Electromagnetic Waves Traveling on a Line of Force and Gravitational Force Waves Traveling along a Line of Force

Abstract

This paper proposes, based on Maxwell's equations and the fundamental fields of the electric flux density vector D [As/m²] and magnetic flux density vector B [Vs/m²] in SI units, that the vector product of D and B can be defined as a quadrupled density q(h), which is equivalent to the electromagnetic impulse density ρ(I). These quantities are mathematically equivalent in unit analysis:

Under the condition that the unidimensional terms satisfy an exact differential equation, and assuming that the derivative of q(h)equals that of ρ(I), the unidimensional Maxwell’s equations (based on permittivity εand permeability μin vacuum) can theoretically establish relationships among energy density ρ(E), impulse density ρ(I), and mass density ρ(m).
These are expressed as:

where b is the speed of wave beam with mass in itself, different from the conventional speed of the light c that is regarded a photon as a particle with no mass, equals the inverse of electromagnetic constant product of permittivity ε and permeability μ, εb=1/μb, εμb2=1.

These relations correspond to Einstein’s mass–energy equation. Furthermore, integrating ρ(I)over an infinitesimal volume dV and spatial element dz leads to an electromagnetic indeterminacy, expressed as the Planck constant wave:

where  dV represents electromagnetic momentum. This expression corresponds to Heisenberg’s uncertainty principle.