An Equation of Motion with Quantum Effect in Spacetime

Abstract

In this paper, we shall present a new equation of motion with Quantum effect in spacetime. To do so, we propose a classical-quantum duality. We also generalize the Schordinger equation to the spacetime and obtain a relativistic wave equation. This will lead a generalization of Einstein's formula $E=m_0{c}^2$ in the spacetime. In general, we have $E=m_0{c}^2+\frac{{\hslash }^2}{12m_0}R$ in a spacetime.

15 pages