ABSTRACT
One can justly say that the unitary theory of Albert Einstein, based on the concept of absolute or distant parallelism [see (Einstein, 1930); see also (Delphenich, 2011) for English translations, a comprehensive bibliography and pertinent commentaries on this subject] represents still another logical attempt – among so many others explored by the great physicist along time – to consolidate the initial idea of theory of relativity, according to which the metric of the world is determined by matter. Einstein must have had realized, as he did in many other cases transparent in the various interventions to amend the theory – see (Goenner, 2004, 2014) and (Renn, 2007), for details, critical discussions and a comprehensive bibliography – that by proposing the metric tensor as unique representative of the matter, he drifted apart from the initial geometrical principle, which states that the matter establishes in fact the space connection, as suggested by the Newtonian theory. Fact is that the space connection can be defined quite independently of the metric. Being nonetheless impossible to give up the idea of metric, Einstein may have searched for a way in which the metric tensor should be correlated with the connection of space, and such a way ensues from the very manner in which the natural connection of a Riemannian metric is calculated (Misner, Thorne & Wheeler, 1973). As a consequence of his idea of distant parallelism – or absolute parallelism; the notion is best described by lie Cartan, in a portrayal that, as indicated before, we would like to term as ‘informational’ (Cartan, 1931) – Einstein proposes the equations of compatibility between metric and connection and not the metric per se, as being theoretically essential. In this case the metric tensor is no more constrained to be a symmetric matrix. In modern terms one can say that the matrix symmetry expressing the invariance of the quadratic metric itself when an arbitrary skew-symmetric part is added to the metric tensor, is broken if the fundamental equations of the theory are the compatibility equations between metric and connection. One can further say that the tensor from which the metric is calculated can be no more just a metric tensor, but a general tensor that should be properly called a fundamental tensor.
