Number 685, May 12, 2004 by Phil Schewe and Ben Stein
Our Universe Has a Topology Scale of at least 24 GPC
Our universe has a topology scale of at least 24 Gpc, or about 75 billion light years, according to a new analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP).
What does this mean? Well, because of conceivable hall-of-mirrors effects of spacetime, the universe might be finite in size but give us mortals the illusion that it is infinite. For example, the cosmos might be tiled with some repeating shape, around which light rays might wrap themselves over and over ("wrap" in the sense that, as in video games, something might disappear off the left side of the screen and reappear on the right side).
A new study by scientists from Princeton, Montana State, and Case Western looks for signs of such "wrapped " light in the form of pairs of circles, in opposite directions in the sky, with similar patterns in the temperature of the cosmic microwave background. If the universe were finite and actually smaller than the distance to the "surface of last scattering" (a distance that essentially constitutes the edge of the "visible universe," and the place in deep space whence comes the cosmic microwaves), then multiple imaging should show up in the microwave background.
But no such correspondences appeared in the analysis. The researchers are able to turn the lack of recurring patterns into the form of a lower limit on the scale of cosmic topology, equal to 24 billion parsecs, a factor of 10 larger than previous observational bounds. (Cornish, Spergel, Starkman, Komatsu, Physical Review Letters, upcoming article; contact Neil Cornish, 406-994-7986, firstname.lastname@example.org.)
The Best Packing of M&Ms
The best packing of M&Ms, filling more than 77% of available volume, has been achieved in a computer simulation performed at Princeton. Actually the new results apply to any ellipsoid object, such as M&M candy, fish eggs, or watermelons.
The modern understanding of dense packing might be said to start in 1611, when Johannes Kepler suggested that the most efficient packing of spheres in a container occurred when the spheres were placed in a face-centered cubic arrangement---the way a grocer stacks oranges. "Kepler's conjecture" was proved in 1998 and the filling factor was worked out to be about 74%. Unlike spheres, which still look the same after you rotate them, ellipsoids' oblateness (they are squashed or stretched in at least one direction) give them orientational degrees of freedom that spheres don't have. Consequentially, ellipsoids can be packed more efficiently than spheres. Depending on the aspect ratio of the ellipsoid, the packing density can be anywhere between 74% and 77%.
The Princeton research (contact Salvatore Torquato, 609-258-3341, email@example.com) has a number of practical implications: it shows that glassy states of matter, in which molecules lie in a disordered arrangement, can have densities almost as high as for crystals; it suggests that because of a high contact number (in the high-density packings ellipsoids can touch 14 of their neighbors) stronger ceramics can be designed; and it encourages researchers to investigate the effect of ellipsoidal shape on evolutionary optimization in fish eggs. (Donev et al., Physical Review Letters, upcoming article.)
Tungsten Inverse Opal
Tungsten inverse opal, created for the first time in a lab at the University of Toronto, is a type of photonic crystal, which in turn is a material that excludes (or nearly excludes) all light at certain wavelengths. In general, opalescence is an optical effect in which light reflected from some object appears milky or pearly, or shimmering with various colors.
Inverse opalescence, then, is the opposite of this---it would be an effect of taking away or forbidding certain kinds of light---which is what a photonic crystals is supposed to do. (Inverse opals, if you were to look at them from the outside would be even shinier than their natural counterparts because they exclude more wavelengths of light.)
Early photonic crystals were built by stacking tiny rods criss cross fashion (or by etching out material from a solid) to create a material which would bottle up radiation of some wavelengths (see, for example, Update 348).
In the University of Toronto case, tiny silica beads are packed into a vessel. Later tungsten metal is introduced in the spaces between the beads and the beads themselves corroded away with acid. The remnant metallic lattice serves as an "inverse opal." It does a fair job of excluding some kinds of light, and possibly even converting what would be waste heat in the form of infrared radiation into more useful wavelengths.
Speaking at the Conference on Lasers and Electro-Optics (CLEO) next week in San Francisco, Georg von Freymann (firstname.lastname@example.org) will report on the creation of his inverse opal material and on various absorption effects in the material. (Meeting website.)