For example, in the case of compactification in R\times S^{3}, what can be said about the vector field on this manifold? Since the flow of the linear tangent to the three-dimensional sphere of the vector field is closed, in this case we can talk about the proper rotation of such a vector field, and the revolutions of the proper rotation can be identified with the phase action of the quantum particle S/h. It is also remarkable that the algebra of tangent vector fields of a three-dimensional sphere is isomorphic to su(2). Moreover, if we consider the random walk of this rotating spherical flow over the manifold R\times S^{3}, we obtain the Schrodinger equation for a free quantum particle.
The space time continuum introduced by Minkowski can be represented in the complex plane that starts with a rotating vector, or a Basic Unit System concept based on Euler's relation with which all the fundamental equations of physics can be deduced. Please again see how SR can be deduced in this new way in which a paradigm shift is necessary,and in which time cannot be reduced to a space dimension.
Edgar Paternina , Thank you, I'll look at your article. I also advise you to look at the works of Arkadiusz Jadczyk.
https://www.researchgate.net/profile/Arkadiusz-Jadczyk/publications
Thank you so much Igor, and regarding my proposal is that it has been texted in IE, and by deducing two important formulas such as that of the pendulum, and wave equation of QM. See plese my paper below. I really would appreciate any comment or criticism.
My best regards
Edgar
I also really like the pendulum. But it may be difficult for you to understand.
Preprint Chaotic dynamics of an electron
Let me clarify the question of the compactification of the Minkowski space. As a result of compactification, the isotropic cone of the Minkowski space turns into a Euclidean space, to the zero point of which a three-dimensional sphere is glued. For clarity, you can reduce the dimension and imagine the plane on which the ball lies.
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