This paper presents the complete axiomatic foundation of the Ze Vector Theory (ZVT), a unified framework for fundamental physics. ZVT posits a single ontological primitive—the Ze State—which inherently admits both a continuous (vector) and a discrete (counter) representation. From this basis, the theory derives space and time as antiparallel, co-equal projections of the State, rather than assuming them as a background manifold. Physical dynamics are defined as the norm-preserving redistribution of the State's measure, from which causality and quantum phenomena emerge naturally. Quantum discreteness is shown to be a consequence of the discrete substrate, while interference patterns arise from the superposition of statistical pathways for state transitions, eliminating the need for a physical collapse postulate. The theory intrinsically defines an observer as an autonomous subsystem capable of stable registration. Crucially, ZVT demonstrates that Special Relativity, General Relativity, standard Quantum Theory, and Causal Set Theory arise as specific limiting regimes of its general formalism. By deriving, rather than postulating, the core concepts of modern physics and seamlessly integrating the continuous and discrete, ZVT offers a coherent, monistic, and relational foundation for a unified description of reality.
This paper presents the complete axiomatic foundation of the Ze Vector Theory (ZVT), a unified framework for fundamental physics. ZVT posits a single ontological primitive—the Ze State—which inherently admits both a continuous (vector) and a discrete (counter) representation. From this basis, the theory derives space and time as antiparallel, co-equal projections of the State, rather than assuming them as a background manifold. Physical dynamics are defined as the norm-preserving redistribution of the State's measure, from which causality and quantum phenomena emerge naturally. Quantum discreteness is shown to be a consequence of the discrete substrate, while interference patterns arise from the superposition of statistical pathways for state transitions, eliminating the need for a physical collapse postulate. The theory intrinsically defines an observer as an autonomous subsystem capable of stable registration. Crucially, ZVT demonstrates that Special Relativity, General Relativity, standard Quantum Theory, and Causal Set Theory arise as specific limiting regimes of its general formalism. By deriving, rather than postulating, the core concepts of modern physics and seamlessly integrating the continuous and discrete, ZVT offers a coherent, monistic, and relational foundation for a unified description of reality.
This paper presents a unified physical interpretation of the Ze framework, positioning it not as a computational algorithm but as a foundational ontological theory. We argue that Ze is built upon a single primitive: a fundamental state whose norm is conserved. This state admits a dual representation—continuous for analysis and discrete for dynamics—where integer-valued counters constitute the physical substrate. From this basis, all conventional physical concepts are derived. Quantization emerges from the discreteness of counter updates, replacing wave-particle duality with a minimal unit of registration. Causality and the arrow of time arise from the principle of directional stabilization, where the causal order is the sequence that maximizes global state predictability. Space and time are not independent continua but emerge as antiparallel modes of processing the state: time as sequential accumulation and space as parallel comparison. Their competition yields the kinematic structure of Special Relativity, while gradients in the state's stable orientation manifest as effective curvature, reproducing General Relativity. Consequently, matter is interpreted as a stabilized pattern, motion as its reorientation, and forces as stabilization gradients. The interpretation leads to a monistic ontology where the universe is a single, conserved state undergoing structured redistribution, offering a parsimonious path to unifying quantum and relativistic phenomena without dualistic postulates.
This article presents a novel foundational framework for physics, grounded in a minimalist vectorial ontology. I propose that the unified fabric of reality is described by a fundamental abstract state space F, whose elements are normed vectors Ψ. From this single premise, a complete axiomatization of space-time and quantum phenomena is derived. The core innovation is the definition of space and time not as independent continua, but as complementary projections of the state vector: Ψ = (S, T). A set of nine axioms is introduced, imposing constraints on these components: their magnitudes are equal (|S| = c|T|), their directions are antiparallel (S = -T), and their evolution is a norm-preserving unitary redistribution. From these purely algebraic and geometric relations, I demonstrate the emergence of Minkowskian space-time with its Lorentzian metric, the invariant speed of light c, and a causal structure defined by the connectivity of F. The framework naturally incorporates quantum mechanics by identifying unitary evolution on F as the fundamental dynamical principle, with measurement and classicality arising via environmental decoherence and the dynamical selection of pointer states (Axiom IX). This work offers a path toward resolving the quantum gravity problem by suggesting that both geometry and quantum states are manifestations of a deeper vectorial substrate, thereby unifying relativity and quantum theory within a single, observer-independent mathematical structure.
