Standard quantum mechanics suffers from unresolved measurement problem and preferred basis problem. Furthermore, there exists a fundamental incompatibility between the quantum formalism constructed on Hilbert spaces and general relativity formulated on four-dimensional spacetime manifolds. In this paper we propose a new quantum interpretation: Global Hilbert-space Boundary-selected Projection Interpretation (GHS-BSI). We postulate that the only fundamental physical reality is the global Hilbert space of a closed universe and its universal quantum state , which satisfies the Wheeler–DeWitt equation and undergoes exclusive unitary evolution, with no physical wavefunction collapse. Four-dimensional Lorentzian spacetime, together with all material fields and interactions, emerges as the orthogonal spectral projection of the universal quantum state onto closed linear subspaces of the global Hilbert space. Spacetime boundary itself is a product of quantum projection, acting as an intrinsic constraint operator to filter quantum subspaces: only quantum branches that can form causally consistent four-dimensional spacetime become observable physical reality, and no parallel worlds exist. We complete the topological mathematical refinement of the boundary selection operator, strictly derive Einstein’s field equations from the distribution of projection weights, resolve the preferred basis problem common to all projection-based interpretations, and revise a series of observable predictions to prioritize prominent signatures detectable with existing datasets. Without introducing extra dimensions or hidden variables, GHS-BSI naturally unifies quantum correlations and relativistic spacetime geometry. It remains empirically consistent with the core conclusions of orthodox quantum mechanics and general relativity, while providing a unified ontological foundation and falsifiable observational predictions for both fundamental theories. Keywords: quantum foundations; measurement problem; global Hilbert space; spectral projection; boundary selection; spacetime emergence; unification of quantum mechanics and relativity; observable predictions
Standard quantum mechanics suffers from unresolved measurement problem and preferred basis problem. Furthermore, there exists a fundamental incompatibility between the quantum formalism constructed on Hilbert spaces and general relativity formulated on four-dimensional spacetime manifolds. In this paper we propose a new quantum interpretation: Global Hilbert-space Boundary-selected Projection Interpretation (GHS-BSI). We postulate that the only fundamental physical reality is the global Hilbert space of a closed universe and its universal quantum state , which satisfies the Wheeler–DeWitt equation and undergoes exclusive unitary evolution, with no physical wavefunction collapse. Four-dimensional Lorentzian spacetime, together with all material fields and interactions, emerges as the orthogonal spectral projection of the universal quantum state onto closed linear subspaces of the global Hilbert space. Spacetime boundary itself is a product of quantum projection, acting as an intrinsic constraint operator to filter quantum subspaces: only quantum branches that can form causally consistent four-dimensional spacetime become observable physical reality, and no parallel worlds exist. We complete the topological mathematical refinement of the boundary selection operator, strictly derive Einstein’s field equations from the distribution of projection weights, resolve the preferred basis problem common to all projection-based interpretations, and revise a series of observable predictions to prioritize prominent signatures detectable with existing datasets. Without introducing extra dimensions or hidden variables, GHS-BSI naturally unifies quantum correlations and relativistic spacetime geometry. It remains empirically consistent with the core conclusions of orthodox quantum mechanics and general relativity, while providing a unified ontological foundation and falsifiable observational predictions for both fundamental theories. Keywords: quantum foundations; measurement problem; global Hilbert space; spectral projection; boundary selection; spacetime emergence; unification of quantum mechanics and relativity; observable predictions
Fundamental physical laws are unitary and reversible, yet observed physical phenomena exhibit irreversibility, thermality, entropy increase, and horizon radiation. Reconciling this apparent contradiction remains a central problem in modern theoretical physics. This work introduces a unified geometric framework, termed selection geometry, in which irreversibility emerges naturally from non-invertible selection acting on projective Hilbert space. We show that physical states are naturally represented as points in projective Hilbert space, whose compactified structure introduces a geometric point at infinity analogous to conformal boundaries in spacetime and the Riemann sphere. Selection mapping acts as a non-invertible projection, compressing spectral degrees of freedom and producing a realized state manifold that is spectrally non-closed. This spectral non-closure provides a geometric origin for thermality, entropy increase, and Hawking radiation. Thermality emerges from circular Euclidean time geometry and the KMS condition, while horizon radiation arises from horizon-induced spectral selection. Event horizons act as selection surfaces that restrict accessible spectral degrees of freedom while preserving global spectral completeness. Within this framework, global spectral evolution remains unitary and reversible, while realized evolution becomes irreversible due to geometric quotient structure induced by selection. This dual structure resolves the black hole information paradox by distinguishing global spectral completeness from realized spectral accessibility. Selection mapping is physically realized as completely positive trace-preserving (CPTP) evolution on density operators. Irreversibility therefore emerges not from dynamical law violation, but from geometric structure. This work establishes selection geometry as a foundational geometric principle underlying quantum mechanics, thermodynamics, and gravitational physics.
