General Principle of Relativity.

1. General remarks. The heuristic strength of the general principle of relativity lies in the fact that it considerably reduces the number of imaginable sets of field equations; the field equations must be covariant with respect to all continuous transformations of the four coordinates. But the problem becomes mathematically well-defined only if we have postulated the dependent variables which are to occur in the equations, and their transformation properties (field-structure). But even if we have chosen the field-structure (in such a way that there exist sufficiently strong relativistic field-equations), the principle of relativity does not determine the field-equations uniquely. The principle of “logical simplicity” must be added (which, however, cannot be formulated in a non-arbitrary way). Only then do we have a definite theory whose physical validity can be tested a posteriori.

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A General Principle of Isomorphism: Determining Inverses

Symmetry ◽

10.3390/sym11101301 ◽

2019 ◽

Vol 11 (10) ◽

pp. 1301 ◽

Cited By ~ 1

Author(s):

Vladimir S. Kulabukhov

Keyword(s):

System Theory ◽

General Principle ◽

Algebraic System ◽

New Paradigm ◽

Principle Of Relativity ◽

The Matrix ◽

Proven Theorem ◽

Derived Rules

The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems.

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