arXiv 1508.062862015-08gr-qchep-th

时空原子的分布函数与引力的性质

Distribution function of the Atoms of Spacetime and the Nature of Gravity

T. Padmanabhan

备注：: Invited review for the special issue on `Entropy in Quantum Gravity and Quantum Cosmology'; 35 pages; no figures
发表信息：: Entropy (2015), 17, 7420-7452
DOI：: 10.3390/e17117420

摘要：

当拉格朗日量加上一个常数时，物质的运动方程保持不变，这一事实表明，假设引力场方程也应该遵守这种对称性。这一原则意味着：（2）在变分原理中，物质的应力张量应通过组合$T_{ab}n^an^b$出现，其中$n_a$是一个辅助零矢量场，它可以变化以得到场方程。这一过程自然地选择了$D$维的Lanczos-Lovelock引力模型和$D=4$维的爱因斯坦理论。将$n_a$与时空中零面的法线等同起来，就可以在宏观极限下对引力进行热力学解释。几个几何变量和描述时空演化的方程获得热力学解释。将这些思想进一步扩展，我们可以从“时空原子”的分布函数中得到这个变分原理，它计算几何的微观自由度的数量。这是基于一个奇怪的事实，即重整化时空赋予每个事件零体积，但有限的面积！

英文摘要：

The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination $T_{ab}n^an^b$ where $n_a$ is an auxiliary null vector field, which could be varied to get the field equations. This procedure selects naturally the Lanczos-Lovelock models of gravity in $D$-dimensions and Einstein's theory in $D=4$. Identifying $n_a$ with the normals to the null surfaces in the spacetime leads to a thermodynamic interpretation for gravity, in the macroscopic limit. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the ``atoms of spacetime'', which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!

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