A non-electromagnetic wavefield in affine [formula omitted]-spacetime with covariance properties under a Lorentz-type of transformation

Abstract

A non-electromagnetic wavefield is constructed that shows covariance properties under a Lorentz-type of transformation of the relevant space–time coordinates and associated field and source quantities in affine (N+1)-spacetime. The construction goes along the lines of the axiomatic physical approach that has served to construct Lorentz-covariant electromagnetic fields in (N+1)-spacetime as a generalization of their (3+1)-spacetime counterparts. In accordance with general concepts about wave phenomena as the carriers of information (in the field quantities) and accompanied by a transfer of energy (descriptive of the wave’s interaction with other thermodynamic systems) and a transfer of momentum (descriptive of the wave’s interaction with mechanical systems), one kind of field and source quantities is taken as a tensor of rank one (vector), the other as an omnidirectional tensor of rank two (which is equivalent to a scalar). The wavelike character of the solutions of the field equations has been ascertained by letting the relative changes in space of the intensive field quantities be counterbalanced by relative changes in time of the extensive field quantities. The existence of covariant field equations under a Lorentz-type of transformation of the special relativity type in (N+1)-spacetime leads to the conjecture that the field under consideration could correspond to some physical field in the universe that (in line with Lorentz’s view on physical cosmology) differs in properties from the electromagnetic one and, if it exists, could couple to the electromagnetic field.