Quantum Mechanics on a background modulo observation
| Title: | Quantum Mechanics on a background modulo observation |
|---|---|
| Authors: | Frugone, Jose A. Pereira |
| Publication Year: | 2023 |
| Collection: | Mathematics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics |
| Subject Terms: | Quantum Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematical Physics |
| More Details: | In this work we will answer the following question: What remains of Quantum Mechanics when we transform the background space-time into a space modularized by observation or measurement regions ? This new moduli space is constructed by identifying regions of space-time where quantum phase comparison (observation, measurement) is implied. We call it Observation Modular space (OM-space). In addition we replace in QM statements the Plank constant (h) by the quantity $\zeta_0 4 \pi^2$ (where $\zeta_0$ is the Plank Length) or otherwise, replacing $P_0$ (the Planck Momentum) by $4 \pi^2$. This maps Quantum Mechanics into a very rich dual Number Theory which we call Observation Modular Quantum Mechanics (OM-QM). We find the OM-dual to the Dirac Equation, the quantum Wave Function and a free particle's mass. The OM-QM counterparts of the Energy turns out to be a simple function of the zeroes of the Riemann zeta function. We also find the OM-QM correspondents to the electron spin, the electron charge, the Electric Field and the Fine Structure Constant. We also find the OM-QM correspondents of the Heisemberg uncertainty relation and Einstein's General Relativity Field equation emerging as certain limits of a unique OM-QM equation. We also get the OM-QM correspondents of the Gravitational Constant and the Cosmological Constant. We find the analog of holography in the OM-QM side and we get an interpretation of spin as a high dimensional curvature. An interpretation of the OM-QM correspondence is proposed as giving the part of QM information which is not measurement or observation dependent. Some potential future applications of this correspondence are discussed. Comment: 23 pages, 5 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2311.12493 |
| Accession Number: | edsarx.2311.12493 |
| Database: | arXiv |
| Description not available. |