Sean Carroll's books decode the universe, blending physics with maths

Sean Carroll challenges the idea that math is not for everyone. In two volumes, he presents physics for amateurs with a touch of math that promises to become pop science classics

The Biggest Ideas in the Universe (Two volumes)

1.   Space Time and Motion

2.   Quanta and Fields

Author: Sean Carroll

Publisher: Harper Collins

Pages: 304 

Price: Rs 450 & Rs 499

 

The physicist Sean Carroll has embarked on an ambitious experiment with a trilogy that discusses the “Biggest Ideas”. Two volumes have been published and both promise to become pop science classics. They bridge an important gap.

 

Physics used to be called Natural Philosophy back in the day because it offers models of natural processes. However, the laws of physics are expressed as beautiful but complex mathematical equations. Some of us love these equations while being aware that it can be hard work to understand them. Yet, when Stephen Hawking was writing A Brief History of Time, he was famously told his readership would halve with every equation, because many otherwise intelligent readers are afraid of maths.

 

Dr Carroll challenges that truism head-on. This series presents physics for “amateurs” with an appropriate leavening of mathematics. The books assume the reader would have some high-school mathematics — enough to follow and understand the physics.

 

Of necessity, such an approach cannot be rigorous because that would take it into textbook territory with the supplying of proofs of whys and wherefores. A textbook would also present hundreds of problems. These books don’t. But the author doesn’t ignore the conceptual underpinnings of the equations of physics. So, he threads a very narrow path, where he produces the equations and coherent explanations of their underlying realities, without delving into the precursor maths. For example, Carroll doesn’t state the rules of differentiation, or integration, or complex numbers and vector algebra. But he does use the relevant equations and explains the specifics of the derivation of momentum, how differential equations work, and the laws of motion.

 

It’s an interesting approach that may require some suspension of disbelief from readers who aren’t conversant with the maths. Also let it be said upfront that some of the maths runs well beyond the high school curriculum. However, the algebra and the calculus is accompanied with excellent diagrams that clearly illustrate the physical processes these equations describe. The books are a delightful walk down memory lane for those readers who do know some physics and maths. Half-forgotten equations trigger memories, and the prose explanations are superb. Dr Carroll wears his erudition lightly and he has a rare gift for the lucid, easy explanations of complexities. He often points out something new about a topic which you thought you had mastered. For example, I had never realised the connection between gravity’s inverse-square law and the dimensionality of space.

 

The attraction of gravity diminishes in proportion to the square of the distance between two objects — if the distance is doubled, the gravitational attraction between these two objects drops to a quarter. The law is inverse-square because space is three dimensional and the surface area of a three dimensional sphere is two dimensional. I knew the inverse square laws (there are others). I knew the formulae for the volume and area of a sphere. I even knew how Newton worked out the inverse square law of gravity by studying Kepler’s Laws of Planetary Motion. But I had never put that information together, and I had never seen this detail pointed out. Another brilliant section in Book One compares the Newtonian approach to the Lagrangian and the Hamiltonian, showing how different world views can be useful even when they lead to equivalent equations.

 

The book often uses humour as a tool. For example, Dr Carroll cites the example of the physicist who tries to improve the milk yield on a dairy farm by assuming the cows are perfectly spherical! This is a great example of how physics sometimes solves problems by making absurd assumptions.

 

Humour and maths apart, the prose is of truly extraordinary quality. The books convey the wonder and the magic of the universe and the big ideas which help us to model it. While book one deals with macroscopic big ideas, book two deals with tiny big ideas. Space time, relativity and other cosmic matters are explored in Book One. While those involve complicated concepts, the mathematics is relatively easy to understand. Also, the average human can mentally relate to balls spinning around under the influence of gravity. Book Two moves into the realm of the quantum, of particles that are waves, and the exoticism of field theory. This is truly weird territory. Many pioneers — Einstein and Schrodinger among them— had trouble accepting the conclusions their own theories threw up. Nobody would believe quantum theory except for the fact that it has been verified experimentally and is foundational to modern technology. The maths is also a little more exotic in book two. But once again, the diagrams help.

 

So the books work for somebody who did study physics and maths, and they can be used as a fun refresher course by the reader who last looked at a physics textbook a few decades ago. They will also work for the young school-goer fascinated by science.

 

How should a reader who doesn’t have the requisite maths, or the curiosity of a bright teenager, approach these books? Treating the mathematics as a combination of interesting hieroglyphics interspersed with comprehensible diagrams. A superficial understanding of mathematics will help you get a feel for the physics. If you absolutely don’t understand the maths, just look at the diagrams, and read the text. You’ll still get the physics!  I look forward to Book Three (Complexity and Emergence) with great expectations.