| Electromagnetic Phenomena | 2003, Vol.3, No.1(9) 3-5 |
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Paul A.M. Dirac
(1902-1984)
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We are approaching the 100th aniversary of Dirac's birth and the 75th aniversary of his famous equations [1], which, in fact, defined, the development of physics in the 20th century. I believe that this event must be widely celebrated by the Journals and scientific groups. Why? I think that his claim of negative energies in its courage may be compared only with the Lorentz-Poincare-Einstein claim of the fact that the time coordinate must be considered on an equal footing with space coordinates. Next, do you think that Dirac became orthodox after receiving the Nobel prize? My answer is "no". Please read his lectures of 1978 in refs. [2,3]: "Any physical or phylosophical ideas that one has must be adjusted to fit the mathematics. Not the other way around. Too many physicists are inclined to start from some preconceived physical ideas and then to try to develop them and find a mathematical scheme that incorporate them. Such a line of attack is unlikely to lead to success... The appearance of this [Dirac] equation did not solve the general problem of making quantum mechanics relativistic. It applied only to the problem of a single electron, not several particles in interaction... When one tried to solve it, one always obtained divergent integrals... Rules for discarding the infinities [renormalization] have been developed. Most physicists are very satisfied with this situation. They argue that if one has rules for doing calculations and the results agree with observation, that is all that one requires. But it is not all that one requires. One requires a single comprehensive theory applying to all physical phenomena. Not one theory for dealing with non-relativistic effects and a separate disjoint theory for dealing with certain relativistic effects. Furthermore, the theory has to be based on sound mathematics, in which one neglects only quantities that are small. One is not allowed to neglect infinitely large quantities. The renormalization idea would be sensible only if it was applied with finite renormalization factors, not infinite ones. For these reasons I find the present quantum electrodynamics quite unsatisfactory. One ought not to be complacent about its faults. The agreement with observation is presumably a coincidence, just like the original calculation of the hydrogen spectrum with Bohr orbits. Such coincidences are no reason for turning a blind eye to the faults of a theory. Quantum electrodynamics ... was built up from physical ideas that were not correctly incorporated into the theory and it has no sound mathematical foundation. One must seek a new relativistic quantum mechanics and one's prime concern must be to base it on sound mathematics." Did we hear him? My answer is "no". It is too risky. "In order to do science as Dirac advised one should be a Dirac!" These are not my words. These are words of one of well known physicist in these days. Therefore, I do not think that I should appeal scientists to do science in this way. However, if nobody follows his advise, I am afraid that we will never come close to the "origin of things". Do you think we know the origin of mass, the Yukawa term , the origin of why the symmetry is SU(3) × SU(2) × U(1). It has been discovered rather phenomenologically. Is this enough? I think not! The prediction ability of the Standard Model is not as strong as it could be. Therefore, we decided to start celebrating his discovery and his birthday giving an example to other Journals and scientific group to do the same, and decided to make a Dirac issue dedicated to him. We apologise if we were not able to collect all significant contributions to the modern-day Dirac-like theories. But our primary intention was the Dirac approach to science. I hope that this task has been fulfilled to a certain degree. I am happy that our secondary aim was successfull, too. You may see that in the Table of Contents. The list of very respectable authors is impressive. As for antecedents, we noted that in the (1/2,0)⊕(0,1/2) representation different equations may exist [4]. However, it seems, that the same observation has been made by Weinberg [5]. "The kinematical classification of particles according to their Lorentz transformation properties is entirely (for finite mass) determined by their familiar representation of the rotation group. It has nothing whatever to do with the choice of one relativistic wave equation rather than another". Of course, one has to take into account the issues related to the representation of the inversion group, namely, the theoretical possibility of unconventional representation of inversions [6], which in the West is called a Wigner type theory. Moreover, independently, physicsts discovered the quantum nature of space-time (or of the corresponding velocity space) [7], and related it to the hydrodinamical theories [8]. All these topics are interested to us. Next, physics approaches again the anti-de Sitter group (which, by the way, also have been studied by Dirac from a group-theoretical viewpoint [9] (see also Kadyshevsky et al [10] and Greiner et al [11]). Physics again approaches the problem of negative-energy solutions and oscillator representation of relativistic quantum mechanics. Who was the first? It was Dirac [12]! I think this is enough. We shall remember Dirac for another 100 years, at least. Does anybody disagree? In the present volume we have some papers related to the aforementioned. I would like to single out the following: S. Blinder considers the classical model of electron and fluid concentrated within a radius of 10-13, which may be an analogue of vacuum polarization. M.N. Célérier and L. Nottale use the formalism of fractal geometry. L. Hannibal discusses some as yet unusual extensions of the Dirac theory to the Riemannnian space. S. Kruglov is for the non-commutative space. He quantizes the Maxwell theory a la Dirac. Kashinov and Ivanov discuss the important (in my opinion) issues of the definitions of Heaviside function and the Dirac delta-function. Kocinski is for the 5th dimension too. Mignani et al. find some relations between 4D and 5D. It is good that they cited the fundamental works of Acad. V. Kadyshevsky and his group. I decided to accept their papers. R. Kuehne suggests several experiments which would be able to find magnetic monopoles (the t'Hooft-Polyakov monopoles?). Horzela and Kapušcik analize the origin of negative energies more deeper. B. Lehnert develops his theory based on the non-zero electric field divergence in the vacuum and applies it to the behaviour of "neutral" particles. It is related to many models proposed in the last fifty years. My question is: is this some new sort of aether (this is left for the reader to answer)? V. Simulik and I. Krivsky's work also has many precedents. It caused a lot of discussions with the referees, as did their paper in the previous special issue of the Editor (in AFDB). This signifies that this paper deserves to be read and carefully checked. Raspini develops a very interesting idea of Tokuoka, SenGupta and Fushchich et al. of the modified Dirac equation with two mass parameters. He might advance even further suggesting the Lagrangian for this model. There are several other contributions in this volume. Many thanks to all who participated in the creation of this special issue. Thanks to the Publsiher, thanks to the Institute for Electromagnetic Research. They did great work. They will do greater.
References
V.V. Dvoeglazov
Universidad de Zacatecas Apartado Postal 636, Suc. UAZ Zacatecas 98062 Zac. Mexico October 2002 |
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