On 21/07/2017 4:17 pm, Russell Standish wrote:
Thanks for the tip. I wasn't aware of this stuff by Zurek. It might be
very relevant.
A good summary by Zurek is given in http://arxiv.org/0707.2832
Bruce
Cheers
On Fri, Jul 21, 2017 at 11:07:52AM +1000, Bruce Kellett wrote:
I have been reading up on Zurek's 'existential interpretation of QM.
This is an interesting attempt to understand unitary QM in an
explicit Everettian 'Relative State' model. In other words, he
claims that one can get a fully unitary model without the necessity
for many worlds -- the observer defines the 'relative state' from
his component of the wave function.
The many worlds arguments of Deutsch and Wallace, among others, are
very heavy on the need for a 'realist' understanding of QM. Wallace,
in particular, seems to think that realism necessitates many worlds
because he wants a realist interpretation of the wave function
itself, or at least a space-time version of this. Zurek sees realism
in different terms, namely, as the objectivity of many observers
agreeing on what the state of the system is, so he concentrates on
the emergence of classical results from the quantum formalism, with
many copies of quantum outcomes coded in the environment -- 'quantum
Darwinism'.
The relevance to your concerns is that he has an interesting
derivation of the Born rule within his approach: a derivation that
avoids the circularity inherent in the Deutsch-Wallace derivation,
and the non-uniqueness of the concept of rationality coming from
their decision theoretic approach. Zurek, on the other hand, relies
on his notion of 'envariance', which is a symmetry of entangled
quantum states. Zurek starts with three axioms of quantum theory:
1. The quantum state is a vector in Hilbert space;
2. Unitary evolution (Schrödinger equation);
3. Immediate repetition of a measurement yields the same outcome.
I think if you get this far, you could perhaps use Zurek's argument
from the symmetries of entanglement to get probabilities and the
Born rule.
I haven't gone into this in detail as yet, but it seems promising to me.
Bruce
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