Pedagoguery

Mass is a quality that we take for granted. We know what it does. It exerts gravity. It has inertia. But at the quantum level, we really lack a basic understanding of why mass exists. From a quantum standpoint, there is no reason why all fundamental particles can't be massless like the photon. From the standpoint of physics, there are two problems arising from mass. The first is, why does it arise at all? The second is, how do different elementary particles gain the precise amount of mass that they have? Intriguing new theories are starting to answer these questions.

The first recorded definition of mass was by Isaac Newton in his Principia: “The quantity of matter is the measure of the same, arising from its density and bulk conjointly.” This definition was good enough for 200 years, but it no more describes why matter has mass than the simple statement “because”. However, as the Standard Model of particle physics is better understood each day, the question of why matter has mass is increasingly becoming a hot topic in physics.

The effective mass of a particle actually has two components. The first is what is called its “rest mass” or the mass of the particle when it is not moving. The second component is its kinetic energy, since energy is related to mass by Einstein's famous equation. In the case of a simple particle, like an electron, this division is very straightforward. However in the case of a compound particle, such as a proton, it is more tricky, since the mass of the proton is composed of the rest mass of the constituent quarks, as well as the kinetic energy of those quarks as well as the massless gluons that hold them together. Physicists can calculate that mass, and it turns out that nearly all of the mass of the proton comes from the kinetic energy of its constituents. That still leaves us with the fundamental question of where truly elementary particles get their mass.

The answer is believed to be something called the Higgs field. In quantum mechanics, fields and particles are interchangeable, to a degree. For example, the photon is the particle associated with the electromagnetic field. In one sense, the Higgs field is just like any other quantum field. However, it differs from other quantum fields in three very distinct ways. The first way is rather technical. All fields carry some kind of angular momentum. That angular momentum is manifested as the angular momentum of its corresponding particles. For example, electrons have an angular momentum of ½ while photons have an angular momentum of 1. (In general, particles which carry some kind of force have a whole number angular momentum.) The Higgs particle, however has an angular momentum of 0. This allows it to appear in the equations of quantum mechanics in a very different way than other particles, and it is also the source of the other two differences of the Higgs field from other fields.

The universe prefers to be in a state of minimal energy. In the case of most fields, the electromagnetic field, for example, this happens when the field value is zero. Take, for example, a deep bowl with curved sides. Drop a ball into the bowl, and it will quickly settle at the center, where the bowl is at its lowest and therefore its energy is at its lowest. Imagine, however, that the bowl has a raised dimple in the middle. The lowest point is now a ring around the dimple, and that is where the ball would settle. The Higgs field is like such a bowl, in that it is at a minimum energy at a non-zero value. Thus, all of space is permeated by a non-zero Higgs field.

The third distinguishing characteristic of the Higgs field is that when a particle interacts with it, that particle behaves as if it has mass. Thus, mass is not an intrinsic property of the particle, it is rather a consequence of its interaction with the Higgs field. To picture this, imagine a hot beach filled with children. This is the Higgs field. If an ice cream vendor were to make his way across the beach, many interactions with the children on the beach would slow him down. A different vendor selling, say broccoli, would have many fewer interactions with the children, and would thus be able to move across the beach much more quickly.

The idea is simple in concept, but in practice, there is still much we do not know. While the Standard Model only requires one Higgs field to get the job done, by no means is it limited to just one. In fact, the most likely successor to the Standard Model, the Supersymmetric Standard Model, will require at least two Higgs fields. Two Higgs fields would give rise to five different Higgs bosons, three that electrically neutral, and two that are charged. In addition, the minuscule masses of neutrinos could conceivable arise from interactions with yet a third Higgs field. Interestingly, Higgs particles would interact with each other quite strongly, leading to high masses for each, on the order of a few hundred times the mass of a proton.

There is good support for the Higgs mechanism in some sort of Supersymmetric Standard Model. For one thing, without the Higgs mechanism, the W and Z particles, the carriers of the weak nuclear force, would be massless like the photon, and the weak nuclear force would be as strong as the electromagnetic force. The predictions of the interactions of the W and Z particles with the Higgs field have been born out through experiment. Given that the Standard Model is a very tightly interlocking structure, and that so many of its predictions are startlingly accurate, physicists are confident that the Higgs particles will be observed some day. The greatest hope is that it will happen with the Large Hadron Collider (LHC) at CERN in Switzerland. That collider is currently under construction, but is schedule to be completed later this year. When the data it collects can be analyzed, maybe then we will truly know what causes mass.

Next issue: Is the universe out of tune?