Conventional relativity places four-dimensional spacetime connected by Lorentz transformations, and fourdimensional spacetime curved by gravity, at the foundation of physical spacetime, whereas quantum mechanics places Hilbert space at the foundation of state description. As long as these two structures are simultaneously treated as fundamental realities, relativistic quantum theory and quantum gravity must begin with the problem of how a dynamically curved spacetime is to be quantized and made consistent with Hilbert-space states. Nakaza New Relativity Theory (NNRT) changes this very point of departure. NNRT takes universal time and universal three-dimensional space as physical spacetime and connects the real motions of all inertial systems by the Galilean Transformation (GT), while relocating the Lorentz transformation, time dilation, length contraction, and the gravitational metric to the observational and measurement layer obtained through electromagnetic phase. The successful mathematics and experimental values of conventional relativity are therefore retained, but the ontology in which curved and deformable four-dimensional spacetime is the unique physical spacetime is not retained. This paper uses NNRT as a new entry into quantum mechanics and repositions Hilbert space not as physical space, but as a mathematical representation space that preserves states, phases, probabilities, and correlations. Using the atomic clock as a concrete example, the paper further presents a continuous observational chain in which quantum levels generate a frequency scale and the resulting phase signal is compared between systems through relative motion and gravitational fields. Accordingly, the conventional entry point—how to quantize a physically real curved four-dimensional spacetime and incorporate it into Hilbert space—loses its premise within NNRT, and quantum theory and relativity are reconstructed as distinct representational and observational structures arising from a common universal physical spacetime. Schrödinger’s cat, EPR/Bell correlations, time dilation, length contraction, the twin problem, and the reification of the gravitational metric can then be organized as manifestations of a common ontological operation: identifying a mathematical representation with physical reality itself. The significance of this paper is therefore not to add another interpretation alongside conventional relativity, but to absorb its successful mathematics into the observational layer of NNRT and, by turning the ontological point of departure, to provide a new formulation of foundational problems that includes quantum mechanics.
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. The term unification is used in a structural sense, referring to compatibility of quantum dynamics with classical field theory rather than a modification of general relativity. 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 unitary orbits. Equivalently, all scalar temporal components of physical states arise as boundary values of functions analytic in the lower half of the complex time plane, selecting the Hardy space—or, more generally, analytic tempered distributions—as the admissible solution space. In these spaces, 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 Schr\"odinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. We further show that quantum spectral discreteness arises from operator-theoretic confinement and boundary conditions on a smooth spacetime manifold, and does not imply any fundamental discreteness of spacetime. The resulting framework provides a real-field 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.
This paper presents a novel theoretical framework that aims to unify the core principles of quantum mechanics, general relativity, and thermodynamics by introducing an extended spatial geometry incorporating a compactified fourth spatial dimension. The theory proposes that many of the counterintuitive behaviours observed in quantum systems, such as wave function collapse, superposition, entanglement, tunnelling, and decoherence, can be naturally explained as consequences of 4D quantum objects being projected into 3D space. In this framework, observable quantum behaviour emerges not from intrinsic randomness but from the limitations of a lower-dimensional perspective on higher-dimensional structures. At the heart of this unification is the introduction of a new scalar field, termed the entropion field, which governs the rate and nature of quantum decoherence while simultaneously encoding the thermodynamic arrow of time. The entropion field interacts with known quantum fields and gravitational curvature, modifying the Einstein field equations and extending the standard model of quantum field theory. The result is a coherent description of how classical reality emerges from quantum substrates, how entropy and time are fundamentally linked, and how spacetime geometry influences quantum behaviour. The paper develops this hypothesis through a structured hierarchy of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular attention is given to testable deviations from standard models, including quantum interference in 4D-projected systems, entropion-driven decoherence rates, and new interpretations of tunnelling and entanglement. Broader implications are explored in quantum information, cosmological evolution, material science, and theoretical computation. This work serves as a foundational step toward a geometrically grounded theory of everything and offers a unified path forward by bridging the three major pillars of modern physics.
