A study of micro space-time theory and time dilation in bound muon decay

Abstract

This paper proposes a space-time theory for describing the physical laws of the micro-world by introducing scalar fields $\mathcal{D}\left(x\right)$ and $\zeta\left(x\right)$. A new field action is constructed, and the Lagrangian for particle motion is rewritten, resulting in a modified space-time relation. The Klein-Gordon equation is theoretically derived using the Hamilton-Jacobi method in four dimensions. To experimentally test the correctness of this theory, we further investigate the time delay between proper time and local coordinate time caused by $\mathcal{D}\left(x\right)$ and discuss the decay rate of bound muons in different elements. The results are consistent with the proposed theory.