Ard: Could you give me one or two of your favourite examples of someone making a theory about the world guided by beauty that then turned out to be empirically true?
FW: Paul Dirac was faced with the problem of devising an equation for electrons that satisfied both the principles of quantum mechanics and the requirements of the special theory of relativity. This was a difficult problem that several people were trying to solve. Dirac, in trying to find an equation, was led by an instinct for simplicity and beauty, and when he found the trick that made it go, it was so compelling that he knew he was on the right track.
He tells a story that he didn’t dare… He didn’t want to work out the consequences because he was afraid it might be wrong. So it took him a while to actually take it out of his desk and do the calculations, but it turns out that that’s correct: that’s called the Dirac equation.
So it solves the problem that you’re trying to solve, but also it has more solutions than he was looking for, of a different character. And what these solutions represented was a new kind of thing, an anti-electron, now called the positron, and that particle was duly found about a year later.
Ard: That was the first time they found anti-matter?
FW: Yes, that was the first example of anti-matter.
David: You said you had a second example.
FW: Well okay, for my second example, thrusting modesty aside, I’m going to talk about my own work, my own early work on the strong force – this is the work for which I got the Nobel Prize.
David: And the strong force is?
FW: There are four basic forces of nature according to our current understanding. There is gravity and electromagnetism, which are the classic forces for which there have been beautiful theories for quite a while. And of course electricity and gravity have been known as forces for a very long time, going back to the Ancient Greeks or even further. People have been falling down for a long time.
But in the 20th century, when physicists started to examine the interiors of atoms, especially what happens inside the cores of atoms, the atomic nuclei, they found that electricity and gravity weren’t sufficient to account for what was going on at all. You needed two, not one but two, distinct new forces, and those were imaginatively called the strong and weak force.
The strong force is what is responsible for holding atomic nuclei together, and at a deeper level, when we learn more about it, we learn that the building blocks of atomic nuclei, protons and neutrons, in fact aren’t the elementary particles: the elementary particles are quarks and gluons out of which the protons and neutrons are built.
So the strong force is the force that is the most powerful force in nature that acts between quarks and gluons. It’s what they do most of the time, and when I was a graduate student, there was no decent theory of the strong force. There was nothing that could remotely be compared with Newton’s equations for gravity or Einstein’s general relativity or Maxwell’s equations for electromagnetism.
Now, you could imagine dreaming up all kinds of equations, but we focussed on equations that were beautiful: equations that had a certain simplicity and mathematical elegance.
David: And you decided to do that?
FW: We decided to do that; it was also all we could do. The calculations aren’t easy to do, first of all, and, secondly, if you start to consider complicated theories, there was not enough experimental information to sort that out.
So the only hope, really, in retrospect, was to follow the principle I discussed earlier in this anthropic explanation of beauty: that is guess that the description is going to be beautiful, work out the consequences, and check whether nature agrees. So in a nutshell that’s what we did. We guessed a particular kind of equation, which is an equation of extraordinary beauty that generalises the Maxwell equations of electromagnetism, in a very… I call it the Maxwell equations on steroids.
David: Was that a joy to discover?
FW: It was a great joy to discover. It was also nerve-wracking because, first of all, gluons at that time were just a word. There had to be some kind of glue that held the quarks together, and quarks were kind of a shadowy notion, too.
David: So this was quite an amazing experience because there is all this vague data around, and what you’re saying is that you took the equations and focussed on what you thought was beautiful, that made completely counter-intuitive predictions that then ended up being true. That must have been an amazing experience, even as an emotional experience just to see that.
FW: Yes, it was quite something.
Ard: And beauty played a big role?
FW: Beauty played an absolutely crucial role because we could only try equations that were beautiful, basically, and if the answer had been complicated, messy, not beautiful, we never would have found it.