The Lazy Universe: An Introduction to the Principle of Least Action

by Jennifer Coopersmith

This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired.

The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

Genres: Physics, Science, Stem, Nonfiction, Mathematics

280 pages, Hardcover

Published July 11, 2017

About the author

Jennifer Coopersmith took her PhD in nuclear physics from the University of London, and was later a research fellow at TRIUMF, University of British Columbia. She was for many years an associate lecturer for the Open University (London and Oxford) honing her skills at answering those 'damn-fool profound and difficult questions' that students ask.

Reviews

[Wendelle · Rating 5 out of 5]

what a splendid book. it is a great prototype of the ideal popular science book, one that actually seeks to explain the physics rather than list the history of physics through the life of famous figures like Einstein or Oppenheimer then regurgitate another inexact analogy about spacetime and blackholes copied from the plethora of such substandard popular science books on the market. it explains the significance of the Principle of Least Action in mechanics and derives and examines slowly and in-depth the core principles of Lagrangian Mechanics. It is good even for Physics students who want to understand the import of and guiding reasons for Lagrangian and Hamiltonian Mechanics beyond the calculational methods they learn to apply in school. it is wordier than some mathematically powerful students may find patience for, and later chapters like Lagrangian and Hamiltonian Mechanics dovetail closely in scope and order with books like Landau's Mechanics so people may find that redundant, but personally this style suited me perfectly.

[Myat Thura Aung · Rating 3 out of 5]

Oh boi, I couldn't finish Chapter 7 (Hamiltonian Mechanics) and related appendices. It's not math that gets in the way tho. It's the concept. And this book is definitely not for those who don't know college-level math. The subject matter is something that needs calculus of variations to be rigorously explained. But the book doesn't require the reader to have learnt calculus of variations. (I haven't learnt it either.) It suffices that we know ordinary calculus (integration, partial differentiation, etc.)

I think the book is splendid except that it is difficult to read (for the likes of us). The subject matter is a hidden gem of theoretical physics. Seriously, it's one of the most important topics but sadly, there are quite a few books about it in popular science literature. No wonder some call this book a rare gem.

[Alexander Miles · Rating 4 out of 5]

I don't usually read a lot of technical books these days, but this one get recommended to me ages ago. I wish I could remember who did that. The book covers the history and development of the Principal of Least Action, starting all the way back with d'Alembert in the 1750s, and tracing each step as it was expanded and re-envisioned to encompass not just statics, but dynamics, and eventually quantum mechanics. There are appendices with worked examples, but the emphasis is on the philosophy and history of the principle - why the approach works rather than how to turn the crank. Cornelius Lanczos's The Variational Principles of Mechanics gets brought up again and again; it seems much of the meat of the book is an effort to make Lanczos' work more accessible. It was interesting seeing how long it took for various leaps in understanding to occur, even something as simple as using time as a parameter of physical systems came far later in the development of physics than I would've imagined.

I had a chance to take courses on Lagrangian and Hamiltonian mechanics during my graduate work, but passed it up to focus on research. This book was my first exposure to those ideas, and the author did a great job pointing out where Newtonian physics falls short and how these 20th century approaches succeed. That said, while I can now claim to be familiar with the concepts and (surprisingly straightforward) equations, it wasn't as in-depth as an actual course where I would need to fight through numerous exercises and corner-cases. The actual prose was a bit stilted at times, but overall an engagingly written book on a topic that takes some chewing to wrap one's head around. I'd recommend this book to anyone looking to expand their understanding of how 19th century physics found it's path into the 20th century.

[Orchasi · Rating 5 out of 5]

if you're someone with questions "how Hamiltonian entered into QM", "why not Lagrangian", "why D'alembert's is true", "Stationary Action vs Least Action" I bet you'll not be disappointed.

"we have done considerable mountain climbing. Now we are in the rarefied atmosphere of theories of excessive beauty.." Lanczos

"I cannot take it anymore better I faint." (myself after reading)

Absolute, Coopersmith did a great Tribute to Lanczos.

