Note: I’ve bumped this post in a probably futile attempt to get it aggregated by Research Blogging.
It’s a little challenging to blog about contemporary optics research, as much of the work being done, though interesting, is of an extremely technical nature and not of much excitement for a general blogging audience.
There are a few research groups out there, however, that work on fundamental optical problems which are conceptually simple but surprisingly subtle in their implications, and one such group, based in Glasgow, recently had a paper come out with the provocative title, “Aether Drag” and Moving Images.
The title is provocative because one hardly expects to see papers with the word ‘aether’ appearing in prestigious journals like Physical Review Letters anymore. ‘Aether’, of course, refers to the incorrect and obsolete idea that light is the vibration of a mysterious, ethereal mechanical substance which permeates all space. The term ‘aether drag’ is a historical holdover, and now is used to refer to the behavior of light fields in moving media. The Glasgow group has taken a fascinating new look at this phenomena, and I provide some details below the fold…
The idea of ‘aether drag’ dates back to astronomical observations of François Arago in 1810 (which I will discuss in more detail in another blog post). Arago attempted to measure the relative motion of the stars by looking for variations in the speed of light. He could detect no such variations, which conflicted with the Newtonian view at the time that light consisted of corpuscles (particles). In 1818, Augustin Jean Fresnel suggested to Arago that the difficulty could be resolved if one assumed: 1. Light is a wave in an as-yet unobserved, mechanical substance referred to as the aether, and 2. The aether gets partially dragged along with moving matter. Fresnel suggested that the velocity of light in a substance moving at velocity v with respect to the aether is given by:
The quantity c‘ is the velocity of light in the moving medium, c is the vacuum velocity of light, v is the velocity of the medium, and n is the refractive index of the moving medium. The quantity f is called the Fresnel drag coefficient. Fresnel’s formula suggests that media with high refractive index drag light more than media with low refractive index. In the limit , i.e. the moving medium is vacuum, there is no drag at all, and in the limit , the speed of light satisfies the Galilean velocity addition formula of Newtonian relativity:
Fresnel’s drag hypothesis helped convince Arago of the wave theory of light, and it held sway as one of the fundamental theoretical results relating to the ‘aether’ until Einstein’s special theory of relativity made the concept moot.
In 1851, Hippolyte Fizeau directly measured the Fresnel drag coefficient using the following ingenious experimental apparatus:
Collimated light from a source (S) is split into two beams at a beamsplitter (P). Part of the light follows path 1 around the interferometer and part of the light follows path 2. The light passes through two tubes of flowing water: light on path 1 is ‘dragged’ forward and arrives at the detector plane (D) faster than light on path 2, which is ‘dragged’ backward by the water. The light beams from path 1 and path 2 interfere on the detector plane and produce interference fringes. If the flow of water is now reversed, the light on path 1 is now the ‘backward dragged’ light and the light on path 2 is now the ‘forward dragged’ light. The interference fringes at D will shift, and from this shift one can deduce the size of the drag coefficient. Fizeau in fact measured results in agreement with Fresnel’s formula.
In modern times, we now know that the aether does not exist, and Fresnel’s drag coefficient can be readily understood using the formulas of Einstein’s relativity. Studies of how light is ‘dragged’ by moving matter continue to provide lots of insight into both optics and relativity, though.
Fizeau’s experiment involved what we might call longitudinal drag: the light and the material are both moving in the same direction. One can also consider the complimentary case of transverse drag, in which the material is moving perpendicularly to the light. The two cases are illustrated below:
In the case of longitudinal drag, the motion of the medium speeds up (or slows down) the light field, while in the case of transverse drag the motion of the medium displaces the position of the beam.
The transverse drag was first directly measured by R.V. Jones in 1971 (“Aberration of light in a moving medium”, J. Phys. A 4 (1971), L1-L3). Jones passed a light beam twice through a rotating glass disk and measured the transverse location of the beam as a function of rotation speed. A simplified diagram of this experiment is shown below:
A light beam coming from a source S passes through a glass disk which is rotating at frequency Ω. It is reflected from a mirror M through the disk a second time and the transverse position is measured by a detector D. The rotating disk drags the light field from its ideal undeviated path (the dashed line), and the amount of displacement the beam experiences depends upon the material properties, the rotation speed, and the thickness of the disk. A similar experiment by Jones showed that the state of linear polarization of the light field can be rotated by the disk as well.
Returning now to the work of the Glasgow group, a theoretical analysis of Jones’ system suggests that images (i.e. pictures) transmitted through a moving medium should be shifted transversely in the same manner as a single light beam. Such investigations are difficult, however, because they require that the medium be moving at a high speed, which introduces many experimental complications. The top speed at which a disk can be rotated, for instance, is much, much lower than the speed of light.
But why not take advantage of Einstein’s theory of relativity? Jones’ experiment involved a light beam incident upon a transversely moving medium. On the surface, it seems that it is experimentally equivalent to consider a transversely moving light beam incident upon a stationary medium. In relativity parlance, the two cases would involve an analysis from the rest frame of the light source and the rest frame of the medium, respectively:
As we will see, this picture is crude and problematic, but for now it gets the basic idea across.
