First posted 31 Oct 2003. I definitely still think there is infinite diversity out there, including many versions of 'me'. I tend now to think of it more as the existence of every possible experience from every possible perspective.
See Scientific American: Parallel Universes [ COSMOLOGY ]; Not just a staple of science fiction, other universes are a direct implication of cosmological observations
Buckle in, 'cause this one's a helluva ride - a real head spinner. You can read the whole article via the link above, but I'm dying to try to summarise it, to see how much of it I 'get'. The gist is that our universe is just part of a multiverse, or actually a part of four tiers of multiverses, with the result being that (based on simple probabilities) an infinite number of you's and me's are 'out there' living through every permutation of our lives. I hope only a few of the me's out there are suffering from my cold at the moment.
Our Hubble Space
The article starts by defining our universe as our visible universe. Since light travels at 300 million metres per second, and since the Big Bang happened about 14 billion years ago, our visible universe (or Hubble space) is a spherical space with a radius of about 10^26 metres. (The article says 4x10^25). This visible universe's radius grows (by definition) by one light year (roughly 10^16 metres) each year, and the light we see emanating from the edge of our Hubble space was emitted at the beginning of time.
Level 1 Multiverse = The Universe
The first level of multiverse, then, is the collection of Hubble spaces. This is what I have always considered and shall continue to call The Universe. If we assume (as current observations suggest) that the overall universe is infinite and that matter is roughly evenly spread throughout it, then there are an infinite number of these Hubble spaces, all with the same physical laws as ours. Now, pick one of those other Hubble spaces. What is the probability that the interaction of fundamental particles and forces over the lifetime of that space just happen to produce another you? Surely unbelievably small. But is it zero? It seems irrational to assume that the probability of another you in any other given Hubble space is absolutely zero, since you have already appeared once, after all. Let's say the chance is one in a gazillion, with a gazillion being the biggest number imaginable. Then there must be another you out there, because any non-zero probability, no matter how small, when applied to an infinite number of cases, will be realised.
Saying that there must be other you's living through every possible permutation of your life is just a special case. We could simply say that anything that is possible (i.e. has non-zero probability) exists. So, somewhere out there is a you with 9 fingers, a you with a squeaky voice, a you who didn't propose to your wife, a you who likes Abba songs, a you who only carries 20p pieces in his pockets. There is you who slept late on your 19th birthday, not to mention a you whose life is exactly the same as yours in this Hubble space. Now you see just how infinite infinity is!
Level 2 Multiverse = The Multiverse
There are a couple of ways to think of a level 2 multiverse, which I will call just The Multiverse. At heart, The Multiverse (i.e. Level 2) is a collection of an infinite number of Universes (i.e. Level 1s), each of which can have very different physical 'constants'. We can think of these Universes as bubbles of non-stretching space within the eternally inflationary Multiverse. Alternatively, we can view The Multiverse as a cycle of continuous birth and destruction of Universes, perhaps with black holes as the agents of mutation and birth. From either angle, we could never communicate between Universes (or gain information about another one), because they are either moving apart from one another at faster than the speed of light or only 'touch' at singularities, through which no information can pass. Still, the existence of The Multiverse would explain the otherwise tricky and highly improbable fine tuning of our own Universe. If ours is just one of an infinite number, then it is no longer surprising that so many specific variables (density fluctuation, relative weights of elements, etc) have values just right for allowing life to emerge and evolve. As regards the multi-me's and multi-you's, if the infinite size of our Universe guaranteed that they were out there, then the existence of The Multiverse, containing an infinite number of Universes, really cements it!
Level 3 Multiverse = Many Worlds (from quantum mechanics)
A level 3 multiverse is another name for the infinite collection of worlds in the 'Many Worlds' interpretation of quantum mechanics. Each quantum event causes a split between worlds, with one proceeding along possible route 1 and the other along possible route 2. Each of those 'worlds' contains an entire Multiverse (i.e. Level 2). Since there are an infinite number of quantum events, there are an infinite number of such splits and an infinite number of worlds, one for each thread that winds its way forward through one 'choice' after another. I (as in this specific Doug in this specific level 1 and 2) only have access to, only experience one of those threads. The other me's see only their specific threads. But all threads exist.
The me's in different Hubble spaces live separate but parallel lives in a different part of space-time. The different me's within the many worlds (Level 3) are not separated from me in spatial terms but in dimensional terms within the overall wave function for the Level 3 multiverse. You can think of these worlds as being perpendicular worlds, as opposed to parallel ones. Jointly, they require an infinite number of dimensions, which the 'Hilbert Space' of the wave function has. Ouch, that hurts my head.
Anyway, the existence of this level depends on whether the wave function's evolution through time is unitary (no, I don't know what that means), which is as yet uncertain but is consistent with observations and wider theory. In one sense, it doesn't matter, because if physics is unitary, then Level 3 adds nothing that doesn't already exist in Levels 1 and 2. No more possibilities are generated, just additional copies of ones that already exist.
Level 4 Multiverse = All possible mathematical structures (or, a bridge too far)
Just a few words on a final, highest level multiverse. The wave function of quantum theory and level 3 multiverse is a mathematical structure, and most physicists today see the universe as fundamentally mathematical. Why not, then, allow for an infinite number of level 3 multiverses corresponding to any imaginable set of (mathematical) laws? Fine with me, but you'll need to check with all the other multi-me's individually.