Q24 Does many-worlds allow free-will?
Many-Worlds, whilst deterministic on the objective universal level, is
indeterministic on the subjective level so the situation is certainly
no better or worse for free-will than in the Copenhagen view.
Traditional Copenhagen indeterministic quantum mechanics only slightly
weakens the case for free-will. In quantum terms each neuron is an
essentially classical object. Consequently quantum noise in the brain
is at such a low level that it probably doesn't often alter, except very
rarely, the critical mechanistic behaviour of sufficient neurons to
cause a decision to be different than we might otherwise expect. The
consensus view amongst experts is that free-will is the consequence of
the mechanistic operation of our brains, the firing of neurons,
discharging across synapses etc and fully compatible with the
determinism of classical physics. Free-will is the inability of an
intelligent, self-aware mechanism to predict its own future actions due
to the logical impossibility of any mechanism containing a complete
internal model of itself rather than any inherent indeterminism in the
mechanism's operation.
Nevertheless, some people find that with all possible decisions being
realised in different worlds that the prima facia situation for free-
will looks quite difficult. Does this multiplicity of outcomes destroy
free-will? If both sides of a choice are selected in different worlds
why bother to spend time weighing the evidence before selecting? The
answer is that whilst all decisions are realised, some are realised more
often than others - or to put to more precisely each branch of a
decision has its own weighting or measure which enforces the usual laws
of quantum statistics.
This measure is supplied by the mathematical structure of the Hilbert
spaces. Every Hilbert space has a norm, constructed from the inner
product, - which we can think of as analogous to a volume - which
weights each world or collection of worlds. A world of zero volume is
never realised. Worlds in which the conventional statistical
predictions consistently break down have zero volume and so are never
realised. (See "How do probabilities emerge within many-worlds?")
Thus our actions, as expressions of our will, correlate with the weights
associated with worlds. This, of course, matches our subjective
experience of being able to exercise our will, form moral judgements and
be held responsible for our actions.
http://kuoi.com/~kamikaze/doc/many-worlds-faq.html