and Subquantum Field model of Electron
Alphonse Bertillon
Georg Hegel
Jacques Hadamard
Albert Einstein |
In the introduction to the work [3] Max Born right after the conclusion concerning the conservatism of hyperbolic motion:
It should be noted that an electron in hyperbolic motion does not have any self-radiation, no matter how great its acceleration is, but hauls its field along. Up to now this circumstance has been known for electrons in uniform motion only. The radiation and radiation resistance only appear at declination from hyperbolic motion.[3]
finishes the next paragraph not less meaningfully:
My theory is in the full accordance with an atomistic instinct of so wide a range of experimenters, that the interesting attempt of Levi-Civita [7] to describe the movement of an electricity as the certain liquid moving freely under the action of its own field and not bound by any kinematic conditions, is hardly worth approval.[3]
The thing is, the field of a single based electron model of the subquantum field theory is nothing more than the central-symmetric stationary two-liquid hyperbolic current of Levi-Civita in its own central-symmetric field. In its turn, the stationary field of a single electron is the sum of the own fields of all the elements of the current of these two unlikely charged electric liquids of Levi-Civita in all space.
Latent from us at the subquantum level, and laying invisibly in the basis of dynamic mechanisms of stable existence of all the quantum bricks of our world, the movement of electricity is similar to the current of the phase liquid moving freely under the action of its own field. The motion of each element of this charged liquid of Levi-Civita should not be bound by any kinematic conditions, imposed from the outside. As for dynamic conditions, imposed on the motion of subcurrents of a single based electron by the requirement of their being strictly hyperbolic (conservative), they have seeming «kinematic» status only for the period of the theory construction and only until the required equations of subcurrents motion in their own field are written down in an explicit form. And these equations are initially selected so that first of all to provide strict conservatism of the motion of subcurrents in the central-symmetric field of an electron. I shall remind, that only the hyperbolic motion of electron subcurrents can pretend to this role by virtue of its conservatism (the absence of energy losses for radiation, in full accordance with Maxwell–Lorentz equations). Only under the condition of being strictly hyperbolic (conservative) in combination with the condition of the central (spherical) symmetry, the required stationary picture of motion of the charged subcurrents in all space, dynamically coordinated with the own field of all this set of subcurrents in all space i.e. with the field of electron can be obtained.
There is no need at the moment to specially stop on the criticism of Born's work [3]. Despite of the well-known confusion in the minds of his contemporaries, coming from the coordination of names of Hermann Minkowski and David Hilbert with this work and natural problems of development of the relativistic paradigm, just two years later Max von Laue would very clearly and firmly declare: – The principle of relativity excludes this possibility [the firm body having a final number of freedom degrees] on the basis of dynamic reasons and consequently any attempt in this direction is unpromising [8]. In this article Laue mentions the participation of Arnold Sommerfeld in the discussion at the assembly of natural scientists in Königsberg and adds in the commentary: – I can't help mentioning that I discussed these questions many times with Sommerfeld.[8]
In itself, this conclusion of Laue concerning legality of the concept of relativistic firm body of Born follows quite trivially from the postulates of the Special Relativity (SR) of Albert Einstein. One can only wonder at why nobody found it necessary and appropriate to publish such a conclusion earlier. Anyway, this delay had nothing to do with the absence of clarity in this question among the main characters outside Göttingen. And there, it seems, the special point of view predominated over this subject, that was coming from David Hilbert, and had an influence, for obvious reasons, not only on works of Born concerning the «due» edition of physical works of Hermann Minkowski, but also on the form of the reaction to these works from the side of the representatives of other scientific centres of Germany.
One should note, that at that point of time an atomistic instinct had just been taking roots in the minds of physicists with reference to atoms. The influence of position of Ostwald and «power engineering specialists» could still be traced. Concerning an electron the situation was very uncertain. The physicists with field instinct of Faraday–Maxwell were still alive and worked actively. There was no unanimity in this question among the young generation as well. A lot of people were confused with open condition of electron model and the absence of correctness in the procedure of replacing extensive electron by point model.
Having failed in the first attempt to solve the problem of stability and atomism of electron within the framework of model of a relativistic firm body, as if uniquely dictated by the postulates of the SR of Einstein, Born did not leave hope for the possibility of constructing a static model of a charged electron-corpuscle. Using the experience of Albert Einstein and Gustav Mie, stored in the business of construction of field theories using nonlinear scheme, Max Born in 1914 proposed his own version of the nonlinear field theory, capable, on the first impression to give adequate and everywhere the regular static solution for electron. The lack of vitality of this approach as well had absolutely not shaken his belief in an atomistic instinct of so wide a range of experimenters, which with time appeared strengthened by the doctrine of static character of an electric charge of a based electron.
