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