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Hi Constantinos,
I enjoyed this paper because it included more of your ideas. Most of your prior papers were 2 or 3 page papers that referenced other 2 or 3 page papers.
I am not challenging the accuracy of Planck's Law. I'm asking which is more fundamental - Planck's Law vs. the Partition functions of Quantum Statistical Mechanics? If Planck's Law is a truism (based on your assumptions involving the properties of exponential functions), then it seems to negate the fundamentality of Fermi and Maxwell statistics. If the Partition Functions are truisms, then all three statistics, Bose, Maxwell and Fermi are allowed.
Planck developed his ideas in 1900. Einstein took Planck's ideas to the next level with his explanation of the Photoelectric Effect in 1905. For all of the talk about Relativity, Einstein won his Nobel Prize for his early development of Quantum Statistical Mechanics - ironically Einstein later questioned Quantum Mechanics...
I see how mechanics can be derived from eta, but also see huge similarities between eta, the Hamiltonion, and Action. I don't consider eta so much of a new concept, as just being a different (perhaps more common-sense?) way to formalize these old concepts.
I have been quiet on the blog site lately. Too many of the discussions sound too similar...
I hope my latest essay is not an incomprehensible code. As a mathematician, you might enjoy some of it. I only have a little bit of physics involving scales, intrinsic spin, and supersymmetry.
Have Fun!
Dr. Cosmic Ray