Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

On Fri, 29 Jul 2005 10:43:19 -0400, sal wrote:
The problem here is really that the "classical" case is a squishy
fiction without hard rules.

True. There were many different "classical" theories of optics, and
many different ideas about how the "ether" interacted with ordinary
matter, if at all. In the context of a historical discussion about
optics, people often refer to first-order effects (in v/c) as
"classical", and to second-order effects as "relativistic". This is
because the "classical" ether theorists were more or less able to
account for all first-order effects (including Sagnac), and were not
forced to adopt the fully relativistic view until second-order
effects came under observation (e.g., Michelson and Morley).

.. in the absence of relativity (or some "aether clone" of
relativity) I don't see any way to predict the correct Sagnac
fringe shift when the signal is carried by an optical fiber with
relatively high index of refraction, rather than by vacuum or air.

Don't under-estimated the ingenuity of the classical theorists. To
account for all first-order effects, including the Fizeau experiment
(which showed how light propagates through a moving column of
water), it was necessary to adopt Fresnel's "partial dragging"
hypothesis.

Oops ... I have a vague memory of reading about Fresnel's hypothesis
but I had completely forgotten about it in this context. And I was
never clear on quite what it was, either.


This meant the ether was neither totally stationary nor
totally dragged along by material bodies. Through a complicated
chain of classical reasoning, Fresnel actually predicted this
partial dragging in 1818, three decades before Fizeau performed his
experiment. According to Fresnel, the speed of light in a medium
with refractive index n moving (along the same line) at speed +- v
should be c/n +- v(1 - n^2), and of course Fizeau confirmed this (up
to first order). If you work out your Sagnac effect with this
partial dragging, you'll see it agrees up to first order with the
relativistic prediction, basically because Fresnel's partial
dragging formula mimics the relativistic speed composition rule up
to first order.

Needless to say, Fresnel's interpretation of the extra term in the
velocity as due to partial dragging of the ether is not entirely
consistent, because the index of refraction in material media varies
with frequency, which means that Fresnel needs infinitely many
ethers, one for each frequency of light, being dragged at slightly
different speeds to account for the observed behavior at all
frequencies. This is the kind of detail that always nagged at ether
theorists, but in general they were happy to just have a theory that
more or less agreed with all the first-order experiments. It was the
second order experiments that made it clear to everyone that the
relativity principle itself, rather than the old mechanical
principles, was the more reliable guide to how things work.

Sagnac himself didn't address the presence of a medium; he assumed
he could ignore the effect of the air in his apparatus, and just
assume the light traveled at C relative to the "fixed frame" (I
think he thought there was an aether but I'm not sure).

Even as late at 1913, for some (particularly French) physicists the
two main competing theories of light were still the ether/wave
theory of Lorentz and the ballistic corpuscle theory of people like
Ritz. Those were the two main traditions, going back to Huygens and
Newton respectively. One major distinction between these theories
is that in an ether theory the speed of light is independent of the
speed of the source, whereas in a ballistic theory the speed of the
source is added to the speed of light. Sagnac's conclusion in his
1913 paper was that (in his words) "the speed of light is
independent of the speed of the source". This, he declared, proves
the existence of an ether.

Say, rather, that it disproves ballistic theory.

Obviously, saying something "proves" a theory correct is an
overstatement, as another experiment some time later may show some
other problem with it. But when an experiment contradicts a theory's
predictions, it's pretty safe to say it "disproves" it, and one must,
at a minimum, find a band-aid for the theory if one is not to reject
it completely.

In any case, while I don't know the exact details of Sagnac's
apparatus, if the air in the apparatus wasn't dragged along with the
disk, then Fox's variant on ballistic theory would still work (since
the air acts as a sort of "ether" and light travels at C/n, n~1,
relative to the air). It's when the tubes carrying the light are
evacuated or a glass fiber is used that ballistic theory really runs
into trouble. I don't see how it can be saved in that case. I don't
know if either of those variants on the experiment had been done when
Fox did his work; I think that was in the '60s.


Needless to say, the independence of light speed from the speed of
the source is a fundamental property of Einstein's relativity theory
too, and this was well known, so no one but the supporters of
ballistic theories was ever bothered by Sagnac's
observations. Sagnac's paper didn't discuss the possibility of a
non-ether theory with invariant light speed. He simply equated the
invariance of light speed with proof of an ether/wave theory.

Crackpots like to claim that Sagnac's result was originally widely
regarded as a refutation of special relativity, but this claim has
no basis in historical fact. Everyone familiar with special
relativity, even critics such as Michelson, always recognized that
the Sagnac effect is a (rather trivial) confirmation of special
relativity, not a refutation.

I think your web page is good, because it points out that Sagnac
devices using fiber optic lines actually involve the Fizeau effect
as well as the Sagnac effect, because they run light in opposite
directions through a rotating medium with an index of refraction
differing significantly from 1. In order to account for the results
in this kind of device, an etherist needs to invoke, at the very
least, Fresnel's partial dragging hypothesis. This makes the device
a somewhat less trivial confirmation of special relativity, because
the Fizeau effect is not trivial. This is seldom mentioned in
discussions of the Sagnac effect, perhaps because people consider
the "pure" Sagnac effect to be represented by a closed loop path
through the vacuum, as distinct from the Fizeau effect of light
propagating in a moving medium. But your point is well taken, that
both of these effects are present in many real Sagnac devices.

Hmmm ... looks like I gotta revise that page yet again... :-)


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

sal wrote:
Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

On Fri, 29 Jul 2005 10:43:19 -0400, sal wrote:
The problem here is really that the "classical" case is a squishy
fiction without hard rules.

True. There were many different "classical" theories of optics, and
many different ideas about how the "ether" interacted with ordinary
matter, if at all. In the context of a historical discussion about
optics, people often refer to first-order effects (in v/c) as
"classical", and to second-order effects as "relativistic". This is
because the "classical" ether theorists were more or less able to
account for all first-order effects (including Sagnac), and were not
forced to adopt the fully relativistic view until second-order
effects came under observation (e.g., Michelson and Morley).

.. in the absence of relativity (or some "aether clone" of
relativity) I don't see any way to predict the correct Sagnac
fringe shift when the signal is carried by an optical fiber with
relatively high index of refraction, rather than by vacuum or air.

