Suggestions: to introduce new units in astronomy and in quantum physics

[Wiljea]

To perform units conversions, these new units have the particularity to be define in SI units with uncertainties. This does not pose problem since DB48x is equipped with Interval Arithmetics (IA). Therefore, conversions will entail uncertainties in their answers due to IA divisions. Here are the conversion factors for each discipline.

1. Solar mass & Earth mass in astronomy
CONTEXT:
It is common practice in astronomy to relate the mass of a celestial body to a known body whose mass serves as a reference. This is typically the case when comparing the masses of different planets to that of the Earth (M🜨). It is also the case when relating the mass of a galaxy or a black hole to the mass of the Sun (M☉). As soon as the characters of ISSUE #1633 will be added and using the updated (extended) version of the constant library (to be available soon), the following will execute in an updated version of DB48x v0.9.15:

- Earth mass ( _M🜨 )

« Duplicate LibraryConstant Swap StandardUncertainty →∆Range »
'LibraryConstant→ΔRange' Store
24 Sig GM🜨 LibraryConstant→ΔRange G LibraryConstant→ΔRange /
   @Expecting 5.97216 78708 07877 12009 435⁳²⁴±1.34220 09508 43057 0517⁳²⁰ kg

This defines the conversion factor:
      1_M🜨 = 5.97216 78708 07877 12009 435⁳²⁴±1.34220 09508 43057 0517⁳²⁰_kg
- Solar mass ( _M☉ )

24 Sig GM☉ LibraryConstant→ΔRange G LibraryConstant→ΔRange /
   @Expecting 1.98840 98717 02381 99416 732⁳³⁰±4.46880 54291 14023 9295⁳²⁵ kg

This defines the conversion factor:
      1_M☉ = 1.98840 98717 02381 99416 732⁳³⁰±4.46880 54291 14023 9295⁳²⁵_kg

2. Planck units in quantum physics
CONTEXT:
In the quest for a theory of quantum gravity, it is becoming increasingly common to consider Planck units as fundamental units. Therefore, in the extended version of the constants library, Planck units of charge, momentum, force, and density have been added to those already existing: length, time, mass, energy, and temperature. The following will execute in the actual, or equivalently, in an updated version of DB48x v0.9.15:

- Planck Length ( _Lpl )

   24 Sig ⒸLpl →Num ⓈLpl →Num →∆Range @Expecting 1.61625 5⁳⁻³⁵±1.8⁳⁻⁴⁰ m
   @THEN 1_Lpl=1.61625 5⁳⁻³⁵±1.8⁳⁻⁴⁰_m

- Planck Time ( _Tpl )

   24 Sig ⒸTpl →Num ⓈTpl →Num →∆Range @Expecting 5.39124 6⁳⁻⁴⁴±5.9⁳⁻⁴⁹ s
   @THEN 1_Tpl=5.39124 6⁳⁻⁴⁴±5.9⁳⁻⁴⁹ s

- Planck Mass ( _Mpl )

   24 Sig ⒸMpl →Num ⓈMpl →Num →∆Range @Expecting 0.00000 00217 6434±2.4⁳⁻¹³ kg
   @THEN 1_Mpl=0.00000 00217 6434±2.4⁳⁻¹³_kg

- Planck Energy ( _Epl )

   24 Sig ⒸEpl →Num ⓈEpl →Num →∆Range @Expecting 1.22089⁳¹⁹±1.4⁳¹⁴ GeV
   @THEN 1_Epl=1.22089⁳¹⁹±1.4⁳¹⁴_GeV

- Planck Temperature ( _T°pl )

   24 Sig ⒸT°pl →Num ⓈT°pl →Num →∆Range @Expecting 1.41678 4⁳³²±1.6⁳²⁷ K
   @THEN 1_T°pl=1.41678 4⁳³²±1.6⁳²⁷_K

- Planck Charge ( _qpl )

