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Planck Length & the Resolution of Zeno's Paradox

McHugh, Joshua Thomas

Published Dec 12, 2025• 0 citations
Publisher

Abstract

This brief note proposes a resolution to Zeno’s paradox by quantising Reason. Arrival is defined as a collapse event governed by Reason, whose limiting behaviours reproduce the paradox’s extremes. Planck-scale discretisation, constrained by the causal limit c, yields a minimal operator framework in which motion emerges as a sequence of discrete epistemic events.

DOI
10.5281/zenodo.17906876

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Europhysics Letters (EPL)•Apr 1, 2013•2 citations
This brief note proposes a resolution to Zeno’s paradox by quantising Reason. Arrival is defined as a collapse event governed by Reason, whose limiting behaviours reproduce the paradox’s extremes. Planck-scale discretisation, constrained by the causal limit c, yields a minimal operator framework in which motion emerges as a sequence of discrete epistemic events.
The Quantum Measurement Problem — the absence of any physical mechanism by which deterministic, unitary Schrödinger evolution transitions into a discrete, probabilistic classical outcome — remains the central open problem in the foundations of quantum mechanics. While environmental decoherence explains the suppression of quantum interference, it does not explain why or when a single outcome is realized. This paper resolves the measurement problem within the Algorithmic Theory of Reality (ATR). By treating the universe as a finite-bandwidth information-processing architecture, we demonstrate that wavefunction collapse is not a mystical observer effect, but a mandatory thermodynamic memory-management protocol. Key Results: The Collapse Threshold: We prove that when a microscopic superposition entangles with a macroscopic apparatus, the entanglement entropy grows until the local Bennett-Landauer processing cost exceeds the local holographic energy budget. This forces a non-unitary state truncation. Quantitative Timescale: The derived threshold yields a quantitative collapse timescale (τc) that mathematically matches the experimentally observed decoherence time. Derivation of the Born Rule: Given pointer-state orthogonality (from decoherence), we rigorously derive the Born Rule (pi = |ci|2) by formulating the forced state truncation as a constrained thermodynamic optimization problem that minimizes the Kullback-Leibler divergence (algorithmic information loss). Scale Unification: The exact same Bennett-Landauer limit that dictates the macroscopic boundaries of the universe (Dark Energy) and galaxies (the MOND scale) is shown to govern the microscopic limits of quantum coherence. The ATR framework mathematically determines when collapse must occur, with what statistics, and in which basis, reducing the single-outcome problem to a single, structurally necessary axiom (the Lüders update). Supplementary Material: The algebraic derivation of the Born Rule (via KL-divergence minimization and Lagrange multipliers), the exponential growth of entanglement entropy, and Monte Carlo statistical validations are independently reproducible via the companion computational verification script, available at: https://github.com/srdrymn/atr-verify-wavefunction-collapse
Planck’s constant sets the fundamental scale at which classical descriptions of nature give way to quantum behaviour, yet it is typically introduced as an empirical parameter rather than derived from first principles. In this work, we show that the existence of a universal minimum unit of action follows necessarily from finite physical registrability. Within the Relational Information framework, time is treated not as a fundamental background parameter but as a relational measure of distinguishable change. We demonstrate that the capacity to register successive events is bounded by physical constraints on localization, energy concentration, and gravitational stability, leading to a maximum realizable environmental cadence. Saturation of this cadence implies a minimum resolvable temporal interval and a corresponding minimum energy–time product. This minimum action scale emerges operationally as the cost of sustaining a single distinguishable registration and is shown to coincide with Planck’s constant. Quantization is thus reinterpreted as a consequence of finite observational bandwidth rather than as evidence for an intrinsically discrete substrate of time or matter. The results provide a quantitative anchor for the Relational Information framework and offer a unified explanation for the emergence of quantum limits without modifying established physical laws.
This paper proposes Informational Flow Ontology (IFO), a minimal metaphysical framework that derives the fundamental categories of reality—time, matter, energy, consciousness, intelligence, free will, and aesthetic experience—from a small set of axioms centered on information, causality, and collapse. IFO treats collapse (the transition from possibility to determinacy) as the primitive event, information as its substrate, and causality as information in motion. Time is identified with causality itself, quantified as the count of micro-collapse events. Energy emerges as the collapsed form of time. The framework posits structural isomorphism between the physical and conscious domains, both governed by a single conservation principle (causal-energy conservation), generalizing Noether's theorem beyond physics. Beauty is defined as the perception of multi-aspect alignment, providing an internal epistemic criterion. The framework is internally closed, structurally minimal, and compatible with frontier physics (causal set theory, quantum information) and classical metaphysical traditions (Spinoza, Leibniz, Whitehead).
The conceptual difficulties of Quantum Mechanics—manifesting as paradoxes of locality, causality, and realism—arise from the fundamental assumption that spacetime is a contin- uous, metric geometry. We propose an alternative framework: The Quantum Loom, which models the vacuum as a discrete, incompressible superfluid network of Planck-scale nodes. By integrating the ER=EPR conjecture with Superfluid Vacuum Theory, we demonstrate that ”Metric Locality” is an emergent approximation, while fundamental reality is governed by ”Topological Connectivity.” In this paper, we apply this framework to resolve eight major foundational paradoxes. We show that ”Temporal Paradoxes” (Wheeler’s Delayed Choice, Quantum Eraser) are re- solved by viewing entanglement as global tension on a closed topological circuit. ”Interaction Paradoxes” (Hardy, Elitzur-Vaidman, Klein) are explained by the non-local interaction of strain fields and dielectric breakdown of the vacuum lattice. Finally, ”Observer Paradoxes” (Wigner’s Friend, Quantum Zeno, and Schr¨odinger’s Cat) are demystified as phase transi- tions: macroscopic superposition is strictly limited by the Topological Jamming density of the network, forcing massive systems to ”flash freeze” into definite states. This model recov- ers objective realism without abandoning non-locality, suggesting that the ”spooky” features of quantum mechanics are simply the hydrodynamics of a pre-stressed vacuum web.