Hendrik Lorentz «Theory of electrons»
Summing up a century-long negative experience accumulated by the efforts of numerous theorists trying to build an electron in the form of a static distribution of charge, one may formulate the following general experimental principle:
An electron cannot be described as a static distribution of charge. Such a model does not correspond to its nature.
As an alternative, a positive guiding principle comes forward:
A model in the form of stationary set of continuously distributed currents corresponds to the nature of an electron at rest.
It prevents from necessity of an additional compensating field and gives real possibility to develop a closed theory. An electron permanently scatters into surrounding space (and simultaneously gathers together) under the influence of its own stationary field (which cannot be reduced to the field of some static distribution of a charge).
These smallest moving parts of a charge of an electron at rest were named ONs. These are marked, colored, mentally isolated, bounded by a closed surface (sphere, cylinder) infinitely small elements of continuously distributed moving charge having common velocity vector. Each element of ON moves independently of the others in accordance with laws of charge motion in a field. Its motion is not influenced by any other bonds. Value and sign of ON charge conserve during its motion. There are no interactions between ON parts (between ONs) since they see the filed of electron only (the sum of fields of all ONs in the whole space), it is the sole and prime reality to them. There is no way to change the motion of neighbors in order to make rise to a question about interaction with them without changing electron field. ONs know nothing about existence of the others even if they move through the same point of the space-time but have different spatial direction of motion. The whole set, two-parameter family of ONs with different directions of velocity vector pass through each world point. In the problem of charge motion in field, ON is an analogue of a trial charge. But ON itself also creates a field that together with fields of all other ONs in the whole space joins an integral field – a field of electron in which ONs generating this field move, etc.
Each point of ON during its motion draws a STREAMLINE, and the set of all streamlines of ON coincides with its spatial track – STREAM TUBE. All streamlines of an electron end in spatial infinity (finite streamlines for electron are excluded as instability sources). Streamlines of an electron at rest are considered symmetrical in respect to velocity sign reversion, i.e. in case of such a reversion they coincide spatially, and ON point draws them in reverse direction. This symmetry is also connected with stability.
ONs' velocity at the infinity is a velocity of light and becomes a unit velocity by selecting a unit system. Since a positron must also exist, ONs' storage at the infinity is doubled by adding similar set with an opposite sign. Such space at the infinity occupied by double uniform and isotropic set of ONs of different charge sign is a model of an invariant empty space.
We shall consider the simplest real problem of a sole electron at rest in an inertial frame of reference, K0, such that its field and streamlines are spherically symmetrical relative to coordinate origin O. Field set of streamlines of an electron at rest defined so is the simplest and maximally symmetrical allowable configuration after a static spherically symmetric distribution of charge.
It is suggested that ONs – SOURCES of ML-FIELD, i.e. field generated by an ON, is defined by Maxwell–Lorentz equations (ML-equations) for potentials. This field may be named ON-FIELD, but it should not be called an electromagnetic field since they have different both structure and origin. Initial and boundary conditions are the symmetries already described above plus those to be described and discovered, and empiric condition imposed on integral field of all ONs (field of electron) in the form of Coulomb asymptotics for large distances from the centre of symmetry of electron.
This, as well as ON definition, is a consequence of a tradition to consider field sources as point sources. (The same applies not only to field sources, and the analysis of it is of a great interest, but in another time and place).
But ML-equations and their solutions, by their structure (nature, essence), more naturally (easily, adequately) describe a field generated by pairs of mutually opposite streamlines. One streamline follows from another by changing sign of velocity in each point. A pair of mutually opposite streamlines transforms into itself in case of reversion of velocity or time sign. This symmetry of a streamline has been already defined and is closely connected to the symmetry of motion law in respect of time reversion to be yet determined. But one should anticipate the law of motion of pairs of streamlines in this case also. Symmetries of streamlines, electron fields, ML-equations and equations of motion are mutually conditioned, related and neither of these symmetries may be eliminated without sacrificing an electron.
Attention! Standard application procedure for the Gauss theorem to calculate field generated by electron is impossible! There is no an area, outer to the field sources representing an electron. Through every spherical surface containing an electron's symmetry centre, the charged field sources (ON-currents) pass in every direction. Some of them come from the infinity inside the area, others leave the inner area for the infinity.
This is the price to be paid for the possibility to move onto subelemental (subquantum) level of internal dynamics of fundamental particles and their fields.
Attention, here is a trap! Let's use stationarity of streamlines and integrate charge density (current density) in each point by two angle parameters and two charge signs and obtain resulting charge density (integral current density is always equal to zero due to symmetry of streamlines) depending on a distance to the centre of symmetry only. Solving this static problem, we shall obtain required scalar potential.
In our approach, these overall densities of charge and current are not ML-field sources! For an arbitrary set of streamlines the field, obtained by the above method (in a symbol form it is ML(Σ) operator affecting all sources of field) will not coincide with the field obtained in accordance with definitions, when at first ML-equations are integrated for each pair of streamlines (or for each ON), and then all these fields are summed up (Σ(ML) operator).
But, maybe, an electron has precisely such set of streamlines that both compound operators give us the same potential up to an accuracy of a constant term? If so, it may be used (as fixing principle) to determine equations of motion and set of streamlines of an electron to be found. This scheme captivates by its elegance, but in the case of electron it is evidently wrong which may be proved or rejected only upon this or that solution of the problem of electron.
|The translation from Russian was made by Yuri Nezhentsev|
Last modifications: November 25 2002
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