Mathematical Physics


On the Geometric Structure of the Spatiotemporal Manifold

Authors: Vu B Ho

In this work we will discuss the geometric structure of the spatiotemporal manifold which appears apparently as a multiverse whose intrinsic geometric structures will be shown to be resulted from geometric interactions between space and time. The geometric and topological structures of the total spatiotemporal manifold are formed from the geometric interactions of the decomposed cells from the base space of the total spatiotemporal manifold which is considered as a fiber bundle. In particular we will discuss in details spacetime which has the mathematical structure of a 6-sphere bundle in which the dynamics of the fibers is resulted from the geometric interactions of different types of decomposed cells that give rise to various relationships between space and time. We also show that the concept of the spatiotemporal manifold being viewed as a multiverse endowed with the structure of a CW complex was in fact suggested by Newton himself in his book Opticks. In Newton’s multiverse, the expansion of space can be seen as a geometric evolution which redistributes to smooth out irregularities of the spatiotemporal manifold.

Comments: 18 Pages.

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Submission history

[v1] 2018-08-12 06:03:49

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