A. Einstein (1955). Relativistic theory of the non-symmetric field: General remarks

Vladimir Leonov

 Vladimir Leonov. A. Einstein (1955). Relativistic theory of the non-symmetric field: General remarks. – E-preprint: Proza.ru, Certificate of publication No. 221092901064, 2021, https://proza.ru/2021/09/29/1064

ANNOTATION WITH COMMENTS

This posthumous article of 1955 is the Scientific Testament of Einstein (1879-1955) in which he abandons his scientific heritage and proposes to start all the work anew with the development of a new theory [1, 2]. “HOWEVER NOW NOBODY KNOWS HOW TO FIND A BASIS FOR SUCH A THEORY,” states Einstein at the end of the article and his life.

So, dear readers, I invite you to get acquainted in the original about what Einstein thought about his scientific work at the end of his life in order to eliminate all speculation on this issue. His opinion is at odds with the generally accepted academic assessment of the General Theory of Relativity (GTR), which was not completed by Einstein on the way to the Unified Field Theory (UFT) – the theory of Superunification.

Therefore, there are practically no references to this article by Einstein, since over the past almost 70 years there has been an unprecedented parasitization of the scientific community on Einstein's works on the General Theory of Relativity (GR), which Einstein himself abandoned at the end of his life. But no one could offer anything fundamentally new, rewriting Einstein's formulas from left to right, and vice versa, in thousands and tens of thousands of articles and books that do not mean anything to science.

This is not about revising Einstein's fundamental ideas in the field of gravity as deformation (curvature) of space-time that are unshakable. And we are talking about a mathematical apparatus in the form of a tensor model of General Relativity (1913) proposed to Einstein by the Swiss mathematician Marcel Grossman (1878-1936) and which played a positive role in the formation of GR. But this mathematical apparatus turned out to be imperfect, and its geometric interpretation of gravitation became obsolete by 1955, as Einstein states in his article. This was facilitated by the failures of Einstein in creating the Unified Field Theory, using the tensor model of GR, on the development of which he spent 30 years of his life in vain. 

Therefore, it is important for us to know the Conclusion of Einstein himself on this article in the original, which he named as "GENERAL REMARKS" in only 1.5 pages of text. This article has 25 pages and many formulas.

It was the "GENERAL REMARKS" that determined the future development of theoretical physics as the creation in 1996-1999 the theory of SUPERUNIFICATION, which includes the theory of quantum gravity [3]. The theory of SUPERUNIFICATION this is the basis of the NEW THEORY, the need for which was pointed out by Einstein in 1955. This fact also applies to GR, already as the Quantum General Relativity (QGR). You can also read on this topic an article by Vladimir Leonov "THE EINSTEIN POSTHUMOUS PHRASE" (2006) [4]. 

The annotation and comments to this article by Einstein were written by Vladimir Leonov on September 29, 2021.

So, we read further A. Einstein himself:

A. Einstein. GENERAL REMARKS (1955) [1] 

A. From my point of view, the theory laid out here is the logically simplest relativistic field theory possible in general. But this does not mean that nature cannot obey more complex field theories.

More complex field theories have been proposed frequently. They can be classified according to the following characteristic features.

a) Increase in the number of measurements of the continuum. In this case, it is necessary to explain why the continuum is obviously limited to four dimensions;

b) Introduction of fields of a different kind (for example, a vector field) in addition to the displacement field and the tensor field g_ik (or g^ik);

c) Introduction of higher order field equations (in the sense of differentiation).

In my opinion, similar more complex theories in their combination should be considered only if there are physical reasons for this based on experiment. 

B. Field theory is not yet fully determined by the system of field equations. Should we admit the existence of singularities? Should we postulate the boundary conditions? As for the first question, my opinion is this: singularities should be excluded. It does not seem reasonable to me to introduce into the theory of continuum points (or lines, etc.) for which the field equations do not hold. Moreover, introducing singularities is equivalent to postulating boundary conditions (arbitrary from the point of view of the field equations) on the “surfaces” surrounding the singularities. This theory will be too vague without such a postulate. The answer to the second question, I think, is that it is imperative to postulate boundary conditions. I will demonstrate this with an elementary example. You can compare the postulate about the potential of the form ф=m/r with the statement that the equation ф = 0 is fulfilled outside material points (in three dimensions). But if we do not add the boundary condition, according to which ф vanishes (or remains finite) at infinity, then there will be solutions that are entire functions of x [for example, 

 x₁²—1/2 (x₂² + x₃²)]

increasing unboundedly at infinity. It is possible to exclude such fields only by postulating the boundary condition if the space is "opens".

C. Can you think that field theory will allow you to understand the atomistic and quantum structure of reality? Almost every answer to this question is "no." But I believe that no one knows anything reliable about this at present, since we do not know how and to what extent the elimination of singularities reduces the set of solutions. You do not have any systematic method for obtaining solutions, free of singularities. Approximate methods are not counted here, since it is never known whether an exact solution free of singularities exists for a particular approximate solution. For this reason, we cannot currently compare with the experience of the content of the nonlinear field theory. Here it can only help the significant progress in the mathematical methods. At present, the prevailing opinion is that the field theory must first be translated by quantization into a statistical probability theory, following more or less established rules. I see in this only an attempt to describe relations of an essentially non-linear character by linear methods.

D. It can be convincingly proved that reality cannot be represented by a continuous field at all. From quantum phenomena, apparently, it follows that a finite system with finite energy can be completely described by a finite set of numbers (quantum numbers). This, it seems, cannot be combined with the theory of the continuum and requires a purely algebraic theory to describe reality. HOWEVER NOW NOBODY KNOWS HOW TO FIND A BASIS FOR SUCH A THEORY [1, 2].

А. Einstein, 1955

This is a translation of Einstein's article into English from the Russian edition [1]. For this reason, you can see some differences between the translation and the original [2].

REFERENCES 

[1]. А. Einstein. Relativistic theory of the non-symmetric field. The collected of scientific papers. Volume 2. Works on the theory of relativity 1921-1955. – Publishing house "Science", Moscow: 1966, p. 849-873, in Russian.

[2]. А. Einstein. Relativistic theory of the non-symmetric field. The Meaning of Relativity. Fifth edition. Princeton, 1955.

[3]. Leonov V. S. Quantum Energetics. Volume 1. Theory of Superunification. Cambridge International Science Publishing, 2010, 745 p.

[4]. Vladimir Leonov. The Einstein posthumous phrase. From book [3], pp. 55-67.