First 3 chapters maybe 4 will be readable for anyone and it's really the most interesting piece of historical physics I ever read (thought I would never say that but here I am) but the most elegant part was the structured flow of information, (D'alembert -> Lagrangian -> Hamiltonian) I would recommend having prior outline of variational mechanics, it really helps to point out the beauty (mechanical ray, mechanical optics) which were being missed (for someone like me!) a part of me is feeling guilty that I acquired these easily,

I still couldn't say I grasped all the information but it really made sense how variational mechanics were developed, and If I have started with this instead of Newtonian (which I feel uneasy even now) my view towards physics would have been much more interesting.

I'll happily recommend to anyone who's interested in physical sciences (which I did already) and I will always pick variational mechanicas over QM, relativity...

[Mike Lisanke · Rating 2 out of 5]

I'd give this book a lower rating but it wasn't poorly written. There Are well written chapters with end notes and lots of references. But, the book that's 200+ pages has a title that implies it'll be explaining Why the Universe is Lazy and seeks to minimize action. This book's author does the prototypical mathematically hand-waving. It'd be a good textbook on mechanics if it was a textbook and didn't wonder between explanation and history of the useful math it could be teaching. But clearly that was not the author's intention. We can never answer whether an author intends to obscure her subject with verbose mathematics just to hide that there is No Explanation. We gain a serious sense of that the author simply believes in 4D space and that traveling in 'straight lines' in curve space explains orbits optics and all EMF and all sorts of useful macro mechanics But that she's willingly dismissive of discussing Mach's Principle means the motivation of Inertia is not on the table. There's no deep physics to learn here and it you want to understand the math, go to a textbook. IMO this should be a pass for most readers.

[Rob · Rating 5 out of 5]

There is nothing quite like this book. It serves as a beautifully written overview of the history and philosophy of classical mechanics (Newtonian, Lagrangian, Hamiltonian, etc) but with a very healthy serve of mathematics and deeper technical insight. It is not really a popular book and not really a textbook. Which makes it perfect if you’re a curious-minded reader who wants to dive deeper than the usual popular treatments and you are comfortable enough to navigate some math (nothing more demanding than basic calculus). I wish there were more books like this!

A step up (in mathematical rigour and depth) from this book would be Jakob Scwichtenberg’s No Nonsense Classical Mechanics. A step down would be Sean Caroll’s Biggest Ideas in the Universe Vol 1 (much broader in scope than this book). Both I highly recommend.

[William Schram · Rating 5 out of 5]

The Lazy Universe goes into the Principle of Least Action. From what I understand, it allows you to cut out the unnecessary portions of equations and reconfigure them to only deal with the energies. Please excuse my gross oversimplification.

The book discusses the Hamiltonian, the Lagrangian, and several other ideas. It is condensed enough to read quickly, but it contains some advanced ideas, too. The main reason it took me so long was my reading environment wasn’t conducive to reading.

I never took Advanced physics, so I had no introduction to any mathematics needed to understand the subject. Learning on your own is perilous.

All in all, this book is amazing. It contains worked examples and is lucidly explained. Thanks for reading my review, and see you next time.

[Ryan · Rating 3 out of 5]

The reading would have been much more enjoyable and comprehensible if I had a deeper background in mathematical physics. A layman could glean some insight from the book, but I would recommend obtaining some proficiency in the actual mathematics required to tackle the examples in the appendices. This book would be a "cherry on top" for those who already have the basics covered; it provides a deeper philosophical understanding for the principle of least action.

[MarkusQ · Rating 3 out of 5]

Good, albeit repetitive and sloppily edited. Basically an homage to Lanczos's textbook (which the author admits up front) that follows the "tell them what you're going to tell them, tell them, tell them what you told them" pattern to a fault.

[Harry Blinks · Rating 5 out of 5]

A great book for someone starting out with variational mechanics, Lagrangians, Hamilton's principle etc. Use it alongside other, more rigorous books - not on it's own - and it will help to improve your general understanding of what you are trying to learn.

[Kris · Rating 4 out of 5]

Gives an intro to principle of least action: a math view of Physics. Good if one has background on linear algebra and functional analysis

[Jalaluddin Abdullah · Rating 5 out of 5]

"Inspired by the monumental work of Lanczos, the author has constructed a beautiful exposition of the philosophical basis underlying classical mechanics. It has enough technical meat to be interesting to an expert, while accessible to a novice." - Gerald Jay Sussman, Massachusetts Institute of Technology.