Superphysics Superphysics
Authors 13

Kuntz, Lasker

15 minutes  • 3097 words
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Professor Dr. J. LE ROUX /RENNES: THE BANKRUPTCY OF RELATIVITY THEORY

(Translated by Dr. E. Ruckhaber)

  1. Einstein’s RTH created a lively intellectual movement and prompted various theoretical and experimental researches which have contributed to the advancement of science. However, the theory in itself does not stand up to thorough scrutiny. In the light of criticism it becomes clear that the given synthesis is an empty semblance that can only be preserved in a favorable, protective semi-darkness.

The connectedness of the arguments and the childlike nature of the hypotheses are of the same kind. The inferences sometimes have no relation to the premises, the basic components of the calculations assume a meaning that does not correspond to the definition in the underlying data. One could perhaps point out the methodological flaws if the results brought real progress to our knowledge. Unfortunately this is not the case. One or the other of the results obtained are independent of theory and cannot in any way serve to support it. It is known that the special RTH originated from the Michelson experiment.

But the author himself did not understand how to properly analyze the results of this experiment. He drew conclusions from them which they in fact do not imply. He then tried to explain these conclusions by means of a series of hypotheses that contradict each other and have no relation to the phenomenon!

The theory of gravity is also very strange. But here, in addition to the lack of ability, there is the enormous dupery in the alleged explanation of the secular progression of the perihelion movementof Mercury. The observed secular forward motion is approximately 374 “. Einstein’s theory gives a displacement of approximately 42” from Newton’s on the basis of current findings, explains this forward movement up to 336 “. In order to deduce from this the superiority of Einstein’s doctrine, something more is necessary than the most blind and abnormal compliance.

The impotence of Relativity in this regard is due to its entire composition. It takes its own principle as its starting point by undertaking material movements through geodetic measurements in the form of quadratic differentials with four variables, represented by spacetime with four dimensions. This hypothesis contradicts gravity. The attempts of mathematicians, who are more conscientious than clear-sighted, to reconcile logically incompatible things, have necessarily failed and will continue to fail.

In the fifteen years or so since the General RTH was established, it was impossible to derive from it an approximate representation of the movement of the solar system or any other system. The promises made are not kept, this is a significant failure.

  1. The Michelson experiment. From the Michelson experiment, Relativity concludes that the relative light propagation speed for the observer is the same in all directions. This conclusion is incorrect. The isotropy of the interference wave does not include that of the propagation wave in itself 1 ).

One can only conclude from this that the means in which the light spreads, aether or otherwise, is homogeneous and isotropic only under certain conditions with respect to a given reference system. If one admits that the ether is influenced by the force of gravity, even the law of propagation can satisfy the following conditions:

a) There is a reference system S in such a way that the means of propagation is homogeneous and isotropic with respect to S in every region remote from the material masses. b) For every light source that is invariably bound to the same reference system, the interference wave is isotropic in a specific area. c) For every light source bound to a material mass and carried along by it, the interference wave is also isotropic in a special area. There are an infinite number of solutions whose common properties are easy to determine. The exact analysis of the phenomenon does not permit the strange conclusions which form the basis of special relativity. The very precise results of Miller’s new experiments are of the greatest interest because they can help us to exercise the influence of the

  1. J. Le Roux, [translated from French->] „Restricted relativity and geometry of undulating systems“, S. 21 (Paris 1922). Journal of Mathematics, S. 223 (1922).

Getting to know matter on the conditions of the propagation of light .3. The relativistic explanation of the Michelson experiment. Having drawn incorrect conclusions from the Michelson experiment, the relativistic school tries to explain it. Since the partial derivative equation for the propagation of the waves does not hold up for the analytic transformation, which is a rectilinear uniform translation, one changes the meaning of the words. The transformation by Voigt-Lorentz, which retains the analytical form of the equation in question, is baptized with the name “translation”.

This is ridiculous sleight of hand. Translation is one thing, Voigt-Lorentz transformation is another. There is a group of translations like there is a Voigt-Lorentz group. The two groups each have their own area and specific meaning in mathematics. Since these are matters of definition, they cannot be confused.

In order to use the Voigt-Lorentz group, Einstein assumes two reference systems; each of them is assigned an observer equipped with a full set of measuring instruments and timers. Each of the two carries out the length measurements in his own system, namely by shifting the scales according to the methods of Euclidean geometry. The observer and the objects have permanent existence and can even, it is said, pass from one system to another. Finally, the relationship between the coordinates of one and the same event point related to both systems using the formulas of Lorentz.

One notices immediately that these hypotheses have nothing in common with the conditions prevailing in the Michelson experiment, where there is only a single observer who neither has to measure his timer nor determine the numerical value of the speed of light.

