The criterion of beauty in physics

In the introduction to my last report I mentioned how sad it is that at the present epoch research in fundamental theoretical physics has reached a point of stagnation similar to that which once affected the physical sciences during antiquity, when geometrical idealism overturned observation as the main criterion for judging the validity of a physical theory. I explained that it is my belief that the current lack of progress in theoretical physics is not merely the consequence of an absence of new observations, but is again in large part attributable to an excessive reliance on mathematics, that is often achieved at the expense of clarity and overall physical consistency. Other researchers in the field have also recognized the existence of such a problem. Some of them, however, go as far as suggesting that mathematical consistency cannot be trusted as a guide to decide if a physical theory is valid. Thus, they suggest that the criterion of mathematical beauty or simplicity should not be used to assess whether a given theory is likely or not to constitute a valid explanation of facts.

It must be clear, though, that this is not what I mean when I emphasize the existence of a problem associated with our growing reliance on mathematics in producing and communicating meaningful results in theoretical physics. What I do believe is that mathematical beauty should not be the only criterion for judging the relevance of a physical theory, even at the most fundamental level. Indeed, the necessity for a model to agree with a large number of implicit, or unrecognized physical principles and philosophical consistency criteria which can be derived from known aspects of reality is often much more constraining a condition for deciding the validity of theory. But many of those criteria are often simply ignored when creating new theories, as if the mathematics itself was alone able to tell the truth. Yet, this doesn’t mean that mathematical beauty and simplicity are not very significant criteria for assessing the value of one theory over another, as in fact they often constitute an indication to the effect that the theory which is being considered agrees with the most general and least constrained ensemble of physical principles.

It is not surprising therefore that the criterion of beauty and simplicity has been emphasized to be of key importance in the formulation of new physical theories by the most successful researchers from Einstein to Dirac. All that one must retain of this discussion is that, while certain models, like supersymmetry, might seem beautiful from a purely technical viewpoint, they are actually very ugly theories when considered from a more general perspective, while they may not even really constitute the simplest or most natural explanation of empirical data. The fact that the most recent experiments may seem to confirm the irrelevance of those once promising theories cannot, therefore, be used as an argument against the validity of a more accurate criterion of beauty. In other words, what appears beautiful to some researchers today, may well prove to be very inelegant and contrived proposals to other researchers who, tomorrow, will invent better and more universally consistent models.