From: "Dan Minette"
>
> From: Robert Shaw wrote:
> > From: "Dan Minette
> >
> > Mescopic physics is fully reducible to microscopic physics and
ultimately
> > the standard model.
>
> Are you familiar with the problem of developing a quantum mechanical
theory
> of quantum mechanical measurements? Zurk (sp) and company have done some
> interesting work with decoherence as a means of explaining how the
collapse
> of the wave function happens. All parties pretty well agree that
> macroscopic physics is where the rubber will meet the road in determining
> the validity of this approach.
>
The collapse of the wave function is a problem, but only Penrose is
suggesting new physics there. Decoherence is a possible feature of
solutions to known physics Without such new physics it is
fully reducible.
> > >
> > > No, all I have to do is show that quantum chaos is involved.
> >
> > That isn't sufficient. Chaos isn't unpredictable, just exponentially
> > harder to predict than linear systems.
> >
> Quantum chaos is inherently indetermanistic. If quantum indeterminacy
isn't
> involved, then its classical chaos. Indeed, I think that's what defines
> each.
>
At worst quantum chaos produces random state transitions but
that doesn't make the system non-computable.
>
> > A chaotic physical system, whether classical or quantum, is
> > still going to be simulatable to arbitrary accuracy by a
> > Turing machine, just not in polynomial time. That means such
> > systems can't do non-algorithmic processes.
> >
>
> Arbitrary accuracy does not exist in the physical world. There is a well
> known limit to which we can simultaneously know, say, momentum and
position.
>
I'm well aware of that.
For a quantum system we can calculate the wavefunction to arbitary accuracy.
> > > > 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.
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.
> > >
> > Such chaos is only a practical barrier to predictability, not a
> theoretical
> > barrier.
>
> Well, let me quickly redo my explanation of a bit ago. Also, I may come up
> with a slightly different number, it may be 2 seconds instead of 1,
because
> I rethought the geometric considerations. (Sorry for any mistakes, but the
> general rules are the same...also I'm using slightly bigger "billiard
balls"
> I think.., so that slows things down).
>
>
> Let us start with the errors set at dp*dx=h. with dx=10^-18m and dp=
> 6.6*10-16 kg m/s. Lets work out the results of multiplying dx by 35 for
> each collision. It turns out that in 1 second, the error would be 2.76
mm,
> very close to the 1 cm target. In 1.1 sec, the error would be 9.65 cm.
>
> Well, lets look at the error from the momentum. A 6.6*10-16 kg m/s error
> is, for a 100 g ball, a 6.6*10-15 m/s error. After .1 sec, this
translates
> into a position error of 6.6*10-16 m. After 1 sec, this translates into a
> position error of 0.25 cm, again close.
>
> So, even with my new numbers, h rears its pretty head within 1 sec. This
> limit is fundamental, BTW; its just not computational. That's the
> difference between quantum and classical chaos.
>
You are mixing quantum and classical descriptions inappropriately.
Start with a fully quantum description.
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 moemnt 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 arbitary accuracy.
> >
> > By definition, H|Universe>=i(d/dt)|Universe>, barring quantum
> > gravitational effects.
> >
>
>
> > If you specify H, how the energy of the universe depends on its states,
> > the time evolution of the universe is fully determined.
> >
>
> 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'
Classically we have du/dt=[u,H]
so knowing the Poisson brackets of the Hamiltonian with anything
is enough to determine its time evolution.
Quantumly we have d<u>/dt=<[u,H]>/(i h-bar)
and knowing how the Hamiltonian commutes with anything
is enough to determine its time evolution. Decoherence suggests
that the apparent collapse of the wavefunction is a consequene
of this equation as applied to large systems. It doesn't challenge
its validity.
In either case all the information about the time evolution of
the system is contained in the Hamiltonian.
--
Matter is fundamentally lazy:- It always takes the path of least effort
Matter is fundamentally stupid:- It tries every other path first.
That is the heart of physics - The rest is details.- Robert Shaw
