## Chameleon-Like Behavior of Neutrino Confirmed 191 191

Anonymous Apcoheur writes

*"Scientists from CERN and INFN of the OPERA Collaboration have announced the first direct observation of a muon neutrino turning into a tau neutrino. 'The OPERA result follows seven years of preparation and over three years of beam provided by CERN. During that time, billions of billions of muon-neutrinos have been sent from CERN to Gran Sasso, taking just 2.4 milliseconds to make the trip. The rarity of neutrino oscillation, coupled with the fact that neutrinos interact very weakly with matter, makes this kind of experiment extremely subtle to conduct. ... While closing a chapter on understanding the nature of neutrinos, the observation of neutrino oscillations is strong evidence for new physics. The Standard Model of fundamental particles posits no mass for the neutrino. For them to be able to oscillate, however, they must have mass.'"*
## Re:What if... (Score:5, Informative)

You'd need a pretty complex theory to get non-mass oscillations to match all the data we got over the past 12 years, which is very compatible with a three-state, mass-driven oscillation scenario. Besides, you'd have to explain more than what the current "new standard model" (the SM with added neutrino masses) does if you want your theory to be accepted. If two theories explain the same data equally well, the simplest is more likely.

## Re:Chameleon-Like Behavior? (Score:3, Informative)

## Re: What if... (Score:3, Informative)

If two theories explain the same data equally well, the simplest is more likely./quote?

Make that "more preferred". In general we don't know anything about likelihood.

The thing about Occam's Razor is that it filters out "special pleading" type arguments. If you want your pet in the show, you've got to provide motivation for including it.

## Re:How in the universe? (Score:5, Informative)

How could something have mass and so weakly interact with normal matter?

Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact). But zero mass and really, really, really small but not zero mass, are two different things.

## Re:How in the universe? (Score:5, Informative)

How could something have mass and so weakly interact with normal matter?

Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact).

The fact that they barely interact with anything has nothing to do with the fact that they are nearly massless. Photons

aremassless and they interact with anything that carries an electric charge. Electrons are much lighter than muons, but they are just as likely to interact with something. The only force that gets weaker as the mass goes down is gravity, which is by far the weakest of the fundamental forces.## Re:What if... (Score:5, Informative)

That's the way I've always understood the mass/oscillation connection too. But then I thought... wait... don't photons oscillate too? They're just coherent oscillations of the EM field; oscillating back and forth between electric and transverse magnetic in free space. If there's something different about neutrino oscillation which makes it necessary for the neutrino to travel at sublight, what is it specifically?

The situation you describe with the EM field is an example of wave-particle duality. Light can behave like both a wave and a particle, but it doesn't make sense to analyze it both ways at the same time. As a wave, it does manifest itself as oscillating electric and magnetic fields and as a particle, it manifests itself as a photon, which doesn't change into a different type of particle. (There's no such thing as an "electric photon" and a "magnetic photon".)

Neutrinos, too, are described quantum mechanically by wavefunctions, and these wavefunctions have frequencies associated with them, related to the energy of the particle. But these have nothing to do with the oscillation frequencies described here, in which a neutrino of one flavor (eg. mu) can change into a different flavor (eg. tau). Quantum mechanically speaking, we say the mass eigenstates of the neutrino (states of definite mass) don't coincide with the weak eigenstates (states of definite flavor: i.e. e, mu, or tau). Without mass, there would be no distinct mass eigenstates at all, and so mixing of the weak eigenstates would not occur as the neutrino propagates through free space.

## Re:Wait a second! Re:What if... (Score:5, Informative)

Light doesn't oscillate in this way. A photon is a photon, and remains a photon. Electric and magnetic fields oscillate, but the particle "photon" doesn't. Neutrinos start as one particle (say, as muon-neutrinos) and are detected as a completely different particle (say, as a tau-neutrino).

The explanation for that is that what we call "electron-neutrino", "muon-neutrino" and "tau-neutrino" aren't states with a definite mass; they're a mixture of three neutrino states with definite, different mass (one of those masses can be zero, but at most one). Then, from pure quantum mechanics (and nothing more esoteric than that: pure Schrödinger equation) you see that, if those three defined-mass states have slightly different mass, you will have a probability of creating an electron neutrino and detecting it as a tau neutrino, and every other combination. Those probabilities follow a simple expansion, based on only five parameters (two mass differences and three angles), and depend on the energy of the neutrino and the distance in a very specific way. We can test that dependency, and use very different experiments to measure the five parameters; and everything fits very well. Right now (specially after MINOS saw the energy dependency of the oscillation probability), nobody questions neutrino oscillations. This OPERA result only confirms what we already knew.

