150 research outputs found
Geometrization of Classical Wave Fields
Geometrical model for material Dirac wave field and for Maxwell
electromagnetic field is suggested where above fields are considered as
propagating regions of the space itself with distorted euclidean geometry. It
is shown that equations for these fields can be considered as relations
describing the space topological defects. These defects, being closed
topological manifolds, are embedded in the outer five-dimensional space, and
observable objects appear to be intersections of above defects with the
physical space. This interpretation explains irrational properties of quantum
objects such as wave-corpuscular duality, stochastic behavior, instantaneous
nonlocal correlation in EPR-paradox, the light velocity invariance and so on.
Wave-corpuscular properties arise as a result of the defect periodical movement
in the outer space relative to its intersection with the physical space, and
just this periodical movement attributes phase to the propagating object.
Appearance of probabilities within the formalism is a consequence of
uncertainty of the closed topological manifold shape, and ensemble of all
possible shapes for the same object can be considered as an ensemble of hidden
variables that leads to probabilistic description. Embedded in the outer space
topological defects provide channels for nonlocal correlations between their
intersections-- noninteracting particles in EPR-experiments, and this means
that the proposed approach can be considered as a nonlocal model with hidden
variables.Comment: 7 pages, Int.Conf.,Quantum Theory: Reconsideration of Foundations-4,
Vaxjo, Sweden. 11-16 June 200
Is Bell's theorem relevant to quantum mechanics? On locality and non-commuting observables
Bell's theorem is a statement by which averages obtained from specific types
of statistical distributions must conform to a family of inequalities. These
models, in accordance with the EPR argument, provide for the simultaneous
existence of quantum mechanically incompatible quantities. We first recall
several contradictions arising between the assumption of a joint distribution
for incompatible observables and the probability structure of
quantum-mechanics, and conclude that Bell's theorem is not expected to be
relevant to quantum phenomena described by non-commuting observables,
irrespective of the issue of locality. Then, we try to disentangle the locality
issue from the existence of joint distributions by introducing two models
accounting for the EPR correlations but denying the existence of joint
distributions. We will see that these models do not need to resort explicitly
to non-locality: the first model relies on conservation laws for ensembles, and
the second model on an equivalence class by which different configurations lead
to the same physical predictions.Comment: Extended with new materia
Priors in quantum Bayesian inference
In quantum Bayesian inference problems, any conclusions drawn from a finite
number of measurements depend not only on the outcomes of the measurements but
also on a prior. Here we show that, in general, the prior remains important
even in the limit of an infinite number of measurements. We illustrate this
point with several examples where two priors lead to very different conclusions
given the same measurement data.Comment: 7 pages; published in AIP Conference Proceedings 1101: Foundations of
Probability and Physics 5, edited by L. Accardi et al, p. 255 (2009
Bohm's quantum potential and quantum force in superconductor
The Bohm's quantum potential, introduced in 1952, and the quantum force in
superconductor, introduced in 2001, allow to describe non-local force-free
momentum transfer observed in the Ahronov-Bohm effects. Comparison of the
Ahronov-Bohm effects in the two-slit interference experiment and in
superconductor ring reveals fundamental difference between the Schrodinger wave
function and the wave function describing macroscopic quantum phenomena. The
Ginzburg-Landau wave function describing the superconductivity phenomenon can
not collapse and an additional postulate, which was implied first by L.D.
Landau, must be used for the description of macroscopic quantum phenomena. It
is note that quantum principles and postulates should not be universal till the
quantum formalism is only phenomenological theory but no description of an
unique reality. A simple Gedankenexperiment is considered which challenges the
universality of the Heisenberg uncertainty relation and the Bohr's
complementarity principle.Comment: 9 pages, 1 figure, the Invited talk was presented at the conference
"Foundations of Probability and Physics-5" Vaxjo University, Sweden, August
24-27, 200
An analog of Heisenberg uncertainty relation in prequantum classical field theory
Prequantum classical statistical field theory (PCSFT) is a model which
provides a possibility to represent averages of quantum observables, including
correlations of observables on subsystems of a composite system, as averages
with respect to fluctuations of classical random fields. PCSFT is a classical
model of the wave type. For example, "electron" is described by electronic
field. In contrast to QM, this field is a real physical field and not a field
of probabilities. An important point is that the prequantum field of e.g.
