Reasons for taking1/2h/c 2 in cgs units as an equivalent in grams for the photon “rest mass” are given. Its numerical value of3.68×10 −48 g corresponds to the minimum mass equivalent energy for one half-cycle of an electromagnetic dipole field distribution, which is discontinuous. For the fluid models that are discussed, this field distribution corresponds somewhat to a hydrodynamic toroidal vortex which is stationary—if we use toroidal coordinates and assume that the ring origin has the radial velocity c, that the (...) gauge is defined by the ring origin diameter, and that free space is represented by a two-fluid model (the fluids oppositely charged). There are mappings which can transform such toroidal entities (photons) into spherical ones. The toroidal entities are possible candidates for the role of “hidden variables.”. (shrink)

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (c) the (...) unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol ϑ and are to be associated with the complex probability eiϑ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory. (shrink)

Although the form of the metric is invariant for arbitrary coordinate transformations, the magnitudes of the elements of the metric are not invariant. For Cartesian coordinates these elements are equal to one and are on the diagonal. Such a unitary metric can also apply to arbitrary coordinates, but only for a coordinate system inhabitant (CSI), to whom these coordinates would appear to be Cartesian. The meaning for a non-Euclidean metric consequently appears to be a simple coordinate system transformation for the (...) appropriate CSI. The conversion of arbitrary coordinates to the flat Cartesian ones can be accomplished by a sequence of isomorphic mappings linking the arbitrary coordinates to the flat Cartesian ones. This is shown for two, three, and four-dimensional spaces. It is also applied to toroidal metrics and fluidfilled spaces for toroidal vortices that are discontinuous, half-wavelength, electromagnetic dipole field distributions. A number of other applications are discussed. (shrink)