Last time, your old Quantum Butcher introduced you to the Keen-O Neutrino, an extremely lightweight, some said massless particle released in nuclear reactions known to occur in the hearts of stars, in the explosions of supernovae, and in the monstrous infernos known as Active Galactic Nuclei (AGN). We discussed the potential implications of "heavy neutrinos" on astrophysics and cosmology, and took a pretty lightweight tour (for lack of time and space) of so-called "Cerenkov Detectors" like Super-Kamiokande and AMANDA that have brought neutrino astronomy to prominence.
Now it’s time to talk about one of the more interesting results to emerge from this work. Last year, at the "Neutrino 98" meeting in Takayama Japan, investigators from the Super Kamiokande project announced their finding of evidence for non-zero neutrino mass. This finding didn’t just pop out of an academic vacuum. There have been hints, for more than a decade now, that the neutrino might have mass. In particular Dr. John Simpson of the University of Guelph found an energy (mass) of 17 keV for the neutrino in the mid 80’s, but his results were met with raised eyebrows and it was strongly suspected his work might have been queered by the use of semimetal crystals. So there were rumblings in the basement of the Standard Model’s tidy house, but most physicists were willing to subscribe to a massless neutrino.
Ultimately, the recent, more definitive demonstration of neutrino mass came out of a vexing, fundamental problem of neutrino physics: the so-called atmospheric neutrino problem. Recall from the last column that when gamma rays strike the earth’s upper atmosphere, they create showers of neutrinos which can then be recorded by Cerenkov detectors like Super-K. For theoretical reasons, the neutrinos produced (and therefore detected) by this process should appear in certain ratios, namely two muon neutrinos for every electron neutrino.
This ratio was not observed. In fact, muon neutrinos and electron neutrinos were observed at an incidence of nearly one-to-one. How to explain such an anomaly? It might be that the theory was incomplete: electron neutrinos might be produced at higher rates than predicted, muon neutrinos at lower rates, or perhaps there were unlikely, as-yet-undetected extraterrestrial electron neutrino sources queering the ratio. Some suggested the problem lay not with the theory, but with the detectors. Clearly, they argued, the detectors were less sensitive to muon neutrinos, or there was some other technical problem creating the observed discrepancy.
A more interesting possibility floated around: perhaps neutrinos were undergoing oscillations. Such oscillations are quantum mechanical effects, in which one particle transforms into another particle with slightly different properties. This is important--if particle a oscillates (transforms) into particle b, the two particles must have different properties. If particles a and b have identical properties, they are the same particle, and to assert that they have undergone an oscillation would be meaningless.
Now, remember that we made much in the last column of the ability of Cerenkov detectors like Super-K and AMANDA to discriminate the trajectories of incoming neutrinos. Using this technology, investigators at Super-K demonstrated the zenith angle dependence of the muon neutrino flux deficit; in other words, they showed that the deficit in muon neutrinos was greatest in the flux from the upcoming direction (i.e., from the center of the earth). When you eliminate confounding variables, such an observation can be best explained by neutrino oscillations. Those neutrinos produced on the opposite side of the earth have to travel through the planet to reach the detector. Their longer flight path gives them more spacetime in which to undergo oscillations, probably into tau neutrinos or a so-called sterile neutrino, before reaching the Super-K observatory.
So, muon neutrinos are undergoing quantum oscillations during their longer flight path through the earth, "fuzzing" into another flavor of neutrino. That is highly significant, because massless neutrinos cannot oscillate. Why not? As noted above, for one particle to oscillate into another, they must have different properties, and in this case that property is mass (energy). If a muon neutrino oscillates into a tau neutrino, the two particles cannot have the same mass. Since they cannot have the same mass, they cannot both have a mass of zero, since 0=0. So at least one of the neutrinos in question has mass, and for theoretical reasons they probably both have mass.
QM
Cool. So the neutrino has mass. And since the cosmos contains a lot of neutrinos, that must account for a big chunk of the so-called "dark matter" known to be lurking in the universe. Perhaps enough to "close" the universe?
