Why and how the constants?

Paul S. Wesson writes "2.11 Fundamental Constants Following on from the comments of the preceding Section, it is useful to recall that there have been numerous attempts to explain the universality and nature of the basic parameters which appear in the equations of physics (like G the Newtonian gravitational constant, h the Planck unit, and e the charge on the electron). There have also been numerous attempts to see if they could be variable, particularly in regard to the age of the universe. The latter attempts have, with a certain small number of questionable measurements, failed. Further, there is no generally accepted explanation for the sizes of the dimensionless numbers formable from the constants, though the numerology of Eddington and the anthropic principle due to Carter are possibilities (see Wesson 1992, 1999 for reviews). It is certainly the case that one can view the so-called fundamental constants as merely parameters that transpose the physical dimensions of other quantities into forms handleable by geometry. Thus (c 2Gρ) 1/2 = [L] converts the density of a fluid to a length, while hmc = [L] does the same for the rest mass of a particle. However, while this enables physical quantities to be related to the geometrical ones of field theories like general relativity, most workers would be more comfortable if there was some systematic rationale for the fundamental constants."?

-- FUNDAMENTAL UNSOLVED PROBLEMS IN PHYSICS AND ASTROPHYSICS Paul S. Wesson Department of Physics University of Waterloo Waterloo, Ontario N2L 3G1 Canada prepared for California Institute for Physics and Astrophysics 366 Cambridge Avenue Palo Alto, California 94306 U.S.A. Email: [email protected]?

(https://www.calphysics.org/problems.pdf)

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While most things change in the Universe, or are specific to certain materials, situations or times, there are quantities that do not change, no matter what or where; these are the fundamental, or universal constants, and are often listed as light speed, c, electron charge, e, electron mass, m sub-e, Planck's constant, h, and the fine structure constant, α. There are others but these are among the first tier. These quantities are the anchors of physics, keeping the relationships stable and the discipline from going too far afield. The composite, α, is given by

α = ke^2/?c

initially associated with atomic theory, it is also associated with the strength of the electromagnetic force. All of these have been considered in previous Letters, but not all at once as a separate topic. In addition to these, light quark mass, m sub-q, was derived. This quantity is not commonly listed as a first tier constant. Considering that all stable matter is based on this quantity (or quantities, given "up" and "down" varieties) this seems no small oversight. Although, like the fine structure constant it was derived earlier as a composite,

(m sub-q)^3 ≈ (A/G)(h/c)^2

where A is the calculated acceleration of the local galactic supercluster. The ratio A/G also appears in derived electron mass,

(m sub-e)^3 ≈ k^2(A/G)(e/c)^4.

When the electron mass relation is divided by the quark,

[(m sub-e)/(m sub-q)]^3/2 ≈ α

so that the fine structure constant might be considered a ratio of the stable matter particles.

The unit, or electron charge, e, was derived by associating the proposed strong force, Fg,1, with the coulomb force at the Planck scale,

Fg,1 ≈> Fcoul; 10^-18 coul ≈> q?≈> e. ??