Critical Analysis of Field Theory (The Correct Criterion of Truth versus Pseudoscience)

A detailed proof of the incorrectness of standard field theory (vector analysis) is proposed. The correct methodological basis for this proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: standard field theory (vector analysis) is a gross error. Gross errors are as follows: (1) field theory is based on differential and integral calculus, which is an incorrect theory; (2) field theory is based on vector calculus, which is an incorrect theory; (3) field theory is formulated within the framework of a geometric coordinate system. But mathematical and physical quantities have no dimension “meter” and cannot be presented (be defined, exist) within the framework of a geometric coordinate system; (4) in the point of view of formal logic and dialectics, the concepts “field in abstracto” and “mathematical field” are identical and meaningless concepts. “Field in abstracto” and “mathematical field” have neither physical properties nor geometric properties; (5) the standard definition of a field is: “A field is a part of space, each point of which corresponds (conforms) to a certain value of some physical quantity”. In the point of view of formal logic, the term “correspondence” is meaningless. The subject-predicate conjunction in a definition must be either “is” or “is not”. Replacement of a dimensionless quantity in mathematical definitions and expressions by a dimensional quantity is an inadmissible operation; 6) a physical field has no points (i.e., values of a physical quantity) in a geometric coordinate system. A material point has coordinates, but a material point is not a point of a physical field. The error is in the assertion that the coordinates of a material point determine (define, identify) the value of a physical quantity; that the value of a physical quantity determines (defines, identifies) the coordinates of a material point; (7) the absurdity is that a dimensionless (i.e., mathematical) quantity is identical to a dimensional (i.e., physical) quantity.