Well, let’s define our terms. If you’re like me you grew up with a notion probably doomed to be considered rather quaint by cosmologists--that the universe has one of three possible destinies. If the universe falls short of critical density, that is, if it lacks the mass to slow itself down from the initial "impetus" of the Big Bang, it will continue to expand forever, until entropy reduces it to an utterly isothermic, utterly isotropic stew of elementary particles. Boring. In this situation, space will be hyperbolic--saddle-shaped. Alternatively, if the universe has just exactly the critical density, the forces of cosmic contraction due to matter/energy density and the forces of expansion from the Big Bang will be in balance, and the universe will slow its expansion at an ever-increasing rate, asymptotically approaching zero velocity. In cosmological terms, W
=1. Space will be flat overall, although of course relativity demands punctuations in spacetime curvature due to the effects of massive bodies or energetic processes. Not only is this vision of the cosmos also Boring, it strikes many cosmologists as a fantastic coincidence, and seems to smack suspiciously of the weak anthropic principle, which I have no time to discuss at present. Finally, if the universe contains enough matter to overcome the expansion of the Big Bang, then spacetime will be spherical, that is, closed. The cosmos will slow, stop, and fall back on itself, crushing into a spacetime singularity. And that, from our point of view, will be that.
I must confess this latter model has always had a profound aesthetic appeal for me. It posits that the universe is, ultimately, a simple harmonic oscillator, an elementary particle undergoing infinite quantum fluctuations, and perhaps occupying a larger cosmos of other particle-universes. And perhaps, as Sagan suggested, every particle in our universe is also a self-contained, closed universe, containing its own elementary particles, an infinite progression up and down the scale from very small to very large.
Alas, one man’s aesthetic is another’s theoretical boondoggle, and while science does have an aesthetic, in the final analysis it’s empirical facts and successful theories that count. Over the last two decades advances in cosmology and astronomy have forever changed our view of the universe and its fate. For quite some time now the closed universe model has been a distinct theoretical underdog. In fact, the question of whether heavy neutrinos would contribute enough dark matter to close the universe (always a doubtful scenario) has become passé in a big way. As Lawrence Krauss declares in the January ‘99 Scientific American, "the standard cosmology of the 1980’s, postulating a flat universe dominated by matter, is dead."
The focus of cosmology has shifted decidedly away from trying to determine whether there’s enough matter, dark or otherwise, to close the universe, and toward reconciling recent observations that confound our most fundamental conceptions of spacetime itself. The standard cosmology of which Dr. Krauss speaks is ultimately the offspring of Hubble’s observations early in this century, that the universe is expanding. The ensuing revolution in astronomy and cosmology raised the questions of "how fast?" "how old?" and "how far?" and compelled Einstein to toss out lambda, the cosmological constant he had incorporated into his theory of general relativity to keep the universe in a steady state. Later, Einstein called lambda his greatest blunder.
Well, not so fast there, Albert. Earlier this year, just in time to throw cosmology into a real quandary for the new millennium, Hogan, Kirschner and Suntzeff performed a series of observations of type Ia supernovae in distant galaxies, hoping to use the instrinsic brightness of these phenomena as a standard candle. The goal was to use such observations to get a more precise measurement of the Hubble Constant, a number that describes the rate of cosmic expansion. Analysis of their observations led Hogan et al reluctantly but inexorably to the conclusion that space is expanding at an accelerating rate. Such a finding implicates the presence of a bizarre cosmic antigravitational force. If these findings hold true, cosmologists will be forced to re-incorporate Einstein’s little lost lambda, the much-maligned cosmological constant, back into the fold of general relativity.
Of course, that’s the easy part. Then they have to explain it. One of the best explanations to emerge so far is the appearance of virtual particles that seethe into and out of existence throughout all of spacetime. But speaking of spacetime, the Quantum Butcher has only limited quantities, and we’ll have to save discussions of the Casimir Effect and quantum foams for another column.
CHECK IT OUT:
If you dig cosmology and neutrino physics, you’ll want to see:
Scientific American, January 1999
The Whole Shebang by Timothy Ferris, Simon and Schuster, c 1997.
http://www-hfm.mpi-hd.mpg.de/CosmicRay/CosmicRaySites.html
http://amanda.berkeley.edu/
http://chico.ncsa.uiuc.edu/Cyberia/Cosmos/CosmosInFF.html
http://www-supernova.lbl.gov/
http://www.phys.hawaii.edu:80/~jgl/nuosc_story.html
