3 0 2 D O C . 3 1 3 O N C U R R E N T S T A T E O F F I E L D T H E O R Y fundamentals. However, it seems hard to believe that the gravitational field and the electromagnetic field should exist alongside each other in space as essentially dif- ferent (although causally connected) entities. The Riemannian theory does not yet permit us to do justice to the unity of the forces of nature, but to doubt it seems quite impossible to the theoretical instinct. After twelve years of searching, full with disappointments, I have now discov- ered a metric continuum structure that lies between the Riemannian and the Euclid- ean ones, and whose elaboration leads to a truly unified field theory. It emerges from the following considerations. Euclidean geometry differs from the more gen- eral Riemannian geometry in that within it, two line elements or vectors at a finite distance can be reasonably compared not only in terms of their lengths, but also of their directions. But the Euclidean continuum is not the only special case of Rie- mannian geometry that has this property indeed, there is a much more general spe- cies of Riemannian continua in which a “distant parallelism”[10] of the vectors is found. The spatial structure that is to be newly introduced can be mathematically described as follows. The existence of a Riemannian metric requires that at every location within the n-dimensional continuum, there is a local “n-Bein orthogonal frame” that acts as a local coordinate system on which the magnitude of a line element is given by the equation1 … .[11] (4) Referred to the general coordinate system, let be the n coordinates on the a-th axis of the n-Bein orthogonal frame. Then the components d xν of the line element are expressed by the formula … . (5) The inverse equations may be written as ,[13] (6) whose coefficients are the normalized subdeterminants of the h quantities defined above. It follows from (4) and (5) that , so that the coefficients g μν of the Riemannian metric can be expressed in terms of the h as . (7) In this theory, the h are the elementary field variables in terms of which the g of the metric can be expressed. 1 Following a suggestion of Weitzenböck, the reference to an axis of the local n-Bein frame is de- noted by an index on the left.[12] ds 2  dx a 2 = h  a dx  h  a d a x = dx a h a  dx  = ds 2 h a  h a  dx  dx  = [p. 131] g  h a  h a  =