The Infinity Puzzle
Author: Frank Close
Publisher: Oxford University Press
Pages: 416
ISBN: 978-0199593507
Aimed at: Technically minded general readers
Rating: 4.5
Pros: Enjoyable and thought-provoking read
Cons: Sometime long-winded, could benefit from a good edit
Reviewed by: Mike James

With the subtitle "How the quest to understand quantum field theory led to extraordinary science, high politics, and the world's most expensive experiment" this sounds like excellent light reading.


The best theory we have at the moment is Quantum Field Theory (QFT), in the sense that it actually produces results of amazing accuracy. If you have any interest in physics then understanding it is a big challenge and a huge desire. It is a very big subject and full of all sorts of mathematical difficulties, not least of which are fields comprised of operators and the infinities that result when you try and work out series approximations. At one level you can rationalize the infinities with the idea that the theory attempts to describe point particles, which are probably a nonsense, but there still remains a nagging doubt about the validity of the renormalization procedures.



Physicist Frank Close has managed to write a book that goes well beyond the sort of glossy books for the lay person that don't actually tell you a thing. As a result, while there are no equations in the book, the ideas presented are quite tough. If, however, you have studied an introduction to QFT then you will find it illuminating. In particular, you will understand the importance of the Higgs boson. It is often described as being the source of mass but its real importance is that it provides a way to give mass to the bosons that arise in gauge theories. Without the Higgs we have to find another way to make the field theories fit the facts and the standard model doesn't look so complete.

The book is an examination of the history of QFT and the experimental side of how it was tested. It goes over the events of the early days right up to today and the LHC. The story is mostly told in terms of the people involved and you get the impression that the author really was there - of course he was. However, the names are often difficult to keep in your head and as a result there is a lot of repetition designed to help you follow. Just occasionally you think "oh no - not again".

There is also a lot of emphasis on who did or who did not get the Noble prize and in particular on whether Abdus Salam deserved it. Personally I found this a little excessive and soul searching - it simply gets in the way of the science and the story of how it was all created. You do get the feeling that science isn't all co-operation with one person borrowing ideas from another without giving credit. It all makes you wonder how progress is ever made with people so paranoid about losing their ideas by careless talk.

There is a similar digression into the naming of the Higgs - should it be called this given the number of people who worked on the idea. The emphasis that the boson should be named after Peter Higgs, because he was the first to state that there would be a boson associated with the field, is a little weak - as particles are always associated with fields. Again I personally grew bored with the long arguments trying to tease out who did what and hence whether it was or was not justified to call the particle the Higgs boson. I would have been much more interested in a discussion of the theory, or even the need to introduce yet another field just to give the boson's mass.

It is worth saying that most of the book is about the invention of the electroweak model and the way that Yang-Mills theories were finally made to work in this context. The author spends a lot of time explaining symmetry breaking, without really getting it over well to even a technical audience. and yet makes no attempt to explain why Yang-Mills theories, which involve local symmetry breaking, and are just as interesting. Perhaps such "gauge" theories are just too well established to be interesting.

Of course there are many insights into what it was like to do science at the time and in particular the primitive state of computing. For example, back in 1963 Martin Veltman decided to use computer algebra to simplify working with the series expansions that are so much part of QFT to try to demonstrate that Yang-Mills theories were renormalizable:

Veltman became interested. However, when he tried to extend Lee's calculations he quickly encountered difficulties. The algebra had "up to 50,000 terms"

... to solve this Veltman pioneered algebraic calculations by computer.

...It looks crazy, adding this weird particle without spin or charge, but I'll take these equations and put them in my computer to see what happens...


Yes, there was no Mathematica back then and yet you can't help wonder why there wasn't more use of programs to compute such horrible expansions.

Not only wasn't there Mathematica there wasn't an internet which made for some interesting problems:

..All his program codes were on the computer at CERN in Geneva. In those days there was no he had to go to Switzerland himself to do the calculations.

Perhaps now it makes more sense that the Web originated in CERN.

There were also some other interesting facts that I had failed to notice from other reading. Perhaps the most worrying is that the renormalizability of Yang-Mills theory with massive bosons has still only been proved using the integral formulation of QM. The algebraic problems inherent in the "canonical formulation" appear to be too great to solve even today. Given that the path integral approach has mathematical difficulties and interpretational difficulties all of its own, this is a little disturbing.

So should you read the book?

Yes, if only to encourage other scientists to write more technical texts aimed at the non-specialist reader. However, if you have no idea what physics is about then my guess is that you just won't get what the book is talking about. Indeed even if you do know a lot of physics, and QFT in particular, what you take away from the book with vary according to what ideas you already understand well. It is a very good book, but very flawed in terms of its role as a polished biography and history of the events. It would benefit from some heavy editing.

For me the one big change in my thinking is that I now see why the Higgs is important for the theory, whereas before I'd believed is was something grafted onto the main structure of QFT and not really that important.

Buy the book, but don't expect to understand all of it and there will be parts that you just have to skip for one reason or another, but it is a very welcome addition to the physics literature.



Expert Performance Indexing in Azure SQL and SQL Server 2022

Author: Edward Pollack & Jason Strate
Publisher: Apress
Pages: 659
ISBN: 9781484292143
Print: 1484292146
Kindle: B0BSWH65ST
Audience: DBAs & SQL devs
Rating: 4 or 1 (see review)
Reviewer: Ian Stirk 

This book discusses indexes, a primary means of improving performance in SQL Server, how does  [ ... ]

Foundational Python For Data Science

Author: Kennedy Behrman
Publisher: Pearson
ISBN: 978-0136624356
Print: 0136624359
Kindle: B095Y6G2QV
Audience: Data scientists
Rating: 4.5
Reviewer: Kay Ewbank

This book sets out to be a simple introduction to Python, specifically how to use it to work with data.

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Last Updated ( Friday, 09 March 2012 )