Re: Simple Sagnac
- From: sal <pragmatist@xxxxxxxxxx>
- Date: Tue, 26 Jul 2005 15:30:55 -0400
On Tue, 26 Jul 2005 15:04:35 +0000, Dirk Van de moortel wrote:
>
> "sal" <pragmatist@xxxxxxxxxx> wrote in message
> news:pan.2005.07.25.15.11.10.44873@xxxxxxxxxxxxx
>> Here's a (relatively) simple view of the Sagnac effect:
>>
>> http://www.physicsinsights.org/sagnac_1.html
>>
>> ...
>>
>> Comments welcome, of course!
>
> If I'm not mistaken, working with a moving medium, in the classical
> treatment you apparently use a dragged, (source speed dependent)
> signal speed u- = k - v, but in the relativistic treatment you use
> standard undragged,
No, it's dragged either way. Perhaps you missed something?
> source speed independent Lorentz composed speed u- = (k-v)/(1-k
> v).
k < c. (well, actually, k <= c.) Again, the signal is dragged either
way. The difference is that the dragging uses CofV in the
relativistic case but uses simple addition of velocities in the
classical case. Indeed, that _is_ the difference between the two
cases, in a nutshell.
In both cases I'm modeling the same thing, which is a signal traveling
in a cable at velocity k < c, with the cable speed = v. Either fiber
optics or electric wire will have a signal propagation speed of c/N
where N is the refractive index of the medium (or the insulator, in
the case of a wire).
Signal speed, classically, should indeed be k +/- v in the stationary
frame, right? And relativistically it's (k-v)/(1-kv) or (k+v)/(1+kv)
(unless I typed a sign wrong). Again, it's the same physical model.
> So you get a discrepancy between classical and relativistic. That
> doesn't surprise me.
Nor me.
I should mention the reason I used a signal speed of k<c, with
dragging, is that, while the common (on-line) mathematical treatments
of the Sagnac effect typically seem to assume signal speed = c, that
implies the signal is light traveling in a vacuum. Nearly all real
Sagnac devices do not use light in a vacuum - they use light in a
medium, either glass or gas, and the medium rotates with the disk.
Running the experiment in vacuum has been done but it takes somewhat
exotic equipment and it's not common, AFAIK. In particular, laser
ring gyros and fiber optic gyros, which are both based on the Sagnac
effect, certainly aren't vacuum filled. So why look at the effect
only in the most uncommon case?
> In other texts the effect is the same classically as
> relativistically.
If they're talking about the effect in glass fibers (not vacuum)
they're wrong if they claim it works classically. But after looking
at your references, that's not what they're saying at all.
> Light speed is taken to be c (or unity) and nothing is dragged or
> composed. No medium is used and closing speed between signal and detector
> is used in both cases. So there is no difference.
Ah so ... what is the signal speed taken to be C=1 relative to? If
you're trying to do it classically, without SR, you need to answer
that question, because not all observers see it as the the same.
Implicit in the "classical" approach is the selection of the
laboratory for the preferred frame, with vacuum for the "medium".
In any case once you allow a little air into the apparatus the
classical argument falls apart, whether or not it worked to start with.
> See for instance sections 1.1 and 1.2 of
> http://www.physics.berkeley.edu/research/packard/Competition/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf
> | "Sagnac (1913) drew on purely classical ideas to
> | predict the effect..."
Did you actually read that paper, Dirk? His later discussion of
derivations of the Sagnac effect touches on aether theory, SR, GR, and
some more exotic approaches. Newtonian mechanics is notably absent
from the set of tricks which will predict it.
As far as I can tell Sagnac's "purely classical" setup involved
passing the beams through air which was stationary in the laboratory
frame. The mirrors moved, but the air, for the most part, didn't.
(Or at any rate Sagnac assumed it didn't.) So, no beam-dragging was
anticipated, and a classical analysis of it worked just fine. But, so
what? Modern sagnac devices spin the whole works, and the beam
certainly should get dragged, and you end up back with k+v and k-v and
no fringe shift if you try to analyze them using Newtonian mechanics.
Early aether theory workers, of whom I believe Sagnac was one,
generally seemed to assume light propagated through the aether at
velocity C relative to said aether even when it was actually traveling
through air. I never understood that -- it seems patently false to
me; else air wouldn't refract light, which it obviously does.
> and even more so:
> http://www.mathpages.com/rr/s2-07/2-07.htm
> | "This analysis is perfectly valid in both the classical and the
> | relativistic contexts."
Uh huh. I'd already seen that page. That sentence comes from the
analysis where he assumes SoL is fixed at C in the stationary frame,
and the signal travels at C in that frame. Of course it's valid
"classically" if you assume that. But he does a lot more on the page,
and later on he says,
"This rules out the ballistic theory of light propagation (as
advocated by Ritz in 1909), according to which the speed of light is
the vector sum of the velocity of the source plus a vector of
magnitude c. Ironically, the original Michelson-Morley experiment was
consistent with the ballistic theory, but inconsistent with the naïve
ether theory, whereas the Sagnac effect is consistent with the naïve
ether theory but inconsistent with the ballistic theory."
So, what you mean by "classical" is a little open to interpretation,
it would seem; ballistic theory is a purely "classical" theory in that
it uses Newtonian mechanics and Galilean transforms for everything.
In any case, as soon as you introduce a medium such as a glass fiber,
as I already said, any attempt at handling it "classically" falls
apart.
> | "It's worth emphasizing that the Sagnac effect is purely a
> | classical, not a relativistic phenomenon,..."
Again, "classical" doesn't seem to be defined here. As far as I can
tell he's saying length contraction doesn't play a role, and you don't
need wicked fast velocities. One thing he certainly is _not_ saying
is that a fiber optic ring gyro can be analyzed using "classical"
(non-relativistic) physics.
Again, I'd be more impressed with the quotes if you explain how you
can use anything other than k+v and k-v for the velocities in the
"classical" case, if you don't happen to have a perfect vacuum on tap
in which to run the experiment.
> These are rather sharply contrasting with your line:
> | "However, from the point of view of Newtonian mechanics, the
> | effect is simply impossible. If anything, the Sagnac effect is
> | a powerful demonstration of the validity of relativity."
Right. For fiber optic loops (which is what I was addressing), the
effect certainly is impossible if you try to analyze it classically,
as I presume you realized as soon as you looked at the equations.
Again, if you disagree, please explain how such an analysis could work.
(Henri would love to know!) (Sagnac didn't assume fiber optic loops,
of course, since they hadn't been invented yet.)
> Other than that, a few typo's/nitpicks:
> - "fiber object" ==> "fiber optic" ?
> - "vaccuum" ==> "vacuum"
> - second part of equation (10)
> g . -v .(-L_S) ==> g .( -v .( -L_S ) )
> - "circular motion introduces centripetal acceleration"
> ==>
> "circular motion requires centripetal acceleration"
> or
> "centripetal acceleration introduces circular motion"
Thanks; fixed (unless I fat-fingered them again!).
--
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