scholarly journals Icosahedral Symmetry and Quantum Gravity

2015 ◽  
Vol 2 ◽  
pp. 33-34
Author(s):  
J.A. de Wet

In this note we will show that Theta functions are a solution of the icosahedron equation and also a solution of the Ernst equation for the stationary axisymmetric case of Einstein’s gravitational equation.

2015 ◽  
Vol 5 ◽  
pp. 1-8
Author(s):  
J.A. de Wet

This Review covers over 40 years of research on using the algebras of Quarternions E6;E8to model Elementary Particle physics. In particular the Binary Icosahedral group is isomorphic to theExceptional Lie algebra E8 by the MacKay correspondence. And the toric graph of E8 in Fig.2 with240 vertices on 4 binary Riemann surfaces each carrying 60 vertices, models a solution of the Ernstequation for the stationary symmetric Einstein gravitational equation. Furthermore the 15 synthemesof E8, consisting of 5 sets of 3,can be identified with algebraic representations of the nucleon,supersymmetric particles,W bosons and Dark Matter.


2016 ◽  
Vol 11 (10) ◽  
pp. 5749-5751
Author(s):  
J.A.de Wet

The Jacobi theta functions are essentially rotations in a complex space and as such provide a basis for the lattices of the exceptional Lie algebras E6;E8 in complex 3-space and complex 4-space.In this note we will show that a choice of the nome q of the theta functions θE6 ;,θE8 leads to the equilateral tritangents of these lattices. Speciffcally we will find quarter period ratios of the real and complex axes. In particular E8 is isomorphic to the binary icosahedral group shown recently to describe Elementary Particle theory and Quantum Gravity so q is fundamental to the structure of space itself.


Author(s):  
K.K. Soni ◽  
D.B. Williams ◽  
J.M. Chabala ◽  
R. Levi-Setti ◽  
D.E. Newbury

In contrast to the inability of x-ray microanalysis to detect Li, secondary ion mass spectrometry (SIMS) generates a very strong Li+ signal. The latter’s potential was recently exploited by Williams et al. in the study of binary Al-Li alloys. The present study of Al-Li-Cu was done using the high resolution scanning ion microprobe (SIM) at the University of Chicago (UC). The UC SIM employs a 40 keV, ∼70 nm diameter Ga+ probe extracted from a liquid Ga source, which is scanned over areas smaller than 160×160 μm2 using a 512×512 raster. During this experiment, the sample was held at 2 × 10-8 torr.In the Al-Li-Cu system, two phases of major importance are T1 and T2, with nominal compositions of Al2LiCu and Al6Li3Cu respectively. In commercial alloys, T1 develops a plate-like structure with a thickness <∼2 nm and is therefore inaccessible to conventional microanalytical techniques. T2 is the equilibrium phase with apparent icosahedral symmetry and its presence is undesirable in industrial alloys.


Author(s):  
J. R. Reed ◽  
D. J. Michel ◽  
P. R. Howell

The Al6Li3Cu (T2) phase, which exhibits five-fold or icosahedral symmetry, forms through solid state precipitation in dilute Al-Li-Cu alloys. Recent studies have reported that the T2 phase transforms either during TEM examination of thin foils or following ion-milling of thin foil specimens. Related studies have shown that T2 phase transforms to a microcrystalline array of the TB phase and a dilute aluminum solid solution during in-situ heating in the TEM. The purpose of this paper is to report results from an investigation of the influence of ion-milling on the stability of the T2 phase in dilute Al-Li-Cu alloy.The 3-mm diameter TEM disc specimens were prepared from a specially melted Al-2.5%Li-2.5%Cu alloy produced by conventional procedures. The TEM specimens were solution heat treated 1 h at 550°C and aged 1000 h at 190°C in air to develop the microstructure. The disc specimens were electropolished to achieve electron transparency using a 20:80 (vol. percent) nitric acid: methanol solution at -60°C.


2019 ◽  
Author(s):  
Vitaly Kuyukov

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.


2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  

Braking effect in quantum gravity


2019 ◽  
Vol 51 (5) ◽  
Author(s):  
S. Ariwahjoedi ◽  
I. Husin ◽  
I. Sebastian ◽  
F. P. Zen

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