When the laws were formulated, though, that term
would have been expressed in terms of the permittivity and permeability
of free space, which are experimentally determined in ways that have
nothing to do with the speed of light. Of course, now that we know light
is an electromagnetic wave, we can say c = 1/squareroot(epsilon_0*mu_0).
But this was only discovered *after* Maxwell had discovered the complete
set of equations, as I mentioned in a previous post. What is your
explanation for this amazing "coincidence", if you don't believe that
the derivation of the speed of light from Maxwell's laws is correct?
Also, note that Maxwell's laws are usually written in the "differential
form" given on the bottom of that page, and that in that form c does not
appear in Ampere's law.
I'll accept Gauss,
I will accept Faraday. Ampere has a speed in it. I dnt care
how many times "physicists" have proven Gauss and Faraday,
I'm not clumping it all together and calling it "Maxwell" proven.
Ampere's law says that moving currents produce a magnetic field, are you
disagreeing with this? It can easily be demonstrated by placing two
wires next to each other and seeing that when a current is run through
both, they either attract or repel each other, depending on whether the
current is flowing in the same or the opposite direction. Maxwell made
one addition to Ampere's equation, predicting something called the
"displacement current", but this is also not too hard to verify
experimentally using a capacitor--see this page:
http://www.ee.byu.edu/ee/em/displace.htm
So there is just as much experimental justification for accepting
Ampere's law as there is for the others. And there is no getting around
the fact that when you put the equations together, they imply that
electromagnetic waves travel at velocity 1/squareroot(epsilon_0*mu_0)
regardless of the velocity of the source (Maxwell was the first to
discover this--the fact that he was the first to see the consequences of
putting all the laws together is why they are called "Maxwell's laws"
even though the individual equations were mostly discovered by others).
Jesse