Fact-checked by Grok 2 weeks ago

Relational quantum mechanics

Relational quantum mechanics (RQM) is an of , proposed by in , that views the state of a quantum system as inherently relative to another physical system acting as an observer, rather than as an absolute or observer-independent reality. In this framework, physical properties and events emerge only through interactions between systems, emphasizing that describes correlations and information accessible from one system's perspective about another, without privileging human observers or classical apparatuses. RQM thus reformulates quantum theory to eliminate the classical-quantum divide, treating all physical systems equivalently and resolving longstanding interpretive issues like the by making value assignments relational rather than requiring or hidden variables. The core principles of RQM rest on three fundamental hypotheses: first, the complete equality of all physical , meaning no is inherently more "observer-like" than another; second, the completeness of as a theory, without need for additional postulates; and third, the relational nature of information, where a 's state relative to another is encoded in correlations that can be probabilistically predicted but not absolutely determined. For instance, in a scenario, the outcome for S relative to observer O (such as a definite ) coexists with a superposition description from another observer P who has not yet interacted with the apparatus, illustrating how different perspectives yield consistent but partial accounts of the same events without contradiction. This relational approach aligns with unitary evolution throughout, avoiding physical modifications to the while interpreting probabilities as epistemic, tied to an observer's limited information. RQM differs markedly from other quantum interpretations by rejecting absolute states or universal wave functions, as in the , and instead adopting a sparse of localized events defined by interactions. It draws inspiration from relational views in and , where properties like or time are frame-dependent, extending this to the quantum to address issues like the Einstein-Podolsky-Rosen () through non-local but non-signaling correlations that remain relative. Since its introduction, RQM has influenced discussions in , , and theory, with ongoing developments exploring its compatibility with and multi-perspective consistency, though it continues to debate questions of and the unity of physical descriptions across observers.

Historical Development

Origins and Motivation

Relational quantum mechanics (RQM) emerged in the mid-1990s as an aimed at resolving longstanding conceptual issues in . The approach was formally published in , marking a shift toward viewing quantum states not as intrinsic properties but as perspectives dependent on interacting systems. A key intellectual root of RQM lies in Machian relationalism, a philosophical stance in physics that prioritizes relations between physical systems over absolute, background-dependent attributes, as exemplified in Ernst Mach's critiques of Newtonian . This relational perspective, which influenced Einstein's development of , resonated with Rovelli's efforts to eliminate privileged frames or structures in fundamental theories. Additionally, influences from theory provided tools to reconceptualize as a theory of correlations and shared information between systems rather than isolated facts. Rovelli's own research background in (LQG), a background-independent approach to quantizing co-developed with Abhay Ashtekar and in the late 1980s, served as a remote but significant motivation for RQM. LQG treats as emergent from quantum relations among gravitational , avoiding a fixed background metric, and Rovelli sought an interpretation of compatible with this relational ontology to bridge quantum theory and gravity without introducing elements. This compatibility was crucial, as standard ' reliance on an external classical observer clashed with the fully quantum, relational nature of LQG. The primary motivations for developing RQM centered on addressing the inherent asymmetry in standard between the observed quantum system and the observing apparatus, which is typically assumed to be classical and privileged. Rovelli argued that this distinction is artificial and unphysical, proposing instead that all physical systems—quantum or otherwise—can serve as observers through interactions, thereby democratizing the role of in the theory. Furthermore, RQM aimed to eliminate the collapse postulate of the wave function, which introduces a non-unitary evolution upon ; by relativizing states to specific observers, the apparent becomes a perspectival update in the information available to that observer, preserving unitary dynamics universally. These motivations stemmed from a desire to render more coherent and ontologically parsimonious, aligning it with the relational principles of .

Key Formulations and Publications

The foundational formulation of relational quantum mechanics (RQM) was presented in Carlo Rovelli's 1996 paper, where he introduced the core ideas of relative states defined through interactions between systems, emphasizing that quantum states are observer-dependent without absolute properties. This work established RQM as an interpretation resolving the by focusing on relational information rather than intrinsic states. Rovelli further elaborated on RQM in his 2004 book , particularly in Chapter 5 on , positioning it as a key interpretive foundation for reconciling with . The chapter integrates RQM's principles into the broader context of background-independent , highlighting its compatibility with approaches. In his 2008 essay "Forget Time," Rovelli linked RQM to thermodynamic and gravitational perspectives, arguing for a timeless quantum framework where interactions define temporal relations.

