The limits of knowledge in classical physics resemble the quantum uncertainty relation

• URL: http://arxiv.org/abs/2503.23698v1
• Date: Thu, 27 Feb 2025 07:02:37 GMT
• Title: The limits of knowledge in classical physics resemble the quantum uncertainty relation
• Authors: David Theurel,
• Abstract summary: This article builds upon a recent analysis of the measurement process in Hamiltonian mechanics.<n>I prove a limitation on the information that can be obtained about a classical system by means of observations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove a thermodynamic limitation on the information that can be obtained about a classical system by means of observations: A direct analogue of the Robertson-Schr\"odinger quantum uncertainty relation controls the acquisition of information at the classical microscale. Central to this theorem is the notion of the "quality" of a measuring probe; a temperature-dependent strictly positive quantity that serves as a figure of merit of the probe, and that plays the role of $1/\hbar$ in the classical uncertainty relation. This study sets the stage for a new area of research into resource theories of classical measurement, in which high-quality measurements and high-information states of knowledge are the limited resources.

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