On Two Fundamental Laws of Nature and the Role of Time in Time—Space Manifold

Abstract

Considering time-space as subordinate to the laws of nature, it becomes possible to explain the internal inevitability of Lorentz invariance and the three-dimensionality of physical space.

Section 1 explains the importance in physics of the concept of symmetry. The possibility is discussed for symmetry to take the place of the Hamiltonian in describing the properties of a dynamical system.

In Sections 2 and 3, two general laws are proposed which are considered to be the most fundamental when we look at physics from the viewpoint of symmetry. One of them is the law describing the relation between symmetry and a conservation law. The other is what I called the law of complexification. In order to state the second law, the concepts of complexification, and its real form describing the relation between linear spaces are generalized, and the complexification and its real form are defined for Lie groups. Then the possibility is shown, using the law of complexification, of deducing Lorentz invariance from rotational invariance in three-dimensional space, and, using the Lorentz transformation, of which the existence is assured by the law of complexification, to build up the freedom of time itself. In other words, the difference is made clear between the role of time and that of space in four-dimensional time-space, or the existence of time is made subordinate to the existence of space.

In the last section, a short explanation is given of the three-dimensionality of physical space, based on the fact that there is no action at a distance in nature.