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The British Journal for the Philosophy of Science

On the Structure and Function of Scientific Perspectivism in Categorical Quantum Mechanics

Vassilios Karakostas, Elias Zafiris

Published Apr 9, 2021• 2 citations
Publisher

Abstract

Contemporary scientific perspectivism is primarily viewed as a methodological framework of how we obtain and form scientific knowledge of nature, through a broadly perspectivist process, especially, with reference to quantum mechanics. In the present study, this is implemented by representing categorically the global structure of a quantum algebra of events in terms of structured interconnected families of local Boolean probing frames, realized as suitable perspectives or contexts for measuring physical quantities. The essential philosophical meaning of the proposed approach implies that the quantum world can be consistently approached and comprehended through a multilevel structure of locally variable perspectives, which interlock, in a category-theoretical environment, to form a coherent picture of the whole in a non-trivial way.

DOI
10.1086/714736

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Contemporary scientific perspectivism is primarily viewed as a methodological framework of how we obtain and form scientific knowledge of nature, through a broadly perspectivist process, especially, with reference to quantum mechanics. In the present study, this is implemented by representing categorically the global structure of a quantum algebra of events in terms of structured interconnected families of local Boolean probing frames, realized as suitable perspectives or contexts for measuring physical quantities. The essential philosophical meaning of the proposed approach implies that the quantum world can be consistently approached and comprehended through a multilevel structure of locally variable perspectives, which interlock, in a category-theoretical environment, to form a coherent picture of the whole in a non-trivial way.
Contemporary scientific perspectivism is re-evaluated and extended to a comprehensive perspectivist methodology and 'mediated' realistic epistemology, especially, with reference to quantum mechanics. In the present study, this is realized by representing categorically the global structure of a quantum algebra of events in terms of structured multitudes of interrelated local Boolean frames, realized as suitable perspectives or contexts for measuring physical quantities. The philosophical meaning of the proposed approach implies that the quantum world can be consistently approached and comprehended through a multilevel structure of locally variable perspectives, which interlock, in a category-theoretical environment, to form a coherent picture of the whole in a nontrivial way. Thus, in contrast to a panoptical "view from nowhere" of the classical paradigm, quantum theory acknowledges in an essential way a perspectival/contextual character of scientific knowledge.
The present study investigates the tension between objectivism and perspectivism in light of the conceptual and philosophical implications of quantum theory. The guiding dictum of objectivism posits that science reveals the underlying structure of reality independently of human cognitive activity, that is, in terms of mind-independent, discourse-independent properties and relations occurring at any spatiotemporal location. It is shown that objectivism’s stance fits with the applicability of the bivalence principle as the semantic foundation of scientific discourse. It becomes then apparent that the non-Boolean logical structure of quantum theory systematically disrupts the objectivist framework. Along this vein, we provide succinct argumentation demonstrating quantum theory’s affinity to perspectivist reasoning. It is contended that the ubiquitous phenomenon of quantum contextuality, as established by Kochen-Specker’s celebrated theorem, strongly suggests that measurement values of quantum observables can, in general, be regarded as pertaining to an object under investigation only within a local probing frame or perspective from which the object-system is considered. The last remark is reinforced when considered within the endo-theoretic perspectivist framework of quantum mechanics. The essential philosophical meaning of the latter implies the view that the quantum world can be consistently comprehended through a multilevel structure of overlapping Boolean probing frames, realized as locally variable perspectives on a quantum system, being capable of forming jointly a coherent picture of the whole in a nontrivial way. Finally, in the appendix, the endo-theoretic perspectivist framework of quantum theory is critically compared to the relational interpretation of quantum mechanics, particularly in its recent development involving the postulate of “cross-perspective links”, revealing thereby the profoundly different picture of the quantum world’s architecture between the two proposals.
According to various no-go results in the foundations of quantum mechanics, for any system associated to a Hilbert space of dimension higher than two, it is not possible to assign definite truth values to all propositions pertaining to the system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton uniqueness theorem is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. On this basis, a perspectivist/contextual account of truth valuation in the quantum domain is produced that satisfies Tarski's criterion of material adequacy for a theory of truth. In light of the latter, perspectivist truth conforms to perspective or context-bound correspondence of a de re nature, designating locally an objectively existing state of affairs. Such an account derives by virtue of the microphysical nature of physical reality in displaying a context-dependence of facts; thus, it essentially opposes a non-perspectival, metaphysically fixed point of reference, or a panoptical standpoint from which to state all facts of nature.
Abstract Perspectivist positions have been proposed in physics, notably in order to address the interpretive difficulties of quantum mechanics. Recently, some versions of perspectivism have also been proposed in general philosophy of science to account for the plurality of scientific practice. Both kinds of views share the rejection of what they metaphorically call the “view from nowhere”. However, beyond this superficial similarity, they are very different: while quantum perspectivism entertains a concrete notion of perspective associated with individual agents or systems or concrete contexts, perspectival realism adopts a more abstract notion associated with explanatory aims or conceptual schemes. The aim of this paper is to clarify what is at stake with perspectivism in general. The general notion of a perspective, as well as the various attitudes one can entertained towards them, are characterised using the concepts of harmless contradiction and cross-perspectival accessibility. A taxonomy of positions ranging from absolutism to relativism is proposed on this basis. Then the framework is applied to quantum perspectivism and perspectival realism to show its fruitfulness. Finally, I argue that abstract versions of perspectivism are bound to be metaphysically weaker than concrete versions.
I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.
It has often been suggested that similar quantum particles may be a counterexample to the principle of the Identity of Indiscernibles. In this article, I discuss the status of indiscernibility in a perspectival approach to quantum mechanics. I argue that adopting an internal physical perspective can have the effect of making entities discernible even if they are not discernible relative to external reference frames, and thus perspectivalism offers a new way to understand the physical meaning of weak discernibility. I discuss whether this approach is circular, and I consider whether the reference frames involved are physically meaningful. I conclude that the Identify of Indiscernibles can probably be maintained in this context, though there are outstanding questions pertaining to the meaning of the quantum state and the way in which a system should be represented in its own reference frame.