In this expression, P(r) is the

electric charge density at the point r and [epsilon] is the permittivity of the surrounding medium.

He derives the potential of a point charge and a sum of point charges in free space for the electric field defined in (5); then generalizes this potential to an integral over a volume V of

electric charge density [[rho].sub.e] and defines the potential for the point of observation r everywhere including points within the charge density of V to get [1, Arts.

Discretized

Electric Charge Density. In this subsection, we attempt to discrete the

electric charge density.

The main trends of the

electric charge density for a given value of the fluid velocity are easily observed in Fig.

In vacuum where

electric charge density [rho] = 0 and electric current density J = 0, Eqs.

Quantity Form Type Units Vector/ Scalar Electric Field Intensity E one-form V E Magnetic Field Intensity H one-form A H Electric Flux Density D two-form C D Magnetic Flux Density B two-form Wb B Electric Current Density J two-form A J

Electric Charge Density Q three-form C P Table 2.

(8), we can obtain the unknown

electric charge density.

As stated in the introduction, the present theory is based on the hypothesis of a nonzero

electric charge density in the vacuum.

The nonzero electric field divergence further gives rise to a local intrinsic

electric charge density within the photon body, whereas there is a vanishing total charge of the latter.

The latter theory is based on a vacuum state that is not merely an empty space but includes the electromagnetic fluctuations of the zero point energy and a corresponding nonzero

electric charge density associated with a nonzero electric field divergence.

The zero-point-energy of the vacuum state, its related electromagnetic vacuum fluctuations, the Casimir effect, and the electron-positron pair formation out of the vacuum support the hypothesis of a local

electric charge density and an associated nonzero electric field divergence in such a state.

The basic physical concept of the present theory is the appearance of a local

electric charge density in the vacuum state in which there are quantum mechanical electromagnetic fluctuations.