Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session Z57: General Physics
11:30 AM–1:18 PM,
Friday, March 10, 2023
Room: Room 303
Sponsoring
Unit:
APS
Abstract: Z57.00005 : On Geometry and Physics Aspects of The Generalized Newton's Laws Triplet (G, h, kB)
12:18 PM–12:30 PM
Presenter:
Zhi an Luan
(University of British Columbia)
Author:
Zhi an Luan
(University of British Columbia)
Collaboration:
Zhi-An Luan
In this paper, I will present an extended Fano geometry and its topological structures: (1). Newton's constant is extended the Newton gravity variety Gi = (miVi)-1 , i = 1,2,3,..., ...n, (2). extended Planck variety hν = 2π×ν, where ν is special real number, such as, 0, ..., √5-1, √3-1, 1, √3, √5, ... ∞. (3). extended Boltzmann variety kBn = 2√3×n, n =1,2,3,4,..., ∞. Notes that: gcd(h, kB) = gcd(2√3×π, 2√3×4) = 2√3, i.e., P1 project. The classical Fano geometry includes only a circle with radial √3, a envelope triangle with boudary length l= 3×6=18 and a square with boundary length 2√3×4 = 8√3= 19.5959179423. This new Quantum Fano geometry has rich topological structure:
the generic enveloped length ln =2√3n tan(π/n)|n→∞ = 2√3π = h. One can obtains that the enveloped area An= 2√3×√3 tan(π), then that the enveloped ratio η= ln /An= 2√3×n tan(π/n) / 2√3 ×√3n tan(π/n) = 2/√3 = 2/3√3 = G√3. For a circle, its enveloped ratio η?= 2π√3 / π√32 =2/√3. It means that all polytopes have an exact same enveloped ratio, which is governed strongly by gravitational constant G.
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