It's summer! A time for relaxation, some fun at the beach,
and intense quantum mechanics. What? Don't look at me like that.
Today, I'm turning to my trusty beach balls to help explain one of the weirdest ideas in quantum
mechanics: neutrino oscillation. Put on some sunscreen and get ready, this is Even Bananas.
A quick refresher on neutrino oscillation. This odd behavior is all about how neutrinos appear
to change as they travel. So an electron neutrino produced in the sun can arrive in a detector on
earth as a muon neutrino. If that neutrino doesn't interact in the detector and travels further,
it can change into a tau neutrino. We've used this animation before to represent oscillation.
It might even be how you imagine it happening at a particle level.
The problem is that it's not quite right. I like to think of it in a different way.
Imagine you have an incredibly stylish pair of sunglasses that let you see only a sliver of the
world. And someone passes you a ball. This ball is red.
You throw the ball to a friend who's also wearing a pair of the special glasses.
Uh, no. This ball is blue. [unison] Wait, what?
You and your friend would be pretty surprised until you realized you were looking at a
beach ball with three different colors on it. This is similar to what happens with
neutrinos. Imagine each color on the beach ball represents a different flavor: electron, muon,
and tau neutrino. Neutrinos actually travel as a mixture of these three different flavors.
And catching the beach ball is like when a neutrino interacts in our detector,
producing its partner particle, or in this case appearing like one single color. In general, if a
muon is producing a detector we say well that must have been a muon neutrino. If we see an electron
we infer an electron neutrino. And if we see a tau, it was a town neutrino. So our original
animation doesn't quite work. The neutrinos aren't literally changing into different particles,
they're traveling as this weird quantum mix of all three. But our vision is
limited and we can only see them when they interact, producing one particular flavor.
Side note: I admit my beach ball analogy isn't perfect, either. When a neutrino interacts,
it fully commits to that one flavor. So a better analogy would be: if the beach ball turned into
a solid color when I caught it. If you have this advanced beach ball technology, please contact me.
One place the beach ball analogy works great though is with this idea of probability.
You never know what color you'll land on or what neutrino flavor you'll get.
But if the red section of your ball is really big then you have a greater chance of seeing
red. And here's the thing, we can have beach balls with different sized stripes. You could imagine
all sorts of different combinations, but there are three mixtures that we're particularly interested
in. We call these the mass states of the neutrino, and there are three of them:
mass state 1, mass state 2, and my state a million. Just kidding, it's mass state 3.
We're so good at naming things. This beach ball here is actually the
right quantum mixture for mass state 2. There's a one-third chance of seeing each flavor muon,
electron, and tau, when it interacts. A very evenly balanced neutrino. My personal favorite.
A mass state 1 neutrino shows up two-thirds of the time as an electron neutrino
and one-sixth of the time as the other flavors.
A mass state 3 neutrino on the other hand almost never shows up as an electron neutrino.
So now we know that there are two totally valid ways to think about neutrinos: as flavor states,
which is how we normally see them interact, and as mass states, which is how they like to travel.
As you might have guessed from the name, the mass states also have mass.
Here's the mind-melting part: these flavor states and mass states don't line up.
So neutrino flavors, which is how we typically end up talking about neutrinos,
don't actually have a well-defined mass. Asking "what is the mass of an electron neutrino"
is like asking "is a banana left-handed?" It's a property they just don't have.
Only certain quantum mixtures have definite masses. Those are our mass states. Quantum
mechanics is weird and it does not care how counterintuitive this seems. It's a really hard
concept to wrap your head around. Each mass state can produce different flavors, the same way the
beach ball is a mixture of three colors, and each flavor is also a mixture of the mass states. After
all, if I think I'm holding a red ball, I could still be looking at any of the three beach balls.
I often get asked "if neutrinos are turning from one flavour into another doesn't that
mean they're changing mass?" Hopefully, the beach ball analogy helps explain that they
aren't the neutrino itself isn't changing, but the probability of seeing a particular flavor.
As it turns out, the different masses were inside them all along, and so were the flavors.
Okay, we've gone into a lot of detail about the flavor and the mass states and I want to bring
it all back home to oscillation. We know that depending on the neutrinos energy and
how far it's travelled, we're more likely to detect certain flavors of neutrino. So what's
the deal? Well now you know the neutrinos are traveling as a mixture of mass states,
and because they have different masses, they're all traveling at very slightly different speeds.
The differences are so small that we actually can't measure them, but it does mean that the
quantum mixture changes as a neutrino travels. Essentially, the stripes on our beach ball are
growing and shrinking over time, and that is what gives us the pattern that we see in oscillation.
When the mix changes, the chance of catching one of our quantum beach balls changes. So the
probability of seeing a particular flavor changes. So all the quantum weirdness boils down to this:
the probability of detecting any given neutrino as any given flavor goes up and down as the neutrino
travels. That's why we call it oscillation and that's how we end up with detectors at different
distances seeing different neutrino flavors. Scientists designing experiments to study
oscillation can work backwards to figure out the best location for their neutrino detectors.
That is, the spot where you see the most neutrinos changing flavor. Once you know how much energy
you'll have in your neutrino beam, you can figure out how long you want it to travel for. A bit of
maths and you can basically draw a circle around the starting point. With the right distance,
find a mine to shield your experiment from cosmic rays and you're ready for some neutrino physics.
If these concepts are a lot to take in, you are not alone. A common saying among physicists
is "if you think you understand quantum mechanics, you don't."
Do you have a different analogy for thinking about neutrinos?
Do you hate beach balls now? We love to hear from you, so let us know in the comments.
A mass state 3 neutrino on the other hand almost never shows up as an electron neutrino. [laughter]
I thought it would go further behind me.