By considering a distribution of complex basic spinors \(W\), satisfying the invariant linear differential equation \(\operatorname{curl}_5 W = 0\) in a 5-dimensional Kaluza space such that the space curvatures are determined by the concomitants of the spinors, a precisely defined mathematical model is obtained. The properties of this model are extremely close to the properties of the physical world. There are light waves which -- on closer examination -- are found to be quantized. There are wave packet solutions which behave as particles, the simplest of which has the correct field and spin to represent an electron. Many quantum effects, such as the Pauli Exclusion Principle, the frequency laws for spectrum, are displayed by the model. Maxwell's equations are not exactly satisfied, but the deviation represents a small oscillation about a zero mean, which would be expected to be unobservable. This paper gives a synthesis between the general theory of relativity and quantum mechanics in a 5-dimensional Kaluza space.