Looking at the night sky we look back in time. The most distant galaxy currently known is 13.2 billion light years away, formed only 480 million years after the Big Bang itself. In the intervening years space itself has expanded and that galaxy is now 41 billion light years distant. So do we live in a universe about 82 billion light years across? Most physicists do not think so. The spatial curvature of the universe is indistinguishable from flat, in which case the universe is most likely spatially infinite. *If* our universe is infinite, then what we can see, including our very selves, will be replicated an infinite number of times. There will be countless copies of you existing right now, forever inaccessible. Welcome to *The Hidden Reality’s *Quilted Multiverse, Brian Greene’s first set of parallel universes, where each “quilt” is an 82 billion light year diameter universe much like our own.

When I first heard this argument I was very skeptical; infinite repetition does not imply *everything *has to happen. After all, the decimal expansion of one third is infinite, but it’s threes all the way down. What makes a difference, however, is quantum theory. In any finite volume there are a very, very large, but still finite number of distinct quantum states. For our visible universe it’s around ten to the power 10^{122}. Once you have more universes than that, repetition is inevitable, there is nowhere else to go. Since there are no magical rules preventing our own universe’s quantum state configuration (after all we’re here, aren’t we?) in an infinite universe, our neighbourhood has to recur, it’s inevitable.

The Quilted Multiverse is rather agnostic about the Big Bang. Current cosmological theories talk about a period of *inflation* at the very beginning. Initially space is assumed to be pervaded with an *inflaton field* which has a non-zero value, and correspondingly vast amounts of potential energy. This situation is inherently unstable and with some probability, at any particular location the field can begin to slide to a lower value, creating an expanding ripple of inflaton field collapse. As it does so, space expands enormously: a region the size of a pea would stretch to larger than the visible universe in 10^{-35 }seconds. In fact the original collapsing volume would only be 10^{-26 }cm across and would weigh about ten grams. In this picture, called *eternal inflation*, the universe is like a gigantic Swiss cheese, the cheese itself being regions where the uncollapsed i field is still driving expansion while the holes are bubble universes, each similar to our own, where the inflaton field has collapsed and its energy has been transformed into galaxies, stars and planets.

You may be sighing in disbelief at all this but there are a couple of things you should know. First of all, the evidence for inflation having occurred is rather good. It explains why the Cosmic Microwave Background (CMB) is so uniform but even more impressively, it explains in a quantitative way the Gaussian fine structure of the CMB. These fine-grained temperature fluctuations are relics of original quantum fluctuations in the inflaton field. Even more strangely, due to the way that collapsing field ripples out from its original source, time is exchanged for space. From the viewpoint of an observer who can see “the whole cheese” a bubble universe is finite; however, from inside such a bubble universe measurements will show it to be flat and spatially infinite. Greene explains this with characteristic clarity and lucidity. So here is our second multiverse, the Inflationary Multiverse consisting of myriads of bubble universes, one of which is our own, embedded within a Swiss cheese space of uncollapsed and still expanding inflaton-field.

Our current best unification of Quantum Theory and General Relativity is String Theory. Many people are familiar with the underlying concepts: elementary particles are not points but tiny strings, their properties encoded in string vibrational modes; to make the equations work, strings live in a ten dimensional space-time, our four large dimensions of space-time plus six extra tiny spatial dimensions, invisibly compactified as Calabi-Yau spaces. In the last ten to fifteen years however, the picture has changed. It was realised that some of those extra dimensions can be large and with size comes inhabitants: branes of 2, 3 or more dimensions. Perhaps our entire universe is a 3-brane-embedded in a higher-dimensional space? We don’t see the extra dimensions because the particles of our world are open strings, with ends anchored on our own brane, all except gravitons, the quanta of gravity. Welcome to the Brane Multiverse, Greene’s third multiverse. Over four chapters he gives a masterly overview of String Theory, its history, present status and contemporary issues. We learn about the Big Bang reconceptualized as Brane collisions possibly implying a Cyclic Multiverse (number 5) and the application of String Theory to Cosmology which leads to the String Landscape of 10^{500} candidate types of bubble universe (number 6).

