On 1/10/2012 12:48 PM, meekerdb wrote:
On 1/10/2012 7:48 AM, Bruno Marchal wrote:
In a way, that strong form of CT might already be false with comp,
only in the 1p sense as you get a free random oracle as well as
always staying consistent(and 'alive'), but it's not false in the 3p
Yes. Comp makes physics a first person plural reality, and a priori
we might be able to exploit the first plural indeterminacy to compute
more function, like we know already that we have more "processes",
like that free random oracle. The empirical fact that quantum
computer does not violate CT can make us doubt about this.
I don't think that is so clear. Nielsen has written some papers on
computations in QM that are not Turing emulable, essentially relying
on the fact that QM uses real numbers. He suggests that QM should be
restricted to avoid this kind of hypercomputation by dropping the
assumption that all unitary operators are allowed.
Could we achieve the same thing by restricting the vector (Hilbert)
space of linear functionals to a finite (but very large) field? Another
possibility is that there is a local preference of basis for a given set
of homomorphisms between the Hilbert spaces of a given pair of
interacting quantum systems. Here is a nice video lecture on the math of
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