Chapter 17: QED, QCD and the Standard Model

Quantum Mechanics has gone on to lead a revolution in physics. Since it was the most popular and explanatory theory that evolved from the discovery of subatomic particles, it has grown and morphed into the edifice that we now call the Standard Model, which may be one of the most accurate, if confounding, models of a physical system that has ever been created.

Quantum Electro Dynamics (QED) was a natural outgrowth from the original quantum theory. QED posits that subatomic fields can also be described utilizing the tools created to describe the atom. It also had one of the most impressive instances of theory predicting reality, a talent sorely lacking in today’s theoretical physics research.

As mentioned previously, the early 20th century was loaded with great physicists, and Paul Dirac was one of that group. He contributed to the development of QED in many respects, including improved notation, resolving inclusion of relativistic effects into the theories (previous calculations required that some of the particles be travelling backward in time, again something that had not been directly observed) but most importantly, Paul Dirac discovered the positron, on paper.

Dirac was looking for a mathematical formation to express the equations of motion of the electron when he stumbled upon the works of an English mathematician, W.K. Clifford who had created an algebraic matrix structure that held the promise of that description, 50 years before. This work was actually based on the original theories of linear algebra and matrix theory proposed by Hermann Grassmann back in 1844, whose work was considered at the time that it was published, almost incomprehensible.

Dirac used this form to create a four component matrix that could successfully describe the motion of the electron, except there was one catch: it required that there be a positively charged antithesis to the electron, an anti-electron, if you will. In the emerging field of experimental particle physics, such a thing had never been observed, yet for the electron, the equation Dirac created was surprisingly descriptive and accurate. Four years later, the positron was discovered and named, and Dirac shared the Nobel with Schrodinger the next year.

Paul Dirac had discovered antimatter through reason, logic and the proper application of QED theory, and the die was cast.

Quantum Chromo Dynamics (QCD) is the application of these principles to the interior of the nucleus. Physicists were trying to determine how the nucleus of an atom could hold together. Since the force created by an electric field gets increasingly stronger as you approach the source, like charges repel each other, and considering that most of the local (earthbound) matter contains nuclei that have many protons (and neutrons, too, but neutrons are considered to have zero charge) there must be some force that can overcome the tendency of the protons to repel each other at the close proximity distances that a nucleus requires. Or else all matter would fly apart and revert to hydrogen.

So the physics community, always resourceful, created a new force, the strong nuclear force that, as the name implies, is strong enough to restrain many protons in a space that is only slightly bigger than the sum of their volumes. The trick was that since there was no evidence of such a force outside of the nucleus, the aptly named Strong Nuclear Force must be able to act only at very short distances, a property that is quite at odds with the other two known forces at the time: gravity and the electromagnetic force, for although these latter two do diminish as the distance from the source is increased, those fields obey an inverse square law with respect to that distance, whereas, the Strong force must terminate very close to the boundary of the nucleus.

This theory brought us quarks (the really fundamental components of matter that compose protons, neutrons and antimatter) and the force carriers, the gluons, as a result of the mathematics created to describe the observations. This force is called the color charge, and it comes in red, green and blue. Quarks come in up, down, top, bottom, strange and charm varieties. Since we have no understanding of what the actual properties of these components are, other than their ability to create forces, their names are, as you can see, somewhat whimsical.

We think that we have seen a gluon (or at least a particle of some sort that has the predicted energy). No one, however has ever seen a quark (although it has been reported that protons are lumpy). Conveniently, the rules for QCD require that quarks can never be seen in a fewer numbers than a pair, the minimum number required, by the ‘laws’, to make a real, observable particle.

The fourth fundamental force, the Weak Nuclear Force was created to allow nuclei to have radioactive decay, and violate the rules of the Strong Force. Go figure. Theoretically, this force has been shown to be within the description of the electromagnetic force at high energies and has led to the creation of the Electroweak description.

These discoveries have led to the creation of what is now referred to as the Standard Model.

The Standard Model is the most successful, if cobbled together, theoretical model ever presented by physicists. It is the progeny of QED, QCD and the results of high energy particle analysis over the last three quarters of a century, yet it remains a model constrained by constants derived from experimental evidence.

