Dimensions and Quantities for UnitSystems
In the base UnitSystems package, simply Float64 numbers are used to generate the group of UnitSystem constants.
However, in the Similitude package, instead constant numbers are used to generate an abstract multiplicative Group, which is only converted to a Float64 value when appropriate or at compile time.
In UnitSystems and Similitude, the spectrum of Group{:Constants} values is generated by a group of 11 mathematical constants (7 Integer primes and 4 Irrational numbers) with 33 physical measurement definitions.
These are 𝟐, 𝟑, 𝟓, 𝟕, 𝟏𝟏, 𝟏𝟗, 𝟒𝟑, φ, γ, ℯ, τ, kB, NA, 𝘩, 𝘤, 𝘦, Kcd, ΔνCs, R∞, α, μₑᵤ, μₚᵤ, ΩΛ, H0, g₀, aⱼ, au, ft, ftUS, lb, T₀, atm, inHg, RK90, KJ90, RK, KJ, Rᵤ2014, Ωᵢₜ, Vᵢₜ, kG, mP, GME, GMJ.
Furthermore, in Similitude there is a dimension type which encodes the dimensional Group{:USQ} for the Quantity type using the same implementation principles as the Group{:Constants}.
This enables the unified usage of Group homomorphisms to transform Quantity algebra elements with varying numbers of dimensionless constants.
Originally, the Newtonian group used for UnitSystems would be made up of force, mass, length, time (or F, M, L, T).
Although force is typically thought of as a derived dimension when the reference gravity is taken to be dimensionless, force is actually considered a base dimension in general engineering UnitSystem foundations.
With the development of electricity and magnetism came an interest for an additional dimension called charge or Q.
When the thermodynamics of entropy became further developed, the temperature or Θ was introduced as another dimension.
In the field of chemistry, it became desirable to introduce another dimension of molaramount or N as fundamental.
To complete the existing International System of Quantities (ISQ) it is also necessary to consider luminousflux or J as a visual perception related dimension.
In order to resolve ambiguity with solidangle unit conversion, angle or A is explicitly tracked in the underlying dimension and Group.
However, this is yet insufficient to fully specify all the historical variations of UnitSystem, including the EMU, ESU, Gauss and LorentzHeavise specifications.
Therefore, there is also a dimension basis for rationalization (denoted R) and lorentz (denoted by C⁻¹).
In combination, all these required base dimension definitions are necessary in order to coherently implement unit conversion for Quantity elements.
Since the existing International System of Quantities (ISQ) is an insufficient definition for dimension, a new Unified System of Quantities (USQ) is being proposed here as composed of force, mass, length, time, charge, temperature, molaramount, luminousflux, angle, rationalization, and a nonstandard dimension (denoted by F, M, L, T, Q, Θ, N, J, A, R, C).
In aggregate, the UnitSystem data generated here constitutes a new universal standardization for dimensional analysis, which generalizes upon previous historical systems up to the 2019 redefinition and unifies them in a common Universe.
This enables a more precise and generalized standardization than the 2019 redefinition, which was comparatively limited in scope.
Specified default UnitSystem values are to be taken as a newly defined mutually-compatible recommended standard, verified to be consistent and coherent.
In fact there is nothing transcendental about dimensions; the ultimate principle is precisely expressible (in Newton's terminology) as one of similitude, exact or approximate, to be tested by the rule that mere change in the magnitudes of the ordered scheme of units of measurement that is employed must not affect sensibly the forms of the equations that are the adequate expression of the underlying relations of the problem. (J.L., 1914)
Specifications for dimensional units are in the UnitSystems.jl and Similitude.jl and MeasureSystems.jl repositories.
The three packages are designed so that they can be interchanged with compatibility.
On its own UnitSystems is the fastest package, while Similitude (provides Quantity type) and MeasureSystems (introduces Measurements.jl uncertainty) build additional features on top of UnitSystems base defintions.
