Monday, October 22, 2012

Stalking the Higgs Boojum, Part 1

It's been noted by a number of people that I am a polymath. This means I have a broad knowledge over many subjects. That does not necessarily presuppose that I know all details about those subjects. To that end I have several fellow scientists expert in those subjects to help me out. Dr. James K. Woosley is an old friend from our graduate school days, and his specialty is particle physics. He's helped me out with a number of books, by looking over my scientific work and pronouncing judgement. So far the judgement has been, in the main, good.

But I thought I'd take the opportunity to let him talk a little bit about the science behind the science fiction. We've all heard the hullabaloo regarding faster-than-light neutrinos and the possible discovery of the Higgs boson (yes, the two are related, because if FTL neutrinos existed, the Higgs couldn't, or likely wouldn't). Let's hear some stuff about it from someone who knows.

-Stephanie Osborn


 If your Snark be a Boojum! For then
You will softly and suddenly vanish away,
 And never be met with again!’

The Hunting of the Snark, by Lewis Carroll

The recent announcement from CERN about the possible discovery of the Higgs boson, called by some the God particle for its supposed role in providing mass to the elementary particles, has stimulated unprecedented interest in particle physics but also a lot of questions about just what it means.

In this article I will discuss what the Higgs boson is, why it is important, and where the particle physics community will go from here. In order to get there, I will take some apparent detours, as well as saying some potentially outrageous things. Well, outrageous to physicists.[1]

The article is divided into sections on the meaning of mass, the standard theory of elementary particles, why the Higgs boson is considered important to the origin of mass, how the search for the Higgs boson was conducted and the results obtained so far, and the future direction of Higgs boson research and the consequences for both physicists and non-physicists.

What is mass, and why do I need to lose weight?

Before we consider how the Higgs boson generated mass, we need to have an understanding of exactly what mass is in the first place.

Ask a classical physicist what mass is, and you will likely get a blank stare. The problem is that, even since the days of Sir Isaac Newton, physicist have had two answers to that question. First, mass is known to be inertia, the resistance of a body to a change in its state of motion. In the simplest form of Newton's laws, the mass m of a body can be defined as the ratio of the quantity of force applied to a body, F, to the acceleration a of that body generated by the applied force; or algebraically,


However, in classical physics, two (or more) bodies generate a force on each other which seems to exist simply because the bodies possess inertial mass. This force, the gravitational force, is such that the force on one body, of mass m, directly proportional to the mass M of the second body in the system, and inversely proportional to the square of the distance r between them,


In this equation, the constant G, called Newton's constant, serves primarily to make sure that the units work out properly. If the two masses are in kilograms (kg), and the distance is in meters (m), then to yield F in the self-consistent metric system units of newtons (N), the constant G has the value of 6.67 x 10-11 Nm2/kg2. This number seems absurdly small (written in decimal notation it is 0.0000000000667), until you realize that it is defined so that, if M is the mass of the Earth, and r is the radius of the Earth, the acceleration experienced by the mass, m, is equal to the acceleration of gravity on the surface of the Earth, 9.8 m/s2. This really just shows how weak gravity is in conventional use, if it takes the entire mass of the Earth to generate just one "g" of gravity.

The identification of two different types of mass, inertial and gravitational, does not answer the question of where mass comes from. Much less the question of why, in consistent units, inertial and gravitation mass are equal. When it came time for Albert Einstein to ponder this question, while developing the general theory of relativity, he just accepted that the two types of mass were the same, a simplified statement of what is known as the principle of equivalence.

However, relativity introduces other concepts necessary to understanding the essence of mass. First, there is a relationship between kinetic energy, or energy of motion, of any material body, and its mass; this is the origin of Einstein's best-known equation, E=mc2. Second, this leads to the definition of rest mass, or the mass of any material body when it is not in motion relative to an observer, usually designated as m0. Third, this also means that the mass of a body in motion (relative to an observer) appears to increase — in particular, part of the energy which a force imparts to the body results in an increase in speed, and part of the energy results in an increase in mass. As the body approaches the speed of light, the mass increases without bound, and so it takes infinite energy just to reach the speed of light, at which point the body has infinite mass.

