Vector aspect of physical quantity unit

Abstract

Based on the vector representation of the physical quantity in the pseudo-Euclidean plane the variants of the corresponding coordinate system expressing the system of quantities units are discussed. The drawbacks of the SI system are indicated - both redundancy and insufficiency. A variant of the system, taking into account the three - dimensional physical space, is proposed, due to which the "dimensional isotopes" disappear - quantities having different physical meaning, but the same dimension in the SI system. It is shown that the mathematical expression of the unit vector norm of the quantity called "system unit" allows judging whether the unit is within the range of uncertainty of this quantity.