 |
Classical Theories, the Sagnac 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, and 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 are not 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 = c/N 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 + v 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 about 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 conspiracy), the 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". How dull...)
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 each 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, then 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 relative to
the emitter. 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 by a factor of the refractive index of the medium. In that case, we might assume light travels at k = c/N relative 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 itself, 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 and v+k for a 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 Sagnac effect.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 of ether 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 Michelson-Morley experiment.
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