Misconceptions in the Standard Field Theory

Abstract

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 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) at the point of view of formal logic and dialectics, the concepts “field in abstraction” and “mathematical field” are identical and meaningless concepts. “Field in abstraction” 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.” 6) a physical field has no points (i.e., values of a physical quantity) in a geometric coordinate system; (7) the absurdity is that a dimensionless (i.e., mathematical) quantity is identical to a dimensional (i.e., physical) quantity.