Each new nonlinear theory of a field was checked by Einstein and other theorists on existence of the everywhere regular, central-symmetric static solution, suitable for the description of electron. The question of the own stationary microcurrents of a charge of electron in its own static field and their possible dynamic inter-conditionality was not put at all. Interpretations of «achievements» of the SR and the quantum theory were rising as basic obstacles, as if prohibiting the use of ether and its currents with classical trajectories of micro-charges motion. This doctrine of static and quantum character of a charge of field sources was not tried either by Levi-Civita or by others mathematicians again. It seems, physicists looked at this problem as at the one lacking common sense completely. They were firmly convinced in the auxiliary if not fictitious character of phase and configuration spaces, in absurdity of concepts about currents of an ether and classical trajectories of micro-charges motion.
The logic, at first sight, was faultless. The set of the experimental data stored by then about physical processes with participation of electrons did not allow physicists to describe them sequentially in concepts of continuous motion of corpuscular point electrons in Space-time of Minkowski (M-space). Physicists based on belief, as if the only sources of an electromagnetic microfield were the charged electrons and protons. From here, in fact, conclusions were drawn of the absence of any latent charged sources of a field and their currents, as well as of impossibility of the description of their motion on classical trajectories in M-space by virtue of the absence of such a possibility for corpuscles-electrons. The more so since the interpretations of waves of Lui de Broglie and the uncertainty relations of Werner Heisenberg seemed to form an irrefutable evidence of continuous character of inflation of concept of classical motion in M-space, as the result of reduction of the characteristic size.
The static model of the point electron, bearing (carrying) on itself quantum a charge and mass, had all chances to be scattered as a house of cards after a recognition of a formalism of wave mechanics of Erwin Schrödinger in many-dimensional (complex) configuration space. Even less possibilities for improvisation remained at physicists' disposal at interpretation of the formalism basing on spinor equation of Dirac. Mathematical structures of equations of Schrödinger and Dirac required, it seemed, the complete refusal from whatever traces of charges-corpuscles at the description of electron-positron field for the benefit of a mixture of two unlikely charged spatial sets of field subcurrents. But here as well, at direct participation of Max Born, physicists managed to offer and protect such an eclectic model of electron-positron field, according to which electron was either a corpuscle or a wave field depending on the point of view of the experimenter or, more precisely, of the experimental setting, which he constructed for this purpose.
The services of Born at all these critical stages of progress and strengthening of an atomistic instinct in bowels of perceiving minds of physicists are doubtless and are very well traced. He, as no one else, in the course of twenty years repeatedly appeared in the thick of significant for all Physics events, and in many respects defined the existing at our disposal physical interpretation of mathematical formalisms used in a microcosm. It's quite another matter, – how long we will still be able to carry on the productive dialogue with nature, without changing our working words, concepts and instincts?
It is necessary to specially note Born's successful use of rather seldom occurring in the works of physicists a concept – an atomistic instinct. With its help the quoted earlier phrase of Born very neatly and fully opens the basic aim of the work [3]. The task was put to construct the proofs of competence and efficiency of an atomistic instinct of so wide a range of experimenters, as well as of his own and David Hilbert's one, with reference to the description of a nature of electron.
Works of physicists-experimenters can be roughly divided into two, very much differing on their capacity, category on the basis of a degree of their critical attitude to some instinct, on the role and the status of this instinct in their research work. Though the picture becomes complicated due to the necessity of relying in every work on the whole group of initial instincts, obviously or tacitly involved in a subject or methods of research, it does not impede to carry out splitting on each of them individually.
Some take (inherit) already worked out by their predecessors and shared by their colleagues an instinct and give to it the status of an initial, base concept for the research. The persuasiveness of obtained results strengthens and deepens this instinct even in that case when the experimenter did not put before himself with all definiteness such an objective, believing this instinct to be certainly righteous and defended by all the previous scientific practice and having need in neither background nor reinforcement.
Others find available and received from predecessors an instinct inconvenient, badly adapted for the adequate description of the elected circle of the phenomena. And they bravely start laying a new instinct, grope for a way of its construction, on the basis of their own vision of specificity of subject matter and possible, let still very hazily felt, prospect.
It is almost needless to remind, how difficult and troublesome work it is, what tests fall upon a head of the rebel, what misunderstanding and sneers is necessary for him to bear from the side of colleagues and the numerous grey mass of adherents of «learning» and keepers of «cleanliness» of a scientific method, which joined them.
Some people obtain satisfaction from the done work and ceremoniously stride in magnificent cloaks under envious looks of colleagues and applauses of enthusiastic public, luxuriate in the streams of approval and gratitude (and at times love) from the side of relatives, obtain well-deserved rewards and the financial help for the further work, successfully advance on the staircase of scientific career and duly serve the science and mankind.
