## On the Motion of Quantum Particles and Euclidean Relativity

**Authors:** Vu B Ho

In this work we discuss the motion of quantum particles when they are viewed as three-dimensional Riemannian manifolds by extending the isometric transformations in classical physics to the isometric embedding between smooth manifolds. According to the Whitney embedding theorem, in order to smoothly embed three-dimensional Riemannian manifolds we would need an ambient six-dimensional Euclidean space. As has been shown in our previous works, a six-dimensional Minkowski pseudo-Euclidean spacetime can be obtained by extending one-dimensional temporal continuum to three-dimensional temporal manifold. While the question of whether it is possible to smoothly embed three-dimensional Riemannian manifolds in six-dimensional pseudo-Euclidean spacetime remains, we will show that it is possible to apply the principle of relativity and the postulate of a universal speed to formulate a special theory of relativity in which the geometry of spacetime has a positive definite metric by modifying the Lorentz transformation. The modified Lorentz transformation gives rise to new interesting features, such as there is no upper limit for the relative speed between inertial reference frames, the assumed universal speed is not the speed of any physical object or physical field but rather the common speed of expansion of the spatial space of all inertial frames. Furthermore, we also show that when the relative speed approaches infinite values, there will be a conversion between space and time.

**Comments:** 6 Pages.

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### Submission history

[v1] 2017-10-22 06:15:08

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