Preface to the lecture, 1

140

 

Positronium

 

 

Fig. 7.3:    Theoretical final state of the positronium 

= static -quant (photon). 

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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).

 

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142

 

dipol moment

 

 

 

Fig. 7.4: Two electrons with oppositely directed spin

 

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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.

 

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