Core Concepts and Principles

The Role of the Observer

In relational quantum mechanics (RQM), the observer is defined as any physical system capable of interacting with another system, thereby resolving the classical-quantum divide that underlies the measurement problem in standard quantum interpretations. This perspective eliminates the need for a privileged classical domain by treating all systems equivalently under quantum mechanics, where interactions serve as the fundamental means of acquiring information about other systems. Observers in RQM are themselves quantum systems that obtain information exclusively through physical interactions, rather than through any special conscious or external agency. Unlike traditional views that might imply a subjective or mental role for observers, RQM emphasizes that any system—be it a particle detector, a measuring apparatus, or even another quantum particle—can function as an observer by establishing correlations via . This relational acquisition of information underscores that quantum descriptions are inherently about the perspectives of interacting systems, without invoking absolute or observer-independent facts. RQM rejects the notion of wave function collapse entirely, maintaining unitary evolution for the combined system of observer and observed throughout all processes. Instead, measurement outcomes are relative to the state of the observer following the interaction, meaning that what constitutes a definite value for a depends on the specific relational context between the systems involved. This approach addresses the by framing quantum events as perspectival, where apparent definiteness arises from the information available to a particular observer, without requiring any modification to the . A illustrative example is the Stern-Gerlach experiment, where an 's is measured relative to the apparatus: post-interaction, the apparatus records the electron as having spin up or down with respect to its own state, but this outcome is not absolute and would differ if described from the perspective of another non-interacting system. The apparatus itself possesses a relative state correlated with the electron, highlighting how both systems are quantum entities without a collapse event. This relational view aligns with the broader principle of state dependence in RQM, where quantum states encode information relative to specific observers.

Observer-Dependent States

In relational quantum mechanics (RQM), the state of a quantum system S relative to an observer O is described by the or that captures the information available to O about S after their interaction. This description arises from the perspective of O, which acts as a interacting with S, thereby establishing a relational framework for the state's properties. Unlike traditional views, this state does not represent an intrinsic or complete reality of S but rather the specific outcomes and correlations discernible from O's standpoint. A core tenet of RQM is the absence of a single for any ; instead, are inherently observer-dependent, with no privileged, description independent of relational interactions. Different observers, such as O and another O', may assign incompatible to the same S, as each bases its description on its own distinct history of interactions and acquired information. For instance, while O might describe S in a definite eigenstate following , O'—not directly interacting with S—could perceive a superposition involving both S and O. This relativity ensures that quantum predictions remain consistent across perspectives without requiring a to a shared . This induces a profound conceptual shift, portraying quantum not as a collection of objective properties but as a dense web of relative facts woven through interactions between systems. Each fact—such as the value of an for S—exists only relative to a specific observer, forming a network where information is exchanged and perspectives interlink without a foundational layer. Stable aspects of this web emerge from repeated or shared interactions, allowing for effective inter-observer agreement, yet the underlying remains purely relational. This view resolves tensions in quantum description by emphasizing perspectival completeness over global objectivity.

Information, Correlations, and Universality

In relational quantum mechanics (RQM), is inherently relative and arises from the entangled correlations between interacting physical . Rather than describing absolute properties of a , the quantum state encodes the that one possesses about another through these correlations, which reduce the number of possible configurations in their joint . For instance, when a measuring apparatus interacts with a quantum , the resulting entanglement correlates the pointer of the apparatus with the 's outcome, providing the apparatus with definite about the relative to itself. This aligns quantum mechanics with , where correlations represent the between subsystems, as formalized by Shannon's framework. A core tenet of RQM is the universality principle, which posits that all physical systems are equivalent and subject to quantum interactions without any fundamental distinction between microscopic and macroscopic scales. Under this hypothesis, no system is privileged as an "observer" a priori; instead, any physical entity—be it an , a laboratory instrument, or a —can acquire relational information about another through during interactions. This universality eliminates the need for a classical-quantum divide, treating the entire as a where all value assignments are relational and perspectival. Experimental evidence supports this equivalence, as macroscopic systems exhibit quantum behavior in controlled settings, such as superconducting qubits. Decoherence in RQM exemplifies these principles as a perspectival phenomenon rather than an objective collapse or loss of coherence in the universe. When a quantum system interacts with a larger environment, the resulting entanglement leads to the suppression of interference terms from the perspective of a subsystem, making relative facts appear stable and classical-like without invoking an absolute state. For example, in the measurement of a spin-1/2 particle by a Stern-Gerlach apparatus, decoherence relative to the apparatus renders the outcome definite for that observer, while the global quantum state remains superimposed from a broader viewpoint. This relational view of decoherence resolves the measurement problem by grounding apparent classicality in the information available to specific systems, consistent with unitary evolution throughout. In a 2023 update, Adlam and Rovelli proposed that information possessed by an observer must be stored in its physical variables, enabling cross-perspective links for consistent descriptions across observers.

