Can Quantum Mechanics be shown to be Incomplete in Principle (original) (raw)
Related papers
A detailed interpretation of probability, and its link with quantum mechanics
Eprint Arxiv 1011 6331, 2010
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can be repeated in similar conditions, and that exhibit 'frequency stabilization'. The central idea of the present article is that the mentioned 'conditions' should be well-defined and 'partitioned'. More precisely, we will divide probabilistic systems into object, environment, and probing subsystem, and show that such partitioning allows to solve a wide variety of classic paradoxes of probability theory. As a corollary, we arrive at the surprising conclusion that at least one central idea of the orthodox interpretation of quantum mechanics is a direct consequence of the meaning of probability. More precisely, the idea that the "observer influences the quantum system" is obvious if one realizes that quantum systems are probabilistic systems; it holds for all probabilistic systems, whether quantum or classical.
The probabilistic roots of the quantum mechanical paradoxes
Indice 2 O. The goal of any mathematical investigation of the foundations of a physical theory is to clarify to what extent the mathematical formalism of that theory is uniquely determined by some clearly and explicitely stated physical assumptions. The achievement of that goal is particularly relevant in the case of the quantum theory where the novelty of the formalism, its being far away from any immediate intuition, the substantial failure met, for many years, by any attempt to deduce the quantum formalism from plausible physical assumptions, intersected with the never solved problems concerning the interpretation of the theory. That with quantum theory a new kind of probability theory was involved, was clear since the very beginnings of quantum mechanics (cf. [28]), even if it was not so clear which of the axioms of classifical probability had to be substituted, which physically meaningful statement had to replace it, how and if a physically meaningful statement could justify the apparently strange quantum mechanical formalism. The lack of clear answers to these questions had a tremendous impact on the process of interpretation and misinterpretation of quantum theory. The attempts to answer these questions motivated the development of a new branch of probability theory -quantum probability-and led to definite mathematical answers to these questions. In the present paper we want to discuss how these mathematical results allow to solve in a rather natural way some old problems concerning the interpretation of quantum theory and its mathematical foundations.
Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic EPR paper (EPR), the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in German. It is plagued with preconceptions about what a physical property is, the 'Uncertainty Principle', and the Principle of Locality. Numerous interpretations of QT vis à vis Reality exist and are keenly disputed. This is the first of a series of articles arguing for a physical interpretation called ‘The Ontic Probability Interpretation’ (TOPI). A gradual explanation of TOPI is given intertwined with a meticulous logico-philosophical scrutiny of EPR. Part I focuses on the meaning of Einstein’s ‘Incompleteness’ claim. A conceptual confusion, a preconception about Reality, and a flawed dichotomy are shown to be severe obstacles for the EPR argument to succeed. Part II analyzes Einstein’s ‘Incompleteness/Nonlocality Dilemma’. Future articles will further explain TOPI, demonstrating its soundness and potential for nurturing theoretical progress.
The interpretation of quantum mechanics: where do we stand?
Journal of Physics: Conference Series, 2009
We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current debate on our best theory, i.e. quantum mechanics itself. We stress that, after the remarkable interest and the many efforts which have lead, in the last years of the past century, to a revival of the subject, and, more important, to new interesting results, we are now witnessing a re-emergence of the vague and unprofessional positions which have characterized the debate in the second quarter of the XXth century. In particular we consider as extremely serious the fact that a completely mistaken position concerning the real meaning of Bell's theorem seems to have been taken by many scientists in the field. *
On the Completeness of Quantum Mechanics
2002
Quantum cryptography, quantum computer project, space-time quantization program and recent computer experiments reported by Accardi and his collaborators show the importance and actuality of the discussion of the completeness of quantum mechanics (QM) started by Einstein more than 70 years ago. Many years ago we pointed out that the violation of Bell's inequalities is neither a proof of completeness of QM nor an indication of the violation of Einsteinian causality. We also indicated how and in what sense a completeness of QM might be tested with the help of statistical nonparametric purity tests. In this paper we review and refine our arguments. We also point out that the statistical predictions of QM for two-particle correlation experiments do not give any deterministic prediction for a single pair. After beam is separated we obtain two beams moving in opposite directions. If the coincidence is reported it is only after the beams had interacted with corresponding measuring devi...
A Semantic Approach to the Completeness Problem in Quantum Mechanics
Foundations of Physics, 2000
The old Bohr-Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground. The completeness problem becomes more tractable, however, if it is preliminarily discussed from a semantic viewpoint. Indeed every physical theory adopts, explicitly or not, a truth theory for its observative language, in terms of which the notions of semantic objectivity and semantic completeness of the physical theory can be introduced and inquired. In particular, standard QM adopts a verificationist theory of truth that implies its semantic nonobjectivity; moreover, we show in this paper that standard QM is semantically complete, which matches Bohr's thesis. On the other hand, one of the authors has provided a Semantic Realism (or SR) interpretation of QM that adopts a Tarskian theory of truth as correspondence for the observative language of QM (which was previously mantained to be impossible); according to this interpretation QM is semantically objective, yet incomplete, which matches EPR's thesis. Thus, standard QM and the SR interpretation of QM come to opposite conclusions. These can be reconciled within an integrationist perspective that interpretes non-Tarskian theories of truth as theories of metalinguistic concepts different from truth.
A Philosopher's View of the Epistemic Interpretation of Quantum Mechanics
2010
There are various reasons for favouring ψ-epistemic interpretations of quantum mechanics over ψ-ontic interpretations. One such reason is the correlation between quantum mechanics and Liouville dynamics. Another reason is the success of a specific epistemic model , in reproducing a wide range of quantum phenomena. The potential criticism, that Spekkens' restricted knowledge principle is counter-intuitive, is rejected using 'everyday life' examples. It is argued that the dimensionality of spin favours Spekkens' model over ψ-ontic models. van Enk's extension of Spekkens' model can even reproduce Bell Inequality violations, but requires negative probabilities to do so. An epistemic account of negative probabilities is the missing element for deciding the battle between ψ-epistemic and ψ-ontic interpretations in favour of the former. * I owe a special thanks to Dr. Jeremy Butterfield for supervising this paper, generously providing encouragement, comments and advice. I also thank Dr. Alex Broadbent and an anonymous reviewer in the History and Philosophy Department, Cambridge University for helpful comments.
QUANTUM MECHANICS AS GENERALIZED THEORY OF PROBABILITIES
It is argued that quantum mechanics does not have merely a predictive function like other physical theories; it consists in a formalisation of the conditions of possibility of any prediction bearing upon phenomena whose circumstances of detection are also conditions of production. This is enough to explain its probabilistic status and theoretical structure. Published in: Collapse, 8, 87-121, 2014
On the missing axiom of Quantum Mechanics
2005
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an Operational Epistemic Theory. In such context the quantum superposition principle has an extraneous non epistemic nature. This leads us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces.