Stellar aberration and Fresnel ether drag

Erland Gadde

I'm interested in the prehistory of the history of relativity. In this
history the nature of light and the ether comes in. One phenomenon that
was debated in this context was stellar aberration: that the positions
of the stars in the sky change slightly, or, more precisely, the
perceived directions of the light beams emitted by the stars change
slightly, depending upon the motion of Earth around the sun. This
phenomenon is equivalent to the percieved change of the direction of
which falling raindrops hit a car, depending upon the motion of the
car.

Stellar aberration is thus easily explained if a light beam is
considered to be a stream of particles (corpuscles or photons), but
with a wave theory of light, stellar aberration shouldn't occur, unless
we use the relativistic Lorentz transformation. Why is it so is
explained in the beginning of this article:

http://www.mathpages.com/rr/s2-05/2-05.htm

Briefly: if we consider a medium denser than air/vacuo moving in a
direction perpendicular to the propagation of incoming planar light
waves, coming from vacuo, and the medium/vacuo boundary is also
perpendicular to the incoming wave motion, then a wave front reaches
every point on the boundary simultaneously. Then, Huygens's principle
implies that the waves must propagate in the medium in a direction
perpendicular to the boundary, that is, in the same direction as the
incoming waves, independently of the velocity of the medium. Thus,
stellar aberration would not be observed.

In the above article, we are told that Fresnel, in 1818 (long before
Lorentz and Einstein) proposed a way around this problem: that the
medium drags the luminoferous ether slightly, so that the part of the
ether which contains the medium is moving in the same direction as the
medium with velocity (1-1/n^2)v, where v is the velocity of the medium
and n is its refractive index.

But I can't see that this solves the problem. On the contrary, the
moving (dragged) ether has the the same boundary to the stationary
ether, in which the incoming waves propagate, as the medium which
drags it. Thus, by the same argument as before, the waves must
propagate in the moving ether in a direction perpendicular to this
boundary, that is, in the same direction as the incoming waves. The
waves will then propagate in the same direction all the time, namely
perpendicularly to the boundary between vacuo and the medium (which is
also the boundary between the stationary and the moving ether), whether
observed by an observer in rest relative to the stationary ether, the
moving ether, or the moving medium. Thus, even with such drag, stellar
aberration wouldn't be observed. So, Fresnel's hypothesis doesn't solve
the problem it was intended to solve!

So I wonder, have I misunderstood something, or this above article
faulty, or what? What was the point with Fresnel's ether drag
hypothesis?

Grateful for all answers and comments,

Erland Gadde

Tom Roberts

Erland Gadde wrote:
> What was the point with Fresnel's ether drag
> hypothesis?

I believe his ether drag hypotheses was intended to explain the
measurements of Fizeau, in which the speed of light in moving water is
increased or decreased. Today we know his drag coefficient is equivalent
to the lowest-order expansion of the relativistic formula for velocity
addition. See, for instance, the Wikipedia article on "aether drag
hypothesis".


Tom Roberts

yaenqzt@yahoo.com

Erland Gadde wrote:
> http://www.mathpages.com/rr/s2-05/2-05.htm
> In the above article, we are told that Fresnel, in 1818 (long before
> Lorentz and Einstein) proposed a way around this problem: that the
> medium drags the luminoferous ether slightly...But I can't see that
> this solves the problem.

As I read the article you cited, the seeming lack of aberration of the
wavefront is explained just by considering how an image is actually
formed in a telescope. But then we should see different amounts of
aberration depending on the index of refraction of the medium filling
the telescope. According to that article, Fresnel's partial drag
hypothesis
was intended to explain why we don't see different amounts of
aberration,
even if we fill the telescope with water (for example).

Tom Roberts wrote:
> I believe his ether drag hypotheses was intended to explain the
> measurements of Fizeau, in which the speed of light in moving water
> is increased or decreased.

Fizeau performed that experiment in 1851, but Fresnel's hypothesis was
in 1818. It's true that Fresnel's hypothesis is consistent with the
outcome
of Fizeau's experiment, but it wasn't proposed specifically to address
Fizeau. (Actually, I believe it was the other way around, i.e., Fizeau
was
trying to test Fresnel and the other dragging hypotheses.)

Beto Pimentel

You are totally right. Fizeau's article of 1859 at the Annalles de Chimie et de Physique make it clear the purpose of the experiment was to choose among three possible models for the relationship between matter and the aether: (1) the aether is unaffected by the motion of transparent bodies; (2) the aether shares the motion of transparent bodies; or (3) part of the aether is dragged along with a mobile transparent body. He claims his experiment with the moving water to be an experimentum crucis of some sort, but when confronted with the result that only (3) agrees with his experimental results, Fizeau asserts that more exploration on the subject is needed before concede this extraordinary hypotheses reflects the true nature of the phenomenon.