Geometric and temporal unit systems

A geometric (or geometrized) unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity. Sometimes Coulomb’s constant, ke, and the electric charge, e, are also set to unity.

The General Conference on Weights and Measures defines the meter as the length of the path traveled by light in vacuum during time interval of 1  ⁄ 299792458 of a second. (17th CGPM; 1983, Resolution 1, CR, 97) In geometric units, every time interval is interpreted as the distance traveled by light during the given time interval so time has the geometric units of length. This is consistent with the notion from special relativity that time and distance are on an equal footing.

One could do the opposite and define a temporal unit system in which every length is interpreted as the travel time of light in vacuum over the given length so length has the temporal units of time. That would show another way in which time can have multiple dimensions.