# Lost in Math: How Beauty Leads Physics Astray

The title of the book says it all, but it may need some explanation. Physicists have learned by experience that mathematics is very effective in describing the physical laws. It has also turned out to be effective when a simpler explanation is preferred over a more complicated one. Simpler means fewer equations, fewer assumptions, and fewer parameters. These simplifications are often the result of symmetry. So physicists came to accept symmetry as a synonym for beauty. This was a success when in astronomy the paradigm shifted from a geocentric to a heliocentric system, and it was useful in particle physics to unify the theory of different forces as in the standard model. But physicists should be warned by the disaster of the models designed and loved by economists for their mathematical beauty but that dramatically crashed in the 1980s with many years of global recession as a consequence.

To arrive at a Grand Unified Theory (GUT) and design the mathematics for quantum gravity, physicists, intoxicated by this concept of symmetry, could only think of going one rung further up the ladder, and blindly proposed supersymmetry (susy for the intimi) as the logical next step. And mathematically, it is indeed a beautiful theory: a supergroup that incorporates all the symmetries of the underlying laws as subgroups. However mathematics is not physics, and physics requires experimental confirmation. Unfortunately the physicists are now erring in the dark since the Large Hadron Collator (LHC) did not reveal all the expected particles predicted by susy. The Higgs boson observed in 2012 was the last success. But the Higgs is at a scale that is so far off the scale of the other particles that it conflicts with another paradigm of physics: *naturalness*. This means that a dimensionless constant should at approximately the same scale as the other parameters. If it is not, then it might be a statistically irrelevant outlier. However if statistics shows that it is an important parameter of the theory, then it needs to be shifted or renormalized, which is called *fine tuning*. The cosmological constant is an example of fine tuning and it is ugly and still a source of much debate. Einstein was the first to introduce the cosmological constant Λ but he did not like it. It was reintroduced to explain the expansion of the universe and dark energy in the ΛCDM (Cold Dark Matter) model, but dark energy is poorly understood.

So the question that Hossenfelder as a theoretical physicist asks herself is whether physicists are blinded by this mathematical symmetry principle of beauty and naturalness and do not realize that they are barking up a dead end. Mathematics should not lead the way for physics. It should be the other way around: the appropriate mathematics should be derived from the physics. In the past this ideal of symmetry and naturalness were not the lead. Symmetry was observed a posteriori when the paradigm shift was made. Also naturalness has not always been avoided. The parallax of the stars that could explain the heliocentric system, was way off the scale of distances in our solar system, and so are the distances between stars and between galaxies as compared to our solar system.

She sets on a mission to ask many of the specialists in the field about their opinion. Skyping and travelling all over the world to interview the leading scientists and everyone who might have an opinion on this matter, trying to convince them (and herself) that physicists have driven research into a cul de sac. This book is a report of her crusade searching for answers. It is clearly her conviction that there is something rotten in the state of physics.

To explain the problem and to understand the arguments given, she also has to discuss the terms and claims of particle physics, cosmology, etc. So at the same time, this book is a very readable popular science book on the subject. Of course there are no technical details, but for the layman, just enough insight into the concepts and problems are given to know what the discussion is about. All this information is nicely interwoven with her travelling experiences, and the interviews. These interviews are related in a very lively and personal way, often in the form of dialogues that she reconstructed from her recordings. So the reader is painlessly introduced to a broad spectrum of concepts. Of course supersymmetry, but also the standard model in particle physics and the concordance model in cosmology, multiverses, strings and branes, dark matter and WIMP, vortex theory, QBism, symmetry and Lie groups, cosmic background radiation, a simplified particle zoo, and many more. But only just enough info to understand the context.

The interviews are also very personal. These "big shots", sometimes very busy running a research group, sometimes old retired emeriti, they are only humans, yet convinced of their opinion, defending the foundations on which they built their career. The place and circumstances in which the interview takes place, the hesitation or silence in the discussion, that sometimes drifts off to a philosophical discourse, it all contributes to an entertaining story. And there are many she has interviewed. From Nobel Prize winners Frank Wilczek, Murray Gell-Mann, and Steven Weinberg, to a wind-surfing non-academic Garrett Lisi, enjoying life and research on Maui, Hawaii, who proposed a so far not very successful Theory of Everything based on the exceptional E8 Lie group, and there are about a dozen more people that are staged.

The frustration of Hossenfelder is that theoretical physicists just go on chasing after mathematical results following these assumptions of beauty and naturalness, and they do not even care about experimental verification, which technically means that they leave science behind. Moreover, they live in a closed, isolated environment, publishing in journals refereed by peers that have the same opinions. The pressure of publishing, getting finances, being accepted by peers, all means that young researchers have to conform themselves to these mainstream ideas. In 2016 the LHC detected something that could not be explained by the standard model. A few months later hundreds of papers had appeared in refereed journals about this so-called diphoton anomaly, when it was announced that the observed bump should be disregarded since it could be explained as noise. This illustrates that theoretical physics can invent explanations for whatever data are presented but so far, no experimental data occurred to confirm susy. Susy is called beautiful, but the concept of beauty can change. Perhaps there are physical laws that are beautiful in an unfamiliar way. Clearly Hossenfelder is throwing a bat in the henhouse. Her message is not very welcome in the community. Will she remain a voice calling in the desert? As a mathematician, (not involved in theoretical physics), I would like the math to triumph, but I think Hossenfelder has some good arguments, and in the past paradigm shifts away from what was considered to be perfect and beautiful have been rewarding. For example it was difficult to abandon the perfectly beautiful circular motion of the planets on epicircles in a geocentric system. However, even though the circles had to be replaced by ellipses in a heliocentric system, it only resulted in an even more general and beautiful mathematical theory. Thus there is no doubt that mathematics will prevail, but nature should be the guide and not the other way around.

I loved reading this bird's-eye vision of the state of confusion and hope against all odds that theoretical physics is in today. It is written in an entertaining and convincing, yet very human way, showing that science is only produced by people. Perhaps it is worthwhile that scientists take a step back from the rat race of producing papers and that they reflect on what they are doing and recall what the ultimate goal of their science is. Reading this book, can be a good start.

**Submitted by Adhemar Bultheel |

**5 / Feb / 2019