| nonlinear commutators -
07-08-2008, 12:23 PM
Total and complete isolation is impossible in the physical world. Although macroscopic systems: planets, stars, and galaxies seem pretty much isolated; their lifetimes are very much less than microscopic systems of electrons and protons. By its definition an isolated system shares neither mass nor energy with its immediate surrounding neighborhood. Still, it causes something to happen. It is directional quantum determinism. Therefore, a system almost completely isolated or near absolute determinism has much uses of no more than 8 commutators or 8 degrees of freedom required by a principle of directional invariance for nonlinear operators.
A set of linear operators: A, B, C, D, E, F, H, G becomes a complete set of commuting operators if and only f any pair has left-right, up-down, or front-back product differences zero: [A, B]=[B, A]=AB-BA=BA-AB=0. Generally, the time evolution of these operators allows the frequent occurrence such that AB≠BA. If wherever and whenever A becomes position operator and B becomes linear momentum operator then by a postulated quantum condition (QC) the 1-dimensional commutator [A, B] is always equal to ih/2p where h is Planck’s constant of action and iis the imaginary unity. This QC or PB (Dirac preferred Poisson Bracket) led to Heisenberg uncertainty principle of non-relativistic quantum mechanics: DADB≥h/4p by the following definition that the product of operational uncertainties is equal to the negative expectation of the imaginary commutator.
On the other hand, nonlinear vacuum commutators are the product of square matrices. Specifically, singular Hadamard matrices symbolized squares of energy for quantum spacetime charges H+ and H-. Commutators of their square roots are [h+, h-]=±x. Moreover, [h+, h+]=+0and [h-, h-]=-0. By Einstein’s energy-mass equivalence, ±0 are converted completely into mass using the simple formula: m=x/c². This gives a spacetime operational uncertainty of DH+DH-≥x² where x is the zero-point energy of the quantum spacetime vacuum.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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Re: nonlinear commutators -
07-08-2008, 12:28 PM
Linear Mode
