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Full Text of the Preface to A Search for the Finite Physics
This publication is a collection of three articles written at different times and on different topics. The first article is the newest and the widest in scope. It will be of interest to physicists whose concerns are the validity of the currently accepted physical laws and the enlargement, if not the complete removal, of these limits. The second article is the oldest and shortest, dealing with a very narrow problem in the general relativity theory. The last article describes a new method of constructing vacuum solutions to the general relativistic field equations.
Of course, the proper places to publish such articles are the refereed physics journals. However, as many physicists realize, such publication is not an easy act to accomplish. This is particularly so if one works alone, without a support group, on topics that are not current, and that do not promote or enhance ideas in progress. The more one deviates from the mainstream of research, the less likely it is that such work will be accepted for publication in a refereed journal, which normally receives more submissions than can be accomodated.
My first article, entitled “Singularity Free Field Equations,” cannot be described as being in line with the main research trends of today. Quite to the contrary, it completely breaks with the traditional direction of research. For reasons enumerated below, it rejects most, if not all, fundamental field equations of physics whose validity has never been questioned before. They are replaced by a set of non-linear field equations that lead to more involved and complex solutions. All this is done for the sole reason that the old field equations lead to particle-like solutions with singularities and the new ones do not. Not much justification for this approach is offered in the article itself and I feel that I owe my readers some explanation for this radical attitude.
There are a number of complaints I harbor toward the prevailing atmosphere in the theoretical physics of today and of the recent past. First, the Electro-magnetic theory (EM) embodied in Maxwell’s equations, both classic and quantum (QED), is considered one of the finest examples of scientific theories. And I have to agree with this opinion as far as the left-hand side of the field equations go. As to the right-hand side, which contains the EM charges and currents, it is, in my opinion, a total failure. By now there are close to a hundred elementary particles carrying primitive electric charges and currents, yet none of them are solutions of either classic or quantum EM field equations. The question is, why aren’t they? Are Maxwell’s equations incapable of producing solutions with charges? Every physicist knows that they are. A sum of terms of the form ei/|r - ri| are the solutions with charges. Do these solutions correspond to any of the observed charged particles? Absolutely not! Not even one fits the bill. The reason is simple enough. Each charged solution represents a particle of infinite mass and of zero spin, whereas all observed particles have finite masses and diverse spins. So why have the EM field equations failed to produce solutions that correspond to real, observed particles? To me, the answer is obvious. The current formulation of the EM field equations is incomplete and deficient and in need of a fundamental change.
Second, in my first exposure to the EM theory it was impressed upon me that whenever and wherever there are charges and currents, they inevitably generate and drag along with them a cloud of the EM field. The EM field can break away from the accelerated charge and propagate as a wave; however, the EM charge can never appear bare without the field. In fact, the charge’s presence is established and detected by the presence of the field itself. Yet in the quantum treatment of charged particles their EM (self)field is left out of consideration and completely ignored as if it were not there. No mention is ever made of why the field is omitted or that an incomplete problem is thus studied.
Finally, it is very puzzling why singular solutions are accepted as good coin in the realm of physics when it is well known that they give not only incorrect, but non-sensical answers of infinite energies mentioned above; moreover, that acceptance of singularities puts limits on the validity of the physical laws. Of course, it is universally acknowledged that the non-sensical infinities are bad and have to be subtracted; however, the blame is never put where it belongs, that is on the field equations that produce singularities. Rather, singularities are treated as local wounds on the body physics to be tolerated and eventually cured as a minor ill. Even the unambiguous experimental result such as the vacuum polarization is interpreted benignly toward the singular solution in the form of the Coulomb law. It is said to be a quantum correction to the law rather than what it actually is - a direct indication that the Coulomb law is invalid, although, under most conditions, a good approximation. If the real problem had been delineated, defined, and discussed, the above trends and directions of research would be understandable and excusable as expedients and temporary measures. However, the real problem was never mentioned, nor defined, nor discussed. There appears to be a silent conspiracy of the physics community not to question the validity of the EM field equations, to consider Maxwell’s formulation of them to be classically correct and the QED modifications to be refinements and alterations also correct, but this time on a different, quantum plane so that the two “correct” theories do not collide.The facts to me, however, are plain. If the vacuum polarization results are correct, then the Coulomb law is not and Maxwell’s equations in the present formulation are incomplete and inadequate to the task.