## Re:What if... (Score:3, Informative)

Thanks. I just found some [uci.edu] equations [ucl.ac.be] that appear to reinforce what you said.

Since the oscillation frequency is proportional to the difference of the squared masses of the mass eigenstates, perhaps it's more accurate to say that neutrino flavor oscillation implies the existence of several mass eigenstates which aren't identical to flavor eigenstates. Since two mass eigenstates would need different eigenvalues in order to be distinguishable, this means at least one mass eigenvalue has to be nonzero. There's probably some sort of "superselection rule" which prevents particles from oscillating between massless and massive eigenstates, so both mass eigenstates have to be non-zero. Cool.

## Re:How measure no charge, no mass? (Score:1, Informative)

## Re:Oscillation and the conservation of energy? (Score:4, Informative)

I'm not a "real" physicist - but I did study this at undergrad level, so here goes:

Heisenberg's Uncertainty Principle ( http://en.wikipedia.org/wiki/Uncertainty_principle [wikipedia.org] ) states that there must always be a minimum uncertainty in certain pairs of related variables - e.g. position and momentum, i.e. the more accurately you know the position of something, the less accurately you know how it's moving. Another related pair is energy and time - the more accurately you know the energy of something, the less accurately you know when the measurement was taken.

(disclaimer - this makes perfect sense when expressed mathematically, it onlysounds like handwavery when you translate it into English, as words are ambiguous and mean different things to different people)

Anyway, this uncertainty means that there is a small but non-zero probability of a higher-energy event occuring in the history of a lower-energy particle (often mis-stated as "particles can borrow energy for a short time, but check the wiki page for a more accurate statement). It sounds nuts, I know, but it has many real-world implications that have no explanation in non-quantum physics. Particles can "tunnel" through barriers that they shouldn't be able to cross, for instance - this is how semi-conductors work.

By implication, there is a small probability of the neutrino acting as if it had a higher energy, and *this* is how neutrino-flipping occurs without violating conservation of energy.

## Re:What if... (Score:4, Informative)

No. All flavour eigenstates MUST be massive: they are superpositions of the three mass eigenstates, one of which can have zero mass. Calling the three mass eigenstates n1, n2 and n3; and the three flavour eigenstates ne, nm and nt, we'd have:

ne=Ue1*n1+Ue2*n2+Ue3*n3

nm=Um1*n1+Um2*n2+Um3*n3

nt=Ut1*n1+Ut2*n2+Ut3*n3

So, if any of n1, n2 or n3 has a non-zero mass (and at least two of them MUST have non-zero masses, since we know two different and non-zero mass differences), all three flavour eigenstates have non-zero masses.

Also, remember that the limit for the neutrino mass is at about 1eV, while it's hard to have neutrinos travelling with energies under 10^6 eV. In other words, the gamma factor is huge, and they're always ultrarelativistic, travelling practically at "c".

Another point is that the mass differences are really, really small; of the order of 0.01 eV. This is ridiculously small; so small that the uncertainty principle makes it possible for one state to "tunnel" to the other.

I really can't go any deeper than that without resorting to quantuim field theory. I can only say that standard QM is not compatible with relativity: Schrödinger's equation comes from the classical Hamiltonian, for example. To take special relativity into account, you need a different set of equations (Dirac's), which use the relativistic Hamiltonian. In this particular case, the result is the same using Dirac, Schrödinger or the full QFT, but the three-line Schrödinger solution becomes a full-page Dirac calculation, or ten pages of QFT. In this particular case, unfortunately, the best I can do is say "trust me, it works; you'll see it when you get more background".

## Re:What if... (Score:3, Informative)

The time-dependent Schrödinger's equation doesn't apply for massless particles. It was never intended to. It isn't relativistic. Try to apply a simple boost and you'll see it's not Poincaré invariant. The main point is that you get the same probabilities if you use a relativistic theory, but you need A LOT of work to get there.

Oscillations work and happen in QFT, which is Poincaré-invariant and assumes special relativity. I can't find any references in a quick search, but I've done all the (quite painful) calculations a long time ago to make sure it works. It's one of those cases where the added complexity of relativistic quantum field theory doesn't change the results from a simple Schrödinger solution.