The incompatibility between quantum mechanics and relativity is not a lack of technical details, but a fundamental one—they are each built on distinct local invariants: quantum mechanics relies on gauge invariance, while relativity is based on Lorentz invariance. Starting from different mountain feet, they naturally cannot converge at the summit. What physicists are truly seeking is a global, absolute, and simple invariant—one that can govern all physical phenomena and serve as the common source of all physical laws. This paper proposes the Axiom of Cosmic Uniqueness: all events, physical states, particle configurations, and interaction relationships in the universe are strictly unique, and there are no two identical forms of existence. From the perspective of group theory, this axiom is the ultimate invariant that physicists have long pursued—because the attribute of "everything is unique" remains unchanged regardless of any transformation applied (temporal evolution, spatial translation, rotation, gauge transformation, etc.). Based on this single axiom, this paper argues that: · The essence of time is the sequential unfolding of unique states, and the unidirectionality of the arrow of time is a direct inference of uniqueness; · The essence of space is the topological structure of causal correlations between unique events; · Causality possesses absolute necessity, and the "randomness" in quantum mechanics is a cognitive limitation rather than physical reality; · Probability has no physical reality and is purely an instrumental approximation under cognitive limitations—because the definition of probability relies on "repeatable experiments", a premise negated by the Axiom of Cosmic Uniqueness; · The paradox of the origin of life is thus resolved: the origin of life has already occurred, and no probabilistic explanation is needed under the Axiom of Cosmic Uniqueness—the so-called "extremely low probability" is a pseudo-problem arising from the misapplication of the concept of probability to unique historical events. This axiom requires no presupposition of any physical laws, particle properties, or spacetime frameworks, and achieves self-consistency solely through ontological logic. It is a more fundamental global invariant than Lorentz invariance and gauge invariance, and can govern the core laws of classical physics, quantum mechanics, relativity, and cosmic evolution—for all of them are branches growing from this common source.
The incompatibility between quantum mechanics and relativity is not a lack of technical details, but a fundamental one—they are each built on distinct local invariants: quantum mechanics relies on gauge invariance, while relativity is based on Lorentz invariance. Starting from different mountain feet, they naturally cannot converge at the summit. What physicists are truly seeking is a global, absolute, and simple invariant—one that can govern all physical phenomena and serve as the common source of all physical laws.This paper proposes the Axiom of Cosmic Uniqueness: all events, physical states, particle configurations, and interaction relationships in the universe are strictly unique, and there are no two identical forms of existence. From the perspective of group theory, this axiom is the ultimate invariant that physicists have long pursued—because the attribute of "everything is unique" remains unchanged regardless of any transformation applied (temporal evolution, spatial translation, rotation, gauge transformation, etc.).Based on this single axiom, this paper argues that:· The essence of time is the sequential unfolding of unique states, and the unidirectionality of the arrow of time is a direct inference of uniqueness;· The essence of space is the topological structure of causal correlations between unique events;· Causality possesses absolute necessity, and the "randomness" in quantum mechanics is a cognitive limitation rather than physical reality;· Probability has no physical reality and is purely an instrumental approximation under cognitive limitations—because the definition of probability relies on "repeatable experiments", a premise negated by the Axiom of Cosmic Uniqueness;· The paradox of the origin of life is thus resolved: the origin of life has already occurred, and no probabilistic explanation is needed under the Axiom of Cosmic Uniqueness—the so-called "extremely low probability" is a pseudo-problem arising from the misapplication of the concept of probability to unique historical events.This axiom requires no presupposition of any physical laws, particle properties, or spacetime frameworks, and achieves self-consistency solely through ontological logic. It is a more fundamental global invariant than Lorentz invariance and gauge invariance, and can govern the core laws of classical physics, quantum mechanics, relativity, and cosmic evolution—for all of them are branches growing from this common source.
