The Higgs boson, whose discovery was confirmed by CERN on July 4th to the exacting 5-sigma level required in particle physics (meaning that the probability that the bulge in the data indicating a particle with mass-energy in the range of ~125 GeV is a random fluke is less than 1 in 3.5 million), is the first and only boson to be predicted to be a very bad ballerina--it can't twirl around!

This part of the story is yet to be confirmed experimentally, and CERN scientists are now working on using their data to confirm this highly peculiar theoretical property of this mysterious particle. To understand what this means, we need to go back to the 1920s.From a high school chemistry course you may remember that two electrons in the same orbital in an atom must differ from one another--their difference is in something called "spin": if one has spin "up" (along a given axis defined in space), the other must have spin "down." The property is due to Wolfgang Pauli and the principle he established in 1925, called the Pauli Exclusion Principle.

Experiments showed that indeed electrons do possess something like a physical spin since they exhibit magnetic properties that resemble those of a spinning electrically-charged object. But at that time, there was no theoretical explanation for something like a spin.

Then one cold night in 1928, Paul Dirac was sitting in front of the fireplace at St. John's College, Cambridge, staring into the fire. Suddenly, he found the answer to a problem that had been occupying his every waking moment for months: how to combine the requirements of quantum mechanics with those of special relativity. The result was the Dirac equation, which as one added bonus resulted in the prediction that the electron must have a spin; and another, more famous outcome, was the prediction of the existence of antimatter. (More on this story can be found in Steven Weinberg,

*The Quantum Theory of Fields*, vol. 1, p. 7.)

So the peculiar property of "spin" now had a theoretical justification. But elementary particles such as the electron are called

*Dirac point particles*: they are like a point in the sense of Greek geometry--they have no

*interior*, i.e., no width, no breadth, no length, no insides. So what does it mean for such a particle to "spin"? How do we visualize an extent-less particle spinning? The answer is that we simply can't. This is one of the many aspects of quantum mechanics that evades all our attempts at a macro-world explanation or visualization. And the story gets much weirder than that.

First of all, the rate of this un-visualizable "rotation" is fixed and quantized. And--worst of all--the electron, and all other particles like it (called *fermions*, after the physicist Enrico Fermi) are defined to have spin 1/2 (in quantized, Planck units), which means something really strange: When such a particle spins around 360 degrees, it *does not* return to where it started from! Instead, its sign reverses.

It is like a ballerina who twirled around full circle and now finds herself dancing on her hands, with her feet straight up in the air! The electron, or any other fermion, only comes back to "normal" after completing *another *full-circle "rotation," to a total of 720 degrees.

It's hard to find everyday-life examples of such weird behavior. But people have tried. The Stanford physicist Leonard Susskind recently showed me a cool example of this phenomenon in our large-scale world. Stand up and hold your hand in front of you, palm up. Put a can of beer (don't open it--or it will spill! but it may help to drink a couple of them before you try this exercise...) on your open palm. Now, rotate your hand, keeping the palm up, counterclockwise (clockwise if you're left handed), meaning inwards, until--this is hard--you've completed a full circle.

Note that you *are not back to where you started, after 360 degrees*, because your arm is twisted now. So *continue *the rotation--very carefully--to complete a second full-circle. If you did this right, you will be exactly where you started. Someone ought to do a video of this--it would be much clearer.

So the fermions--electrons and quarks and other "matter" elementary particles--are all like that. They obey what are called Fermi-Dirac statistics: they can't occupy all the same quantum states--they have to differ from one another on at least

*something*, often the spin; they are governed by Pauli's exclusion principle. The bosons (force carriers, when elementary particles), on the other hand, which are particles with

*integer*spins, follow Bose-Eintstein statistics: they like to "get together" and share the same quantum properties.

This is how we get laser light--light in which the photons are all coherent, sharing their quantum properties. And this is also how we get something called a Bose-Einstein condensate, in extremely low, close-to-absolute-zero, temperatures: the particles (these are now atoms that have integer spins) come together in such a way that their individual quantum-mechanical wave functions actually

*merge*into one large wave; essentially, they become a

*single quantum object*(whose size actually brings them to our macro-world scale!).

So what about the Higgs? Well, for theoretical reasons that have to do with how its field interacts with other fields, the Higgs must have

*zero*spin. Since zero is still an integer, the Higgs is a boson. But it is a

*scalar*boson. In fact, Peter Higgs, a modest individual by all accounts, still calls "his" boson the "scaler boson" (of course he does this in recognition of the fact that five other physicists had the same idea that led to the particle's prediction in the same year, 1964). The photon, gluon, W+, W-, and Z bosons all have spin 1 and are defined as

*vector*bosons (you can think of it this way: if you spin, you have a direction, defined by the right-hand rule; even though in quantum mechanics everything is a mixture, including the "directions").

A particle that doesn't spin is considered a scalar, and not a vector (it has no defined direction). As such, the Higgs would make a very bad ballerina--one who can't twirl around. Does it, in reality?--CERN promises to let us soon know the answer.

P.S. Are there any

*other*kinds of bosons? The answer is: Maybe. If gravity can be made into a quantum field theory, then the boson carrying out the action of the force of gravity would be the

*graviton*. This hypothetical particle has never been discovered, but for theoretical reasons that have to do with the fact that mass curves space--as Einstein's general theory of relativity has taught us--the graviton, if it exists, must have a spin of 2. I will leave you to conjecture about just what this may mean!

Thank you for passing on this 'beer can' exercise. I found it easier to do than the old 'spinor spanner'. It shows a property of a system (more complex than a particle) to only return to the way it was after 720 degrees. These examples generally work by having an arm (or strings) attached to your shoulder or something else.

Point particles, viewed as irreducible representations of a double cover of rotations, manage to exhibit this behaviour without strings attached, so maybe a caution should be included not to take the analogy too far?