  1. Incompatibility of Einstein’s requirements. But even more: Einstein’s hypotheses are themselves logically incompatible with one another.

Two systems with variables S (x, y, z, t) and S ‘(x ’, y’, z ’, t’) may correspond to one another according to Lorentz’s formulas. Should a point in the. System S ‘be fixed, so x’, y ‘, z’ must be constant, while t’ remains arbitrary. The equation which determines t’ then plays no role.

Under these circumstances, all points bound to S ’suffer a straight, uniform translation with respect to S; but the variables x ’, y’, z ’do not mean Cartesian right-angled coordinates in the sense of S. The same obviously applies if one assumes x, y, z fixed and t as arbitrary.

Einstein did not differentiate between the fixed instantaneous values and the variable arbitrary values of t and t ’ between a permanent object and a momentary event. Now, however, the observers, their yardsticks and timepieces must be viewed as permanent things in the system to which they are bound.

According to one of Einstein’s basic hypotheses regarding the length measures in one of the systems, two identical objects that lie in the same system are related to one another by means of a Euclidean transformation made on the variables of this system.On the other hand, according to the hypotheses made, the observers, the yardsticks and the timepieces are mutually related from one system to the other. All of these assumptions would require that the transformation of a Euclidean substitution by means of a Lorentz transformation still remains a Euclidean substitution - which is not the case. Einstein’s interpretation of the Lorentz group thus encounters a logical contradiction. The entire special RTH rests on this fragile foundation.

  1. Space and spaces. In the General RTH there is a mixture of two things which mathematicians wrongly use the same name: geometric space and analytical spaces. In the cases where n variables occur, the analysts often name a system of numerical values that are shared with these variables “analytical point” and all these points the name “analytical space”. The number of dimensions of the analytic space envisaged is the number of variables that make it up. These definitions are purely analytical and independent of the concrete meanings of the given variables.

The geometer’s point of view is different. For him, the number of dimensions is not a property of space, but a property of the space element. This requires an explanation.

The position of a geometric point is determined by three coordinates. The totality of the positions of the geometric points would thus form an analytical three-dimensional space. But a straight line is determined by four numbers, which are also called their coordinates; the position of a solid body is determined by six coordinates, etc. If one regards the straight line as an element, the totality of the possible positions forms an analytical space of four dimensions (Plücker’s ordered space). The totality of the positions of a solid body would also define a six-dimensional analytic space. For the geometer, the location of the points is the same as that of the straight line or the solid: it is always the same space.

The space considered as a place in the sense of the geometer does not have a certain number of dimensions.

Classical mechanics considers systems whose position depends on any number n of parameters. The totality of the possible positions of this system forms an analytical space of n dimensions; the place of these possible positions always belongs to the same indefinite space of the geometer. The point of an event in the relativistic sense is determined by three position coordinates that are linked to a time value. Their entirety forms a four-dimensional analytical space. But if the event is composed of the simultaneous consideration of two point positions and a time value, the whole forms an analytical space of seven dimensions.

The totality of the possible connections between two completely independent event points would form an analytical space of eight dimensions.Further examples are superfluous. The ones given here suffice to make it clear which essential difference there is for the geometer between the local space and the total space. They are two different terms that are referred to by the same name.

  1. The relativistic spacetime and the analytic space of Newtonian gravity. Relativity has only a four- dimensional spacetime in mind, which it examines in the form of quadratic differentials; this should play a role similar to that of the line element of a surface in geometry.

The force of gravity would hereafter be determined by starting from this square shape. The natural motion of a material point would be represented by a geodetic line of the differential form in question. This geodesic line is his world line. A geodetic line corresponds to every movement. Something similar can be found in classical mechanics. The principle of the smallest effect leads to the fact that the representation of the motion of a system is based on a geodetic line in the form of quadratic differentials. But one has in the eye the movement of a whole system, which is viewed as a solid whole, and more that of a single element. The quadratic form then comprises as many variables as are necessary to determine the position of the system, and it is the movement of the whole that is represented by a line from the form in question. If, for example, one imagines the universe as formed by a total of n mass points, the position of the whole will depend on 3n variables. The corresponding analytical space will have 3n dimensions. Time is not a supplementary coordinate, because the movement of a timepiece of whatever kind leads away from the entirety of the movements of the universe.

The square shape mentioned is as follows:

In it U denotes a function of the coordinates of the system. The calculation involves the introduction of an auxiliary variable t, which is defined by the equation is determined. This allows the geodetic differential equations to be reduced to the usual form of the equations of mechanics. This auxiliary variable t is the canonical time of classical mechanics. The canonical frame of reference is the one for which the kinetic energy of the observable universe is minima.

