In a post from 2013, I summarized the findings of my original 1997 paper (updated in 2007) documenting a new FineStructureConstant (α) based set of definitions for the fundamental constants (c, ħ, GN, and H0) . This post was due to updates from 2013 Planck spacecraft CMB (H0) results and the 2012 LHC confirmation of finding the mass of the Higgs boson (mHiggs).
About the same time, Wolfram Mathematica deprecated their PhysicalConstants package in order to provide for more robust curated datasets (e.g. CODATA ParticleData) which includes Quantity (exact or with experimental uncertainties) and UnitConvert capability.
Until now, I had maintained my own version of this package in order to add a custom UoM with conversions between it and the SI UoM based on my analysis of a possible unification of the fundamental constants and dimensional relationships of (L)ength, (T)ime, (M)ass, and (C)harge. These strongly indicate an 8D (E8) fine structure linked a posteriori particle mass prediction of the Higgs boson mass=124.44 GeV/C2 and cosmological constants of gravity (GN) and H0.
This post provides for the integration of that newer Wolfram Mathematica capability as well as the 2019 redefinition of the SI UoM which replaced some measures with exact unit definitions. These changes are described on Wikipedia here and by Wolfram’s Chief Scientist Michael Trott here.
My Powerpoint overview is here with the first slide shown below:
This new Time Unified UoM identifies a UnitLength= α/Rydberg Constant (R∞) associated with atomic mass spectroscopy and UnitAcceleration that is 4π(cH0=Acceleration AssociatedWith CosmologicalExpansion Rate) as a a dimensionless unit with UnitLength=(complexified UnitTime)2. It links the macro (cosmological) to the micro (nuclear/chemical) scales via integer exponents (dimensions) related to the FineStructureConstant (α). Other notable defining constants are a 4D (TimeUnit4) UnitCharge and 8D c=α-8 UnitVelocity, h=α-8 UnitAction, and Newton’s GravitationalConstant (GN~4πH0~α8/UnitTime).
See below a list of the constants and UoM elements for SI, Natural (Planck) units, and my own “more Natural” Time Unified UoM, which includes the Higgs mass (a posteriori) postdiction. The list is sorted by n where (Tn) is the unified (reduced) time dimension of the physical constant or UoM.