Oh, and there’s one other thing: the Standard Model does not include gravity.

This is not considered by most to be especially significant or troublesome, since the force of gravity is so weak compared to the other forces at the level of interest for Quantum Mechanics, but clearly, since it is presently thought that gravity is the major force that shapes the universe, without gravity, the Standard Model cannot be said to be a definitive description of matter.

Still, it is the Standard Model which dominates the thinking of our current brain trust of theoretical particle physicists, and it is through the laws, assumptions and mathematical structures that we currently interpret the observations that we make, especially when we are smashing particles together at high velocities.

The relative strengths of this theory and the structure that it envisions will not be addressed here, but it should be pointed out that as long as one follows its precepts, it is a very accurate, inclusive and internally consistent theory, and is obviously very popular, at least among physicists.

There are however, a few problems with the Standard Model as it exists today that should be pointed out. They are:

  • All interactions are considered to be between point-like particles, that is, particles that have no lower level boundary. The real problem with this assumption will surface in one of the following bullets, but for the time being, let’s just note that this assumption does not match the reality of particles, particularly like the proton and the neutron, which are real and do have a measurable size.
  • As stated previously, the Standard Model does not include gravity. Well, three out of four still gets you a ‘C’ in school.
  • It relies heavily on probabilistic theory. This works, but is not philosophically satisfying.
  • It assumes that neutrinos have no mass. (Note for those of you who do not know what a neutrino is: the name is Italian for ‘little one’, and it is a particulate byproduct of neutron decay and fusion. They are so small and interact so weakly with other matter that a beam of them, if you could make one, would pass straight through the Earth relatively unscathed). We now know that they do have mass. Added to this problem is that there are three types, each with different masses that can somehow change from one type to the other without releasing or absorbing energy. This is a much bigger problem with this theory than it appears to be for most.
  • It relies on 18 different and particular empirically determined constants, well 21 if you count the speed of light (c), Planck’s Constant (h) and Newton’s gravitational constant (G). Being that there are only 12 different particulate categories, this seems like a lot of information that cannot be determined by the theoretical construct.
  • In order to generate mass in the particles in the Standard Model, they must pass through a mysterious field created by the Higgs boson, named after its creator, Peter Higgs. At the time of this writing, some empirical evidence of the Higgs boson exists, and the estimates for its mass (hence, energy) cover a relatively wide range of energy distribution. They might have found it with the Large Hadron Collider (where they commonly refer to it as “the God Particle”), but at this point in time, although they have found a ‘particle’ at about the assumed energy level, none of the assumed properties have been evidenced and there is still some discussion as to the validity of the findings. So for now, lacking absolute proof of its existence, it remains another hole in the theory, since without the Higgs, there can be no mass in the universe
  • Most disturbing of all is the tendency for some of the terms utilized to tend toward infinity or zero. A good example of this comes from the formula for the mass energy of an electron. The expression for that is:

Mem = q2/8πre

Where: Mem is the mass energy

q is the chrage

And re is the radius is the distance from the point source.

  • Since the electron is considered to be a wave-particle without a true surface, the value of the radius, re, can go just as low as we want it to. As it tends toward zero, the value of the mass energy, Mem in this equation goes to infinity (as the denominator tends toward zero). This does not match observations. So in order to circumvent the consequences of the formulation, the clever quantum mechanics physicists have invented a process called renormalization; which roughly translates to mean that since we know that the answer is finite, we can just ignore the calculated answer and substitute in the empirical value whenever we need to. (OK, it’s really not quite that blatant, but in principle, it is.) This is not the only renormalization necessary to keep the Standard Model from blowing up.

The underlying message from this very limited discussion of Quantum Mechanics and the Standard Model is this: although it has proven to be a very useful theoretical framework with which to describe the subatomic universe, and despite the fact that these theories have proven very powerful and have driven the creation of many of the more recently conceived devices, such as lasers, LED’s and transistors (and quantum computing if it ever comes of age), they are founded on some untenable assumptions, rely heavily on empirical data and involve calculation techniques that in many instances, are questionable at best.

In order to provide a comprehensive definition of the universe of matter and energy, we must do better than this.

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