``Despite the unrivaled empirical success of quantum theory, the very suggestion that it may be literally true as a description of nature is still greeted with cynicism, incomprehension and even anger...''
Ian Murray
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So I went to Deutsch's website and did manage to sort of read mathematical physics for New Years. It seemed to be more interesting than getting drunk or stoned and watching a bad movie. Maybe it's the same, but I couldn't tell. Try:
http://xxx.lanl.gov/abs/quant-ph/0104033
for the mathematical version of the multiverse. I think what this is, is something like a discretized Hilbert space, my image of which is an exfoliated onion.
The difference that Deutsch adds though is to transform the quantum world, into the universe, which is a world of information about itself. In other words, the physical world is modeled as if it were an information universe. Just to twist your mind around, here are his concluding remarks on the mathematical model:
``Since a generic quantum computational network does not perform anything like a classical computation on a substantial proportion of its qubits for many computational steps, it may seem that when we extend the above conclusions to the multiverse at large, we should expect parallelism (ensemble-like systems) to be confined to spatially and temporally small, scattered pockets. The reason why these systems in fact extend over the whole of spacetime with the exception of some small regions (such as the interiors of atoms and quantum computers), and why they approximately obey classical laws of physics, is studied in the theory of decoherence (see Zurek 1981, Hartle 1991). For present purposes, note only that although most of the descriptors of physical systems throughout spacetime do not obey anything like classical physics, the ones that do, form a system that, to a good approximation, is not only causally autonomous but can store information for extended periods and carry it over great distances. It is therefore that system which is most easily accessible to our senses indeed, it includes all the information processing performed by our sense organs and brains. It has the approximate structure of a classical ensemble comprising `the universe' that we subjectively perceive and participate in, and other `parallel' universes.
In Section 1 I mentioned that the theory presented here does roughly the same job for the multiverse as the theory of foliation into spacelike hypersurfaces does for spacetime in general relativity. There are strong reasons to believe that this must be more than an analogy. It is implausible that the quantum theory of gravity will involve observables that are functions of a c-number time. Instead, time must be associated with entanglement between clock-like systems and other quantum systems, as in the model constructed by Page and Wootters (1983), in which different times are seen as special cases of different universes. Hence the theory presented here and the classical theory of foliation must in reality be two limiting cases of a single, yet-to-be-discovered theory the theory of the structure of the multiverse under quantum gravity...'' (Deutsch, The Structure of the Multiverse, 19-20p)
On the other hand there are some very subtle problems that lurk within this mathematical formalism, most of which I don't understand, except to perceived as in a heavy fog.
The first of these problems is something like Occam's razor or the parsimony test. Do we need to postulate all these foliations to explain anything meaningful for our physical or scientific understanding of the world?
Deutsch's answer is yes, and he gives Zeno's paradox as the reason. How can you get to the end, if each step is only one step in an infinite path of such steps? Or alternatively, if there are a fixed discrete number of such steps, what happens to you between steps? Deutsch's answer is you need the multiverse to resolve this dilemma.
Another problem is something I think of as Hegel's mistake. The mistake is to conflate the phenomenology of mind with the phenomenology of the world. This makes the assumption that the world and its processes are knowable because there is no meaningful difference between the world and the mind that experiences the world. The two are somehow reciprocally interchangeable. The problem here is, if this assumption is accepted, then there is no method available to distinguish between, what I consider two distinct realms: the world, and the mind (or in collective terminology, then the human and physical worlds). This solves the problem of knowledge by subjectifying the world, or conversely objectifying the mind.
The transposition of this mistake into the case of mathematical models is that there is no meaningful distinction to be made between the mathematical models of the world (activities of mind) and the physical world itself (processes of material reality). In other words, advanced physical science makes the same romantic mistake as its arch rival, the great grand-daddy of postmodernism his own bad self, George Wilhelm Fredrick.
To my thinking, David Hawking has reached the terminal phase of this mistake, when he postulates what he calls the strong anthropic principle, ``We see the universe the way it is because we exist.'' [124p. Brief History of Time]. He later extrapolated this idea into a potential argument for the existence of god in some subtly about the infinite, but bounded universe, that escapes me at the moment. If you re-read Deutsch above, you will see a permutation on a similar anthropic principle.
In some intuitive sense, I see all these problems and even Deutsch's multiverse (world as information) as symptoms of a cultural terminus on the plateau of reason, the postmodern turn, the horizon of the knowable. On the other hand, I don't want to launch immediately into some bizarre and convoluted discussion of meaning and linguistics, or get lost delving into some other hermeneutic realm as an alternative.
It seems to me, that it is possible to simply hold all of this in suspension, as potentials none of which have yet crystallized into anything resembling what we might later look back on and call science, art or history.
Chuck Grimes