102 research outputs found
A Continuous Transition Between Quantum and Classical Mechanics (I)
In spite of its popularity, it has not been possible to vindicate the
conventional wisdom that classical mechanics is a limiting case of quantum
mechanics. The purpose of the present paper is to offer an alternative
formulation of classical mechanics which provides a continuous transition to
quantum mechanics via environment-induced decoherence.Comment: Revised version, to appear in Found. of Phy
Continuous Transitions Between Quantum and Classical Electrodynamics
The Maxwell equations in the presence of sources are first derived without
making use of the potentials and the Hamilton-Jacobi equation for classical
electrodynamics is written down. The manifestly gauge invariant theory is then
quantized to write down the Hamilton-Jacobi equation in quantum
electrodynamics. Finally, an interpolating field theory is proposed that
describes continuous transitions between quantum and classical electrodynamics.
It is shown that energy flow lines are identical for quantum and classical
fields in the case of the double-slit arrangement but differ in the case of
vortex beams.Comment: 7 pages, no figures; section 1.1 edited and shortened to make it more
transparen
The Quantum-like Face of Classical Mechanics
It is first shown that when the Schr\"{o}dinger equation for a wave function
is written in the polar form, complete information about the system's {\em
quantum-ness} is separated out in a single term , the so called `quantum
potential'. An operator method for classical mechanics described by a
`classical Schr\"{o}dinger equation' is then presented, and its similarities
and differences with quantum mechanics are pointed out. It is shown how this
operator method goes beyond standard classical mechanics in predicting coherent
superpositions of classical states but no interference patterns, challenging
deeply held notions of classical-ness, quantum-ness and macro realism. It is
also shown that measurement of a quantum system with a classical measuring
apparatus described by the operator method does not have the measurement
problem that is unavoidable when the measuring apparatus is quantum mechanical.
The type of decoherence that occurs in such a measurement is contrasted with
the conventional decoherence mechanism. The method also provides a more
convenient basis to delve deeper into the area of quantum-classical
correspondence and information processing than exists at present.Comment: 9 pages, no figure
Quantum Mechanics and Quantum Information Science: The Nature of
An overview is given of the nature of the quantum mechanical wave function.Comment: 8 pages, no figure; typo correcte
The Unfinished Search for Wave-Particle and Classical-Quantum Harmony
The main purpose of this paper is to review the progress that has taken place
so far in the search for a single unifying principle that harmonizes (i) the
wave and particle natures of matter and radiation, both at the quantum and the
classical levels, on the one hand and (ii) the classical and quantum theories
of matter and radiation on the other hand. The famous paradoxes of quantum
theory, the mysterious nature of measurements in quantum theory and the
principal no-go theorems for hidden variables are first briefly reviewed. The
Koopman-von Neumann Hilbert space theory based on complex wave functions
underlying particle trajectories in classical phase space, is an important step
forward in that direction. It provides a clear and beautiful harmony of
classical waves and particles. Sudarshan has given an alternative but
equivalent formulation that shows that classical mechanics can be regarded as a
quantum theory with essentially hidden non-commuting variables. An extension of
KvNS theory to classical electrodynamics provides a sound Hilbert space
foundation to it and satisfactorily accounts for entanglement and
Bell-CHSH-like violations already observed in classical polarization optics. An
important new insight that has been obtained through these developments is that
entanglement and Bell-like inequality violations are neither unique signatures
of quantumness nor of non-locality---they are rather signatures of
non-separability. Finally, Sudarshan's proposed solution to the measurement
problem using KvNS theory for the measuring apparatus is sketched to show to
what extent wave and particles can be harmonized in quantum theory.Comment: 28 pages, 3 figures; Journal of Advanced Physics, special issue on
"Tests of Foundations of Quantum Mechanics", 201
Nonquantum Cognition
The Hilbert space structure of classical field theory is proposed as a
general theoretical framework to model human cognitive processes which do not
often follow classical (Bayesian) probability principles. This leads to an
extension of the circumplex model of affect and a Poincar\'{e} sphere
representation. A specific toy field theoretic model of the brain as a coherent
structure in the presence of noise is also proposed that agrees qualitatively
with Pavlovian fear conditioning studies.Comment: 24 pages, 2 figure
Entangling successive single-photons from quantum dots
A method is proposed for generating and discriminating Bell states of high
fidelity from consecutive single-photons generated in a semiconductor quantum
dot. The use of a non-symmetric beam splitter is found to be essential and
sufficient, and no nonlinear optical process such as SPDC is required at any
stage. This should be of considerable importance for testing the foundations of
quantum mechanics.Comment: 10 pages, 1 figur
Comments on "On Bohm trajectories in two-particle interference devices" by L. Marchildon
Marchildon's arguments against my earlier work are refuted.Comment: 4 pages, revtex, no figure
A Cosmology Inspired Unified Theory of Gravity and Electromagnetism: Classical and Quantum Aspects
Milne cosmology has recently been shown to be in broad agreement with most
cosmological data while being free of the problematic notions of standard
cosmology such as the dark sector. In this paper a broken symmetric unified
theory of gravity and electromagnetism is introduced which has a Milne metric
under a certain geometric condition. Strikingly, particles (dyons) emerge as
topological charges in this theory provided the torsion vector is
curl-less.Comment: 10 pages, no figure
Comments on Struyve and Baere's paper on experiments to distinguish Bohmian mechanics from quantum mechanics
It is shown in detail why the arguments put forward by Struyve and Baere
(quant-ph/0108038) against my conclusions are incorrect
- …