Quantum Mechanics describes particles as vibrations in time and space. The intensity of the vibration in time (i.e. – when it is) reflects the particle’s energy; the intensity of the vibration in space (i.e. – where it is) reflects its momentum.

In large-scale reality, such as baseballs and buildings, those vibrations are way too small to influence the results of experiments. In studying these “classical” systems, physicists discovered certain mathematical laws that govern the relationship between momentum (p) and energy (E). Believing that these rules should still be manifested in the quantum realm, they were used as guidelines in building theories of vibration.

In Special Relativity, that relationship is (m is the mass of the particle):

m² = E² – p²

In the case of electromagnetic waves, we have m = 0. Using a fairly simple mathematical analogy, the equation above becomes a wave equation for the electromagnetic potential, A. An electric field (that drives electricity down a wire) arises from the gradient of the potential; a magnetic field (that causes the electricity to want to turn) arises from the twisting of the potential.

The contribution of P.A.M. Dirac was to find a mathematical analogy that would describe the massive particles that interact with the electromagnetic potential. When the meaning of the symbols is understood, that equation is not hard to write down, but explaining the symbols is the subject of advanced courses in physics. So here I’ll focus on describing the nature of the equation. Let’s pick an electron for this discussion. The electron is a wave, and so is represented by a distribution ψ.

Physically, the electron is like a little top: it behaves as though it is spinning. When it is moving, it is convenient to describe the spin with respect to the motion. If we point our right thumb in the direction of motion, a “right-handed” electron spins in the direction of our fingers; a “left-handed” electron spins in the opposite direction. To accommodate this, the distribution ψ has four components: one each for right- and left-handed motion propagating forward in time, and two more for propagation backwards in time.

Dirac’s equation describes the self-interaction of the particle as it moves freely through space (without interacting with anything else). Now from the last post, we know that nothing moves freely through space, because space is filled with Dark Energy. But when Dirac wrote his equation, Einstein’s axiom that space was empty still ruled the day, so it was thought of as “self-interaction”. That self-interaction causes the components of the electron to mix according to m, E and p. When the self-interaction is applied twice, we get Einstein’s equation, relating the squares of those terms.

So what does the mass term do? Well, it causes right-hand and left-hand components to mix. But here’s the funny thing: imagine watching the electron move in a mirror. If you hold up your hands in a mirror the thumbs pointed to the right, you’ll notice that the reflection of the right hand looks like your left hand. This “mirror inversion” operation causes right and left to switch. In physics, this is known as “parity inversion”. The problem in the Dirac equation is that when this is applied mathematically to the interaction, the effect of the mass term changes sign. That means that physics is different in the mirror world than it is in the normal world. Since there is no fundamental reason to prefer left and right in a universe built on empty space, the theorists were upset by this conclusion, which they call “parity violation”.

Should they have been? For the universe indeed manifests handedness. This is seen in the orientation of the magnetic field created by a moving charged particle, and also in the interactions that cause fusion in the stars and radioactive decay of uranium and other heavy elements.

But in purely mathematical terms, parity violation is a little ugly. So how did the theorists make it go away? Well, by making the mass change sign in the mirror world. It wasn’t really that simple: they invented another field, called the Higgs field (named after its inventor), and arbitrarily decided that it would change sign under parity inversion. Why would it do this? Well, there’s really no explanation – it’s just an arbitrary decision that Higgs made in order to prevent the problem in the Dirac equation. The mass was taken away and replaced with the Higgs density and a random number (a below) that characterized its interaction with the electron: m ψ was replaced with a H ψ.

Now here’s a second problem: if space was empty, why would the Higgs be expected to have a non-zero strength so that it could create mass for the electron? To make this happen, the theory holds that empty space would like to create the Higgs field out of nothingness. This creation process was described by a “vacuum” potential with says that when the Higgs density is zero, some energy is available to generate a density, until a limit is reached, and then increasing the density consumes energy. So space has a preferred density for the Higgs field. Why should this happen? No reason, except to get rid of the problem in the Dirac equation.

And what about the other spinning particles? Along with the electron, we have the muon, tau, up, down, strange, charm, bottom, top and three neutrinos, all with their own masses. Does each particle have its own Higgs field? Or do they each have their own random number? Well, having one field spewing out of nothingness is bad enough, so the theory holds that each particle has its own random number. But that begs the question: where do the random numbers come from?

So now you understand the concept of the Higgs, and its theoretical motivations.

Through its self-interaction, the Higgs also has a mass. In the initial theory, the Higgs field was pretty “squishy”. What does this mean? Well, Einstein’s equation says that mass and energy are interchangeable. Light is pure energy, and we see that light can be converted into particle and anti-particle pairs. Those pairs can be recombined to create pure energy again in the form of a photon. Conversely, to get high-energy photons, we can smash together particles and anti-particles with equal and opposite momentum, so that all of their momentum is also converted to pure energy (this is the essential goal of all particle colliders, such as those at CERN). If the energy is just right, the photons can then convert to massive particles that aren’t moving anywhere, which makes their decay easier to detect. So saying that the Higgs was “squishy” meant that the colliding pairs wouldn’t have to have a specific energy to create a Higgs particle at rest.

Of course, there’s a lot of other stuff going on when high-energy particles collide. So a squishy Higgs is hard to detect at high energies: it gets lost in the noise of other kinds of collisions. When I was in graduate school, a lot of theses were written on computer simulations that said that the “standard” Higgs would be almost impossible to detect if its mass was in the energy range probed by CERN.

So it was with great surprise that I read the reports that the Higgs discovered at CERN had a really sharp energy distribution. My first impression, in fact, was that what CERN had found was another particle like the electron. How can they tell the difference? Well, by looking at the branching rations. All the higher-mass particles decay, and the Higgs should decay into the different particle types based upon their masses (which describe the strength of the interaction between the Higgs field and the particles). The signal detected at CERN was a decay into two photons (which is also allowed in the theory). I am assuming that the researchers at CERN will continue to study the Higgs signal until the branching ratios to other particles are known.

But I have my concerns. You see, after Peter Higgs was awarded the Nobel Prize, his predecessor on the podium, Carlo Rubia (leader of the collaboration that reported the top particle discovery) was in front of a funding panel claiming that the Higgs seemed to be a bizarre object – it wasn’t a standard Higgs at all, and the funding nations should come up with money to build another even more powerful machine to study its properties. Imagine the concern of the Nobel committee: was it a Higgs or not? Well, there was first a retraction of Rubia’s claim, but then a recent paper that came out saying that the discovery was not a Higgs, but a “techni-Higgs”.

One of the characteristics of the scientific process is that the human tendency to lie our way to power is managed by the ability of other scientists to expose fraud by checking the facts. Nobody can check the facts at CERN: it is the only facility of its kind in the world. It is staffed by people whose primary interest is not in the physics, but in building and running huge machines. That’s a really dangerous combination, as the world discovered in cleaning up the mess left by Ivan Boesky and his world-wide community of financial supporters.