We introduce physical phase invariance as a minimal, observer-independent principle capable of unifying quantum theory and relativity. By identifying the physical phase with the classical action measured in units of Planck’s constant, the framework assigns phase a direct operational meaning. Spacetime structure, Lorentz invariance, and quantum probabilistic behavior emerge as effective descriptions of underlying phase dynamics rather than fundamental postulates. Time is defined relationally through phase evolution, and classical motion arises from stationary phase conditions. A simple dynamical equation for the phase field is proposed, while quantum probabilities are shown to result from statistical coarse-graining over unresolved phase degrees of freedom. This approach provides a coherent conceptual foundation linking quantum mechanics, special relativity, and gravitation.
We introduce physical phase invariance as a minimal, observer-independent principle capable of unifying quantum theory and relativity. By identifying the physical phase with the classical action measured in units of Planck’s constant, the framework assigns phase a direct operational meaning. Spacetime structure, Lorentz invariance, and quantum probabilistic behavior emerge as effective descriptions of underlying phase dynamics rather than fundamental postulates. Time is defined relationally through phase evolution, and classical motion arises from stationary phase conditions. A simple dynamical equation for the phase field is proposed, while quantum probabilities are shown to result from statistical coarse-graining over unresolved phase degrees of freedom. This approach provides a coherent conceptual foundation linking quantum mechanics, special relativity, and gravitation.
We propose that the unobservability of absolute scale constitutes a foundational principle of physics. Starting from the requirement that physical predictions must be invariant under rescalings of the action, we show that only phase-based quantities remain well defined. This requirement uniquely selects a complex amplitude description, leading directly to the structure of quantum mechanics, including linear superposition, Hilbert space, and the Born rule. Within this framework, the classical notion of action loses absolute meaning, and physical observables arise from invariant phase relations. Quantum mechanics is therefore not postulated, but emerges as the minimal consistent description of systems in which scale cannot be directly observed. The formal structure of quantum theory is shown to follow from this principle without additional axioms. We further demonstrate that the same principle implies the existence of a dynamical scale field, which governs the effective quantum scale and connects naturally to cosmological models with a time- dependent Planck mass. In this way, the structure of quantum mechanics and the large-scale dynamics of the Universe are linked through a common origin. This framework provides a unified perspective in which quantum behavior and cosmological evolution arise from a single underlying principle, suggesting a new approach to the relationship between fundamental physics and cosmology.
Physical theory remains fragmented across classical, quantum, thermodynamic, and gravitational regimes despite deep mathematical overlap. This work proposes phase coherenceas a primitive organizing principle governing physical evolution. By formalizing dynamics as extremization of a global coherence functional over admissible phase states, classicalequations of motion, unitary quantum evolution, thermodynamic irreversibility, quantumnonlocal correlations, and probabilistic structure emerge without independent postulation.Gravitation is reinterpreted as curvature of a coherence metric rather than a fundamentalforce. The framework is explicitly falsifiable and forbids objective wavefunction collapse,fundamental time asymmetry, and point-like graviton degrees of freedom.
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 persistent challenge of unifying quantum mechanics with general relativity is often traced to a series of apparent structural tensions: complex versus real ontology, probabilistic versus deterministic dynamics, linear versus nonlinear evolution, and spectral discreteness versus geometric continuity. We argue that these tensions do not signal a fundamental incompatibility between the theories, but rather originate from surplus structure in the conventional formulation of quantum mechanics. Beginning from the physically indispensable requirement of matter stability, we prove that the Hamiltonian spectrum can always be shifted to become non-negative. The consequent positivity of energy enforces one-sided temporal frequency support for all physical states, selecting the Hardy space of analytic signals as the admissible solution space. In this space, the real and imaginary parts of the wave function are not independent; they are linked uniquely via the temporal Hilbert transform. Hence, the complex structure of quantum mechanics emerges as a representational artifact of an underlying real operator algebra. Building on our earlier work on Unified Quantum Mechanics and the Unified Real Wave Equation, we establish a rigorous proof of exact equivalence between the real-field evolution and the Schrödinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. The resulting framework provides a realfield formulation of quantum mechanics and gravitation, with stability and causality implemented as foundational principles, and demonstrates that the Einstein field equations are compatible with a unified field-theoretic description of spacetime and matter. Extending the same analyticity principle to spacetime geometry, we propose an analytic formulation of the Einstein field equations, from which classical general relativity is recovered exactly as the real projection.
The principle of action plays a central role in both classical and quantum mechanics, yet its physical meaning is often introduced in a purely formal manner. In this work, the concept of action is examined from a scale-based perspective that clarifies its role in the quantum–classical correspondence. By emphasizing the dimensionless ratio S/ℏ, we show that the emergence of classical dynamics can be understood as a consequence of quantum phase coherence rather than as an independent postulate. Within the path integral formulation, classical trajectories arise naturally from stationary-phase conditions when the action associated with a physical process becomes large compared to Planck’s constant. This interpretation provides a unified conceptual framework in which variational principles, quantum interference, and classical determinism are linked through the scale of action. The analysis highlights the role of Planck’s constant as a universal parameter governing the physical relevance of alternative histories, analogous to the function of Boltzmann’s constant in statistical physics. Beyond its theoretical implications, the proposed perspective offers pedagogical value by providing a coherent bridge between classical and quantum mechanics suitable for advanced undergraduate and early graduate physics education.
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.