691 research outputs found
Quantum models of classical mechanics: maximum entropy packets
In a previous paper, a project of constructing quantum models of classical
properties has been started. The present paper concludes the project by turning
to classical mechanics. The quantum states that maximize entropy for given
averages and variances of coordinates and momenta are called ME packets. They
generalize the Gaussian wave packets. A non-trivial extension of the
partition-function method of probability calculus to quantum mechanics is
given. Non-commutativity of quantum variables limits its usefulness. Still, the
general form of the state operators of ME packets is obtained with its help.
The diagonal representation of the operators is found. A general way of
calculating averages that can replace the partition function method is
described. Classical mechanics is reinterpreted as a statistical theory.
Classical trajectories are replaced by classical ME packets. Quantum states
approximate classical ones if the product of the coordinate and momentum
variances is much larger than Planck constant. Thus, ME packets with large
variances follow their classical counterparts better than Gaussian wave
packets.Comment: 26 pages, no figure. Introduction and the section on classical limit
are extended, new references added. Definitive version accepted by Found.
Phy
Einstein, incompleteness, and the epistemic view of quantum states
Does the quantum state represent reality or our knowledge of reality? In
making this distinction precise, we are led to a novel classification of hidden
variable models of quantum theory. Indeed, representatives of each class can be
found among existing constructions for two-dimensional Hilbert spaces. Our
approach also provides a fruitful new perspective on arguments for the
nonlocality and incompleteness of quantum theory. Specifically, we show that
for models wherein the quantum state has the status of something real, the
failure of locality can be established through an argument considerably more
straightforward than Bell's theorem. The historical significance of this result
becomes evident when one recognizes that the same reasoning is present in
Einstein's preferred argument for incompleteness, which dates back to 1935.
This fact suggests that Einstein was seeking not just any completion of quantum
theory, but one wherein quantum states are solely representative of our
knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to
clarify his views on quantum theory and the circumstance of his otherwise
puzzling abandonment of an even simpler argument for incompleteness from 1927.Comment: 18 pages, 8 figures, 1 recipe for cupcakes; comments welcom
Founding quantum theory on the basis of consciousness
In the present work, quantum theory is founded on the framework of
consciousness, in contrast to earlier suggestions that consciousness might be
understood starting from quantum theory. The notion of streams of
consciousness, usually restricted to conscious beings, is extended to the
notion of a Universal/Global stream of conscious flow of ordered events. The
streams of conscious events which we experience constitute sub-streams of the
Universal stream. Our postulated ontological character of consciousness also
consists of an operator which acts on a state of potential consciousness to
create or modify the likelihoods for later events to occur and become part of
the Universal conscious flow. A generalized process of measurement-perception
is introduced, where the operation of consciousness brings into existence, from
a state of potentiality, the event in consciousness. This is mathematically
represented by (a) an operator acting on the state of potential-consciousness
before an actual event arises in consciousness and (b) the reflecting of the
result of this operation back onto the state of potential-consciousness for
comparison in order for the event to arise in consciousness. Beginning from our
postulated ontology that consciousness is primary and from the most elementary
conscious contents, such as perception of periodic change and motion, quantum
theory follows naturally as the description of the conscious experience.Comment: 41 pages, 3 figures. To be published in Foundations of Physics, Vol
36 (6) (June 2006), published online at
http://dx.doi.org/10.1007/s10701-006-9049-
Reality, measurement and locality in Quantum Field Theory
It is currently believed that the local causality of Quantum Field Theory
(QFT) is destroyed by the measurement process. This belief is also based on the
Einstein-Podolsky-Rosen (EPR) paradox and on the so-called Bell's theorem, that
are thought to prove the existence of a mysterious, instantaneous action
between distant measurements. However, I have shown recently that the EPR
argument is removed, in an interpretation-independent way, by taking into
account the fact that the Standard Model of Particle Physics prevents the
production of entangled states with a definite number of particles. This result
is used here to argue in favor of a statistical interpretation of QFT and to
show that it allows for a full reconciliation with locality and causality.
