Re: Simple Sagnac


"Bilge" <dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message news:slrndeisl0.7ma.dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> sal:
>
> >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.
>
> 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. then,
>
> vt_1 = ct_1/n = 2\pi r + wrt_1 => t_1 = 2\pi r/[(c/n) - wr]
>
> vt_2 = ct_2/n = 2\pi r - wrt_2 => t_2 = 2\pi r/[(c/n) + wr]
>
>
> t_2 - t_1 = 2 n\pi r [(1/(c - nwr)) - (1/(c + nwr))]
>
>
> = 2pi r [ 2nwr/(c^2 - (nwr)^2)]
>
> = 4\pi r^2 [ (n^2 w)/(c^2 - (nwr)^2 ]
>
> >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.
>
> The index of refraction for air at STP for 590 nm is about,
> 1.00029. Rearranging the above gives:
>
>
> t_2 - t_1 = 4\pi w r^2/[(c/n)^2 - (wr)^2]
>
> for n = 1.00029. 1/n^2 = 0.99942 or 99.942% c.
>
> The index of refraction is irrelevant. The only point that it
> would enter the calculation differently than just replacing
> c by c/n, is if the ring was rotating fast enough that the
> frequency dependence of n == n(w) mattered.
>
> [...]
> >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.)
>
> Replace c with c/n.

The thing that puzzled me, and still does, is that he says
that both the "classical" u- = k - v and the relativistic
u- = (k-v)/(1-k v) are 'dragged'. Yet, if we take the case
where k = 1, the relativistic speed reduces to u- = 1, which
is something I wouldn't call dragged. And it's no closing
speed either. But again, I might be mistaken. Need more
from the sideline.

Dirk Vdm


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