Cosmic Rays Report from the Structure of Space

Figure 7

According to the principle of least action an infinitesimal change (blue arrow) in the kinetic energy () along the least-time path (black arrow) equates with an infinitesimal change (green arrow) in the scalar potential () and infinitesimal change (red arrow) in dissipation (). Thus the familiar Lorentz factor follows when the curved least-time path is approximated by straight sections.