If one finally determines U according to a minimum requirement for the energy of the accelerations, one finds where mi and mk denote the masses of two elements and rik denote their distance. This is Newton’s first law. The equations of motion then have the form These equations contain not only the coordinates of the point under consideration, but also those of all other points in the system, which gives the whole thing closed 1). An interesting fact of relativity, which classical mechanics reveals but escaped Einstein’s school, is the relative character of the principle of the equality of action and counteraction. This principle does not express a property of matter: it is a property that comes from the choice of the frame of reference.

  1. On the impossibility of representing the phenomena of gravity by Einstein’s theory. It remains to be shown that it is impossible to represent the phenomena of gravity, starting from Einstein’s basic hypothesis.

Let T be a quadratic form of differentials of four variables x1 , x2 , x3 , x4 . The equations of the geodetic lines of this form can be written as follows:

  1. J. Le Roux, [French translation->] “Mathematical principles of the theory of Gravitation” Paris

They allow three of the coordinates to be expressed as a function of the fourth and any six integration constants. The only difference between two solutions is the numerical values of these six constants.

Let us consider two solutions that represent the movements of any two material elements. Under y1 , y2 , y3, y4 are to be understood the coordinates of the elements of the first, under z 1 , z2 , z3 , z4 those of the second. You can for example, assume that y1 , y2 , y3 are expressed as a function of y4, and also z1 , z2 , z3 as a function of z4. But there is no necessary relationship between y4 and z4 : there is generally no necessary relationship from element to element between two geodetic lines. Onecould evidently manufacture such a product by i.e. set y4 = z4 = t, where t denotes a time. However, this agreement is by no means essential. Nothing in the differential equations (2) would be changed if for the first line y4 = t and for the second set z4 = t + α , where α means any constant. The lack of a regular relationship between the points of occurrence of two different geodetic lines is the main reason that Einstein’s theory is unsuitable for representing the phenomena of gravity. One can derive differential equations from theory which will more or less approximate those of the motion of a single point; but one will never be able to derive the equations for the motion of any solid system from it. It is not the difficulty of the problem or the inability of the authors to blame for the failure of the attempts that have been made in this sense, but rather it is grounded in the essential contradiction that exists between the principle of Einstein’s theory and the fact of unity. It has not even been possible to set up the equations for the motion of a system of two bodies that are related to a reference system that does not have one of these bodies as its starting point. The secret of this powerlessness lies in the restriction of the analytical space corresponding to the problem of gravitation to four dimensions.

Analytical mechanics, free from the superstition of spacetime, cleanly and accurately solves the problem by introducing the necessary number of variables. Relativistic mechanics stomps in the same place, unable to get out of its four-dimensional prison. The four-dimensional analytic space of Einstein does not contain the 3 n-dimensional analytic points which correspond to each position of a whole of n material elements. While for this reason relativity can only treat the elements individually, classical mechanics treats the whole of the observable universe in its totality.

  1. Gravity is a property of the observable universe considered in its entirety. It is common to see gravity as a law of acceleration or interaction. But in this way the problem is robbed of its true nature. The so-called Newtonian effect, which is inversely proportional to the square of the distance, only applies to movements related to certain reference systems. Since these systems are oriented towards the starry sky, they actually depend on the totality of the stars observed. The wording of the law of attraction also presupposes the choice of a special point of reference for the time so that the acceleration can be determined. This canonical time is also established, theoretically by considering the entire universe, practically by the apparent rotation of the starry sky. It is always the whole of the universe that comes into its own. The concept of two equal and directly opposite actions at a distance seems at first to contradict our understanding. However, we prove that:Whatever the nature of a moving whole, whatever the movements of the elements that compose it - there are always systems of reference which are so constituted that the relative movement of the whole with respect to any particular one within it seems to take place solely on the basis of two mutual, equal, and directly opposite effects. The mutual remote effects are therefore essentially a fact of relativity which results from the determination of the reference system. Einstein’s method did not make it possible to uncover this important result. In order to finally express the law of mutual effect in a form that is independent of the choice of the reference variable, one would have to use the totality of the parameters that serve to determine the position of the observable universe as a whole. That too is beyond the capabilities of Einstein’s method. The results confirmed by the relativistic school only appear satisfactory if they are admitted without criticism. This applies e.g. from the deceptive indication of 42 “for Mercury instead of 374” and the inability of the method to explain the rest.

  2. Conclusion.

These general statements make it unnecessary to go into the various irregularities of the method and the pseudo-geometric theories of relativity. One gets the same impression from them and finds the same lack of criticism, combined with some assertions that are downright absurdities. My very clear conclusion is that Einstein’s RTH does not belong to the field of positive science.

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