turbulence与量子引力的类比：超越Kolmogorov的1941年理论
Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory
摘要：
最近，基于量子涨落一般性质的简单论证已经表明，时空的量子涨落服从与均匀不可压缩湍流中速度涨落相同的标度律，如Kolmogorov 1941（K41）标度理论所描述的。然而，很少有人注意到的是，这种类比排除了分形量子时空的可能性，这与量子引力研究中越来越多的证据相矛盾。在本注中，我们证明了分形量子时空的概念可以通过将湍流和量子引力之间的类比扩展到K41理论的范围之外来恢复。特别是，它表明，最近的Horava-Lifshitz方案的量子引力的分形量子时空的兼容性，意味着奇异的量子波函数。最后，我们提出了一个基于扩展自相似技术的操作过程，来检验量子引力涨落的（多）标度特性。
英文摘要：
Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.
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