Theories versus models: QED, QCD, axiomatic abstractions, and experimental data
A student of mine spent this past summer in a nuclear physics research program at Jefferson National Laboratory where he learned a good deal about QED and QCD. In class recently, he brought this up in relation to the difference between a theory and a model. He argued that QED was a theory because it has a specific idea or two behind it. For example, if you could sum it up, it basically predicts that the change in the number of vertices in a set of Feynman diagrams is proportional to the fine structure constant (that’s a very rough way of saying it). My student argued that QCD was more of a model precisely because it lacked any unifying element, any grand idea so to speak, as QED does. To him it really is a collection of mathematical models of observed phenomena. I honestly do not know QCD well enough to comment, but I think the premise of the question is intriguing.
James Schombert at the University of Oregon describes QCD and QED in a different way. In his description both might be viewed as models. To a colleague of mine, everything is simply a model. What intrigued me about my student’s comment, though, was the similarity his description of QCD had to Tom Moore’s description of quantum mechanics in his textbook Six Ideas That Shaped Physics. Essentially, Moore views most theories as being structured as follows:
- There is an underlying physical reality upon which is a layer of observable phenomena.
- Upon that is layered a conceptual description of that phenomena, i.e. what it is, what it means, etc.
- Upon that is layered a mathematical description of that phenomena.
Moore then describes quantum mechanics as missing layer number 2, the conceptual description. It’s not that he contends there is no conceptual description, it is that he contends there is no consistent and universally agreed upon conceptual description. My student, thus, views QCD in this light while he views QED in a different light entirely.
I see things another way. In truth I haven’t much thought about the whole QED/QCD thing since my knowledge of QCD is not as sophisticated as it could be. But I understood the point he was trying to make. What I think of in instances such as this is less a difference between “theories” and “models” and more a difference between “theorists” and “modelers.” They represent different ways of approaching a problem (both completely valid) and perhaps has some relation to the difference between mathematical physicists and applied mathematicians that I discussed a few weeks ago. Theorists, such as myself, often (though perhaps not always) have some sort of unifying idea that drives our research and, at its heart, our research is often axiomatic and very often abstract. That is, we use the rules of logic to argue from some axiomatic premise through to some conclusion, in the process using a lot of math that is very general and abstract in that we don’t necessarily always consider actual numbers. Our goal, nonetheless, is a prediction of future experimental results (at least, that should be our goal, however indirectly – as Carl Caves once said, roughly paraphrased, physics is an inherently experimental science at its core). A modeler, on the other hand, tends to work from sets of data, trying to fit various mathematical techniques to that data in such a way that those mathematical techniques may later be used to predict future data. In this day and age, modelers often work extensively with computers. Numerical modeling, of course, is a major discipline in its own right. But computers are not a necessary prerequisite for modeling nor, even, hard numbers since we could substitute “repeatable behavior” for the latter.
To answer the QED versus QCD question, then, one would need to look at the details of the “theories” themselves to glean whether or not there was some sort of grand physical idea behind the mathematics or not. It is possible a grand physical idea came out of the mathematics after they had been applied, but is that idea unifying in some respect? Does it seek to bring together seemingly disparate physical phenomena? Perhaps some readers would like to comment on this.