Contemporary Perspectivism as a Framework of Scientific Inquiry in Quantum Mechanics and Beyond

Abstract

Contemporary perspectivism is viewed as a framework of scientific inquiry concerning the origin, generation and systematization of scientific knowledge of nature by focusing on the conditions under which such knowledge may arise in perspectivist terms and investigating the essential ramifications of these conditions. To this end, we develop the conceptual, methodological and semantic framework of contemporary perspectivism according to the norms of the proposed endo-theoretic approach. Implementation of the preceding three-fold scheme in quantum mechanics implies that the global structure of a quantum algebra of events can be consistently comprehended through a multilevel structure of locally variable Boolean perspectives, interconnected in a category-theoretic environment, yielding jointly all the information encoded in the former. In this respect, the proposed approach validates the perspectivist/contextual nature of quantum mechanics at a fundamental level of discourse. Furthermore, due to its general character, it may acquire the form of a theoretical pattern of scientific inquiry in the natural sciences, especially when dealing with complex trans-perspectival phenomena, the analysis of which requires the use of information resulting from more than one perspective. Finally, in the appendix, we provide a concise comparative assessment between our perspectivist framework of quantum theory and Rovelli’s relational interpretation of quantum mechanics.

Appendices

Appendix

It is instructive to attempt a concise comparative assessment between our perspectivist framework of quantum theory and Rovelli’s relational interpretation of quantum mechanics (RQM) focusing on their essential differences, thus revealing the profoundly different apprehension of the quantum world’s architecture between the two proposals. The appendix is partly based on comments and clarificatory questions raised by the reviewer, giving us the opportunity to explicate on certain issues ranging from the concept of perspective to the way different perspectives may relate to each other and from the meaning of perspectivist truth to issues concerning the ontology of quantum events and their impact on the comprehension of reality.

[A] Methodology and Mechanism for Relating Perspectives – Intersubjectivity

We initially point out that both our proposed endo-theoretic perspectivist framework and Rovelli’s RQM, particularly in its recent development involving the postulate of “Cross-Perspective Links" (CPL), affirm the intersubjective agreement on empirical facts among agents under certain conditions. However, the underlying conceptual and formal methodology by which this agreement is established, and indeed the very notion of “perspective", differ significantly. For brevity, we shall call henceforth the updated version of RQM, as modified by the addition of the CPL postulate, RQM+.

• 1. Rovelli’s Relational Quantum Mechanics and the CPL Postulate

  • RQM: In Rovelli’s [24] initial formulation of RQM, the state of a system S is always relative to an observer O. Facts—namely, values of physical quantities—are established only during interactions and are relative to the interacting systems. Comparisons of facts relative to different observers (e.g., Alice’s measurement outcome relative to Alice, and Bob’s measurement outcome relative to Bob) are only meaningful from the perspective of a third observer W who interacts with both Alice and Bob [46]. This led to concerns about “island universes" of information [47], where an observer cannot, in principle, know anything beyond their immediate present experience or confirm empirical facts relative to other observers. The implied lack of intersubjectivity regarding measurement outcomes seemed to challenge the character of the scientific practice or even undermine scientific objectivity itself.

  • Introducing CPL: To address the aforementioned intersubjectivity issues, Adlam & Rovelli [48, p. 7] proposed a new postulate, the “cross-perspective links" (CPL), formulated as follows: “In a scenario where some observer Alice measures a variable V of a system S, then provided that Alice does not undergo any interactions that destroy the information about V stored in Alice’s physical variables, if Bob subsequently measures the physical variable representing Alice’s information about the variable V, then Bob’s measurement result will match Alice’s measurement result".

    • Under the CPL process, point-like quantum events—that is, the actualization of a value in an interaction—become absolute, observer-independent features of reality [48, p. 12]. However, quantum states remain relational, describing the relationship between systems.

