I'll try to keep this as unmysterious as I can.
>
> For a quantum system we can calculate the wavefunction to arbitrary
accuracy.
>
We can, until the wavefunction collapses. Then we can calculate no further
until we determine which eigenstate it collapsed into.
>
> > > > > In known physics the movement of the human brain through its
> infinite
> > > > > dimensional phase space can be precisely predicted by using the
> > > > > Hamiltonian operator.
> > > >
> > > > I would like to see that worked out. If it is true, I'd be very
> > > surprised.
> > >
> > > If it isn't true, then classical quantum physics is false.
> > >
> >
> > Are you absolutely sure about that? I've posted this stuff on
sci.physics
> > and didn't see any contradictions from the professional physicists
there.
>
> They were probably talking about what is practical, within the physical
> universe.
>
Hmm, well I was a participant in the conversation. We did explicitly discuss
the
possibilities for free will. At some point, we have to have collapses of
the wavefunction. Neurons are not in superpositions.
> Penrose agrees that all known physics is computable, that the brain can
> only be non-algorithmic if known physics is incomplete on the mesoscale.
> If the brain could be non-algorithmic within known physics Penrose would
> say so.
I think I need to clarify something, because it is fairly clear to me that
we are miscommunicating. I am not arguing that anything in the present
theory of QM is non-computable. What I am arguing is that we can only
calculate the probability of future states existing from QM. We cannot
calculate what the future states will be. Penrose is trying to do something
different from what I was trying to
do: he is trying to see how there can be a scientifically based free will.
I'm trying to determine if free will can be seen to be consistant with
science.
>
> We have two particles in a rectangular box whose wavefunctions
> can be expanded in terms of the energy eigenfunctions. The actual
> interaction term is complicated but it can be approximated by the
> probability of collisions in any pair of states and the probability
> of transitions between states at the moment of collision. On doing
> this you get a set of first order ODEs for the probability of
> being in each energy eigenstate, which is a computable problem,
> solvable to arbitrary accuracy.
>
I think we really did misscommunicate here. We do know the probability of
finding the balls, but we cannot predict where the balls will be. After 10
seconds, a minute for sure, all we can say is that the balls will be on the
table (assuming the table is, say, 5 meters by 5 meters).
What I was saying about the human brain is that its future states cannot be
predicted from its present states. After a very short amount of time, all
one could say is "that human will live or die by time t+dt" from knowing the
state of the brain as precisely as possible at time t. So, we cannot
predict the future states of human beings, even in principal.
My requirement for accepting free will is that it is consistent with what we
know about the brain, not that it is reducible to it. If we could prove
that our actions are, in principal, predictable, then there would be no room
for free will. As it stands now, all one has to do is presume that
observations present an incomplete picture, not a false picture. After all,
from observations alone, there is no reason to require us to be self aware.
> >
> > Well, I'll agree that the amount of energy in the universe is fully
> > determined (unless some of that new astrophysical stuff requires a basic
> > change in physics...I don't think it will but it is certainly possible).
> > Insofar as you can ignore the details, then the Hamiltonian of the
> universe
> > is constant. But, that's boring and useless. Think about a classical
> > problem, the orbit of planets around a sun. One express the
Hamiltonian,
> > not for the energy of the solar system as a whole, but as a function of
> the
> > potential and kinetic energy of each planet. Then, we get the equations
> of
> > motion.
>
> Of course, that's what I meant by 'how the energy of the universe
> depends on its states'
>
I understand how what you said is true; but on the other hand, it isn't
fully true. From time to time, the wavefunction collapses. There is no way
to determine the future evolution of the collapsed state until one
determines which eignenfunction(s) the wavefunction collapsed into.
>
> In either case all the information about the time evolution of
> the system is contained in the Hamiltonian.
>
Including which eignestate the system will collapse into? Yes, I know how
the formalism works, but you also need to consider what we do with the
formalism.
Dan M.
