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Routledge eBooks

Exploring the depths of existence

Sudip Patra, Menas C. Kafatos

Published May 26, 2026• 0 citations
Publisher

Abstract

We have referred to general organising principles of quantum mechanics (QM) in the previous chapter, which can be extended (as principles) to several other domains. Among such principles, contextuality-complementarity is perhaps most important in its applicability to different domains of reality. There is a consensus now ( Khrennikov, 2022 ) that these principles emerged through the original works of N. Bohr. Khrennikov (2025) has produced a seminal work in which contextuality becomes the basis of reformulation of QM, and even non-locality, which is argued to be a central feature in the orthodox QM interpretation (rather than the Copenhagen(ish) approaches), can also be reformulated in terms of local contextuality. We will hold a different approach to non-locality later in the chapter, which builds upon our earlier works ( Nadeau and Kafatos, 2001 ). We also mention here that some authors ( Plotnitsky, 2022 ) have attempted to formulate a ‘reality without realism’ view based on Bohr’s original insights. In this chapter, we provide a more detailed view of Copenhagen(ish) approaches to contextuality-complementarity. Since we think that a quantum-like framework (QLF) is also related to such approaches, contextuality-complementarity in QLF can also be formulated in the same line.

DOI
10.4324/9781003688198-5

Related papers

Quantum-like reality, subjective experiences, and the quantum physical world

Sudip Patra, Menas C. Kafatos

The current chapter is a continuation of the previous chapter, since it explores more general principles which provides the basis of quantum-like reality proposal. We argue in this book that the contextuality principle, which is becoming revealed as a central principle of quantum mechanics and quantum information theory, is also a central principle for cognitive and social decision-making domains. Recently, multiple general logico-philosophical frameworks have been proposed to describe contextuality in general, and the current chapter is in the same direction.

Routledge eBooks•May 26, 2026•0 citations

Information Interpretations of Quantum Mechanics

Andrei Yu. Khrennikov

We start with discussion on Bohr’s response to the EPR argument andexplain how Bohr was able to sail between Scylla (incompleteness) andCharybdis (nonlocality) towards the consistent interpretation of quantumtheory. We call the latter the Bohr interpretation and distinguish it fromthe commonly used orthodox Copenhagen interpretation. We point to connectionbetween the complementarity principle and the information interpretationof QM and briefly discuss its versions, starting withSchrödinger and continuing to the information quantization interpretation(Zeilinger, Brukner), QBism (Fuchs et al.), reality without realism (RWR,Plotnitsky), the Växjö interpretation (Khrennikov), and derivations of thequantum formalism from the information axioms (e.g., D’Ariano et al.). Oneof the main distinguishing features of the information interpretation is the possibility of structuring thequantum foundations without nonlocality and spooky actionat a distance.

Cambridge University Press eBooks•Nov 28, 2024•0 citations

Bohr's complementarity

Diego S. Starke, Jonas Maziero, Marcos L. W. Basso +1 more

Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.

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Quantum contextuality in the Copenhagen approach

Gregg S. Jaeger

The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 16, 2019•18 citations

Entanglement limits duality and vice versa

Xiao‐Feng Qian, A. Nick Vamivakas, Joseph H. Eberly

Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.

arXiv:1803.04611•Optica•Jul 30, 2018•91 citations

Truth by fiat

Álvaro Balsas, A. L. L. Videira

The purpose is, first, to review the occurrences which led to the acceptance by the bulk of physicists of the instrumentalist approach to quantum mechanics (QM) as the only one worth considering as truly rendering nature at the atomic level. Formulated soon after the creation of QM it outright refused the local realist interpretation. Next, to bring out the successive waves of dissenting voices, which still go on unabated. Finally, to recall that – in spite of the pervading dominance of the Copenhagen reading of quantum phenomena – the manifold questions concerning the interpretation of QM continue to be the subject-matter of forceful interventions claiming that the foundational basis of QM is far from being definitely closed.

Revista Brasileira de História da Ciência•Dec 27, 2013•1 citation
We have referred to general organising principles of quantum mechanics (QM) in the previous chapter, which can be extended (as principles) to several other domains. Among such principles, contextuality-complementarity is perhaps most important in its applicability to different domains of reality. There is a consensus now ( Khrennikov, 2022 ) that these principles emerged through the original works of N. Bohr. Khrennikov (2025) has produced a seminal work in which contextuality becomes the basis of reformulation of QM, and even non-locality, which is argued to be a central feature in the orthodox QM interpretation (rather than the Copenhagen(ish) approaches), can also be reformulated in terms of local contextuality. We will hold a different approach to non-locality later in the chapter, which builds upon our earlier works ( Nadeau and Kafatos, 2001 ). We also mention here that some authors ( Plotnitsky, 2022 ) have attempted to formulate a ‘reality without realism’ view based on Bohr’s original insights. In this chapter, we provide a more detailed view of Copenhagen(ish) approaches to contextuality-complementarity. Since we think that a quantum-like framework (QLF) is also related to such approaches, contextuality-complementarity in QLF can also be formulated in the same line.
The current chapter is a continuation of the previous chapter, since it explores more general principles which provides the basis of quantum-like reality proposal. We argue in this book that the contextuality principle, which is becoming revealed as a central principle of quantum mechanics and quantum information theory, is also a central principle for cognitive and social decision-making domains. Recently, multiple general logico-philosophical frameworks have been proposed to describe contextuality in general, and the current chapter is in the same direction.
We start with discussion on Bohr’s response to the EPR argument andexplain how Bohr was able to sail between Scylla (incompleteness) andCharybdis (nonlocality) towards the consistent interpretation of quantumtheory. We call the latter the Bohr interpretation and distinguish it fromthe commonly used orthodox Copenhagen interpretation. We point to connectionbetween the complementarity principle and the information interpretationof QM and briefly discuss its versions, starting withSchrödinger and continuing to the information quantization interpretation(Zeilinger, Brukner), QBism (Fuchs et al.), reality without realism (RWR,Plotnitsky), the Växjö interpretation (Khrennikov), and derivations of thequantum formalism from the information axioms (e.g., D’Ariano et al.). Oneof the main distinguishing features of the information interpretation is the possibility of structuring thequantum foundations without nonlocality and spooky actionat a distance.
Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.
The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.
Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.
The purpose is, first, to review the occurrences which led to the acceptance by the bulk of physicists of the instrumentalist approach to quantum mechanics (QM) as the only one worth considering as truly rendering nature at the atomic level. Formulated soon after the creation of QM it outright refused the local realist interpretation. Next, to bring out the successive waves of dissenting voices, which still go on unabated. Finally, to recall that – in spite of the pervading dominance of the Copenhagen reading of quantum phenomena – the manifold questions concerning the interpretation of QM continue to be the subject-matter of forceful interventions claiming that the foundational basis of QM is far from being definitely closed.