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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.07264 |
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| _version_ | 1866909102229159936 |
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| author | Frugone, Jose A. Pereira |
| author_facet | Frugone, Jose A. Pereira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum state collapse on a Riemann-Hilbert space modulo observation Frugone, Jose A. Pereira Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Quantum state collapse on a Riemann-Hilbert space modulo observation |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.07264 |