Stathis Papaioannou wrote:
> 2009/2/22 Stephen Paul King <stephe...@charter.net>:
>> Ok, my difficulty lies in the notion of "copying". If we are going to
>> use a method X to derive a conclusion, does it not make sense that X must be
>> sound? QM forbids the cloning or copying of states:
>> "The no cloning theorem is a result of quantum mechanics which forbids the
>> creation of identical copies of an arbitrary unknown quantum state. It was
>> stated by Wootters, Zurek, and Dieks in 1982, and has profound implications
>> in quantum computing and related fields.
>> The state of one system can be entangled with the state of another system.
>> For instance, one can use the Controlled NOT gate and the Walsh-Hadamard
>> gate to entangle two qubits. This is not cloning. No well-defined state can
>> be attributed to a subsystem of an entangled state. Cloning is a process
>> whose end result is a separable state with identical factors.
>> "No-cloning in a classical context
>> There is a classical analogue to the quantum no-cloning theorem, which we
>> might state as follows: given only the result of one flip of a (possibly
>> biased) coin, we cannot simulate a second, independent toss of the same
>> coin. The proof of this statement uses the linearity of classical
>> probability, and has exactly the same structure as the proof of the quantum
>> no-cloning theorem. Thus if we wish to claim that no-cloning is a uniquely
>> quantum result, some care is necessary in stating the theorem. One way of
>> restricting the result to quantum mechanics is to restrict the states to
>> pure states, where a pure state is defined to be one that is not a convex
>> combination of other states. The classical pure states are pairwise
>> orthogonal, but quantum pure states are not."
> But the brain changes from moment to moment due to chemical reactions
> and thermal motion and we still remain the same person. If tolerances
> were so tight that the no-cloning theorem is relevant then the brain
> couldn't possibly function.
Exactly. Anything that is going to produce useful information
processing must ultimately be classical. Even quantum computers must
have their results projected out classically. Tegmark and others have
shown that brain processes involve actions many orders above Planck's
constant - so a most quantum effects would produce small random effects.
Of course if you reject the idea that thinking is information
processing, then you could attribute it some other aspect of quantum
state evolution and ride off on Depak Chopra's horse.
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