In recent decades, some notable popular-science writers have produced books claiming that theoretical physicists at the frontier of their field are doing it all wrong—Lee Smolin’s The Trouble with Physics, in 2006, Peter Woit’s Not Even Wrong, that same year, and 2018’s Lost in Math, by Sabine Hossenfelder. Generally speaking, these books make the same argument: For centuries, physics advanced by means of experiment, observation, and measurement. The results of experiments drive the formulation of theories, from which scientists extract novel predictions, which then lead to new experiments resulting in the successful application of theory in reality. But today, with the massive success of the two greatest of all theories—general relativity (which pertains to gravity) and quantum field theory (which describes the other fundamental forces)—there is little experimental or observational evidence to guide us about where to go next. David Lindley’s The Dream Universe is the newest contribution to this line of argument. He contends that what has evolved into a purely mathematical approach to physics has yielded more incorrect predictions than successful ones about the physical world. Over the past 50 years, it’s brought us wondrous ideas such as supersymmetries, supergravity, extra dimensions, grand unification, and string theory—but no new physical discoveries. Instead, we have dazzling failures.

Lindley, a trained physicist  turned science writer, divides the book into four sections, with the first two devoted to what some physicists see as ancient history: the field of physics prior to 1900. He draws a sharp distinction between the logicians and philosophers whose differing schools of thought dominated the ancient world and shaped the emergence of modern science in the early 1600s. This contrast is not new, but Lindley successfully makes some older examples especially relevant to the current state of physics.

There is, for example, Zeno of Elea’s famous paradox. Zeno imagined a frog that wants to travel a certain distance from one place to another. In order to cover that distance, it must first make it through the first half of the journey. To travel the distance that remains, it must then travel half of what’s left: a quarter of the original distance. No matter how many “halves” the frog crosses, there will always be a non-zero distance remaining. That leftover fraction will continue to get smaller but will never disappear entirely. And therefore, the paradox states, motion from one location to another should be impossible.

Of course, this line of thought is incorrect, as motion clearly occurs in the world. Frogs really do complete their journeys from one point to another. Yet for around 2,000 years, philosophers and intellectuals were unable to resolve this paradox satisfactorily. That changed with the arrival of Galileo, the primary subject of the book’s first section. Galileo applied what was then an entirely novel concept to the physical motion of objects: velocity, or the rate at which motion occurs. As the frog traverses the first half of its journey, it does so in a specific amount of time. It then travels half the remaining distance but requires only half of the time of the previous jump. Each subsequent “half” for the distance it travels takes only half the amount of time, even as the distance jumps are allowed to get infinitesimally small. Looking at distance alone doesn’t provide you with the full picture, Galileo demonstrated. You need to examine how distance and time change together; you need to understand the rate of motion.

This, Lindley argues, is a solid illustration of how science should work. Yes, there are mathematical relationships between various quantities, but they’re only important insofar as they relate to observable, measurable properties of the universe. He lauds Galileo as a tipping-point figure in the birth of modern science. Galileo abandoned the ancient notion that the natural world could be understood by thought and mathematics alone and asserted that mathematics is useful only as a tool for understanding the quantitative relationships between observable phenomena.

In the book’s second section, figures such as Newton, the Bernoullis, and Faraday leverage new techniques and concepts in their work, but the fundamental essence of science remains the same as it was for Galileo. It’s about what can be observed and measured, with mathematical frameworks serving as tools to make the connections between an underlying theory and what is observed. One of the most useful tools, expounded upon at length by Lindley, is the differential equation, which first arises in the context of Newton’s calculus. Lindley eloquently explains: “For a given set of conditions, it tells you what happens a moment later; and when that moment has elapsed, the same differential equation tells you what happens after the next moment has elapsed.” Any system in the universe evolves continuously in time, and both Newtonian mechanics and classical electromagnetism successfully allow us to determine how that time-evolution occurs.

