The standard paradigm for the cosmos is composed of 3 main parts: (1)
the standard model of particle physics, (2) the standard Big Bang
model, and (3) the Inflationary Scenario. To be sure there are other
components, but these three main components are interwoven and together
they constitute our general paradigm for understanding nature.

This post concerns identifying ways in which to clearly distinguish
between the standard paradigm and the Discrete Fractal paradigm (see
www.amherst.edu/~rloldershaw for details). I believe that I have found
another major, and promising, distinction between these two paradigms.

Within the context of the standard model of particle physics, there is
virtually no question about the Planck Scale, at which General
Relativity plays an equally important dynamical role with QED. The
conventional Planck length is about 1.6 x 10^-33 cm and the Planck mass
is about 2 x 10^-5 g.

According to the Discrete Fractal paradigm, nature has a discrete
spacetime structure and each of the fundamental scales in nature's
unbounded discrete hierarchy has its own unique value for the
gravitational "constant".

Numerically the relationship between G values on neighboring scales is:
G(n-1) = 3.27 x 10^38 G(n), where G(n) = 6.67 x 10^-8 cgs.
That means G(n-1) for the atomic scale would be equal to 2.31 x 10^31
cgs.
When you put G(n-1) into the conventional equations for the Planck
length and the Planck mass, because you want all atomic scale
"constants" for uniformity, you get:

Planck length = 3 x 10^-14 cm (= 0.4 times the proton radius)

Planck mass = 1.2 x 10^-24 g (= 0.8 times the proton mass).

Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

So we have identified another example of a fundamental, very large,
difference between the two paradigms. Unlike the definitive Dark Matter
Test, the reality of the two differing Planck Scales is not so easily
tested empirically. However, if the radically different revised Planck
Scale of the DF paradigm should lead to promising new ideas in quantum
field theory, that could lead to a re-examination of the standard
particle physics model's Planck Scale, and, in turn, to a
re-examination of the foundations of the standard cosmological
paradigm.

Robert L. Oldershaw