X-Message-Number: 16901
From: 
Date: Fri, 6 Jul 2001 11:04:42 EDT
Subject: The Schrodinger's limit, basic

The Schrodinger's limit.

The Schrodinger's quantum mechanics is built on an infinite dimensional 
function space, for example: sin(x),..., sin(nx), with n any positive 
integer. The wavelenght of each dimension get smaller as n increase. the 
largest dimension may be definned as the scale where the force associed to 
the quantum effect overcomes the classical domain. This is the scale of atoms 
or 0.000 000 01 cm. (10^-8 cm). The smallest dimension is given by the scale 
of the Planck's lenght, that is: 1.6 x 10^-33 cm. That allows 10^25 
dimensions or so in quantum mechanics, this is a big number in itself, but it 
is far from infinite.

I have said before that, because of the Casimir effect extracting energy from 
the vacuum, real quantum systems have very few dimension not nihil, about 6 
to 10 only. is this enormous domain with up to 10^25 dimensions really empty? 
The physics answer is yes, I don't think so. Introducing sin(x/n) dimensions 
may soak up vacuum energy and expand the quantum scale to larger system, 
given a value N of n, we can couple the dimensions: sin(Nx) and sin(x/N) 
without asking or getting energy from the outside.

A quantum system is conserved if it remains coherent (its wave function is 
not destroyed). Any interaction with an outside element, that is another 
nearby quantum system will produce a decoherence effect. If there are only 
something as 6 dimensions not empty, all is said, on the contrairy, if the 
x/n dimensions are added, thing get more interesting.

There is some part of the original wave function in these high n number 
dimensions, for the x/n one, the scale is larger and so the nearby stranger 
quantum system able to produce a decoherence effect is included in the x/n 
scale. For these high n dimensions, the stranger is no more a stranger and so 
it don't produce decoherence effects.

What is the limit of that process? for n near 10^25, the x/n scale is near 
0.1 light year, far larger than the solar system. So here is the possibility, 
at the scale of the solar system, to have a single quantum wave with nearly 
no decoherence effect.

Assume we watch a quantum system at small scale with few dimensions, we will 
see it decay with time. Now, if we look at a larger dimension pack, we will 
see in higher dimensions the remains of the past wave function, that is the 
quantum system history. Going to more and more dimensions, we will see the 
elements of longer ago past histories. The limit beeing the solar system 
formation, when the gas cloud was interacting on a scale larger than .1 light 
year.

 Yvan Bozzonetti.

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