In this investigation, we explore previously unknown relations between natural constants by taking the following steps: (1) We discard Dirac’s constant
ℏ from the universal man-made constants of physics, which we redefine in terms of Planck’s constant
h. (2) Working in the SI system of units, we determine Newton’s gravitational constant
G from Boltzmann’s constant
and the elementary charge
e, recognizing the entropy of matter as their common underlying characteristic. (3) By comparing the mass of 1 mole of electrons to the
h-defined Planck mass
, we deduce nature’s own molar constant (
0.1 mol) that contains a ‘reduced Avogadro number’
of particles, where
is Avogadro’s number and
is the associated Avogadro factor. (4) From the new effective gravitational constant
, where
is the vacuum permittivity, we obtain MOND’s universal constant
and its critical acceleration
, recognizing the Newtonian source of gravity as the common underlying characteristic and repudiating the need for a principle of equivalence of masses. (5) We derive the gravitational coupling constant
solely from
. (6) We adopt the measured value of the
h-defined fine-structure constant (FSC)
and the value of
(or, equivalently, nature’s
), and we determine the relative ratio
precise to 10 significant digits. (7) We derive the relative strong ratio
directly from the Avogadro factor
. (8) We determine the coupling constants of weak and strong interactions (
and
, respectively) in terms of the FSC
. (9) The relation
leads to a determination of the mass of the W boson
from the measured values of
and the reduced Fermi constant
. (10) Using the Planck mass as a principal constant (
, where
is the electron mass), we obtain new classical definitions of
, and the Compton radius
; and we reformulate in a transparent, geometrically clear way several important QED equations, as well as the extended Planck system of units itself. We discuss the implications of these results, and we pave a way forward in exploring the unification of the fundamental forces of nature.
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