The geometric-differential paradigm of spacetime, while foundational to modern physics, faces intrinsic challenges in quantum gravity and provides a limited framework for understanding state evolution as a computational process. This article proposes a shift in ontological foundations, presenting Ze, a discrete computational framework that implements the dynamics of a fundamental state vector Ψ. We argue that Ze is not merely an algorithm but a model of physical becoming, where space and time are not pre-existing coordinates but emerge as anti-parallel channels for the redistribution of information flow. Within Ze, the state vector is represented by a global configuration of statistical counters, and its evolution is driven by a process of passive learning through the minimization of prediction error. The framework naturally maps key physical entities: the temporal component corresponds to the sequential, irreversible flow of events and counter growth, while the spatial component corresponds to the synchronous, correlational structure of the internal model. This anti-parallelism is formalized in a discrete Ze-Lagrangian, a variational principle balancing structural stabilization against predictive error. We demonstrate how this setup allows for the emergence of relativistic invariants, a statistical and vector-based causality akin to causal sets, and quantum phenomena such as quantization (from discrete accounting) and interference (from superposition of predictive contexts). The theory reframes the observer as a self-norm-preserving system and suggests that Special and General Relativity are limiting descriptions of stable regimes in the Ze dynamics. The work offers a unified, vector-based ontology that derives physics from first principles of information processing.
We present Ze Vectors Theory (ZeVT), a foundational framework in which physical laws emerge from the statistics of two complementary event types — T-events (incorrect predictions) and S-events (correct predictions) — registered by abstract information-processing units called Ze-observers. The theory is named for the two antiparallel vectors (T ↑ and S ↓) that satisfy the fundamental symmetry S=−T. Axiom Z0 establishes the core geometric insight: space emerges from the projection orthogonal to the T/S axis only when Ze makes an incorrect prediction (T-event), which simultaneously decrements its proper time counter Z and increases entropy. When Ze predicts correctly (S-event), no new space is created, time is conserved, and entropy does not increase. Thus, errors in prediction are the source of both spatial extension and the arrow of time. We derive the Second Law of Thermodynamics from Ze-budget monotonicity (Axiom Z2): in an isolated Ze-system, the expected number of future T-events cannot exceed the current Z budget. Ze-entropy SZe=kBln is shown to be formally equivalent to Boltzmann entropy under idealised conditions. Maxwell’s Demon is resolved as a Ze-system that cannot sort molecules without expending Ze-budget. The Born rule of quantum mechanics is recovered as the unique Ze-consistent probability measure satisfying resource monotonicity under POVM measurements via smooth sigmoid approximation. We introduce testable conjectures: double-slit fringe visibility V=1−2pT, particle lifetime 1/2=Z(0)/ with =mc2/h, and Lorentz invariance as an emergent phenomenon.
