Abstract The no-go theorems of Bell and Kochen and Specker could be interpreted as implying that the notions of system and experimental context are fundamentally inseparable. In this interpretation, statements such as ‘spin is “up” along direction $x$’ are relational statements about the configurations of macroscopic devices which are mediated by the spin and not about any intrinsic properties of the spin. The operational meaning of these statements is provided by the practically infinite resources of macroscopic devices that serve to define the notion of a direction in three-dimensional space. This is the subject of ‘textbook quantum mechanics’: the description of quantum systems in relation to an experimental context. Therefore, the subject that textbook quantum mechanics treats as a formally closed system is not a physically isolated system. The subject rather describes the physical relation that a microscopic system holds with some macroscopic environment. Can one go beyond that? Relational quantum mechanics endeavours to provide a relational description between any quantum systems without the necessity of involving macroscopic devices. However, by applying ‘textbook quantum mechanics’ in such situations, it implicitly assumes infinite resources, even for simple quantum systems such as spins, which have no capacity to define an experimental context. This leads to conceptual difficulties. As an alternative, we analyse Penrose’s spin network proposal as a potential formalisation of quantum theory that goes beyond the textbook framework: a description in presence of finite resources, which is inherently relational and inseparable in the system-context entity.
Abstract The no-go theorems of Bell and Kochen and Specker could be interpreted as implying that the notions of system and experimental context are fundamentally inseparable. In this interpretation, statements such as ‘spin is “up” along direction x’ are relational statements about the configurations of macroscopic devices which are mediated by the spin and not about any intrinsic properties of the spin. The operational meaning of these statements is provided by the practically infinite resources of macroscopic devices that serve to define the notion of a direction in three-dimensional space. This is the subject of ‘textbook quantum mechanics’: the description of quantum systems in relation to an experimental context. Therefore, the subject that textbook quantum mechanics treats as a formally closed system is not a physically isolated system. The subject rather describes the physical relation that a microscopic system holds with some macroscopic environment. Can one go beyond that? Relational quantum mechanics endeavours to provide a relational description between any quantum systems without the necessity of involving macroscopic devices. However, by applying ‘textbook quantum mechanics’ in such situations, it implicitly assumes infinite resources, even for simple quantum systems such as spins, which have no capacity to define an experimental context. This leads to conceptual difficulties. As an alternative, we analyse Penrose’s spin network proposal as a potential formalisation of quantum theory that goes beyond the textbook framework: a description in presence of finite resources, which is inherently relational and inseparable in the system-context entity.
The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the (neo-)Copenhagen interpretation of quantum theory to measurement contexts, and in QBism to the beliefs of the agents. In contrast to the other two interpretations, in RQM any interaction between two quantum systems counts as a "measurement", and the terms "observer" and "observed system" apply to arbitrary systems. We show, in the form of a no-go theorem, that in RQM the physical description of a system relative to an observer cannot represent knowledge about the observer in the conventional sense of this term. The problem lies in the ambiguity in the choice of the basis with respect to which the relative states are to be defined in RQM. In interpretations of quantum theory where observations play a fundamental role, the problem does not arise because the experimental context defines a preferred basis.
Quantum mechanics has transformed our understanding of reality, yet deep philosophical puzzles remain unresolved. Is there a consistent way to describe quantum measurement, the emergence of space and time, and the role of observers within one coherent ontology? This paper introduces Relational Quantum Dynamics (RQD), an interpretation that places relationships and information—not isolated objects—at the foundation of physics. Unlike traditional views, such as the Copenhagen interpretation, Everett’s many-worlds theory, or hidden-variable approaches, RQD denies a single observer-independent reality, instead proposing that facts only become definite within specific observational contexts. It explicitly addresses foundational no-go results, including Bell’s theorem, the Kochen–Specker theorem, and the Frauchiger–Renner paradox, by replacing absolute facts with relational, context-dependent truths. RQD rests on five interlocking principles: (1) quantum states are contextual and observer-relative, (2) time emerges from quantum interactions rather than existing as an external parameter, (3) space is constructed from patterns of quantum entanglement, (4) observers emerge as systems with highly integrated information, and (5) classical reality appears through quantum decoherence without special wavefunction collapse. Philosophically, RQD aligns with ontic structural realism, proposing that the fundamental ontology of the universe consists entirely of informational relations. It avoids collapsing into relativism or solipsism by ensuring intersubjective agreement through physical interactions. Ultimately, RQD may offer a unified picture in which quantum mechanics, spacetime, and observers are no longer separate domains but aspects of one interconnected informational web.
