Lost in Math

Lost in Math: How Beauty Leads Physics Astray 
by Sabine Hossenfelder. Basic Books, June 2018. Reviewed by Steven Willing, MD

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“Physical laws should have mathematical beauty”. Paul Dirac, Nobel Laureate*

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Way back in 1973, the world of theoretical physics reached a dead end. That year marked the last successful prediction of any elemental particles - the top and bottom quarks - which were experimentally verified in 1995 and 1977 respectively. (The Higgs boson, finally detected in 2012, had been predicted in the 1960’s). Since then, there has been no successful prediction that would supersede the standard model.  

In the intervening decades, dozens of additional particles have been predicted; not one has been found. String theory evolved and gained wide acceptance, without a shred of experimental verification. Proton decay has been sought but never observed. Dark matter remains dark to our own investigations. The search for a grand unified theory, based on the the holy grail of supersymmetry, has gone nowhere. Eighty years of effort failed to combine general relativity with the standard model. More exotic concepts - the multiverse, wormholes, extra dimensions, mini black holes - have eluded observation and may never be testable. Some ideas are untestable, even in theory.  

Not that we are lacking in achievement. What physicists call the “standard model” - where all matter and forces except for gravity are accounted for by 25 elemental particles and forces - has been wildly successful both in experimental validation and its predictive power. The same is true of quantum theory. There’s only one problem. Physicists hate them both. Nature, it seems, is too unnatural for their tastes. 

The standard model has been denigrated as “ugly and contrived” (Michio Kaku), “ugly and ad hoc” (Stephen Hawking), “ugly and baroque” (Brian Greene), with “the air of unfinished business” (Paul Davies). What troubles them so? Fine-tuning. Too many improbable coincidences. Too hard to understand or explain. Quantum mechanics is “magic”.  Too many arbitrary constants. (In the standard model, there are at least 19 unique constants that cannot be predicted by the model. They can only be determined by scientific measurement).  

The mass of the Higgs boson serves as a case in point.   Its mass depends on the contribution from quantum fluctuations multiplied by the fermion/boson sum. Quantum fluctuations contribute an amount to the mass of the Higgs boson 10¹⁵ greater than what is measured. To achieve the measured mass, the quantum fluctuation effect must be perfectly offset by a factor of 10^-15, with a precision extending to fourteen digits.   In the eyes of physicists, such fine-tuning is not “natural”. It is an improbable coincidence. Fine-tuning is “a badge of shame” (Lisa Randall), “a sickness” (Howard Baer). It seems to demand an explanation. It is “ugly”. There are other trouble spots of fine tuning: the cosmological constant, the “strong CP problem”, and the great disparity between gravity and other forces (the “hierarchy problem”).

Theoretical physicist Sabine Hossenfelder suggests one reason physicists have hit a wall: in their philosophical quest for “Beauty” the world of theoretical physics has gotten “Lost in Math”. The popular perception of a scientist is that of one driven by cold, hard, objective, unswerving logic. Despite the stereotype, the theoretical physicists interviewed and cited  by Hossenfelder - all leaders in their field - seek, hope for, even insist upon solutions that are aesthetically satisfying.  To them, the ultimate explanation for everything should reveal elegance,  naturalness,  symmetry - all shrouded in mathematical beauty. Yet, there is a danger in this approach. If our present laws of nature were not beautiful, would we ever have found them?  Surely an ugly explanation beats no explanation at all. If a more fundamental theory is not “beautiful”, will we fail to find it? Or even look for it? What if ultimate reality is “ugly"? 

There are other barriers to progress. As high energy experiments from the Large Hadron Collider eliminate from consideration various testable hypotheses, successive hypotheses must assume even higher energy levels which may not be testable, ever: 

If we wanted to directly reach Planckian  energies, we’d need a particle collider about the size of the Milky Way. Or if we wanted to measure a quantum of the gravitational field - a graviton - the detector would have to be the size of Jupiter….Clearly, these aren’t experiments we’ll get funded anytime soon. 

To escape the current predicament, there are calls to abandon the scientific method by eliminating the requirement of experimental verification.  Physicist, philosopher, and string theory proponent Richard Dawid is advocating “non-empirical theory assessment”. With declining prospects of empirical validation, Dawid concludes that “the scientific method must be amended so that hypotheses can be evaluated on purely theoretical grounds.” But “if we can’t test it, is it science?” asks Hossenfelder. 

Hossenfelder is at various times lively, comic, and probing. She quips “Theoretical physicists used to explain what was observed. Now they try to explain why they can’t explain what was not observed…There are many ways to not explain something”.  

In her journey through the rarified world of particle physicists and cosmologists, Hossenfelder voices concern for how hostility to the idea of a God on the part of some harms the public image of science. In the course of their conversation, cosmologist George Ellis recalls his review of a book by Victor Stenger claiming that science disproves the existence of God: 

"I opened this book with great anticipation, waiting to see what was the experimental apparatus that gave the result and what did the data points look like and was it a three-sigma or five-sigma result? Of course, there is no such experiment. These are scientists who haven’t understood basic philosophy.” (God, the Failed Hypothesis, by Victor Stenger, reviewed by George Ellis in Physics World) 

“Lost in Math” portrays a community of researchers in philosophical crisis. The esteemed physicists interviewed in this book and its impressive author are to be congratulated on their efforts and their honesty. The genuine achievements of science are acknowledged and celebrated, while the limitations of science and of scientists are admitted frankly. Scientists are human, after all. 

Naturalness, beauty, simplicity are aesthetic and philosophical concepts, not scientific ones. While aggressive proponents of secularism accuse believers of irrationality for believing in a God that - they claim - cannot be proven, their rear guard is crumbling. The field of theoretical physics faces a headwall where empirical validation of foundational theories may no longer be possible. More foundational theories may ultimately be embraced on faith alone - so long as the mathematics is beautiful! 

In the world of physics, we find fine-tuning and mystery from the subatomic to the cosmic scale with rapidly diminishing prospects of natural explanation. It is possible we may never see deeper than we are currently able, that we have reached our limit of comprehension regarding the essence of underlying reality. Meanwhile, what can be proven is distressingly improbable. God must be smiling.

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*In her biography of Paul Dirac, historian Helge Kragh noted that in the last 49 years of his life Dirac “largely failed to produce physics of lasting value”.