On Thu, 1 May 2008 15:39:40 -0600, "Steve Bell"
wrote:


This belief of "an independent external world" of mine actually has nothing
to do with any mathematical development, it is purely philosophical, I would
say. My "world view" is that there exists an independent external world,
doing its "thing," and we as scientists and observes are just trying to
figure out what this "thing" is. In the Scale Relativity papers, given they
are really talking about deterministic chaos theory, why would a
deterministic world behave differently just because we gain better and
better resolution in our observations?

This is a very rough and ready response because its a while since I
looked at a Scale Relativity paper, but I think one answer would be
that there is only one world and it does what it does at all levels.
However, when we examine its behaviour at a microphysical level we see
quantum behaviour, because then we are using a resolution at which
that becomes visible, and when we examine at a coarser resolution we
see classical behaviour, because that is what is visible at that
level. As to the question of how Nature maintains these different
levels of behaviour that would seem to be one of emergence.

I am not sure how well Scale Relativity handles that, but there is at
least this paper:
Quantum-classical transition in Scale Relativity
http://arxiv.org/abs/quant-ph/0609161

That might provide a viable answer, though I can't promise.

I am being called away from my computer for a while, so I will comment
later on the rest of your post which looks very interesting.

Cheers,
Surfer

They seem to be tying a fundamental
characteristic of a physically chaotic deterministic system, i.e., the
degree of its "fractal-ness", to us and our ability to observe. If you
believe the external world is deterministic, its deterministic character to
me, is what it is, regardless of how accurate and precise we can observe.
And even if the progression from the present to the future is truthfully
stochastic, that is still to me, a characteristic of an independent world
that just makes it harder for use to figure out what the hell is going on,
more so than if it were deterministic. Either way, what we can or cannot
intuit from observation changes not the true character of the external
world. Not in my opinion, anyway.

This issue of truthful determinism or truthful stochasticism is unbelievably
important to me. I used to think the motion of electrons, say, in atoms, was
truthfully stochastic. But I think I'm changing my mind now because of chaos
theory. If the motion of electrons in the atomic world, and all particles
everywhere for all time were/are actually deterministic, but just really,
really complicated, that is a hard thing to accept too, because that means
all events, from the beginning of the universe were predetermined by the
initial conditions from that point onward. There is no "free will" or
anything like that. We've just been "faked out" into thinking such things as
"we have free will" because this tremendous deterministic complexity makes
it look like "nothing is cast in stone." But maybe it is. In certain ways,
that's comforting because "what will be will be," but them it's depressing
to think I can't do anything about tomorrow. I believe philosophers have
been struggling with this for decades, if not from the first time a
Neanderthal buried one of their dead with ceremony.

But the equations are beautiful. I worked up the tensor algebra of the Kerr
equations of motion (field equations) as linear algebra, for the purpose of
computation. You can see this representation at:

http://physics.clarku.edu/cip/sbell/suppl.pdf

There is no actual derivation in the above of the Kerr metric, but I
followed very nearly Wald's syntax. It's a fairly quick explanation of to
how get to the computational equations. I must stress, that to a true
GR'ist, I took "license" with issues of coordinate contraction/expansion,
this was mainly to basically get what one would see with our "inertial
brains". I wrote an orbit simulation, "fully Kerr," and generated the
following plots:

http://physics.clarku.edu/cip/sbell/fig1.pdf
http://physics.clarku.edu/cip/sbell/fig2.pdf

It's in FOTRAN, I've been meaning to convert it to C, but for computation
speed on a Windows PC, FORTRAN is just as fast as C. The source code is
available, if you wish. This is for a 10 solar mass black hole (remember,
this is no-where as complicated as n-body) with a test body (the satellite)
starting off with 0.14c at a 45 deg angle to x-y. The beginning eccentricity
was 0.5, the reason for the loop-to-loops. With ecc = 0, nice round circles
are produced, with beautiful deterministic frame-dragging effects bringing
the orbits out-of-plane. A shell can be produced like this. The second pdf
shows how if continued, a torus will be formed. This shows the wide
plasticity of Kerr orbits with their nonlinear frame-dragging effects
(geomagnetism). If GP-B doesn't find this, that would be a blow.

It could be at the birth, very small, almost differential, slight
differences in initial conditions of what-ever-the-hell were the particles
back 13.7 by ago, has by now, produced a gigantic chaotic, but
deterministic, "settling in to some gigantic attractor." The chaos could
have evolved very rapidly (inflation) attaining almost that of today's
complexity in a very small amount of time, and now we are just along for the
ride. The resolution of this with quantized jumps in the world of the small
(atoms) is very difficult. But phase space quantized to h_bar will help.

Steve Bell