  An important feature of Kaluza-Klein theories is their ability to relate
fundamental physical constants to the radii of higher dimensions. In previous
Kaluza-Klein theory, which unifies the electromagnetic field with gravity as
dimensionless components of a Kaluza-Klein metric, i) all fields have the same
physical dimensions, ii) the Lagrangian has no explicit dependence on any
physical constants except mass, and hence iii) all physical constants in the
field equations except for mass originate from geometry. While it seems natural
in Kaluza-Klein theory to add fermion fields by defining higher dimensional
bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do
not satisfy conditions (i), (ii), and (iii). In this paper, we show how
conditions (i), (ii), and (iii) can be satisfied by including bispinor fields
in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent
teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor
equation, since conditions (i), (ii), (iii) imply a special relation among the
terms in the Kaluza-Klein or teleparallel Lagrangian that would not be
satisfied in general.
