物理空间的数字量子描述与连续统描述
On a digital quantum description of physical space versus the continuum description
摘要：
实数连续统在力学和场论中很好地作为物理空间的模型。然而，这是一个动机良好和流行的想法，在基本普朗克尺度下，引力和量子效应的结合迫使我们重新评估空间（和时间）的概念，并期望某种离散性或粒度。在这里，我们研究了一个立方网格的点代表基本体积的空间，并推导出频谱的动量和波数，这是不一般的比例。对于有限网格，动量是有界的和离散的。不确定原理必须修正以反映小尺度空间非定域性，但在连续极限下，它与标准不确定原理是一致的。我们在这项工作中只考虑运动学，不讨论时间或能量或动力学演化。
英文摘要：
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum effects forces us to re-evaluate the concept of space (and time), and some sort of discreteness or granularity is expected. Here we study a cubic grid of points representing fundamental volumes of space and derive the spectra of momenta and wave number, which are not generally proportional to each other. The momentum is bounded and discrete for a finite grid. The uncertainty principle must be modified to reflect small scale spatial non-locality but it is consistent with the standard uncertainty principle in the continuum limit. We only consider kinematics in this work, and do not discuss time or energy or dynamical evolution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
