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
self-similar 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), and for this post 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.

Could the conventional Planck Scale values be way out of the ball park?

Robert

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
self-similar 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), and for this post 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.

Could the conventional Planck Scale values be way out of the ball
park?

Could the conventional Planck Scale values be way out of the ball
park?

Yes, they could be. But I don't expect it would be like you are stating
above. I would expect something more dynamical.

FrediFizzx wrote:
Could the conventional Planck Scale values be way out of the ball
park?

Yes, they could be. But I don't expect it would be like you are
stating
above. I would expect something more dynamical.


Well, the Discrete Fractal paradigm ( www.amherst.edu/~rloldershaw )
views hadrons as Kerr-Newman black holes and uses a G value of ~2.2 x
10^31 cgs. So GR plays as important a role as EM *within* Atomic Scale
systems. These ideas seem to have quite a bit of dynamical content.

Hi Rob,

I do think that hadrons as black holes of any kind has been rule out
already. No? However, the confinement mechanism may be similar to a
black hole's event horizon concept. I don't know what your G ~= 2.2E31
cgs means? Cgs is centimeter, gram, second? I suppose this is some
kind of relative strength of gravity? Relative to what? I will try to
take a look at your website in more detail when I get more time. But I
would expect that G disappears (goes to zero) into a unification at
small scales with the other forces. We have a hexagonal fractal lattice
structure for the quantum "vacuum" that you can check out at the links
below.