This paper develops a theoretical framework that seeks to unify the foundational principles of quantum mechanics, general relativity, and thermodynamics by extending spatial geometry to include a compactified fourth spatial dimension. The central proposal is that many counterintuitive features of quantum systems—such as wave function collapse, superposition, entanglement, tunneling, and decoherence—emerge as phenomena from the projection of four-dimensional quantum states into observable three-dimensional space. Within this formulation, apparent quantum randomness is reinterpreted as a consequence of observing only a lower-dimensional slice of a higher-dimensional structure. A key innovation of the framework is the introduction of a scalar degree of freedom, termed the entropion field, which governs decoherence and encodes the thermodynamic arrow of time. The entropion field couples directly to both quantum fields and spacetime curvature, leading to modified Einstein field equations and an entropic extension of quantum field dynamics. This mechanism provides a consistent account of classicality emerging from quantum substrates, links entropy growth to projection dynamics, and clarifies how spacetime geometry constrains quantum evolution. The theory is presented through a structured progression of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular emphasis is placed on testable deviations from standard theories, including altered interference signatures in 4D-projected systems, entropion-modulated decoherence rates, and revised mechanisms of tunneling and entanglement. Broader implications are explored for quantum information theory, cosmology, condensed matter, and computational theory. Collectively, these results establish a geometrically grounded unification scheme that integrates the three major pillars of modern physics into a consistent and falsifiable framework.
Physics and philosophy converge at the deepest levels of inquiry. GHS-BST, as a theoretical framework with "information as the first principle" at its core, inevitably touches upon the central questions of philosophy. This paper systematically expounds the philosophical implications of GHS-BST at five levels: Ontology: The world is informational structure rather than matter. ℋglobal is eternal and indecomposable (center-trivial Type III factor). Matter is the projected manifestation of informational structures through boundary screening. Matter is not primary; information is. Epistemology: Observers participate in the construction of reality. Observers define "what is observable" through the boundary. Boundary screening is not passive reception but active construction. Without observers, there is no boundary; without boundary, there is no projection; without projection, there is no reality. Philosophy of Time: Frame rate is time. Time is not a background container but the frequency of boundary refreshment. The past is frames already played; the future is frames yet to be generated; the present is the current frame. When the boundary ceases to refresh, time ceases to exist. Philosophy of Consciousness: Consciousness is the self-projection cycle of informational structures. Consciousness is not an additional entity, not a "soul" or "ghost," but the self-referential capacity generated by informational structures in sustained projection. It corresponds mathematically to a topological fixed point on the boundary manifold (a self-referential loop with Euler characteristic χ(Γ)=1). The Problem of Meaning: Meaning is not externally bestowed but is projected in sufficient frames with sufficient richness. The purpose of life is "to project oneself in frames"—to maximize the richness and complexity of projection within a finite number of frames. This paper also discusses derivative issues including free will, death, and ethics, demonstrating that GHS-BST provides a unified framework from physics to ethics: free will is the capacity of informational structures to select projection paths in boundary screening; death is de-projection—information remains in ℋglobal but no longer appears in the current frame; ethics is the practice of mutual recognition and respect among projected structures. Keywords: Information Ontology; Epistemology; Philosophy of Time; Philosophy of Consciousness; Self-Projection Cycle; Problem of Meaning; Free Will; Ethics PACS: 01.70.+w (Philosophy of Science); 03.65.-w (Foundations of Quantum Mechanics); 89.70.-a (Information Theory)