Lost in Math

Sabine Hossenfelder’s new book Lost in Math provides a well-informed take on the current situation in fundamental physical theory. The author is completely honest, utterly fearless, and often quite funny. Mathematician readers should be warned that the title of the book may mislead them: there is little about mathematics as such, or the topic of its complex relations with modern theoretical physics. The usage of “Math” in the title is more like the everyday usage as meaning “calculation”, making a claim that theorists have gotten lost in endless calculations in ever more complex models, unable to find a route towards genuinely new ideas that could lead to connection to experiment and real progress.

The author is a theoretical physicist whose specialty is the study of the possibility of experimentally accessible signatures of quantum gravitational effects. Besides this research specialty, she is engaged in many activities designed to communicate with the public, maintaining an excellent blog entitled Backreaction as well as a Twitter account well worth following. She also writes for publications like Quanta and Forbes, and periodically even produces and sings in music videos with physics themes.

Her career has coincided with a difficult period for fundamental theoretical physics, with many decades of little progress towards the goals of improving on the Standard Model of elementary particles and finding a consistent and testable quantum theory of gravity. This has led her over the years to devote a great deal of time and effort to thinking about whether the organization of research in theoretical physics might be responsible for these difficulties, and these concerns are a recurring theme throughout the book.

Over the past few years, results have finally started to arrive from the Large Hadron Collider (LHC) at CERN in Geneva. These results have included the 2012 discovery of the Higgs particle, completing the Standard Model, but also strictly negative results showing no evidence for suggested enlargements of the Standard Model. The most popular of these enlargements has always been the so-called “supersymmetric” version of the Standard Model, based on replacing the fundamental Poincaré Lie algebra of spacetime symmetries by a certain Lie super-algebra extension. This introduces new “supersymmetry” generators, which should relate known particle states to conjectural “superpartner” states. The problem is that such superpartners had not been seen in earlier experiments, with the LHC somewhat of a last hope for finding them.

Now that the negative LHC results are in, long-standing ideas guiding research in particle theory are in trouble, and many theorists have started to refer to the situation as a “crisis”, or even a “nightmare scenario.” The central theme of Hossenfelder’s book is that of trying to understand this crisis, what is responsible for it, and what can be done about it. Part of what she does is address the problem in a characteristically direct manner, by going to talk to those responsible and ask them what they have to say for themselves. A large part of the book consists of fascinating interviews with leading figures in the field, in particular with Nima Arkani-Hamed, Steven Weinberg, Frank Wilczek, and Joe Polchinski, as well as several other physicists who are not as well known. Put together, these interviews give an insightful and comprehensive view of what experts are thinking as they try and come to terms with the implications of the failure of long-held hopes.

The main framing device that Hossenfelder uses throughout the book is that of questioning the idea of “beauty” as a criterion for evaluating the promise of speculative new ideas about physics. I’m afraid that this choice of language will mislead many who don’t read carefully enough to see what she is trying to get at. By “beauty”, she is referring to a specific set of ideas that physicists have extrapolated from their successful use in the Standard Model, ones that she describes with the terms “symmetry, unification and naturalness.” “Symmetry” refers to the use of certain Lie groups (e.g. \(SU(3)\), \(SU(2)\) and \(U(1)\) in the case of the Standard Model) and their finite dimensional representations. “Unification” refers to the realization of these groups as subgroups of a larger group, and “naturalness” to the expectation that, lacking a reason otherwise, calculated dimensionless numbers will be of order one. All of these ideas arise out of successes in the development of the Standard Model, and one can assign them some aesthetic meaning, but I’m not convinced that doing this is enlightening. At various points Hossenfelder makes it clear that her worry is that physicists are getting stuck due to outdated notions of “beauty”, while at the same time she still believes that successful new ideas will come with their own new form of “beauty”.

The book ends with the following summary, making clear the author’s position on the beauty question:

We know that the laws of nature we presently have are incomplete. To complete them, we have to understand the quantum behavior of space and time, overhauling either gravity or quantum physics, or maybe both. An the answer to this will without doubt raise new questions…

…There’s much work to do. The next breakthrough in physics will occur in this century.

It will be beautiful.

Peter Woit is Senior Lecturer in the mathematics department at Columbia University and since 2004 has been blogging on topics in physics and mathematics. He is the author of Not Even Wrong (2006) and Quantum Theory, Groups, and Representations (2017).