时空几何测量的量子极限
Quantum limits to the measurement of spacetime geometry
摘要：
这封信分析了量子力学对时空几何测量精度的限制。通过将计算物理学应用于时钟系综，如GPS，我们提出了量子几何极限的协变版本，它指出，可以包含在半径为r，时间范围为t的四个时空体积中的时钟滴答声和探测器滴答声的总数小于或等于rt/pi x_P t_P，其中x_P，t_P是普朗克长度和时间。量子几何边界限制了在四体积时空中可以发生的事件或“操作”的数量，并且与全息边界相一致和互补，全息边界限制了在三体积时空中可以存在的比特数量。
英文摘要：
This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the physics of computation to ensembles of clocks, as in GPS, we present a covariant version of the quantum geometric limit, which states that the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to rt/pi x_P t_P, where x_P, t_P are the Planck length and time. The quantum geometric bound limits the number of events or `ops' that can take place in a four-volume of spacetime and is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a three-volume of spacetime.
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