# SIG

A galactic system of measures used be several species to communicate with each other in a SF universe in my head. This is an explicitly designed system of units. Base 16 is used because of the importance of binary. Aliens might find caesium-133 as easy to use as humans do. I don't use multiples of the plank length—which might seem like the natural thing to do—because measuring the constant of gravitation accurately is harder than measuring the elementary charge, speed of light in vacuum, Planck's constant, or Boltzmann's constant. But my unit of electrical charge is √(2)×16^15 times the Planck charge.

L = length unit = wavelength of radiation from the transition between hyperfine ground states of caesium-133 atoms at absolute zero, as that radiation passes through a perfect vacuum = 3.26122557 centimeters = 0.0326122557 meters. (The length unit is exactly 299792458/9192631770 meters.)

T = time unit = 16^8 × (Length unit / speed of light in a vacuum) = 0.467218464 seconds. Or the duration of 16^8 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at rest at a temperature of 0 K. (The time unit is exactly 4294967296/9192631770 seconds.)

M = unit of mass = 16^32 × Planck's constant / (speed of light × length unit) = 0.0230618313 kg, which makes plank's constant 16^-24. [I'm not sure of a nice way to state this definition.] (This unit is only as good as our measurement of Planck's constant, currently with an uncertainty of around 5×10^-8. But we're still arguing about how to define the kilogram.) [In the galaxy, the simplest way to realize this definition is to ask the most scientifically advanced species you can find to make a measurement of Planck's constant with minimal uncertainty and manufacture a few 1-unit-of-mass artifacts.]

Update 2020-09-18: note that the kilogram was redefined in terms of Planck's constant in 2019:

1 kg := (Planck's constant) / (6.62607015×10^-34 m²/s)

Therefore the following is exact:

1 M = (16^32 × 6.62607015 × 10^-34 × 9192631770 / (299792458 × 299792458)) kg

C = unit of current = 52.3615416 amperes. The Current Unit is a constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 Length Unit apart in a vacuum, would produce between these conductors a force per length equal to 1/(2π) M×L/T²/L.

E = unit of energy = M×L²/T² = 0.000112360968 joules

P = unit of temPerature = 7.05881935 Kelvins, which makes Boltzmann's constant 16^-16. One defines temperature in terms of the ideal-gas-law behavior of an ideal gas: the temperature of an ideal gas is defined to equal (16^16)(pressure)(volume)/(number of particles).

Therefore,

c = speed of light = 16^8 L/T (by definition)

h = Planck's constant 16^-24 = M×L²/T (by definition)

qe = elementary charge = 16^-16 × √(2 × the fine-structure constant) C×T (measured)

G = Newtonian constant of gravitation = 9.6853×10^-9 L³/M/T² (measured)

ε₀ = electric constant = vacuum permittivity = 16^-16 T⁴×C²/L³/M (by definition)

μ₀ = magnetic constant = vacuum permeability = 1 M×L/T²/C² (by definition)

kB = Boltzmann's constant = 16^-16 M×L²/T²/P (by definition)