This working paper proposes a speculative ontological framework in which selected quantumphenomena are interpreted as three-dimensional manifestations of higher-dimensional spatialstructures. The central hypothesis is that fundamental particles are not complete objectsconfined to accessible three-dimensional space, but higher-dimensional structures whose observableproperties correspond to constrained projections, slices, or manifestations within a coherentthree-dimensional layer. In this framework, time is not treated as a spatial dimension. Instead,time is defined as the computational ordering of state transitions. Measurement is interpretedas a physical interaction that constrains higher-dimensional possibility into a definite three-dimensional outcome. The double-slit experiment is used as a guiding example: superposition isinterpreted as multiple compatible three-dimensional manifestations of one higher-dimensionalentity, while which-path detection corresponds to a constraint that eliminates interference byforcing one stable observable manifestation. The framework does not replace standard quantummechanics. Rather, it proposes an ontological interpretation of why quantum formalism maybe required for observers whose access is restricted to a three-dimensional domain. Major openproblems include deriving the Born rule, reproducing the full formalism of quantum mechanicsand quantum field theory, explaining relativistic effects under computational time, and generatingtestable predictions.
This working paper proposes a speculative ontological framework in which selected quantumphenomena are interpreted as three-dimensional manifestations of higher-dimensional spatialstructures. The central hypothesis is that fundamental particles are not complete objectsconfined to accessible three-dimensional space, but higher-dimensional structures whose observableproperties correspond to constrained projections, slices, or manifestations within a coherentthree-dimensional layer. In this framework, time is not treated as a spatial dimension. Instead,time is defined as the computational ordering of state transitions. Measurement is interpretedas a physical interaction that constrains higher-dimensional possibility into a definite three-dimensional outcome. The double-slit experiment is used as a guiding example: superposition isinterpreted as multiple compatible three-dimensional manifestations of one higher-dimensionalentity, while which-path detection corresponds to a constraint that eliminates interference byforcing one stable observable manifestation. The framework does not replace standard quantummechanics. Rather, it proposes an ontological interpretation of why quantum formalism maybe required for observers whose access is restricted to a three-dimensional domain. Major openproblems include deriving the Born rule, reproducing the full formalism of quantum mechanicsand quantum field theory, explaining relativistic effects under computational time, and generatingtestable predictions.
Understanding whether the mathematical structure of quantum mechanics is fundamental or emergent remains a central question in the foundations of physics. In particular, the special role played by time in quantum theory, appearing as an external evolution parameter rather than a dynamical observable, suggests that the formalism itself may arise from deeper structural considerations. In this work, we investigate the emergence of quantum mechanical formalism from classical wave dynamics by adopting a dimensional framework in which time is treated as a +1 evolution parameter relative to the dimensions through which physical phenomena (fields or disturbances of a field) propagate and interact. Within this perspective, different fields may evolve with respect to different effective dimensions, while remaining embedded in a common higher-dimensional space, allowing time to acquire a relational and context-dependent role. This means that in our proposed model, time is not a fixed dimension which is experienced the same way for every field or field interaction of any dimensionality. In that sense, time for one physical phenomenon can behave as space for a higher dimensional physical phenomenon, whose time is a different +1 dimension. The central objective of this paper is to determine how a higher-dimensional deterministic field can be consistently represented by a lower-dimensional description that lacks direct access to its full set of evolution parameters and evolves through a spatial (for the higher-dimensional field) dimension. To this end, we introduce a general projection framework in which a higher-dimensional field is mapped to a reduced field through an interaction-based recording process. Crucially, we do not assume the form of this mapping a priori. Instead, we impose the requirement that it preserve the maximum amount of physically accessible information. In particular, we demand the faithful encoding of phase relations, interference structure, and spectral composition, including the relative contributions of different Fourier modes and their superposition. We first demonstrate, within a purely classical 3+1-dimensional wave framework that these constraints severely restrict the admissible form of the reduced description and naturally lead to complex amplitudes, linear superposition, Hilbert space structure, and canonical operator relations. This analysis provides an intuitive and mathematically explicit route to quantum-like descriptions without assuming quantum postulates. We then generalize the construction to a 4+1-dimensional framework, introducing an additional evolution parameter and showing that under the same information-preserving constraints, the Schrödinger equation appears as an effective low-energy description of the reduced dynamics, while a relativistic dispersion relation emerges simultaneously through the encoding of the hidden evolution parameter as an invariant frequency scale. In this way, both quantum mechanical and relativistic structures arise from the same underlying requirement: the consistent and information-preserving representation of higher-dimensional wave propagation in a lower-dimensional observational framework. The results suggest that the formal structure of quantum mechanics need not be postulated a priori, but may instead be understood as the unique mathematical language required to encode the observable remnant of a higher-dimensional deterministic dynamics under strict constraints of symmetry, invariance, and information preservation.
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.
Abstract Quantum mechanics and relativity are extraordinarily successful mathematical theories, yet their conventional physical interpretations rely on substantially different conceptual frameworks. The Theory of Space (TS) proposes a fourth dimension defined by the Planck-related interval, with interpreted as a longitudinal dimension associated with energy (cτ), rather than as the conventional Minkowski spacetime interval. This fourth dimension does not coexist continuously with the observable three spatial dimensions as a conventional four-dimensional manifold. Instead, TS proposes an oscillatory existence between observable 3D presence and a non-observable fourth-dimensional phase. Through this oscillation, the quantum system undergoes repeated dimensional projection into observable 3D, with individual eigenstates manifested probabilistically while the underlying quantum state continues to evolve. Within this framework, phenomena including measurement, the Born rule, the arrow of time, entropy, entanglement, tunneling, and Bell-type correlations acquire a common physical interpretation. Heisenberg uncertainty and non-commutativity are interpreted as consequences of physical parameters associated with different phases of the dimensional oscillation and therefore not simultaneously manifested within the same 3D instance. TS further distinguishes between the quantum system’s spatial component and its compact physical entity. Their coexistence within the complete system provides a proposed physical basis for quantum interference and phase-dependent phenomena, including the double-slit experiment and the path-integral description of quantum evolution. As an extension of the model, TS proposes that the periodic displacement and replacement of quantum space generate a pulsed inward spatial flow. This mechanism provides a possible basis for a quantized gravitational interaction and suggests that gravitational energy may be represented by a positive contribution. Related developments, including spiral spatial flows, follow naturally from the same dimensional-oscillation mechanism. The Theory of Space therefore seeks to provide a common conceptual framework for quantum, relativistic, and gravitational phenomena without replacing the established mathematical equations that successfully reproduce experimental observations. The present work develops this framework and invites critical examination of its assumptions, physical implications, and potential experimental consequences. Keywords: relativity; Lorentz transformation; quantum superposition; quantum superposition; collapse; entanglement; quantum gravity
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 presents the Dimensional Ontological Triad Law, a recursive structural law governing transitions across dimensions: n-dimensional change = (n+1)-dimensional entity = (n+2)-dimensional adjective. Through pure logical reasoning and thought experiments, 22 original discoveries were made, including a unified explanation of 8 major quantum mechanical anomalies (superposition, entanglement, tunneling, measurement problem, wave function collapse, double-slit experiment, observer effect, and decoherence) under a single dimensional-projection principle. The framework identifies two types of projections — free-axis projection and constraint-axis projection — that systematically account for all known quantum phenomena as shadows of four-dimensional reality perceived from three-dimensional perspective. This research was conducted in collaboration with Claude (Anthropic) as AI Exploration Partner. Both English and Japanese versions of the paper are included. Note on Dimensional Definitions: In this framework, dimensional definitions are intentionally shifted by one level from conventional academic usage. For example, what is traditionally called the "fourth dimension (time)" is treated here as the third-dimensional being's projective name for the fourth axis. This shift is a deliberate methodological choice to avoid conceptual constraints imposed by lower-dimensional terminology when describing higher-dimensional structures. Call for Collaboration: The author welcomes collaboration from researchers in quantum foundations, philosophy of science, and mathematical physics — particularly for mathematical formalization of the framework and experimental prediction derivation. Contact: ikoma.yuudai@gmail.comCompanion paper: DOI 10.5281/zenodo.18523074
The formal system of quantum mechanics has been empirically successful, but its underlying concepts—such as the physical nature of the collapse of wave functions, the non-localization of quantum entanglement, and the transition from quantum to classical—have not yet been recognized as ontological interpretations [1]. This paper proposes a new conceptual framework called "dynamic dimension theory". The framework takes an ontological leap: it interprets three-dimensional physics as a dynamic projection of a higher-dimensional "dynamic axis field" rather than a self-consistent quantum whole. Its core mechanism, "stability selection", reconstructs the collapse of the wave function into a finite time physical relaxation process. Therefore, the problems of quantum entanglement such as non-locality are obtained based on high-dimensional integrity and synchronous projection. The theory is based on three basic postulates: (1) there is a diffuse, non-spatial high-dimensional physical field, that is, the "dynamic axis field"; (2) The three-dimensional physical reality is the projection of the dynamic state of the field to its subspace; (3) The evolution of the field is governed by the expansion form of the principle of minimum action, and naturally tends to the most stable state of information-energy architecture. The core of this theory is that it reinterprets the collapse of the wave function as a finite dynamic process, that is, "high-dimensional stability selection", rather than an infinite mathematical instantaneous mutation. From this, the theory naturally explains multiple phenomena: quantum entanglement is revealed as an associative projection of the same high-dimensional dynamic axis structure in three-dimensional space ("high-dimensional replication" model), and its non-localized association is the result of the synchronous projection of the overall event; The quantum-classical boundary is triggered by the complexity of the macroscopic system on the stability of the dynamic axis. This framework also resonates deeply with the holographic principle and the ER=EPR conjecture on physical images [2-3]. In order to transform this conceptual concept into a testable scientific theory, this paper proposes three clear and falsifiable experimental test paths, which constitute a complete verification system from micro to macro: 1. Microdynamic test: The detection of the "synchronization window" effect for entangled photon pairs is predicted and designed. This experiment aims to directly measure the finite time scale of the quantum projection process and is a decisive test of the theoretical dynamics kernel. 2. Energy conservation extended test: A full-cycle energy statistical monitoring experiment of "preparation-collapse-decoherence" was designed on the superconducting qubit platform to verify the hypothesis of "interdimensional energy cycle" predicted by the theory and face the compatibility problem with the law of conservation of energy. 3. Cosmological origin test: It is predicted that the coupling of dynamic axial field and expansion field in the early universe will produce characteristic non-Gaussian imprints (f_NL^loc ∼) in the primordial perturbations, and a complete analysis scheme is given for detection using next-generation galaxy survey data (e.g., DESI, Euclid) [4]. This paper systematically expounds the principle, deduction and dialogue between dynamic dimensionalism and the existing physical framework. Its primary value is to try to integrate the interpretation of a series of basic problems into a single and testable physical mechanism, and to put forward clear and concrete experimental predictions. Whether these predictions are confirmed or falsified, this work will open up new and fruitful directions for quantum-based experimental exploration.