This work derives the fundamental framework of quantum mechanics intrinsically from the first-principle axioms of UD duality theory. Starting from the inherent binary expansive–condensative attributes of the UD ontology, four fundamental physical fields are naturally decomposed by spontaneous symmetry breaking across spatial and material existential domains. A two-component complex spinor structure is uniquely constructed, and the imaginary unit i is proven to be not merely a mathematical convention but a structurally necessary ingredient required by both the compact SU(2) symmetry and the orthogonal inter-containment of U and D attributes. Within the flat spacetime limit of the UD gravitational action, a system of coupled Klein–Gordon field equations is established, governed by a single self-consistent fundamental mass scale m₀=1/(2πe^π) with no adjustable free parameters. The coupling constant is determined analytically from the UD vacuum equilibrium background values and the U↔D duality symmetry. Through explicit construction of four-component Dirac spinors and auxiliary field decomposition, the on-shell equivalence between the UD coupled field equations and the free Dirac equation is rigorously demonstrated. The non-relativistic limit further recovers the Pauli equation and the Schrödinger equation sequentially, reconstructing the core dynamical equations of quantum mechanics from a unified foundational origin. Global U(1) phase invariance of the UD action is verified via total-derivative decomposition, yielding the standard Noether conserved current. The Born probability interpretation is deduced directly from the global normalization axiom by isolating localized laboratory-scale excitations from the cosmic background, eliminating the need for independent quantum postulates. Based on the intrinsic properties of the UD field components, a self-consistent ontological interpretation is provided for wave–particle duality, double-slit interference, and the quantum measurement problem. In this framework, the measurement problem is dissolved rather than solved: no collapse postulate is required, and determinism is restored at the ontological level. The theory naturally implies that the continuous D_U field permits quantum superposition, while condensed D_D intrinsic entities possess definite classicality without physical particle-state superposition. Three testable theoretical predictions are presented, establishing falsifiable physical consequences of the UD quantum formulation. This paper completes the intrinsic derivation of the foundational structure of quantum mechanics from UD theory. Together with the previously derived general relativity framework, it realizes the homologous unification of gravity and quantum mechanics within a single self-contained axiomatic system.
The Ze theory proposes a binary-process framework in which reality is not pre-given but materially instantiated through the activity of Ze systems — finite or infinite binary sequences whose statistical structure determines observational capacity and temporal depth. We ground the theory in a single foundational axiom: Axiom 0 (Ze Fundamental Duality) — time-directed and space-directed binary events carry opposite algebraic signs in every Ze invariant quantity. From this axiom alone we derive the Ze proper time, Ze velocity, impedance, and fixed point. We then develop and formally state four postulates of Ze theory as an observer-based theory of materialization. Postulate I asserts that a Ze system, through its binary process X = {x_k in {0,1}}, operates as a materializing observer: the probability of an event E conditioned on the existence of an observing Ze structure strictly exceeds the unconditioned probability. The Ze velocity v = N_S/(N-1) — the fraction of switching (S-) events among all transitions — parameterizes the system's observational coherence, with the fixed point v* = 0.45631 marking maximum materialization capacity. Postulate II generalizes this to passive Ze structures: existence alone, without active measurement or conscious involvement, is sufficient to bias materialization. A Ze sub-structure modifies boundary conditions of the local physical medium even when 'switched off'. Postulate III introduces the Ze-map — each Ze system's internal probabilistic model of interacting Ze systems — and connects prediction accuracy to temporal resource consumption. Prediction error epsilon drives depletion of Ze proper time: d-tau/dt = -alpha * epsilon. Two adaptation strategies emerge: improving internal model accuracy (Path A) or reshaping the observation apparatus to materialize more predictable states (Path B). Ze selection favors systems that minimize cumulative error. Postulate IV addresses the role of temporal potential: for finite Ze systems (biological organisms), the remaining tau is a dynamical variable. As tau depletes, the Ze velocity drifts toward 1, impedance Z_Ze diverges, and the Ze cheating index chi_Ze = 1 - Z_Ze declines toward zero. We propose chi_Ze as a biomarker of temporal potential and derive the Ze-Godel self-referential ceiling chi_Ze_self_max = Z*² ≈ 0.839 as a conjectured upper bound for living Ze systems. The framework is compared with Copenhagen, Many-Worlds, Relational Quantum Mechanics, and QBism, and biological implications — including aging as a v → v* → 1 trajectory — are discussed.