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| Elav |
 Posted: Sat Sep 30, 2006 9:05 am |
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Guest
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Hi all
There are many posts in this group talking about locality and realism
these days and I've recently read this very interesting paper :
Célérier M.N. & Nottale L., 2004, J. Phys. A 37, 931-955
"Quantum-classical transition in scale relativity"
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"It is worth stressing here that a non-differentiable and fractal
spacetime is essentially non-local, since the 'particles' are
identified with bundles of geodesics. Therefore, we recover the
non-locality of the wavefunction of standard quantum mechanics.
Moreover, having now derived the Dirac equation and the bi-spinor
nature of the wavefunction exactly in its standard quantum mechanical
form (there is no missing or additional variable in the
non-differentiable spacetime representation, but only a change of
variables with the same number of degrees of freedom), some profound
aspects of quantum mechanics such as the EPR paradox and the breaking
of Bell inequalities are also recovered in the new framework."
.....
So, have any of you read about Laurent Notalle's work ? He's
generalizing current physics by dropping the assumption of
differentiability of space-time (going from C2 to C0 class). It really
looks like promising, in my honnest opinion.
Any comments ? |
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| Panties On Head |
| Posted: Sat Sep 30, 2006 1:21 pm |
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Guest
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Any comments ?
--------------------------------------------
I'm not a professional physicist, and so my opinions are not mainstream, but
I'll toss in my 2 cents anyway.
First, I think that alot of modern physics has been very contorted and
convoluted because some fundamental issues have never been addressed
properly by mathematics. If the mathematical tools are not available, then
you will have all kinds of wierd theories which attempt to answer questions
but only dance around the issue. Just imagine trying to model probabilistic
behaviour of dice without the concept of randomness !
Second, I think that Nottale is definately correct in his attempt to use the
concept of scale. He is on the right track. Scale is certainly one of the
most important things in physics, of equal importance to the very concept of
energy. It is fundamental, in my opinion. So, his work is certainly
important.
My criticism is as follows.
First, I think that his work is based on a scalar calculus which is a
Clifford calculus (?). I dont know how this calculus works, but I'm pretty
sure that it does not really address causality, uniqueness, triviality, or
nonexistence. From what little I know of his work, it does not seem to match
up with my own views on what such a scalar calculus should accomplish.
Second, the idea that the fine structure is fractal. I think that one should
ask what the fractal is made of. What does it consist of. What is it
composed of. The answer must be dimension. And so, in my opinion, the fine
structure is a place where you will find order and disorder. A fractal is
self similar on all scales, and we dont know that all scales even exist. So,
you could have a "scalar truncated" fractal, no problem. And, it might even
be possible to have a genuine fractal, but that needs to be explained how
that could occur on infinitely small scales.
Third, fractals dont always even look like fractals. Many fractals can only
be discovered with Poincare' sections, or they will occur in the time
domain. You can be looking at something which seems pretty mundane, but in
the time domain it is really a fractal. So, what is and is'nt a fractal
often depends on how something is observed. And while I strongly suspect
that Nottale is indeed correct that fractals exist in the fine structure,
there is currently no experiment yet devised which can confirm this.
As an ancillary comment, the orbit of Pluto was recently reported to be
chaotic. While this statement may be correct if one is looking at a
Poincare' section, it is not neccesarily correct if Pluto is observed in a
different fashion. The statement becomes false if one observes Pluto for
only 1 Earth day. The statement probably becomes false if one is only
observing Pluto's mean distance from Sun or some other parameter. And the
original findings become problematic if you consider that they must have
been based on calculation, and not observation.
Lastly, this is not Nottale's fault. A formalized understanding of order and
disorder has not yet been achieved by mathematics. We are limited by the
tools that we have at our disposal, and I dont think that it's possible to
address causality without a discussion of triviality and nonexistence. I do
not believe it possible. When you start to think about partial causality,
partial existence, partial order-disorder, all roads seem to lead to
triviality and nonexistence and this has not been formalized by mathematics.
I think that Nottale and Wolfram have some things in common. They are both
truly great scientists and I hope that history remembers them that way. But
they have one more thing in common - they are both lacking an order-disorder
continuum, and this, in my opinion, is the only thing standing in the way to
a revolutionary implementation of both of these truly great ideas.
The concept of randomness is simply insufficient.
http://sciphysicsopenmanuscript.blogspot.com/
http://sciphysicsopenmanuscript.blogspot.com/
http://order-disorder-randomness.blogspot.com/
http://order-disorder-randomness.blogspot.com/ |
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