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arXiv · 2402.07264

Quantum state collapse on a Riemann-Hilbert space modulo observation

Jose A. Pereira Frugone
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Abstract

In a previous work we constructed a new kind of moduli background space by identifying regions of space-time where an observation of space-time is implied. We called it Observation Modular space (OM-space). Quantum Mechanics (QM) on this moduli space gets mapped into a very rich and highly non trivial dual Number Theory which we call Observation Modular Quantum Mechanics (OM-QM). In this work we extend the scope of this modularization to include observations of quantum states. We call the resulting extended space Observation Modular Riemann-Hilbert space (OM-RH space). It has the mathematical structure of a Riemann Surface. We find the OM-QM analogue of quantum base states and mixed states. This allows us to find the OM-QM analogues to the quantum State Reduction postulate and the Born rule. The OM-QM analog to quantum state collapse turns out to be totally deterministic and unitary in OM-RH space. It is shown to be equivalent to an Elliptic Curve Encryption-decryption protocol. Finally we obtain the OM-QM analog of entangled quantum states. As an example we apply this to the OM-QM interpretation of the EPR experiment.

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Jose A. Pereira Frugone. 2024-02-11. Quantum state collapse on a Riemann-Hilbert space modulo observation. https://arxiv.org/abs/2402.07264

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