X-Message-Number: 21790
From: 
Date: Sat, 24 May 2003 07:37:05 EDT
Subject: Beyond  quantum domain

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Some time ago, there has been some messages about quantum domain and if it 

was the end of the story. There is a hint about a structure that could go beyond
quantum domain:

I have said before that the dynamics of a point in 3 D space may be figured 
out in a 6 dimensional phase space with sign of squared coordinates: +++ - - - 
, the natural representation being done by the Jacobi formalism. Because it 
use as basic element the so called action, a product of energy and time, it 

needs in fact an infinite number of dimension to define it. Because the function
serie is limited to 3 terms by the number of space dimensions, there is a 
remainder or action uncertainty, what we call the Planck's constant. Jacobi + 

Planck's constant would define the most basic quantification, but Erwin 
Schrodinger 
found a simpler substructure using only the +++ dimensions and turning a 

difference operator into a true derivative in Jacobi. It was then realized than

the minus dimensions could be recovered as supplementary quantifications: Dirac,
Klein-Gordon-Einstein, Dual.

The duality make a difference between + - and - + for example, so we must 
look at: 
- - - +++ space too with three more quantifications. The fourth minus sign is 
known to give the supersymetry and the fifth the brane theory. I have said 

before that a proper formalism for it would be the Clifford's algebra. There is
yet a problem: that algebra would be supported by the five element group Z5, 
but there are too 4 more lookalike structures called loops. A loop is a 

multiplicative group structure without the associative law. For example the 3 
element 
product: abc has no meaning because a(bc) is different from (ab)c.

Strangely, these loops satisfy a kind of associative laws called Jacobi's 
identities. These are at the root of Lie's groups used in the definition of a 

quantification. So at the five elements level we have one Clifford's algebra on 
a 
group symmetry quantification and 4 more without group but with 
quantification.

The last minus is more interesting: The step after Clifford is something as a 
Fourier transformed algebra, it is called a Virasoro algebra. There is no 

simple group with 6 elements, so there is only loops. There are 107 such loops,
some satisfy the Jacobi's identities and so have a Lie's substructure giving a 
quantification and some have not.

For such loops, the Virasoro algebra can't be used on a quantification, we 
have here the first example of a post-quantum theory.

Now, next time you'll ponder about the possibility of some post quantum 
reality, you'll know what to search for on google :-)

Yvan Bozzonetti.

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