Formal Framework

Algebraic Structure

In relational quantum mechanics (RQM), the algebraic structure is grounded in the standard formalism of , where physical systems are described by Hilbert spaces and characterized by orthomodular lattices of possible measurements, such as yes/no questions about the system. Observables correspond to operators, whose spectral decompositions determine the possible outcomes of measurements. The fundamental non-commutativity of is enforced by relations such as [q, p] = i \hbar for and operators. States in RQM are not absolute but relative to another , reflecting the of one with respect to another. This relational approach treats the as a tool for encoding information about correlations between systems, rather than an intrinsic property of an isolated entity. For two interacting systems S and O, where O acts as the reference (or observer), the state of S relative to O emerges from the joint description. The relative state formalism operationalizes this through the reduced density operator, obtained via over the reference system's following their interaction. Specifically, if |\psi_{SO}\rangle denotes the entangled joint of S and O, the relative density operator for S with respect to O is given by \rho_{S|O} = \operatorname{Tr}_O \left( |\psi_{SO}\rangle \langle \psi_{SO}| \right), which captures the conditional probabilities and expectations for observables on S as perceived by O. This construction ensures that all information is encoded in the , aligning with the observer-dependent of quantum descriptions in RQM.

Dynamical Evolution

In relational quantum mechanics (RQM), dynamical evolution proceeds unitarily across the entire of the universe, encompassing all interacting systems without any privileged foliation of or absolute reference frame. This global unitary dynamics ensures that the evolution of any subsystem is described relative to another system acting as an observer, with relative states emerging from the correlations established during interactions. Unlike interpretations that invoke , RQM maintains that the full evolves deterministically and linearly, preserving all relational information about the system without introducing non-unitary processes. The standard Schrödinger equation governs this evolution on the universal scale: i \hbar \frac{d |\psi \rangle}{dt} = H |\psi \rangle where |\psi \rangle is the state vector in the full Hilbert space and H is the total Hamiltonian. For a specific observer, such as system O interacting with system S, the relative state of S with respect to O updates through the unitary operator U(t) = e^{-i H t / \hbar}, which entangles the subsystems and correlates their outcomes. Post-interaction, the relative perspective of O on S yields definite values for observables, derived from the reduced density matrix or conditional states, without requiring a physical projection or measurement-induced collapse. This relational actualization of values arises solely from the interaction dynamics, ensuring consistency across different observers' descriptions. RQM eschews any preferred basis in the , as the emergence of definite outcomes depends on the specific interaction rather than an external . The dynamics thus conserve the relational structure of information, where probabilities and correlations between systems remain invariant under unitary evolution, resolving apparent paradoxes like the by relativizing the notion of "outcome" to the observer-system pair. This framework aligns with the of , where observables and states are defined relationally, but emphasizes the temporal unfolding of these relations through continuous unitary flow.

