Classical Theories, the Sagnac Effect,
and the Michelson-Morley Experiment
On the Sagnac effect page
on this site, I
stated that the Sagnac effect is classically impossible.
However, numerous people pointed out to me that I was wrong, and that,
in fact, Sagnac
himself used a "classical" model to predict the effect.
The primary problem is with what we mean by "classical". There
are a number of "classical" theories of dynamics, and not all of them
are inconsistent with the results of the Sagnac effect. For
example, if we consider the Sagnac effect
only in the case where the medium in which the light travels is vacuum,
if we assume that the velocity of light in vacuum is c
relative to the "stationary" frame of the laboratory, then the effect
simple and inevitable. If the light
goes around the path at c
relative to a stationary observer,
but the disk is spinning, then it gets there sooner when it goes
"against" the spin because the detector is "coming to meet it".
When it goes "with" the spin, the detector is "running away from it"
and it takes longer for the light to get there. (It appears that
this is the model Sagnac used to predict the effect, though his device
actually was filled with air, not vacuum.)
There is another issue here, however. Sagnac effect
devices which are commonly available
filled with vacuum. The light is either carried
in gas-filled tubes, or it is carried in glass, in an optical
fiber. In glass, and perhaps in gas, we would surely expect the
light to be "dragged" along with the medium, so that the velocity of
the light will be k
relative to the
medium, where N
is the refractive index of the medium.
And in that case, classical (Newtonian) vector addition of velocities
leads us to the conclusion that there should be no Sagnac effect
That's a false conclusion: there is
a Sagnac effect. So,
the simple but "classical" model of the light traveling at k
relative to the medium, and in turn moving at velocity k
relative to the laboratory (if the medium is, itself, moving at v
must be wrong.
But there is no single "classical" theory of
dynamics. On the remainder of this page I'll talk very briefly
the implications of the Sagnac effect for several versions of
"classical" dynamics, and I'll also discuss -- even more briefly --
the implications of the Michelson-Morley experiment.
I've included no data or references here. This page just contains
brief comments on the classical theories and their relationships with
the Sagnac and Michelson-Morley experiments. These topics
are widely covered. If you're looking for more infromation, you
can find accessible
discussions of these theories and experiments in any reasonable
encyclopedia, such as Wikipedia or Scienceworld. If you use
google to research
them, however, be aware that there are many "crank" pages out there
which purport to show such things as that relativity was proved wrong
wrong by experiments done in the 1800's (belief in relativity is a
Universe isn't expanding, the Sun is solid rather than gaseous, the
world is just 6,000 years old, and the Sun revolves around the Earth,
to name just a few which I've seen seriously proposed. For
reasons I can't explain the Sagnac effect has seemed to attract a
dispropotionate number of crank pages. (This page which
you are currently reading is not a crank page -- there may be errors on
this page or on this website,
but aside from that, the physics is purely "mainstream".
The Michelson-Morley Experiment
Before talking about any classical theory we need to mention the
Michelson-Morley experiment, which I haven't discussed elsewhere.
(This is a very, very
brief sketch of the "MMX", as it's often
called. There are many references online which cover it in
substantial detail. See, for instance, Wikipedia
In MMX, light is passed through two paths, oriented at 90 degrees to
other. The velocity of the light as it passes through the two
paths is compared. One path is oriented parallel to the motion of
the Earth; the other path is perpendicular to the motion of the
Earth. If there is an "ether" through which light propagates,
and relative to which light travels at fixed velocity C
the speed of light should vary depending on whether it's going parallel
or perpendicular to the motion of the Earth as the Earth moves through
the "ether". However, no difference in travel time between a path
parallel to Earth's motion and one perpendicular to Earth's motion has
been detected. (The experiment has been done with evacuated tubes
as well as air-filled tubes; it made no difference.)
Ballistic (or "Emission") Theory
According to ballistic theory, light travels at C
. Within a medium, such as a glass fiber, the
light travels at C
relative to the medium
Composition of velocities is done by vector addition (purely
Newtonian). One could, therefore, say that the light is fully
"dragged" by the medium.
Emission theory, therefore, predicts no
Sagnac effect, as we
saw on the Sagnac page
Emission theory, on the other hand, is fully consistent with the
observed (null) results of the Michelson-Morley experiment.
Ether Theory with No "Dragging"
In ether theory it's assumed that there is a "luminiferous ether"
through which electromagnetic radiation propagates, much like
sound waves propagate through air. Light may then travel at c
relative to the ether regardless of how fast anything else is going.
In a medium such as glass, light travels slower than c
factor of the refractive index of the medium. In that case, we
might assume light travels at k
to the ether
, where N
is determined by the
medium. In that case, when light passes through a moving fiber
optic cable, the light would actually be moving at k
relative to a fixed observer
rather than relative to the glass
, and we would indeed observe a Sagnac effect -- but it
wouldn't match the one that's actually measured. If the disk is
rotating counterclockwise, then for counterclockwise ("positive"
direction) signal travel, we'd have:
For clockwise signal travel, we'd have:
And the difference would be:
Immediately we notice that the difference is not independent of the
signal velocity. This result is obviously different from the
difference predicted by relativity, and the interference fringes would
shift to a different degree if this result were correct. Since
the effect, as observed, matches the prediction of special relativity,
we can therefore conclude that the assumption that the light is not
dragged at all by a moving medium must be incorrect, as is the model
that assumes the light is dragged but velocity composition is by
classical vector addition.
The predictions of ether theory with no "dragging" also do not match
the results of the Michelson-Morley experiment.
Ether Theory with Dragging
As far as I know nobody ever proposed that the ether might be "dragged
along" exactly as fast as the medium moves. But we can still ask
what would happen in that case. If the ether were "fully
dragged", the behavior would be identical to
that predicted by emission theory, which, as we've already noted,
doesn't match the results of Sagnac's experiment.
Ether Theory with Partial Dragging
There is another possibility, proposed by Fresnel back in the
1800's. Fresnel proposed that the ether would be partially
dragged by a moving medium, and the velocity observed by a stationary
observer, if the signal traveled at k
relative to a stationary
fiber, would be between k
fiber moving at v
. That's a qualitative
description; Fresnel proposed a a quantitative model which
produced precise predictions. Fresnel's predictions matched the
values observed in the Fizeau experiment, done some years after
Fresnel's death. His theory also predicts, to good precision, the
However, ether theory with partial dragging conflicts with the
Michelson-Morley experiment: The partially dragged ether should
be traveling at a different velocity relative to a beam of light
traveling along the motion of the Earth versus a beam traveling across
the motion of the earth, resulting in a different velocity of light in
the two directions, and no such difference has been found.
"Lorentz Ether Theory"
There is one more variant on ether theory which should be
mentioned. Lorentz proposed that objects moving through the ether
are physically foreshortened. Clocks moving through the ether may
also be also physically affected. The transforms which
describe the changes due to motion through the ether are the "Lorentz
transforms", familiar from special relativity.
As far as I know, at least in the area of mechanics, Lorentz's version
theory produces predictions which are identical to those produced by
special relativity. So, "Lorentz ether theory"'s predictions are
also consistent with the Sagnac effect, and with the results of the
The chief criticism leveled against so-called LET is that the ether is
necessarily completely undetectable -- our motion through it is exactly
masked by the "Lorentz contraction". If that were not true, then
the Michelson-Morley experiment would not have produced a consistently
null result. But this leads us to the realization that, if the
centerpiece of the theory, the "ether", is something which, by
assumption, can't be detected, then there is no reason to believe it
exists! Postulating an invisible, undetectable object as part of
a theory is not reasonable if there's an alternative.
Back to the Sagnac page