In “The Biggest Ideas in the Universe”, Sean Carroll reveals the beauty behind physics equations.

As an undergraduate toiling my way through physics and organic chemistry, I found classes immensely satisfying for the most part. Science worked for me, at least on one level. I enjoyed the explanations and the theory behind the opaque terms that filled my textbooks. The real world applications and the theoretical possibilities physicists derived by working with equations fascinated me. That “wow” factor, the real world tie-in between science and the everyday, is basically what the entire pop-culture sci-comm industry is built on, from the Science Guy to all the YouTube-full-time-science-teacher/part-time-influencers.

That said, without fail, my enthusiasm ground to an equally emphatic halt when the time came to solve equations. I really sucked at that part. By extension, the remainder of my scientific career pretty much followed a similar, halting trajectory. It was pretty disheartening, yet I never lost the joy and sense of wonder that I experienced watching new worlds and alternate realities blossom from an equation scribbled on a blackboard (remember those?). It was an experience I would later enjoy scraping through the dense constellation of metaphors in William Carlos William’s masterpiece Patterson (but that’s a whole ‘nother story). 

Sean Carroll’s new book, The Biggest Ideas in the Universe: Space, Time, and Motion (Dutton) distills the magic of the equations-based physics universe and allows his readers to enjoy a rarified view of the world. It fits somewhere in between a college Intro to Physics textbook and a popular science book. His aim is to equip his readers with a solid grasp of the ideas that have shaped modern physics. In order to achieve that goal, he turns to the equations associated with them and explains the way the variables relate to each other and what the various relationships imply. Where popular science books introduce an idea then attempt to illustrate it metaphorically or by example – essentially moving away from the nuts and bolts of the theory – Carroll invites his readers to fall into it. In his words, “we’re not going to teach you how to solve the equations. But you will learn to understand the equations, even ones that are considered relatively advanced by physics-textbook standards. That turns out to be enormously easier.”

While I cannot vouch for anything being easier, it certainly makes working through sections of the book that much more satisfying, not to mention more interesting. Turns out, a little more ammo in the mental arsenal goes a very long way.

The Biggest Ideas in the Universe deals with theories physicists have spent entire careers trying to understand. Luckily, readers aren’t asked to dig that deep. And that’s okay. Carroll is quick to point out that the first step in addressing complex concepts is by simplifying them. That fact, in and of itself, is like some switched the light on in pitch-black room. It solves many a layperson’s mystery regarding how scientists’ work can be so specific at times, yet eventually lead to far-reaching discoveries.

In order to explain the concept, Carroll tells a physics joke referred to as the Spherical Cow: 

A dairy farmer is struggling with milk output at the farm and decides to ask a scientist at the local university for help. For reasons that remain unexplained, they consult with a theoretical physicist. The physicist goes off to do some complicated calculations and returns with an impressive-looking stack of equations. “I’ve solved your problem, I think,” says the physicist. “What is it?” replies the farmer excitedly. “Well, first assume a spherical cow…”

Carroll explains,

It’s an example of a general principle – namely, idealize a difficult problem down to a simple one by ignoring as many complications as you can. Get an answer to the simple problem. Then put the complications back in and calculate how they affect the answer to the simple problem.

It’s gems like this that turn muddles of words, concepts, and formulas into really satisfying a-ha moments.

Unlike textbooks that sort of meander through surveys of topics, ticking boxes along the way to ensure thoroughness, The Biggest Ideas in the Universe works toward a defined goal –  a discussion of black holes. Carroll balances history and scientific theory as he charts the evolution of a given theory. The meat, however, is centered completely in the equation. As Carroll notes in his introduction

Here’s the thing about equations: they are not that scary. They are just a way to compactly summarize a relationship between different quantities. It’s one thing to be told that, according to Einstein’s theory of general relativity, “mass and energy cause spacetime to curve.” It is quite another to be given Einstein’s equation… You can read all the words you like, but until you understand this equation, you won’t really understand Einstein’s theory.

The Biggest Ideas in the Universe starts off simple. It uses the understanding of motion during Aristotelian times as a launch point. It isn’t some random decision either. The comprehension of how bodies move spurred the first law of physics – conservation of momentum. It would lay the groundwork for the line of inquiry that led to the discovery that not only did the planets revolve around the sun but they also followed elliptical paths. 

In explaining the nuances of classical mechanics, The Biggest Ideas in the Universe retreads the Newtonian laws we’re all familiar with. However, Carroll also makes a necessary detour into the field of Hamiltonian mechanics in order to paint a clearer picture of the relationship between velocity and momentum in order to draw an adequate picture of space (not the “thing” with all the planets, stars, and galaxies, rather the “thing” we occupy in relation to other objects). It’s an important concept because, together with time, it forms that special dimension known as spacetime that is central to Albert Einstein’s theories of special and general relativity. 

Einstein’s theory of general relativity sits at the heart of The Biggest Ideas in the Universe. It may actually be the Biggest of the Biggest Ideas so far as Carroll’s book goes. The theory alone has been responsible for the prediction of many phenomena years before they were observed, including black holes, gravitational waves, gravitational lensing, the expansion of the universe, and the different rates clocks run in a gravitational field. Of all of its predictions, the existence of black holes stands out as one of its most profound. 

According to general relativity, whenever the ratio of an object’s mass to its radius becomes sufficiently large, a black hole can form. It physically deforms spacetime. It is a region of spacetime where gravity is so strong that nothing – no particles or even electromagnetic radiation such as light – can escape from it with the boundary of no escape called the event horizon. Although it has a great effect on the fate and circumstances of an object crossing it, it has no locally detectable features according to general relativity. 

Carroll follows the breadcrumbs left by general relativity until he reaches his final destination. Those ominous circular voids countless sci-fi yarns have been spun around. The fact that The Biggest Ideas in the Universe culminates in a chapter on black holes is important because it gets to the core of what makes science science and not a belief system. This elegant equation – – has the ability to accurately make predictions, in this case predicting the existence of something that is beyond the imagination. According to Carroll,

This equation has ended up correctly predicting the evolution of the universe, the existence of black holes, the propagation of gravitational waves, and other phenomena that Einstein had no inkling of at the time. That’s the power of a good scientific theory: it knows much more than the people who first write it down do.

The Biggest Ideas in the Universe asks readers to step out of their comfort zone. With a little bit of trust and smidgen of active reading, the rewards are immense. As a writer and explainer, Carroll instinctively knows when to push, when to relax, and when to provide some much needed encouragement. He gives his readers the opportunity to gain a deeper understanding of physics. While his approach can be challenging at times, it also shows a great deal of faith in his readers’ ability to comprehend complex ideas. It’s the ultimate compliment.

WORDS: Marc Landas.

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