    • The value of a variable V obtained by Alice is still initially relativized to Alice, since, at the beginning, she is the only one with that information, yet CPL establishes that this information, being physical and “stored in Alice’s physical variables", is accessible in principle through measurements to any other observers. The CPL postulate introduces a specific mechanism that has been added on an already existing structure for linking different observers’ information but now about absolute quantum events.

    • The CPL modification, while confronting at least theoretically the intersubjectivity problem, leads to the de-relativization of facts, thereby potentially undermining the distinctively relational aspects of the classical formulation of RQM.

• 2. Karakostas & Zafiris’ Endo-Theoretic Perspectivist Framework: The K&Z Approach

  • Nature of Perspective: In our framework, a “perspective" is not primarily an individual observer’s interaction history but is formally defined as a Boolean probing frame. This is a complete Boolean algebra of projection operators associated with a set of compatible and thus comeasurable observables. It represents a particular experimental context by partitioning the “space" of possible outcomes. Furthermore, it constitutes a local structural invariant within the global non-Boolean quantum event algebra, satisfying the general desiderata put forward in Section 1 concerning the suitability of a structural unit to be qualified as a perspective.

  • Intersubjectivity: Intersubjective agreement on the determinateness and repeatability of empirical facts, among agents sharing the same perspective, is an explicit consequence of the logical status characterizing a Boolean frame.

    • If agents Alice and Bob share the same perspective, it means they are operating within or have adopted the same Boolean frame ${\mathbb M({B}_A)}$ (as defined in Section 6).

    • Within such a definite Boolean frame, propositions are assigned bivalent truth values. Thus, each proposition in ${\mathbb M({B}_A)}$ is assigned at any given time t a definite truth value, “true" or “false". The Kochen-Specker theorem, although globally forbids a bivalent truth-value assignment to all quantum mechanical propositions, nonetheless, does not prohibit such local assignments within a selected Boolean subalgebra.

    • Therefore, if Alice and Bob are considering propositions and performing measurements within the same explicitly defined Boolean frame, the empirical facts established—namely, the outcomes of measurements corresponding to projection operators within that frame—will be determinate and repeatable for both, simply because they are operating under identical logical conditions provided by that shared frame.

  • The Interrelation Mechanism Codified – From Local Perspectives to a Global Structured Whole: These local Boolean frames are not isolated “island universes". They are systematically related to each other as homomorphic images via the modeling functor ${\mathbb M}$ within the overarching, non-Boolean quantum event algebra L. The K&Z categorical perspectivist framework provides the precise syntax of perspectives for how they interconnect:

    • Functor of Boolean Frames on L: For any quantum event algebra L, we define a functor ${\mathbb {R}}(L)$ whose action on any Boolean algebra B provides the set of all possible Boolean probing frames of the type B that can be adjoined to L. This functor, ${\mathbb {R}}(L)={Hom_\mathcal {L}}({\mathbb M}(-),L)$, captures the totality of all possible local perspectives on L (Section 5.2).

    • Compatibility and Gluing: The framework establishes rigorous compatibility conditions for how these frames overlap consistently. When two Boolean frames, say, $\psi _B: {\mathbb M} (B) \rightarrow L$ and $\psi _C: {\mathbb M} (C) \rightarrow L$, are not disjoint, their relationship is governed by their pullback. This ensures that any information they share is consistent. The cocycle conditions for the gluing isomorphisms guarantee that these local perspectives can be “pasted" together seamlessly into a coherent global structure [6, Section 4.2]. This mechanism explicitly prevents fragmentation.

    • Synthesis – The Colimit Construction: The actual assembly of the global structure from these coherently interconnected local Boolean frames is performed by a universal mathematical construction known as the colimit. Our central result is that the global quantum event algebra L is precisely the colimit of the diagram formed by all of its local Boolean probing frames:

      $$\begin{aligned} L= Colim({\mathbb {R}}(L))\,. \end{aligned}$$

      This means L is the unique object that synthesizes all the information contained in the local perspectives composing ${\mathbb {R}}(L)$ in a way that respects all their interrelations. It is the “universal solution" that arises from gluing all the locally variable perspectives together (Section 5.3).