Don't under-estimated the ingenuity of the classical theorists. To
account for all first-order effects, including the Fizeau experiment
(which showed how light propagates through a moving column of
water), it was necessary to adopt Fresnel's "partial dragging"
hypothesis.

Oops ... I have a vague memory of reading about Fresnel's hypothesis
but I had completely forgotten about it in this context. And I was
never clear on quite what it was, either.


This meant the ether was neither totally stationary nor
totally dragged along by material bodies. Through a complicated
chain of classical reasoning, Fresnel actually predicted this
partial dragging in 1818, three decades before Fizeau performed his
experiment. According to Fresnel, the speed of light in a medium
with refractive index n moving (along the same line) at speed +- v
should be c/n +- v(1 - n^2), and of course Fizeau confirmed this (up
to first order). If you work out your Sagnac effect with this
partial dragging, you'll see it agrees up to first order with the
relativistic prediction, basically because Fresnel's partial
dragging formula mimics the relativistic speed composition rule up
to first order.

Needless to say, Fresnel's interpretation of the extra term in the
velocity as due to partial dragging of the ether is not entirely
consistent, because the index of refraction in material media varies
with frequency, which means that Fresnel needs infinitely many
ethers, one for each frequency of light, being dragged at slightly
different speeds to account for the observed behavior at all
frequencies. This is the kind of detail that always nagged at ether
theorists, but in general they were happy to just have a theory that
more or less agreed with all the first-order experiments. It was the
second order experiments that made it clear to everyone that the
relativity principle itself, rather than the old mechanical
principles, was the more reliable guide to how things work.

Sagnac himself didn't address the presence of a medium; he assumed
he could ignore the effect of the air in his apparatus, and just
assume the light traveled at C relative to the "fixed frame" (I
think he thought there was an aether but I'm not sure).

Even as late at 1913, for some (particularly French) physicists the
two main competing theories of light were still the ether/wave
theory of Lorentz and the ballistic corpuscle theory of people like
Ritz. Those were the two main traditions, going back to Huygens and
Newton respectively. One major distinction between these theories
is that in an ether theory the speed of light is independent of the
speed of the source, whereas in a ballistic theory the speed of the
source is added to the speed of light. Sagnac's conclusion in his
1913 paper was that (in his words) "the speed of light is
independent of the speed of the source". This, he declared, proves
the existence of an ether.

Say, rather, that it disproves ballistic theory.

Obviously, saying something "proves" a theory correct is an
overstatement, as another experiment some time later may show some
other problem with it. But when an experiment contradicts a theory's
predictions, it's pretty safe to say it "disproves" it, and one must,
at a minimum, find a band-aid for the theory if one is not to reject
it completely.

In any case, while I don't know the exact details of Sagnac's
apparatus, if the air in the apparatus wasn't dragged along with the
disk, then Fox's variant on ballistic theory would still work (since
the air acts as a sort of "ether" and light travels at C/n, n~1,
relative to the air). It's when the tubes carrying the light are
evacuated or a glass fiber is used that ballistic theory really runs
into trouble. I don't see how it can be saved in that case. I don't
know if either of those variants on the experiment had been done when
Fox did his work; I think that was in the '60s.


Needless to say, the independence of light speed from the speed of
the source is a fundamental property of Einstein's relativity theory
too, and this was well known, so no one but the supporters of
ballistic theories was ever bothered by Sagnac's
observations. Sagnac's paper didn't discuss the possibility of a
non-ether theory with invariant light speed. He simply equated the
invariance of light speed with proof of an ether/wave theory.

Crackpots like to claim that Sagnac's result was originally widely
regarded as a refutation of special relativity, but this claim has
no basis in historical fact. Everyone familiar with special
relativity, even critics such as Michelson, always recognized that
the Sagnac effect is a (rather trivial) confirmation of special
relativity, not a refutation.

I think your web page is good, because it points out that Sagnac
devices using fiber optic lines actually involve the Fizeau effect
as well as the Sagnac effect, because they run light in opposite
directions through a rotating medium with an index of refraction
differing significantly from 1. In order to account for the results
in this kind of device, an etherist needs to invoke, at the very
least, Fresnel's partial dragging hypothesis. This makes the device
a somewhat less trivial confirmation of special relativity, because
the Fizeau effect is not trivial. This is seldom mentioned in
discussions of the Sagnac effect, perhaps because people consider
the "pure" Sagnac effect to be represented by a closed loop path
through the vacuum, as distinct from the Fizeau effect of light
propagating in a moving medium. But your point is well taken, that
both of these effects are present in many real Sagnac devices.

Hmmm ... looks like I gotta revise that page yet again... :-)


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

Nice web page. A very clear simple explaination of the Sagnac effect.
Just a few quibles.

Your statement about the inability of Newtonian mechanics to explain
Sagnac is backwards. Sagnac has often been used in this group in
attempts to show that light travels at c+v or c-v in a moving frame.
Why else would it take different times to go in opposit directions
around the ring To claim that the single clock is out of sync with
itself is really grasping at straws. Some might even say that is
absurd

Sagnac does not prove SR wrong because SR excludes rotations. In
"Relativity" Einstein wrote,

"If, relative to K, K' is a uniformly moving co-ordinate system devoid
of rotation, then natural phenomena run their course with respect to K'
according to exactly the same general laws as with respect to K. This
statement is called the principle of relativity (in the restricted
sense)."

The signal is partially dragged in media for both classical and
relativistic models, as it must be to agree with experiment. That is
what Fizeau proposed and varified experimentally before SR existed.
The media slows the signal to less than c, but slows it less when the
media is moving in the same direction as the signal. The signal cannot
be fully dragged or the signal speed could exceed c in the stationary
frame with a fast moving media.

One error I noticed in your classical view of the stationary frame is
that you used 2pi r for the distance traveled by the signals. That is
only true when there is no rotation. On the 28th Bilge wrote.

" Why not? If the ring rotates with an angular velocity, w, then
the light in the direction of rotation has to travel a distance:


s = 2\pi r + wrt_1


Where t is the time required for the light to reach the point on the
ring that it started, since the ring rotated by a distance wrt in that
time. Similarly, in the opposite direction, the distance traveled is
s = 2\pi r - wrt_2. The speed of light in the ring is v = c/n, so it
travels a distance s = vt_1 in the direction of rotation and s = vt_2
in the opposite direction."

