Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by Max Tegmark, Allen Lane, RRP£25 / Knopf RRP$30, 432 pages

As recently as the 1990s, most scientists regarded the idea of multiple universes as wild speculation too far out on the fringe to be worth serious discussion. Indeed, in 1998, Max Tegmark, then an up-and-coming young cosmologist at Princeton, received an email from a senior colleague warning him off multiverse research: “Your crackpot papers are not helping you,” it said.

Needless to say, Tegmark persisted in exploring the multiverse as a window on “the ultimate nature of reality”, while making sure also to work on subjects in mainstream cosmology as camouflage for his real enthusiasm. Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone. Now a physics professor at Massachusetts Institute of Technology, he presents his multiverse work to the public in Our Mathematical Universe.

Other cosmologists, such as Brian Greene and John Barrow, have also published good books recently arguing that our universe – the region of space born in the Big Bang 13.8bn years ago – is one of an infinite collection of universes that has existed and will exist for ever. What makes this book stand out is the way Tegmark weaves his own life, from Swedish childhood to American academic celebrity, through the complex mathematics.

Physics could do with more characters like Tegmark. He combines an imaginative intellect and a charismatic presence with a determination to promote his subject – and himself. One story shows how keen Tegmark was to make his mark on arrival as a research student at the University of California, Berkeley. To his horror, he discovered that his then-surname, Shapiro, unusual in Sweden, was “about as unique in international academia as Andersson had been back home”. So, before publishing his first paper, he adopted his mother’s maiden name, Tegmark.

To grasp the four levels of multiverse that make an appearance in Our Mathematical Universe, we need at least a rudimentary understanding of two key underlying concepts: “cosmic inflation” and quantum theory. Inflation is the idea that, an infinitesimal fraction of a second after the Big Bang, space expanded at an exponential rate – sowing the seeds of everything astronomers can observe today. In our region of space, inflation soon stopped but Tegmark argues that elsewhere it continues indefinitely, creating an infinite cosmos with exactly the same physical laws as ours: the Level I multiverse. Everything that is happening now in our universe, like you reading this article, is mirrored in an infinite number of other Level I universes.

The Level II multiverse consists of universes with laws of physics that share the same mathematical framework as ours but have different values for the various fundamental particles and forces. Level III is quite distinct. It is based on the “many worlds” interpretation of quantum mechanics, in which reality is constantly splitting into an unimaginably large number of directions because anything that is physically possible takes place and leads to a new parallel universe.

Level IV is even harder to grasp. Tegmark believes that the multiverse is ultimately a mathematical structure, which can adopt an infinite number of different mathematical forms corresponding to different fundamental laws of physics. In his words: “We’re on a planet in a galaxy in a universe that I think is in a doppelgänger-laden Level I multiverse in a more diverse Level II multiverse in a quantum-mechanical Level III multiverse in a Level IV multiverse of all mathematical structures.”

Although only a physicist or mathematician is likely to understand everything in Our Mathematical Universe, enough will be comprehensible for non-scientific readers to enjoy an amazing ride through the rich landscape of contemporary cosmology. There are many interesting diversions from the main argument, from an assessment of threats to human civilisation (such as a 30 per cent risk of nuclear war) to the chance of intelligent life elsewhere in our galaxy (lower than astrobiologists like to think). Written in a lively and slightly quirky style, it should engage any reader interested in the infinite variety of nature.

Clive Cookson is the FT’s science editor

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