Albert Einstein, in searching for the transformation group for his unified field theory, wrote: "Every attempt to establish a unified field theory must start, in my opinion, from a group of transformations which is no less general than that of the continuous transformations of the four coordinates.
"[1]The Poincaré group, the transformation group of special relativity, being orthogonal, the inverse of a transformation equals its transpose, introducing discrete reflections.
This, in turn, violates Einstein's dictum for a group "no less general than that of the continuous transformations of the four coordinates".
Available parameters are thus reduced, from the 16 needed to express all transformations in a curved spacetime, per the general principle of relativity, ∂xμ′/∂xν, to the 10 of the Poincaré group.
[2] The Einstein group can be obtained by factorizing the squared spacetime invariant interval into a quaternion-valued form and its conjugate, ds ds*, where and qμ(x) is a four-vector of Hermitian quaternions.