I'm sure the 2\pi is a typo for 2*pi. The important thing here is that
he included the wrt factor. Leaving out the + or - wrt is what caused
your time to come out the same in both directions.

Bruce

On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


sal wrote:
Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

[ snip ]

Nice web page. A very clear simple explaination of the Sagnac
effect. Just a few quibles.

Your statement about the inability of Newtonian mechanics to explain
Sagnac is backwards. Sagnac has often been used in this group in
attempts to show that light travels at c+v or c-v in a moving frame.

Which just shows the level of silliness in some of the arguments in
this group.


Why else would it take different times to go in opposit
directions around the ring To claim that the single clock is out
of sync with itself is really grasping at straws. Some might even
say that is absurd

SR is intuitively unappealing. That's not news.


Sagnac does not prove SR wrong because SR excludes rotations.

Untrue. Einstein's SR paper didn't treat acceleration, and
accelerated _observers_ are beyond the ability of SR to handle with
any grace, but accelerated _objects_ can be handled just fine in most
cases without stepping outside the math of SR. (If you want to be
nit-picky about it you need to add the "clocks postulate" to SR in
order to allow you to conclude anything about accelerated objects.)

And the reason Sagnac doesn't disprove SR is that SR predicts the
effect, and is, in that sense, confirmed by it, rather than
contradicted by it. To handle it strictly within the bounds of SR you
must look at it from the fixed frame, but from that point of view it's
a trivial bit of algebra to derive the effect.


In "Relativity" Einstein wrote,

"If, relative to K, K' is a uniformly moving co-ordinate system
devoid of rotation, then natural phenomena run their course with
respect to K' according to exactly the same general laws as with
respect to K. This statement is called the principle of relativity
(in the restricted sense)."

The signal is partially dragged in media for both classical and
relativistic models, as it must be to agree with experiment.

Right. Composition of velocities automatically gives partial
dragging. In aether theory partial dragging must be glued on somehow,
which is what Fresnel did, 'way back when. In ballistic theory it's
even harder to come up with a scenario in which partial dragging makes
sense.


That is what Fizeau proposed and varified experimentally before SR
existed. The media slows the signal to less than c, but slows it
less when the media is moving in the same direction as the signal.
The signal cannot be fully dragged or the signal speed could exceed
c in the stationary frame with a fast moving media.

And that reasoning leads almost directly to the Lorentz transforms and
the composition of velocities formula, and suddenly you're looking at
what's commonly called "Lorentz ether theory" in this newsgroup; it
has been stated many times that its predictions are identical to those
of SR.

Since SR uses no "ether" one must conclude that this is another way to
say there is no evidence for the "ether" assumed by the so-called
Lorentz ether theory.


One error I noticed in your classical view of the stationary frame
is that you used 2pi r for the distance traveled by the signals.

No, I didn't. Equation (2) shows the time to go around clockwise,
given that the signal travels at velocity u(-) as viewed in the lab
frame to go around the ring that way. First line of (2):

u(-) t(-) = 2 pi r - v t(-)

Term by term:

u(-) is the signal speed going clockwise, viewed from fixed frame

t(-) is the time to go from the emitter to the detector

2 pi r is the full circumference of the ring

v t(-) is the distance traveled by the detector in that time

So the total distance traveled, as given in that equation, is

2 pi r - v t(-)

which is less than the full circumference. And t(-) is time to get
from the emitter to detector, not time to go all the way around the
circle. The detector is "coming to meet" the detector in that case.

Going the other way, it's given by equation (4), and is

2 pi r + v t(-)

and is, of course, longer than the full circumference, because the
detector is "running away" from the signal in that case.


That is only true when there is no rotation. On the 28th Bilge
wrote.

"Why not? If the ring rotates with an angular velocity, w, then the
light in the direction of rotation has to travel a distance:


s = 2\pi r + wrt_1

Which is exactly what I said on that page. Bilge assumed k=u=c which
I did not, but aside from that it's the same formula.

Note that w = omega = angular velocity in the fixed frame, r = radius
in the fixed frame, and wr = v in my formula (2). Again, it's the
same formula.


Where t is the time required for the light to reach the point on the
ring that it started, since the ring rotated by a distance wrt in
that time. Similarly, in the opposite direction, the distance
traveled is s = 2\pi r - wrt_2. The speed of light in the ring is v
= c/n, so it travels a distance s = vt_1 in the direction of
rotation and s = vt_2 in the opposite direction."

I'm sure the 2\pi is a typo for 2*pi.

No it certainly is not a typo. Bilge uses "\pi" to mean "the symbol
for pi" and juxtaposition of terms in an expression implies
multiplication, according to common modern usage. Bilge wrote what he
intended.


The important thing here is that he included the wrt factor.

As did I.


Leaving out the + or - wrt is what caused your time to come out the
same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to the
cable (rather than C relative to the fixed frame), combined with
vector addition of velocities, which leads to the time coming out the
same in both directions.


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

"sal" wrote in message
news | Your statement about the inability of Newtonian mechanics to explain
| Sagnac is backwards. Sagnac has often been used in this group in
| attempts to show that light travels at c+v or c-v in a moving frame.
|
| Which just shows the level of silliness in some of the arguments in
| this group.

Yours among them.
|
|
| Why else would it take different times to go in opposit
| directions around the ring To claim that the single clock is out
| of sync with itself is really grasping at straws. Some might even
| say that is absurd
|
| SR is intuitively unappealing. That's not news.

Don't be silly, I've had plenty of fun with it. Of course it's
appealing.
Watching you struggle trying to put the x coordinate into
tau(x',0,0,t) has been hilarious.
If x' =x-vt and x = 0, what is tau (-vt, 0,0,t)?

[snip the rest, funny as it was]

Androcles

sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


sal wrote:
Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

[ snip ]

Nice web page. A very clear simple explaination of the Sagnac
effect. Just a few quibles.

Your statement about the inability of Newtonian mechanics to explain
Sagnac is backwards. Sagnac has often been used in this group in
attempts to show that light travels at c+v or c-v in a moving frame.

Which just shows the level of silliness in some of the arguments in
this group.

Oh, I see, anything that doesn't agree with your point of view is
silly.

Why else would it take different times to go in opposit
directions around the ring To claim that the single clock is out
of sync with itself is really grasping at straws. Some might even
say that is absurd

SR is intuitively unappealing. That's not news.

