Definition
In geometric units, every time interval is interpreted as the distance travelled by light during that given time interval. That is, one second is interpreted as one light-second, so time has the geometric units of length. This is dimensionally consistent with the notion that, according to the kinematical laws of special relativity, time and distance are on an equal footing.
Energy and momentum are interpreted as components of the four-momentum vector, and mass is the magnitude of this vector, so in geometric units these must all have the dimension of length. We can convert a mass expressed in kilograms to the equivalent mass expressed in metres by multiplying by the conversion factor G/c2. For example, the Sun's mass of 2.0×1030 kg in SI units is equivalent to 1.5 km. This is half the Schwarzschild radius of a one solar mass black hole. All other conversion factors can be worked out by combining these two.
The small numerical size of the few conversion factors reflects the fact that relativistic effects are only noticeable when large masses or high speeds are considered.
In the table below are listed all conversion factors that are useful to convert between all combinations of the SI base units, and if not possible, between them and their unique elements, because ampere is a dimensionless ratio of two lengths such as, and candela (1/683 ) is a dimensionless ratio of two dimensionless ratios such as ratio of two volumes = and ratio of two areas =, while mole is only a dimensionless Avogadro number of entities such as atoms or particles:
Conversion from kg,s,C,K into m:
- G/c2
- c
- ((G/(4πε0))1/2)/c2
- (G kB)/c4
Conversion from m,s,C,K into kg:
- c2/G
- c3/G
- 1/(G4πε0)1/2
- kB/c2
Conversion from m,kg,C,K into s
- 1/c
- G/c3
- ((G/(4πε0))1/2)/c3
- (G kB)/c5
Conversion from m,kg,s,K into C
- c2/((G/(4πε0))1/2)
- (G 4πε0)1/2
- c3/((G/(4πε0))1/2)
- (kB(G 4πε0)1/2)/c2
Conversion from m,kg,s,C into K
- c4/(G kB)
- c2/kB
- c5/(G kB)
- c2/(kB(G 4πε0)1/2)
All these units represents nothing else than length along dimension, thus revealing SI as redundant in comparison to geometrized units.
Read more about this topic: Geometrized Unit System
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