  • The Boolean frames-quantum adjunction: The preceding solution is based on the Boolean frames-quantum adjunction, which ensures that local information can be globally synthesized (Section 5.3). This adjunction provides a bi-directional mechanism for encoding (from Boolean to quantum) and decoding (from quantum to Boolean) information in perspectivist terms. Instead of being an added postulate, it is a fundamental consequence of the category-theoretic representation of quantum event structures via the action of Boolean probing frames, conceived as perspectives applied on a quantum system. It establishes that the global structure of a quantum algebra of events can be consistently comprehended through a multilevel structure of locally variable Boolean perspectives, interconnected in a category-theoretic environment, yielding jointly all the information encoded in the former. Thus, inter-perspectival consistency is an essential feature of the proposed framework.

    • The structural concept of “perspective", our methodology on the conditions under which knowledge is possible, as analyzed in Section 2, the explicit use of category theory, and the Boolean frames-quantum adjunction, are unique to our endo-theoretic approach in providing a consistent perspectivist framework of quantum mechanics.

[B] Explicating the Meaning of the Perspectivist/Contextual Correspondence Theory of Truth

We are addressing the following clarificatory questions raised by the reviewer in relation to our proposed account of truth: (1) Is a given measurement valid only for those agents sharing the context C? (2) What happens if somebody is outside C? Can the measurement result be different or indeterminate? (3) According to the proposed account of truth, once an experimental context is set up and a measurement is performed, its result depends on the context. In what sense this result may be considered observer independent? (4) Furthermore, such contextualization criterion is very different from saying that scientific truths depend on what an epistemic community agrees upon, as usually said in perspectival considerations.

• 1. Agents Sharing Context C

  • In quantum mechanics, a global Boolean context of measurement does not exist, and by virtue of Kochen-Specker’s theorem, only single local contexts, as defined by our concept of a perspective, can be considered as being definite, thus capturing Boole’s “conditions of possible experience" (Section 2.2). Henceforth, in the endo-theoretic approach to perspectivism, truth valuation is localized and subsequently contextualized with respect to distinct Boolean probing frames conceived as perspectives targeting the quantum system of interest. That is, bivalent truth-value assignments hold consistently only within a perspective and its associated measurement context C. The proposition “P-in-C" is only well-defined and capable of possessing a determinate truth value with respect to C. Consequently, the truth of “P-in-C" characterizes an objectively existing state of affairs, as delineated by C. Any agent, who wishes to evaluate P in the context C, would arrive at the same truth value, assuming access to the relevant empirical facts.

• 2. Agent “Outside" Context C

  • If an agent is “outside" C, it means they are operating within a different context $C^{\prime }$ (a different Boolean frame), or perhaps they have not adopted any specific Boolean frame relevant to P.

  • If C and $C^{\prime }$ are incompatible contexts, corresponding to non-commuting sets of observables, then a proposition P meaningful in C might not even be well-defined in $C^{\prime }$, or a related proposition $P^{\prime }$ in $C^{\prime }$ might yield a different outcome. This is a standard feature of quantum contextuality as revealed by Kochen-Specker’s theorem. For example, if C involves measuring spin-z and $C^{\prime }$ involves measuring spin-x, the outcomes correspond to different complementary aspects of reality, which, in principle, cannot be realized simultaneously.

  • From the standpoint of an agent in $C^{\prime }$, the truth value of “P-in-C"—a proposition tied to a different, potentially incompatible context—might be considered indeterminate from $C^{\prime }$’s perspective. However, the truth value of “P-in-C" itself is determinate within its own defining context C. Our framework aims to show how these determinate truth-valuations from different perspectives can be systematically interrelated—to the degree authorized by quantum mechanics—via the use of the functorial apparatus of category theory (Section 5.2).

