A neutrino identity crisis?
The strange disappearance of both atmospheric muon neutrinos and solar electron neutrinos can be understood as a process of "neutrino oscillation". What that means is that, given the proper conditions, a neutrino of one type can change into one of a different type; if all three neutrinos have a mass of zero, or even the same mass of any value, this would not be allowed.
If neutrinos have mass and therefore are able to change their stripes, both the atmospheric and solar neutrino anomalies could be solved. This is because muon neutrinos from the atmosphere which oscillate into tau neutrinos would be experimentally undetectable (in a practical sense). Similarly, if electron neutrinos from the Sun change into muon or tau neutrinos, they too will interact at a significantly lower rate.
The term neutrino "oscillation" was coined because the transition between neutrino types is not one-way. In other words, a muon neutrino which (say) transforms into the tau type will actually transform back and forth as it sails along. This process is a probabilistic consequence of quantum mechanics. Given a neutrino produced as a certain type, after travelling a certain distance, the neutrino will become a mixture of two (or three) types. A rigorous mathematical explanation of neutrino oscillation is beyond the scope of this introduction, but the outlines can be sketched out for the simplified case where there are only two neutrinos involved in the process. It is not an easy phenomenon to explain without resorting to math, but those willing to read on may find some of their questions answered. For the truly curious, a mathematical derivation using quantum mechanics is also available.
It has long been known that particles of matter behave, in some circumstances, akin to waves instead (the effect has been observed for electrons and many other familiar particles. When particles behave like waves, they exhibit a sort of frequency which is proportional to their energy . Normally, this behavior is unimportant, since no physically observable quantity depends on whether the particle at a peak or a trough along its "matter wave".
Catching a wave
The situation changes, however, if one wave can undergo "interference" with another. Interference has a very specific meaning in connection with wave behavior, namely it either means one wave's "peaks" add together with another wave's "peaks" to produce an even bigger peak ("constructive interference") or one wave's peaks add together with another wave's troughs to cancel out both waves ("destructive interference"). When two waves moving together add or subtract in this way, there is still no dramatic effect if the waves have the same wavelength (or equivalently, frequency), since in that case the resulting wave is simpler a larger or smaller copy of the original ones.
If, on the other hand, the interfering waves have different frequencies, the resulting wave is not simply an enlarged or reduced version of either of the original waves. In fact, the resulting wave has no definite wavelength; at some points the two waves interfere constructively, and at others they interfere destructively. At points where one wave is crossing zero (i.e. steeply rising or falling) and the other is at a minimum or maximum (i.e. is approximately flat), the combined wave appears to have the frequency of the first wave. At other points, the situation is reversed and the combined wave has a frequency close to that of the second wave. The frequency at which this phenomenon repeats is related to the arithmetic difference in the two original frequencies. In effect the combined wave changes its behavior from being like one wave to being like the other with a new frequency equal to the difference in the individual frequencies. In the case of a matter wave, where the particle has a mass much smaller than its energy, it can be shown that the frequency is proportional to the square of the mass, divided by the momentum.
This is getting to sound a pretty similar to neutrino oscillation (waves alternating back and forth between different characteristics). It sounds great, except if a given neutrino is one matter wave, where is the other matter wave which is interfering with it to produce this flip-flopping? The answer is that (in our simplified case of two neutrinos) the neutrino actually interferes with itself. Putting it another way, a neutrino can propagate not as a single wave, but as pre-packaged combination of two. The reason is that neutrinos are produced in weak interactions, as either an electron neutrino, a muon neutrino, or a tau neutrino. But what if the electron neutrino itself acts like one of our combined waves? That is, what if the electron neutrino does not have a definite mass, but instead acts like our schizophrenic wave?
Mixing it up
That is the unstated premise of neutrino oscillation; an electron neutrino, when produced must be in a quantum mechanical state which has, in effect two different masses. A muon neutrino is a similar, complementary mixture of the two masses. Conversely, a neutrino with exactly one, definite mass must be a mixture of electron and muon neutrinos. So when an electron neutrino (and its combined matter wave) is produced and starts to propagate, the two different mass values interfere with each other. Depending on the difference in frequency between the two waves, the initial electron neutrino combined wave will sometimes be dominated by one or the other waves subcomponents which has a specific mass and frequency. But if a neutrino with a definite mass is a mixture of both electron and muon neutrinos (this pre-condition for oscillation is termed "mixing"), what started as a pure electron neutrino with a mixture of masses has become a neutrino with a pure mass and a mixture of electron neutrino and muon neutrino properties. In fact the combined electron neutrino matter wave, as the two matter wave components with different masses irregularly add and cancel with each other, may even at times very closely resemble the combined muon neutrino matter wave. If the neutrino interacts a point where it is not in a definite state of being either an electron neutrino or a muon neutrino, which one it behaves like at that moment is anybody's guess.
Conclusion or Confusion?
The above is an attempt to sketch out the plausibility of the idea of neutrino oscillations and the implication of unequal (and hence non-zero) neutrino mass if the phenomenon is observed. It may reassure the skeptical reader to know that an essentially identical interference/mixing/oscillation scenario has in fact been experimentally observed for 20 years between two other subatomic particles called kaons. There is no question that if neutrino have different (non-zero) masses, and if they mix so that each neutrino represents a mixture of two or more different masses, neutrino oscillations will occur. Similarly, there is no known or imagined mechanism by which massless neutrinos would oscillate.
Still think we're pulling your leg? In physics, an equation (or two) is worth a thousand words. Check our math as you follow along with the derivation!