Opinion 173: Theoretical Physics Is Turning Into Metaphysics, and it is JUST AS WELL

By Doron Zeilberger

Written: Aug. 20, 2019

A year ago I finished reading a fascinating book by Sabine Hossenfelder, where she makes a very good point that large parts of theoretical physics were "lead astray" by [mathematical] beauty, that is quickly replacing "agreement with experiments" as their driving force and raison d'être.

Whether you agree or disagree, I strongly recommend her book. In addition to being very insightful and well-argued, it is extremely entertaining. A large part of the fun is her irreverent and ironical depiction of the leading luminaries of string theory and high-energy physics, making them look (perhaps sometimes unfairly) as pompous and full-of-themselves.

A few days ago, I finished reading another interesting book, by Graham Farmelo, that covers more or less the same ground, but from the opposite standpoint. It is an admiring, almost hagiographic, narration of the history of string theory, that contrasted sharply with Hossenfelder's critical (and sometimes mocking) prose.

While, at the concluding chapter, Farmelo is paying some lip-service to the criticism voiced by Hossenfelder (but completely ignoring her book), he asserts (citing Paul Dirac and Albert Einstein) that using mathematical beauty as a guiding criterion to evaluate theoretical work is basically a good thing.

Whether it is good or bad, it seems that it is inevitable, and even Stephen Weinberg concedes (p. 257, line 6) that it is faute de mieux, i.e. better than nothing. The good old methodology of the "scientific method" just ran out of energy (both literally and metaphorically), at least in high-energy physics, and it is a big waste of the tax-payer's money to build yet another mega-accelerator, with its exponentially diminishing returns.

So call the kind of research done today by string theorists "metaphysics", if you will, but what if it is? If nothing else, string theory lead to lots of great mathematics and mathematics is also a science.

Speaking of metaphysics, there is room for yet another kind of meta-physics, that would hopefully justify renouncing the dogma of "experimental confirmation". That new kind of metaphysics is not that of Aristotle and Kant, but the physics analog of meta-mathematics, that explores the limits of mathematics. Gödel, Church, Turing, and others meta-proved that there is only so much that math can do. More recently, Cook, Karp, Levin and others pointed out that there is only so much that even computers can do in real time. These are both deep and flourishing subjects. Even before that, the history of mathematics had lots of disappointing "shocks", where central problems that many brilliant minds tried to solve, turned out to be (inherently) unsolvable.

[For example: proving the parallel postulate; squaring the circle; solving a quintic; deciding whether there is something between ℵ0 and 20.]

Once this "physics undecidability", or at least "physics intractability", is made precise using a yet-to-be developed "meta"-physical theory, we will come to grips with the fact that we will never be able to confirm experimentally our proposed theories, even in principle, regardless of their beauty, and learn to live with virtual realities, each theory with its own virtual reality, and since beauty is in the eyes of the beholder, we can each have our own favorite theory of everything.

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