[Paper Review] Physical unknowables

Svozil Karl|arXiv (Cornell University)|Jan 15, 2007

Quantum Mechanics and Applications4 citations

TL;DR

This paper explores physical unknowables—limits to omniscience, omnipredictability, and omnipotence—by reducing them to recursively unsolvable problems. It argues that quantum indeterminacy, classical chaos, and Gödel-Turing undecidability impose fundamental, irreducible limits on physical knowledge, suggesting that randomness in both classical and quantum domains may stem from deep logical and computational constraints rather than mere epistemic ignorance.

ABSTRACT

A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.

Motivation & Objective

• To investigate the existence of fundamental physical limits to knowledge, prediction, and control, beyond mere epistemic uncertainty.
• To examine whether physical unknowables arise from logical incompleteness (Gödel-Turing), classical chaos, or quantum indeterminacy.
• To challenge the assumption of physical determinism and the possibility of a theory of everything by identifying intrinsic limits to computability and predictability.
• To explore whether classical and quantum randomness are ontologically distinct or both rooted in deeper undecidability and contextuality.
• To propose that value indefiniteness and contextuality in quantum mechanics may reflect limitations in physical description rather than intrinsic randomness.

Proposed method

• Reduction of physical unknowables to recursively unsolvable problems, leveraging results from computability theory and logic.
• Analysis of classical chaotic systems as exhibiting instability under initial condition variations, leading to practical and theoretical unpredictability.
• Examination of quantum indeterminacy through the lens of value indefiniteness, complementarity, and contextuality (Kochen-Specker, Bell-type theorems).
• Use of thought experiments involving indistinguishable random sources (e.g., 'Born' vs. 'Poincaré' boxes) to test operational distinguishability of classical and quantum randomness.
• Application of operational and normalization criteria (von Neumann, Samuelson) to assess the consistency of probabilistic models.
• Speculative reconstruction of physical reality based on undecidability, granular spacetime, and epistemic interpretations of mixed states and contextuality.

Experimental results

Research questions

• RQ1 Can physical unknowables be formally reduced to problems that are recursively unsolvable?
• RQ2 To what extent is classical chaos a source of physical unknowability, and is it fundamentally different from quantum indeterminacy?
• RQ3 Is the randomness in quantum mechanics ontic or epistemic, and can it be traced to contextuality or measurement context translation?
• RQ4 Can the distinction between classical and quantum randomness be operationally tested, and if so, under what conditions?
• RQ5 What are the implications of Gödel-Turing undecidability for the possibility of a complete physical theory or a theory of everything?

Key findings

• Physical unknowables—lack of omniscience, omnipredictability, and omnipotence—are provably unavoidable due to reduction to recursively unsolvable problems.
• Classical chaos leads to practical unpredictability, but such systems may still be formally computable, making their unknowability epistemic in nature.
• Quantum indeterminacy, including value indefiniteness and contextuality, cannot be explained by hidden variables or classical determinism, as shown by Kochen-Specker and Bell-type theorems.
• There exists no operational method to distinguish between classical and quantum random sources (e.g., 'Born' vs. 'Poincaré' boxes) when no labels or hints are given.
• The assumption of classical continua may be a convenient abstraction; abandoning it could resolve apparent paradoxes in classical randomness.
• Mixed quantum states may be epistemic, representing ignorance of underlying pure states, and quantum randomness may arise from context translation rather than intrinsic indeterminism.