Key Implications and Applications

Resolution of Quantum Non-Locality

The Einstein-Podolsky-Rosen (EPR) paradox, introduced in , highlights an apparent tension in arising from entanglement, where measurements on spatially separated particles seem to imply instantaneous influences across distances, suggesting non-locality or incompleteness of the theory. In the standard formulation, two entangled particles are prepared in a shared , such that measuring one particle's property (e.g., ) appears to determine the other's outcome immediately, regardless of separation, challenging relativistic locality without invoking hidden variables. Relational quantum mechanics (RQM) resolves this paradox by rejecting the notion of an , observer-independent , instead positing that and properties are inherently relational, defined only relative to a specific observing . Correlations between entangled systems are thus local to each observer's perspective: there is no shared global that undergoes instantaneous collapse, eliminating any violation of locality or signaling. This approach maintains the completeness of without hidden variables, as the apparent non-locality stems from assuming an , which RQM discards in favor of observer-relative descriptions. A concrete example involves two observers, , each interacting with one particle from an entangled pair, say in a singlet state. From Alice's viewpoint, her yields a definite outcome for her particle, and the state of Bob's particle relative to her is now determined accordingly, reflecting the full correlation. Similarly, Bob's defines the state of Alice's particle relative to him, with outcomes consistent due to their prior shared with the entangled . No superluminal influence is required, as each observer's about the joint evolves locally through their interactions, ensuring statistical consistency without a common absolute reality. This relational consistency arises naturally from the dynamical evolution described in RQM's formal framework.

Relational Networks and Coherence

In relational quantum mechanics (RQM), physical systems interact to form networks of relative facts, where each interaction generates information accessible only relative to the participating systems, building a web of observer-dependent descriptions without invoking an absolute reality. These networks emerge as systems exchange quantum information, ensuring that descriptions remain consistent across interactions while remaining perspectival; for instance, the state of one system relative to another defines localized facts that propagate through the network via correlations. This relational structure underscores that quantum reality is constructed collectively from pairwise relations, avoiding the need for a global wave function. Coherence in RQM is maintained relationally rather than as an intrinsic, property of isolated systems, arising from the preservation of quantum superpositions within specific contexts. In multi-observer scenarios, reflects the alignment of relative facts across the network, where terms remain intact unless disrupted by further interactions, thus ensuring intersubjective consistency without collapsing to a single perspective. This approach integrates information correlations between systems, allowing coherent narratives to emerge from the totality of relations. Decoherence in RQM appears as a relative , stemming from environmental interactions that suppress from the viewpoint of a particular observer, yet it does not eliminate underlying relational superpositions for other systems. For an observer entangled with a large , such as a measuring device, decoherence manifests as the effective classicalization of outcomes, but this is perspectival—other isolated systems may still perceive coherent quantum behavior. This relational decoherence resolves apparent paradoxes in multi-system setups by localizing the loss of to specific viewpoints, without requiring universal . The implications for macroscopic superpositions in RQM highlight their persistence relative to isolated observers, where large-scale quantum effects endure in descriptions decoupled from environmental entanglement. For example, a macroscopic object in superposition may appear definite to an interacting observer due to decoherence, but remains superposed relative to a non-interacting , preserving the quantum nature across the relational network. This framework thus accommodates the absence of observed macroscopic in everyday scenarios while affirming its relational existence, bridging microscopic quantum principles with emergent classicality.

Integration with Quantum Gravity and Cosmology

Relational quantum mechanics (RQM) aligns seamlessly with (LQG), a non-perturbative approach to quantizing , by emphasizing relational states that eschew a fixed . In LQG, emerges from discrete quantum excitations known as spin networks, which encode geometric relationally through interactions among of volume and area, rather than presupposing a continuous manifold. This compatibility arises because RQM's of relative between systems complements LQG's background-independent formulation, where physical properties are defined only with respect to local observers or subsystems. In , RQM provides a for describing the as an interconnected relational of subsystems, without invoking an external observer to a universal . This view is crucial for interpreting the Wheeler-DeWitt , the canonical in that governs the timeless of the , \hat{H} \Psi = 0, where \hat{H} is the Hamiltonian and \Psi is the of the . Relationally, the is recast in terms of partial observables—physical variables that evolve relative to one another—yielding transition amplitudes between eigenstates of these observables as the basis for predictions, rather than a static global configuration. A key implication of this integration is that time emerges dynamically from correlations between subsystems, such as a acting as a clock and the gravitational , obviating the need for an absolute temporal parameter. In this relational setting, the ""—the apparent frozen dynamics implied by the Wheeler-DeWitt equation—is not a fundamental issue but a artifact of seeking absolute evolution; instead, the universe's history unfolds through the web of these inter-system relations, consistent with RQM's dynamical framework of evolving relative states.

