We propose a physical redefinition of reference frames as finite, interaction-defined spacetimedomains sustained by coherence in an active vacuum. Unlike General Relativity, where frames aremathematical and local, frames in the present framework possess finite spatial extent and temporalduration determined by interaction reach and vacuum polarization. We show that the Heisenberguncertainty relations arise naturally as structural constraints on the existence of such frames, ratherthan as independent quantum postulates. A covariant spacetime uncertainty relation is derived,unifying spatial–momentum and time–energy uncertainties. Exact inertial frames and perfectlylocalized states are shown to be physically forbidden. The framework provides a consistent bridgebetween relativity, quantum mechanics, and vacuum physics, and extends earlier vacuum-basedapproaches to quantization and gravitation.
We propose a physical redefinition of reference frames as finite, interaction-defined spacetimedomains sustained by coherence in an active vacuum. Unlike General Relativity, where frames aremathematical and local, frames in the present framework possess finite spatial extent and temporalduration determined by interaction reach and vacuum polarization. We show that the Heisenberguncertainty relations arise naturally as structural constraints on the existence of such frames, ratherthan as independent quantum postulates. A covariant spacetime uncertainty relation is derived,unifying spatial–momentum and time–energy uncertainties. Exact inertial frames and perfectlylocalized states are shown to be physically forbidden. The framework provides a consistent bridgebetween relativity, quantum mechanics, and vacuum physics, and extends earlier vacuum-basedapproaches to quantization and gravitation.
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities, this perspective naturally leads to the concept of quantum reference frames (QRFs). We investigate the perspective-dependence of position and momentum uncertainties, correlations, covariance matrices, and entanglement within the QRF formalism. We show that the Robertson-Schrödinger uncertainty relations are frame-dependent, and so are correlations and variances, which satisfy various constraints described as inequalities. However, the determinant of the total covariance matrix, linked to the uncertainty volume in phase space, as well as variance-based entanglement criteria, remains invariant under changes of reference frame. Under specific conditions, the purities of subsystems are also invariant for different QRFs, but in general, they are perspective-dependent. These invariants suggest fundamental, robust measures of uncertainty and entanglement that persist despite changes in observational perspective, potentially inspiring dedicated quantum information protocols as well as further foundational studies.
Abstract Fundamental discrepancies exist among the foundational postulates of classical mechanics, relativity and quantum mechanics, leaving long-standing open physical puzzles including the origin of the arrow of time, quantum measurement collapse and the nature of spacetime. This paper proposes a self-consistent unified physical paradigm: the physical essence of a reference frame is the selective filtering of the full degrees of freedom of a system. All classical, relativistic and quantum physical theories constitute effective reduced descriptions of degrees of freedom under specific rules imposed by reference frames. Core phenomena such as temporal irreversibility, wave-function collapse, the constancy of the speed of light and the quantum-classical transition are not fundamental ontological properties of the universe, but emergent effects arising from filtering mappings introduced by finite-bandwidth observers. This work establishes an axiomatic framework for reference frames and degree-of-freedom filtering, defining projection filtering mappings, the principle of vanishing relative degrees of freedom, and the dimensionless filtering ratio. Within this framework, we reconstruct classical mechanics, special and general relativity, quantum decoherence and quantum measurement theory. Three categories of irreversible mechanisms — statistical coarse-graining, environmental partial-trace decoherence and time-domain sampling truncation — are integrated into a single mathematical structure. A universal dimensionless filtering ratio is defined. We clarify that the continuity of the control parameter does not imply that observables must evolve smoothly. Conceptually, the system can exhibit three regimes: quantum superposition, intermediate transition and classical state. Experiments on quantum bits at the Weizmann Institute provide preliminary observational hints, yet further verification is required; no specific form of the response curve is assumed in this paper. Three falsifiable quantitative predictions are put forward, involving attosecond spectroscopy, decoherence of superconducting qubits and cold-atom interferometry. We compare the present paradigm with relational quantum mechanics, QBism and consistent histories, discuss the ontological implications of time, observers and irreversibility, and outline extensions towards quantum gravity and cognitive science.