Defaults are shared: Metric, SI2019, CODATA, Conventional, International, InternationalMean, MetricTurn, MetricGradian, MetricDegree, MetricArcminute, MetricArcsecond, Engineering, Gravitational, FPS, IPS, British, English, Survey, Gauss, LorentzHeaviside, EMU, ESU, IAU, IAUE, IAUJ, Hubble, Cosmological, CosmologicalQuantum, Meridian, Nautical, MPH, KKH, MTS, FFF, Planck, PlanckGauss, Stoney, Hartree, Rydberg, Schrodinger, Electronic, Natural, NaturalGauss, QCD, QCDGauss, QCDoriginal.
julia> using Similitude # or UnitSystems or MeasureSystemsAn optional environment variable ENV["SIMILITUDE"] induces UnitSystems.similitude() to return true, giving flexibility for building dependencies whenever it is desirable to toggle usage between UnitSystems (default) and Similitude (requires environment variable specification). For example, in MeasureSystems and Geophysics this option is used to increase flexibility with variety in local compilation workflow.
A UnitSystem is a consistent set of dimensional values selected to accomodate a particular use case or standardization.
It is possible to convert derived physical quantities from any UnitSystem specification into any other using accurate values.
Eleven fundamental constants kB, ħ, 𝘤, μ₀, mₑ, Mᵤ, Kcd, θ, λ, αL, g₀ are used to govern a specific unit system consistent scaling.
These are the constants boltzmann, planckreduced, lightspeed, vacuumpermeability, electronmass, molarmass, luminousefficacy, angle, rationalization, lorentz, and gravity.
Different choices of natural units or physical measurements result in a variety of unit systems for many purposes.
Main documentation is at https://units.crucialflow.com/unitsystems
Historically, older electromagnetic unit systems also relied on a rationalization constant λ and a lorentz force proportionality constant αL.
In most unit systems these extra constants have a value of 1 unless specified.
UnitSystem{kB, ħ, 𝘤, μ₀, mₑ, Mᵤ, (Kcd, θ, λ, αL, g₀, ...)}Fundamental constants of physics are: kB Boltzmann's constant, ħ reduced Planck's constant, 𝘤 speed of light, μ₀ vacuum permeability, mₑ electron rest mass, Mᵤ molar mass, Kcd luminous efficacy, θ angle measure, λ Gauss rationalization, αL Lorentz's constant, and g₀ gravitational force reference.
Primarily the Metric SI unit system is used in addition to the historic English engineering unit system.
These constants induce derived values for avogadro, boltzmann, molargas, planck, planckreduced, lightspeed, planckmass, dalton, protonmass, electronmass, newton, einstein, vacuumpermeability, vacuumpermittivity, electrostatic, and
additional constants molarmass, luminousefficacy, gravity, angle, turn, spat, stefan, radiationdensity, magnetostatic, lorentz, biotsavart, rationalization, vacuumimpedance, elementarycharge, magneton, conductancequantum, faraday, magneticfluxquantum, josephson, klitzing, hartree, rydberg, bohr.
Physics constant documentation is at https://units.crucialflow.com/constants
Standardized unit/derived quantities are hyperfine, loschmidt, wienwavelength, wienfrequency, mechanicalheat, eddington, solarmass, jupitermass, earthmass, lunarmass, earthradius, greatcircle, radarmile, hubble, cosmological, radian, steradian, degree, squaredegree, gradian, arcminute, arcsecond, second, minute, hour, day, gaussianmonth, siderealmonth, synodicmonth, year, gaussianyear, siderealyear, jovianyear, angstrom, inch, foot, surveyfoot, yard, meter, earthmeter, mile, statutemile, meridianmile, admiraltymile, nauticalmile, lunardistance, astronomicalunit, jupiterdistance, lightyear, parsec, bubnoff, ips, fps, fpm, ms, kmh, mph, knot, mps, barn, hectare, acre, surveyacre, liter, gallon, quart, pint, cup, fluidounce, teaspoon, tablespoon, grain, gram, earthgram, kilogram, tonne, ton, pound, ounce, slug, slinch, hyl, dyne, newton, poundal, poundforce, kilopond, psi, pascal, bar, barye, technicalatmosphere, atmosphere, inchmercury, torr, electronvolt, erg, joule, footpound, calorie, kilocalorie, meancalorie, earthcalorie, thermalunit, gasgallon, tontnt, watt, horsepower, horsepowerwatt, horsepowermetric, electricalhorsepower, tonsrefrigeration, boilerhorsepower, coulomb, earthcoulomb, ampere, volt, henry, ohm, siemens, farad, weber, tesla, abcoulomb, abampere, abvolt, abhenry, abohm, abmho, abfarad, maxwell, gauss, oersted, gilbert, statcoulomb, statampere, statvolt, stathenry, statohm, statmho, statfarad, statweber, stattesla, kelvin, rankine, celsius, fahrenheit, sealevel, boiling, mole, earthmole, poundmole, slugmole, slinchmole, katal, amagat, lumen, candela, lux, phot, footcandle, nit, apostilb, stilb, lambert, footlambert, bril, neper, bel, decibel, hertz, apm, rpm, kayser, diopter, gforce, galileo, eotvos, darcy, poise, reyn, stokes, rayl, mpge, langley, jansky, solarflux, curie, gray, roentgen, rem.