What you are doing is not SR. I already provided you with one quote
that said, "K' is a uniformly moving co-ordinate system devoid of
rotation". What part of "devoid of rotation" do you not understand?
If you look in "On The Electrodynamics Of Moving Bodies" you will find,
"in a state of parallel translatory motion parallel to the axis of X"
Do you understand what that is saying? Your example deviates from
normal SR practice for clock sync. Two clocks resting at the same
point are supposed to show the same time in SR. A slow transported
clock is not supposed to go out of sync in SR.

Sagnac does not prove SR wrong because SR excludes rotations.

Untrue. Einstein's SR paper didn't treat acceleration, and
accelerated _observers_ are beyond the ability of SR to handle with
any grace, but accelerated _objects_ can be handled just fine in most
cases without stepping outside the math of SR. (If you want to be
nit-picky about it you need to add the "clocks postulate" to SR in
order to allow you to conclude anything about accelerated objects.)

And the reason Sagnac doesn't disprove SR is that SR predicts the
effect, and is, in that sense, confirmed by it, rather than
contradicted by it. To handle it strictly within the bounds of SR you
must look at it from the fixed frame, but from that point of view it's
a trivial bit of algebra to derive the effect.

In SR all frames are equal. Here you are saying that you can do
something in one frame but not the other. Why is that? Because the
frames are not equal and you are not working with SR.

In "Relativity" Einstein wrote,

"If, relative to K, K' is a uniformly moving co-ordinate system
devoid of rotation, then natural phenomena run their course with
respect to K' according to exactly the same general laws as with
respect to K. This statement is called the principle of relativity
(in the restricted sense)."

The signal is partially dragged in media for both classical and
relativistic models, as it must be to agree with experiment.

Right. Composition of velocities automatically gives partial
dragging. In aether theory partial dragging must be glued on somehow,
which is what Fresnel did, 'way back when. In ballistic theory it's
even harder to come up with a scenario in which partial dragging makes
sense.

When dicussing the Fizeau experiment in "Relativity" Einstein glued on
dragging by stating, "In accordance with the principle of relativity we
shall certainly have to take for granted that the propagation of light
always takes place at the same velocity w with respect to the liquid,
whether the latter is in motion with reference to other bodies or not."

That is what Fizeau proposed and varified experimentally before SR
existed. The media slows the signal to less than c, but slows it
less when the media is moving in the same direction as the signal.
The signal cannot be fully dragged or the signal speed could exceed
c in the stationary frame with a fast moving media.

And that reasoning leads almost directly to the Lorentz transforms and
the composition of velocities formula, and suddenly you're looking at
what's commonly called "Lorentz ether theory" in this newsgroup; it
has been stated many times that its predictions are identical to those
of SR.

The Lorentz transforms are not needed for a classical explaination, nor
is LET. And the classical explaination works with absolute time, so
there are no clocks going out of sync with themselves.

Since SR uses no "ether" one must conclude that this is another way to
say there is no evidence for the "ether" assumed by the so-called
Lorentz ether theory.

And what explaination does SR provide for how light energy gets from
point A to point B?

One error I noticed in your classical view of the stationary frame
is that you used 2pi r for the distance traveled by the signals.

No, I didn't. Equation (2) shows the time to go around clockwise,
given that the signal travels at velocity u(-) as viewed in the lab
frame to go around the ring that way. First line of (2):

u(-) t(-) = 2 pi r - v t(-)

Term by term:

u(-) is the signal speed going clockwise, viewed from fixed frame

t(-) is the time to go from the emitter to the detector

2 pi r is the full circumference of the ring

v t(-) is the distance traveled by the detector in that time

So the total distance traveled, as given in that equation, is

2 pi r - v t(-)

which is less than the full circumference. And t(-) is time to get
from the emitter to detector, not time to go all the way around the
circle. The detector is "coming to meet" the detector in that case.

Going the other way, it's given by equation (4), and is

2 pi r + v t(-)

and is, of course, longer than the full circumference, because the
detector is "running away" from the signal in that case.

My bad. I was looking for a rotation and did not see v as representing
one.

That is only true when there is no rotation. On the 28th Bilge
wrote.

"Why not? If the ring rotates with an angular velocity, w, then the
light in the direction of rotation has to travel a distance:


s = 2\pi r + wrt_1

Which is exactly what I said on that page. Bilge assumed k=u=c which
I did not, but aside from that it's the same formula.

Note that w = omega = angular velocity in the fixed frame, r = radius
in the fixed frame, and wr = v in my formula (2). Again, it's the
same formula.


Where t is the time required for the light to reach the point on the
ring that it started, since the ring rotated by a distance wrt in
that time. Similarly, in the opposite direction, the distance
traveled is s = 2\pi r - wrt_2. The speed of light in the ring is v
= c/n, so it travels a distance s = vt_1 in the direction of
rotation and s = vt_2 in the opposite direction."

I'm sure the 2\pi is a typo for 2*pi.

No it certainly is not a typo. Bilge uses "\pi" to mean "the symbol
for pi" and juxtaposition of terms in an expression implies
multiplication, according to common modern usage. Bilge wrote what he
intended.


The important thing here is that he included the wrt factor.

As did I.


Leaving out the + or - wrt is what caused your time to come out the
same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to the
cable (rather than C relative to the fixed frame), combined with
vector addition of velocities, which leads to the time coming out the
same in both directions.

Ah, so you found your error, And I assume you will correct it on your
web site

--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

Hey, Sock, who's your puppeteer?


On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:



Leaving out the + or - wrt is what caused your time to come out the
same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to the
cable (rather than C relative to the fixed frame), combined with vector
addition of velocities, which leads to the time coming out the same in
both directions.

Ah, so you found your error, And I assume you will correct it on your web
site

Ah, so you intentionally misunderstand.

That was the reason that a purely Newtonian argument with fixed signal
speed relative to the cable which leads to no Sagnac ... it wasn't any
"mistake" on my web page, nor any mistake in relativity.

Whoever your puppeteer is, you're boring.

**plonk**


--
Nospam becomes physicsinsights to fix the email

sal wrote:
Hey, Sock, who's your puppeteer?