24 Sig 'ROUND(CONVERT(√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc);1_C);XPON(UVAL(Ⓡε₀/2*√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc)))-XPON(UVAL(√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc)))-2)' →Num Eval 
'CONVERT(ROUND(UBASE(Ⓡε₀/2*ROUND(CONVERT(√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc);1_C);XPON(UVAL(Ⓡε₀/2*√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc)))-XPON(UVAL(√(4*Ⓒπ*Ⓒε₀*Ⓒℏ*Ⓒc)))-2));-2);1_C)' 
→Num Eval →∆Range @Expecting 1.87554 60384 2⁳⁻¹⁸±1.5⁳⁻²⁸ C 
@Or equivalently, using the updated version of DB48x v0.9.15
   24 Sig Ⓒqpl →Num Ⓢqpl →Num →∆Range @Expecting 1.87554 60384 2⁳⁻¹⁸±1.5⁳⁻²⁸ C
   @THEN 1_qpl=1.87554 60384 2⁳⁻¹⁸±1.5⁳⁻²⁸ C

- Planck Momentum ( _ppl )

'ROUND(CONVERT(√(Ⓒℏ*Ⓒc↑3/ⒸG);1_kg·m/s);XPON(UVAL(ⓇG/2*√(Ⓒℏ*Ⓒc↑3/ⒸG)))-XPON(UVAL(√(Ⓒℏ*Ⓒc↑3/ⒸG)))-2)' →Num Eval 
'CONVERT(ROUND(UBASE(ⓇG/2*ROUND(CONVERT(√(Ⓒℏ*Ⓒc↑3/ⒸG);1_kg·m/s);XPON(UVAL(ⓇG/2*√(Ⓒℏ*Ⓒc↑3/ⒸG)))-XPON(UVAL(√(Ⓒℏ*Ⓒc↑3/ⒸG)))-2));-2);1_kg·m/s)' 
→Num Eval →∆Range @Expecting 6.52478 6±0.00007 2 kg·m/s 
@Or equivalently, using the updated version of DB48x v0.9.15
   24 Sig Ⓒppl →Num Ⓢppl →Num →∆Range @Expecting 6.52478 6±0.00007 2 kg·m/s
   @THEN 1_ppl=6.52478 6±0.00007 2_kg·m/s

- Planck Force ( _Fpl )

'ROUND(CONVERT(Ⓒc↑4/ⒸG;1_N);XPON(UVAL(ⓇG*Ⓒc↑4/ⒸG))-XPON(UVAL(Ⓒc↑4/ⒸG))-2)' →Num Eval 
'CONVERT(ROUND(UBASE(ⓇG*ROUND(CONVERT(Ⓒc↑4/ⒸG;1_N);XPON(UVAL(ⓇG*Ⓒc↑4/ⒸG))-XPON(UVAL(Ⓒc↑4/ⒸG))-2));-2);1_N)' 
→Num Eval →∆Range @Expecting 1.21025 6⁳⁴⁴±2.7⁳³⁹ N 
@Or equivalently, using the updated version of DB48x v0.9.15
   24 Sig ⒸFpl →Num ⓈFpl →Num →∆Range @Expecting 1.21025 6⁳⁴⁴±2.7⁳³⁹ N
   @THEN 1_Fpl=1.21025 6⁳⁴⁴±2.7⁳³⁹_N

- Planck Density ( _ρpl )

'ROUND(CONVERT(Ⓒc↑5/(Ⓒℏ*ⒸG²);1_kg/m³);XPON(UVAL(ⓇG*2*Ⓒc↑5/(Ⓒℏ*ⒸG²)))-XPON(UVAL(Ⓒc↑5/(Ⓒℏ*ⒸG²)))-2)' →Num Eval 
'CONVERT(ROUND(UBASE(ⓇG*2*ROUND(CONVERT(Ⓒc↑5/(Ⓒℏ*ⒸG²);1_kg/m³);XPON(UVAL(ⓇG*2*Ⓒc↑5/(Ⓒℏ*ⒸG²)))-XPON(UVAL(Ⓒc↑5/(Ⓒℏ*ⒸG²)))-2));-2);1_kg/m³)' 
→Num Eval →∆Range @Expecting 5.15485⁳⁹⁶±2.3⁳⁹² kg/m↑3 
@Or equivalently, using the updated version of DB48x v0.9.15
   24 Sig Ⓒρpl →Num Ⓢρpl →Num →∆Range @Expecting 5.15485⁳⁹⁶±2.3⁳⁹² kg/m↑3
   @THEN 1_ρpl=5.15485⁳⁹⁶±2.3⁳⁹² kg/m↑3

End.