3.1 Maxwell Equations define Physics of Sources

3.1  Maxwell Equations define Physics of Sources

Out of numbered streamlines of an electron, one line L may be chosen with peak in point p relative to which the line is symmetric (Op distance and velocity v(p) are minimal). The center of infinitesimal circle δS0 orthogonal to the streamline L passes through p at zero moment of time. Within time period δt, surface δS draws volume element δV0 between δS0 and δS1 and lateral surface of stream tube. Countable set of elements of the current tube δVn is constructed in such a way that δVn–1 and δVn have only common surface δSn, being an image of initial circle δS0. Each element δVn+1 is an image of preceding element δVn, and thus an image of initial element δV0. It remains to complete this set with symmetrical one in relation to Op axis and to double obtained set by adding the same set but with reverse velocity sign. Constructed in such a way linear set of ONs of same charge sign is a CURRENT THREAD. It is self-dual by definition (reverse to itself, transforms into itself with reversal of sign of velocity). Current thread is a set of ONs obtained out of an initial peak ON by special time shifts and time reflection. Each such ON carries common to all quantity of charge δq.

The question arises about scalar potential field to which the current thread L gives rise. It is ML(L), i.e. a result of integration of ML-equations with ON sources of the current thread L. In this case

L = Èn(δqn+) + Èn(δqn–), (1)

where union taken over all integers n (from minus infinity to plus infinity). Thus:

ML(L) = Σ n(ML(δqn+) + ML(δqn–)). (2)

Operator ML affecting individual ONs may be represented as a linear combination of retarded and advanced solutions of Lienar–Wiechert:

ML = αLVret + βLVadv, (3)
LVret(δqn+) = δq(n-i)+/(rrv), (4)
LVret(δqn+) = δq(n+j)+/(r + rv), (5)
LVadv(δqn–) = δq(n+j)–/(rr(–v)), (6)
LVadv(δqn–) = δq(n-i)–/(r + r(–v)), (7)

where velocity vectors v for ONs δqm– are expressed through velocity vectors v of ONs δqm+, and vectors v and r are taken for retarded and advances ONs shifted by i and j in appropriate direction. These i and j are selected, as is usual, from the condition of equality of time necessary for ON δqm* to coincide with ON δqn* to the time when signal from ON δqm* arrives to observation point (point of field calculation) with unit velocity.

The following equalities become obvious:

LVret(δqn+) = LVadv(δqn–), (8)
LVadv(δqn+) = LVret(δqn–), (9)

being the major objective of our preceding efforts. It is clearly visible that the advanced field of ON δqn– is indistinguishable from the retarded filed of ON δqn+, and advanced part of the field of ON δqn+ coincides with retarded component of the field of ON δqn–. If to proceed from solution for ON field in any of these three forms:

ML = 2LVret,    ML = 2LVadv,    ML = LVret + LVadv, (10)

The result will be one and the same field of the current thread L.

ONs δqn+ and δqn– are mutually inverse and absolutely equal. «+» and «» signs, as well as «ret» and «adv», are conventional and relative and are determined by form of notation and its imperfection. Advanced field is as natural as retarded one, it is one and another – simultaneously (with equal rights). These field components are unextractable from general field of current thread L, as individual ONs of this thread are unextractable objectively. In terms of scalar potential, one should interpret each summand as a semisum of «retarded» and «advanced» parts of a field of two definite ONs of the current thread.

Natural and inherent character of this symmetry of solutions of ML-equations with sources in form of current threads makes them distinguishable, makes these field sources more natural, more adequate to ML-equations.

To give Michael Faraday due for his genius and efforts in discovery and description of the FIELD, its investigation and promotion of this idea, this fundamental field should be named – FM-FIELD (Faraday–Maxwell field).

The nature of fundamental FM-field has prompted the physical essence of field sources through ML-equations and the structure of their general solution. But these sources current threads – appeared to be more profound physical level than elementary particles and four known types of interaction (this number is conventional and may be varied depending on ways of description of interaction between particles). All of them, both elementary particles and fields of inter-particle interaction, are just visible indications of interaction between fundamental FM-field and its sources. This is a program, but at this stage it became possible to formulate it (catch its tail).

The surprising fact is that ML-equations that govern the structure of elementary particles and their fields were discovered in their primordial form on the basis of study of interaction of macroscopic objects at low energy consumption. Partially it «makes clear» an amazing ability of a human to catch the essence of phenomena despite their appearance. Maybe the harmony of these two mysterious and amazing laws can make them closer and create an illusion of conceivability, humanity. This is as if a human recollects something forgotten rather than discovers something new, as if these forgotten things have searched ways themselves, helped a human to get this possibility, to get ready to remember, to restore a harmony in a soul, to get something natural, predestined. Insights are not similar to discoveries, it is rather ability to see, understand, read texts of nature, which sets a human on the right path and helps him to get understanding.

We have not yet exhausted all the wisdom which remains encoded in ML-equations, we are still to be shocked by the depth and information capacity of these looking so simply linear equations which sometimes seem to be out-dated, invalid in the world of atoms, requiring cancellation or generalization. These equations give rise to both the relativity and quantization in a natural way. The only thing to be done is to read correctly this amazing story, to decode FML-CODE of these phenomena.

 The translation from Russian was made by Yuri Nezhentsev
Last modifications: November 27 2002
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