Along with all other quantum objects, an electron is partly a wave and partly a particle. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment. When an electron looks more like a particle it has no shape, "point particle", according to the Standard Model, meaning that it interacts as if it is entirely located at a single point in space and does not spread out to fill a three-dimensional volume. Therefore, in the sense of particle-like interactions, an electron has no shape. In this paper, a new theory is proposed in which the electron has a structure and a shape. The central idea is that an electron is a frictionless vortex with conserved momentum made out of condensed vacuum generated in the Big Bang from massless virtual photons that acquire mass when moving in the vortex at the speed of light. Using Hydrodynamics laws and applying them on the superfluid vacuum the basic properties of the electron are described here forth. This study provides mathematical models to calculate the mass, kinetic energy, density, volume, time, charge, and particle-wave duality. Such mathematical formulations are presented to confirm the theory. We conclude that the shape of the electron is accessible to human imagination, knowing its shape helps to determine its properties and shed a light on how matter is made and to explain the interactions of sub-atomic particles.

The nature of gravitation and G is not well understood. A new gravitation mechanism is proposed that explains the origin and essence of the gravitational constant, G. Based on general relativity, the vacuum is considered to be a superfluid with measurable density. Rotating bodies drag vacuum and create a vortex with gradient pressure. The drag force of vacuum fluid flow in the arm of the vortex is calculated relative to the static vacuum and a value that is numerically equal to that of G is obtained. Using Archimedes' principle, it is determined that G is the volume of vacuum displaced by a force equivalent to its weight which is equal to the drag force of the vacuum. It is concluded that the gravitational constant G expresses the force needed to displace a cubic metre of vacuum that weighs one kg in one second. Therefore, G is not a fundamental physical constant but rather is an expression of the resistance encountered by the gravitational force in the vacuum.

A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as "particle" and "wave" were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck's theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie's wavelength; furthermore, Compton's and de Broglie's wavelengths were also differentiated.

Charge is a fundamental physical property of matter that is responsible for its interactions with electromagnetic fields. The real nature and the essence of charge are unknown. In this paper, a new theory is presented to describe the nature and the essence of electric charge is formulated based on the vortex model of the electron which has a finite size and has an irrotational vortex structure. This theory and the vortex model of the electron enables us, for the first time, to describe the origin of bivalency, stability, quantization, equality of the absolute values of the bivalent charges, to derive a simple formulation to calculate the electric charge based on hydrodynamics without the use any constant. The difference between negative and positive charge, is revealed and the charged particles interactions are described. The electric charge is an expression of accelerated spherical mass per area reduced by the stiffness of the vacuum which has the units ε 0 ML 3 /T 2 . The calculated results based on these equations comply accurately with the experimental results.

In this study, the essence and origin of the magnetic constant are discussed and a mechanism that allows real estimations of the magnetic constant based upon the vacuum density description is proposed. By considering the vacuum as a liquid with a measurable density and the electron as a vortex, hydrodynamic laws are applied to measure the diminished momentum of a rotating electron in a vacuum, thus obtaining a value similar to the experimentally derived value of the magnetic constant. A consequence of this description is that the magnetic constant can be expressed as the shear stress per unit time of the vacuum; this means that it is an observable vacuum parameter and not a fundamental constant.