Comparisons with Other Interpretations

Similarities and Differences with

Relational quantum mechanics (RQM) shares significant similarities with the , particularly in its pragmatic emphasis on observer-dependent predictions over a commitment to an absolute of quantum states. Both interpretations prioritize the outcomes of measurements as relative to the observing system, avoiding the need for hidden variables to explain quantum phenomena. In RQM, as in , the theory is formulated to yield empirical predictions without invoking additional metaphysical structures beyond the standard quantum formalism. A key difference lies in the nature of the observer: the typically posits a classical apparatus or human observer that induces , distinguishing between and a classical context. In contrast, RQM treats all physical systems—quantum or otherwise—as potential observers, eliminating the privileged role of classical entities and allowing interactions between any two systems to define relative states. This "democratization" of observers in RQM extends the framework by integrating the observer fully into the quantum domain. Furthermore, while Copenhagen relies on a non-unitary collapse postulate to transition from superposition to definite outcomes, RQM maintains unitary evolution throughout, with apparent collapses arising solely from the relativity of information between systems. This unitary approach in RQM resolves longstanding critiques of Copenhagen's by providing a consistent, observer-relative description without collapses, effectively realizing "Copenhagen without the ."

Contrasts with Hidden-Variable Theories

Hidden-variable theories seek to supplement with underlying definite properties or variables that exist independently of observation, aiming to provide a more complete, deterministic description of physical reality. For instance, Bohmian mechanics introduces particle trajectories guided by a non-local wave function, positing objective, pre-existing values for all observables. In stark contrast, relational quantum mechanics (RQM) rejects the notion of intrinsic, observer-independent states, asserting that all physical properties are relational—defined only relative to interactions with other systems—and that quantum mechanics already offers a of these relations, obviating the need for variables. RQM's compatibility with the Bell theorem further highlights this divergence: while hidden-variable theories must either accept non-locality (as in Bohmian mechanics) or invoke to reproduce quantum predictions without violating Bell's inequalities, RQM accounts for the observed correlations by relativizing facts to observers, thereby violating local realism in a perspective-dependent way without additional assumptions. This relational violation preserves the appearance of non-locality only from an absolute, non-relational viewpoint, which RQM discards. A key critique of hidden-variable approaches from the RQM perspective is their introduction of excess structure incompatible with ; for example, the instantaneous non-local influences in Bohmian mechanics conflict with the locality and causal structure of , requiring ad hoc modifications like preferred foliations to attempt relativistic extension. RQM avoids such issues by grounding descriptions in local interactions constrained by light cones, ensuring natural compatibility with relativistic without superfluous ontological commitments.

Relations to Everettian and Consistent Histories Approaches

Relational quantum mechanics (RQM) shares foundational similarities with the Everettian relative-state formulation, particularly in emphasizing the relativity of quantum states to interacting systems. Both approaches reject and treat states as relative rather than , building on the idea that quantum descriptions depend on the perspective of or system involved. For instance, Everett's universal allows states to be defined relative to subsystems, akin to RQM's relational states between interacting entities. However, RQM diverges by adopting a strictly perspectival where facts are relative to specific interactions without implying an underlying , whereas Everett's posits a single, absolute universal that branches into multiple coexisting worlds. In contrast to the Everettian many-worlds interpretation, RQM avoids ontological multiplicity and branching realities, maintaining a single, consistent world described differently from various relational viewpoints. Everett's approach accommodates all possible outcomes as equally real across parallel branches, leading to a proliferation of worlds upon measurement-like interactions. RQM, however, resolves apparent indeterminacy through observer-system interactions without multiplying realities, viewing differing perspectives as complementary descriptions of the same events rather than distinct ontological branches. This distinction underscores RQM's commitment to relationalism, where the state of a system is always defined with respect to another, eliminating the need for an absolute state or global branching. RQM also exhibits affinities with the consistent histories approach, particularly in their mutual reliance on decoherence to explain the emergence of stable, classical-like facts from quantum superpositions. Both frameworks leverage environmental interactions and decoherence to suppress between potential outcomes, allowing for probabilistic assignments to histories or events without invoking . In , decoherence ensures that sets of histories are consistent—meaning their projectors commute—enabling a non-standard where propositions about the system's evolution can be meaningfully assigned truth values. RQM incorporates similar ideas but frames facts as inherently relational, tied to specific observer-system pairs, rather than requiring global consistency across an absolute framework. A key difference lies in how they handle facts and consistency: consistent histories emphasize selecting compatible families of histories for probability calculations, treating the framework as observer-independent but requiring internal coherence. In RQM, facts are perspectival and may not align globally, with stable facts emerging only when histories from different perspectives commute and share information, thus avoiding the need for a privileged global description. This relational treatment of facts distinguishes RQM from the more framework-centric approach of . RQM can thus serve as a conceptual bridge between these interpretations by integrating decoherence mechanisms to account for apparent classicality and shared realities, without committing to either Everett's multiplication of worlds or the ' emphasis on globally consistent frameworks. This allows RQM to incorporate the effective role of decoherence in establishing relational among systems, while preserving its relational .