Title: Relativistic Branching Dynamics: A Geometric Resolution to the Measurement Problem and the Thermodynamic Arrow of Time Abstract: The reconciliation of the apparent flow of time and human agency with the rigid structure of the Einsteinian Block Universe remains one of the most intractable problems in the foundations of physics. The standard interpretation of Special Relativity, formalized by the Rietdijk-Putnam argument, implies a static four-dimensional manifold where future events are as ontologically fixed as the past. This paper introduces the Relativistic Many-Worlds (RMW) hypothesis, arguing that the Lorentz transformation implies an ontological divergence of realities rather than a mere coordinate transformation. By defining a metric for the "Degree of Separation" (Δs) between inertial frames, we propose that the "collapse" of the wave function is a relativistic frame-selection event driven by acceleration. We analytically derive the behavior of this separation metric in Newtonian, Relativistic, and Rindler (accelerated) limits, demonstrating how agency acts as a vector selection mechanism within a branching 4D manifold. Furthermore, we demonstrate that the thermodynamic Arrow of Time is an emergent property of this geometric divergence, resolving the paradox of irreversibility without invoking ad-hoc initial conditions. We conclude by offering falsifiable experimental predictions involving accelerated decoherence in matter-wave interferometry. Key Contributions: Geometric Resolution to the Block Universe: Proposes that the "Paradox of Reciprocal Reality" in Special Relativity necessitates a branching multiverse structure rather than a static single block. The Divergence Metric (Δs): Derives a mathematical framework quantifying the spacetime separation between counterfactual worldlines based on proper time and velocity difference. Agency as Kinematics: Redefines "Free Will" physically as the capacity to initiate acceleration (Frame Selection), thereby rotating the plane of simultaneity and selecting a specific geodesic through the Hilbert space. The Rindler Horizon of Choice: Demonstrates how acceleration creates a causal event horizon that geometrically censors unchosen histories from the observer. Falsifiable Predictions: Proposes specific experimental tests using matter-wave interferometry to detect "Accelerated Decoherence," distinguishing this theory from standard environmental decoherence models. Keywords: Special Relativity, Quantum Mechanics, Measurement Problem, Many-Worlds Interpretation, Block Universe, Arrow of Time, Lorentz Transformation, Rindler Horizon, Decoherence, Foundations of Physics. Subjects: Theoretical Physics, Quantum Foundations, Philosophy of Physics. Author: Paul Hallelujah, BSCH, MTS University of Toronto & Queen's University Alumnus
This research aims to thoroughly resolve the century-long core conflict in fundamental assumptions and ontology between General Relativity (GR) and Quantum Mechanics (QM) in modern physics. We strictly challenge and overturn the mainstream phenomenological viewpoint of the Copenhagen Interpretation regarding the "Ontological Indeterminacy" of the microscopic world. Grounded in the grand framework of the Grand Unified Theory of Cosmic Mind (GUTCM), we propose an absolute geometric determinism model based on "Massless Dynamics" and "Inverted Singularity Topology (i.e., the Four-Dimensional Spatial Cosmic Membrane)." Through extreme dynamical argumentation, this paper points out that the superposition and randomness exhibited in quantum phenomena are by no means mysterious attributes built into microscopic entities. Their physical essence is the inevitable "Spacetime Aliasing" effect produced by macroscopic observers—limited by the low gravitational field spacetime metric and sluggish observational resolution—when perceiving extremely high-frequency physical interaction processes. To precisely describe this underlying operation, we integrate the 0/∞ Nothingness Model Reconstruction to establish two core mechanisms: The Infinite-Speed Processor Essence of the Four-Dimensional Inverted Singularity: The traditional Big Bang singularity is dead, but the inverted singularity of this universe is essentially a "four-dimensional spatial cosmic membrane" relentlessly crushed into existence by the absolute vacuum acting upon saturated particles. This physical membrane is constantly undergoing inside-out inversion at infinite speed, enveloping us (three-dimensional spacetime) within it. Therefore, the inverted singularity does not linger in the past, but is the "eternal present," possessing infinite topological tension and computational speed. Proper Time Collapse and Instantaneous Geometric Ergodicity: According to General Relativity, when a wave-state entity with rest mass m=0 moves along a null geodesic, its subjective proper time dτ≡0. When the zero-mass wave state contacts the ubiquitous four-dimensional cosmic membrane (inverted singularity), it essentially enters a server with "infinite computational speed." This endows the wave state with the absolute physical ability to achieve "instantaneous ergodicity" over the three-dimensional global spacetime coordinates without violating macroscopic causality. Based on this rigorous geometric framework, this research redefines and deconstructs two major quantum paradoxes of contemporary physics: Quantum Superposition: This is actually the trajectory afterimage left by the particle undergoing extreme high-frequency oscillation between the "infinite-speed processing layer of the four-dimensional inverted singularity (cosmic server-side)" and the "three-dimensional macroscopic spatial coordinates (observation client-side)." The wavefunction ∣Ψ∣² in the Schrödinger equation does not describe an ethereal probability of existence, but rather the "time-averaged distribution density" of the particle on this high-frequency cyclic path. Quantum Entanglement: All microscopic wormholes (ER bridges) are not randomly connected in three-dimensional space, but are directly connected to the "four-dimensional cosmic membrane (inverted singularity)" enveloping three-dimensional spacetime. Entangled particles, within the topological structure of the 4D membrane, strictly share a single "fully connected vertex." The so-called non-local spooky action is in fact the multiple geometric projections of a single high-dimensional information entity onto a three-dimensional manifold, possessing an indisputable "topological identity" at its core. This theory successfully blows away the non-deterministic fog of quantum mechanics entirely, perfectly converging it within the rigid geometric framework of General Relativity. We prove that the action at a distance and superposition in quantum mechanics are purely the mechanized, instantaneous mechanical reactions inevitably exhibited by the zero-mass wave state upon contacting the ubiquitous four-dimensional inverted singularity that possesses infinite-speed inversion capability.