On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:



Leaving out the + or - wrt is what caused your time to come out the
same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to the
cable (rather than C relative to the fixed frame), combined with vector
addition of velocities, which leads to the time coming out the same in
both directions.

Ah, so you found your error, And I assume you will correct it on your web
site

Ah, so you intentionally misunderstand.

Not sure what you are talking about here but I don't intentionally
misunderstand things. It is not my intention to be a troll. I commend
you for the effort you have put into building your site. I was just
trying to correct a few things that I knew were not quite right. It
wasn't meant as an attack. Sorry if it came off as one.

As for my being a crank, I do not claim that there is anything wrong
with relativity. And I am not the only one that said there were a few
questionable things about your page. Bill Hobba questioned the use of
SR with a rotating system. Your own page says that you can not sync
clocks in a rotating frame. That should have been a clue that
something was wrong. What you have done is show why SR can't be used
in rotating frames. Bilge and Dirk also raised some questions. Are
they puppets as well?

That was the reason that a purely Newtonian argument with fixed signal
speed relative to the cable which leads to no Sagnac ... it wasn't any
"mistake" on my web page, nor any mistake in relativity.

The reason it was a mistake is because you claimed to be viewing things
classically from the stationary frame. Making the "fixed signal speed
relative to the cable" is right out of relativity, and frame jumping to
boot.

Whoever your puppeteer is, you're boring.

**plonk**


I have no puppeteer. Bruce S Richmond


--
Nospam becomes physicsinsights to fix the email

On Thu, 04 Aug 2005 18:57:33 -0700, wrote:

I have no puppeteer. Bruce S Richmond

Well, my sincere apologies, indeed. It seems that I took your post
rather differently from the spirit in which it was given.

Luckily I messed up my filter file or I wouldn't have seen your
followup post. You may rest assured I'll be less trigger happy in the
future.

I'll start over again here, and this time I'll be a bit more polite
.... :-(


sal wrote:

On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


Leaving out the + or - wrt is what caused your time to come
out the same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to
the cable (rather than C relative to the fixed frame), combined
with vector addition of velocities, which leads to the time
coming out the same in both directions.

Ah, so you found your error, And I assume you will correct it on
your web site

Ah, so you intentionally misunderstand.

Not sure what you are talking about here but I don't intentionally
misunderstand things. It is not my intention to be a troll. I
commend you for the effort you have put into building your site. I
was just trying to correct a few things that I knew were not quite
right. It wasn't meant as an attack. Sorry if it came off as one.

As for my being a crank, I do not claim that there is anything wrong
with relativity. And I am not the only one that said there were a
few questionable things about your page. Bill Hobba questioned the
use of SR with a rotating system. Your own page says that you can
not sync clocks in a rotating frame. That should have been a clue
that something was wrong.

The thing that is wrong was my assertion that "classically" the effect
is inexplicable. (More on that, below.) The use I made of relativity
is fine, however.

You should, by the way, notice something: Noplace on that page do I
use the term "special relativity". It just happens that the only math
I used was math which one encounters in special relativity.


What you have done is show why SR can't be used in rotating frames.

This is debatable and is really a point of semantics.

The semantic issue is: "What is special relativity"? From _general_
relativity ... and from experiments ... we know that acceleration,
itself, does not affect time. We also know there's nothing magical
about rotation -- it's just linear motion combined with centripetal
acceleration.

Einstein's original SR papers didn't deal with acceleration. However,
that doesn't mean we can't apply the same techniques to accelerated
bodies, and, in fact, knowing what we know about relativity in
general, there's no reason not to.

Again, the issue is one of semantics: If, when you say "Special
Relativity" you mean "What Einstein discussed in 1905", then
accelerated frames are indeed left out. BUT if when I say "Special
Relativity" I mean "Relativity in the absence of gravitational fields,
and in which we restrict our analysis to use only coordinate systems
in which the metric is Lorentz's", then I can study accelerated
objects with no problem, and, with due caution, I can even examine
accelerated frames.

About any (non-singular) point one can construct a "local Lorentz"
frame, or a "momentarily comoving reference frame". This is an
inertial frame which coincides with the frame you started with at one
particular instant in time and one particular place. If one works
through the behavior of a signal moving around the rim of a disk with
velocity k relative to the disk's rim, and the rim of the disk is
moving at velocity v, one will indeed find that the velocity of the
signal as viewed by an observer in the "stationary" frame is given by
the composition of velocities law. That's (a sketch of) the
justification for the first part of the page in which I discuss the
effect from the "fixed frame".

One can include as much or as little detail as one wants in the
analysis; however, if one keeps in mind that the behavior of an
accelerated reference frame is _locally_ just like the behavior of an
inertial frame which happens to be comoving with it, _AND_ if one
keeps in mind that the acceleration here is always transverse to the
velocity, one can see immediately that the "local Lorentz frame" is
just the frame that's moving tangentially to the disk, and the signal
speed must obviously be given by CofV. One can then skip the messy
math because the result is obvious up front.

Now, as to the analysis from the point of view of the cable -- we can
again note that the acceleration doesn't affect time, and from that we
at once see that it's just the same as the "straight" case, save that
it's bent. The bend itself is irrelevant. (Magnify the picture
enough, and you can't even see the bend; and it's in the "magnified"
view that we actually take all the derivatives, which are what we're
concerned with here.)

From there, just picturing it makes it clear that the man walking
around the rim carrying a watch must see things just exactly the same
way the man walking down a straight moving cable would see them. The
fact that he's accelerating inward, again, doesn't affect his watch,
and doesn't affect his measurements of tangential lengths. So, the
result _must_ come out the same as if the cable where laid out
straight.

If we want to be totally complete in our picture, we can also imagine
that we're using light pulses to synchronize closely spaced clocks all
around the rim of the disk. They're close enough together that we
don't have to worry about the acceleration. If we ask ourselves what
will happen, it's pretty clear that we'll get exactly the same result
that way as we would if we did it on the straight moving cable -- when
we get to the "other end" we've got what looks like a time skew
relative to the starting point from the point of view of someone in
the stationary frame.

Finally, given that the "composition of velocities" approach is
clearly correct, that provides a second demonstration that the
"wrapped straight cable" approach is correct: The two produce the same
answer.

Obviously I didn't include all these extra words on the page. In
fact, the original reasoning consisted of just the illustrations; the
words on the page all came later, and all the additional stuff about
MCRFs and so forth didn't seem likely to contribute at all to the
clarity of the page.

