论文标题
离散的希尔伯特空间，诞生的规则和量子重力
Discrete Hilbert Space, the Born Rule, and Quantum Gravity
论文作者
论文摘要
量子引力效应表明，planck长度的阶段的长度最小或时空间隔。这反过来表明，希尔伯特空间本身可能是离散的，而不是连续的。一个含义是，不存在一些非常小的阈值的量子状态。在没有崩溃的量子力学中，埃弗里特所谓的小牛分支的排除对于出生的规则是必不可少的。我们在量子重力的背景下讨论了这一点，表明离散模型（例如简单或晶格量子重力）确实提出了一个具有最小规范的离散希尔伯特空间。这些考虑因素与量子重力产生的变形历史（时空几何以及物质场）中发现的细晶粒的最终水平有关。
Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.
