2,284 research outputs found
On Spontaneous Wave Function Collapse and Quantum Field Theory
One way of obtaining a version of quantum mechanics without observers, and
thus of solving the paradoxes of quantum mechanics, is to modify the
Schroedinger evolution by implementing spontaneous collapses of the wave
function. An explicit model of this kind was proposed in 1986 by Ghirardi,
Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the
wave function. We point out how, by focussing on the essential mathematical
structure of the GRW model and a clear ontology, it can be generalized to
(regularized) quantum field theories in a simple and natural way.Comment: 14 pages LaTeX, no figures; v2 minor improvement
Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)
The 1964 theorem of John Bell shows that no model that reproduces the
predictions of quantum mechanics can simultaneously satisfy the assumptions of
locality and determinism. On the other hand, the assumptions of \emph{signal
locality} plus \emph{predictability} are also sufficient to derive Bell
inequalities. This simple theorem, previously noted but published only
relatively recently by Masanes, Acin and Gisin, has fundamental implications
not entirely appreciated. Firstly, nothing can be concluded about the
ontological assumptions of locality or determinism independently of each other
-- it is possible to reproduce quantum mechanics with deterministic models that
violate locality as well as indeterministic models that satisfy locality. On
the other hand, the operational assumption of signal locality is an empirically
testable (and well-tested) consequence of relativity. Thus Bell inequality
violations imply that we can trust that some events are fundamentally
\emph{unpredictable}, even if we cannot trust that they are indeterministic.
This result grounds the quantum-mechanical prohibition of arbitrarily accurate
predictions on the assumption of no superluminal signalling, regardless of any
postulates of quantum mechanics. It also sheds a new light on an early stage of
the historical debate between Einstein and Bohr.Comment: Substantially modified version; added HMW as co-autho
Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Since the analysis by John Bell in 1965, the consensus in the literature is
that von Neumann's 'no hidden variables' proof fails to exclude any significant
class of hidden variables. Bell raised the question whether it could be shown
that any hidden variable theory would have to be nonlocal, and in this sense
'like Bohm's theory.' His seminal result provides a positive answer to the
question. I argue that Bell's analysis misconstrues von Neumann's argument.
What von Neumann proved was the impossibility of recovering the quantum
probabilities from a hidden variable theory of dispersion free (deterministic)
states in which the quantum observables are represented as the 'beables' of the
theory, to use Bell's term. That is, the quantum probabilities could not
reflect the distribution of pre-measurement values of beables, but would have
to be derived in some other way, e.g., as in Bohm's theory, where the
probabilities are an artefact of a dynamical process that is not in fact a
measurement of any beable of the system.Comment: 8 pages, no figures; for Peter Mittelstaedt Festschrift issue of
Foundations of Physic
Does quantum nonlocality irremediably conflict with Special Relativity?
We reconsider the problem of the compatibility of quantum nonlocality and the
requests for a relativistically invariant theoretical scheme. We begin by
discussing a recent important paper by T. Norsen [arXiv:0808.2178] on this
problem and we enlarge our considerations to give a general picture of the
conceptually relevant issue to which this paper is devoted.Comment: 18 pages, 1 figur
Non-local Realistic Theories and the Scope of the Bell Theorem
According to a widespread view, the Bell theorem establishes the untenability
of so-called 'local realism'. On the basis of this view, recent proposals by
Leggett, Zeilinger and others have been developed according to which it can be
proved that even some non-local realistic theories have to be ruled out. As a
consequence, within this view the Bell theorem allows one to establish that no
reasonable form of realism, be it local or non-local, can be made compatible
with the (experimentally tested) predictions of quantum mechanics. In the
present paper it is argued that the Bell theorem has demonstrably nothing to do
with the 'realism' as defined by these authors and that, as a consequence,
their conclusions about the foundational significance of the Bell theorem are
unjustified.Comment: Forthcoming in Foundations of Physic
Response to Nauenberg's "Critique of Quantum Enigma: Physics Encounters Consciousness"
Nauenberg's extended critique of Quantum Enigma rests on fundamental
misunderstandings.Comment: To be published in Foundations of Physic
Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'
The starting point of the present paper is Bell's notion of local causality
and his own sharpening of it so as to provide for mathematical formalisation.
Starting with Norsen's (2007, 2009) analysis of this formalisation, it is
subjected to a critique that reveals two crucial aspects that have so far not
been properly taken into account. These are (i) the correct understanding of
the notions of sufficiency, completeness and redundancy involved; and (ii) the
fact that the apparatus settings and measurement outcomes have very different
theoretical roles in the candidate theories under study. Both aspects are not
adequately incorporated in the standard formalisation, and we will therefore do
so. The upshot of our analysis is a more detailed, sharp and clean mathematical
expression of the condition of local causality. A preliminary analysis of the
repercussions of our proposal shows that it is able to locate exactly where and
how the notions of locality and causality are involved in formalising Bell's
condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and
Confirmation", edited by Dieks, et a
On a recent proof of nonlocality without inequalities
Recently a quite stimulating paper [1] dealing with the possibility of
exploiting the nonlocal aspects of a superposition of states of a single photon
appeared. We regard as greatly relevant the results which have been obtained.
However we think that the presentation of the matter and the way to derive the
conclusion are not fully satisfactory and do not put the necessary emphasis on
some subtle basic aspects like locality and realism. In view of its interest we
consider it useful to reconsider the line of reasoning of ref.[1] and to derive
once more its results by following a procedure which seems to us more lucid and
which makes fully clear the role of the various conceptual aspects of the
treatment. We hope that our analysis will contribute to clarify and to deepen
the interesting results of ref.[1]
Observables have no value: a no-go theorem for position and momentum observables
A very simple illustration of the Bell-Kochen-Specker contradiction is
presented using continuous observables in infinite dimensional Hilbert space.
It is shown that the assumption of the \emph{existence} of putative values for
position and momentum observables for one single particle is incompatible with
quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments
adde
Nonlocality of Two-Mode Squeezing with Internal Noise
We examine the quantum states produced through parametric amplification with
internal quantum noise. The internal diffusion arises by coupling both modes of
light to a reservoir for the duration of the interaction time. The Wigner
function for the diffused two-mode squeezed state is calculated. The
nonlocality, separability, and purity of these quantum states of light are
discussed. In addition, we conclude by studying the nonlocality of two other
continuous variable states: the Werner state and the phase-diffused state for
two light modes.Comment: 7 pages, 5 figures, submitted to PR
- …