[AntonioLao]

Ohm is the macroscopic unit of electrical resistance. Macroscopic resistance in its phenomenological appearance is an intensive variable and as a scalar is temperature dependence. It has a well defined value at every point within the conducting solid media. This linearity is usually true for solids but exceptional for liquids and gases. This value remains practically constant regardless of the changes in shape and size as long as the ratio of conductor length to its cross section is the constant of an inverse variation for both resistance (R) and conductance (g). The quantum theory of electrons in solids allows precise and accurate measurements. However, the temperature dependence has been extended to the microscopic domain near absolute zero of temperature.

Since 1827 the macroscopic form of Ohm’s law as discovered by Georg Simon Ohm (1787-1854) becomes the most basic and most widely used laws of electricity. Initially, it was derided and condemned by the purported scientific community as a detraction of the dignity of all physical laws of nature known by the middle of the 19th century. These are embellished with mathematical sophistications using calculus and differential and integral equations. However, a complete microscopic form of Ohm’s law is critical for understanding the mysterious phenomenon of high-temperature superconductivity. Low-temperature theories are now considered foregone conclusions since the BCS theory of 1957. The dawn of high-temp superconductivity was the surprise discovery made by Georg Bednorz and Karl Müller in 1986.

The microscopic form of Ohm’s law can be a single vector equation if and only if the current density (J) is in the same direction parallel to the electric field (E) with g as the scalar constant of direct variation: J=gE. g is defined as the conductance which is the reciprocal of R: g=1/R. If the directions or orientations of J and E are different with respect to each other then g becomes a tensor or vector depending on the microscopic configurations. Superconductivity could become temperature independence if and only if the conductance takes on the forms of Hadamard vectors or matrices. These are necessary for understanding spacetime ohm (resistance).