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.
The quest to reconcile quantum mechanics with gravitational theory motivates the exploration of frameworks that treat quantum uncertainty and spacetime geometry under a unified approach. A promising candidate that emerges from this pursuit is the relativistic quantum phase space (QPS) formalism, which extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, providing a unified setting where the uncertainty principle and relativistic covariance coexist. For the signature (1,4), we construct a scalar from the mean values and the inverse variance-covariance matrix and prove its invariance under linear canonical transformations (LCTs). Motivated by the form of the variance-covariance matrix in a particular reference frame, we identify this invariant as Γ=L2/ℓ2 for states that saturate the uncertainty relations, where L and ℓ are two fundamental length scales that can be identified with the de Sitter radius and the Planck length, respectively. From this invariant, we obtain a geometric equation that unifies mean values and quantum fluctuations. In the limit ℓ→0, the equation reduces to the de Sitter spacetime equation; in the limit L→∞, it yields a curved momentum space reminiscent of Born reciprocity. In the Minkowski limit (both ℓ→0 and L→∞), the familiar relativistic relations for rest mass and proper time emerge. These limiting cases show how the Planck length and the cosmological constant can be unified within a single geometric constraint, establishing the QPS geometry as a promising framework for exploring the interplay between quantum mechanics and gravity.
We present a unified theoretical framework in which both General Relativity (GR) and quantum dynamics emerge from first principles associated with a structured, phase‑coherent vacuum. Rather than quantizing spacetime geometry or postulating intrinsic randomness, the vacuum is modeled as a deterministic continuum endowed with conserved density and phase degrees of freedom. General Relativity arises uniquely from general covariance and conservation laws, while relativistic and nonrelativistic quantum equations emerge as reduced descriptions of vacuum phase dynamics under symmetry breaking and coarse‑graining. Probability is shown to be epistemic, originating from incomplete access to vacuum phase information rather than fundamental indeterminism. The framework reproduces Einstein’s field equations, the Newtonian limit, and the Schrödinger equation, while providing a consistent pathway toward relativistic quantum dynamics and testable deviations in strong‑field regimes.
The Theory of Temporal Relativity proposes a unified theoretical framework that extends Special and General Relativity into the complex domain, integrating aspects of Quantum Mechanics within a single geometrical structure. The theory introduces a generalized Hilbert-space geometry and interprets quantum states as observer-dependent, arising from complex temporal relations between reference frames. Theory of Temporal Relativity is a theoretical framework proposing a unified extension of Special and General Relativity into the complex domain, with the goal of incorporating aspects of Quantum Mechanics within a consistent geometrical model. The theory generalizes Hilbert-space geometry and relativistic invariance to complex coordinates, introducing observer-dependent descriptions of physical quantities and a reinterpretation of quantum states as complex-phase relations between reference frames. Within this model, fundamental constants such as c, G, and h are not strictly universal but can exhibit apparent local variations arising from the observer’s position in the complex spacetime manifold. These variations preserve global covariance and CPT symmetry while reconciling quantum non-locality with relativistic kinematics. The framework predicts experimentally testable effects, including measurable phase shifts in interferometric experiments, possible frequency modulations in non-inertial systems, and small local deviations of physical constants detectable in condensed-matter and gravitational contexts. The supplementary work, “Quantum Uncertainty, Planck’s Constant, and Ontological Insights from Complex Spacetime Geometry and Local Metric Deformations”, develops the principle of Temporal Relativity as a foundational element of the theory. It formalizes the connection between quantum uncertainty, metric deformations, and complex temporal structures, within an alternative logical framework (AU). This extension provides both an ontological interpretation of the wavefunction and a basis for the emergence of quantum indeterminacy from geometric causes. Together, these works present a coherent attempt to unify the relativistic and quantum domains under a single complex-geometric view of spacetime, maintaining mathematical rigor while providing clear experimental pathways for empirical validation.