The above views have driven me to reject the field equations that lead to singularities and to search and replace them with a set that offers a choice of particle-like solutions that are regular everywhere.
The next two articles are concerned with the vacuum solutions of the general relativistic (GR) field equations and as such have nothing directly to do with the singularity free field equations. However, their indirect influence on the inclusion of the GR theory into the plan for modification is unmistakable.
The first, short article is unusual in that it requires no mathematical work at all in spite of the fact that it offers a first, as far as I know, multiparticle vacuum solution to the GR field equations. Due to the general covariance, the coordinates in any exact solution of the GR field equations do not possess an absolute meaning in that they can be replaced by a set of new coordinates which are functions of the old ones. Taking advantage of this freedom, I replaced the radial coordinate of the Schwarzschild solution with the reciprocal of Newton’s gravitational potential for N particles, where N is any positive integer. And - lo and behold ! - I obtained an exact vacuum solution to the GR field equations for N particles. In 1993, I submitted this result to the Physical Review Letters. The editor replied that the metric so constructed was not a solution and hence rejected the paper. I knew better and resubmitted it. This time an expert from Chicago admitted that the metric was a solution, but that it was not a new solution. On that basis he recommended not to publish the paper. It is inconceivable to me that an expert would not see the difference between a function with one singularity and a function with N singularities. So far, I have not heard that my solution has appeared anywhere in print. This indicates to me that the expert indeed may have missed both the physical and the mathematical difference in the two functions, and more importantly, its physical significance. I have decided to include the short article in this collection to get credit for it, to communicate it to the physics community for whatever use they can make of it, and, most importantly, because it opened my eyes to the new aspect of the GR field equations. The fact that they allowed such a wide new family of solutions convinced me that the GR field equations are not as exclusive as I thought they were, and that there must exist a method to generate these, and possibly other, solutions directly by mathematical means.
This conviction persisted and I began an effort to find such means. While pursuing this goal, I happened to come upon an expression whose addition to the common field equations made them yield solutions that were free of singularities. Having spent many years searching for such an expression, I was very excited with this new find in spite of the fact that it required an unusual form, an integral over the field rather than an algebraic expression in the field. At this time I abandoned the work on the last article and started to explore how to construct the singularity free field equations. It seemed a good idea to start with the simplest field equations and to progress to the more complex ones as I gained experience. This is how the work evolved and how it is presented. The Newton’s gravity, the Klein-Gordon (K-G) field, and the Dirac field modifications were for me the learning steps and are to be< treated as such by the reader. The culmination of this effort was the EM field equations. After I derived the masses for the three leptons it became clear to me that the fundamental equations of physics are not the K-G fields or the Dirac fields which deal with specific species of particles and contain such global properties as spins and masses. The fundamental equations are those of the EM fields containing no global characteristics and only their densities. Any particle properties found in nature should be derivable from these densities by integration and quantization, provided the theory contains a sufficient number of free parameters.
At this stage I went back to the last article to finish it. The initial joy of having laid bare such a difficult problem was clouded by what the results implied. The high degree of arbitrariness in the vacuum solutions of the GR field equations made it difficult for me not to do something about it. As a result of this dilemma, added to my general and persistent desire to get rid of singularities, I decided to formulate a new set of field equations for the general relativity. The set is based on the wave propagator to insure that the solutions are “physical,” and they are formulated in the flat spacetime to endow them with the energy- momentum tensor and a high degree of tractability. In spite of all these simplifications the general covariance is preserved at all levels. It is presented as a last section in the first article. The theory is free of singularities and at long distances its solution coincides with the conventional solution to the first order in 1/r. Beyond that, all its other achievements are only aesthetic.
No doubt there are some physicists so used to singularities that they will miss them. My field equations can accommodate them if the constants of integration are selected with care. I am ready to reintroduce singularities whenever and wherever mother nature should call for such drastic measures.
BOHDAN SHEPELAVEY |
