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Flip Tanedo | USLHC | USA

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The secret lives of particles

Up next on your favorite sensationalist news program: What do quantum particles do when we’re not looking? Probably not what you’d expect.

Quantum physics is weird… but most readers of this blog probably already knew that.

While the mathematical formalism ‘behind the scenes’ is perfectly well-defined and the predictions by the theory are completely sensible (and rigorously tested), it is often difficult to interpret the mechanism of quantum theory into ideas that make sense relative to everyday experiences. You’ve probably already heard of several examples of quantum weirdness:

  • At very small scales pop in and out of existence like the bubbles in a quantum root beer
  • Somehow the cat-in-the-box is both dead and alive (who put the cat in such a dangerous box?)
  • Particles behave like waves… or maybe waves behave like particles

The subject of quantum physics is too broad and deep for me to give an complete summary of the nuts and bolts, but the three popular examples above are all related to one very neat feature of quantum theory:

Particles behave very differently (perhaps even misbehave) when nobody is looking*.

A quantum system looks just fine when you observe it, but between observations some seriously funky things can occur. I’m being deliberately vague when I say “observation,” suffice it to say that it could be anything from peeking to look at the cat-in-the-box or looking for the remnants of an exotic particle in a collider. Here’s the point: once we make an observation, everything makes sense. Energy and momentum are conserved, the cat is either dead or alive (but certainly not both), etc.

Quantum Billiards

An analogy is in order. In high school physics people love to talk about billiard balls. They’re the perfect example of Newtonian physics: if you know the positions and the momenta of the cue ball, you can calculate (up to friction) the trajectories of all the other balls. Thus if you only knew the initial an final configurations of the billiard balls, you could work out everything that happened in between. Consider, for example, the following picture of my friend and colleague, Sven:

untitled-1

Between these two photos one can work out all of the kinematics of the billiard balls. As a string theorist, however, Sven knows that nature is quantum mechanical.

Quantum mechanics tells us that when you’re not looking, all sorts of crazy stuff happens. If we “close our eyes” between the initial and final configurations, the balls ought to have taken any of an infinite number of arbitrary paths (as shown above). In fact, to be technically correct, they take a combination of all the paths. In one possible path, the eight ball can hit the side bumper and then fly off to the moon at faster-than-the-speed-of-light and return to the table to innocently come to rest just short of the corner pocket.

quantumbilliard

The “sum” of all of these possible (if non-sensical) histories conspire to give a final configuration of billiard balls which just happens to obey all of our rules about conservation of momentum, etc.

Okay, let’s stop right here. You should be angrily jumping up and down saying,

But that’s not science, that’s mumbo-jumbo! Where is the experimental evidence? You’re just making up stories about what happens when nobody is looking, then you’re saying that everything magically works out when someone is looking! Isn’t this just another version of the, “if a tree falls in the woods and there’s nobody there to hear it” paradox?

To this I would say, “good job!” You’re thinking like a scientist. Indeed, up to now what I’ve been telling you is a story and you have no reason to believe it. It turns out, however, that one can set up situations where the effect of this quantum “sum over histories” can actually be made manifest. Let’s start by being a little more concrete about what I’m trying to sell you.

“Hacked” Quantum Mechanics

Here’s a somewhat idiosyncratic introduction to quantum mechanics. It’s not rigorous, but should give a flavor of what’s actually being done. (And I’ll refer back to this in future posts.) Suppose you have a particle that you’ve observed at point A. We would like to know the probability of finding the particle at point B at some later time.

  • For each path between A and B, no matter how funky, we associate a complex number called the amplitude of that path.
  • If we sum together all of these numbers, we get a complex number called the amplitude for the particle to go from A to B.
  • The probability of finding the particle at B is given by the squared absolute value of the amplitude for it to go from A to B.

When we say that a particle takes “all possible paths” between A and B we are really referring to this sum over amplitudes. For those who like fancy words, this is known as Feynman’s “path integral formulation” of quantum mechanics.

Here’s the interesting thing about these amplitudes: complex numbers have relative phases (i.e. angles) and they can “interfere,” i.e. they can sum in a way that partially or completely cancel each other out. This is exactly the same interference when we say quantum mechanics displays wave-particle duality. What usually happens is that the amplitudes for very exotic paths end up canceling each other out, leaving only the contribution from more mundane paths. In particular, this usually leaves behind the classical path as the dominant contribution.

We can set up situations, however, where there are two different classical paths that should both give “dominant contributions.” In this case, one can observe that these two paths exhibit quantum interference. The most well-known example of this is the famous double-slit experiment, where the distribution of electrons on the other end of a barrier with two slits shows a pattern characteristic of quantum interference. In fact, one can “read” the distribution of electrons as a way of hinting at the existence of two slits in the barrier. This experiment is usually presented as proof that electrons behave like waves. In this context I present it as evidence that electrons obey a “sum over histories.” The formalism of quantum mechanics tells us that these are actually the same thing. Thus all this quantum “sum over histories” is not just mumbo-jumbo and really does make testable predictions.

Not-so-secret lives of particles at the LHC

So far I’ve given a very hand-wavy discussion of what is meant when physicists say “a particle takes all possible paths between two points.” This has been rather abstract and it’s not clear why it’s so useful since, as we’ve mentioned, most of the time the punchline is that the result of the quantum effects is to reproduce something classical.

The point is this: one way to describe the program at the LHC is that we’re trying to reveal the “secret lives of particles.” When we smash particles together at the LHC we end up with a lot of stuff coming out. We know that the stuff that we’re colliding are protons. We also know what most of the stuff we’re detecting: light baryons and leptons. None of these things are directly interesting to me: these are all rather boring Standard Model junk that we’ve known about for a long time. We’re not going to directly observe the Higgs boson, or supersymmetry, or extra dimensions in our detectors. Those things would all decay into the boring junk before we have any chance of observing them. (This is looking grim…)

What we can observe, however, is the distribution of the “boring junk.” In between the collision point and the detector, the quantum particles take all possible “paths.” This includes some ‘paths’ that involve creating a Higgs boson (or other exotic particle) which then promptly decays into boring junk. Even though we don’t detect the Higgs directly, we can see its imprint on the distribution of boring junk in the same way that one could “read” the distribution of electrons in the double-slit experiment.

Further Reading**

I’ve been unfortunately terse in my description here. After getting to know some of the readers from their comments, I’m sure many will want to learn about these ideas in somewhat more detail. Allow me to suggest two excellent reference by Richard Feynman, both of which are accessible to a lay audience,

-Flip

* — For Doctor Who fans, the best analogy to a quantum system I can think of is the award-winning episode Blink. Here statues of weeping angels (actually aliens) stalk about when nobody is looking andcreep up on people to attack them. (Supremely creepy.)

** — I recently found out that my favorite childhood television show, Reading Rainbow, has unfortunately completed its last show and will not be continuing due to lack of funding. At the end of each episode LeVar Burton would suggest some books that kids might be interested in picking up in their local library.

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