X-Message-Number: 21790 From: Date: Sat, 24 May 2003 07:37:05 EDT Subject: Beyond quantum domain --part1_17.39bc2c44.2c00b361_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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. --part1_17.39bc2c44.2c00b361_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=21790