By Michael Clive Price
Many-Worlds, whilst deterministic on the objective universal
level, is indeterministic on the subjective level so the situation
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
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
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 face 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.