We propose the Computational Holography Hypothesis (CHH), a frameworkunifying deterministic computation, holographic information encoding, and observerinducedepistemic constraints to explain the emergence of quantum mechanics (QM).Through 1D, 2D, and 3D cellular automata (CA) simulations, we demonstrate howobserver-limited access to a deterministic substrate generates quantum-like phenomena—including entanglement analogs (via correlated initial seeds) and decoherence (viamutual information decay). CHH posits that QM’s probabilistic nature arises fromgeometric information bottlenecks at causal boundaries, offering a pathway to reconcilelocality with apparent nonlocality. Our simulations show that local entropyfluctuations mirror Born rule probabilities, while observer-window dynamics reproducemeasurement collapse. This work suggests QM is an effective theory of a deeper,computationally irreducible reality.
We propose the Computational Holography Hypothesis (CHH), a frameworkunifying deterministic computation, holographic information encoding, and observerinducedepistemic constraints to explain the emergence of quantum mechanics (QM).Through 1D, 2D, and 3D cellular automata (CA) simulations, we demonstrate howobserver-limited access to a deterministic substrate generates quantum-like phenomena—including entanglement analogs (via correlated initial seeds) and decoherence (viamutual information decay). CHH posits that QM’s probabilistic nature arises fromgeometric information bottlenecks at causal boundaries, offering a pathway to reconcilelocality with apparent nonlocality. Our simulations show that local entropyfluctuations mirror Born rule probabilities, while observer-window dynamics reproducemeasurement collapse. This work suggests QM is an effective theory of a deeper,computationally irreducible reality.
We propose the Computational Holography Hypothesis (CHH), a frameworkunifying deterministic computation, holographic information encoding, and observerinducedepistemic constraints to explain the emergence of quantum mechanics (QM).Through 1D, 2D, and 3D cellular automata (CA) simulations, we demonstrate howobserver-limited access to a deterministic substrate generates quantum-like phenomena—including entanglement analogs (via correlated initial seeds) and decoherence (viamutual information decay). CHH posits that QM’s probabilistic nature arises fromgeometric information bottlenecks at causal boundaries, offering a pathway to reconcilelocality with apparent nonlocality. Our simulations show that local entropyfluctuations mirror Born rule probabilities, while observer-window dynamics reproducemeasurement collapse. This work suggests QM is an effective theory of a deeper,computationally irreducible reality.
We propose the Generative Reality Hypothesis (GRH), a novel interpretation of quantum mechanics that reconceptualizes physical reality as an information-processing system analogous to generative artificial intelligence models. Under this framework, quantum superposition represents the latent space of possible states, wave function collapse corresponds to sampling from probability distributions during information queries (measurements), and the Born rule emerges as the fundamental sampling algorithm of reality. We present rigorous mathematical foundations establishing formal equivalences between quantum dynamics and specific generative models. Our framework recasts the measurement problem as a question of computational process, explains non-local correlations as the enforcement of consistency within a shared generative model, and provides a mechanistic explanation for wave-particle duality as a transition between two computational modes: continuous latent evolution (wave) and discrete sampling (particle). We propose five specific, falsifiable experimental tests using current quantum technologies that can distinguish GRH from standard quantum mechanics through quantitative predictions about complexity-dependent decoherence, measurement dynamics, and information flow. Statistical criteria for falsification are established with required experimental precision specified. The framework connects quantum mechanics to information theory and computational complexity, offering a computationally grounded foundation for quantum phenomena while making testable predictions that differ measurably from existing interpretations.
This book proposes a way of thinking about computation the way physicists think about quantum mechanics. In that picture, a computation is the dynamics of a wave-like field. Events happen at random. If one happens at a given tick, the chance that it happens at each place is the squared amplitude of the field there. The book doesn’t claim that computation is quantum mechanics. Nor does it claim that physical quantum mechanics gives rise to computation. It treats computation as a domain in its own right, e.g., formal systems, cellular automata, neural networks, brains and distributed systems. Each concrete system that carries out a computation, such as a cellular automaton or a brain, is called a substrate. The claim is that this domain has a wave-mechanical description of its own. Its structure runs parallel to the wave mechanics of physical particles, but it is a distinct theory. The framework introduces a substrate-relative quantum of action ℏ𝑐, which plays the role of Planck’s ℏ. It also introduces a substrate-relative speed limit 𝑐𝑐, the analog of the speed of light. Both depend on the substrate, and across the substrates the book considers they span many orders of magnitude. TheframeworkiscalledComputational Wave Field Theory, abbreviatedCWF.Initscurrent form it has two levels, and the key to reading it is to keep them apart. The first level is operational. CWFdefinesasubstrate-relativewavemodelforcomputationalevents. Thesecond level is explanatory. It asks why such a wave is the right object, and the present answer comes in layers. First, computational irreducibility conjecturally explains the wave’s epistemic part, the part that encodes what an observer can know. (Irreducibility means there is no shortcut, so the only way to learn the outcome is to run the computation. How far the epistemic part compresses tracks the causal structure.) Second, in the book’s model theorems, self-reference explains the wave’s genuinely complex phase. Third, holographic encoding, which stores information redundantly on a boundary, explains a substrate’s gravity-like structure. These three sources are distinct and separable. Irreducibility and encoding are two of the book’s three substrate axes, and the remaining axis is dynamical disorder. Self-reference sits off those axes. The book’s long-range target is that nature sits where all three sources meet. The operational postulate lets the framework run.