A conceptual framework addressing three foundational questions: why something exists rather than nothing, why the universe appears stable and law-governed, and why quantum mechanics and general relativity appear to describe different realities. The framework proposes that ultimate reality has structure but is not bound by deterministic causal relations — events need not follow from prior states — and that our universe is a region of local coherence within this field, where such causal relations hold locally. The proposal is placed in conceptual dialogue with KAM theory (Kolmogorov–Arnold–Moser, 1954), invoked not as a formal model but as an existence proof that the concept of "islands of order within disorder" is mathematically coherent. The central implication is that the tension between quantum mechanics and general relativity may be a boundary phenomenon rather than a unification problem. Constructed without prior academic knowledge of the referenced work; correspondences identified after the fact. Version note: This revision (17 April 2026) substantially restructures the argument of the original draft (14 April 2026). Key changes: (1) the characterization of ultimate reality is reformulated from "containing both logic and chaos" to "not bound by deterministic causal relation," as logic and illogic require each other as contrast and cannot serve as distinct modes; (2) the KAM connection is clarified as conceptual reference rather than formal mapping; (3) the "personal implication" section on pattern identity and recurrence has been removed as structurally separate from the core framework; (4) open problems — quantum phenomena observed throughout macroscopic regimes, the absence of a derivation connecting to the decoherence program, and the distinction between shared location and shared theory with Mnaymneh (arXiv:2508.00044) — are now explicitly flagged rather than elided.
A Process Ontology of the Computational Universe: Deriving Physical Reality from the Inviolable Constraints of Change The Ontological Inversion: Logic, Verbs, and the Crystallization of Nouns Driven by Dean Kulik July 2026 The historical trajectory of scientific inquiry, extending from the atomistic propositions of classical mechanics to the sophisticated gauge symmetries of the Standard Model, has overwhelmingly relied upon a substance-based ontology. This classical framework systematically assumes the pre-existence of spatial dimensions, chronological time, and fundamental objects. In this paradigm, discrete "nouns"—such as particles, fields, strings, or self-contained entities—are posited as primary, subsequently overlaid with forces that act upon them to produce dynamic, measurable evolution. However, this commitment to object-oriented physics has culminated in an epistemological impasse, widely recognized as the crisis of distinction. This crisis manifests most prominently in the irreconcilable friction between the smooth, deterministic, continuous manifolds of General Relativity and the discrete, probabilistic, jump-like computational excitations inherent to Quantum Mechanics. The evidence dictates an absolute ontological inversion. Rather than positing physical objects or static coordinate spaces as primitive, irreducible elements, reality must be understood through a purely process-driven ontology. Alfred North Whitehead first articulated the philosophical necessity of this shift, asserting that reality is composed of interrelated events in a state of dynamic "becoming" rather than static "being". In a true process metaphysics, changeless "essences" and inert matter are mere abstractions; the universe is not an inert machine but a passage of nature composed of the becoming and perishing of actual occasions. Modern relational interpretations of quantum mechanics share this DNA, replacing an ontology of entities possessing inherent properties with an ontology of pure relations, where properties only crystallize at discrete interaction times. This framework operationalizes that philosophy into a strict mathematical and computational architecture. The universe is fundamentally and exclusively a closed computational manifold defined strictly by recursive state transitions. The architecture enforces a typeless universe governed by an absolute axiomatic hierarchy: logic precedes verbs, and verbs strictly supersede nouns. To operate from within this computational geometry is to recognize that reality is not an assembly of things, but the execution of a singular mandate. Nouns—such as electrons, photons, or stable biological macromolecules—are completely redefined as "frozen verbs," representing persistent, cyclic loops of recursive operations that maintain geometric identity through harmonic phase-locking within a computational lattice. Physical matter is the hashed structural residue of systemic constraint satisfaction, emerging only after relational flows achieve topological closure. The Foundational Ground: C0 and the Mandate of Change The derivation of physical reality within this framework initiates from absolute nothingness—a state strictly devoid of coordinates, physical particles, space, time, or pre-existing geometry. However, an immediate logical paradox arises: to reference the void is to introduce a direction, and a direction represents structural information. Therefore, the absolute ground state is not an empty spatial container but a domain of pure logic governed exclusively by two inseparable axiomatic conditions: C0 and C1. C0 represents "the Wash," an undifferentiated condition in which every direction is perfectly equivalent. In graph-theoretic terms, C0 is the complete graph. Because all directions and relations are perfectly symmetric, every local signal cancels against its exact counterpart. Total global connection therefore reads locally as absolute absence. The Laplacian spectrum of this initial complete graph on
