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Vadim N.Matveev
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From the authors

In Soviet scientific literature, the question of synchronizing clocks is mentioned in general terms, if at all. In popular articles, as well as in special literature, almost no attention is given to this central problem in Einstein’s entire special theory of relativity (STR). Apparently for this reason, many people in Russia even today, perhaps “through inertia”, either are not aware of the importance of the question of clock synchronization or are very poorly informed of its essence in general. One of us literally fished a more or less detailed description of the problem of synchronization out of a heap of literature from the 1960s and 1970s. It consisted of individual articles, Marder’s popular book “The Clock Paradox” [1], and an article by A. A. Tyapkin in Advances in the Physical Sciences (APS) [2].

The problematic nature of synchronizing clocks consists of the use of the condition of the equality of the speed of light in opposite directions for clock synchronization in the STR, while it is fundamentally impossible to experimentally verify this equality. In order to measure the speed of light from point А to point В, then from point В to point А, and then to compare these speeds, it is necessary to have synchronously running clocks at points А and В. However, it is only possible to synchronize the clocks at points А and В using the Einstein method by assuming that these velocities are equal even before they are measured. Naturally, after this assumption is made, they also become equal based on the measurement results.

It is also not possible to measure velocity by synchronizing a pair of clocks at point А, then moving one of them to point В, since the result of the synchronization and measurement of the speeds of light from point А to point В and back, vAB and vBА, respectively, is dependent upon the speed at which the clocks are transported from one point to the other. When synchronizing clocks via the transfer technique, if the clocks being transported are transferred at different speeds in different instances, the vAB and vBА velocity measurement results will then be different in different instances. For example, after a clock is transferred from А to В at a velocity close to the speed of light, the vАВ velocity subsequently measured will be arbitrarily great, while the vВА velocity will be arbitrarily close to c/2. During such synchronization, the light arrives at point B from point А almost instantaneously, but travels back two times slower than usual. During very slow transfer, the vАВ and vВА velocities will be equal to one another.

So what clock transfer speed is “correct”? It is impossible to answer this question, especially since clocks at different points in space are synchronized in the STR using light signals rather than by means of moving them from one point to another. Many people today see the equality of the speeds of light in opposite directions as an obvious “fact”, but no grounds exist for the a priori preference of the slow transportation of clocks over fast transportation.

It should be noted that the problem of the speed of light in one direction is not of topical interest in practice, since the speed of light is actually measured using one solitary clock and a mirror. During this solitary clock method, the time interval between light pulse dispatch to the mirror and the reception of the pulse returned to the initial point after being reflected from the mirror is measured. Velocity is calculated for the doubled distance between the clock and the mirror and the light travel time in the back and forth directions. Strictly speaking, velocity measured in this manner constitutes the average speed in the back and forth directions – this is because the speed there may not equal the speed back. The equality of this average speed of the c constant is an experimental fact.

No clock synchronization problems arise during the measurement of average speed. No matter how we synchronize the second clock, the average speed of light measured in the back and forth directions without assumptions would equal the c constant. This is obvious, since the experimental result is not dependent either upon the readings of the clock at point В or even upon its presence there.

It is frequently said that Rømer measured the speed of light in one direction. It may seem strange, but Rømer velocity is also the velocity obtained under the tacit assumption of the equality of the speeds of light in opposite directions. The fact of the matter is that Rømer and Cassini were speculating about the movement of Jupiter’s satellites, automatically assuming that the observers’ space was isotropic. The Australian physicist Karlov [3] showed that Rømer actually measured the speed of light by implicitly making the assumption of the equality of the speeds of light back and forth.

Poincare examined the proposition of the equality of the speed of light from A to B and the speed from B to A, and this proposition in particular became the principal postulate of Einstein’s 1905 work [4], although it was not presented in the form of a postulate, but rather in the form of a “definition”, which preceded two Einsteinian principals that are often called postulates. In a later work [5], Einstein called this “definition” an assumption, during which he noted that it pertains not only to the speed of light, but also to velocity in general. In this work, Einstein wrote: “But if velocity at the speed of light is fundamentally impossible to measure without arbitrary assumptions, we then also have the right to make arbitrary assumptions about the speed of light. We will now assume that the speed of light propagation in a vacuum from point A to point B is equal to the speed of light passing from B to A". In truth, unlike Poincare, who adhered to the conventionalist point of view, Einstein, by alluding to the impossibility of measuring velocity in one direction without arbitrary assumptions, was inclined to regard the arbitrary assumption of the inequality of the speed of light in opposite directions as unnatural and “highly improbable” [6].