Others are expelled, in overwhelming majority, from the temple of science as apostates of faith and instinct and are buried in oblivion. Refusal from tested system of fundamental concepts in the mastered before area of the phenomena, raised through the mechanism of scientific inheritance to an instinct, is perceived by vast majority as display of a nocuous mutation, impending to destroy the clear-cut work of an organism of science. The carrier of attributes of rebelliousness appears to be the subject to treatment and isolation from the representatives of a healthy part of scientific community, sometimes with application of very rigid sanitary measures.
And only few of them manage to continue the begun work if they in time find themselves strong enough to drop over themselves a more or less skilful mask of decency and reliability, having hidden for the time being their heretical plans. The number of such lucky persons is not so great by virtue of rebellious arrangement of their personalities badly adapted to the show and acting. And only very few of them, minions of fortune, achieve success and enter their name in an imperishable fabric of inherited intellectual memory of descendants in the form of an instinct. However, these elects of gods themselves receive such honour, as a rule, only after the death and the change of generations. Cases of occurrence of lifetime certificates of nascency of a new instinct in physicists' thinking during some last centuries can be counted using the fingers of one hand. The nature of such quite an abnormal phenomenon is possible to explain by the extremely hardly probable, but nevertheless possible result of interaction, interference of our Rebel's efforts with pioneer work of another Genius in the same direction. Bright an example of such happy interference is the appearing in the world Faraday–Maxwell sheaf and their joint child – a field instinct.
An availability of characteristic instinctive constituents in any scientific theory, inseparable from its historically specific set of carriers in flesh, and regular display of specificity of these constituents in the mechanisms of heredity and variability of scientific theories, is well coordinated to famous thesis of Max Planck:
The final victory of Boltzmann in the fight against Ostwald and power engineering specialists for me was… the fact self-understood… At the same time I managed to establish one, in my opinion, remarkable fact. Usually new truths win not by the way of convincing their opponents and making them accept they were wrong, but mostly when these opponents gradually die out, and the rising generation just acquires the truth at once.[16]
For the description and the analysis of the phenomena of scientific life, the evolution of scientific theories and all range of the phenomena concerned, it is deemed useful to use the language and methods of the evolutionary theory in addition to the standard, describing the process of cognition in terms of relations between the theory and experiment. Application of the methods of the evolutionary theory allows very convexly and evidently to grasp the essence of many processes which are taking place with the scientific theories, which are badly describable in the language of interaction of ideas and their complexes, torn off from their carriers – people.
The result of activity of some placed at the moment in the shade an instinct-obstacle, which was chaining the creative person of any scale, can be revealed with the help of steadfast supervision and analysis of all implicit fragments used at reception of the absurd solution. Chaining, ill-wresting instinct-obstacle's influence on the process of cognition can be illustrated to the present reader on examples of «errors of the great» who were making their errors some centuries prior to the occurrence of our educated in these questions «I», doomed to make already own mistakes in other situations, that still have quite similar (invariant) structure. As samples-textbooks for the improvement of clearing technique, putting in order our own cognizing «I», – a small fragment from the remarkable book of Morris Kline «Mathematics. The Loss of Certainty»:
Decartes also rejected complex roots and coined the term imaginary. He said in his Geometry, «Neither the true nor the false [negative] roots are always real; sometimes they are imaginary». He argued that whereas negative roots can at least be made «real» by transforming the equation in which they occur into another equation whose roots are positive, this cannot be done for complex roots. These, therefore, are not real but imaginary; they are not numbers.
Not even Newton regarded complex roots as significant, most likely because in his day they lacked physical meaning. In fact, he said in his Universal Arithmetic (2nd ed., 1728), «But it is just that the Roots of Equations should be often impossible [complex], lest they should exhibit the cases of Problems that are impossible». That is, problems which do not have a physically or geometrically meaningful solution should have complex roots.
The lack of clarity about complex numbers is illustrated by Leibniz's oft-quoted statement, «The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity». Though Leibniz worked with complex numbers formally, he possessed no understanding of their nature. To justify the use he and John Bernoulli made of them in the calculus, Leibniz said no harm came of it.
Despite the lack of any clear understanding during the 16th and 17th centuries, the operational procedures with real and complex numbers were improved and extended. In his Algebra (1685) Wallis showed how to represent geometrically the complex roots of a quadratic equation with real coefficients. Wallis said, in effect, that complex numbers are no more absurd than negative numbers and, since the latter can be represented on a directed line, it should be possible to represent complex numbers in a plane. He did give an incomplete representation of complex numbers and also a geometrical construction for the roots of ax2+bx+c=0 when the roots are real or complex. Though Wallis's work was correct, it was ignored because mathematicians were not receptive to the use of complex numbers.[17,ch.V]
This book and books like this should be read and studied repeatedly at various stages of self-improvement by each researcher who wishes to clearly look inside himself at the correlation between the logical structure of his scientific models and their instinctive constituents. By virtue of our knowledge of «correct» answers, – it is easier for us to trace this correlation in quite remote from us documentary copies of adventures of creative idea of the great. Results of the done work can render invaluable service to everyone, who sincerely wishes to get rid of various intuitive «clips» in bowels of his own cognizing personality. Such «clips» are an obstacle in the way of our creative potential's opening, they block productive activity of our scientific «I», aimed at researching the unknown. If in time to realize the utility and necessity of such a step, to distinguish in oneself the display of similar intuitive and instinctive «clips», and to start their elimination by definition and clear-cut verbalization of the instincts and intuitive «postulates» put in depths of consciousness, to transfer them into the rank of «working hypotheses» accessible to the logical analysis and the critic, – results will not keep themselves waiting.
