An Interdisciplinary Journal

* 2004, Vol.7, No.2, pp.129-139*

In this paper an approach is developed which allows to
propose Quantum Mechanics with Fundamental Length
as the theory to describe quantum-mechanical behavior of
nature at Planck's scale (that is at the Early Universe). Such
approach seems to be logically supported, since in all known
methods for researching quantum-gravitational effects, somehow or
other, a fundamental length of the Planck-scale order appears.
Quantum Mechanics with Fundamental Length is obtained by
deformation of Quantum Mechanics. The novelty of the presented
approach is in carrying out a deformation of density matrix,
instead of deforming commutators (in other words, a deformation
of Heisenberg's algebra) as it was done up to now. In our approach
two fundamental features of Quantum Mechanics are conserved.
Namely, the probabilistic interpretation of the theory and the
well-known measuring procedure corresponding to that
interpretation (at the moment in first approximation). Some
dynamical aspects of the theory are discussed. An explicit form of
deformed Liouville equation is given. Some implications of
obtained results are analyzed. In particular, the problem of
singularity and the hypothesis of cosmic censorship are tried. The
Density-entropy concept is introduced, improving the definition of
statistical entropy. Density of entropy is used to deal with
the problem of information loss in
black holes. Bekenstein-Hawking's formula for black hole entropy
is deduced from the first principles.

*Key words: *
fundamental length, general uncertainty
relations, density pro-matrix, deformed
Liouville's equation, density of entropy,
Bekenstein-Hawking formula

Full text:
Acrobat PDF (165KB)
PostScript (303KB)
PostScript.gz (138KB)

Copyright © Nonlinear Phenomena in Complex Systems.
Last updated: *June 29, 2004*