## “Aether Drag” and Moving Images: A different sort of “twin paradox”

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:

${\bf c'} = {\bf c}/n + f{\bf v}$,

where

$f = 1-1/n^2$.

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 $n\rightarrow 1$, i.e. the moving medium is vacuum, there is no drag at all, and in the limit $n\rightarrow\infty$, the speed of light satisfies the Galilean velocity addition formula of Newtonian relativity:

${\bf c'} = {\bf c}/n+{\bf v}$.

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 $\alpha$ and which have a frequency difference $\delta \omega$ 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

$\Delta x = \frac{v}{c}L(n-1/n)$,

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

$\Delta x = \frac{v}{c}L(n-1)$,

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

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### 14 Responses to “Aether Drag” and Moving Images: A different sort of “twin paradox”

1. Alessia says:

Thank you for a very clear description, understandable even by those like myself not versed in the field of optics.

In case you were wondering, ResearchBlogging did pick up your post, for I found it via their RSS feed.

2. Hi Alessia,

Thanks for the comment! Yes, I seem to have finally figured out how to make ResearchBlogging work with WordPress…

3. IronMonkey says:

Thanks for this very interesting report. I would like to offer a little more insight on the concept of Aether. As stated in the introduction, this concept is indeed obsolete in modern science. In my opinion, it is unfortunate that the word Aether is imbued with mysticism. Paul Dirac attempted to revive the search for Aether through quantum-mechanical arguments [Nature, vol.168 (1951)]; unsurprisingly, he was immediately met with much criticisms [Nature, vol.169, January and April (1952)].
The reason why I think this concept is still relevant is simple: intuitively, any form of energy which travels in a wavelike motion may need a medium through which it propagates. From my understanding, the latter fact is true for water waves, sound, and many more physical phenomenae; except for electromagnetic waves which we assume can travel trough “free space”, or in other words, “vacuum”. Is this really the case?

4. IronMonkey: Thanks for the comment. You stated that, “The reason why I think this concept is still relevant is simple: intuitively, any form of energy which travels in a wavelike motion may need a medium through which it propagates.”

The ‘catch’ in your sentence is in the word, ‘intuitively’. If I were to summarize the greatest contribution that Einstein’s relativity made to the philosophy of science, it was to demolish the role of intuition. Scientists had spent the hundred years before Einstein running around in circles trying to quantify the properties of the aether, and made very little progress. Einstein came along and said, in essence, “Why are you so convinced there is an aether at all?” Most scientists thought about it a bit and realized that it was their everyday intuition that had convinced them the aether existed.

The problem with ‘intuition’ is that it is based on an extremely limited terrestrial worldview. We live in a quiet corner of a galaxy, in a relatively weak gravitational field, moving at relatively slow speeds compared to anything around us. Our eyes can only observe an almost negligibly small range of the electromagnetic spectrum, and we cannot readily observe objects smaller than a tenth of a millimeter. It is an extremely big reach to assume that all phenomena in the universe must be easily reconcilable with everyday experience.

That isn’t to say that intuition isn’t useful: it can be a useful guide at times in understanding phenomena, but should always be backed up with direct experimental evidence. Einstein made researchers of his time realize that their notions of an aether were based purely on intuition. (Ironically, the more one understands Einstein’s theory of relativity, the more intuitive it gets. I can hardly imagine any other theory of relativity now.)

You wrote: “From my understanding, the latter fact is true for water waves, sound, and many more physical phenomenae; except for electromagnetic waves which we assume can travel trough “free space”, or in other words, “vacuum”.”

This is, in fact, why scientists of the early 1800s postulated an aether in the first place! This was what was known as the ‘mechanical theory of light propagation’. Since that time, though, we have another important group of waves which propagate in vacuum: all matter in the universe has wavelike properties. If we assume these wavelike properties are also due to an ‘aether’, we either need a second aether for matter or we need our original aether to support both light and matter waves. In either case, we end up making an even more complicated aether model and don’t gain any scientific insight.

Who knows? It may turn out, in some distant future research, that we find that light propagation is based in some sort of mysterious substance. The problem right now is that any aether model would involve aetherial matter which behaves completely unlike any other matter in existence. Once your ‘mechanical theory of light propagation’ starts to look completely unlike any other form of mechanical wave propagation, the reasonable conclusion is that nothing is gained by holding that mechanical point of view.

• Stephen says:

I would suggest that because light accelerates after leaving glass that the aether is spinning at the speed of light. It works similar to the cogs in a clock or watch, in that the cogs are spinning alternatively left and right (positive/negative) which gives the light wave a second dimension of spin energy. Thus, light has both spin and wave energy. The cogs only come into contact when a light sources pushes them together. Otherwise, they just just spin freely and are invisible to us. When one of the cogs stop spinning it becomes a neutron or black hole attractor which forms matter. Thus, aether is the source of the universes energy (dark matter).

5. IronMonkey says:

Thanks Skullsinthestars for your comment on my comment. Indeed, intuition itself may not be a valid starting point for pursuing scientific endeavour. This is in fact a mistake Einstein himself may have made in his later years when he refused to acknowledge the statistical predictions of quantum theory. “God does not play dice…”

As you pointed out, in the current state of knowledge, we don’t necessarily need an aethereal substance to describe physical phenomenae already explained by the theory of relativity. This is absolutely true.

