WITHDRAWN

jiazheng liu

Published Aug 10, 2025• 0 citations

Abstract

The fundamental nature of time—continuous or discrete—remains unresolved across physics, mathematics, and philosophy. This work introduces , the minimum observable response time, as a universal lower bound on temporal resolution derived from thermodynamic and information-theoretic principles. We prove that, under the constraint, continuous-time and discrete-time formulations become observationally equivalent: no conceivable experiment can distinguish between them. This equivalence arises because any measured time series is inherently quantized into multiples of , regardless of the underlying temporal structure. We formalize this result mathematically, extend it to a generalized uncertainty relation for time measurement, and demonstrate its consistency with known physical limits such as the Nyquist–Shannon sampling theorem and the Heisenberg uncertainty principle. Philosophical implications are discussed, showing that defines a hard epistemic boundary for empirical science regarding the ontology of time.

DOI: 10.31234/osf.io/fuwmq_v1

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