Dirac Sphere Potentials

The discrete elements of nature are the negative and positive unit potential point charges, aka the electrino and positrino, respectively. These point charges continuously emit an electric potential field from their current position (t, s). That electric potential expands spherically at a radial speed @.

Geometrically each expanding spherical potential is defined as a Dirac sphere, which is a term I coined. I presume there may already be a geometrical object for this purpose, and will update the terminology once I become aware.

The electrino emits a Dirac sphere which propagates from (t, s) with radial velocity @ and has value –δ/r where r = @ times Δt, where Δt is the absolute time since the potential was first emitted on the path of the electrino.

Likewise, the positrino emits a Dirac sphere which propagates from (t, s) with radial velocity @ and has value +δ/r where r = @ times Δt, where Δt is the absolute time since the potential was first emitted on the path of the positrino.

A unit potential emits a continuous stream of Dirac sphere potentials along its path history in space and time. When a Dirac sphere potential stream encounters a point charge, action occurs. Each point charge may be considered to be constantly encountering the Dirac sphere stream of itself and every other point charge in the universe.

The path history of velocity of the point charge that emitted the Dirac sphere stream determines the vector potential. The velocity of the point charge that encounters a Dirac sphere stream is a factor in determining the action upon the point charge.

If a point charge is traveling at a velocity v < @ then it stays within the spheres of it’s own Dirac sphere stream and no self action occurs, or rather the action is null.

When the velocity of a point charge exceeds @, then the point charge is outside the spheres it has just emitted and is exploring its own prior emissions in a path dependent fashion and self action occurs.

When the velocity of a point charge equals @ this is a symmetry breaking point, since self action will change the point charge velocity.

Note that there are no infinities at small r nor zeros at large r. The magnitude of each Dirac sphere is somewhere on the |δ/r| curve. That said, at large distances, the magnitude is a very small real number and not only that superposition of negative and positive unit potentials will tend to cancel out.

Locally we think about action in terms of the path history of all significantly interacting point charges, including the self, where ‘significantly’ is defined relative to the scale of the problem to be solved. In this way we can compute each individual action and then sum all the action to determine how the point charge will move along its path.

As a matter of convenience, we define the term ‘aura‘ as the scalar and vector potentials that result from the superposition of all Dirac spheres at the current location of the point charge, i.e. (t,s), beyond those point charges in an assembly or set of local assemblies. That is to say, “aura” represents the churning background potential from far enough away to not be part of the typical behaviour of the assembly or reaction. The aura certainly has influence on the path of point charges, but that influence is generally very small compared to the nearby point charges. Occasionally superposition can result in a change in the aura that is in the right location and the right time and with the right magnitude to influence a reaction.