At this point Greene changes tack as he considers Hugh Everett III’s *Many Worlds Interpretation of Quantum Mechanics*. This is a familiar concept in science fiction (e.g. Brasyl). We think we are familiar with concepts such as observation “splitting worlds” and the like. Greene considers such talk misleading. There’s the math and there’s the interpretation of the math in the world. In the math Everett is conservative. He’s content to let Schrödinger’s wave equation plot the evolution of a particle’s wavefunction through an act of observation. He doesn’t want any smuggling in of collapse-talk. How to explain, therefore, why we see the electron as being exactly *here*, rather than some kind of probability-smear? If the combined electron-observer wavefunction didn’t collapse, then the observer has to be a collection of disparate realities too, that’s just the way it is. Welcome to multiverse number 6.

The Quantum Multiverse appeals to many physicists who have come to accept the dictum ‘just believe in the math’. It’s not without its problems though. The main challenge is how to recover the probabilistic interpretation of the squared wavefunction amplitude. If everything possible happens, how do we get that some outcomes are enormously more likely than others? It’s still a work in progress.

Having climbed the foothills, Greene now contemplates one of the hardest conceptual problems of contemporary physics, the so-called Holographic Multiverse. You may have heard that the maximum amount of information that can be stored in a volume is proportional not to the volume but to the enclosing surface area. You may even have heard rumors that everything we do in this universe is a pale shadow of something happening way out on some far surface. Confused? Then this is the chapter for you but be warned, even Brian Greene’s legendary intelligence and clarity of thought can’t penetrate the fundamental obscurities in this area.

Greene starts with a good story about Black Hole entropy and then goes for the AdS/CFT correspondence. This has been an exciting and high profile topic of contemporary physics research since Juan Maldacena showed that a ten dimensional string theory (including gravity) defined within a bulk was exactly equivalent (i.e. dual) to a four dimensional (and quite well understood) quantum field theory (QFT), without gravity, defined on its surface. For example, black holes modelled by string theory in the bulk were equivalent to clouds of hot gas modelled by QFT on the surface. Suddenly hard computations could be replaced by equivalent calculations which were easy. So here is the Holographic Multiverse, number 7, a parallel surface universe corresponding to our bulk one. Except: is this meant to be real or is it just the way the math works out? Nobody knows.

Another change of tack for the next multiverse. In 1964 I first encountered Daniel F. Galouye’s Counterfeit World. In this novel the hero gradually comes to realize he lives in a simulation. Towards the end, by great ingenuity, he manages to bootstrap himself up a level to the world which developed the simulation. He now asks himself: “Is this it, or is this world too a simulation?”. How could you ever tell? The Simulated Multiverse, number 8, isn’t really physics per se. *Any* physical laws which permit a simulation to work could be programmed. Greene talks a little about discrete vs. continuum models of space-time, and about how much computing power is really needed. It’s entertaining and probably more familiar to most readers than the hard science. Oh, and Greene does not think he lives in a simulation. Incidentally, pursuing the logic of universe-simulation to its ultimate end leads to Dust Theory (not discussed in *The Hidden Reality*), memorably described in Greg Egan’s Permutation City.

The final piece of the puzzle, the Ultimate Multiverse (number 9) explores a principle Greene learned from his philosophy tutor, the *principle of fecundity*. We give up on the worry as to what makes our own universe special, or even “why there is something rather than nothing” (Leibniz). *Every *mathematically-consistent universe actually exists “somewhere”. It is possible that there are only two people who believe in the Ultimate Multiverse: one was Professor Robert Nozick, Greene’s philosophy tutor; the other is MIT’s Max Tegmark.

The Hidden Reality is a first class tour around the state-of-the-art in theoretical physics. Greene is incredibly smart and totally on top of his material – he has something fresh and insightful to say about pretty much everything, and he never talks down to the reader. You are assumed intelligent and interested, and he will do the rest. Much more material is covered than I have reviewed above. He has a lengthy discussion about the controversies surrounding String Theory, which he describes as “speculative”; he treats the “anthropic principle” in depth; his coverage of the cosmological constant, dark energy and the expansion of the universe is a model of clarity. His greatest achievement, however, is that as you turn the last pages you have the illusion that, at least at the level of the big ideas, *you too understand this stuff*.