Numerical Methods and Causality in Physics

Abstract

We discuss physical implications of the explicit method in numerical analysis. Numerical methods have there own condition for causality, known as the Courant-Friedrichs-Lewy condition. It is proposed that numerical causality merges with physical causality as the grid interval size approaches zero. We discuss the implications of this proposition on the numerical analysis of the wave equation. We also show that, insisting on physical causality, the numerical analysis of Schrodinger's equation implies that the minimum space interval should satisfy $\Delta x \ge a_0 \lambda_c$, where $\lambda_c$ is the reduced Compton wavelength and $a_0$ is a constant of the order unity.