An Equation of Motion with Quantum Effect in Spacetime

TL;DR

This paper introduces a new relativistic equation of motion incorporating quantum effects in spacetime, generalizing Einstein's energy-mass relation through a classical-quantum duality and a spacetime Schrödinger equation.

Contribution

It proposes a novel equation of motion with quantum effects in spacetime, extending classical and quantum duality and relativistic wave equations.

Findings

Derived a generalized energy-mass relation in spacetime.

Formulated a relativistic quantum wave equation.

Established a connection between quantum effects and spacetime curvature.

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 $E=m_0c^2$ in the spacetime. In general, we have $E=m_0c^2 + \frac{\hbar^2}{12m_0}R$ in a spacetime.