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Journal of Physics Conference Series

Structural Realism and the underdetermination of the physical meaning

Ovidiu Cristinel Stoica

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Abstract I point out an underdetermination of physics, in particular of Quantum Mechanics: that of the relation between the operators and their physical meaning. The set of operators for which we attribute physical meaning is, from relational, structural, and dynamical points of view, indistinguishable from any set of operators obtained from the former by a unitary transformation that commutes with the Hamiltonian. The same is true for the structures inhabiting the world, in particular there are structures isomorphic to the structure of an observer, but they would attribute the meaning of position and other physical meanings to different operators. In particular, space itself is underdetermined from the structure of the theory. Different structures that are isomorphic to an observer would call “position” different observables, and consequently would call “space” different structures. I show that they are highly non-unique. A solution would be that all possible assignments of physical meaning to the operators allowed by the symmetries of the formalism are equally valid. But this leads to a problem: there would be no correlation between the content of the mind of an observer about the external world, and the actual properties of the external world. This has unexpected consequences: it refutes structural realism, and it shows that, in addition to the structure, the substance underlying the structures matters for consciousness to exist.

DOI
10.1088/1742-6596/2948/1/012014

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Abstract I point out an underdetermination of physics, in particular of Quantum Mechanics: that of the relation between the operators and their physical meaning. The set of operators for which we attribute physical meaning is, from relational, structural, and dynamical points of view, indistinguishable from any set of operators obtained from the former by a unitary transformation that commutes with the Hamiltonian. The same is true for the structures inhabiting the world, in particular there are structures isomorphic to the structure of an observer, but they would attribute the meaning of position and other physical meanings to different operators. In particular, space itself is underdetermined from the structure of the theory. Different structures that are isomorphic to an observer would call “position” different observables, and consequently would call “space” different structures. I show that they are highly non-unique. A solution would be that all possible assignments of physical meaning to the operators allowed by the symmetries of the formalism are equally valid. But this leads to a problem: there would be no correlation between the content of the mind of an observer about the external world, and the actual properties of the external world. This has unexpected consequences: it refutes structural realism, and it shows that, in addition to the structure, the substance underlying the structures matters for consciousness to exist.
As far as classical physics is concerned, it is possible to trace causal relations between physical objects (i.e. particles in this case) back to intrinsic properties of these objects (such as their mass and charge). On this view, causal relations turn out to be internal instead of external relations, supervening on intrinsic properties of the relata (as proposed by Heil and Lowe). However, one can raise doubts about this view already in Newtonian mechanics. The decisive blow to this view comes from quantum physics, with Bell’s theorem proving that no dynamics based on local, intrinsic properties of quantum objects can yield the empirical predictions of quantum mechanics. Nonetheless, quantum entanglement by no means implies that we have to abandon an ontology of objects (i.e. substances such as particles) in favour of an ontology of structures (as claimed by French and Ladyman). Any of the known proposals for a quantum ontology of matter in space-time is committed to objects. However, on any of these proposals, what determines the dynamics of these objects are not local, intrinsic properties, but a global or holistic property instantiated by all the objects together – that is, a structure that takes all the objects in the universe as its relata. The view set out in this paper thus amounts to combining ontic structural realism with an ontology of objects that can be conceived as substances. This suggestion is illustrated by drawing on the ontology of quantum physics worked out by Bohm and Bell. 1.
Abstract Both empirical and theoretical objective science can only access relations, revealing nothing about the intrinsic nature of the entities “in relation”. We typically refer to these entities as “matter”, assuming their nature is irrelevant and that relational structures alone explain all phenomena, including consciousness. This would imply that consciousness arises not from matter itself but solely from its structural configurations. Consequently, if two worlds possess isomorphic structures and obey identical dynamical laws, isomorphic systems within these worlds should be equally sentient or insentient. I demonstrate that if this premise held true, the memories within an observer’s brain would bear no correlation to the external world. Yet since we do acquire knowledge of the external world, structure alone must be insufficient: there exists something beyond relations, the intrinsic essence of the “stuff in relation”. This essence imbues the observer’s structure with sentience, metaphorically “breathing fire” into it. In turn, the observer confers physical meaning upon the world’s structures. Remarkably, this conclusion emerges directly from physics and mathematics. Without acknowledging this intrinsic element, we would be incapable not only of subjective experience but also of acquiring any objective knowledge about the physical world.
Recent attempts to turn Standard Quantum Theory into a coherent representational system have improved markedly over previous offerings. Important questions about the nature of material systems remain open, however, as current theorizing effectively resolves into a multiplicity of incompatible statements about the nature of physical systems. Specifically, the most cogent proposals to date land in effective empirical equivalence, reviving old anti-realist fears about quantum physics. In this paper such fears are discussed and found unsound. It is argued that nothing of global skeptical or agnostic significance follows from the kind of underdetermination presently encountered in fundamental quantum theory. The case is instructive, however, for what it shows about the characteristics and prospects of scientific realism as a perspective in contemporary philosophy of science.
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that are both simple and well-known. The representations are unitarily inequivalent because the spectra of the position and momentum operators are different, and spectra are invariant under unitary transformations. The existence of these representations can have consequences that run from the merely unexpected to the barely conceivable. To start with, states of a single particle that belong to inequivalent representations will always be mutually orthogonal; they will never interfere with each other. This property, called superseparability elsewhere, is well-defined mathematically, but has not yet been observed. This article suggests two single-particle interference experiments that may reveal its existence. The existence of inequivalent irreducibile representations may be traced to the existence of different self-adjoint extensions of symmetric operators on infinite-dimensional Hilbert spaces. Analysis of the underlying mathematics reveals that some of these extensions can be interpreted in terms of topological, geometrical and physical quantities that can be controlled in the laboratory. The tests suggested are based on these interpretations. In conclusion, it is pointed out that mathematically rigorous many-worlds interpretations of quantum mechanics may be possible in a framework that admits superseparability.
Scientific realism has traditionally maintained that our best scientific theories can be regarded as more or less true and as representing the world as it is (more or less). However, one of our very best current theories—quantum mechanics—has famously resisted such a realist construal, threatening to undermine the realist stance altogether. The chapters in this volume carefully examine this tension and the reasons behind it, including the underdetermination generated by the multiplicity of formulations and interpretations of quantum physics, each presenting a different way the world could be. Authors in this volume offer a range of alternative ways forward: some suggest new articulations of realism, limiting our commitments in one way or another; others attempt to articulate a ‘third way’ between traditional forms of realism and antirealism, or are critical of such attempts. Still others argue that quantum theory itself should be reconceptualised, or at least alternative formulations should be considered in the hope of evading the problems faced by realism. And some examine the nature of these issues when moving beyond quantum mechanics to quantum field theory. Taken together they offer an exciting new set of perspectives on one of the most fundamental questions in the philosophy of modern physics: how can one be a realist about quantum theory, and what does this realism amount to?