36 research outputs found
Entwined Paths, Difference Equations and the Dirac Equation
Entwined space-time paths are bound pairs of trajectories which are traversed
in opposite directions with respect to macroscopic time. In this paper we show
that ensembles of entwined paths on a discrete space-time lattice are simply
described by coupled difference equations which are discrete versions of the
Dirac equation. There is no analytic continuation, explicit or forced, involved
in this description. The entwined paths are `self-quantizing'. We also show
that simple classical stochastic processes that generate the difference
equations as ensemble averages are stable numerically and converge at a rate
governed by the details of the stochastic process. This result establishes the
Dirac equation in one dimension as a phenomenological equation describing an
underlying classical stochastic process in the same sense that the Diffusion
and Telegraph equations are phenomenological descriptions of stochastic
processes.Comment: 15 pages, 5 figures Replacement 11/02 contains minor editorial
change
Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas
Recently, a new perspective of gravitational-thermodynamic duality as an
entropic force arising from alterations in the information connected to the
positions of material bodies is found. In this paper, we generalize some
aspects of this model in the presence of noncommutative Schwarzschild black
hole by applying the method of coordinate coherent states describing smeared
structures. We implement two different distributions: (a) Gaussian and (b)
Lorentzian. Both mass distributions prepare the similar quantitative aspects
for the entropic force. Our study shows, the entropic force on the smallest
fundamental unit of a holographic screen with radius vanishes. As a
result, black hole remnants are unconditionally inert even gravitational
interactions do not exist therein. So, a distinction between gravitational and
inertial mass in the size of black hole remnant is observed, i.e. the failure
of the principle of equivalence. In addition, if one considers the screen
radius to be less than the radius of the smallest holographic surface at the
Planckian regime, then one encounters some unusual dynamical features leading
to gravitational repulsive force and negative energy. On the other hand, the
significant distinction between the two distributions is conceived to occur
around , and that is worth of mentioning: at this regime either our
analysis is not the proper one, or non-extensive statistics should be employed.Comment: 15 pages, 2 figures, new references added, minor revision, Title
changed, to appear in EPJ Plu
The Effect of Folding on Covering Spaces, Immersions and Bifurcation for Chaotic Manifolds
Renormalization approach to the dimension of diffusion in Cantorian space
AbstractA simple renormalization group method is used to drive the Hausdorff dimension for a critical Cantorian space. The results reinforce previous ones regarding the role played by the Golden Mean dimension, Cantor triadic set and the Sierpinski gasket. Connection to diffusion and interference are also considered