proof ______________________________________________________________ 141
7.3 Positronium
But before the two elementary vortices, the electron and the positron, are annihilated
under emission of radiation, they will for a short time take a shell-shaped, a bound state, in
which one vortex overlaps the other.
Its formation we can imagine as follows: an electron, flying past a resting positron, is
cached by this for reason of the electromagnetic attraction and spirals on an elliptic path
towards the positron. In doing so its angular velocity increases considerably. It will be
pulled apart to a flat disc for reason of the high centrifugal forces, to eventually lay itself
around the positron as a closed shell.
Now the red positron sees the electron vortex so to speak "from the inside" and doing so it
sees as well red; because the green vortex has a red centre and vice versa! The result is the
in fig. 7.3 given configuration.
The number of field lines, which run from the red border of the positron in the direction of
the centre, is identical to the number, which point towards the green border of the electron.
Here already the same state has been reached as in the centre, which corresponds to the
state at infinity. That means that no field lines point from the green border to the outside;
seen from the outside the particle behaves electrically neutral. It doesn't show any
electromagnetic interaction with its surroundings.
If the particle were long-living, then it undoubtedly would be the lightest elementary
particle
besides the electron; but without stabilizing influence from the outside the
positronium can't take the in fig. 7.3 shown state at all. The positron takes up the kinetic
energy which is released if the electron becomes a shell around it. But before the bound
state can arise, which would identify the positronium as an elementary particle, the equal
rights of both vortices comes to light. With the same right, with which the electron wants
to overlap the positron, it itself vice versa could also be overlapped.
If the stabilization of the one or the other state from the outside doesn't occur, then the
stated annihilation under emission of y-quanta is the unavoidable consequence (fig. 4.6).
142
dipol moment
Fig. 7.4: Two electrons with oppositely directed spin
proof
143
7.4 Dipole moment
As electrically charged spheres elementary vortices have a magnetic dipole moment along
their axis of rotation as a consequence of the rotation of their own (fig. 7.4). This is
measurable very precisely and for the most important elementary particles also known
quantitatively. In contrast to the angular momentum the magnetic moment can't be
constant according to the here presented theory. It should slightly change, if we increase
the field strength in the laboratory.
In a particle consisting of several elementary vortices the vortices mutually increase the
local field strength. Therefore we measure at the proton, which consists of three vortices,
not the triple, but only the 2,793-fold of the nuclear magneton which can be expected for
reason of its mass. Also the neutron has instead of the double only the 1,913-fold nuclear
magneton. The deviations therefore are explicable as a consequence of the surrounding
fields.
Prerequisite for this point are two other, still unanswered, key questions of quantum
physics:
XII: Why is measured for the proton approximately the triple of the magnetic dipole
moment which can be expected for reason of the charge?
XIII: Why does the neutron, as an uncharged particle, actually have a magnetic
moment?
These questions can only be brought to a conclusive answer, if we have derived the vortex
structures of the respective particles.
The elementary vortex, as a consequence of the spin along its axis, forms a magnetic north
pole and a south pole. Another possibility to interact with an
external field or with other
particles is founded on this property. This shall be studied by means of two electrons.
which form an electron pair.
For reason of the equal charge the two electrons at first will repel each other. If they rotate
of their own they however will mutually contract, which, seen from the outside, is
interpreted as a force of attraction. And in addition will they align their axes of rotation
antiparallelly. While they now rotate in the opposite direction, a magnetic force of
attraction occurs.
As is shown in fig. 7.4, the magnetic dipole field in this way is compensated towards the
outside, as is clarified by the field line (H) with a closed course. Between both electrons a
space free of E-field stretches. If both vortices are a small distance apart they lay
themselves around this space like two half-shells of a sphere. A particle forms which seen
from the outside is magnetically neutral, but it carries the double elementary charge (fig.
7.4b).
The exceptional affinity is always restricted to two vortices of equal charge with an
opposite direction of rotation. Further vortices can't be integrated anymore and are
repelled. This property of vortices covers the quantum condition (Pauli's exclusion
principle) for the spin quantum number perfectly.