115 research outputs found
Quantum Cybernetics: A New Perspective for Nelson's Stochastic Theory, Nonlocality, and the Klein-Gordon Equation
The Klein-Gordon equation is shown to be equivalent to coupled partial
differential equations for a sub-quantum Brownian movement of a ''particle'',
which is both passively affected by, and actively affecting, a diffusion
process of its generally nonlocal environment. This indicates circularly
causal, or ''cybernetic'', relationships between ''particles'' and their
surroundings. Moreover, in the relativistic domain, the original stochastic
theory of Nelson is shown to hold as a limiting case only, i.e., for a
vanishing quantum potential.Comment: 21 pages; published in Phys. Lett. A 296 (2002) 1 -
Definition and evolution of quantum cellular automata with two qubits per cell
Studies of quantum computer implementations suggest cellular quantum computer
architectures. These architectures can simulate the evolution of quantum
cellular automata, which can possibly simulate both quantum and classical
physical systems and processes. It is however known that except for the trivial
case, unitary evolution of one-dimensional homogeneous quantum cellular
automata with one qubit per cell is not possible. Quantum cellular automata
that comprise two qubits per cell are defined and their evolution is studied
using a quantum computer simulator. The evolution is unitary and its linearity
manifests itself as a periodic structure in the probability distribution
patterns.Comment: 13 pages, 4 figure
The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics
By assuming that a particle of energy hbar.omega is actually a dissipative
system maintained in a nonequilibrium steady state by a constant throughput of
energy (heat flow), the exact Schroedinger equation is derived, both for
conservative and nonconservative systems. Thereby, only universal properties of
oscillators and nonequilibrium thermostatting are used, such that a maximal
model independence of the hypothesised sub-quantum physics is guaranteed. It is
claimed that this represents the shortest derivation of the Schroedinger
equation from (modern) classical physics in the literature, and the only exact
one, too. Moreover, a "vacuum fluctuation theorem" is presented, with
particular emphasis on possible applications for a better understanding of
quantum mechanical nonlocal effects.Comment: 39 pages; sign error in equ. (3.2.29) now correcte
An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations
A classical explanation of interference effects in the double slit experiment
is proposed. We claim that for every single "particle" a thermal context can be
defined, which reflects its embedding within boundary conditions as given by
the totality of arrangements in an experimental apparatus. To account for this
context, we introduce a "path excitation field", which derives from the
thermodynamics of the zero-point vacuum and which represents all possible paths
a "particle" can take via thermal path fluctuations. The intensity distribution
on a screen behind a double slit is calculated, as well as the corresponding
trajectories and the probability density current. The trajectories are shown to
obey a "no crossing" rule with respect to the central line, i.e., between the
two slits and orthogonal to their connecting line. This agrees with the Bohmian
interpretation, but appears here without the necessity of invoking the quantum
potential.Comment: 26 pages, 6 figures; accepted version to be published in Annals of
Physics (2012
A classical explanation of quantization
In the context of our recently developed emergent quantum mechanics, and, in
particular, based on an assumed sub-quantum thermodynamics, the necessity of
energy quantization as originally postulated by Max Planck is explained by
means of purely classical physics. Moreover, under the same premises, also the
energy spectrum of the quantum mechanical harmonic oscillator is derived.
Essentially, Planck's constant h is shown to be indicative of a particle's
"zitterbewegung" and thus of a fundamental angular momentum. The latter is
identified with quantum mechanical spin, a residue of which is thus present
even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic
Quantum Walks and Reversible Cellular Automata
We investigate a connection between a property of the distribution and a
conserved quantity for the reversible cellular automaton derived from a
discrete-time quantum walk in one dimension. As a corollary, we give a detailed
information of the quantum walk.Comment: 15 pages, minor corrections, some references adde
Quantum features derived from the classical model of a bouncer-walker coupled to a zero-point field
In our bouncer-walker model a quantum is a nonequilibrium steady-state
maintained by a permanent throughput of energy. Specifically, we consider a
"particle" as a bouncer whose oscillations are phase-locked with those of the
energy-momentum reservoir of the zero-point field (ZPF), and we combine this
with the random-walk model of the walker, again driven by the ZPF. Starting
with this classical toy model of the bouncer-walker we were able to derive
fundamental elements of quantum theory. Here this toy model is revisited with
special emphasis on the mechanism of emergence. Especially the derivation of
the total energy hbar.omega and the coupling to the ZPF are clarified. For this
we make use of a sub-quantum equipartition theorem. It can further be shown
that the couplings of both bouncer and walker to the ZPF are identical. Then we
follow this path in accordance with previous work, expanding the view from the
particle in its rest frame to a particle in motion. The basic features of
ballistic diffusion are derived, especially the diffusion constant D, thus
providing a missing link between the different approaches of our previous
works.Comment: 14 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz
von Foerster Conference 2011)", see
http://www.univie.ac.at/hvf11/congress/EmerQuM.htm
On the absence of homogeneous scalar unitary cellular automata
Failure to find homogeneous scalar unitary cellular automata (CA) in one
dimension led to consideration of only ``approximately unitary'' CA---which
motivated our recent proof of a No-go Lemma in one dimension. In this note we
extend the one dimensional result to prove the absence of nontrivial
homogeneous scalar unitary CA on Euclidean lattices in any dimension.Comment: 7 pages, plain TeX, 3 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); minor changes (including
title wording) in response to referee suggestions, also updated references;
to appear in Phys. Lett.
On the digraph of a unitary matrix
Given a matrix M of size n, a digraph D on n vertices is said to be the
digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is
an arc of D. We give a necessary condition, called strong quadrangularity, for
a digraph to be the digraph of a unitary matrix. With the use of such a
condition, we show that a line digraph, LD, is the digraph of a unitary matrix
if and only if D is Eulerian. It follows that, if D is strongly connected and
LD is the digraph of a unitary matrix then LD is Hamiltonian. We conclude with
some elementary observations. Among the motivations of this paper are coined
quantum random walks, and, more generally, discrete quantum evolution on
digraphs.Comment: 6 page
Quantization in classical mechanics and reality of Bohm's psi-field
Based on the Chetaev theorem on stable dynamical trajectories in the presence
of dissipative forces, we obtain the generalized condition for stability of
Hamilton systems in the form of the Schrodinger equation. It is shown that the
energy of dissipative forces, which generate the Chetaev generalized condition
of stability, coincides exactly with the Bohm "quantum" potential. Within the
framework of Bohmian quantum mechanics supplemented by the generalized Chetaev
theorem and on the basis of the principle of least action for dissipative
forces, we show that the squared amplitude of a wave function in the
Schrodinger equation is equivalent semantically and syntactically to the
probability density function for the number of particle trajectories, relative
to which the velocity and the position of the particle are not hidden
parameters. The conditions for the correctness of the Bohm-Chetaev
interpretation of quantum mechanics are discussed.Comment: 16 pages, significant improvement after 0806.4050 and 0804.1427. (v2)
revised and reconsidered conclusion
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