• 3. Perspectivist/Contextual Truth is an Empirical Fact

  • Let us initially remind that in the endo-theoretic approach to perspectivism, the kind of the experimental context to be utilized corresponds to the specification of a particular Boolean probing frame C. Once C is fixed, the measurement outcome for a proposition P defined within C yields a truth value for “P-in-C". The latter truth value is objective and observer-independent given that context C; it corresponds to an objective, yet contextually delimited, state of affairs. Any observer or agent correctly applying the rules of quantum mechanics within that specific context C will ascertain the same result. Since the truth of P is context-dependent upon C, if a different context $C^{\prime }$, incompatible with C, were chosen, a different set of propositions would become determinate. In the quantum domain, perspectivist/contextual truth is an empirical fact of reality. For, within any well-defined experimental context (or Boolean probing frame), measurements yield definite, repeatable, and intersubjectively confirmable outcomes.

• 4. Contextualization Criterion – Epistemic Community Agreement

  • Our contextualization criterion should be distinguished from typical perspectival theses in the general philosophy of science where truth usually depends on an epistemic community’s agreement. In the endo-theoretic approach to perspectivism, truth is context-bound correspondence to an objective state of affairs. When applied to quantum mechanics, the “context" is a structural feature of the physical theory—a Boolean algebra of compatible observables—not an epistemic community. The agreement of agents within that context is then a consequence of this objective, context-bound truth, yielding empirically confirmed facts. This is a contemporary form of perspectival realism, associated to the philosophy and conceptual foundations of quantum mechanics, where the consideration of a perspective forms an essential feature of the theoretical landscape for describing consistently microphysical reality (Section 6).

[C] The K&Z Approach Compared to Rovelli’s RQM

We proceed to a concise comparison between our perspectivist framework of quantum theory and Rovelli’s relational interpretation of quantum mechanics giving emphasis on certain features that reveal the essentially different accounts of the quantum world’s architecture between the two proposals.

• 1. Notion of Perspective

  • RQM: A “perspective" is tied to an observer and their interaction history, including the probabilistic predictions that the ensemble of events relative to the observer entails [49].

  • K&Z Approach: A “perspective" is an endo-theoretic structural unit, a Boolean probing frame serving as a window on physical reality. It constitutes a local structural invariant within quantum theory itself, characterizing a maximal set of comeasurable observables, or, equivalently, a complete Boolean algebra of commuting projection operators generated by this set. Such a kind of perspective constitutes the principal structural unit for investigating reality at her microphysical dimension. It provides experimental accessibility on the investigated system, functions locally as a probing frame for the individuation of events, resolves a targeted object of inquiry, generally, probes consistently the physical world.

• 2. Role of the Observing or Measuring System

  • RQM: It is a core thesis of the relational interpretation that any system can acquire the status of an “observer" (or “observing system") in a physical interaction. Accordingly, a measurement is considered as the obtainment of mutual information between the physical variables of two interacting systems, in which either system can undertake the role of the “observer" while the other stands in the role of the “observed system". This equivalence relation between different systems in their status of possible observers reflects the radically relational character of RQM.

  • K&Z Approach: In the endo-theoretic approach to perspectivism, given a quantum system under investigation, the observer, apart from selecting the observable to be measured and thus specifying the perspective applied on the system, plays no special role. During the measurement process, the observer or the experimentalist is naturalized in terms of a measuring apparatus. Every reference is exclusively related to the possible results of interactions between the measuring apparatus and the measured system as parts of the experimental set-up. Values of quantum mechanical observables or outcomes of measurement processes are perspective-dependent since they are context-dependent. Their relational character is with respect to the context of measurement, not between any two interacting systems. Hence, in our approach, the measuring system cannot be any physical system, as in relational quantum mechanics, but a suitable measuring apparatus by means of which outcomes of measurements are irreversibly recorded. This is reminiscent of Wheeler’s [20, p. 189] expression: “Until the act of detection the phenomenon-to-be is not yet a phenomenon". In the quantum domain, the individual character of the quantum phenomenon removes the possibility for comparing consistently what is with what might have been.

