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April 3, 20260 citationsOpen Access

Windowed Action Formalism and Five Experimental Manifestations of Finite-Domain Localization in Quantum Physics

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SHShawn Hackett

Key Points

  • This work aims to demonstrate the importance of finite-domain localization in quantum physics and its implications.
  • Introduces a windowed action principle using a smooth window function
  • Analyzes five different experimental phenomena in quantum physics
  • Derives windowed Noether identities relevant to local dynamics
  • Examines non-conservation of local currents due to domain restrictions
  • Compares findings across distinct quantum physical regimes
  • Identifies a single localization window responsible for observable effects across all cases
  • Shows that apparent non-conservation of currents arises from finite-domain restrictions
  • Demonstrates that finite-domain localization serves as a unifying principle in quantum physics
  • Validates that modifications to traditional quantum mechanics were not necessary to explain findings
  • Links results to established phenomena like the Unruh effect and dynamical Casimir effect

Abstract

Time in fundamental physics is typically treated as a globally defined background parameter,despite the fact that all physical interactions are instantiated over finite temporal and spatial do-mains. In practice, detector couplings are switched on and off, boundaries are driven for limiteddurations, quenches occur over finite ramps, and scattering processes involve nonzero preparationand detection times. These finite-domain features are usually treated as technical or experimentalnecessities rather than as physically meaningful structure. In this work, I show that the formalconsequences of restricting a field-theory action to a finite spacetime domain via a smooth windowfunction ♢(x) are not auxiliary but arise in a unified way across a wide range of experimentally es-tablished phenomena. Introducing a windowed action principle yields windowed Noether identitiesthat preserve all local dynamics while explicitly restricting the operational domain of conservedquantities. Apparent non-conservation of local currents in the boundary layer is not a symmetryviolation but an exact consequence of domain restriction, mathematically identical in structure toopen-system flux terms in decoherence theory. Applying this framework, I analyze five distinctexperimental cases: the timelike Unruh effect in trapped-ion detectors, the dynamical Casimir ef-fect in superconducting circuits, quench-induced currents in cold-atom systems, ultrafast coherentcontrol with femtosecond laser pulses, and finite-time scattering theory. Across all five cases, asingle localization window and one experimentally constrained boundary-layer timescale accountfor observed spectral structure, apparent non-conservation, and finite-time effects without modi-fying the underlying quantum mechanics or quantum field theory. The results demonstrate thatfinite-domain localization is not a case-specific artifact but a unifying formal principle across thesephysically distinct regimes.

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Cite This Study

Shawn Hackett (2026) studied this question.

synapsesocial.com/papers/69cf5ced5a333a821460a828https://doi.org/10.5281/zenodo.19363333
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