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January 17, 20260 citationsOpen Access

When Is a Configuration Physical? Rethinking the Vacuum Selection Problem

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PNPeter Nero

Key Points

  • The central aim is to rethink vacuum selection in physics, challenging the assumption of uniform definition across configuration space.
  • Critically analyze existing vacuum selection methods in quantum gravity and cosmology.
  • Introduce the notion of conditional constructions in Hilbert spaces and effective field theories.
  • Examine how stability and spectral separation affect vacuum configurations.
  • Identification of disconnected regions in configuration space where physics is well defined.
  • Demonstration that traditional landscape scans are ineffective due to misassumptions about vacuum selection.
  • Shift in focus from counting vacua to discerning where physical definitions are valid.

Abstract

The problem of vacuum selection has resisted resolution across quantum gravity, string theory, cosmology, and effective field theory, often framed as choosing among vast landscapes using statistical or anthropic arguments. We argue that this difficulty reflects a mis-posed question: the implicit assumption that physics is defined everywhere in configuration space. Core physical structures—Hilbert spaces, probabilities, effective field theories, and renormalization group flows—are conditional constructions that presuppose stability, boundedness, and spectral separation. These conditions need not hold globally. Selection therefore cannot act pointwise on vacua, but only on admissible regions defined by dynamical and spectral inequalities. Such regions may be disconnected and inaccessible by continuous deformation, rendering standard landscape scans ineffective by construction. Recasting vacuum selection as an admissibility problem explains why existing approaches have struggled to converge and shifts emphasis from counting or weighting vacua to identifying where physics is well defined at all. The paper is intentionally theory-agnostic and aims to clarify the conceptual structure underlying selection rather than propose a new fundamental model.

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Cite This Study

Peter Nero (2026) studied this question.

synapsesocial.com/papers/696b2616d2a12237a9349574https://doi.org/10.5281/zenodo.18255208
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