From Simplicity to Complexity: Understanding QCD and Related Theories from First Principles

How would you describe the surface of the Earth? Looking from space, it would be described in terms of oceans and land-masses. Looking from a helicopter, it would be described in terms of mountains and valleys, rivers and cities. On foot, it would be described in terms of everyday things such as buildings, roads and even other people. All of these descriptions apply to the same thing, the Earth, and yet each would appear to us to be very different. What this shows is that the relevant features of a system at one scale are very different from those of the same system when observed at another scale. This idea - that the description of a system should be appropriate to the scale at which it is observed - is an invaluable tool in trying to understand the universe at its most fundamental level. Now imagine zooming in on a human. From an initial description in terms of bones and organs, we move to a description in terms of cells - and from cells to molecules and from molecules to atoms. Zooming in on the atom, we see a nucleus surrounded by a cloud of electrons, and zooming in on the nucleus we see protons and neutrons. What comes next? Physicists are certain that the proton and neutron are composed of yet smaller objects called quarks, which are held together by particles called gluons. The theory that describes the way in which quarks and gluons interact with each other is called Quantum Chromodymanics (QCD). But here there is a problem. We have a theory of quarks and gluons; we know that this theory should describe the proton and the neutron; but nobody has actually succeeded in understanding the proton and neutron in terms of its constituents. The reason for this comes down to describing things using features relevant to the scale of observation. At scales much smaller that the proton (but not small enough to start asking what quarks and gluons are made of) life is easy. Here, quarks and gluons interact weakly with each other and the mathematical techniques exist to extract predictions from QCD. These predictions have been stringently tested against experiment and provide firm support that QCD really does describe nature. So, if QCD makes predictions at scales much smaller than the proton, why are there difficulties in describing the proton itself? At the scale of the proton, quarks and gluons no longer interact weakly with each other, but interact strongly - so strongly, that the quarks are held together to form the proton itself. And this is the problem: the mathematical techniques do not exist to extract predictions when the interactions become strong - the quarks and gluons are interacting too frantically with each other! The ultimate aim of my research is into a possible way to overcome the mathematical difficulties. The key is to reverse our thinking and to stop zooming in, and start zooming out. Suppose that we start at scales small enough so that we understand QCD. If we had a mathematical tool to tell us how the description changes as we zoom out then, starting from small scales which we understand, we could work up to the scale of the proton. The way in which we describe the proton would be different from the description used at the scale we started at, but the mathematics would relate the two. In other words, we would have a relationship between something we do understand and something we want to understand. In principle, this could help to solve the real, physical problem of why the proton and the neutron are the way that they are. Indeed, this problem is considered to be one of the most important in science. QCD is at the heart of the `Standard Model' of particle physics which, together with Einstein's theory of General Relativity, represents the pinnacle of human understanding about how the universe operates at its most fundamental level. A fuller understanding of QCD would greatly help in the quest to peel back the next layers of mystery about how the universe really works.