Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by Max Tegmark

Max Tegmark is a leading proponent of the idea of the multiverse, a concept familiar to many as the “parallel worlds” of science fiction, but also one taken increasingly seriously by sober scientific theorists. Several variations on the theme tell us that there must be an infinite number of versions of our Universe (capital “U”), other universes (small “u”), some indistinguishable from our own, some with minor differences, many with significant differences, and all separated from us in space and/or time. But Tegmark, a professor of physics at the Massachusetts Institute of Technology, is careful to not frighten his readers by making such seemingly outrageous claims at the start of this book. Instead, he leads us gently by the hand through the traditional story of our place in the Universe, from the Sun and Solar System outwards, before wading into deeper waters.

Even this familiar story is enlivened by the author’s personal touch, with anecdotes from his childhood and early life in research. So by the time he gets to the tricky bit, he feels like an old and trustworthy friend. This is just as well, because things get very tricky indeed.

The first step into deep water is the easiest. If space is infinite, our visible Universe can be regarded as a bubble within that infinite space, analogous to the bubble of visibility surrounding a person walking through a fog. It is possible to calculate the number of particles (neutrons, protons and the like) in that bubble, and to calculate the number of ways they could be arranged. This is an enormous number but, crucially, it is not infinite. So in infinite space, there must be other bubbles – other universes – with exactly the same arrangement of particles as in our Universe. This is the Type I multiverse, and it is almost common sense.

The Type II multiverse is only slightly more complicated. It takes on board the currently favoured idea of inflation, which explains the present appearance of our Universe as resulting from an epoch of very rapid expansion at the time of the Big Bang. Each universe is an inflating bubble within some kind of superspace. But it is the Type III multiverse that is familiar from science fiction.

This is where quantum physics comes into the story, with Schrödinger’s famous “dead and alive cat” and the idea that every time the world is faced with a choice of possibilities at the quantum level it splits to allow all possible developments. In fact, no “splitting” is required, and it is equally valid, as Schrödinger himself pointed out, to think of all quantum possibilities existing alongside each other “all the time”, whatever that means in this context.

Let me spell that out. In the famous thought experiment, a (purely hypothetical) cat is trapped in a box with a quantum device that ensures that it has a 50:50 chance of being dead or alive. When the box is opened, one possibility is realised. The “splitting” idea says that, at that moment, the Universe divides in two, one universe with a dead cat and one with a live cat. The “parallel” idea says that there are always two universes, each initially with a cat in the same situation, in one of which the cat dies while in the other it lives, with no splitting involved. “Parallel universes,” Tegmark says, “are not a theory, but a prediction of certain theories.”

All of this is allowed – some would say required – by the known laws of physics, or as Tegmark prefers, the known laws of mathematics. As Galileo said, nature is “a book written in the language of mathematics”. But Tegmark isn’t finished yet. He goes on (further than would most physicists) to consider the Type IV multiverse, in which different universes are governed by different laws of mathematics. This leads on to speculation about the nature of reality and our place in it, the future of life and the future of the Universe. All a far cry from early chapters on our place in the Universe, and discussion of the sizes of planets and stars, but somehow a natural development, thanks to Tegmark’s gift for storytelling, from those beginnings. As he says, “physics is the ultimate intellectual adventure”; this is a great place to join in that adventure.