I hope this helps a bit with understanding why I didn't feel the need
to use anything beyond CofV and some Lorentz transforms in the
analysis!



Bilge and Dirk also raised some
questions. Are they puppets as well?

No, not at all.


That was the reason that a purely Newtonian argument with fixed
signal speed relative to the cable which leads to no Sagnac ... it
wasn't any "mistake" on my web page, nor any mistake in relativity.

Again, there are several ways of approach this "classically".

There's (classic) ballistic theory, which assumes the signal in vacuum
travels at C relative to the emitter, and at C/N in a glass fiber
relative to the fiber. That matches what I called the "classic" case
and it leads to a conclusion of no Sagnac effect.

There's classical aether theory, in which one can assume any degree of
"dragging" of the signal by the medium. On the page I talk about no
dragging (signal moves at fixed velocity relative to the lab frame)
and I talk about "full dragging" (just like the BaT case: signal
moves at C/N relative to the medium).

But the case I did not discuss -- which I really need to add! -- is
the case where there is "partial dragging". That notion dates from
some time in the 1800's and actually explains the Sagnac effect. So,
it _is_ explainable "classically", and I need to update the page to
say so.

*****************************************

Now, let me see what else I overlooked in your earlier post...

On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


sal wrote:
Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

[ snip ]

Nice web page. A very clear simple explaination of the Sagnac
effect. Just a few quibles.

Your statement about the inability of Newtonian mechanics to
explain Sagnac is backwards. Sagnac has often been used in this
group in attempts to show that light travels at c+v or c-v in a
moving frame.

Which just shows the level of silliness in some of the arguments in
this group.

Oh, I see, anything that doesn't agree with your point of view is
silly.

No, that's not what I meant at all.

I meant it's silly to claim that the Sagnac effect _refutes_
relativity in any way. However, that exact claim is often made. I
don't understand why -- the only "proof" I've ever seen that the
effect contravenes relativity comes down to proof by assertion. And,
after working it out for myself, it obviously doesn't do any such
thing.


Why else would it take different times to go in opposit directions
around the ring To claim that the single clock is out of sync
with itself is really grasping at straws. Some might even say
that is absurd

SR is intuitively unappealing. That's not news.

I can expand on this. I didn't mean "a single clock is out of sync
with itself". That's obviously absurd.

The trick here is to get from (my) figure 4 to figure 5, and see that
they're the same thing.

Take a linearly moving cable, with the clocks in sync in the
_stationary_ frame. Now, without changing anything -- particularly
without changing its linear velocity -- wrap it around the spinning
disk.

You get figure 5. And if someone walks around the disk holding a
clock, if there are clocks all along the length of the cable that are
in sync in the "lab frame", the walker will see them getting farther
and farther from his/her clock as he/she moves around the rim.

It's a purely visual argument, but it matches the math.


What you are doing is not SR.

So what? It's relativity. It's based on pseudo Riemannian geometry,
applied in flat space where there is a global Lorentz frame.


If you look in
"On The Electrodynamics Of Moving Bodies" you will find, "in a state of
parallel translatory motion parallel to the axis of X" Do you understand
what that is saying? Your example deviates from normal SR practice for
clock sync.

So what?


Two clocks resting at the same point are supposed to show the same
time in SR. A slow transported clock is not supposed to go out of
sync in SR.

So? A clock which is carried around the ring is _NOT_ "slow
transported" in the local inertial frame of someone who is situated at
one point on the ring!

Consider: When the clock is situated diametrically across from the
"ring-stationary observer" the clock is moving at velocity -V in the
observer's MCRF. That's not "slow"! So, it's not slow transport, and
there's no surprise that the clock goes out of sync.

Just _how_ it goes out of sync is a interesting question which
deserves some calculations and graphs of its own. I don't claim to
have exhausted the subject -- I have barely scratched the surface.


Sagnac does not prove SR wrong because SR excludes rotations.

Untrue. Einstein's SR paper didn't treat acceleration, and
accelerated _observers_ are beyond the ability of SR to handle with
any grace, but accelerated _objects_ can be handled just fine in
most cases without stepping outside the math of SR. (If you want
to be nit-picky about it you need to add the "clocks postulate" to
SR in order to allow you to conclude anything about accelerated
objects.)

And the reason Sagnac doesn't disprove SR is that SR predicts the
effect, and is, in that sense, confirmed by it, rather than
contradicted by it. To handle it strictly within the bounds of SR
you must look at it from the fixed frame, but from that point of
view it's a trivial bit of algebra to derive the effect.

In SR all frames are equal. Here you are saying that you can do
something in one frame but not the other. Why is that? Because the
frames are not equal and you are not working with SR.

So what? I'm happy with GR. I just didn't show any math beyond what
you're familiar with from SR on that page.

In any case the frame which is "different" is the accelerated frame,
and, yes, that's "different", all right.

Accelerated _bodies_ are, as a rule, easily handled in SR.
Accelerated coordinate systems are not.


In "Relativity" Einstein wrote,

If, relative to K, K' is a uniformly moving co-ordinate system
"devoid of rotation, then natural phenomena run their course with
respect to K' according to exactly the same general laws as with
respect to K. This statement is called the principle of
relativity (in the restricted sense)."

The signal is partially dragged in media for both classical and
relativistic models, as it must be to agree with experiment.

Right. Composition of velocities automatically gives partial
dragging. In aether theory partial dragging must be glued on
somehow, which is what Fresnel did, 'way back when. In ballistic
theory it's even harder to come up with a scenario in which partial
dragging makes sense.

When dicussing the Fizeau experiment in "Relativity" Einstein glued
on dragging by stating, "In accordance with the principle of
relativity we shall certainly have to take for granted that the
propagation of light always takes place at the same velocity w with
respect to the liquid, whether the latter is in motion with
reference to other bodies or not."

I'd say that's just the principle of relativity at work. Why don't
you think so?


That is what Fizeau proposed and varified experimentally before
SR existed. The media slows the signal to less than c, but slows
it less when the media is moving in the same direction as the
signal. The signal cannot be fully dragged or the signal speed
could exceed c in the stationary frame with a fast moving media.