• 3. Nature of Truth

  • RQM: In the classical formulation of RQM, facts are observer-dependent. The value of a variable for system S becomes definite relative to observer O upon interaction. Another observer $O^{\prime }$ might not have this fact actualized relative to them. Since a comparison of measurement results between any pair of observers is only meaningful in RQM by invoking a third observer W, truth is radically relative to an observer’s perspective.

  • RQM+: Quantum events become now absolute. If Alice measures variable V on S and gets v, this event, relative to Alice, is an absolute fact. The CPL postulate ensures that Bob, as any other observer, can later access this information about Alice’s past relative fact. While the initial value ascription is to Alice’s perspective, the event itself has an absolute status. To the extent, therefore, that the information gained by Alice when a variable becomes definite relative to her is in principle accessible to any observer who measures Alice’s variable in the right basis, then the existence of an empirical fact is absolute, as absolute or observer-independent is in the CPL scenario the instantaneously realizable set of point-like quantum events [48, p. 11].

  • K&Z Approach: Truth is perspectivist/contextual correspondence of a de re nature. Truth assignment is contextual since it depends on the selected Boolean frame C. Once C is specified, the truth of “P-in-C" is an objective matter determined by correspondence to the state of affairs carved out by C. Different Boolean frames $C^{\prime }$, $C^{\prime \prime }$, ..., provide locally possible perspectives onto the quantum world. The category-theoretic formalism establishes how the various perspectival truth assignments across perspectives are globally coherent. In the relational interpretation, the cross-perspective links is a specific postulate added on an already existing structure for achieving inter-observer agreement about past events. In contradistinction, our framework’s consistency and interrelation of perspectives arise from the mathematical coherence of the categorical perspectivist representation of a quantum event structure via Boolean probing frames, which is of sheaf-theoretic nature. The quantum event algebra itself is comprehended functorially as a sheaf over the base category of Boolean probing frames, meaning that it is “constituted" or “glued" together from these locally variable perspectives in a consistent way [6].

• 4. Determining the Existence of a Preferred Basis

  • RQM (pre- & post-CPL): Unlike the relational interpretation, we take the prevalent view that while every measurement presupposes an interaction between two systems—the measuring system and the system under measurement—nonetheless, every interaction does not qualify as a measurement. RQM, functioning under pure unitary quantum dynamics, cannot single out a unique variable that should take on definite values during an interaction that leads to a quantum event [51]. Furthermore, two quantum systems, forming an entangled state, admit correlations of a different kind depending on the selected basis to represent the state, as in a Bell-type entangled state of two spin-half particles. Consequently, lacking an exact method for determining a preferred definite basis, there exists an inherent ambiguity in RQM associated to the theoretical feasibility that an “observer" may assign multiple distinct relative states to the same “observed system".⁹

  • K&Z Approach: In the endo-theoretic approach to perspectivism there is no such ambiguity since the perspective, materialized as an experimental context, defines locally the preferred basis, that is, the eigenbasis of the set of observables that are compatible with the observable to be measured.

• 5. Global Event Ontology

  • RQM+: As a direct implication of the CPL postulate, quantum events, once radically relational in the classical version of RQM, are considered now as absolute, observer-independent facts of reality. The CPL process achieves intersubjective agreement among observers at the expense of inducing a nonlocal dependence of quantum events on one another, in the sense that the choice of which variable becomes definite in a quantum event at a given time will generally be dependent on the values of variables of previous events. In order to avoid potential compatibility issues with relativity theory, Adlam [52, p. 33] suggests that “we must allow that the network of events is determined in an ‘all-at-once’ manner, rather than being generated in some temporal order". Accordingly, this introduces in the context of RQM+ an ontology of a mosaic of absolute events whose distribution is obtained in an instantaneous, structureless and fragmented manner, impossible to be calculated or characterized as a whole [48, p.12].

