Principle of ``Superrelativity'' has been proposed in order to avoid the contradiction between principle of relativity and foundations of quantum theory. Solutions of a newly derived non-linear Klein-Gordon equation presumably may be treated as primordial nonlocal elements of quantum theory. It is shown that in the framework of CP(N-1) model supplementary elements which are non-local in spacetime but local in the projective Hilbert space permit us to avoid at least one of the main difficulties of quantum theory-the necessity to relate the ``reality'' of a quantum state with a measuring process. In the framework of superrelativity the geometry of the projective Hilbert space (Fubini-Study metric and connection) together with the non-linear wave equation are full and closed quantum scheme.
Principle of Superrelativity'' has been proposed in order to avoid the contradiction between principle of relativity and foundations of quantum theory. Solutions of a newly derived non-linear Klein-Gordon equation presumably may be treated as primordial nonlocal elements of quantum theory. It is shown that in the framework of CP(N-1) model supplementary elements which are non-local in spacetime but local in the projective Hilbert space permit us to avoid at least one of the main difficulties of quantum theory-the necessity to relate the reality'' of a quantum state with a measuring process. In the framework of superrelativity the geometry of the projective Hilbert space (Fubini-Study metric and connection) together with the non-linear wave equation are full and closed quantum scheme.
In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories in the sense that the affine connection of this theory is constructed from first derivatives of the Fubini-Study metric tensor in the projective Hilbert space of the pure quantum states CP(N). That is we have not merely analogy with general relativity but this construction should presumably provide a unification of general relativity and quantum theory.
A new type of gauge quantum theory (superrelativity) has been proposed. This differs from ordinary gauge theories in sense that the affine connection of our theory is constructed from first derivatives of the Fubini-Study metric tensor. That is we have not merely analogy with general relativity but this construction should presumably provide a unification of general relativity and quantum theory. Here we shall discuss the physical meaning of metric properties of the projective Hilbert space and manifestation of its nontrivial physical character.
We develop a comprehensive axiomatic framework for quantum-inspired distance metrics on projective Hilbert spaces, providing a unified foundation that organizes and generalizes existing measures in quantum information theory. Starting from five fundamental axioms, projective invariance, unitary covariance, superposition sensitivity, entanglement awareness, and measurement contextuality, we show that any admissible distance depends solely on state overlap and establish the uniqueness of the Fubini-Study metric as the canonical geodesic distance. Our framework further yields a hierarchy of comparison results relating the Fubini-Study metric, Bures distance, Euclidean distance, measurement-based pseudometrics, and entanglement-sensitive distances. Key contributions include an entanglement-geometry complementarity principle, high-dimensional concentration bounds, and operational interpretations connecting distances to state discrimination and quantum metrology. This work places the geometry of quantum state spaces on a rigorous axiomatic footing, bridging abstract metric theory, information geometry, and operational quantum principles.
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection rule. In order to avoid the subjective nuance, I emphasis that the notion of "measurement" here, is nothing but the covariant differentiation procedure in the functional quantum phase space CP(N−1), having pure objective sense of evolution. Transition to the local moving quantum reference frame leads to some particle-like solutions of quasi-linear field PDE in the dynamical space-time. Thereby, the functionally covariant quantum dynamics gives the perspective to unify the Einstein relativity and quantum principles which are obviously contradictable under the standard approaches.
The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space ←→ time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (‘framespaces’), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck’s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck’s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.
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.