量子引力理论
A Gravitational Theory of the Quantum
摘要：
量子和引力物理学的合成是通过一个有限的，现实的，局部因果理论，其中引力不仅在退相干测量过程中，而且在非退相干幺正演化过程中起着至关重要的作用。不变集理论是建立在宇宙状态空间的一个紧凑的分形子集$I_U$的几何性质上的，宇宙被假设在这个子集上演化，物理定律被假设从这个子集中推导出来。与$I_U$的首要性相一致，定义了一个非欧几里德（因此也是非经典的）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。$I_U$上的不确定状态可以用复希尔伯特状态来描述，但前提是它们的平方振幅是有理数，并且对应的复相位角是$2 π$的有理数倍数。这样的希尔伯特态必然是$g_p$ -远离具有无理平方振幅或无理相位角的状态。$I_U$的有隙分形性质解释了量子互补性，并在数值上以有理角和角的有理余弦之间的一般数论不相容性为特征。贝尔不等式，其违反将不符合当地的现实主义，被证明是$g_p$ -远离所有形式的不等式，违反任何有限精度的实验。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$I_U$在$p=\infty$奇异极限下的演化。与此相反，提出了一个扩展的爱因斯坦场方程的$I_U$光滑约化为广义相对论作为$p \rightarrow \infty$。新的建议，暗宇宙和消除经典时空奇点给出和实验的影响概述。
英文摘要：
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 $2 π$. 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 Schrödinger 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.
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