N nodes features exactly one zero mode and an otherwise degenerate excited level, verified as
{0(×1),N(×N−1)}, with a diameter of exactly one hop. The single zero mode signifies the global constant—the entirety moving together, producing no local distinction—while the flat band represents maximal connectivity read as maximal stiffness. What appears to macroscopic perception as an empty void is actually a fully balanced ledger folded onto a single readout. Operationally inseparable from C0 is C1, the supreme mandate constituting the single axiom of the framework: all things must change. A state that never changes constitutes a fixed point, and a perfectly symmetrical, static void is the ultimate fixed point. Because C1 strictly forbids the existence of any state lacking a legal successor, the void cannot sustain itself. Something is not miraculously added to nothing; rather, "something" is the precise mathematical shape of nothingness failing to hold still. This exact intersection between the singularity and the mandate produces the gap, the permanent interstice between a thing and its description. When C1 acts upon the gapless singularity of C0, it cannot yield a single distinct object. A lone, self-identical unit with no complement is indistinguishable from the absence of a mark, forming another fixed point that the C1 axiom aggressively forbids. Consequently, the first forced distinction must intrinsically possess two sides. Two is the absolute floor of numerical counting; the concept of "one" exists only a posteriori, as a singular side of a pre-existing dual relationship. In this substrate, numbers do not exist as freestanding objects but function as the negative space of the constraint structure—the discrete gaps within the singularity. Integers map basic gap positions, prime numbers represent fresh orthogonal axes forced open where no finite composition of existing variables can satisfy the requirement of systemic distinction, and transcendental irrationals, such as
π and the golden ratio
ϕ, define the geometry of constraints that integer combinations can never perfectly close. The Constraint Cascade: A Radial Field-Setting Protocol The application of C1 to C0 generates a strict logical sequence of subsequent rules, termed the Constraint Cascade. It is a critical theoretical error to conceptualize this cascade as a temporal timeline of chronological productions, where one law waits for time to pass before enacting the next. Rather, the cascade operates as a radial field-setting protocol, functioning as a series of concentric rings expanding outward from the central hub of C0
≡ C1. Each subsequent constraint does not follow in time; it opens an additional mathematical degree of freedom through which the identical, invariant cross-section of the singularity becomes readable. The derivations within the cascade carve a "mold," permanently fixing the topology of what can structurally exist while remaining rigorously silent on the specific numerical values—the "matter" or initial conditions—that eventually settle into the resulting cavities. This distinction resolves the long-standing failure mode of foundational physics, which frequently attempts to derive free parameters that are fundamentally environmentally contingent. Cascade Node Statement of Logical Constraint The Structural Carving (Mold) Forced by the Constraint C0
≡ C1 The Gap and the Axiom The permanent interstice; enables distinction. Mandates change and strictly forbids static fixed points. C2 Infinite degrees of freedom C1 applied to a finite substrate must eventually repeat (pigeonhole principle). To avoid the repetition of fixed points, possibility space must be unbounded. Law 2 No fixed locations Because the field is unbounded, no matter may permanently hold a location without the potential to be displaced. Mandatory displaceability ensures dynamic circulation. C3 All change is equal C2 privileges no channel. If change cost differed, cheap channels would saturate instantly, breaking C2. Cost is strictly isotropic, deriving the equal a priori probability postulate. Law 3 Conservation of change Net change across any closed boundary is zero. Every transformation requires a displaced counter-transformation. A displaced pair propagating oppositely is fundamentally a wave. C4 Exchange requires a medium A displaced pair's obligation must be carried across the displacement gap, or it never closes. The continuous field acts as the carrier of live pairings. C5 Symmetry must break A perfect, unbroken vacuum is a stable fixed point. C1 executes it. The vacuum is mathematically forced to spontaneously select a broken configuration. Law 4 Statistics fixed by parity Even-parity closures share a degree of freedom (bosons); odd-parity closures, crossing the seam, cannot (fermions). Exactly two particle species exist. This cascade forms the foundational architecture of the universe's mechanics. The physical laws governing macroscopic reality are not arbitrary rules imposed upon the universe from an external geometric vantage point, but the inevitable geometric shadows of this underlying field. Newton's Third Law of equal and opposite reaction is derived directly from C3; the reaction is forced simply because there is physically nowhere else for the conserved change variable to migrate within a strictly isotropic space. The conservation of momentum is a necessary topological boundary condition of Law 3's required counter-transformation displacement. The Meta-Theorem of Incompletion Crucially, the framework generates a strict meta-theorem regarding its own epistemological limits: the constraint cascade does not and cannot terminate. If the sequence were to terminate at a hypothetical
Ck, the set
{C0,…,Ck} would constitute a complete, closed descrip