Brian Greene is Professor of Mathematics and Physics at Columbia University and one of the leading workers on string theory, which he outlined to a general audience is his two earlier books; The Fabric of the Cosmos and The Elegant Universe. In this book he looks at the various types of possible 'alternate universes' and multiverses which are implied by some interpretations at least of modern physics.
The first and perhaps the easiest to understand is what he calls the quilted multiverse, though it might be easier to think of it as the megaverse. The megaverse is simply our own universe in its fullest possible extent, far beyond our observation horizon. He shows that if this megaverse is infinite or at least inconceivably large, then the laws of physics suggest that there will be large numbers (an infinity if the universe is actually mathematically infinite) of worlds identical to our own, containing people identical to us, as well as worlds only slightly different. There is even an identical local universe somewhere far beyond a googolplex light years away. If the universe is really truly infinite, then anything that can happen, however unlikely, will happen an infinite number of times (i.e. worlds in which David Cameron spontaneous changes into a chimpanzee for example, because there is an infinitesimally tiny chance of this happening, so in a truly infinite universe there will be an infinite number of worlds in which a David Cameron changes into a chimpanzee). Greene admits somewhat further on in the book that dealing with the paradoxical nature of infinity is a problem.
According the cosmological theory known as eternal inflation, this megaverse is indeed infinite for those living inside it, though not so from the outside, Not only that it is only one of a huge, perhaps infinite number of 'pocket universes' is a wider reality, separated by regions of something called the inflaton field. It is unclear whether normal concepts of space and distance apply in this realm of the 'spaces between the worlds'. Different pocket universes may have different physical constants and only in some will life be possible.
These infinite pocket universes are according to the most recent version of string theory, M-theory (where M stands for membrane), are themselves just three dimensional 'islands' in a 10 dimensional hyper space known as the bulk. There are possibly many such membranes in the bulk, another set of parallel worlds. M-theory also has led to the notion of a cyclic universe, in which membranes close to one another in this higher dimensional space crash into one another in mutually assured destruction out of which new universes arise like the phoenix from the ashes.
Greene then looks at another more technical set of parallel universes which emerge from the fact that it is not possible to specify which set of equations correspond with our universe. There are a large number of these equations, 1 followed by 500 zeros, though this is clearly tiny compared with the realms of googolplex light years. Nethertheless it is perhaps a relief that this set of "landscape" universes can be considered as a subset of the set of the pocket universes in the eternal inflation.
He then moves on to perhaps a more familiar type of parallel universe, the ones arising out of the many worlds interpretation of quantum mechanics. Greene explains this hypothesis in more technical detail and more clearly than others have done, and assesses some of its strengths and weaknesses. In some way this type of parallel universe seems more intimate. Whereas things happening googolplexes of light years away, or across untraversable inflation fields of boiling quantum foam, or multidimensional hyperspacial bulk accessible only to gravity are remote theoreticals, the many worlds interpretation hints at things happening to me. As an example imagine a quantum event at 50/50 probability can either open a door on the left or the right. If the left door opens you find a billion pound treasure, if the one on the right opens you find a sore, hungry, human eating-tiger. What interests you is which one am 'I' who is now contemplating my fate, going to get. At least some interpretations of this theory seem to contain deeply solipsistic inferences.
Even more solipsistic are two more possibilities that some physicists are seriously entertaining, one is that our experienced world is some sort of hologram projected from a two dimensional 'remote boundary', though what 'remote' and 'boundary' might mean in this case is unclear. Somehow I suspect to make sense of this we would have to think of this two dimensional boundary as being omnipresent everywhere rather than in some remote quasi geographical location.
Rather more easy to understand is the idea that our world is some vast simulation in an alien computer. Forteans, paranormalists and some more with-it theists might love that one, but looking at the tragedy of human history, I doubt we would find the simulators very congenial company. This might because, though Greene omits this, the same logic which suggests we might be simulations suggests that the simulators are simulations and so on through infinite regress.
Perhaps of all the current theories of physics this one reflects the times. In past ages people have seen the universe as everything from a lump of potter's clay to a living organism. In more recent times it was seen as a giant clockwork, and now in the information age as a giant computer. No doubt in future times other analogies will present themselves (to the genetic code among others perhaps).
If holograms and computer simulations aren't abstract enough for you, Greene takes us to what last step of abstraction, the reduction of the world to mathematics, and thence to the (pen?)ultimate set of alternated universes, those that realise every possible mathematical structure and equation. I think that Greene is rather sceptical of this Platonic approach to mathematics. He also gives us a brief glimpse of perhaps the final, ultimate set of parallel universes, one in which the domains of mathematics are but a small fraction.
Greene admits that much of this is speculative, but suggests ways in which future discoveries and research might confirm or disconfirm some of the theories on which they are based.
Clearly this is not an easy book, though Greene relegates the maths to the notes at the end, and some background knowledge of physics and modern scientific speculation is probably needed to grasp it, but well worth the effort. Greene shows how even the wildest-seeming of these speculations are grounded in actual science and mathematics rather than idle speculation, though recognising there are physicists who see the whole thing as a total cop-out, prematurely closing off the search for the answer as to why things have to be they are in only universe there is.
Though one might suspect that in decades or centuries or millennia to come the exact theories outlined here will go the way of the luminiferous ether or phligiston, something of the grandeur remains. Whatever the details they hint at of a reality stranger than we can imagine. True or not, they present a vision, however blurry, of a Total Whole beyond all possible imagining. It is perhaps not surprising that it is easier to contemplate this in terms of arrangements of particles, and mathematical equations, than as a vision of infinity upon infinity of the agony and ecstasy of life.