Standard physics units are at https://geophysics.crucialflow.com/dev/units
Additional reference UnitSystem variants: EMU, ESU, Gauss, LorentzHeaviside, SI2019, SI1976, CODATA, Conventional, International, InternationalMean, Engineering, Gravitational, IAU, IAUE, IAUJ, FPS, IPS, British, Survey, Hubble, Cosmological, CosmologicalQuantum, Meridian, Nautical, MPH, KKH, MTS, FFF; and natural atomic units based on gravitational coupling and finestructure constant (Planck, PlanckGauss, Stoney, Hartree, Rydberg, Schrodinger, Electronic, Natural, NaturalGauss, QCD, QCDGauss, and QCDoriginal).
Unit conversion documentation is at https://units.crucialflow.com/convert
Derived Unit conversions:
Mechanics: angle, solidangle, time, angulartime, length, angularlength, area, angulararea, volume, wavenumber, angularwavenumber, fuelefficiency, numberdensity, frequency, angularfrequency, frequencydrift, stagnance, speed, acceleration, jerk, snap, crackle, pop, volumeflow, etendue, photonintensity, photonirradiance, photonradiance,
inertia, mass, massflow, lineardensity, areadensity, density, specificweight, specificvolume, force, specificforce, gravityforce, pressure, compressibility, viscosity, diffusivity, rotationalinertia, impulse, momentum, angularmomentum, yank, energy, specificenergy, action, fluence, power, powerdensity, irradiance, radiance, radiantintensity, spectralflux, spectralexposure, soundexposure, impedance, specificimpedance, admittance, compliance, inertance;
Electromagnetics: charge, chargedensity, linearchargedensity, exposure, mobility, current, currentdensity, resistance, conductance, resistivity, conductivity, capacitance, inductance, reluctance, permeance, permittivity, permeability, susceptibility, specificsusceptibility, demagnetizingfactor, vectorpotential, electricpotential, magneticpotential, electricfield, magneticfield, electricflux, magneticflux, electricdisplacement, magneticfluxdensity, electricdipolemoment, magneticdipolemoment, electricpolarizability, magneticpolarizability, magneticmoment, specificmagnetization, polestrength;
Thermodynamics: temperature, entropy, specificentropy, volumeheatcapacity, thermalconductivity, thermalconductance, thermalresistivity, thermalresistance, thermalexpansion, lapserate,
molarmass, molality, mole, molarity, molarvolume, molarentropy, molarenergy, molarconductivity, molarsusceptibility, catalysis, specificity, diffusionflux,
luminousflux, luminousintensity, luminance, illuminance, luminousenergy, luminousexposure, luminousefficacy.
Other similar packages include UnitSystems.jl, MeasureSystems.jl, PhysicalConstants.jl, MathPhysicalConstants.jl, Unitful.jl, UnitfulUS.jl, UnitfulAstro.jl, UnitfulAtomic.jl, NaturallyUnitful.jl, and UnitfulMoles.jl.