Re: Stellar/Atomic Self-Similarity

You should look into renormalization groups
and stuff like Pisot / beta geometry.
The Ising type of dependence on a Pisot seems to be
just one way nature has these scaling constants built in.
The standard model has alpha for electromagnetic
and alpha1, alpha2 and alpha3 weak and strong coupling interactions.
And yes, in the early universe ( very high temperatures) they were all supposed to be the same:
symmetry breaking took place as the universe cooled.

The basic scaling constant
is Weyl hbar*c/e which is very close to,
the gravitational constant G.
The number hbar*c/e^2=1/Alpha seems to be the basic scaling constant for both small and large scales.
Cosmologists go into fits over 137, ha, ha...
I certainly encourage you in your quest for
knowledge and hope you will be successful in your search.
The radial numbers Sqrt[hbar*G/c^2]
and it's inverse pretty much make limits in the large and small
on which the new second order uncertainty ideas of the last fews years have been based. There are mass limits along with them,
small and large. The toral/ torus model of cosmology is based on this Planck scale inversion
and it's limitations to the physical universe.
rloldershaw@xxxxxxxxxx u wrote:
I promise to look through your derivations, but consider two points.

1. The scaling constant for lengths and times, which is Lambda (not
gamma), is a dimensionless constant. Possibly it is a pure number that
can only be determined empirically. The same may be true for D.

2. But the main point is that if we only focus on the derivation of the
scaling equations, we risk ignoring the main result of the paper: that
there might be a discrete self-similar relationship between atomic and
stellar systems.

I think it makes sense to tentatively accept the simple scaling rules
as heuristic, empirical axioms. Then we ask the question: does nature
obey these axioms? If yes, then finally we go back and ask the
question: is a deeper understanding of the scaling rules possible?

I'm still working on the middle part and wondering if people believe
the evidence for discrete self-similarity between RR Lyrae stars and He
atoms in Rydberg states undergoing single-level transitions in the
principal quantum number range of 7 to 10. It seems to me that the
evidence is specific, unique and comprehensive enough to answer the
middle question in the affirmative. But I seem to be the only person
on the planet who believes that. Is that because there is an error in
my thinking? Or because it is a new idea and others do not quite know
how to respond to it?

At any rate, thanks Roger. I am also very interested in the question
scaling rule derivations.

Rob

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