# The Kinetic and Gravitational Scaling of the Units of Electricity and Magnetism

An effective means of incorporating the time dilation effect into relativity theory is to

assume that the unit of time is directly proportional to γ (u) = (1-u2/c2)-0.5 on an object such as a light source that has been accelerated to speed u relative to the laboratory. In recent work it has been shown that a similar theoretical approach can be applied to other physical quantities such as length and inertial mass, and as a result, to all other mechanical properties in the mks system. This concept of uniform scaling can also be applied successfully for gravitational interactions. The question as to how the units of electromagnetic quantities such as electric charge and magnetic induction change with both acceleration and varying position in a

gravitational field is therefore of considerable interest. Since the unit of electric charge can be chosen independently of the value of the permittivity of free space ε0, it is shown that all electromagnetic quantities can also be assigned units directly in the mks system, thereby making it a trivial matter to deduce their kinetic and gravitational scaling behavior. For example, the unit of electric charge can be 1 J as long as ε0 has units of 1 N. A table is given that makes a comprehensive comparison of the standard units in the Giorgi system with those in two such direct mks schemes. A simple procedure is also described for changing the numerical values of the units in a systematic manner by dividing the various electromagnetic

quantities into five distinct classes. This allows one to equate the value of ε0 to 1/4π, for example, similarly as for the Gaussian system of units, while still retaining the same formulas as in the Giorgi system.