And that reasoning leads almost directly to the Lorentz transforms
and the composition of velocities formula, and suddenly you're
looking at what's commonly called "Lorentz ether theory" in this
newsgroup; it has been stated many times that its predictions are
identical to those of SR.

The Lorentz transforms are not needed for a classical explaination,
nor is LET. And the classical explaination works with absolute
time, so there are no clocks going out of sync with themselves.

The classical explanation which works requires an assumption of
"partial dragging of the aether".


Since SR uses no "ether" one must conclude that this is another way
to say there is no evidence for the "ether" assumed by the
so-called Lorentz ether theory.

And what explanation does SR provide for how light energy gets from
point A to point B?

Ask God.

While you're at it ask Him what "energy" is to start with.

The proof of a theory is whether its predictions are correct, not
whether you feel it gives you an intuitive "explanation" of how things
might work.


[ snip point of agreement ... yes, we had one... ]


Leaving out the + or - wrt is what caused your time to come out
the same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to
the cable (rather than C relative to the fixed frame), combined
with vector addition of velocities, which leads to the time coming
out the same in both directions.

Ah, so you found your error, And I assume you will correct it on
your web site

Again, the error is that there were more kinds of "classical
analysis" than I allowed for, and classical aether theory with partial
dragging can account for the effect.

And someday soon I'll be rewriting part of the page to reflect that.


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

sal wrote:
On Thu, 04 Aug 2005 18:57:33 -0700, wrote:

I have no puppeteer. Bruce S Richmond

Well, my sincere apologies, indeed. It seems that I took your post
rather differently from the spirit in which it was given.

Luckily I messed up my filter file or I wouldn't have seen your
followup post. You may rest assured I'll be less trigger happy in the
future.

I'll start over again here, and this time I'll be a bit more polite
... :-(


sal wrote:

On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


Leaving out the + or - wrt is what caused your time to come
out the same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to
the cable (rather than C relative to the fixed frame), combined
with vector addition of velocities, which leads to the time
coming out the same in both directions.

Ah, so you found your error, And I assume you will correct it on
your web site

Ah, so you intentionally misunderstand.

Not sure what you are talking about here but I don't intentionally
misunderstand things. It is not my intention to be a troll. I
commend you for the effort you have put into building your site. I
was just trying to correct a few things that I knew were not quite
right. It wasn't meant as an attack. Sorry if it came off as one.

As for my being a crank, I do not claim that there is anything wrong
with relativity. And I am not the only one that said there were a
few questionable things about your page. Bill Hobba questioned the
use of SR with a rotating system. Your own page says that you can
not sync clocks in a rotating frame. That should have been a clue
that something was wrong.

The thing that is wrong was my assertion that "classically" the effect
is inexplicable. (More on that, below.) The use I made of relativity
is fine, however.

You should, by the way, notice something: Noplace on that page do I
use the term "special relativity". It just happens that the only math
I used was math which one encounters in special relativity.

If it quacks like a duck ....

What you have done is show why SR can't be used in rotating frames.

This is debatable and is really a point of semantics.

The semantic issue is: "What is special relativity"? From _general_
relativity ... and from experiments ... we know that acceleration,
itself, does not affect time. We also know there's nothing magical
about rotation -- it's just linear motion combined with centripetal
acceleration.

Einstein's original SR papers didn't deal with acceleration. However,
that doesn't mean we can't apply the same techniques to accelerated
bodies, and, in fact, knowing what we know about relativity in
general, there's no reason not to.

With Einstein's SR clock syncing provides one and only one time
coordinate for a given location in a frame. You yourself have said it
is absurd to have a clock out of sync with itself, but that is what you
end up with when you go full circle. A curve is not a straight line.
You can only perpetuate that lie so long before it comes around and
bites your backside.

Again, the issue is one of semantics: If, when you say "Special
Relativity" you mean "What Einstein discussed in 1905", then
accelerated frames are indeed left out. BUT if when I say "Special
Relativity" I mean "Relativity in the absence of gravitational fields,
and in which we restrict our analysis to use only coordinate systems
in which the metric is Lorentz's", then I can study accelerated
objects with no problem, and, with due caution, I can even examine
accelerated frames.

About any (non-singular) point one can construct a "local Lorentz"
frame, or a "momentarily comoving reference frame". This is an
inertial frame which coincides with the frame you started with at one
particular instant in time and one particular place. If one works
through the behavior of a signal moving around the rim of a disk with
velocity k relative to the disk's rim, and the rim of the disk is
moving at velocity v, one will indeed find that the velocity of the
signal as viewed by an observer in the "stationary" frame is given by
the composition of velocities law. That's (a sketch of) the
justification for the first part of the page in which I discuss the
effect from the "fixed frame".

One can include as much or as little detail as one wants in the
analysis; however, if one keeps in mind that the behavior of an
accelerated reference frame is _locally_ just like the behavior of an
inertial frame which happens to be comoving with it, _AND_ if one
keeps in mind that the acceleration here is always transverse to the
velocity, one can see immediately that the "local Lorentz frame" is
just the frame that's moving tangentially to the disk, and the signal
speed must obviously be given by CofV. One can then skip the messy
math because the result is obvious up front.

Whether you can see it or not the curve is still there. When you are
pushing a new system of measurement because it is more accurate than
the old, it seems sort of foolish to say that it is better if you don't
look too close, or in this case look so close that you don't see the
big picture.

Now, as to the analysis from the point of view of the cable -- we can
again note that the acceleration doesn't affect time, and from that we
at once see that it's just the same as the "straight" case, save that
it's bent. The bend itself is irrelevant. (Magnify the picture
enough, and you can't even see the bend; and it's in the "magnified"
view that we actually take all the derivatives, which are what we're
concerned with here.)

From there, just picturing it makes it clear that the man walking
around the rim carrying a watch must see things just exactly the same
way the man walking down a straight moving cable would see them. The
fact that he's accelerating inward, again, doesn't affect his watch,
and doesn't affect his measurements of tangential lengths. So, the
result _must_ come out the same as if the cable where laid out
straight.

If we want to be totally complete in our picture, we can also imagine
that we're using light pulses to synchronize closely spaced clocks all
around the rim of the disk. They're close enough together that we
don't have to worry about the acceleration. If we ask ourselves what
will happen, it's pretty clear that we'll get exactly the same result
that way as we would if we did it on the straight moving cable -- when
we get to the "other end" we've got what looks like a time skew
relative to the starting point from the point of view of someone in
the stationary frame.

