We extend the representation frame formalism, previously introduced to account for key cosmological observations in the Einstein static universe, to non-relativistic quantum mechanics. In this framework, each inertial observer is associated with a flat representation referential Robs, defined as the tangent space to the spatial manifold at the observer’s position, in which all measurements are represented. The Euclidean structure of Robs allows quantum systems to be described using the standard Schrödinger formalism, avoiding the technical ambiguities that arise when quantising directly on curved manifolds. We derive the relation between the Hamiltonian governing quantum dynamics in Robs and its counterpart defined on the physical manifold U, and show that curvature effects enter as observer-dependent modifications of effective potentials. Although the resulting quantum description depends on the observer’s representation frame, we show that this does not lead to contradictions between observers: consistency of measurement outcomes follows from the standard structure of quantum correlations established by physical interactions. We illustrate the formalism with explicit applications, including the hydrogen atom in an Einstein static universe and quantum systems in the vicinity of a black hole, highlighting how spacetime curvature manifests itself in the observer’s quantum description.
We extend the representation frame formalism, previously introduced to account for key cosmological observations in the Einstein static universe, to non-relativistic quantum mechanics. In this framework, each inertial observer is associated with a flat representation referential Robs, defined as the tangent space to the spatial manifold at the observer’s position, in which all measurements are represented. The Euclidean structure of Robs allows quantum systems to be described using the standard Schrödinger formalism, avoiding the technical ambiguities that arise when quantising directly on curved manifolds. We derive the relation between the Hamiltonian governing quantum dynamics in Robs and its counterpart defined on the physical manifold U, and show that curvature effects enter as observer-dependent modifications of effective potentials. Although the resulting quantum description depends on the observer’s representation frame, we show that this does not lead to contradictions between observers: consistency of measurement outcomes follows from the standard structure of quantum correlations established by physical interactions. We illustrate the formalism with explicit applications, including the hydrogen atom in an Einstein static universe and quantum systems in the vicinity of a black hole, highlighting how spacetime curvature manifests itself in the observer’s quantum description.
Abstract Quantum coherence is a fundamental resource underlying interference, entanglement-assisted processes, quantum information transfer, and the operational distinction between classical and quantum states. In laboratory-scale systems, coherence is commonly analysed relative to approximately inertial observers and weak gravitational environments. A more complete description becomes necessary when quantum systems are considered in accelerated reference frames, strong gravitational fields, or curved spacetime geometries. Under such conditions, the definition of particles, field modes, temporal evolution, and observable quantum correlations can depend on the observer and on the spacetime structure used to describe the system. This article examines the conceptual and physical behaviour of relativistic quantum coherence in non-inertial frames and curved spacetime environments without relying on a formulation based on explicit mathematical expressions. Particular attention is given to accelerated observers, horizon-related mode restrictions, observer-dependent vacuum descriptions, gravitational frequency shifts, field localization, and the transformation of accessible quantum information. Coherence is treated not merely as an intrinsic property of an isolated microscopic object but as a relational quantity affected by the physical decomposition of a quantum field into operationally accessible degrees of freedom. The analysis distinguishes coherence degradation from fundamental destruction of quantum information and emphasizes the role of inaccessible field sectors, measurement limitations, and observer-dependent subsystem definitions. Curved spacetime is further considered as a structured environment capable of modifying mode propagation, phase relationships, and correlations without behaving as a conventional material reservoir. The discussion establishes a conceptual framework relevant to relativistic quantum information, quantum field theory in non-inertial settings, gravitational quantum sensing, and future experiments involving quantum systems operating across different gravitational potentials or accelerated trajectories. The resulting perspective indicates that quantum coherence remains meaningful in relativistic physics only when the observer, field decomposition, measurement procedure, and spacetime geometry are specified consistently.
The theories of special relativity and quantum mechanics both rely on continuous rotation groups to describe physical systems, yet one is formulated on a real spacetime manifold while the other employs a complex Hilbert space. This work investigates whether this distinction may arise from the treatment of time itself. By examining the consequences of describing a relativistic system using a single global time parameter, we explore whether such a description naturally requires a mathematical structure capable of encoding observer-dependent proper times as complex phase information. Within this framework, quantum superposition is investigated as a possible coordinate-level representation of unresolved relativistic frame assignments, while wavefunction collapse is conceptualised as the physical resolution of this ambiguity through interaction. exploring whether aspects of the quantum formalism may be understood as consequences of describing the invariant structure of Minkowski spacetime from a local perspective using a rigid notion of time.
Abstract Quantum coherence is a basis-dependent resource whose operational meaning becomes particularly subtle when quantum fields are observed from non-inertial reference frames or propagate through curved spacetime. In relativistic settings, the distinction between particles, modes, and accessible subsystems depends on the observer, while gravitational or accelerated horizons can restrict portions of the field from direct measurement. These effects imply that coherence assigned to one set of field modes need not coincide with that reconstructed by another observer. The problem becomes more intricate under non-stationary relativistic conditions, where acceleration, spacetime geometry, or mode structure changes with time and no single global decomposition into positive- and negative-frequency components remains universally preferred. This study develops a conceptual framework for analysing observer-dependent quantum coherence in such environments. The discussion combines quantum field theory in curved spacetime, the Unruh and Hawking effects, relativistic quantum information, and the resource-theoretic description of quantum coherence. Curved-spacetime field theory establishes that the concept of a particle is not generally observer independent [1]. Algebraic and geometric formulations further demonstrate that physically meaningful observables can remain well defined even when global particle interpretations become ambiguous [2]. Resource theory provides a complementary language for distinguishing coherence intrinsic to a chosen state representation from changes caused by observer-dependent mode decomposition [7]. Particular attention is given to accelerated observers, horizons, Bogoliubov mode mixing, time-dependent acceleration, dynamically changing accessibility of field sectors, and the distinction between genuine decoherence and redistribution of coherence into inaccessible degrees of freedom. Non-stationary relativistic motion is treated as a dynamical source of basis change rather than merely a perturbation of a stationary accelerated frame.
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.
Abstract In general relativity, the dynamics of objects is governed by the curvature of spacetime, which is caused by the presence of matter and energy. In contrast, in quantum mechanics, the dynamics is governed by the wavefunction, which completely describes the behavior of the particles. There is an ongoing effort to explore analogs of space and spacetime curvature in the context of quantum mechanics. Such analogies may reveal a deeper structure of quantum reality and its possible relations with Einstein’s theory of gravity. In this note, by coupling the non-relativistic Schrödinger equation with the heat equation and using the hydrodynamical formulation of quantum mechanics, we find that the dynamics of the particle is fully characterized by the normalized curvature of the wavefunction’s amplitude. Such a curvature obtains an analogy to the Ricci curvature of curved space in a Riemannian manifold. The proposed geometric correspondence provides a new pathway to explore quantum dynamics through the lens of differential geometry, the language of general relativity.
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of their commutation relations including the energy-time relation. These commutators also describe the relativistic shifts undergone under frame transformations, not only for inertial frames but also for uniformly accelerated frames. The quantum redshift laws differ from their classical counterparts while still obeying universal metric properties. The paper presents this approach in terms closely connected to the seminal Einstein conception of localisation in space-time and refers to already published papers for more technical developments.