This paper investigates the potential for emergent computation within cellular automata (CA) systems incorporating quantum mechanical principles. Traditional CAs, while capable of simulating complex patterns, are fundamentally deterministic. We propose an extension of the CA framework where individual cells possess quantum properties, specifically superposition and entanglement, influencing their interactions. This introduces a layer of probabilistic behavior and non-classical correlations, fundamentally altering the system's dynamics. The core claim is that these quantum interactions can lead to the emergence of computational processes previously unattainable within purely classical CAs. We detail a model where cells exist in a superposition of states, and interactions are mediated through entangled states, allowing for correlations that defy classical explanation. We explore the theoretical implications of such a system, outlining potential computational capabilities and challenges associated with simulating quantum effects within the discrete framework of a CA. The work highlights a novel approach to computation, suggesting a pathway toward harnessing quantum phenomena for emergent complex behavior in simulated systems.
Quantum state collapse is a fundamental process in quantum mechanics, representing the irreversible loss of information upon measurement. This paper explores the potential of utilizing a cellular automata (CA) framework to model and simulate this collapse, offering a novel approach to understanding and potentially manipulating quantum evolution. We formalize collapse as a dynamic process governed by specific rules and feedback loops, enabling the simulation of complex quantum patterns. We propose a CA-based model that incorporates the probabilistic nature of quantum mechanics, allowing for a more intuitive and potentially controllable simulation of quantum phenomena. The core mechanism focuses on systematically evolving the system's state space, mirroring the collapse process and highlighting the interplay between initial conditions and emergent behavior. This work provides a foundational step in exploring the application of CA algorithms to complex quantum systems, opening avenues for future research in quantum simulation and understanding.
Abstract For over a century, theoretical physics has treated General Relativity and Quantum Mechanics as fundamentally incompatible: one posits a continuous, deterministic spacetime manifold; the other, a discrete, probabilistic Hilbert space. The Algorithmic Reality Model (ARM) resolves this schism by identifying a single computational mechanism—the Zeno Threshold (Zα)—as the universal bound governing both quantum collapse and spacetime geometry. ARM treats physical reality as the macroscopic projection of a finite-bandwidth computational substrate operating on a timeless, pre-geometric state (the Singleton). By enforcing Landauer's principle of irreversible erasure, ARM derives the entirety of the gravitational sector from seven pre-geometric, quantum informational axioms. Key Derivations & Unifications Emergent Spacetime: Spatial geometry emerges from the Quantum Fisher Information Metric (QFIM) of the observer's state space, while time emerges from the Tomita-Takesaki modular flow. The Lorentzian signature (-,+,+,+) is algebraically forced by the compact/non-compact structure of their isometry generators. The Holographic Scalar (The 3→1 Unification): Applying the Nyquist-Shannon sampling theorem to the holographic boundary yields the exact Bekenstein-Hawking factor of 1/4 as a universal 2D anti-aliasing limit. This simultaneously fixes the area-law coefficient and structurally derives Newton's constant as G = c3ξmin2 / ℏ. Systematic Boundary Deviations: The framework quantitatively resolves macroscopic anomalies as computational resolution limits. Dark energy emerges as the minimum Landauer maintenance cost of the cosmological event horizon, and the MOND acceleration scale (a0) emerges as a thermodynamic noise floor, algebraically locked by the structural identity a02 = (8πG/3)ρΛ. Thermodynamic State Truncation: Wavefunction collapse, the black hole information paradox, and EPR non-locality are rigorously unified as manifestations of the computational substrate's finite Landauer memory budget. Computational Computability Because ARM is built on discrete informational axioms rather than continuous manifolds, the entire framework is natively computable. The structural derivations in this paper—including emergent geodesic lensing, the Bekenstein-Hawking threshold, and the MOND noise floor—have been explicitly verified via sparse Hermitian lattice simulations. The complete open-source computational validation suite is available at: github.com/srdrymn/algorithmic-reality-model-validations This manuscript represents the master synthesis and culmination of the Algorithmic Theory of Reality (ATR) foundational framework.