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![A graph of the binning state, λ≡{ni}\documentclass[12pt]{minimal}...](publication/329043561/figure/fig1/AS:961466937131058@1606242989710/A-graph-of-the-binning-state-lnidocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs’ general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must, the fundamentally statistical character of quantum mechanics. This is illustrated by drawing an analogy with an...
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Citations
... Such a theorem had a remarkable resonance [13][14][15][16][17][18][19][20][21][22][23][24][25], and questions about its actual meaning are still discussed today: on the one hand, some authors believe that it rules out interpretations of QM where merely represents information. On the other hand, it has recently been shown by other scholars that non-trivial epistemic as well as statistical approaches to QM are not refuted by the PBR argument [10,[26][27][28][29]. ...
In this paper we show that ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontic models, as defined by Harrigan and Spekkens (HS), cannot reproduce quantum theory. Instead of focusing on probability, we use information theoretic considerations to show that all pure states of ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontic models must be orthogonal to each other, in clear violation of quantum mechanics. Given that (i) Pusey, Barrett and Rudolph (PBR) previously showed that ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-epistemic models, as defined by HS, also contradict quantum mechanics, and (ii) the HS categorization is exhausted by these two types of models, we conclude that the HS categorization itself is problematic as it leaves no space for models that can reproduce quantum theory.
... Such a theorem had a remarkable resonance [13][14][15][16][17][18][19][20][21][22][23][24][25], and questions about its actual meaning are still discussed today: on the one hand, some authors believe that it rules out interpretations of QM where ψ merely represents information. On the other hand, it has recently been shown by other scholars that non-trivial epistemic as well as statistical approaches to QM are not refuted by the PBR argument [10,[26][27][28][29]. ...
... The ket represents an ensemble of possibilities. 41,42,43 This means that in the superposition state (15) consists of an ensemble some members of which have a dead cat and some members have an alive cat. And, in the filled out view, each member has a guiding wave structure one element of which is the same as any other member. ...
A simple way, accessible to undergraduates, is given to understand measurements in quantum mechanics. The ensemble interpretation of quantum mechanics is natural and provides this simple access to the measurement problem. This paper explains measurement in terms of this relatively young interpretation, first made rigorous by L. Ballentine starting in the 1970's. Its facility is demonstrated through a detailed explication of the Wigner Friend argument using the Stern Gerlach experiment. Following a recent textbook, this approach is developed further through analysis of free particle states as well as the Schrodinger cat paradox. Some pitfalls of the Copenhagen interpretation are drawn out.
... The ensemble interpretation is used to explain the real meaning PBR theorem in Rizzi[7].2 For the analysis in the ensemble interpretation see Reference[3]. ...
A recent no-go theorem gives an extension of the Wigner’s Friend argument that purports to prove the “Quantum theory cannot consistently describe the use of itself.” The argument is complex and thought provoking, but fails in a straightforward way if one treats QM as a statistical theory in the most fundamental sense, i.e. if one applies the so-called ensemble interpretation. This explanation is given here at an undergraduate level, which can be edifying for experts and students alike. A recent paper has already shown that the no-go theorem is incorrect with regard to the de Broglie Bohm theory and misguided in some of its general claims. This paper’s contribution is three fold. It shows how the extended Wigner’s Friend argument fails in the ensemble interpretation. It also makes more evident how natural a consistent statistical treatment of the wave function is. In this way, the refutation of the argument is useful for bringing out the core statistical nature of QM. It, in addition, manifests the unnecessary complications and problems introduced by the collapse mechanism that is part of the Copenhagen interpretation. The paper uses the straightforwardness of the ensemble interpretation to make the no-go argument and its refutation more accessible.
... Despite this, many still view the quantum mechanical state as wholly or partly epistemic [213,216,217]. Their view is tenable given the clear scope to reject or challenge one or more of the explicit or implicit assumptions [ [219][220][221][222]. Ongoing arguments for the ontic view [223] appear to be similarly inconclusive [217,224]. ...
This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.
... Since the inception of Quantum Mechanics (QM), there has been an on-going discussion on the ontology of the theory and its interpretations. In particular, there has been recently an intense debate on the validity of the so-called statistical interpretation of QM, see 1,2 . The ontological problem of QM is manifested especially clearly in the measurement problem. ...
The main contribution of this paper is to explain where the imaginary structure comes from in quantum mechanics. It is shown how the demand of relativistic invariance is key and how the geometric structure of the spacetime together with the demand of linearity are fundamental in understanding the foundations of quantum mechanics. We derive the Stueckelberg covariant wave equation from first principles via a stochastic control scheme. From the Stueckelberg wave equation a Telegrapher’s equation is deduced, from which the classical relativistic and nonrelativistic equations of quantum mechanics can be derived in a straightforward manner. We therefore provide meaningful insight into quantum mechanics by deriving the concepts from a coordinate invariant stochastic optimization problem, instead of just stating postulates.
... Despite this, many still view the quantum mechanical state as wholly or partly epistemic [213,216,217]. Their view is tenable given the clear scope to reject or challenge one or more of the explicit or implicit assumptions [ [219][220][221][222]. Ongoing arguments for the ontic view [223] appear to be similarly inconclusive [217,224]. ...
This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.