It is obvious that signals transmitted in opposite directions around
the disk do not get back to the starting point at the same instant.
Saying that it is the same instant when timed by two different clocks
at the same location doesn't sound very convincing. Classical theory
can get the two different times measured with one clock. Which sounds
more reasonable? Now what did we do with that razor?

Finally, given that the "composition of velocities" approach is
clearly correct, that provides a second demonstration that the
"wrapped straight cable" approach is correct: The two produce the same
answer.

Obviously I didn't include all these extra words on the page. In
fact, the original reasoning consisted of just the illustrations; the
words on the page all came later, and all the additional stuff about
MCRFs and so forth didn't seem likely to contribute at all to the
clarity of the page.

I hope this helps a bit with understanding why I didn't feel the need
to use anything beyond CofV and some Lorentz transforms in the
analysis!



Bilge and Dirk also raised some
questions. Are they puppets as well?

No, not at all.


That was the reason that a purely Newtonian argument with fixed
signal speed relative to the cable which leads to no Sagnac ... it
wasn't any "mistake" on my web page, nor any mistake in relativity.

Again, there are several ways of approach this "classically".

There's (classic) ballistic theory, which assumes the signal in vacuum
travels at C relative to the emitter, and at C/N in a glass fiber
relative to the fiber. That matches what I called the "classic" case
and it leads to a conclusion of no Sagnac effect.

There's classical aether theory, in which one can assume any degree of
"dragging" of the signal by the medium. On the page I talk about no
dragging (signal moves at fixed velocity relative to the lab frame)
and I talk about "full dragging" (just like the BaT case: signal
moves at C/N relative to the medium).

But the case I did not discuss -- which I really need to add! -- is
the case where there is "partial dragging". That notion dates from
some time in the 1800's and actually explains the Sagnac effect. So,
it _is_ explainable "classically", and I need to update the page to
say so.

*****************************************

Now, let me see what else I overlooked in your earlier post...

On Wed, 03 Aug 2005 21:59:15 -0700, wrote:


sal wrote:
On Tue, 02 Aug 2005 21:32:21 -0700, wrote:


sal wrote:
Thanks for the informative response.

On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:

[ snip ]

Nice web page. A very clear simple explaination of the Sagnac
effect. Just a few quibles.

Your statement about the inability of Newtonian mechanics to
explain Sagnac is backwards. Sagnac has often been used in this
group in attempts to show that light travels at c+v or c-v in a
moving frame.

Which just shows the level of silliness in some of the arguments in
this group.

Oh, I see, anything that doesn't agree with your point of view is
silly.

No, that's not what I meant at all.

I meant it's silly to claim that the Sagnac effect _refutes_
relativity in any way. However, that exact claim is often made. I
don't understand why -- the only "proof" I've ever seen that the
effect contravenes relativity comes down to proof by assertion. And,
after working it out for myself, it obviously doesn't do any such
thing.


Why else would it take different times to go in opposit directions
around the ring To claim that the single clock is out of sync
with itself is really grasping at straws. Some might even say
that is absurd

SR is intuitively unappealing. That's not news.

I can expand on this. I didn't mean "a single clock is out of sync
with itself". That's obviously absurd.

The trick here is to get from (my) figure 4 to figure 5, and see that
they're the same thing.

Take a linearly moving cable, with the clocks in sync in the
_stationary_ frame. Now, without changing anything -- particularly
without changing its linear velocity -- wrap it around the spinning
disk.

You get figure 5. And if someone walks around the disk holding a
clock, if there are clocks all along the length of the cable that are
in sync in the "lab frame", the walker will see them getting farther
and farther from his/her clock as he/she moves around the rim.

It's a purely visual argument, but it matches the math.


What you are doing is not SR.

So what? It's relativity. It's based on pseudo Riemannian geometry,
applied in flat space where there is a global Lorentz frame.


If you look in
"On The Electrodynamics Of Moving Bodies" you will find, "in a state of
parallel translatory motion parallel to the axis of X" Do you understand
what that is saying? Your example deviates from normal SR practice for
clock sync.

So what?


Two clocks resting at the same point are supposed to show the same
time in SR. A slow transported clock is not supposed to go out of
sync in SR.

So? A clock which is carried around the ring is _NOT_ "slow
transported" in the local inertial frame of someone who is situated at
one point on the ring!

Consider: When the clock is situated diametrically across from the
"ring-stationary observer" the clock is moving at velocity -V in the
observer's MCRF. That's not "slow"! So, it's not slow transport, and
there's no surprise that the clock goes out of sync.

Just _how_ it goes out of sync is a interesting question which
deserves some calculations and graphs of its own. I don't claim to
have exhausted the subject -- I have barely scratched the surface.

If the clock is moving with the disk then it has no velocity for anyone
on the disk. Its coordinates are not changing, so it is not moving.
If you are going to jump frames and say that it is moving at some huge
velocity due to the rotation of the disk, then there is no slow
transport of any clock on the earth's surface.


Sagnac does not prove SR wrong because SR excludes rotations.

Untrue. Einstein's SR paper didn't treat acceleration, and
accelerated _observers_ are beyond the ability of SR to handle with
any grace, but accelerated _objects_ can be handled just fine in
most cases without stepping outside the math of SR. (If you want
to be nit-picky about it you need to add the "clocks postulate" to
SR in order to allow you to conclude anything about accelerated
objects.)

And the reason Sagnac doesn't disprove SR is that SR predicts the
effect, and is, in that sense, confirmed by it, rather than
contradicted by it. To handle it strictly within the bounds of SR
you must look at it from the fixed frame, but from that point of
view it's a trivial bit of algebra to derive the effect.

In SR all frames are equal. Here you are saying that you can do
something in one frame but not the other. Why is that? Because the
frames are not equal and you are not working with SR.

So what? I'm happy with GR. I just didn't show any math beyond what
you're familiar with from SR on that page.

In any case the frame which is "different" is the accelerated frame,
and, yes, that's "different", all right.

Accelerated _bodies_ are, as a rule, easily handled in SR.
Accelerated coordinate systems are not.


In "Relativity" Einstein wrote,

If, relative to K, K' is a uniformly moving co-ordinate system
"devoid of rotation, then natural phenomena run their course with