A five-dimensional perspective on the Klein–Gordon equation

Austin Blaquière

K. B. Wharton

Morton D. Kostin

Sergio Giardino

Helge Kragh

In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein–Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the usual Schrödinger equation. In most of the early versions the Klein–Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil.

A. BLAQUIt

The purpose of this paper is to bring out some connections between the work of Isaacs and physics. The first five sections are devoted to classical dynamics. The theories of Hamilton and Jacobi are revisited via the geometrical approach to optimal control and de Bro- glie's ideas. The other sections contain a stochastic-type generalization, leading to the Klein-Gordon equation of relativistic wave mechanics.