The Ze Framework proposes that relativistic and quantum effects emerge from the statistics of causal event updates rather than from the fundamental geometry of spacetime. This paper presents eight falsifiable predictions (FP-1 through FP-8) of the Ze Framework, formally restated in precise mathematical language. Four predictions are verified computationally: FP-1 (universal Lorentz scaling τ(v)/τ₀ = √(1−v²), confirmed to residuals < 10⁻⁵ across 21 velocity values and N = 10⁷ events); FP-2 (implementation equivalence — i.i.d., Markov, and deterministic streams with identical (N_T, N_S) yield identical τ); FP-3 (acceleration independence — four p-profiles with equal effective velocity produce equal τ/τ₀); FP-5 (causal chain length determines proper time — τ = √(L_c² + 2L_c·N_S) matches the Minkowski interval exactly). FP-6 (twin paradox) is verified to agree with the SR prediction to within statistical fluctuations O(1/√N). FP-4, FP-7, and FP-8 are critically assessed: FP-4 is reformulated as an analytic limit statement; FP-7 and FP-8 are identified as theoretical programme goals requiring future formal development. All computationally tested predictions pass their pre-specified falsifiability thresholds. The Ze Framework is found to be self-consistent within its defined domain and fully compatible with the established structures of special relativity at the level of counter dynamics.
The Ze Framework proposes that relativistic and quantum effects emerge from the statistics of causal event updates rather than from the fundamental geometry of spacetime. This paper presents eight falsifiable predictions (FP-1 through FP-8) of the Ze Framework, formally restated in precise mathematical language. Four predictions are verified computationally: FP-1 (universal Lorentz scaling τ(v)/τ₀ = √(1−v²), confirmed to residuals < 10⁻⁵ across 21 velocity values and N = 10⁷ events); FP-2 (implementation equivalence — i.i.d., Markov, and deterministic streams with identical (N_T, N_S) yield identical τ); FP-3 (acceleration independence — four p-profiles with equal effective velocity produce equal τ/τ₀); FP-5 (causal chain length determines proper time — τ = √(L_c² + 2L_c·N_S) matches the Minkowski interval exactly). FP-6 (twin paradox) is verified to agree with the SR prediction to within statistical fluctuations O(1/√N). FP-4, FP-7, and FP-8 are critically assessed: FP-4 is reformulated as an analytic limit statement; FP-7 and FP-8 are identified as theoretical programme goals requiring future formal development. All computationally tested predictions pass their pre-specified falsifiability thresholds. The Ze Framework is found to be self-consistent within its defined domain and fully compatible with the established structures of special relativity at the level of counter dynamics.
The Ze framework proposes that proper time is not a geometric parameter but a count of effective information updates, with relativistic kinematics emerging statistically from the dynamics of event processing rather than from assumed spacetime structure. This paper presents a comprehensive experimental programme to test four core Ze postulates across multiple domains. The foundational digital experiment employs identical processors receiving identical input streams operating in maximally sequential versus maximally parallel modes, predicting update count ratios τ_B/τ_A = √(1 - v²) where v represents the proportion of parallel correlations—a functional form identical to the Lorentz factor of special relativity. Physical clock experiments compare internal transition counts in systems with different internal complexity (trapped ions, molecular clocks, optical lattice clocks) under identical relativistic conditions, testing whether proper time correlates with update statistics rather than merely with velocity. Non-inertial experiments subject systems to periodic correlation modulation without changing average velocity, predicting that proper time accumulation depends on causal structure rather than path length alone. Quantum-level experiments leverage programmable quantum computers (IBM, IonQ) to test whether interference corresponds to parallel update distribution and whether the quantum Zeno effect reflects mode switching with measurable update deficits. The Ze framework does not claim special relativity is incorrect but seeks to show it arises as an effective theory from deeper informational principles. Structural convergence with causal set theory, twistor theory, and emergent spacetime frameworks provides indirect support. The digital experiment offers the most direct test: if the relativistic curve emerges from pure information dynamics, it demonstrates that relativistic kinematics are not unique to physics but reflect universal constraints on information processing. Independent replication by multiple groups and derivation of relativity without assuming it would constitute sufficient evidence to attract serious scientific engagement. All proposed experiments are feasible with current technology, and their falsification conditions are clearly specified, ensuring the Ze framework meets the highest standards of empirical testability.
To present Ze Theory as an interpretive framework for quantum mechanics, reformulating known quantum phenomena in the language of Ze-observers—quantum systems by construction that possess proper time and act under conditions of struggle for existence. A Ze-observer is defined as a tuple (H, ρ_Z, {M_i}, τ_Z, θ_Z), where H is a Hilbert space, ρ_Z is a belief state, {M_i} is a POVM, τ_Z is a proper time counter, and θ_Z is a prediction threshold. The dynamics of τ_Z follow the rule: for a correct prediction (S-event), τ_Z is preserved; for an incorrect prediction (T-event), τ_Z decreases by 1. Two fundamental survival strategies of Ze are derived: internal adaptation (filtering of rare events) and external adaptation (niche construction). Within the proposed framework: (1) the arrow of time emerges from the decrease of τ_Z during T-events; (2) aging is interpreted as the dominance of the filtering strategy; (3) quantum entanglement corresponds to Ze generated by a common parent; (4) the double-slit experiment is reinterpreted through strategy choice; (5) spacetime is constructed from partial order and the commutation matrix of POVMs. Ze Theory offers a coherent interpretive framework for quantum mechanics, consistent with evolutionary epistemology. Open problems include deriving the Born rule from selection pressure, Lorentz invariance from Ze network dynamics, and the emergence of gravity.
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.
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.
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.
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.