"Surfer" wrote in message
...
A scale-relativistic derivation of the Dirac Equation
http://arxiv.org/abs/hep-th/0210027
Scale calculus and the Schrodinger equation
http://arxiv.org/abs/math/0211071
On a closer reading of these two links, I would have to say that myself
personally, do not accept one of their fundamental tenets. In the first
link
it is said:
"Giving up the assumption of differentiability has important physical
consequences: one can show [2,3] that spaces of topological dimension D_T
,
which are continuous but non-differentiable, are characterized by a D_T
measure which becomes explicitly dependent on the resolution (i.e., the
observation scale) epsilon at which it is considered and tends to
infinity
when the resolution interval epsilon tends to zero."
In the second link, in Section 3.2, the uncertainty principle (UP) is
introduced, and a fundamental characteristic of motion is tied to
measurement error.
To me, this says some physical characteristic of the external world,
e.g.,
the nature of motion and the differentiability of spatial dimensions, is
tied to observational error. This in my opinion is a huge conceptual
mistake, the same essential one in the UP of QM. To me, there is no need
to
assume that, and still think chaotic nonlinear GR dynamics is the way to
go.
In this idea, the determinism of motion and the differentiability of
spatial
dimensions are still maintained, but the essence of physical motion,
which
has nothing to do with observing the motion, is extremely dynamically
complicated. Considering observation, then yes, it looks stochastic, but
in
fundamental essence, it is not.
But, at least, these ideas are advancing towards a better understanding
of
things. Hopefully these researchers will realize that an introduction of
measurement error into the true character of motion is a significant
observatory-centric bias producing a conclusion that there is no
"external
world, independent of the perceiving subject." Einstein did not accept
this.
He though that "A belief in an external world, independent of the
perceiving
subject, is the basis of all natural science." I think we should adopt
Einstein's philosophy wholeheartedly, and stop being so
observatory/measurement-centric minded in our theory.
Those are interesting observations. Its possible the Quantum State
Diffusion approach is closer to reality. There is a link to a paper
here that I looked at a few years ago.
"Quantum State Diffusion: from Foundations to Applications"
http://arxiv.org/abs/quant-ph/9701024
I have noticed that Process Physics papers sometimes refer to QSD.
Interestingly, one of the QSD authors expressed this view
"Quantum measurement breaks Lorentz symmetry"
http://arxiv.org/abs/quant-ph/9906005
But I have not seen much written on QSD recently.
Surfer
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? 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