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Book review

Our Mathematical Universe

My Quest for the Ultimate Nature of Reality

by Max Tegmark

I found this a thoroughly entertaining account by Max Tegmark of some of the “big questions” of modern physics, with a particular slant towards cosmology – what is our universe composed of, how did it come into being, what might be its ultimate fate, that kind of thing. Initially I wasn’t sure about the very personal style in which it was written, but after a few chapters I began to like it. Tegmark has been at the forefront of a number of these discoveries, and there are lots of semi-autobiographical anecdotes in here: ultimately, the cheerful and enthusiastic style did win me over, and I found it definitely added to my enjoyment of the book.

I realised as I was reading this that I haven’t really read a popular science account of these topics for perhaps 20 years, so I was definitely behind the curve with regard to things like dark matter and dark energy, and their abundance in the universe (making up something like 20% and 70% of all the stuff out there, respectively). This was a great account of all these theories, working through the evidence in particular from the cosmic microwave background, which has yielded two different Nobel physics prizes.

Tegmark moves the reader through all this at the same time as he elucidates his view of how it all comes together with quantum mechanics. I was pleased here to see the increasing acceptance by physicists of Everett’s “many worlds” interpretation of quantum mechanics, and how it’s taken over from the more historically popular Copenhagen interpretation, with its reliance on the horribly ill-defined “observer” causing a collapse of the quantum wave function. To the very limited degree that I’ve ever managed to get my head around quantum mechanics, it’s always seemed a complete fudge to say “these equations describe the universe as we know it to thirteen decimal places, but I don’t really like what they say about the nature of reality, so I’m just going to paper it over with this observer thing and then I’ll feel more comfortable”!

At this point, Tegmark starts to roll out the big guns of his theory. Not only are there multiple physically separate universes (because the initial expansion phase was so fast that light will never be able to travel from one to another), but also these universes will have different starting conditions. This provides an explanation as to why our universe is so “well tuned” for life – there are 30 or so physical constants whose values would only need to vary by a very small amount to have prevented life ever existing. Well that’s straightforward in this view- those other variations are just in other universes (inaccessible to our light cone). And quantum mechanics now says that physical reality also has other places where the alternate paths of quantum interactions are playing out – in some of these parallel worlds, Schrodinger’s famous cat is alive, in others it’s dead, and that’s all ok (unless perhaps you are the cat!)

Ultimately, Tegmark comes to argue that in fact these different worlds may not only have different starting conditions, but also entirely different laws. Not just (for example) different numbers of space or time dimensions, which is weird enough, but different kinds of physical existences. All our physical laws, he argues, are the result of mathematical symmetries – all the different kinds of particles (quarks, photons, etc) are predicted by symmetries in group theory, for example. Thus there will be other universes with other symmetries, based on other groups. An overwhelming number of these will be too simple to do anything very interesting, but some of them will be complex – perhaps complex enough to form other kinds of particles, and indeed other kinds of life, too strange to even imagine!

Since I recently read Group Theory and Physics, I was pleasantly surprised by how much I sympathised with Tegmark’s thesis here. It’s even reflected in science fiction in books like Distress, which again I read recently, and which is about how a “theory of everything” might decide which universe (which mathematical symmetries) we really live in. I’m obviously being swept up in a wave of theories and stories all about this – perhaps the cosmos really is trying to tell me something!?

Ultimately, these kinds of questions about the underlying nature of reality are profound, and perhaps even beyond our real knowing, but they’re great fun to think about, and Max Tegmark is exactly the sort of person who you’d want to be sat beside in the pub while you explored it all. This book is as close as I’m ever going to get to that, and I thoroughly enjoyed the opportunity.

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