Many different “aether” theories have been proposed. The formulation of “aether” by Paul Dirac is not mechanical; it is statistical. In essence, what he proposed was that vacuum, or aether, must be subject to quantum mechanical laws. Thus “perfect vacuum” as we know it becomes an ideal unattainable state. This formulation of vacuum (aether) is consistent with relativity within his “New theory of electrodynamics” [Proc. Roy. Soc. London, (1951),(1952),(1954)]. Of course, this is just a theory, and any theory must be confirmed by experimental facts. Obviously, when trying to rigorously describe what vacuum is, one may reach the limit of knowledge.

6. Sili says:

Stupid question, but isn’t part of the reason that light travels without a medium that it in sense carries its own medium with it?

I mean, it’s Electro-Magnetic waves. One induces the other, so the magnetic wave serves as a medium for the electric one and vice versa. Or is that too far-fetched?

7. “…but isn’t part of the reason that light travels without a medium that it in sense carries its own medium with it?”

That’s an interesting idea that I hadn’t heard before. Personally, I think there are two problems with such an interpretation: 1. It assumes that a medium is absolutely necessary for wave propagation. 2. It helps not at all with the other ‘mediumless’ wave: ordinary matter. All matter has wavelike properties, and those waves are not associated with E/M waves.

I think I’ve got a real-world example to further elucidate these points, but I’ll leave it for a separate post, after I’ve fleshed out the details…

8. You say:
“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.”
You missed that the non traveling twin feels the acceleration of gravity, which the traveling twin does not. According to the equivalence theorem you (your atoms) cannot tell the difference. As such, you have not accounted for the acceleration of the stay behind twin. Your logic is flawed!

• Really? Two points:

1) The original twin paradox is formulated to resolve a seeming contradiction in special relativity, not general relativity. The important point is that special relativity does not violate common sense, without even having to worry about gravity. However,

2) The equivalence principle doesn’t imply that both twins feel absolutely identical forces. If we take gravity into account, the stationary twin feels a constant force of gravity, while the traveling twin necessarily feels a time-varying force of gravity (in one direction on the way out, and in the opposite direction to go back. The resolution of the paradox is still that the two twins have different experiences — namely different forces — and therefore there is no problem with arguing that they can both agree on who has aged more.

• Bruce Williams says:

Not really. Imagine that instead of a linear motion, the leaving twin travels on a circular path such that he and his atoms experience a continuous 1g field while accelerating and decelerating, just as the earth bound twin feels 1g of earths gravity. This leaves only the speed change as a factor.
Now, who is older when the leaving high speed twin gets home? Forces are all the same, just one went at a high speed for a while. Now, which one aged more?
Choosing experimental conditions, such as is done in the twins paradox, which leave multiple variables is invalid. You should know that!

9. Bruce Williams says:

P.S. Equivalence (of Gravity and Acceleration) is valid in both General and Special Relativity. And if not, then the entire theory falls apart. Just read Einsteins papers on the matter.

10. M Khan says:

That acceleration does not produce changes in time is well known. Time dilation of particles moving in circular particle accelerators can be
precisely calculated by using only the velocities and completely ignoring the acceleration. This also is clear in the so called twin paradox.
The time dilation of the traveling twin cannot be explained by acceleration. The acceleration can be made to be instantaneous then the only
difference between the twins is the velocity.

Let us look at the twin paradox. In this modified version twin A (Traveling twin) and twin B (stay home twin) both initially start the journey
together and undergo a large but brief acceleration to achieve the same large velocity. Twin A continues journey at a high velocity while twin B
after achieving the same velocity immediately undergoes deceleration and turnaround acceleration and deceleration to stop at home. Twin A
completes a high speed journey at a uniform velocity for a certain prolonged period then does exactly similar deceleration acceleration (as
twin B) followed by return journey and deceleration.

By design the acceleration deceleration of both the twins is exactly the same and also very brief. The twins only differ in the time spent in
traveling at uniform velocity. From here we can see that time dilation is only related to motion through space including the velocity present
during acceleration. Also we know clearly from Lorentz’s and Einstein’s equations for time dilation that only velocity is involved and that time
dilation is not caused by acceleration.

The same logic should be applied to acceleration in gravity. It should be clear from above that acceleration in gravity or in motion does not
produce time dilation. Around large masses differential expansion of space creates time differential which then produces gravitation
acceleration.

From our hypothesis and from observation we can see that all motion is due to expansion of space. Also if total motion imparted by
expanding space is a constant then we expect to see slowing of time in an object if its external motion is increased. Similarly if a mass
composed of billions of atoms moving at tremendous velocities is placed in a time a differential (gravity) it is natural to expect that it will move
towards slower time and the internal motion will get converted to an external linear motion.

Twin paradox as well as the problem of acceleration seen in a rotating object is present only if you deny motion through space. Just as a
moving object can be differentiated from a non moving object because of its slower time and so can a rotating mass be differentiated
from a non rotating mass due to presence of acceleration. Objects set into motion produce a curvature in space while objects at rest do
not. If Einstein had applied the concept of curved space to motion then there would not be any talk of twin paradox.

11. J Thomas says:

I woke up from a dream this morning about the Fizeau experiment. In the dream scientists were performing the Fizeau experiment across a distance of 100 light years. They had a way to estimate both the average thickness of the interstellar gas and the average velocity by doing the experiment, but they were having some kind of problem because the star they were modifying to make the signal was interfering with their time travel. It almost made sense, like dreams do sometimes.

As I was waking up, I started to wonder. There’s a very thin gas in intergalactic space. Could it create a Fizeau effect?

If it was on average traveling in one direction, could you get a red shift in one direction and a blue shift in the other?

Could that be enough to explain the observed red shift? When people measure that kind of thing, is the effect from interstellar gas big enough that they have to correct for it? Or is it in fact so small that it can be ignored?

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