Monday, September 26, 2011

Physics surprise - or is it?

kw: science, physics

In the CNET article Physics Shocker - Neutrinos clocked faster than light, work is reported that measured the speed of neutrinos that traveled 732 kilometers through solid rock, from CERN in Switzerland to Italy, and arrived 61 nanoseconds "too soon". That is, they arrived sooner than the time it would take light to cover the same distance in a vacuum, which is supposed to be the shortest travel time possible. By the way, the caption to the article's illustration mentions "neutrons", which is an error.

This is no surprise to me, because of a well-known property of x-rays: they have a refractive index less than one in most media. Refractive index is the ratio of the velocity of a phenomenon through a medium to its velocity in vacuum. Thus, one variety of crown glass has a refractive index of 1.51 for a certain wavelength of visible light; this implies its velocity through the glass is 1/1.51 times c, or 0.662c. The refractive index of an x-ray of moderate energy (30 KeV, wavelength 0.0413 nm) in water is 0.99999974, which implies that the x-ray's phase speed is 1.00000026c. I say "phase speed" rather than velocity because it is one of two ways wave speed is measured for a wave packet (The two are equal in a standing wave); refractive indexes are formally defined as the ratio of phase speeds.

Try this sometime on a windless day: throw a small stone into a pond, then watch the ripples carefully. The expanding ring of ripples, typically about ten wavelets, will show a kind of rolling effect; new wavelets appear at the trailing edge, travel through the thickness of the ring, and die out at its forward edge. These wavelets are moving at the phase speed, while the slower speed of the ring is called the group speed. Standard physics analysis indicates that x-ray photons travel at the group speed, but have an internal structure that exhibits phase speed "rolling", and this is what interacts with the medium to refract it at an angle we measure to determine the refractive index.

This leads to an interesting property of x-rays: total external reflection. Anyone who has taken an elementary physics course will know about total internal reflection: at angles shallower than the critical angle all the light moving from the medium to vacuum (or air) is reflected. Thus, when you are under water and look toward the surface, there is a circle in which you can see what is above the surface, and outside that circle, the water's surface appears as a mirror reflecting things below the surface. With x-rays it is just the opposite. At very shallow angles all the x-rays that hit a surface, such as of polished aluminum, are reflected outward with no losses (Aluminum's refractive index for x-rays is in the range of 0.99999). This behavior was exploited to make the focusing mirrors of the Spitzer X-Ray Telescope, which gathers x-rays from an area roughly a meter in diameter to a spot a micron wide, producing images with resolution similar to a telescope with an 8-inch (20 cm) aperture.

An x-ray lens was invented that exploits a different result of this sub-unit refractive index. A rod of aluminum or boron can be drilled with small holes that cross the central axis at various angles. Each hole does a little focusing in one plane, and by having various angles (three is common), a diverging beam of x-rays can be focused into a parallel or even converging beam. We are talking very small angles here. The effect makes it possible to focus x-rays, but has limited utility because even in Al or B, x-rays are gradually absorbed, so the thickness of material needed for elaborate focusing would use up most of the beam's energy.

The experiment in Italy is surprising because it was set up to measure the group speed of the neutrinos. If further investigations support this result, it will be necessary to repeat them with the neutrinos moving through vacuum over similar distances, such as between the CERN reactor and the ISS. Very careful timing (and careful synchronization of clocks to account for relativistic effects with satellite velocity in the 5km/s range) will be needed to ascertain whether this is a refractive index situation or a property of the neutrinos that is independent of the medium. Maybe they'll turn out to be the fabled tachyons! (I kinda doubt it, but fun to dream…)

No comments: