This exploratory paper proposes a mathematical model in which three-dimensional space and an additional coordinate, c, remain independently defined, while their interaction is activated by an observer’s conscious recognition of occupying three-dimensional space. It presents the model’s postulates, mathematical proofs, an exact solution, and requirements for empirical testing. The proposal has not been experimentally validated or peer reviewed.
This exploratory paper proposes a mathematical model in which three-dimensional space and an additional coordinate, c, remain independently defined, while their interaction is activated by an observer’s conscious recognition of occupying three-dimensional space. It presents the model’s postulates, mathematical proofs, an exact solution, and requirements for empirical testing. The proposal has not been experimentally validated or peer reviewed.
If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction with the universe should be further developed with consciousness being the driving force.
Perceiver Collapse: Dual-Location Quantum Physics and Dimensional Pooling This paper explores a conceptual extension of Dual-Location Quantum Physics in which two entities can remain independently located and represented while becoming progressively unified within the dimensional space accessible to a perceiver. Rather than treating observation as a conventional physical collapse of the entities themselves, the paper investigates whether perception can instead be modelled as a process of dimensional pooling. Within the framework, each entity possesses its own independent multidimensional representation. The two entities therefore remain distinct in their underlying state and location. A perceiver, however, does not necessarily engage with every available dimension equally. Attention establishes a dimensional scope: selected dimensions become coupled through the perceptual process, while dimensions outside that scope remain independent. The paper formalizes this process using Hilbert-space operators, density states, entropy, and effective dimensionality. Attention is represented as an operator-space coupling between the two otherwise independent entities. As attention increases, the distinguishability associated with an attended dimension progressively contracts, producing a lower effective dimensional representation. Dimensions outside the perceiver's scope remain unaffected. This creates a distinction between ontological separation and perceptual dimensionality. Two entities may continue to exist separately in their respective locations while their representation within an observer's accessible dimensional space becomes increasingly pooled. Complete attention-driven pooling therefore does not require the physical entities to merge; it corresponds instead to the disappearance of relative degrees of freedom within the perceived representation. The resulting framework provides a mathematical language for exploring how a higher-dimensional dual-location state might give rise to a lower-dimensional perceptual representation. It is deliberately presented as a formal exploratory model rather than as a claim that consciousness or physical observation has been experimentally demonstrated to cause dimensional collapse. Its purpose is to establish a reproducible operator framework in which perception acts as dimensional scope, and dimensional scope determines which distinctions remain accessible to the observer.
This exploratory preprint studies a controlled quantum-scattering toy model with an additional harmonically confined coordinate w. It compares a fixed-width one-dimensional barrier, the exact shrinking observable slice V(x,0), and the full coupled (x,w) Hamiltonian. The identical-slice control shows that the non-monotonic transmission turn is not unique to an additional coordinate, while the coupled calculation produces a quantitatively distinct transmission curve and a converged transverse-broadening signal. The action-coordinate hypothesis is S_E = f(w), with A = S_E / ħ. The original eleven-point parameter sweep gives a monotonic nonlinear locus when A is plotted against the center broadening Δw_rms. A new matched-state stress test independently changes longitudinal energy or transverse confinement and retunes the barrier to reproduce Δw_rms = 0.08, 0.18, and 0.35. The corresponding WKB actions spread by 50.2%, 31.1%, and 22.7% relative to the baseline; the exact-scattering exponent agrees, and a refined-grid calculation is stable. Thus a universal one-variable proxy A = F(Δw_rms) fails without refitting. This result does not falsify an otherwise unspecified microscopic relation S_E = f(w), because Δw_rms is an observable moment rather than the coordinate or tunneling path w. It shows that broadening alone is insufficient and that a richer state description or path-level definition is required. The work is non-peer-reviewed and does not claim evidence that nature has an accessible fourth spatial dimension. The supplement contains the calculation scripts, CSV data, numerical metadata, convergence checks, and figures; AI assistance is disclosed in the manuscript.
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 non-peer-reviewed exploratory preprint tests whether a coupled quantum Hamiltonian with one additional spatial coordinate can produce barrier transmission distinct from ordinary one-dimensional quantum mechanics when both calculations share exactly the same observable slice V(x,0). A prescribed self-similar Gaussian barrier is compared using three calculations: fixed-width 1D, shrinking identical-slice 1D, and full coupled (x,w) scattering with harmonic confinement. The shrinking 1D slice is itself non-monotonic, so an upward turn is not uniquely extra-dimensional. The full model nevertheless gives a quantitatively different curve, with a sampled minimum near V0=18 and T=9.87e-3 at V0=64 versus 6.09e-9 for the identical slice. This is a reproducible coupled-channel result within a mathematical toy Hamiltonian, not evidence that nature has an accessible fourth spatial dimension. The barrier family is prescribed rather than derived from a constitutive field law. The record includes the manuscript and a supplement containing code, complete numerical results, metadata, and convergence checks. ChatGPT and Sarvam AI assisted with brainstorming and language development. ChatGPT also assisted with literature triage, control design, numerical implementation and auditing, and drafting. AI systems are not authors. Chaman Prakash Kanth remains responsible for the manuscript, assumptions, metadata, and publication decision.