A few questions about neutrino oscillation

Even though I don’t understand the process, I do recognize that neutrinos can oscillate. In other words the three neutrino types can change into one and other, and then back again. I recognize, further, that the existence of such oscillations implies that neutrinos have a non-zero (rest) mass (and, therefore, that they travel at less than the speed of light).

Question 1: Are the differences in their masses the only difference among the neutrino types?

Question 2: As a neutrino travels (say from the Sun to the Earth) it oscillates, and hence its mass changes. Does this mean that its velocity also changes, but in a reciprocal way, in order to allow for conservation of energy?

Question 3: Is there an intuitive, non-technical way to appreciate the fact that ‘if neutrinos oscillate they must have non-zero mass’? As an example of what I mean by “an intuitive, non-technical way”, it is fairly intuitive to appreciate that if a neutrino is traveling at less than the speed of light, it’s possible that it can be its own anti-particle. This is the case since an observer could (theoretically) get in front of, or be behind, a neutrino traveling at velocities < c, with the resulting change in perspective reversing the apparent direction of its spin, i.e. changing it into its anti-particle. OTOH, if the neutrino is traveling at light speed, one can never “get in front of it” to witness the change in the direction of its spin. Ergo, it can’t be its own anti-particle. Is there any sort of “analogous analogy” to illustrate why neutrino oscillation implies non-zero neutrino mass?


I don’t know the answers to 1 and 2, but here’s a stab at 3: If it’s observed to oscillate, that means it had time to oscillate. Objects that experience time have to be going less than c. If an object is massless, it must travel at c, so anything moving at less than c must have mass.

First of all, you have to be careful when you say “the three kinds of neutrinos”. There are, in fact, three different kinds of neutrino, with those three being the electron neutrino, the mu neutrino, the tau neutrino, the nu-1, the nu-2, and the nu-3.

Clear as mud? OK, think of it this way: There’s a sort of three-dimensional “neutrino space”, and the three kinds of neutrino are three mutually-perpendicular axes in this space. There are many different ways you can set up these axes, but since the space is three-dimensional, you can never have more than three sets of mutually-perpendicular axes. So there are three different kinds of neutrino, but what those three kinds are is a matter of context.

Now, you could have any number of different sets of axes, but two in particular are of interest to physicists. First, there’s a set of axes that corresponds with how the particles interact via the weak force. A W particle can decay into an electron-like particle and a neutrino, and which neutrino you get is determined by which electron-like particle you get: You could get an e+ and an electron neutrino, or a mu+ and a mu neutrino, or a tau+ and a tau neutrino, from a W+.

But it turns out that these three “flavor neutrinos” don’t have definite masses. They’re each a mixture of three other neutrino-axes which do have definite masses (but don’t have a definite way in which they interact with the weak force). These are called nu-1, nu-2, and nu-3, in order of increasing mass. Last I saw, the emerging consensus is that the electron and mu neutrinos are almost in the 1-2 plane (that is, they’re each mostly a mixture of the lightest and second-lightest neutrinos, with only a very small admixture of the heaviest kind), and lie at approximately 45 degree angles to the 1 and 2 axes (this is called a mixing angle), while the tau neutrino lies almost along the 3 axis (that is, the tau neutrino is almost entirely the heaviest neutrino, with just a little bit of the others).

Now, as for oscillation: You can think of neutrinos traveling through space as being a mixture of three waves (one each for the 1, 2, and 3 neutrinos), with the relationship between the phases of the waves telling you whether it’s an electron, mu, or tau neutrino. But the wavelength of these waves depends, in part, on the mass of the particle. Since the 1, 2, and 3 neutrinos have different masses, they have different wavelengths, so as the wave propagates, the relationship between their phases changes, and hence the flavor changes. If you could somehow create a pure beam of exclusively one mass (say, nu-1), then it wouldn’t oscillate, since it’d have only a single mass, but it wouldn’t have a well-defined flavor, and could interact with electrons, muons, and tauons with various probabilities.

Thank you,** Chronos**. I am still digesting what you said, but even after my first read, “a bit of the veil was lifted” from my eyes. Many of the concepts you described were totally new to me. But, wow, were they interesting (and instructive)! I really appreciate all the effort you put into it. Thanks!

I don’t ever think I’ve seen that explanation either. When atoms were simple solar systems, who’d have predicted that something as straightforward as a particle could behave that way? Wait until the folks who want simple answers to QM read that. We’ll see heads exploding all the way to Orion’s Belt. :slight_smile: