Complementarity as a Pathway to a Perspectivist Metaphysics

*Perspectivism and Quantum Mechanics, 50 minutes + 15 minutes Q&A (3 October 2023)

Abstract:

Quantum Reconstruction—Bridging Two Cultures of Inquiry

Reviving a Phenomenological Approach to Quantum Mechanics: The French View of London, Linköping, Sweden, 66 minutes + 34 minutes Q&A (13 September 2023)

Abstract: For a century, quantum theory has posed a fundamental challenge to philosophical thinking. On its face, it repudiates many if not most of the key features of the mechanical conception of physical reality. However, the challenge of developing a precise, coherent alternative to that conception has yet to be met [4]. The quantum reconstruction program is the perhaps the most important advance in the foundations of physics of the last half-century, and opens up rich opportunities for philosophical reflection. However, despite the development of many reconstructions of various parts of the quantum formalism over the last twenty years, the reconstruction program has yet to engage the serious attention of the majority of philosopher engaged in the philosophy of physics [1].

In this paper, I describe some of the obstacles and misconceptions that stand in the way of the embrace of the quantum reconstruction program; explain how interpretation of quantum reconstructions can avoid many of the pitfalls of implicit metaphysics that is inherent in the conventional approach of direct interpretation of the quantum formalism; and describe the exciting possibilities that certain reconstructions (e.g. [2, 5]) open up, such as the prospect of developing a rigorous metaphysical understanding of such enigmatic notions as complementarity [3] and entanglement.

[1] Philipp Berghofer. Defending the quantum reconstruction program.

[2] Philip Goyal. Derivation of quantum theory from Feynman’s rules. Phys. Rev. A, 89:032120, 2014. doi: https://doi.org/ 10.1103/PhysRevA.89.032120.

[3] Philip Goyal. Persistence and nonpersistence as complementary models of identical quantum particles. New J. Phys., 21: 063031, 2019. doi: https://doi.org/10.1088/1367-2630/ab152b.

[4] Philip Goyal. The role of reconstruction in the elucidation of quantum theory. In Philipp Berghofer and Harald. A. Wiltsche, editors, Phenomenological approaches to quantum physics. 2023. To appear. Available at http://philsci-archive.pitt. edu/21405/.

[5] Philip Goyal, Kevin H. Knuth, and John Skilling. Origin of complex quantum amplitudes and Feynman’s rules. Phys. Rev. A, 81:022109, 2010. doi: https://doi.org/10.1103/PhysRevA.81.022109.

Persistence and Reidentification in Systems of Identical Quantum Particles

Seminar at Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, 44 minutes + 10 minutes Q&A (28 June 2023)

Abstract: The quantum symmetrization procedure that is used to handle systems of identical quantum particles brings into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability that are attributed to classical particles. However, we presently lack a coherent conception of matter composed of entities that lack one or both of these fundamental characteristics [1]. In particular, the canonical view that identical particles are indistinguishable is at odds with operational assumptions (of persistence and reidentifiability) implicit in the experimental procedures used to investigate the microphysical realm. We also lack a clear a priori understanding of why systems of identical particles (as opposed to non-identical particles) require special mathematical treatment, and this only in the quantum mechanical (as opposed to classical mechanical) setting.

Here, on the basis of a conceptual analysis of a recent mathematical reconstruction of the quantum symmetrization procedure [2, 3], we argue that the need for the symmetrization procedure originates in the confluence of identicality and the active nature of the quantum measurement process. We propose a conception in which detection-events are ontologically primary, while the notion of individually persistent object is relegated to merely one way of bringing order to these events.

From this perspective, we show that the symmetrization procedure is not a mathematical expression of the idea that identical particles are indistinguishable. Rather, it is a formal means of synthesizing two different object-models of the same detection-event data. Consequently, indices in a symmetrized state do not refer unequivocally to particles, and non-symmetric measurement operators are physically meaningful.

1. "Persistence and Reidentification in Systems of Identical Quantum Particles: Towards a Post-Atomistic Conception of Matter", Philip Goyal, http://philsci-archive.pitt.edu/id/eprint/21849

2. "Informational approach to the quantum symmetrization postulate", Philip Goyal, New J. Phys., 17:013043, 2015. doi: https://doi.org/10.1088/1367-2630/17/1/013043

3. "Persistence and nonpersistence as complementary models of identical quantum particles", Philip Goyal, New J. Phys., 21:063031, 2019. doi: https://doi.org/10.1088/1367-2630/ab152b

Persistence and Reidentification in Systems of Identical Quantum Particles

Seminar at Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, 44 minutes + 10 minutes Q&A (28 June 2023)

Abstract: The quantum symmetrization procedure used to handle systems of identical quantum particles brings into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability that are attributed to classical particles. However, we presently lack a coherent conception of matter composed of entities that do not possess one or both of these fundamental characteristics. We also lack a clear a priori understanding of why systems of identical particles (as opposed to non-identical particles) require special mathematical treatment, and this only in the quantum mechanical (as opposed to classical mechanical) setting.

Here, on the basis of a conceptual analysis of a recent mathematical reconstruction of the quantum symmetrization procedure [1, 2], I argue that the need for the symmetrization procedure originates in the confluence of identicality and the active nature of the quantum measurement process [3]. I propose a conception in which detection-events are ontologically primary, while the notion of individually persistent object is relegated to merely one way of bringing order to these events. On this basis, I describe a new interpretation of the symmetrization procedure, which gives a new physical interpretation to the indices in symmetrized states and to non-symmetric measurement operators, and may provide a new approach to the vexing question of entanglement in identical particle systems.

[1] P. Goyal, Informational approach to the quantum symmetrization postulate, New Journal of Physics 17 013043 (2015) https://iopscience.iop.org/article/10.1088/1367-2630/17/1/013043

[2] P. Goyal, Persistence and nonpersistence as complementary models of identical quantum particle, New Journal of Physics 21 063031 (2019) https://iopscience.iop.org/article/10.1088/1367-2630/ab152b

[3] P. Goyal, Persistence and Reidentification in Systems of Identical Quantum Particles: Towards a Post-Atomistic Conception of Matter (2023) http://philsci-archive.pitt.edu/21849/

Have Some Physicists Always Been Phenomenologists?

The Nuts and Bolts of Phenomenological Qualitative Research: Reflecting on Methodological Challenges, SDU, Odense, Denmark, 35 minutes + 35 minutes Q&A (8 June 2023)

Abstract:

Information and the Structure of Quantum Theory

"Information & Interactions: Eddington, Wheeler, and the Limits of Knowledge" Workshop, Trinity College, Cambridge, 34 minutes (22 March 2014)

Abstract: Introductory talk that describes the informational perspective on the physical world, and outlines a information-based reconstruction of quantum theory.

Information Physics: Towards a New Conception of Physical Reality

"Bayesian Inference and Maximum Entropy Methods in Science and Engineering 2011" Workshop, Waterloo, Canada, 87 minutes (10 July 2011)

Abstract: The central tenet of information physics is that the concept of information is as fundamental to developing an understanding of the physical universe as are the classical concepts of space and time, matter and energy.

In this talk, I shall sketch the developments—in physics and elsewhere—that have given rise to the field of information physics, and indicate some of the many rather deep insights that ‘informational thinking’ has provided into the structure of physical theory, in particular into the mathematical structure of quantum theory. I shall also briefly sketch the emerging conception of reality (or ontology) to which these developments seem to naturally lead.

The Logic of Process, and the Origin of Quantum Theory

"Laws of Nature" Workshop, Perimeter Institute, 64 minutes (21 May 2010)

Abstract: Description of the the project of reconstructing quantum theory, and a presentation of the reconstruction of quantum theory based on the paper "Origin of Complex Quantum Amplitudes and Feynman's Rules" (2010).

The talk itself is 42 minutes long, followed by a followed by a ~20 minute Q&A.

Recordings of the talks given at the workshop are available here.

