Re: Simple Sagnac

On Fri, 29 Jul 2005 10:43:19 -0400, sal <pragmatist@xxxxxxxxxx> 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. 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.

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.
.

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