Foreword: Lost in Math

The Icelandic Publishers of Sabine Hossenfelder's first book, Lost in Math asked me if I would write a foreword for the book, which will appear later this year. Here it is, in English. :)

(This will appear in Icelandic, in Rammvillt í reikningskúnstum: Hvernig fegurð villir um fyrir eðlisfræði. Translated by professor Gunnlaugur Björnsson and Baldur Arnarson. )

I first got to know Sabine Hossenfelder when she invited me to a scientific meeting at her institution in Germany to discuss issues associated with Quantum Gravity.  She was a wonderful host who ran a very interesting meeting, with an eclectic but excellent group of participants.  I think that I actually met her earlier briefly when she was in town at my institution to interview the physicist Frank Wilczek for her book.  I did not know at the time that she could sing and play the guitar, nor that she could explain scientific concepts with a freshness and novelty that I continue to find refreshing every time I either listen to her or read something she has written. 

This is not to say we agree on everything.  We don’t.  I still think, for example, that evidence for the dark matter apparently dominating the mass of galaxies is best explained by a new sort of elementary particle, while Sabine thinks it is most likely due to changes in gravitational interactions on the scale of galaxies.

But the great thing about science is that one can disagree about such things, have useful conversations, and actually learn something in the process, if one is willing to be honest, both with your interlocutor and with yourself. 

We do agree on perhaps about the most important facet of science, however.  The power of science is governed first by careful observations and next by the ability to make predictions. Neither of us has much time for beautiful theories that make no predictions, or elegant theories whose predictions are wrong.

In this regard, when I think of Sabine’s writing, the word honest springs to my mind.  She speaks her mind, and says what she thinks, whether or not her views conform to those of the majority.  Indeed, she speaks out particularly when her views don’t so conform.   We need such informed critics.  Science is, after all, a dialectic.

Informed is a key word here.  Many people may not be persuaded by ideas floating around at the forefront of physics.  But most of them have no idea what those ideas are really all about.   Sabine does—she is an accomplished researcher in theoretical physics whose work has touched on fundamental issues.   This is important. 

When I was asked to write this introduction to Lost in Math, I turned to words I had recently written about Sabine and her writing.  I want to quote them here because I think they capture my views of Sabine and her popular impact in a way that applies equally well to this book.

“Part gonzo journalist, part curious child, part teacher, and part accomplished researcher, Sabine Hossenfelder is a unique writing talent and a unique science popularizer. One cannot help being provoked reading her prose, as she knows how to push your buttons. But she also abhors bullshit, which makes her take on the deepest human questions and what physics has to say about them worth looking at, and also ensures that it will be different than those other physics books of grand verbosity about frontier physics. You might agree with her. You might not. But you will come away from the experience enriched, and will think about the world differently than you did before.”  

Lost in Math is in large part about the tension between truth versus beauty in science.  This tension exists because scientists, unlike, say mathematicians, sometimes have to choose between the two. The great German mathematical physicist Herman Weyl betrayed on which side of the mathematics/physics fence he dwelled when he wrote the words: “My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.”This is a luxury that mathematicians have but physicists don’t. 

Ultimately, Lost in Math is motivated by Sabine’s concern that too many physicists have lost their way, following Weyl’s example, rather than, say, Richard Feynman, whose priority was whether theory conformed to nature as revealed by the results of experiments.

With the popular rise of what has become known as String Theory in the 1980’s, fundamental physics research took a relatively new departure away from the measurable universe and into mathematical speculations regarding universes about which we might have no empirical handles.  Initial predications about the need for 26 dimensions gave way to the possibility of ten or eleven dimensions, and then to the possibility that dimensions themselves might be an illusion, and that the universe of our experience exist as a holographic projection of a higher dimensional space. Strings themselves, once considered the heart of the mathematical framework of these theories, gave way to more complex objects called branes, and the mathematics became ever more complex—so complex in fact that physicists were inventing new mathematics as they went along. 

The sociology of elementary particle physics transformed during the 1990’s as a combined result of two factors.  First, no significant new empirical data had emerged from particle accelerators that could guide the theoretical speculations of physicists.  There is a well-known phenomenon when individuals are placed in sensory deprivation facilities.  They begin to hallucinate. The lack of empirical direction in particle theory over the final two decades of the 20th century had a similar effect on theorists, who, in the absence of empirical constraints, created a host of possible, and sometimes beautiful ‘Beyond The Standard Model’ theories, many of which did not pass the test of subsequent experiments, and none of which, alas, has yet turned out to have any experiment support. 

Second, in the absence of experimental verification as an adjudicator of good versus bad theories, a new social dynamic emerged.  Mathematical elegance, and sometimes mathematical complexity, became the arbiter of excellence.  For almost a decade, young mathematical physicists, many of whom showed no interest in any physics that might relate in any way to ongoing experimental investigations, began to populate physics departments, and, if they were string theorists, they might get tenure within a few years of receiving their degrees.

