标题： 量子力学在观测背景下的模运算 显示英文标题

标题： Quantum Mechanics on a background modulo observation

摘要： 在本工作中，我们将回答以下问题：当我们将背景时空转化为由观测或测量区域模化的空间时，量子力学还剩下什么？这个新的模空间是通过识别量子相位比较（观测、测量）被暗示的空间时间区域来构建的。我们称之为观测模空间（OM空间）。此外，我们在量子力学陈述中将普朗克常数（h）替换为量$\zeta_0 4 \pi^2$（其中$\zeta_0$是普朗克长度）或者否则，将$P_0$（普朗克动量）替换为$4 \pi^2$。这将量子力学映射到一个非常丰富的对偶数论，我们称之为观测模量子力学（OM-QM）。我们找到了狄拉克方程、量子波函数和自由粒子质量的OM对偶。能量的OM-QM对应物实际上是黎曼zeta函数零点的简单函数。我们还找到了电子自旋、电子电荷、电场和精细结构常数的OM-QM对应物。我们还找到了海森堡不确定性关系和爱因斯坦广义相对论场方程的OM-QM对应物，它们作为唯一OM-QM方程的某些极限出现。我们还得到了引力常数和宇宙学常数的OM-QM对应物。我们在OM-QM方面找到了全息理论的类似物，并得到了自旋作为高维曲率的解释。提出了OM-QM对应关系的一种解释，即提供不依赖于测量或观测的量子力学信息部分。讨论了这种对应关系的一些潜在未来应用。 显示英文摘要

摘要： 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.