From: Robert Shaw wrote:
> From: "Dan Minette"
>
> > I'm going to focus on one aspect of Robert Shaw comments for the moment.
> > >
> > > There isn't room in physics for new stuff on a scale that affects the
> > > workings of the brain. Penrose appeals to nonlinearities in quantum
> > > theory connected with gravity but there is no independant evidence
> > > of such effects. Quantum gravity is even less likely to be relevant.
> > >
> >
> > Actually, there might be room in macroscopic physics. I'm not counting
on
> > this room for my answer, but its still worth noting. Macroscopic
physics
> is
> > probably the most likely area for something fundamentally new and usable
> to
> > be found in physics. Quantum gravity will be new, but it probably will
> not
> > have applications.
>
> 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.
Penrose is of the opinion that there will significant new physics here. I
tend to differ with him on this, but he is reasonable in stating that this
is a prime area for new physics.
> >
> > > It's not possible in practice but proving it impossible in principle
is
> > > much harder. You need to discover new physics which has a significant
> > > effect on processes at the energy levels and time scales found in the
> > brain.
> >
> > 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.
> 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.
> >
> > > 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. I
certainly can make mistakes, but I've pushed this idea past a number of
folks. Also, Bohr believed this. That doesn't make it true, but it does
make it quite unlikely that the idea is inherently inconsistent with basic
QM..
> > Think about perfect billiard balls on a perfect table traveling at 10
> meters
> > per second and interacting (on average) every meter. Quantum chaos is
> > involved in their position within 1 second.
> >
> 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 consider perfect "billiard balls" traveling 10 meters a second, on a
perfect table, interacting with each other about once per meter. (I'll have
them do it exactly once per meter to simplify things.) Let each of these
billiard balls be 8 cm in diameter, and have a mass of 100 g (a bit light,
but it simplifies the calculations.) The momentum of the ball, is then, 1
kg*m/s.
Let us consider a collision, and the uncertainties therein. Assuming that
errors are small, an error of x at a collision n, will result in an error of
25x at collision n+1. (The distance is 100 cm, the radius of the balls is 4
cm) Now, there are two balls to consider, and each may have error. So, at
collision n we need to consider the RMS addition of the error in each ball:
a factor of sqrt(2). So, roughly, the error in the position of each ball is
multiplied by a factor of 35 in each collision.
The same is true, of course, of the error in the momentum of the ball. At
collision, a ball that has a position error of x cm will have a momentum
error of .01 kg m/s.
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.
>
> 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.
In order to predict the future states of the universe one has to consider
the details of the Hamiltonian. Its true that one can often make classical
approximations, but one has to be careful when one does that.
Dan M.
> It's not practical to specify H that precisely, but it is possible in
> principle.
> The mere existence of a algorithm that can simulate the universe to
arbitrary
> accuracy is enough to imply that nothing within the universe can perform
> any non-algorithmic procedure, even if the universe simulating algorithm
is
> neither constructible nor executable within the universe being simulated.
>
> --
> Robert
>
>
