In this lecture we will discuss some of the big questions in High Energy Physics: Unification of the Forces, the Hierarchy problem, Dark Matter, Dark Energy, Supersymmetry. This is a bit of a lark for me. I am no expert on these things, but have been to enough talks to know some of the lingo. I have some skepticism of the value of some of these questions (which may be born of having too simplistic a view of them) but it is fun nonetheless to talk about them.

Hierarchy Problem

There are a series of questions which are sometimes raised as the "big questions" in High Energy Physics, which boil down to "why are the equations of motion for the universe the way they are." This is kind of a strange way of thinking. A classical example is "why is gravity an inverse square law, and not $r^{-2.1}$?" Such "why" questions are clearly outside the range of physics. To give the particle theorists their due, these are smart people, and often the "Why" questions are actually "How" questions in disguise. For example, consider this long-winded question "Experiment suggests that the weak interaction is described by a Lorentz invarient gauge theory -- but other experiments suggest that the gauge Bosons have mass. How are these two consistent with one-another?" We know that the Higgs mechanism provides the "how." In public lectures one simply says that the Higgs mechanism is the explanation for ``why" the $W$ and $Z$ bosons have mass. In this spirit one can ask ``why is the Higgs mass so light?" This is known as the Hierarchy problem. The real problem has to do with structures of quantum gauge theories. For our little toy problem, we studied a classical gauge field. You run into problems when you start including quantum fluctuations. The standard story is that excitations of the Higgs field hybridize with fluctuations in the quark fields. When you add up all these fluctuations you get an infinite mass for all the particles -- ie. the Higgs mechanism works too well. Actually, you only get an infinite mass if you believe your field theory to arbitrarily high energies. Since we don't have a theory of quantum gravity, we know our field theory should break down at the Plank scale. This cuts off our divergences. Consequently we expect the Higgs mass to be of order the Planck scale. Of course there is one simple way around things. We just make the coupling between the Higgs and the other fields really really really weak. A small number times a big number can be a reasonable size number. This solution is known as ``fine tuning." Theorists don't like fine tuning because it puts them out of a job. There is nothing to explain -- nature just gave us some crazy values of the coupling. A more popular solution is ``supersymmetry." This means one doubles the standard model. For every bosonic field in the standard model we add a fermionic field. For every fermionic field we add a bosonic one. These ``superpartners" have exactly the same properties as the normal standard model particles. They even give them silly names: for example the bosonic counterparts of quarks are squarks. This "solves" the hierarchy problem in the sense that the quantum fluctuations from these new fields exactly cancel those from the old, and the divergence which started our worries disappears. Unfortunately we then have to explain why nobody has seen these ``superpartners." A typical story is that the "supersymmetry" is only a partial symmetry, and the superpartners are much heavier than the standard model particles. How heavy? Well lets just say that the next generation accelerators are sure to find them...

Dark Matter

A more serious question is that of "Dark Matter," or more precisely "non-baryonic dark matter." If you look at the rotation curves of galaxies you can estimate their mass density as a function of radius. It turns out that there is a lot more matter than you can see. Apparently we understand the observations well enough to rule out "boring" dark things like black holes or rocks. What is all that mass? A second clue comes from the "large-scale structure" of the universe. By modeling the stelar dynamics, you can relate the mass density of the universe to the size distribution of intergalactic structures. A third clue is anisotropies in the cosmic microwave background radiation. You can also relate these to the mass density of the universe. They too point to a lot more mass than we can see. The clincher comes from our models of big bang nucleosynthesis. Apparently there is not even enough baryonic matter in the universe to account for all that mass. One hypothesis is that there is some particle -- as yet unspecified -- which does not interact with regular matter except through gravity. Such "weakly interacting massive particles" are just what is needed to explain the observations, but until they are directly observed they are just a fiction. Some even use this as a feature rather than a bug --they hypothesize that the dark matter is the superpartners to the standard model particles.

Dark Energy

An equally serious question is that of "Dark Energy." This is really a code word referring to the fact that the expansion of universe is accelerating. What is the force driving this expansion?

Structure of the Standard Model

Here are some "silly" questions: Why are there three generations of quarks? Why is the weak interaction so strange (breaking all those symmetries)? Why are the constants of nature what they are?

Unification of Forces

I always thought that the "unification" of forces sounds really cool. Unfortunately I don't know what it means. I tried to do some reading for this lecture. Unfortunately, the more I read, the more I realized I didn't understand what the game is. I can certainly sympathize with the idea that it would be great if there was one "theory" which explained everything in a unified picture. Apparently there is some hope that at high enough energies the theory of matter simplifies, and grand unified theories are attempts to write down this simplified limit. Of course we can't do experiments at those energies, so one has to work with other guiding principles.

Quantum Gravity

How does one produce a theory of quantum gravity? The crux of this problem has to do with the zero-point motion of very high momentum modes of the fields (at the Planck scale). Since energy is mass, these zero-point fluctuations have a gravitational signature. The funky thing is that their energy density is high enough that if quantum field theory can be applied past the Planck scale, the universe should be permeated with little teeny tiny black holes. Needless to say this leads to some unphysical predictions. Clearly the solutions is to have a theory which does not allow arbitrarily high energy fluctuations. One approach is to upgrade our field theory to a "string theory." The finite length of the strings ends up cutting off the divergences.