But what do we mean by a ‘transversely moving light beam’? It is completely impractical to move the actual light source, for the same reason that it is difficult to move the medium itself: it can’t be moved very fast. Instead, the Glasgow group uses a stationary light source whose field contains a moving interference pattern. They interfere two beams at an angle and which have a frequency difference between them. Looking directly into the beam, one would see a behavior as shown in the animation below:
This is obviously a slowed-down, idealized view of the true behavior: in the actual experiment, the fringes are moving at a speed on the order of 10 km/s! This beam was used as the ‘moving’ light field, and the transverse drag on the field was measured as a function of the fringe velocity.
Here’s where things get a bit unusual. According to the experimental work of Jones, in which a light field travels through a moving medium, the transverse displacement should satisfy the formula
where v is the speed of the medium, c is the speed of light in vacuum, L is the thickness of the medium, and n is the refractive index. However, for a ‘moving’ light field passing through a stationary medium, the Glasgow group experimentally found a displacement of the form
where v here represents the transverse speed of the fringes. In short, the ‘moving’ light field results in a different displacement than the moving medium!
Naively we might have expected that the displacement should be the same in both cases: according to Einstein’s relativity, it would seem that the only difference between the two cases is the choice of one’s ‘point of view’ (i.e. reference frame). But here we have different experimental results for different ‘points of view’. What’s going on?
One can view this ‘paradox’ as similar in spirit, and in its resolution, to the famous ‘twin paradox’ of special relativity. A brief summary of the twin paradox follows:
According to Einstein’s theory of relativity, 1. the laws of physics are the same for all observers in inertial frames of reference, and 2. moving clocks run slower than stationary clocks. We imagine twin brothers, one of whom hops into a spaceship and travels at very nearly the speed of light on a round trip to a distant star. The Earthbound brother observes that time passes slower for the traveling twin, and so when the traveling twin returns, he is younger than his Earthbound counterpart. From the point of view of the Earthbound brother, this is illustrated below:
But, one might argue, since all motion is relative, can’t we just as well look at the scenario from the point of view of the traveling brother? From his point of view, it appears that the Earth rockets off at very nearly the speed of light, and comes back. Using this argument, one would say that the traveling brother would find that his Earthbound counterpart is younger:
But both brothers cannot be right; in fact, the ‘correct’ point of view is that of the Earthbound brother; the traveling twin indeed would return younger. Where, then, is the flaw in the argument above?
The answer is in the initial statement of relativity given above: 1. the laws of physics are the same for all observers in inertial frames of reference. An inertial reference frame is one which does not accelerate. The traveling twin must turn around in order to return to the Earth, and that turn around involves a change in velocity. Physically, the traveling twin will feel the deceleration of his spacecraft, while the Earthbound twin will feel no comparable deceleration. Only the Earthbound twin stays in an inertial reference frame. Although the two brothers seem at first glance to be in physically identical situations, they are not.
A similar argument can be made for the problem of moving light/stationary medium vs. moving medium/stationary light. The two cases seem at first glance to be physically identical, but in fact there is a subtle but important difference: the direction of motion and energy flow of the light field.
The differences between the Jones experiment and the Glasgow experiment are schematically illustrated below, both in the lab frame and the medium reference frame (adapted from the paper):
In the Jones experiment, in the moving medium frame, the Poynting vector S (which indicates power flow) and the wavevector k (which indicates the ‘direction’ of the wavefronts of the wave) are parallel. If we look at the same experiment from the rest frame of the medium, the Poynting vector and wave vector are now approaching the medium at an angle, but remain parallel.
In the Glasgow experiment, in the rest frame of the medium, the field is normally incident upon the medium, so that the wavevector is normal to the surface. The Poynting vector, however, is actually pointing at a slight angle to the wavevector. If we look at the same experiment in the moving frame of the medium, there is still a slight angle between the two vectors. It therefore turns out that setup of the Glasgow experiment is not identical in a relativistic sense to the experiment by Jones!
The subtle difference is that the Glasgow experiment is using a light field with two frequencies, which produces a ‘bias’ in the energy flow which favors the higher-frequency wave. Another way to explain the difference is that the Glasgow experiment is arranged so that no refraction of the light wave occurs on entering the medium (k is perpendicular to the medium in the medium’s rest frame). The experimenters modified their setup by tilting the medium to add the missing refraction, and then found their results in agreement with Jones.
With this question settled, the researchers also demonstrated the predicted rotation of an image due to ‘aether drag,’ almost as an afterthought.
Investigations such as this one are in a sense simple to implement, but the interpretation of the results can be difficult. The researchers suggest that studies of light propagation in moving media may help to solve one outstanding controversy of optics, the so-called Abraham-Minkowski controversy. This controversy, involving the proper definition of momentum for light propagating in matter, has not been completely sorted out over a hundred year span.
Leach, J., Wright, A.J., GÃ¶tte, J.B., Girkin, J.M., Allen, L., Franke-Arnold, S., Barnett, S.M., Padgett, M.J. (2008). â€œAether Dragâ€ and Moving Images. Physical Review Letters, 100(15) DOI: 10.1103/PhysRevLett.100.153902