标题： 量子引力理论 显示英文标题

标题： A Gravitational Theory of the Quantum

摘要： 通过一种有限、现实的局部因果理论，寻求量子物理和引力物理的综合，其中引力不仅在非相干测量期间起着关键作用，而且在非非相干的幺正演化期间也起着关键作用。 不变集理论建立在一个紧致分形类似子集$I_U$的几何特性上，该子集属于宇宙状态空间，假设宇宙在其上演化，并且物理定律假设由此得出。 与$I_U$的优先性一致，定义了一个非欧几里得（因此是非经典的）状态空间度量$g_p$，它与数论中的$p$-adic 度量相关，其中$p$是一个大但有限的毕达哥拉斯素数。 在$I_U$上的不确定态使用复希尔伯特态来描述，但仅当它们的振幅平方是有理数且对应的复相位角是$2 \pi$的有理倍数时才如此。 这样的希尔伯特态必然与具有无理平方幅值或无理相位角的态保持$g_p$的距离。 $I_U$的间隙分形性质解释了量子互补性，并通过有理角度和角度余弦之间的通用数论不和谐性进行数值表征。 贝尔不等式，其违反与局域实在论不一致，被证明与任何有限精度实验中被违反的不等式形式保持$g_p$的距离。 通过$I_U$的计算不可约性解决了延迟选择悖论。 薛定谔方程和狄拉克方程描述了在$I_U$上的演化，在$p=\infty$的奇异极限下。 相比之下，提出了在$I_U$上爱因斯坦场方程的扩展，在$p \rightarrow \infty$时它平滑地减少到广义相对论。给出了关于暗宇宙的新提议以及消除经典时空奇点的方法，并概述了实验意义。 显示英文摘要

摘要： The synthesis of quantum and gravitational physics is sought through a finite, realistic, locally causal theory where gravity plays a vital role not only during decoherent measurement but also during non-decoherent unitary evolution. Invariant set theory is built on geometric properties of a compact fractal-like subset $I_U$ of cosmological state space on which the universe is assumed to evolve and from which the laws of physics are assumed to derive. Consistent with the primacy of $I_U$, a non-Euclidean (and hence non-classical) state-space metric $g_p$ is defined, related to the $p$-adic metric of number theory where $p$ is a large but finite Pythagorean prime. Uncertain states on $I_U$ are described using complex Hilbert states, but only if their squared amplitudes are rational and corresponding complex phase angles are rational multiples of $2 \pi$. Such Hilbert states are necessarily $g_p$-distant from states with either irrational squared amplitudes or irrational phase angles. The gappy fractal nature of $I_U$ accounts for quantum complementarity and is characterised numerically by a generic number-theoretic incommensurateness between rational angles and rational cosines of angles. The Bell inequality, whose violation would be inconsistent with local realism, is shown to be $g_p$-distant from all forms of the inequality that are violated in any finite-precision experiment. The delayed-choice paradox is resolved through the computational irreducibility of $I_U$. The Schr\"odinger and Dirac equations describe evolution on $I_U$ in the singular limit at $p=\infty$. By contrast, an extension of the Einstein field equations on $I_U$ is proposed which reduces smoothly to general relativity as $p \rightarrow \infty$. Novel proposals for the dark universe and the elimination of classical space-time singularities are given and experimental implications outlined.