  • K&Z Approach: Our framework provides a constructive and structural account resulting in an ontology that is fundamentally different from a primitive, instantaneous, fragmented collection of events.

    • Holistic and Structured: Now, the global event ontology is not analogous to a mosaic of disparate event-flashes. It is a unified, coherent, and highly structured algebraic object, the quantum event algebra L, forming a complete, atomic, orthomodular lattice. The relations between events—such as inclusion, orthogonality, compatibility, and so on—are intrinsic to this algebraic structure. The structure is neither imposed externally nor is it realized in an “all-at-once" manner.

    • Calculable and Characterizable as a Whole: Far from being impossible for a distribution of quantum events to be calculated or characterized as a whole, the critical point of the K&Z framework is to demonstrate that the global object L is the characterization of the whole, and that it is uniquely determined by the synthesis of its local perspectival manifestations. The colimit construction provides the universal categorical solution for this characterization. The guiding principle, therefore, is not that the world is a mere collection of fragmented facts but that the world is a structured whole which is knowable through a multiplicity of partial, internally consistent perspectives.

• 6. The Nature of Events and Nonlocality

  • In our framework, as in standard quantum mechanics, an “event" corresponds to an element of the global quantum algebra L; it is represented by a projection operator.

  • This event does not acquire a pre-given, absolute, context-independent truth value. The global algebra L is inherently value-indefinite, which is the logical-structural meaning of the Kochen-Specker theorem.

  • An event obtains a definite truth value and thus it becomes an actual fact, only perspectivally, that is, within a Boolean probing frame or perspective from which the quantum system is considered (Section 6).

  • Quantum nonlocality and constraints on probabilistic correlations among quantum physical observables are not the result of peculiar nonlocal influences between absolute, fragmented events. They are a direct consequence of the non-Boolean, holistic structure of the global quantum algebra L. The entangled correlations of an EPR pair, for instance, are encoded in the global state vector of the compound system, which defines the relations within the tensor product algebra $L_{A} \otimes L_{B}$. A local measurement that involves the adoption of a Boolean frame, say, at system B projects out a specific slice of this global structure, revealing information that is constrained by the whole. The correlation is thus structural, not causal.

• 7. “All-at-Once" Realization vs. Structural Constitution

  • In RQM, including the CPL postulate, the strongly nonlocal dependencies of quantum events on one another force an “all-at-once", atemporal explanatory stance for the entire mosaic of facts. Within our framework, such an “all-at-once" realization of events is redundant. The non-Boolean quantum algebra L, equipped with the projective geometry of Hilbert space, encodes generic kinematic (pre-dynamic) constraints on probabilistic correlations between measurement outcomes (events), ensuring the consistent incorporation of probabilities in a physically indefinite world. The relationship between the global structure and local measurements is explicated by the Boolean frames-quantum adjunction, which formalizes a bi-directional, structure-preserving information flow between these two hierarchically distinct structural levels. This provides a structural explanation for how local contexts, within a generic non-Boolean quantum framework, reveal global properties, surpassing the need for an “all-at-once" hypothesis concerning the realization of disparate events.

In conclusion, the K&Z approach offers in comparison to RQM+ a profoundly different picture of the quantum world’s architecture. Instead of postulating a distribution of absolute but fragmented events and then seeking an external hypothesis of an “all-at-once" realization that induces a generic form of nonlocality, we demonstrate how a holistic indefinite quantum reality, conceptualized as a global quantum event algebra, is mathematically constituted by the coherent synthesis of all possible, locally variable Boolean perspectives. The distribution of events is neither instantaneous nor fragmented; it is an expression of the intricate non-Boolean probabilistic correlations within a single unified quantum event structure.