Twistor algebraic dynamics in complex space-time and physical meaning of hidden dimensions

We review the algebraic field theory based completely on a nonlinear generalization of the CR complex analiticity conditions to the noncommutative algebra of biquaternions. Any biquaternionic field possesses natural twistor structure and, in the Minkowski space, gives rise to a shear-free null congruence of rays and to a set of gauge fields associated with it. In the paper we develop the algebrodynamical scheme in the complex extension of Minkowski space-time – in the full vector space of biquaternion algebra. This primodial space dynamically reduces to the 6D observable'' space-time of the complex null cone which in turn decomposes into the 4D physical space-time and the 2D internal spin space’‘. A set of identical point charges (duplicons'') -- focal points of the congruence -- arises in the procedure. Temporal dynamics of individual duplicons is strongly correlated via fundamental twistor field of the congruence. We briefly discuss some new notions inevitably arising in the considered algebrodynamical scheme, namely those of complex time’’ and of ``evolutionary curve’', as well as their hypothetical links to the quantum uncertainty phenomenon.