Summers, Benjamin (2026) The Nonexistence of the Instantaneous Present. [Preprint]

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Abstract

Much of theoretical physics rests on the idealization that a physical system possesses a complete state at each instant of time—a state sufficient to determine all future evolution. We present independent arguments that this idealization is physically unjustified. First, the state at a temporal point is constructed as the limit of states over intervals; the ε-δ definition of a limit explicitly excludes the limit point from its own construction, guaranteeing convergence of the value in the neighborhood of the point while remaining formally silent on what properties the point itself carries. Second, the joint application of quantum mechanics and general relativity guarantees that the limiting process δt → 0 physically self-destructs at the Planck scale; quantum-mechanical clock bounds independently constrain the measurability of time intervals from below; and special relativity independently requires infinite energy to compress proper time to zero—three distinct mechanisms by which established physics prevents the temporal point from being physically realized. Third, quantum field theory has known since the 1940s that physics evaluated at a spacetime point is pathological—a fact encoded in ultraviolet divergences, systematized by the renormalization program, and given physical interpretation by Wilson's demonstration that the divergences reflect the finite domain of validity of any effective description, not a deficiency of any particular calculational method. These lines of evidence converge on a single conclusion: the instantaneous present—a temporal point carrying complete dynamical information—does not exist. Any dynamical framework that presupposes it, including the Chapman-Kolmogorov factorization condition central to the theory of stochastic processes, rests on an assumption that established physics contradicts.

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Item Type:	Preprint
Creators:	Creators Email ORCID Summers, Benjamin bsummers@adagioinstitute.org 0000-0002-1725-8492
Keywords:	stochastic indivisibility, Chapman-Kolmogorov condition, instantaneous present, measurement problem, temporal limits, Planck scale, renormalization, stochastic-quantum correspondence
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Depositing User:	Benjamin Summers
Date Deposited:	23 Mar 2026 21:00
Last Modified:	23 Mar 2026 21:00
Item ID:	28724
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Date:	20 March 2026
URI:	https://philsci-archive.pitt.edu/id/eprint/28724

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