Within such an interpretation, as Ballentine and Jarret pointed out long ago,
Bell's theorem does not demonstrate any nonlocality.Comment: 15 pages. Published versio
Hidden variables with nonlocal time
To relax the apparent tension between nonlocal hidden variables and
relativity, we propose that the observable proper time is not the same quantity
as the usual proper-time parameter appearing in local relativistic equations.
Instead, the two proper times are related by a nonlocal rescaling parameter
proportional to |psi|^2, so that they coincide in the classical limit. In this
way particle trajectories may obey local relativistic equations of motion in a
manner consistent with the appearance of nonlocal quantum correlations. To
illustrate the main idea, we first present two simple toy models of local
particle trajectories with nonlocal time, which reproduce some nonlocal quantum
phenomena. After that, we present a realistic theory with a capacity to
reproduce all predictions of quantum theory.Comment: 16 pages, accepted for publication in Found. Phys., misprints
corrected, references update
Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality
We investigate possible explanations of quantum correlations that satisfy the
principle of continuity, which states that everything propagates gradually and
continuously through space and time. In particular, following [J.D. Bancal et
al, Nature Physics 2012], we show that any combination of local common causes
and direct causes satisfying this principle, i.e. propagating at any finite
speed, leads to signalling. This is true even if the common and direct causes
are allowed to propagate at a supraluminal-but-finite speed defined in a
Newtonian-like privileged universal reference frame. Consequently, either there
is supraluminal communication or the conclusion that Nature is nonlocal (i.e.
discontinuous) is unavoidable.Comment: It is an honor to dedicate this article to Yakir Aharonov, the master
of quantum paradoxes. Version 2 contains some more references and a clarified
conclusio
Violation of local realism vs detection efficiency
We put bounds on the minimum detection efficiency necessary to violate local
realism in Bell experiments. These bounds depends of simple parameters like the
number of measurement settings or the dimensionality of the entangled quantum
state. We derive them by constructing explicit local-hidden variable models
which reproduce the quantum correlations for sufficiently small detectors
efficiency.Comment: 6 pages, revtex. Modifications in the discussion for many parties in
section 3, small erros and typos corrected, conclusions unchange
Quantum Mechanics and Leggett's Inequalities
We show that when the proper description of the behaviour of individual
photons or spin 1/2 particles in a spherically symmetric entangled pair is done
through the use of the density matrix, the Leggett's inequality is not violated
by quantum mechanics.Comment: 7 pages, no figures. A missing global sign in the r.h.s. of eq.
(4.10) in section 4 of version 1 (v1) invalidates the conclusion of that
particular section, which is then suppressed in the present version (v2
On Uniqueness of the Jump Process in Quantum Measurement Theory
We prove that, contrary to the standard quantum theory of continuous
observation, in the formalism of Event Enhanced Quantum Theory the stochastic
process generating individual sample histories of pairs (observed quantum
system, observing classical apparatus) is unique. This result gives a rigorous
basis to the previous heuristic argument of Blanchard and Jadczyk. Possible
implications of this result are discussed.Comment: 31 pages, LaTeX, article; e-mail contact [email protected]
A novel determination of the local dark matter density
We present a novel study on the problem of constructing mass models for the
Milky Way, concentrating on features regarding the dark matter halo component.
We have considered a variegated sample of dynamical observables for the Galaxy,
including several results which have appeared recently, and studied a 7- or
8-dimensional parameter space - defining the Galaxy model - by implementing a
Bayesian approach to the parameter estimation based on a Markov Chain Monte
Carlo method. The main result of this analysis is a novel determination of the
local dark matter halo density which, assuming spherical symmetry and either an
Einasto or an NFW density profile is found to be around 0.39 GeV cm with
a 1- error bar of about 7%; more precisely we find a for the Einasto profile and for the NFW. This is in contrast to the
standard assumption that is about 0.3 GeV cm with an
uncertainty of a factor of 2 to 3. A very precise determination of the local
halo density is very important for interpreting direct dark matter detection
experiments. Indeed the results we produced, together with the recent accurate
determination of the local circular velocity, should be very useful to
considerably narrow astrophysical uncertainties on direct dark matter
detection.Comment: 31 pages,11 figures; minor changes in the text; two figures adde
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