Quantum Theory from Complementarity, and its Implications

"Perimeter Institute–Australian Foundations (PIAF) 2009 Conference: New Perspectives on the Quantum State", Perimeter Institute, 31 minutes (1 Oct 2009)

Abstract: Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this talk, we show how it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair.

By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes. We then discuss how complementarity—the key guiding idea in the derivation—can be understood as a consequence of the intrinsically relational nature of measurement, and discuss the implications of this for our understanding of the status of the quantum state.

[0–11 mins] When we ask the question "What is a quantum state?", what kind of answer are we looking for? To what extent have existing methodologies in quantum foundations been successful in providing these answers?

[12–24 mins] Sketch of a reconstruction of quantum theory based on the paper "Origin of Complex Quantum Amplitudes and Feynman's Rules"

[25–27 mins] Implications of this reconstruction for our understanding of the nature of quantum reality, and the prospects for obtaining a direct, intuitive understanding of it.

[27–31 mins] Audience Questions & Answers.

Why Quantum Theory is Complex

"Reconstructing Quantum Theory" Workshop, Perimeter Institute, 88 minutes (11 August 2009)

Abstract: Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. We show that it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair.

By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes

[0–3 mins] The current status of our understanding of quantum theory. Reconstructing of quantum theory as a next logical step.

[3–46 mins] Description of a reconstruction of quantum theory described in the paper "Origin of Complex Quantum Amplitudes and Feynman's Rules"

[46–88 mins] Audience Questions & Answers.

All workshop talks are available here.

From Information Geometry to Quantum Theory

"The Clock and the Quantum: Time and Quantum Foundations" Workshop, Perimeter Institute, 31 minutes (29 September 2008)

Abstract: The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value—not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. However, such articulation has traditionally been hampered by the fact that the quantum formalism consists of postulates expressed in an abstract mathematical language to whose elementary objects (complex vectors and operators) our physical intuition cannot directly relate.

Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates.

In this talk, I describe a very simple reconstruction of the finite-dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, and the importance (or lack thereof) of assumptions concerning separated systems.

Foundations of Quantum Mechanics (Introductory Lecture, No. 2)

"New Horizons In Fundamental Physics" Lecture Series, Perimeter Institute, 85 minutes (28 February 2008)

Abstract: Second of two introductory talks on quantum foundations given as part of Perimeter Institute's New Horizons in Fundamental Physics lecture course for undergraduates.

This talk focusses explicitly on the strategy of reconstruction as a way to understand quantum theory—that is, attempting to derive the mathematics of quantum theory from a small number of physically well-motivated postulates.

Please note that these two introductory talks follow on from Owen Maroney's first four talks on quantum foundations in the same series, and presuppose them. However, this second talk is essentially self-contained.

Foundations of Quantum Mechanics (Introductory Lecture, No. 1)

"New Horizons In Fundamental Physics" Lecture Series, Perimeter Institute, 78 minutes (26 February 2008)

Abstract: First of two introductory talks on quantum foundations given as part of Perimeter Institute's New Horizons in Fundamental Physics lecture course for undergraduates.

This talk addresses the broad question of what kind of understanding of quantum theory we seek, and proceeds to discuss the various strategies that have been employed to gain an understanding of quantum theory, and what they have achieved.

Please note that these two talks follow on from Owen Maroney's first four talks on quantum foundations in the same series, and presuppose them. However, roughly the first half of this talk is self-contained.

An Information-Theoretic Approach to Quantum Theory

Quantum Foundations Seminar, Perimeter Institute, 79 minutes (22 January 2007)

Abstract: The mathematical formalism of quantum theory has many features whose physical origin remains obscure. In this paper, we attempt to systematically investigate the possibility that the concept of information may play a key role in understanding some of these features. We formulate a set of assumptions, based on generalizations of experimental facts that are representative of quantum phenomena and physically comprehensible theoretical ideas and principles, and show that it is possible to deduce the finite-dimensional quantum formalism from these assumptions. The concept of information, via an information-theoretic invariance principle, plays a central role in the derivation, and gives rise to some of the central structural features of the quantum formalism.