Of course, Lindley reminds us, what constitutes a good scientific theory depends on the scientific context of its time. Surely not, you might think; don’t proper scientific theories have to satisfy timeless criteria such as explaining all the phenomena the theories they displace are able to, being able to make testable predictions, being repeatable, and so on? Well, yes, but here is where we get to Lindley’s central thesis: Contemporary theoretical physicists seem to have reverted to the idealized philosophy of Platonism. As he puts it, “The spirit of Plato is abroad in the world again.” Is this true? Plato’s stance was that it was enough to think about the universe. Surely, we can do better than that today, with our far more powerful mathematical tools and an abundance of empirical data to test our theories against. No physicist I know would say that to understand the laws of nature it is sufficient to think about them.
While it’s clear that nature obeys mathematical rules, a happy middle ground between Plato and Aristotle would seem to be preferable: to make the math our servant, not our master. After all, mathematics alone cannot entirely explain reality. Without a narrative to superimpose on the math, the equations and formulas lack a connection with physical reality. Lindley makes this point forcefully: “I find it essentially impossible to think of physical theories and laws only in mathematical terms. I need the help of a physical picture to make sense of the math.” About this, I am in total agreement. The mathematics can be as pretty and aesthetically pleasing as you like, but without a physical correlative, then that is all it is: pretty math.
According to Lindley, something happened in 20th-century theoretical physics that caused some in the field to “reach back to the ancient justifications for mathematical elegance as a criterion for knowledge, even truth.” In 1963, the great English quantum physicist Paul Dirac famously wrote, “It is more important to have beauty in one’s equations than to have them fit an experiment.” To be fair, Dirac was a rather special individual, since many of his mathematical predictions turned out to be correct, such as the existence of antimatter, which was discovered a few years after his equation predicted it. But other physicists took this view to an extreme. The Hungarian Hermann Weyl went as far as to say, “My work always tried to unite the truth with the beautiful, and when I had to choose one or the other, I usually chose the beautiful.” Lindley argues that this attitude is prevalent among many researchers working at the forefront of fundamental physics today and asks whether these physicists are even still doing science if their theories do not make testable predictions. After all, if we can never confirm the existence of parallel universes, then isn’t it just metaphysics, however aesthetically pleasing it might be?
But Lindley goes further by declaring that much fundamental research, whether in particle physics, cosmology or the quest to unify gravity with quantum mechanics, is based purely on mathematics and should not be regarded as science at all, but, rather, philosophy. And this is where I think he goes too far. Physics has always been an empirical science; just because we don’t know how to test our latest fanciful ideas today does not mean we never will.