Le 30-nov.-06, à 08:10, Maurice (for-list) wrote :
> It was hoped by some that the study of quantum gravity might deliver
> something along these lines.
> This may be the wrong place to ask, but does anyone know if string
> theory and so on offer any hope in this direction?
Interesting question.
I have related questions.
Take "loop gravity" (the main competitor of string theory for the
marriage between GR and QM). In loop gravity, the GR idea that gravity
force = curvature of space is kept all along, so that quantization of
gravity leads to quantization of space and time. So there exists, in
loop gravity, atoms of space time, and so the physical reality is
eventually completely discrete, except for the complex quantum wave
amplitudes.
Now we can also replace the use of complex numbers by gaussian integers
(a+bi with a and b in the set of integers or rationals or algebraical).
Due to the linearity of the SWE, this is "mathematically" enough.
But then such a loop gravity theory would entail that the number of
worlds (of the MWI) are always finite (unless we posit at the start
some infinite "Garden of Eden).
In that sense String Theory is more coherent with both the comp hyp in
the cognitive science and David Deutsch view that the
splitting/differentiation is a multiplication by 2^aleph_0 (the
continuum).
Now about the many world in String theory I remember having read by
Witten that the wave aspect of the string theory is not yet well worked
out, but a priori, given that string theory is entirely based on the
quantum theory (without collapse, it seems to me), the MW should fit in
without much problem.
Sometimes I think that string theory will even lead to a MW with a
vengeance, that nature tries not just all consistent histories, but
tries all number systems as well (like the p-adic fields, finite
fields, etc.) and all possible topologies, in which those consistent
histories can be implemented. Don't know...
I have another question: could a quantum chaotical system (as far as we
know what that is) be turing universal? Any comments are welcome.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Dec 01 2006 - 09:45:09 PST