标题： 因果结构中量子涨落的角谱 显示英文标题

标题： Angular spectrum of quantum fluctuations in causal structure

摘要： 标度论证用于限制宏观因果钻石边界上由普朗克尺度真空涨落引起的因果一致量子引力所产生的畸变的角谱。位移的小角度谱来源于一种尺度不变性：在横向物理分离$c\tau\ll R$处，半径为$R$的因果钻石表面上垂直于表面的畸变的方差和涨落率应仅依赖于$\tau$，其归一化由普朗克时间$t_P$确定，并且不应依赖于$R$。 对于尺度$R$上的测量，该原理导致在角尺度$\Theta$、$\langle\delta\tau^2\rangle_\Theta\simeq\tau\:\!t_p\sim\Theta R\:\!t_P/c$和角功率谱$C_\ell\sim (R\:\!l_P)/\ell^3$上的方差具有普遍标度，位于$\ell\gg1$。 该谱与基于因果相干虚拟零引力冲击的关系模型的全息噪声一致，这是对所有$\ell$的一般性猜想。 高$\ell$的缩放与某些其他量子模型的预测形成对比，这些模型在角波数$\ell$上相差一个幂次，并被证明会预测来自远处源的图像过度模糊。 显示英文摘要

摘要： Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: the variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius $R$ at transverse physical separation $c\tau\ll R$ should depend only on $\tau$, with a normalization set by the Planck time $t_P$, and should not depend on $R$. For measurements on scale $R$, the principle leads to universal scaling for variance on angular scale $\Theta$, $\langle\delta\tau^2\rangle_\Theta\simeq\tau\:\!t_p\sim\Theta R\:\!t_P/c$, and angular power spectrum $C_\ell\sim (R\:\!l_P)/\ell^3$ at $\ell\gg1$. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all $\ell$. The high $\ell$ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wavenumber $\ell$ and are shown to predict excessive blurring of images from distant sources.