Princeton University Press recently began a Frontiers in Physics series whose purpose is to provide “short introductions to some of today’s most exciting and dynamic research areas.” The first few volumes focused on astronomy, but the series’ latest offering deals with mainstream physics and carries the intriguing title, Can the Laws of Physics Be Unified? The author is Princeton University senior scientist and University of Pennsylvania emeritus professor Paul Langacker, who published a respected scholarly book, The Standard Model and Beyond, in 2010, with a second edition issued in 2017.
The audience for The Standard Model and Beyond is graduate students and researchers in elementary-particle physics. In the introduction to Can the Laws of Physics Be Unified?, however, Langacker writes that he has in mind a much broader readership: “This book is written for an undergraduate physics student, a practicing scientist in a related field, or any interested reader familiar with the basic ideas of classical physics, quantum theory, and relativity.” Since the standard model is one of the crowning achievements of modern science, Langacker’s goal is admirable. But it is also a challenging one, given that the standard model is expressed in the language of relativistic quantum field theory and requires the knowledge of gauge theories.
At 271 pages, the book is short and sweet and is published in a nice 5- by 8-inch size that encourages casual reading—I brought my copy along on vacation. Although I can attest to the accuracy of the text, it is not clear that I am the best judge of how the book will be received by its intended audience. The author and I are about the same age (seventyish), and our careers have coincided with the golden years of particle physics, beginning in the late 1960s. Today we know that the standard model describes nearly all aspects of elementary-particle interactions.
Thus, as I read through the 80 pages introducing readers to the standard model and its implications, I was comfortable with the presentation and could fill in the blanks when Langacker simplified things. It was a pleasure to have those matters described by someone who really understands them.
The casual reader, however, may be dismayed by the plethora of ideas being offered—gauge theory, asymptotic freedom, quarks, gluons, nonabelian fields, creation and annihilation operators, spontaneous symmetry breaking, the Higgs mechanism, Yang–Mills theory, color, quantum chromodynamics, accelerators, electroweak theory, CP (charge conjugation–parity symmetry) violation, and quark and neutrino mixing, to name just a few. I have had nearly half a century of study to assemble all those ideas into a coherent package in my mind. Absorbing them all in an afternoon would be considerably more challenging.
Following the introductory material, the chapter called “What don’t we know?” summarizes a range of questions raised by the standard model. Many of them are long-standing and well known. An example is the fine- tuning problem. Feynman diagrams with loops in them often produce infinities, which are presumably cut off by an unknown high-energy interaction. If that missing interaction is gravity, then the relevant cutoff scale would presumably be the Planck energy—the combination of Newton’s constant, Planck’s constant, and the speed of light with units of energy, which is on the order of 1019 GeV.
Since the physical value of a quantity such as the Higgs mass is given by the sum of its bare value plus the loop correction, a huge loop contribution must be compensated by a very carefully chosen bare value. That sort of cancellation—fine tuning—seems unnatural. Langacker discusses that and other standard model enigmas, including the mystery of why the theta term contribution to CP violation is so tiny.
The closing chapter looks beyond the standard model to seek solutions to some of the outstanding questions. One possibility is some sort of grand unification. Having studied how electrodynamics unifies electric and magnetic phenomena and how standard electroweak theory unifies the weak and electromagnetic interactions, theorists have sought for many years to find a single theory that would incorporate quantum chromodynamics with the electroweak interaction. Any such picture, however, would of necessity include a plethora of new particles that have not yet been seen and would require the proton to decay, which is also yet to be observed.
Another popular unification effort is the search for supersymmetry, which relates fermions and bosons. The existence of supersymmetry would be useful for resolving the fine-tuning problem, since cancellations of Feynman diagrams with boson and fermion loops would mean that there exists no quadratically divergent loop contribution to, for example, the Higgs mass. However, once again many new particles would be required, none of which have yet been seen. Then there are string theories, which attempt to eliminate divergences by replacing point systems with extended strings and allowing the inclusion of gravity in the unification. But identifying the correct theory among the numerous possibilities is difficult, and in any case many additional spacetime dimensions must be dealt with. Langacker also discusses future accelerator programs that might shed light on outstanding issues.
Overall, Can the Laws of Physics Be Unified? is an interesting and enjoyable read, and it describes the vast landscape of particle physics in a comprehensive and authoritative fashion. My only concern is whether the book is truly accessible to its intended audience of nonexperts. I have my doubts, but maybe they are unfounded. Five or six decades ago, when I was a young person trying to digest books like George Gamow’s One, Two, Three . . . Infinity (1947), I struggled to comprehend numerous concepts. But that lack of easy understanding was what led to my fascination with those subjects, and eventually to my undertaking a scientific career to attempt to comprehend them. If Paul Langacker’s book can provide similar motivation for today’s readers, it will have accomplished a great deal.
Barry Holstein is retired from the University of Massachusetts Amherst after a career that focused on problems at the interface of particle and nuclear physics.