electron contains the irreducible contribution of the background field, vacuum
fluctuations. In principle, the traditional QM-formalism can be considered as a
special regularization procedure: subtraction of averages with respect to
vacuum fluctuations. In this paper we derive a classical analog of the
Heisenberg-Robertson inequality for dispersions of functionals of classical
(prequantum) fields. PCSFT Robertson-like inequality provides a restriction on
the product of classical dispersions. However, this restriction is not so rigid
as in QM. The quantum dispersion corresponds to the difference between e.g. the
electron field dispersion and the dispersion of vacuum fluctuations. Classical
Robertson-like inequality contains these differences. Hence, it does not imply
such a rigid estimate from below for dispersions as it was done in QM
What's wrong with this rebuttal?
A recent rebuttal to criticism of Bell's analysis is shown to be defective by
fault of failure to consider all hypothetical conditions input into the
derivation of Bell Inequalitites.Comment: 2 page
About Essence of the Wave Function on Atomic Level and in Superconductors
The wave function was proposed for description of quantum phenomena on the
atomic level. But now it is well known that quantum phenomena are observed not
only on atomic level and the wave function is used for description of
macroscopic quantum phenomena, such as superconductivity. The essence of the
wave function on level elementary particles was and is the subject of heated
argument among founders of quantum mechanics and other physicists. This essence
seems more clear in superconductor. But impossibility of probabilistic
interpretation of wave function in this case results to obvious contradiction
of quantum principles with some fundamental principles of physics.Comment: 5 page
Understanding quantization: a hidden variable model
We argue that to solve the foundational problems of quantum theory one has to
first understand what it means to quantize a classical system. We then propose
a quantization method based on replacement of deterministic c-numbers by
stochastically-parameterized c-numbers. Unlike canonical quantization, the
method is free from operator ordering ambiguity and the resulting quantum
system has a straightforward interpretation as statistical modification of
ensemble of classical trajectories. We then develop measurement without wave
function collapse \`a la pilot-wave theory and point out new testable
predictions.Comment: 16 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz
von Foerster Conference 2011)", see http://iopscience.iop.org/1742-6596/361/
Classical signal model reproducing quantum probabilities for single and coincidence detections
We present a simple classical (random) signal model reproducing Born's rule.
The crucial point of our approach is that the presence of detector's threshold
and calibration procedure have to be treated not as simply experimental
technicalities, but as the basic counterparts of the theoretical model. We call
this approach threshold signal detection model (TSD). The experiment on
coincidence detection which was done by Grangier in 1986 \cite{Grangier} played
a crucial role in rejection of (semi-)classical field models in favor of
quantum mechanics (QM): impossibility to resolve the wave-particle duality in
favor of a purely wave model. QM predicts that the relative probability of
coincidence detection, the coefficient is zero (for one photon
states), but in (semi-)classical models In TSD the
coefficient decreases as where is
the detection threshold. Hence, by increasing this threshold an experimenter
can make the coefficient essentially less than 1. The
TSD-prediction can be tested experimentally in new Grangier type experiments
presenting a detailed monitoring of dependence of the coefficient
on the detection threshold
Embedding Quantum Mechanics Into a Broader Noncontextual Theory: A Conciliatory Result
The extended semantic realism (ESR) model embodies the mathematical formalism
of standard (Hilbert space) quantum mechanics in a noncontextual framework,
reinterpreting quantum probabilities as conditional instead of absolute. We
provide here an improved version of this model and show that it predicts that,
whenever idealized measurements are performed, a modified
Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality holds if one takes into
account all individual systems that are prepared, standard quantum predictions
hold if one considers only the individual systems that are detected, and a
standard BCHSH inequality holds at a microscopic (purely theoretical) level.
These results admit an intuitive explanation in terms of an unconventional kind
of unfair sampling and constitute a first example of the unified perspective
that can be attained by adopting the ESR model.Comment: 24 pages, standard Latex, Extensively revised versio
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