Preface to the lecture, 1
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Field-theoretical approach Einstein:___________________________________________________ "Is it conceivable, that a field theory permits us to understand the atomistic and quantum structure of reality? This question by almost all is answered with No. But I believe that at the moment nobody knows anything reliable about it"
. Pauli:______________________________________________________ "The electric elementary quantum e is a stranger in Maxwell-Lorentz' electrodynamics" . _______ Fig. 3.2: The field-theoretical approach
Vieweg, Braunschweig 1974. Braunschweig 1961, entnommen aus: H. G. Kussner: Grundlagen einer einheitlichen Theorie der physikalischen Teilchen und Felder. Musterschmidt-Verlag Gottingen 1976, S. 161. Field-theoretical approach:
Approach ___________________________________________________________________________ 43
3.2 Field-theoretical approach The field-theoretical approach is the very much older one. Until the last turn of the century the world in this respect still was in order. Max Planck, by the discovery of quanta, has plunged physics into a crisis.
Albert Einstein, who, apart from his lightquanta hypothesis, in his soul actually was a field theorist, writes: ,,Is it feasible that a field theory allows us to understand the atomistic and
q u a n t u m structure of reality?". This question by almost all is answered with No. But I believe that at present nobody knows anything reliable about it ".
By the way the "No" can be justified by the fact that the field description after Maxwell is by no means able to the formation of structure so that it is not possible for quanta to
appear as a consequence. The field-theoretical approach could, obstructed by Maxwell's field theory, not further be pursued and to this until today nothing has changed.
Nevertheless it would be an omission to not at least have tried this approach and have it examined for its efficiency. Maybe the above mentioned problems of causality let
themselves be solved much more elegantly. For this however the Maxwell theory must be reworked to a pure field theory. With the well-known formulation it offends against the claim of causality, since it is field theory and quantum theory at the same time. To
Maxwell himself the quanta were still unknown, but today we know that the fourth Maxwell equation is a quantum equation:
(3.4)
After this the electric field is a source field whereby the individual charge carriers, like e.g. electrons, act as sources to form in their sum the space charge density p el . The other three Maxwell equations are pure wave equations. In this way the third equation identifies the magnetic field as source free:
div B = O . (3.3)
This for Pauli probably was the reason to call, "the electric elementary quantum e - a
stranger in Maxwell-Lorentz' electrodynamics" .
Let's return to the principle of causality according to which in the field-theoretical approach the fields should act as a cause and not the particles. In a corresponding field description quanta logically have not lost anything. It is only consistent to likewise demand freedom of sources of the electric field:
Div D = O . (3.7)
When the electric field is not a source field, then what is it? The magnetic field is a vortex field. Hence it would be obvious to also conceive the electric field as a vortex field. Numerous reasons speak for it: 1. A non-vortical gradient field, like it is formed by charge carriers, merely represents a
special case of the general vortex field. Only by the generation of quanta a source field can form as a special case. 2. The electromagnetic wave teaches us the duality between the E- and the H-field that
are directed perpendicular to each other and are in a fixed relation to each other. If one of them is a vortex field then also the dual field must be a vortex field.
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Duality
Fig. 3.3: The dual field description
Dual approach according to Jackson or Lehner : Div B = because of the 4 th Maxwell equation: Div D = (3.4) magnetic monopoles should exist, otherwise dual extension (3.8) not allowed! Caution: closed loop conclusion! Maxwell theory proves the correctness of the Maxwell theory. Result: search for magnetic monopoles unsuccessful. : J. D. Jackson, Classical Electrodynamics, 2 nd Ed. , John Wiley, New York, 1975, S. 251 - 253
berg 1990, S. 35 - 36 und S. 533 ff.
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