Epistemic Horizons: This Sentence is 1/√2(|True> + |False>) (original) (raw)
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Epistemic Horizons and the Foundations of Quantum Mechanics
Foundations of Physics, 2018
In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to F. W. Lawvere that illuminates and unifies the different perspectives on self-reference.
Epistemic Horizons: This Sentence is 1/√2(|True> + |False>) (Book Version)
Undecidability, Uncomputability, and Unpredictability, 2021
In [Found. Phys. 48.12 (2018): 1669], the notion of epistemic horizon was introduced as an explanation for many of the puzzling features of quantum mechanics. There, it was shown that Lawvere's theorem, which forms the categorical backdrop to phenomena such as Gödelian incompleteness, Turing undecidability, Russell's paradox and others, applied to a measurement context, yields bounds on the maximum knowledge that can be obtained about a system, which produces many paradigmatically quantum phenomena. We give a brief presentation of the framework, and then demonstrate how it naturally yields Bell inequality violations. We then study the argument due to Einstein, Podolsky, and Rosen, and show how the counterfactual inference needed to conclude the incompleteness of the quantum formalism is barred by the epistemic horizon. Similarly, the paradoxes due to Hardy and Frauchiger-Renner are discussed, and found to turn on an inconsistent combination of information from incompatible contexts.
We offer the hypothesis that the paradoxical element which surfaced as a result of the EP R argument—due to the perceived conflict implied by Bell's inequality between the, seemingly essential, non-locality required by current interpretations of Quantum Mechanics, and the essential locality required by current interpretations of Classical Mechanics—may merely reflect a lack of recognition that any mathematical language which can adequately express—and effectively communicate—the laws of nature, may be consistent under two, essentially different but complementary and not contradictory, logics for assigning truth values to the propositions of the language, such that the latter are capable of representing—as deterministic—the unpredictable characteristics of quantum behaviour. We show how the anomaly may dissolve if a physicist could cogently argue that: (i) All properties of physical reality are deterministic, but not necessarily mathematically predetermined—in the sense that any physical property could have one, and only one, value at any time t(n), where the value is completely determined by some natural law which need not, however, be representable by algorithmically computable expressions (and therefore be mathematically predictable). (ii) There are elements of such a physical reality whose properties at any time t(n) are determined completely in terms of their putative properties at some earlier time t(0). Such properties are predictable mathematically since they are representable by algorithmically computable functions. The values of any two such functions with respect to their variables are, by definition, independent of each other and must, therefore, obey Bell's inequality. The Laws of Classical Mechanics determine the nature and behaviour of such physical reality only, and circumscribe the limits of reasoning and cognition in any emergent mechanical intelligence. (iii) There could be elements of such a physical reality whose properties at any time t(n) cannot be theoretically determined completely from their putative properties at some earlier time t(0). Such properties are unpredictable mathematically since they are only representable mathematically by algorithmically verifiable, but not algorithmically computable, functions. The values of any two such functions with respect to their variables may, by definition, be dependent on each other and need not, therefore, obey Bell's inequality. The Laws of Quantum Mechanics determine the nature and behaviour of such physical reality, and circumscribe the limits of reasoning and cognition in any emergent humanlike intelligence. In this paper we formally define the common language, but distinctly different logics, of such functions, and suggest a perspective from which to view the anomalous philosophical issues underlying some current concepts of quantum phenomena such as indeterminacy, fundamental dimensionless constants, conjugate properties, uncertainty, entanglement, EPR paradox, Bell's inequalities, and Schrödinger's cat paradox. We also briefly indicate the significance of such a perspective for defining the concept of emergence in a mechanical intelligence.
Einstein, Incompleteness, and the Epistemic View of Quantum States
Foundations of Physics, 2010
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.
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.
A new model for quantum mechanics and the invalidity of no-go theorems
In this paper we define and study the new model for quantum mechanics (QM) – the hybrid epistemic model. The new feature of this model consists in the fact that it does not contain the formal definition of the measurement process but the measurement process is one of possible processes inside of QM. The hybrid-epistemic model of QM is based on two concepts: the quantum state of an ensemble and the properties of individual systems. We show the local nature of EPR correlations in the hybrid-epistemic model of QM in all details. We define precisely the epistemic and the ontic models of QM for the goal to prove that these three models give the same empirical predictions, i.e. that they are empirically equivalent. We show that the no-go theorems (Bell’s theorem, the Leggett-Garg’s theorem and others theorems) cannot be proved in the hybrid-epistemic model of QM. This is one of the main results of this paper. We shall consider the possible inconsistences of the ontic model of QM. We introduce the property-epistemic model of QM which is the special simple case of the hybrid-epistemic model.
Bell’s Theorem Tells Us Not What Quantum Mechanics Is, but What Quantum Mechanics Is Not
Quantum [Un]Speakables II
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything, then it is rather the significance of the principle of Bohr, but even this is not a clear implication. Non-locality is a necessary consequence of Bell's theorem only if we reject complementarity by adopting some form of realism, be it additional hidden variables, additional hidden causes, etc., or counterfactual definiteness. The essay contains two largely independent parts. The first one is addressed to any reader interested in the topic. The second, discussing the notion of local causality, is addressed to people working in the field.
The hybrid-epistemic model of quantum mechanics and the possible solution to the measurement problem
In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr's view (the ontic model) and the Einstein's view (the epistemic model).
The Problem of Truth in Quantum Mechanics
Global Philosophy (Axiomathes), 2023
There is a large literature on the issue of the lack of properties (i.e. accidents) in quantum mechanics (the problem of "hidden variables") and also on the indistinguishability of particles. Both issues were discussed as far back as the late 1920's. However, the implications of these challenges to classical ontology were taken up rather late, in part in the 'quantum set theory' of Takeuti (1981), Finkelstein (1981) and the work of Décio Krause (1992)-and subsequent publications). But the problems created by quantum mechanics go far beyond set theory or the identity of indiscernibles (another subject that has been often discussed)-it extends, I argue, to our accounts of truth. To solve this problem, i.e. to have an approach to truth that facilitates a transition from a classical to a quantum ontology one must have a unified framework for them both. This is done within the context of a pluralist view of truthmaking, where the truthmakers are unified in having a monoidal structure. The structure of the paper is as follows. After a brief introduction, the idea of a monoid is outlined (in §1) followed by a standard set of axioms that govern the truthmaker relation from elements of the monoid to the set of propositions. This is followed, in §2, by a discussion of how to have truthmakers for two kinds of necessities: tautologies and analytic truths. The next section, §3, then applies these ideas to quantum mechanics. It gives an account of quantum states and shows how these form a monoid. The final section then argues that quantum logic does not, despite what one might initially suspect, stand in the way of a account of quantum truth.
On the Bell Experiment and Quantum Foundation
The Bell experiment is discussed in light of a new approach towards the foundation of quantum mechanics. It is concluded from the basic model that the mind of any observer must be limited in some way: In certain contexts, he is simply not able to keep enough variables in his mind when making decisions. This has consequences for Bell's theorem, but it also seems to have wider consequences.