I want to make a brief comment about what Gilles Henri
said to Hal Finney some days ago:
>I think that nobody answered me satisfactorily on the problem of
>"interpreting" or recognizing" a string. I could compare this problem to
>gauge invariance in physics. It's well known that all physical theories
>admit many equivalent representations or gauge transformations. However, to
>represent "physically" something, they must contain quantities invariant
>upon these transformations, that allow to recognize intrinsic features :
>e.g. proper interval in general relativity, curvature of space-time and
>more generally the action in any known theory.
>You seem to admit as obvious that a computation or a string can represent,
>or better *be* a physical state of the Universe. However when you think of
>a real way to connect them, it seems obvious that you have to precize a way
>of doing that. If you want to describe the positions of all atoms, or the
>values of a field, you have to precise the coding of real numbers and so
>on. When Bruno says that the UD will solve Wheeler-DeWitt equation, it
>assumes some coding that allows to recognize the solution in a string. I
>may be wrong, but I don't see how you can definie intrinsic physical
>quantities (like the curvature of the space time for example) independantly
>on these representations (same problem with the "matching pattern" of Hal).
>It means also that the same string can represent (under different coding
>schemes) different, and even quite different Universes. So it cannot posses
>intrinsically all physical properties, and for example the presence of
>living beings. Maybe I am wrong and you know works proving the contrary?
You must take into account the fact that the "interpreter" is itself encoded in the string. If you do that, you will be able to use a lot of existing invariance results from theoretical computer science for ascribing RELATIVE representational content to computationnal states. These "contents" depend on the existence of a representation for the interpreter and the data, but are invariant with respect to the choice of a representation.
You can take this with a grain of salt, for the "invariance" results are only true in some limit. Here we encounter the corresponding problem faced by those who asks for a non-frequentist(°) interpretation of probabilities in Everett interpretation of QM.
My feeling is that the UD argument (the PE-omega thought experiment) provide something like a definitive clue why we must indeed take the limit into account, both in MWI and/or COMP.
Bruno
(°) A nice introduction to this problem is given in the Quantum Computation course by Preskill
http://www.theory.caltech.edu/people/preskill/ph229/
Note that some people, like David Albert in his book "Quantum Mechanics and Experience, Harvard University Press, 1992" really discard Everett-like interpretations with this "probability" interpretation problem.
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Received on Wed Mar 24 1999 - 02:09:44 PST