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February 2, 20260 citationsOpen Access

Universal Finite Resolution: A Unified Causal Foundation for Time, Entropy, and Quantum Gravity

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ARAlexei A. Rivera

Key Points

  • The research aims to explore a unified causal foundation underlying time, entropy, and quantum gravity, challenging existing theories.
  • Proposed the Universal Finite Resolution hypothesis based on bandwidth-limited systems.
  • Modeled the universe as a self-organized critical system similar to a sand pile cellular automaton.
  • Derived implications for the arrow of time, origin of entropy, wave function collapse, and ultraviolet cutoff.
  • Introduced a non-zero integration time that requires a breakdown of unitarity at the Planck scale.
  • Offered a new approach incorporating decoherence into the Von Neumann equation.
  • Provided a testable framework applicable across various physical systems at different energy scales.

Abstract

What if physical reality, from an electron to the universe itself, cannot perceivethe Present, but only an approximation of the Present? We propose the hypothesisof Universal Finite Resolution, which challenges the assumption of continuoustime fundamental to standard Quantum Mechanics and General Relativity. Drawingupon the modern concept of a ”Bandwidth-Limited System,” we posit that all physicalinteraction is bounded by a non-zero integration time τmin. Modeling our universe as aself-organized critical system analogous to a ”Sand Pile” cellular automaton, we derivethat this temporal lower bound necessitates a breakdown of unitarity at the Planckscale. This introduces an intrinsic, irreducible decoherence term to the Von Neumannequation, offering a unified causal mechanism for: (1) the Arrow of Time, (2) theorigin of Entropy, (3) objective Wave Function Collapse, and (4) a natural ultravioletcutoff for singularities. Unlike String Theory or Loop Quantum Gravity, which modifyspacetime geometry or particle content, UFR adjusts the processing rate of the vacuumitself, governed by a Twistor-formulated mass-scaled Lindblad Master Equation. Thisframework is experimentally testable across independent physical systems at vastlydifferent energy scales and offers immediate retroductive solutions to a wide range ofexisting anomalies.

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Cite This Study

Alexei A. Rivera (2026) studied this question.

synapsesocial.com/papers/6980ffa4c1c9540dea812462https://doi.org/10.5281/zenodo.18426202
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