We relate physical time with the topology of magnetic field vortices. We base ourselves on a formulation of unimodular gravity where the cosmological constant Λ appears as the canonical dual to a variable which on-shell becomes four-volume time. If the theory is restricted to a topological axionic form (viz. a parity-odd product of an electric and a magnetic field), such a time variable becomes the spatial integral of the Chern-Simons density. The latter equates to helicity, so that unimodular time is transmuted into the linking number of the vortices of the topological magnetic field, times their flux. With the added that this flux is a universal constant, the flow of time can thus be interpreted as the progressive weaving of further links between magnetic field vortices, each link providing a quantum of time with value related to the fixed flux. Non-abelian extensions, and targetting parameters other than Λ are briefly examined, exposing different types of vortices and a possible role for inter-linking leading to new phenomenology.

中文翻译：

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涡旋、拓扑和时间


我们将物理时间与磁场涡旋的拓扑联系起来。我们基于幺模引力的公式，其中宇宙常数 Λ 表现为变量的正则对偶，在壳上变成四体积时间。如果理论仅限于拓扑轴子形式（即电场和磁场的宇称奇积），那么这样的时间变量就成为陈-西蒙斯密度的空间积分。后者相当于螺旋度，因此单模时间转化为拓扑磁场涡旋的链接数乘以它们的通量。补充说，该通量是一个通用常数，因此时间的流动可以解释为磁场涡旋之间进一步链接的渐进编织，每个链接提供一个时间量，其值与固定通量相关。简要检查了非阿贝尔扩张和 Λ 以外的目标参数，揭示了不同类型的涡流以及相互链接导致新现象学的可能作用。