But then things get murkier. In the second half of the book, Lindley takes us into the 20th and 21st centuries, when classical notions of space, time, positions, momenta, and determinism were replaced with relativistic and quantum notions. Mathematics, rather than empiricism, becomes a driving force in making new predictions about the universe. Although the results weren’t immediate, this approach had some impressive triumphs. The positron (and antimatter in general), predicted by Paul Dirac in 1928, was confirmed a few years later. Other predictions, such as the neutrino, the Higgs boson particle, and gravitational waves, took decades or even a century to be confirmed.

But most of what the new mathematical paradigm predicted has not come to pass. There are no supersymmetric particles, no proton decay, no evidence for additional spatial dimensions, to name just a few. Much to Lindley’s frustration, these ideas continue to dominate fundamental physics.

Yet Lindley fails to make the best case for the paradigm he attacks before attacking it. He could have taken more care to separate out what is scientifically known (and supported by the type of science he lauds) and what is speculation, philosophy, or interpretation layered on top of it. He’s critical of cosmological inflation, for example, because of its untestable prediction of multiverses and the idea of the string landscape that pervades much of the relevant literature. But he makes no mention of the enormous successes of cosmic inflation—the idea that the universe underwent a period of relentless, exponential expansion prior to the hot big bang—from a physical cosmology perspective. At least four independent predictions arose from the theory in the 1980s that were subsequently verified and validated by observations of the universe itself. Instead, Lindley focuses only on the untestable—and arguably, unscientific—predictions that emerged from cosmological inflation. Additionally, he often attempts to bolster his case by merely quoting those with whom he agrees. Instead of noting that Alan Guth says X, Paul Steinhardt says Y, and Sabine Hossenfelder says Z, he could pull out what’s empirically true and separate it from opinion and speculation.


So what should we do about fashionable theorists who explore mathematical spaces and devise constructs that are hopelessly divorced from observable and measurable quantities? Lindley doesn’t say. He argues that such trends transform physics into an unscientific pursuit, similar to how the pre-Galilean philosophers sought to divine the nature of the entire universe through pure reason (and perhaps mathematics) alone. In this, I largely agree with him and the aforementioned Smolin, Woit, and Hossenfelder. But simply deeming the current approach flawed is unsatisfying. While Lindley offers a compelling account of the history of physics, The Dream Universe ultimately disappoints.

Lindley’s failing here is understandable. While it’s easy to recognize what’s wrong, it’s far more difficult is to explain what “doing it right” looks like. You can hearken back to Galileo, Newton, and Faraday and point out the superiority of the empirical approach. But, in fact, many scientists at the frontiers of discovery are already taking this approach. Astrophysicists have uncovered overwhelming empirical evidence for dark matter and dark energy, while demonstrating that the universe is made of matter (and not antimatter) everywhere in space. Particle physicists have empirically revealed each and every particle of the standard model and measured the behaviors and properties of every known quantum of matter to unprecedented precision. Relativity and quantum field theory have been validated with exquisite precision, with experiments continuing to push forward on all those frontiers. Even at the time of this writing, efforts to build a next-generation, higher-energy particle collider are under way; ground-based telescopes are planned with light-gathering powers that are a factor of 10 greater than today’s largest; four separate proposed NASA missions (LUVOIR, HabEx, Lynx, and Origins) seek to push the observable cosmos beyond the limits of Hubble, James Webb, or any of NASA’s great observatories.

Would more theorists working on phenomenology—which teases out near-term predictions for experiments and observations under various theoretical scenarios—be an improvement over the status quo? Would a greater investment in alternative (non-string theory) approaches to quantum gravity yield better results? The problem is, when you’re walking down a blind alley, you can’t know whether or not it’s a blind alley until you get to the end. Lindley can’t be faulted too much for not knowing the correct way forward; none of us do. It’s eminently possible that fundamental physics really has lost its way, as The Dream Universe contends. But without the requisite evidence to guide us, the only option is to keep moving forward.

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