The alternative is not that Einstein was wrong, but that neutrinos have imaginary mass rather than real mass. This is consistent with observations. We can't measure neutrino mass in experiments, only mass squared, and the error bars on those measurements persistently include some small negative numbers. (And some of these measurements virtually exclude any positive mass^2 values. Other measurements purporting to exclude negative mass^2 values may be the result of over-correction and wishful thinking.)
Imaginary-mass particles are consistent with relativity and were first theorized in the 1960s and given the name "tachyons". High-energy tachyons move near the speed of light; low-energy tachyons move at unlimited velocities. This accounts for the fact that the neutrinos from the 1987A supernova were only 18 hours ahead of the light from the explosion, despite the distance -- they were extremely high energy tachyons.
If neutrinos are tachyons, this could account for a couple of odd things about them - the exceptionally low cross section (likelihood of interaction) and their oscillating between different flavors (electron, muon, tau). Exactly how is a job for the theoreticians, but it seems to me that a neutral particle moving effectively backward in time and at unlimited velocities coupled with low energies is not often going to interact, and imaginary mass could be likened to a rotation or oscillation, much like many other things involving imaginary numbers in physics.
Physicist John Cramer talked about the idea back in 1992 in his Analog column: Neutrino Physics: Curiouser and Curiouser (Alternate View Column AV-54) [washington.edu]
Quoted Text
of the six most recent experimental determinations of neutrino mass, all have given negative values of the mass-squared to within the statics of the measurements. The experimental observation is that in the vicinity of the end point the yield of electrons lies above the zero-mass line, while for neutrinos with non-zero real mass, the electron yield should lie below this line. The measured mass-squared values are negative to an accuracy of several standard deviations in the most recent of these experiments.
These experimenters have been strangely quiet about mass-squared measurements with negative values. If the results had been positive by the same amount, the literature would be filled with claims that a non-zero value for the neutrino mass had been established. But a negative mass-squared is not something that can be easily publicized.
You obtain the measured mass value from a mass-squared measurement by taking the square root of the measured value. However, the square root of a negative number is an imaginary number. Thus the measurements could, in principle, be taken as an indication that the electron neutrino has an imaginary mass.
What are the physical implications of a particle with an imaginary rest mass? Gerald Feinberg of Columbia University has suggested hypothetical imaginary-mass particles which he has christened "tachyons". Tachyons are particles that always travel at velocities greater than the speed of light. Instead of speeding up when they are given more kinetic energy, they slow down so that their speed moves closer to the velocity of light from the high side as they become more energetic. Feinberg argued that since there are no physical laws forbidding the existence of tachyons, they may well exist and should be looked for.
Here's a link to another, slightly more technical look at the idea: Neutrinos Must be Tachyons [arxiv.org] by Eue Jin Jeong. Googling "neutrino tachyon" also turns up several previous discussions.
(Blatantly ripped from an intelligent sounding post on Slashdot:
http://science.slashdot.org/comments.pl?sid=2441350&cid=37488580)
Don't throw away your Flux Capacitor yet!
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