The Photon Push-Me Pull-You
A few weeks ago, over at Built on facts, I threw Matt a bit of a knuckleball in the comments.
[C]onsider a solid bar of the same index [as water]. You send in the pulse of light (assume a really good AR coating so there’s no reflection). What happens to the speed of the bar?
This was sneaky because it is one of the unsolved issues in physics (I feel no remorse for doing this, and Matt realized that something was up) — the theory is complicated enough that it’s really easy to miss out on some of the subtleties and end up with an invalid answer. There are two schools of thought: Minkowski, who had taken the approach that the photon’s momentum in the medium should be nE/c, and Abraham, whose approach gave the momentum as E/nc. Clearly, the results are at odds, and this came to be known as the Minkowski-Abraham momentum controversy.
I found a number of articles on the topic, but perhaps the best one is a review article from Reviews of Modern Physics. Momentum of an electromagnetic wave in dielectric media by Pfeifer et. al, No. 4, October–December 2007 pp. 1197-1216. (link is to a pdf file) The article points out that this isn’t a simple problem, because a photon in a medium can’t be naively treated as just a photon — both solutions have merit, but must include the interactions with the medium, which are obviously different depending on the approach you take — in the end there can be only one you can only have one answer for the momentum of the system.
The article describes a number of attempts to measure the effect, and how these were misinterpreted. One experiment, from Ashkin and Dziedzic, was to shine a laser onto water and observe the surface — if Minkowski was correct it should bulge outward to conserve momentum, but the Abraham solution would require the surface to compress. It bulged outward, but was later determined to be because there was a dipole force on the surface, owing to the Gaussian beam profile. There were other experiments, each one a bit murky because of the complicated nature and small magnitude of the effect.
The latest salvo has landed. The ArXiv blog has posted The embarrassing lightness of photons in which yet another measurement has been made, this time with optical fiber. I recall being told about an experiment such as this that had been proposed, and I don’t know if this is the same group, but they (Weilong She, Jianhui Yu, Raohui Feng at Sun Yat-Sen University) have made the measurement by observing the motion of the tip of the optical fiber when the photons leave, and their answer is that it moves back and to the left so Abraham was right — the photon momentum is reduced in the medium, and the fiber must recoil when the photons leave and their momentum increases.
SFN RSS
The two models diverge as n^2. What fiber has the biggest n? Germanium hits n = 4.10 at 2060 nm, cinnabar hits n_D = 3.256 (for n_e). Fused silica, though convenient, is a wuss with n_D = 1.4584.
http://www.almazoptics.com/Ge.htm
http://www.translume.com/m_optical.htm
Ah, that was a tough one! I spent a few hours that day wondering if I was just a terrible physicist for not being able to quickly figure out such an “easy” problem.
Al: I believe transmittance will be the problem there. The laser has to be strong enough to produce an observable effect, but not so strong as to wreck the transmitting medium. Looks like the transmittance of Ge is not better than .5 anywhere in the spectrum.
Given two media of refractive index n0 and n1, reflectance R at normal incidence is
R = [(n0 − n1)/(n0 + n1)]^2
Given n0 = 1. for air and n1 = 4.1 for Ge, then R = 36.9% for the interface. That makes Ge internal transmission at least 52.3% plus 36.9% or 89.2%. Not so bad, especially if pulsed. Long runs of Ge fiberoptic are not advertised, perhaps from polycrystalline scattering. Does single crystal germanium fiber grow by edge-defined growth? Does cinnabar form a glass phase like quartz? An important divergence between two theories should be decided by more than one observation.
That’s a different effect. I’m taking about absorption with the material, like x-rays in lead. The light that makes it past the interface will heat the material – possibly enough to screw up the experiment.
Fused silica refractive index,
Fused silca, n_D = 1.45840; Fused germania, n_D = 1.6075
( 1.6075/1.45840)^2 = 1.215
For commercial optical glass, SF66 n_D = 1.9228 and K-PSFn214 n_D = 2.14297 (Sumita Optical Glass),
Fused silca, n_D = 1.45840. Commercial optical glass K-PSFn214 n_D = 2.14352,
(2.14352/1.45840)^2 = 2.16 signal advantage “8^>)
http://techon.nikkeibp.co.jp/article/HONSHI/20070424/131621/
Poynting predicted exactly the opposite: when light enters or leaves dielectric, it pulls the dielectric outwards. (Philosophical Magazine, vol. 9, p. 393, 1905). Was Poynting wrong? Hard to believe.