Chapter V with the beautiful heading «Illogical development of the most logical science» in the book of Morris Kline [17] opens with harmonious to our efforts epigraph of Wordsworth: No, we should not grieve for the past – we have to look for powers there. This «illogicality» is natural to interpret as «illegal» presence of the «foreign» bases – the instincts, that take a role of logically picked up and tested postulates and principles. So we also shall not grieve for the past and shall take the wise advice. We shall endeavour to obtain authority above our own instincts, improving the last ones up to such a degree that the descendants would believe, that our instincts were shaped under the supervision of wise ideas, so that they would not have to convict us of the opposite, proving the domination of our dense instincts above our most illogical ideas. And hope we will have the luck of faceting our own instincts in such a way, that they will begin to sparkle with divine light inside us, illuminating our ways of knowledge, cleared of an excessive cargo of self-conceit, admiring our former forms of an ascension to treasured truths.
As the first, tentative «proof» of the possibility of correction of our own instincts during the intellectual development (individual ontogenesis), I shall refer to Richard Dawkins: – we are constructed as the machines for genes and grown as the machines for mimes, but we are in forces to rise against our creators. We are the only creatures on the Earth, capable to rise against the tyranny of egoistic replicators.[29] I shall postpone to the future subsequent «proofs» of the possibility declared above, not having denied myself right here of a small pleasure to refer to precedent of my own ontogenesis… It will be necessary to return to the additional analysis of thesis of Dokins about our capacity to rise against the tyranny of egoistic replicators both during the process of collective historical phylogenesis of our scientific theories, and in case of individual ontogenesis of the specific person-researcher, which seems to be especially problematic and difficult for realization.
The retrospective analysis of the reasons of origin of predecessors' mistakes obvious to us gives us a possibility to convict and to neatly classify the instincts guilty in it, the imperatives of intuition and implicit methodical installations similar to them, to make their explicit description, comprehensive inventory and the analysis. On the one hand, – we easily overcome this site, already traversed by others before us, and we have comprehensive maps of logical structure of this area and are almost insured from the recurrence of mistakes. And on the other hand, – we get an invaluable experience of recognition and drawing on maps a various sort of artful traps for our own knowledge, that will occur on our way as well in still an unknown area.
Both the overcoming of various in their form but not in essence the barriers arising on our ways of knowledge, and the development of various languages (techniques) their description (overcoming) gradually elaborate in us the proper reaction on their most unexpected occurrence in various forms of phenomena and acts of nature similar to them. We do not panic any more, we do not rush blindly into unknown, checking feverishly the available equipment on the way. The experience saved up by us suggests by the words of Einstein, – God is refined, but not ill-intentioned. We quietly have a seat and we concentrate profoundly on the adventure which has fallen down on us, the possible versions of construction of the equipment appropriate to the situation.
It is very regrettable to observe how managers from science in every possible way involve us in this crucial period into public shows of different kind and purpose, in every possible academic races with obstacles, finding-out and the account of merits of participants, various priority suits… Such methods worked out still at the organization of fights of the Roman gladiators, can very probably assist the birth of successful «sports» idols of the public thirsting for shows, or the selection of stars of show business and so forth, but can not assist the success of our candidate in Prometei. At a cradle of our civilization bloody Roman collisions of dark animal instincts were played, but there was also the stage of the Greek theatre where dramas of the ideas cleared from being concrete of their carriers were played, there were the fine muses attracting up, bringing up harmonious aspirations of our souls…
The great gift of heavens to Newton was a happy and fruitful isolation (1665–1667) in communication which was a result of the plague raging around in England, the isolation which presented us with an essential part of the Science of new time. We can and are obliged in memory of feats and sufferings of the predecessors to expose precautionary signs and beacons, and as worthy of their intellectual efforts monuments to shape effective toolkit (like a map, a compass, a telescope, a microscope etc.), the organized protective mechanism (immunity) standing on guard of our creative health and allowing to orientate oneself with more confidence in the dark back streets of our cognizing «I».
| The translation from Russian was made by Masha and Natasha Zazerska Last modifications: March 20 2003 | RU | Back to Contens |
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