Criticisms and Recent Advances

Open Problems and Debates

One prominent in relational quantum mechanics (RQM) concerns the precise definition of an "" or "fact" within its relational framework. In RQM, events are posited to exist only relative to interactions between , but the theory lacks a clear criterion for when such an interaction constitutes a definite , leading to ambiguities in identifying relational facts. This issue manifests as circularity in observer interactions, particularly in scenarios like the "third-person problem," where one observer (P) attempts to describe the state relative to another observer (O) during a ; the relational state assignment becomes self-referential and ill-defined without an external . Critics argue that this circularity undermines RQM's claim to resolve the , as the reduction of the wave function remains unaccounted for in purely relational terms. A related philosophical debate centers on whether RQM implies , given that physical facts are relativized to individual observers, potentially rendering the external world inaccessible beyond one's own perspective. Proponents counter that is avoided because observers are defined broadly as any physical systems capable of , and inter-observer emerges from shared relational networks, ensuring empirical agreement across descriptions. However, detractors maintain that this response does not fully dispel solipsistic concerns, as the theory struggles to validate facts relative to or hypothetical observers without invoking subjective . Technical challenges further complicate RQM's formulation, particularly in handling continuous interactions rather than discrete events. The original framework emphasizes instantaneous interactions for state relativization, but real often involve ongoing entanglements, making it unclear how to delineate boundaries for relational facts amid evolving superpositions. Additionally, RQM's absence of a preferred —lacking a slicing akin to —poses difficulties in ordering events, especially in contexts requiring temporal coordination, such as successive measurements. These issues highlight ongoing debates about RQM's applicability to dynamical processes beyond idealized cases.

2023 Revision and Subsequent Developments

In 2023, Emily Adlam and proposed a significant revision to relational quantum mechanics (RQM) through their introduction of "cross-perspective links" (CPL), shifting the framework toward a perspectival that emphasizes observer viewpoints while incorporating absolute quantum events. This revision replaces the earlier postulate of relativity of comparisons with CPL, which posits that possessed by one observer can be physically stored and accessed by others through interactions, ensuring intersubjective agreement on measurement outcomes. Unlike the original RQM's strict relational facts, this update introduces observer-independent "quantum events" or "flashes" as primitive, absolute facts about reality, defined by interactions where physical variables become definite relative to an observer but occur independently of any specific perspective. This new addresses prior critiques of RQM's purely relative facts by grounding the theory in a structure of absolute events and perspectival states, thereby resolving issues of ontological . Building on this revision, developments in 2024 and 2025 extended RQM's perspectival approach into broader interpretive frameworks. In 2025, E. Zaghi introduced Relational Quantum Dynamics (RQD), an that reframes quantum reality as a non-dual web of relationships, drawing analogies to the ancient metaphor where phenomena arise interdependently without isolated entities. RQD integrates by treating quantum states as relational information flows, linking RQM to consciousness-centered and category-theoretic models that emphasize holistic, non-local interconnections. Concurrently, 2025 papers debated the implications of in RQM, with some advocating "soft " to balance relationalism against infinite regresses of observer dependencies, while others explored its compatibility with quantum . These advancements enhance RQM's compatibility with theory by formalizing how perspectival facts enable shared protocols and error correction across observers, and with relativistic principles by treating events as frame-invariant anchors. The revisions directly counter critiques, such as those concerning the status of facts, by providing a clearer metaphysical foundation that supports empirical consistency without invoking hidden variables or absolute states.