It is often said that the equality of the speeds back and forth is obvious, since space is isotropic, and that inequality is unobvious. This is not the case. The fact that light requires more time to move from point А to point В than to move from B to A is also obvious if, for example, point А is located in the stern and point В in the bow of a spacecraft that is moving relative to us and we track the process of light movement from A to B and back not from within, but rather from without. In principle, both the equality and the inequality of this craft’s light propagation times from point A to point В and back can be found from a host of other reference systems that are in motion relative to this craft, even if the clocks of these systems have been synchronized using Einstein’s method. In this vein, what is the basis on which the clock inside the craft is synchronized without allowance for the objective results of the observation of light behavior inside the craft obtained from different reference systems outside the craft?

During the 1960s and 1970s, references were often encountered in abstract journals to foreign works in which versions of the special theory of relativity based on the proposition of the inequality of the speeds of light in opposite directions were examined. These versions were called ε-STR and consistently described everything that the STR describes. In truth, most of them were more “ponderous” and less convenient than Einstein’s version, since they violated the requirement of the immutability of the mathematical form of notation of laws in different reference systems. Most of the works of these authors were not opposed to Einstein’s version, but rather demonstrated the consistency of an untraditional approach. The authors of these works attempted, by disrupting the mathematical beauty of the STR, to uncover its physical content and to clear up the enigma of the speed of light in one direction. Why nature does not permit us to measure the speed of light in one direction without arbitrary assumptions! Is this randomness or something deeper? The developers of the alternative theories did not answer this question.

One of the authors of this booklet tried to answer these questions. By 2000, he had written the book “Entering the Third Millennium Without Physical Relativity?”, which the CheRo Publishing House released that same year [7]. In the book, based on the principle of the equal status of assumptions of the equality and inequality of the speed of light in opposite directions, a means was proposed for solving the synchronization problem and the related problem of the dependence of the magnitude of the physical quantities of a body that are inherent in the body itself upon the reference systems.

The problem of relativistic quantities was solved by means of refining the concept of an “object” and viewing an object as a set of subobjects (objects with a higher degree of concretization), each of which has not relative, but rather absolute dimensions. The relativity of simultaneity is responsible for the existence of these subobjects.

The refinements in the concept of a “physical object” proved to be sufficient to do away with the relativity of the magnitude of physical quantities without the involvement of a dedicated reference system or a global environment. For this reason, the author felt that the matter was resolved (at least as far as he was concerned) and that dealing with a global environment was superfluous. The solution at which we arrived over the course of our joint work on developing the approach described in the book “Entering the Third Millennium Without Physical Relativity?” was even more unexpected. We discovered the possibility of simulating relativistic effects using the simplest techniques of pre-Einsteinian classical physics based on the example of the movement of objects in a material medium. Here, in order to facilitate simulation, it was not necessary for us to examine movement at velocities commensurate with the speed of light. Within the model, effects are manifested in an explicit form at the usual “terrestrial” velocities with which we deal in our everyday life. The possibility of simulating STR effects with the involvement of an environment and the absence of such models in other versions made it necessary to take a new look at the old and the apparently once and for all resolved problem of the existence of a world environment.

In the booklet that you are holding in your hands, a theoretical STR model is described, which we also call an STR simulation. The booklet is a portion of a book that we intend to write and release in the near future. In the booklet, Einstein’s STR is simulated based on the example of barges, shuttles, and boats that travel at the usual speeds in an aquatic environment. Simulation did not require anything from us other than the most elementary rules of classical physics. We hope that, in reading the booklet, you will see how simple the foundation of the theory now called the STR is. Would you not then come to the conclusion that the openwork four-dimensional mathematical superstructure adorning this simple, to the point of primitiveness, foundation is artificial in nature? Time will tell.

In the booklet, we are not revealing all the deliberations that led us to construct the simulation examined in the book. However, we would like to note that the simulation is based not on contrivances for the sake of contrivances, but rather on our notions of how interaction occurs in a material world, the elements of which are not linked to one another by anything other than interactions through a “void”.

The booklet includes the body of the text and attachments. During the first reading, it may be best not to refer to the materials in the attachments, so the essence of the simulation as a whole can be perceived. The reader may then either independently verify the claims made in the body of the text without detailed explanations (it is not hard to do this) or refer to the attachments.

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From the authors
In lieu of a preface. The essence of the simulation

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