  where \(\lambda\) is understood to be an arbitrary function of position in the four-dimensional world. Here the factor \(\bfrac{e}{ch}\), where \(- e\) is the charge of the electron, \(c\) is the speed of light, and \(\bfrac{h}{\pi}\) is the quantum of action, has been absorbed in \(f_{p}\). The connection of this “gauge invariance” to the conservation of electric charge remains untouched. But an essential difference, which is significant for the correspondence to experience, is that the exponent of the factor multiplying \(\psi\) is not real but purely imaginary. \(\psi\) now assumes the role that \(ds\) played in Einstein’s old theory. It seems to me that this new principle of gauge invariance, which follows not from speculation but from experiment, compellingly indicates that the electromagnetic field is a necessary accompanying phenomenon, not of gravitation, but of the material wave field represented by \(\psi\). Since gauge invariance includes an arbitrary function \(\lambda\) it has the character of “general” relativity and can naturally only be understood in that context.