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The Biggest Ideas in the Universe: Space, Time and Motion - Sean Carroll *****

In the brilliant Yes Minister/Yes Prime Minister TV series, an idea would be described as bold or brave it was stupid or career wrecking. In The Biggest Ideas in the Universe, Sean Carroll has done something extremely bold and brave. But - for the right audience (and we'll come back to that) - it is absolutely brilliant. A quick aside about the unwieldy title: this is the first entry in the 'Biggest Ideas' trilogy with two more to follow.

There are two broad ways to write about physics. You can take the popular science approach which is descriptive, gives context and, if done well, makes it possible to a good idea of what the science is about without bumping against the maths. Or you can write a textbook, which builds on a foundation of heavy duty mathematics. This will describe what physics is really about, but will be impenetrable to anyone without an appropriate degree. (And often exceedingly dull too.) Carroll has built a bridge between the two - something I thought was impossible until now.

Famously, Stephen Hawking was told that the audience for a book halved with every equation that was included. If this is really true, Carroll has a problem, because his book contains plenty of them. Starting simply with conservation and introducing the first equation in the definition of momentum, Carroll builds surprisingly rapidly. Not only does he approach change and dynamics using conventional analysis approaches, he also introduces Hamiltonians and Lagrangians (and, of course, partial differentials) when you are less than a third of the way through the book. By the end we've got both the special and general theories of relativity under our belt and have dealt with matrices, tensors and more.

This is astonishing - Carroll doesn't just throw in equations and loosely explain them, he gives quite detailed descriptions of where they've come from and how they are used. What we don't get, which a textbook would do, is any attempt to solve these equations or expect the reader to do anything too strenuous with them, but the amount of detail is remarkable.

Does it all work? No - almost inevitably. I have seen, for example, more approachable descriptions of the principle of least action, starting with the Baywatch Principle and least time, rather than plunging straight into least action. Yet, for the right audience (and we're nearly there), it is rarely the case that the reader is left bewildered. Carroll builds everything impressively in a way that is quite different from anything I've ever seen before.

So, the audience thing. Carroll says about equations 'they are not that scary.' He tells us he dreams of a world where 'as kids are running around at a birthday party, one parent says "I don't see why anyone thinks there should be new particles near the electroweak scale," and another immediately replies "Then how in the world are you going to address the hierarchy problem?"' I'm sorry, Sean, but dream on. It's not going to happen. There are two big problems here for a truly general audience.

One is that I think Carroll totally underestimates the depth of many people's struggle with maths. It's not so much that equations are scary for those who say they don't like maths as that they repel readers without any information going into the brain. I don't think Carroll's beautiful build of the maths underlying physics will help such people at all. The other problem is that it would be possible to absorb everything in this book and you still wouldn't get the kind of conversation Carroll envisages - getting a better understanding of how physicists do their work will not allow you to go beyond what you've learned to pose those kind of questions.

A while ago I was listening to Mark Kermode and Simon Mayo's film podcast. They had asked for a simple physics explanation of multiverses. These aren't stupid people. Yet the point at which they wen't into 'This is too complicated, it's beyond me' was when the physicist said something like 'When you think of a quantum particle like an electron'. Their minds had already blanked out. Does anyone really think that such people, intelligent but not science-oriented, would ever come round to Carroll's way of thinking? 

I see the audience of this book as twofold. For people like me who have a decades old physics degree to get some nostalgic reminder of what I once knew, and for young people who are about to go to university to study physics to get a wonderful introduction to what lies beneath the mathematical slog they are about to go through and why it's all worthwhile. Any idea this will convert people who aren't already excited by physics, I'm afraid, is fantasy. But for the right people, this book is magnificent.

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Review by Brian Clegg - See all of Brian's online articles or subscribe to a weekly digest for free here
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