The String Theory heyday of the 1990’s subsided in the early 2000’s, in part due to exciting new data from astrophysics and cosmology that provided fundamental challenges for physical theory, and ultimately a decade later, after the discovery of the Higgs particle many left the string ship—which, if not sinking, appeared to be listing dangerously to its side—in favor of explorations aimed at producing good predictive calculations of phenomena associated with the Higgs.   Nevertheless, the legacy of mathematical elegance, and theoretical beauty remained as the seeming goals of much of fundamental physical theory work.

It was in the context of these developments that Sabine Hossenfelder’s book Lost in Math appeared, and as is typical of her no-nonsense attitude, Sabine took issue with this new scientific culture in her own unique style. 

One of the areas that has led her to some consternation is the emergence of a concept called ‘naturalness’ that has come to guide particle physics.  This is not a vague notion, but a well-defined mathematical concept, first emphasized by the brilliant Nobel Prizewinning theorist Gerard ‘t Hooft.  A particle physics model is ‘natural’ if it is impervious to the quantum effects of as of yet unknown new physics at high energy scales.

The best known example of an ‘unnatural’ theory is, in fact, the Standard Model of Particle Physics, and in particular the part of that model that involves the famous Higgs particle.   One of the most perplexing aspects of the Standard Model is the question of why the mass of the Higgs particle, which sets the scale for the unification scale of two of the four forces in nature—electromagnetism and the weak force—falls over 16 orders of magnitude below the scale where quantum effects in gravity become important, and over 14 orders of magnitude below the scale that many physicists presume will see the unification of all three non-gravitational forces in nature.

This “Hierarchy Problem”, as it has become known is particularly perplexing because withing the context of the Standard Model, if there is new physics that becomes relevant at these extremely high energies, quantum effects should feed down into the Standard Model and drive the magnitude of the Higgs particle mass up to these very high energies.  Nothing in the theory protects this from happening, and the theory is therefore ‘unnatural.’

The Hierarchy Problem is one of the main motivators for the mathematical proposal that a new symmetry of nature, called Supersymmetry might become manifest at high energies.  This new symmetry can protect the Higgs mass from the vicissitudes of high energy physics, and keep the scale of electro-weak unification at the observed experimental value, at least as long as new ‘supersymmetric partner’ particles of ordinary matter appear soon at the Large Hadron Collider in Geneva.

Unfortunately, to date, no such particles have been observed.

One can then take this result in one of two different ways.  Either there is more motivation for looking for other new phenomena near the Higgs, or, naturalness is not a good guide.  Time may tell.  Of course, it could be that we simply don’t observe anything new in current or future machines, and accelerator experimental particle physics dies out, and with it interest in whether the Hierarchy Problem or naturalness issues may lead to compelling new physics.  

As physicists continue to debate beauty in physics, or elegance of models, it is worth thinking of Einstein’s development of General Relativity as a historical object lesson.   In retrospect, General Relativity is a triumph of mathematical elegance, in which differential geometry proved to beautifully describe the nature of curved spacetimes in a way that naturally incorporated Newton’s Universal Law of Gravity.

Nevertheless, as mathematically elegant as General Relativity is, we must remember that the key fact that convinced Einstein he was right wasn’t the mathematical beauty of his theory, but the fact that it allowed a correct calculation of the perihelion of Mercury, which up until that time had remained an observational mystery.   He reported to a friend that he had heart palpitations the moment that he realized his model gave a correct prediction of the puzzling motion of that planet.  He never wrote in these words about the mathematics he had learned to develop his model. 

This ultimately points the way out of our current preoccupation with beauty or elegance in theories.  It will come from data.  The imagination of nature far exceeds that of humans, which is why we need to keep exploring the universe with our laboratory experiments and our great observatories. 

When James Clerk Maxwell first developed his fundamental equations of electromagnetism, heralded today as one of the pillars of theoretical physics, emblazoning T-shirts of undergraduate physicists from around the world, the theory didn’t look particularly beautiful, and Maxwell’s attempt to explain its underpinnings by use of analogies to mechanical wheels and pulleys was at best awkward.  But it predicted that light was a wave, and that its speed could be calculated from first principles, and lo and behold, the calculations agreed with experiment.

Whenever a deep empirical puzzle in physics is resolved by a theoretical insight, no one stops to ask if the idea is beautiful enough to be true, but whether it is true enough to be beautiful.

(I am happy to add that earlier this year Sabine recently kindly penned a lovely comment on my recent book, The Edge of Knowledge/The Known Unknowns: “With the ease of a master, Lawrence Krauss takes us on a sightseeing tour to the biggest unknowns in the universe. A breathtaking trip to the frontiers of knowledge and beyond.” I should note that neither my foreword, nor her kind remarks were exchanged in any quid pro quo way… Be wary of confusing correlation with causation! )