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February 8, 20260 citationsOpen Access

Integer Quantization from Global Constraint Resolution in Quantum Measurement

WHWilliam He

Key Points

  • The aim is to explore how quantization can be understood through global constraints imposed on continuous state spaces without altering quantum dynamics.
  • Develop a structural framework based on global constraint enforcement.
  • Analyze the role of symmetry, topology, and conservation laws in quantization.
  • Draw analogies with elliptic divisibility sequences to illustrate integer enforcement.
  • Establish that quantized observables can be reinterpreted as resolutions under global constraints.
  • Demonstrate that quantization can arise solely from the global structure without additional modifications to quantum mechanics.

Abstract

Discrete measurement outcomes are a defining feature of quantum mechanics, yet the origin of quantization itself remains conceptually unresolved. This work presents an interpretive and structural framework in which quantization arises from global constraint enforcement—due to symmetry, topology, and conservation laws—on continuous state manifolds. Standard quantized observables are reinterpreted as admissible resolutions under these constraints. A formal analogy with elliptic divisibility sequences illustrates rigid integer enforcement arising from global structure alone. The framework does not modify quantum dynamics, introduce collapse mechanisms, or posit hidden variables. The manuscript is currently under consideration at Foundations of Physics.

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Cite This Study

William He (2026) studied this question.

synapsesocial.com/papers/6988277b0fc35cd7a884650bhttps://doi.org/10.5281/zenodo.18506325
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