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Geometrized unit system

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In physics, especially in the general theory of relativity, geometrized units or sometimes geometric units, is a physical unit system in which all physical quantities are expressed in the unit of length: meter. In this system, the speed of light c and the gravitational constant G are set to one, c = 1 and G = 1 (and sometimes also Boltzmann constant k = 1). In this system, formulas appear simpler because all constants drop out.

A time interval is in geometrical units expressed in meters, the distance travelled by light in that interval.

In exactly the same way as we can use light-seconds as a distance in meters, we can express a mass (kilogram) as "mass-meters". The Sun has a mass (in conventional units 2×1030 kg) which is expressed in mass-meters as 1.5 km.

The conversion from conventional units (kg) is
mass [meters] = G/c2 mass [kg] = 0.742 × 10-27 (m/kg) mass [kg]

Other conversions are given in the table by expressing the number 1.0 in different ways.


Converting geometrized units to conventional units
1.0 = c = 2.997930 ×108 m/s
1.0 = G/c2 = 0.7425×10-27 m/kg
1.0 = G/c4 = 0.826×10-44 m/N
1.0 = Gk/c4 = 1.140×10-67

m/K

See also

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