Re: Simple Sagnac


"sal" <pragmatist@xxxxxxxxxx> wrote in message news:pan.2005.07.26.19.30.50.888284@xxxxxxxxxxxxx
> 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.

What if you allow London and Van der Waal's forces to act between
the earth and the glass fiber ?

Sue...

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


.

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