This paper deconstructs traditional physical paradigms that assume continuous spacetime and fixed material entities. Instead, we present a unified theoretical framework establishing phase streams on a countable space $\Lambda^4$—comprising countably infinite discrete nodes—as the true substrate of the physical world. In Chapters 1 through 4, the smoothness of spacetime, intrinsic properties of elementary particles (mass, charge, spin), and the phenomenon of "wave function collapse" upon observation are algebraically and topologically redefined as spontaneous phase locking (algebraic closure phase transitions). This occurs when the multi-body coupling strength $K$ with environmental nodes exceeds a critical threshold $K_{\text{crit}}$. Extending these insights into quantum computing, Chapter 5 and the Appendix propose a conceptual model for a "Non-Phase-Transition Quantum Processor (NPQP)." In contrast to conventional paradigms relying on physical isolation, NPQP actively cancels coupling topology to permanently restrict the system within $K < K_{\text{crit}}$ (the probabilistic regime), thereby structurally suppressing decoherence. This framework provides a novel unified perspective on fundamental physical interactions and establishes a theoretical guidepost for next-generation quantum computing.
This paper deconstructs traditional physical paradigms that assume continuous spacetime and fixed material entities. Instead, we present a unified theoretical framework establishing phase streams on a countable space Λ4—comprising countably infinite discrete nodes—as the true substrate of the physical world. In Chapters 1 through 4, the smoothness of spacetime, intrinsic properties of elementary particles (mass, charge, spin), and the phenomenon of "wave function collapse" upon observation are algebraically and topologically redefined as spontaneous phase locking (algebraic closure phase transitions). This occurs when the multi-body coupling strength K with environmental nodes exceeds a critical threshold Kcrit. Extending these insights into quantum computing, Chapter 5 and the Appendix propose a conceptual model for a "Non-Phase-Transition Quantum Processor (NPQP)." In contrast to conventional paradigms relying on physical isolation, NPQP actively cancels coupling topology to permanently restrict the system within K<Kcrit (the probabilistic regime), thereby structurally suppressing decoherence. This framework provides a novel unified perspective on fundamental physical interactions and establishes a theoretical guidepost for next-generation quantum computing.
AbstractThis work presents a unified geometric framework for quantum reality through four interconnected papers. It proposes that the coherent, non-separable correlations described by Hilbert space originate from an unobservable Energy Space, a fundamental substrate beyond spacetime that preserves perfect coherence and all conservation laws, thereby providing a geometric interpretation of quantum entanglement. Within this framework, the relation E = hf is interpreted as an encoding relation rather than a statement of physical energy actualization. During measurement, structural branching may occur, but Energy Space ensures that only one geometrically valid branch undergoes physical localization. Spacetime emerges from Energy Space as a passive geometric medium with intrinsic dynamic capabilities, giving rise to quantum objects and their interactions.Quantum objects are interpreted as dynamic geometric patterns of spacetime possessing an encoded geometric identity. Their physical properties, including mass, charge, spin, momentum, energy, wavelength, and phase, are fundamentally encoded in Energy Space and become physically actualized according to the interaction context and the degree of coherence or decoherence. The stability, transformation, and propagation of quantum objects are determined by their geometric compatibility with spacetime and with other quantum geometries.Electromagnetic, weak, and strong interactions are interpreted as direct interactions between compatible quantum-object geometries, whereas gravity is regarded as an indirect geometric interaction mediated through spacetime geometry. Geometric interactions may produce superposition, transformation into new quantum-object geometries, or the formation of larger composite geometric structures, providing a unified geometric interpretation of interactions, confinement, and composite systems.Within this geometric framework, a recursive geometric scaling parameter satisfying the invariant relation is proposed. Based on this hierarchy, phenomenological recursive scaling relations are developed for the lepton and quark families, suggesting a possible underlying geometric structure governing fermion masses, generational hierarchy, and relative stability.Finally, the Peak-Coupling Theory proposes that quantum localization and decoherence occur through discrete peak-coupling events between interacting quantum geometries at oscillatory extrema within a quantum wave packet. The wave envelope and phase continuously modulate the distribution of possible coupling events, while observable interaction probabilities may emerge from the squared magnitude of local coupling amplitudes, providing a possible geometric route toward the emergence of Born-rule probabilitiesTogether, these four papers present a unified conceptual framework in which Energy Space, spacetime, quantum objects, physical interactions, particle hierarchies, quantum measurement, and localization are interpreted as interconnected manifestations of an underlying geometric reality.These ideas are developed across four papers: Paper 1: Energy Space and Geometric Nature of Quantum Objects and Spacetime Paper 2: Quantum Geometry Paper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
Modern quantum mechanics operates under a profound ontological inversion: it misinterprets the mathematical remnants of a physical interaction as the fundamental causal mechanism of the state itself. By prioritizing wave-function collapses, probability amplitudes, and observer-driven measurements, mainstream physics continuously attempts to derive the nature of the source from the morphology of its artifact. This paper establishes the Framework of Substrate Realism (PSR), structurally redefining quantum mechanics by demonstrating that non-locality, superposition, and entanglement are objective, intrinsic states of a continuous physical substrate. These phenomena operate independently of external measurement matrices, observer interventions, or classical instrumentation thresholds. By integrating density-driven screening constraints derived from unified informational tensors, we show that subatomic entities are distinct wave phase-profiles within this continuous substrate. The apparent "particle state" is exposed as an anthropic post-processing illusion generated by the hardware-locking thresholds of classical instrumentation and the evolutionarily rigid perceptual matrices of human neurological architectures. We bypass the constraints of Bell's theorem by establishing a non-local field holism, clarify the non-linear topological nature of multi-wave coupling, and resolve the quantum-relativistic paradox through primordial chrono-energetic co-genesis. Finally, we provide an engineering roadmap for stable quantum information architectures and propose concrete, non-human artificial intelligence (AI) verification protocols operating at pre-threshold raw analog data streams to validate the substrate's continuous evolution.