However, this assessment doesn't apply to photons, the individual quantum particles that make up light. Since, by obvious definition, light travels at the speed of light, photons are very different from any material body. Photons are thus considered to be massless - they have no mass, and thus are constrained to always move at the speed of light to maintain their existence. (In principle, the other force carrying particles of the standard model — the intermediate vector bosons of the weak force, the gluons of the strong force, and the gravitons of the gravitational force — are also expected to be massless. This is clearly not true for the intermediate vector bosons, as we will discuss in the next section; the gluons and gravitons will be considered in the final section.) However, photons still possess energy, by virtue that they also possess momentum, and one central tenant of Einstein's general theory of relativity is that gravitational forces can also affect photons. In the theory, this is because the gravitational forces act by warping space-time, which changes the pathways along which the massless photons travel, leading to such phenomena as gravitational lenses which are becoming a useful tool in astronomy. However, the same effect would be encountered if the gravitational force is assumed to act on energy densities, rather than on masses, and Einstein's theory also makes that assumption.

And thus, we come to the classical "handle" on the origin of gravitational mass: any concentration of energy reacts to gravity, and thus gravity maybe a phenomenon of energy concentrations rather than of masses. All of this is true, but it is well hidden in gravitation theory. The relevant equation, which is what physicists refer to as Einstein's equation (not the much better known and much simpler; it is provided here primarily because it has recently appeared (bizarrely, and with a small error) in a popular movie[2]


where the quantities R (a 4 x 4 matrix in the dimensions of space-time) describe the curvature of spacetime, the quantities g, called the metric, defines the coordinate system used to describe space time, and the quantity T is the energy density which causes the gravitational field.

But as noted, gravity is not the only force. The electromagnetic force is significantly more powerful; the electromagnetic force between two electrons is stronger than their mutual gravitational force by a factor of 1040 or 10,000,000,000,000,000,000,000,000,000,000,000,000,000. Other than the direct effects of gravitation — falling bodies, the unsightly numbers we observe every time we step on the scale (if we can look down that far) — everything else we observe on a macroscopic scale on earth is due to the electromagnetic force. We feel the shock when we pick up static electricity walking across a carpet - that shock represents only a very small number of electrons. The forces that hold all of matter together, from the table I am keyboarding this on to the cells in my body, are the result of slight imbalances in electrically neutral matter due to the distribution of negative (electron) and positive (proton) charges therein.

And how massive is a single electron? Well, consider the electric field, the field which measures the strength of interaction between electrons, of an electron at rest relative to the observer. I won't write the equation, except to note that it is similar to the gravitational force equation above, only it is expressed in terms of the electric charge instead of the mass. The force generated by this field causes changes in kinetic energy of the particles which pass through it, and so it is said to have a potential energy which balances the kinetic energy changes. This potential energy can be summed to obtain an overall energy density, and a total energy of the field. By a surprising coincidence, the total energy of the field of a single electron, is equal to the mass of the electron, multiplied by the square of the speed of light.

Astonishingly, that coincidence is not assumed to have any relevance to the Standard Model as described next week.

1 In his column "Best of the Web Today" for Friday 24 August 2012, James Taranto of the Wall Street Journal paraphrases physics professor Jerry Peterson of the University of Colorado at Boulder, discussing changes in Colorado laws regarding concealed carry of firearms on campus, as saying "… he simply wants his students to feel safe to engage in discussions that could become controversialreiterated that the presence of guns in his classroom 'would destroy the learning environment.'" Taranto then asks, "What in the world are they talking about that is so controversial it would lead to gunfire in a physics class?" ( I don't intend that this essay should be an answer to his question, but you never know.

2 Expendables 2, where the alcoholic mercenary is stated to be a chemical engineer by training, with a corresponding level of scientific knowledge.

We'll continue the discussion in the following weeks. I can say, however, that he helped me immensely in writing the Displaced Detective series by verifying that my interpretation and implementation of M theory in those books was a legitimate one, thereby preparing me to write Extraction Point! with Travis S. Taylor. Jim has also helped me develop concepts for compact power supplies for the Displaced Detective series, but that hasn't been published...yet.
-Stephanie Osborn