A mixed bag of neutrinos

If we represent electron neutrinos (νe), muon neutrinos (νμ), and tau neutrinos (ντ) by pure red, pure green and pure blue, respectively, the three neutrino mass states (ν1, ν2 and ν3) would be fuchsia, lime and periwinkle, a mixture of the primary colors.

Quantum mechanics is an everyday fact of life for particle physicists. Most particles are short-lived and decay before they can be directly observed, and the weirdest quantum shenanigans are perpetrated by systems that can’t be observed. Neutrinos behave quantum mechanically, and even though they are not short-lived, neutrinos are so difficult to observe that they can maintain a mixed quantum state even while traveling large distances.

A quantum state—the current value of some aspect of a quantum system—is like a light switch. It can be off or on, but never in between. Before discovering quantum mechanics, physicists expected a system’s properties to be like dimmer switches that smoothly slide between off and on, but they’re not. In addition, quantum properties can also take on multiple values simultaneously—off and on, as illustrated by the figure below. Each possible state contributes some amount, such as 30 percent off and 70 percent on. This mixing allows neutrinos to spontaneously change from one type to another, a phenomenon known as neutrino oscillations.

Neutrinos are categorized by how they they are produced: Electron neutrinos are produced along with electrons, muon neutrinos along with muons and tau neutrinos along with tau particles. They can also be categorized by mass: Neutrino 1, neutrino 2 and neutrino 3 all weigh different amounts. A neutrino cannot be categorized by production mode and by mass at the same time, however. A pure production state is a quantum mixture of all three mass states and a mass state is a quantum mixture of all three production states. A muon neutrino, produced along with a muon in the LBNE beamline for instance, would travel for hundreds of miles from Fermilab as a mixture of quantum states and may be observed in a detector in South Dakota as an electron neutrino.

This interplay between production states and mass states is what allows neutrinos to oscillate, or change from one production state to another and back again. The probability of each state actually wavers back and forth, the way the pitch of a gong wobbles as it resounds. The gong wobbles with a beat frequency because of a competition between two nearly matched resonances, which are analogous to the differences between neutrino masses in neutrino oscillations.

Physicists use production state transitions to learn more about the neutrino mass states. Neutrino masses are so small that it’s hard to measure them any other way, though they have cosmic significance. There are enough neutrinos in the universe that their feeble masses could affect how galaxies form and how space expands. The exact way that production states and mass states mix might even be associated with the disappearance of antimatter in the early stages of the Big Bang.

—Jim Pivarski

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A classical (pre-quantum) system can take any single value between off and on, while a quantum system can be off, on or both, but never in between.