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The Quantum Field Paradox: Resolution via Saladini's Theorem

Gabriele Saladini

Published Feb 17, 2026• 0 citations
Publisher

Abstract

This paper addresses the Infinite Quantum Field Paradox. Using the Saladini Theorem, it proves that divergences arise only from the impossible assumption of infinite field mode processing.-Finite Capacity: Agents cannot access, process, or measure an infinite number of field modes simultaneously.-Logical Nullification: Divergences are non-operational for finite physical systems.-Systemic Collapse: The paradox is logically and physically nullified within finite comprehension.

DOI
10.5281/zenodo.18673032

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This paper addresses the Infinite Quantum Field Paradox. Using the Saladini Theorem, it proves that divergences arise only from the impossible assumption of infinite field mode processing.-Finite Capacity: Agents cannot access, process, or measure an infinite number of field modes simultaneously.-Logical Nullification: Divergences are non-operational for finite physical systems.-Systemic Collapse: The paradox is logically and physically nullified within finite comprehension.
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We present a resolution of the Wigner's Friend paradox within a framework of quantum mechanics (QM) on the hybrid space RxQ_{p}, where Q_{p} denotes the field of p-adic numbers, regarded as a model of discrete microscopic space at the Planck-Bronstein scale. In this framework, wavefunction collapse is not an independent postulate but a dynamical consequence of the Schrödinger equation with non-local Hamiltonians: wavefunctions localize onto compact supports during measurement interactions, producing definite pointer readings without the intervention of observers or the exchange of information between subsystems. We model both Wigner and his Friend as classical apparatuses and show that each produces a definite reading through independent applications of the collapse mechanism, thereby eliminating the conflict between their descriptions of reality. The framework is consistent with the principal no-go theorems in finite- and infinite-dimensional Hilbert spaces associated with extended Wigner's Friend scenarios -- including those of Frauchiger-Renner, Brukner, Bong et al., and Guérin et al. -- since it requires no agents capable of recording or reasoning about outcomes, thereby vacating the observer-dependent assumptions that drive those theorems. We illustrate the collapse mechanism explicitly through a toy model of a particle in a box, comparing the standard description with the new one. The non-locality intrinsic to QM on L2(RxQ_{p}) permits realism at the cost of locality, and the Absoluteness of Observed Events holds in our framework without requiring observer independence.
The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event horizon, namely, that the Hilbert space factorizes. While valid in quantum mechanics, this fails drastically in quantum field theory, and hence a deeper understanding of entanglement is required if further progress is to be made. Recently, ideas from algebraic quantum field theory have provided new insight into this issue, and show promise for elucidating the connection between entropy and horizons that underlies black hole thermodynamics.