Rovelli’s relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute but is relative to the observer itself. The interpretation goes further and proposes a set of axioms. In standard non-relational language, one of them states that an observer can only retrieve a finite amount information from a system by means of measurement. Our contribution starts with the observation that quantum mechanics, i.e., quantum field theory (QFT) in dimension 1, radically differs from QFT in higher dimensions. In higher dimensions, boundary data (or initial data) cannot be characterized by finitely many measurements. This calls for a notion of measuring scale, which we provide. At a given measuring scale, the observer has partial information about the system. Our notion of measuring scale generalizes the one implicitly used in Wilsonian QFT. At each measuring scale, there are effective theories, which may be corrected, and if the theory turns out to be renormalizable, the mentioned corrections converge to determine a completely corrected (or renormalized) theory at the given measuring scale. The notion of a measuring scale is the cornerstone of Wilsonian QFT; this notion tells us that we are not describing a system from an absolute perspective. An effective theory at that scale describes the system with respect to the observer, which may retrieve information from the system by means of measurement in a specific way determined by our notion of measuring scale. We claim that a relational interpretation of quantum physics for spacetimes of dimensions greater than 1 is Wilsonian.
In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties within the orthodox formalism of quantum mechanics. Through an analysis of the meaning of physical invariance and quantum contextuality we will derive a Corollary to KS theorem that proves that a vector in Hilbert space cannot be interpreted coherently as an object possessing (objective) physical properties. As a consequence, the notion of quantum object can be only defined in terms of nomological properties. We conclude the paper by analyzing the consequences of this Corollary to KS theorem for the ongoing debate about quantum individuality.
Quantum mechanics has transformed our understanding of reality, yet deep philosophical puzzles remain unresolved. Is there a consistent way to describe quantum measurement, the emergence of space and time, and the role of observers within one coherent ontology? This paper introduces Relational Quantum Dynamics (RQD), an interpretation that places relationships and information, not isolated objects, at the foundation of physics. Unlike traditional views, such as the Copenhagen interpretation, Everett's many-worlds theory, or hidden-variable approaches, RQD denies a single observer-independent reality, instead proposing that facts only become definite within specific observational contexts. It explicitly addresses foundational no-go results, including Bell's theorem, the Kochen-Specker theorem, and the Frauchiger-Renner paradox, by replacing absolute facts with relational, context-dependent truths. RQD rests on five interlocking principles: (1) quantum states are contextual and observer-relative, (2) time emerges from quantum interactions rather than existing as an external parameter, (3) space is constructed from patterns of quantum entanglement, (4) observers emerge as systems with highly integrated information, and (5) classical reality appears through quantum decoherence without special wavefunction collapse. Philosophically, RQD aligns with ontic structural realism, proposing that the fundamental ontology of the universe consists entirely of informational relations. It avoids collapsing into relativism or solipsism by ensuring intersubjective agreement through physical interactions. Ultimately, RQD may offer a unified picture in which quantum mechanics, spacetime, and observers are no longer separate domains but aspects of one interconnected informational web.
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it is expected to hold the key to quantum advantage. Yet, despite its long recognised importance in quantum foundations and, more recently, in quantum computation, the structural essence of contextuality has remained somewhat elusive - different frameworks address different aspects of the phenomenon, yet their precise relationship often remains unclear. This issue already looms large at the level of the Bell-Kochen-Specker theorem: while traditional proofs proceed by showing the nonexistence of valuations, the notion of state-independent contextuality in the marginal approach allows to prove contextuality from seemingly weaker assumptions. In the light of this, and at the absence of a unified mathematical framework for Kochen-Specker contextuality, the original algebraic approach has been widely abandoned, in favour of the study of contextual correlations. Here, we reinstate the algebraic perspective on contextuality. Concretely, by building on the novel concept of context connections, we reformulate the algebraic relations between observables originally postulated by Kochen and Specker, and we explicitly demonstrate their consistency with the notion of state-independent contextuality. In the present paper, we focus on the new conceptual ideas and discuss them in the concrete setting of spin-1 observables, specifically those in the example of [S. Yu and C.H. Oh, Phys. Rev. Lett., 108, 030402 (2012)]; in a companion paper, we generalise these ideas, obtain a complete characterisation of Kochen-Specker contextuality and provide a detailed comparison with the related notions of contextuality in the marginal and graph-theoretic approach.