Abstract This work presents a unified geometric framework for quantum reality through four interconnected papers. It proposes that the coherent, non-separable correlations described by Hilbert space originate from an unobservable Energy Space, a fundamental substrate beyond spacetime that preserves perfect coherence and all conservation laws, thereby providing a geometric interpretation of quantum entanglement. Within this framework, the relation E = hf is interpreted as an encoding relation rather than a statement of physical energy actualization. During measurement, structural branching may occur, but Energy Space ensures that only one geometrically valid branch undergoes physical localization. Spacetime emerges from Energy Space as a passive geometric medium with intrinsic dynamic capabilities, giving rise to quantum objects and their interactions. Quantum objects are interpreted as dynamic geometric patterns of spacetime possessing an encoded geometric identity. Their physical properties, including mass, charge, spin, momentum, energy, wavelength, and phase, are fundamentally encoded in Energy Space and become physically actualized according to the interaction context and the degree of coherence or decoherence. The stability, transformation, and propagation of quantum objects are determined by their geometric compatibility with spacetime and with other quantum geometries. Electromagnetic, weak, and strong interactions are interpreted as direct interactions between compatible quantum-object geometries, whereas gravity is regarded as an indirect geometric interaction mediated through spacetime geometry. Geometric interactions may produce superposition, transformation into new quantum-object geometries, or the formation of larger composite geometric structures, providing a unified geometric interpretation of interactions, confinement, and composite systems. Within this geometric framework, a recursive geometric scaling parameter satisfying the invariant relation is proposed. Based on this hierarchy, phenomenological recursive scaling relations are developed for the lepton and quark families, suggesting a possible underlying geometric structure governing fermion masses, generational hierarchy, and relative stability. Finally, the Peak-Coupling Theory proposes that quantum localization and decoherence occur through discrete peak-coupling events between interacting quantum geometries at oscillatory extrema within a quantum wave packet. The wave envelope and phase continuously modulate the distribution of possible coupling events, while observable interaction probabilities may emerge from the squared magnitude of local coupling amplitudes, providing a possible geometric route toward the emergence of Born-rule probabilities Together, these four papers present a unified conceptual framework in which Energy Space, spacetime, quantum objects, physical interactions, particle hierarchies, quantum measurement, and localization are interpreted as interconnected manifestations of an underlying geometric reality. These ideas are developed across four papers: Paper 1: Energy Space and Geometric Nature of Quantum Objects and SpacetimePaper 2: Quantum GeometryPaper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
This work proposes a theoretical framework reinterpreting particle motion andfield excitation propagation as emergent phenomena arising from sequences of discrete transition events, rather than traditional continuous trajectories or waves.We develop an operator algebra to explore how fundamental physics might emergefrom such transitions, which could operate at either discrete or infinitesimal scalesdepending on spacetime’s structure. The spacetime-agnostic architecture accommodates both continuous and discrete models while offering fresh perspectives on paradoxes of particle identity, field localization, and quantum measurement. Testable predictions for mass-dependent quantum interference phenomena are derived, providing potential experimental pathways to probe the transition-based paradigm.
This paper, authored by Aidan McGill in October 2024, proposes a novel reinterpretation of quantum decoherence by framing it as a physical phase transition in probability distributions. It challenges conventional interpretations, such as the Copenhagen and many-worlds theories, which rely on the concept of wave function "collapse" driven by an external observer or measurement. Key aspects of this framework include: Observer-Independent Decoherence: The model removes the necessity of an observer, proposing that classical behavior is an emergent property of quantum complexity rather than a separate reality. The Phase Transition Mechanism: Decoherence is defined as a transition in the probability distribution of a system's wave function, triggered when interactions with external systems cross a specific threshold of complexity. Information and Energy Dynamics: The shift from quantum to classical behavior is driven by informational exchanges and energy transfers between a system and its environment. Empirical Alignment: The framework is supported by real-world examples, including buckyball double-slit experiments and superconducting qubits, which demonstrate quantum effects in macroscopic systems. Consistency with the Born Rule: This reinterpretation maintains the probabilistic outcomes of standard quantum mechanics and remains fully consistent with the Born rule. By focusing on the intrinsic properties of system interactions, this work offers a unified view where quantum mechanics governs all scales, and classical reality is a byproduct of informational complexity.
This work presents a topological phase framework in which time is treated as a generated quantity arising from phase collapse rather than as a fundamental background dimension. In this model, space corresponds to a completed manifold of resolved states, while time emerges as an index of unresolved phase transitions between spatial configurations. Quantum measurement, consciousness, and computation are described as different projections of the same underlying phase-selection process. The framework introduces formal definitions for phase collapse, dual-sphere manifolds, and projection operators linking physical, computational, and cognitive domains. These structures provide a unifying basis for phase-based physics, large-scale computation, and emergent intelligence architectures. This work was developed independently and does not rely on operator-theoretic or quantum-information formalisms, instead adopting a phase-theoretic and topological perspective.