A Fluid Perspective of Relativistic Quantum Mechanics

In previous papers, it has been shown how Schrödinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour is derived from Fisher information terms added to the classical Lagrangian, showing that a quantum mechanical system is driven by information and not only electromagnetic fields. This program was applied to Pauli's equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful, there were terms that did not admit interpretation, a number of which can be easily traced to the relativistic Dirac theory. Here, this analysis is repeated for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.