The lazy universe

Jennifer Coopersmith

Why I looked at this book

Newtonian physics is fairly intuitive: there are forces which cause things to move the way they do. But this behaviour can also be framed in terms of the principle of least action. To me this seems a bit weird: it's as if particles were intentionally trying to economise on the use of certain stuff. Given that it's such a powerful principle should the teaching of physics include it from the start, or should it begin with ideas which are more intuitively grasped? I'm looking to this book to discuss such issues and help me better understand the principle of least action.

First impressions

In the first chapter Coopersmith lists the advantages of the principle of least action. One that I find important is the ability to link together different viewpoints. For instance the underlying models in Newtonian gravity and General Relativity look totally different, but in many situations their predictions are very similar. I'm hoping that least action may help to show their similarities.

This book is dedicated to Cornelius Lanczos, and is based on his textbook The Variational Principles of Mechanics, the idea being that Coopersmith offers a more accessible explanation of the concepts. I realised, though, that she is the author of Energy, the subtle concept, which I found a bit intimidating when I started to read it. This book seems a bit wordy at times, but I'm hoping that it is easier to get into, although I wouldn't say that it was written as a 'popular' book. I'll have to see how it turns out. Maybe I'll look at Lanczos' textbook to check how much this book makes the concepts easier to understand.

Main review

In the introduction Coopersmith compares physics to the beautiful garden in Alice in Wonderland that Alice so wanted to enter. To wander in the garden requires a knowledge of mathematics, but maybe without mathematics we could look through the keyhole. The implication is that this book is written to give the reader such a look. The trouble is that the book doesn't live up to this. It does in fact contain some pretty difficult mathematics, and early on there is a chapter on mathematical foundations to prepare the reader for the rest of the book. But I felt that even that seemed to introduce difficult concepts without sufficient explanation.

To my mind the book is more suited to those who are studying the principle of least action and would like to get a wideer viewpoint regarding it's different forms an applications. The book examines the historical antecedents of the principle and explains how it gave rise to Lagrangian and Hamiltonian mechanics. There is also a look at the Hamilton-Jacobi principle, progressing to the links between particle mechanics and the motion of a wavefront.

At one point in the book there was the suggestion that the principle might be applied to less mathematical systems, such as a guinea pig eating a biscuit. This wasn't really expanded upon though, which I thought was a pity as I would have liked more discussion on how the least action principle might be applied more generally (for instance in economics).

In summary, I think the book might be suited to those studying physics at an undergraduate level, (rather than the postgraduate level of Lanczos' book), but it is clearly not aimed at a 'popular science' readership.