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Heuristic Schrodinger equation of quantum mechanics QM perfectly describes the micro-world phenomena, but remains an axiomatic hypothesis having no logical explanations and properly formulated correspondence principle with classical mechanics. However, resent investigations demonstrate immanent presence of this basic QM law in pure mathematics of hyper complex quaternion – Q numbers. We outline the logics and stages of this discovery.
A deeper analysis of the Q-algebra whose “imaginary” units behave as a vectors initiating a 3D Cartesian frame involving the spectral theorem of the theory of matrices reveals existence of a pre-geometric fractal surface, a “square-root slice” of a 3D space. Simple distortions oscilla-tion and stretching of the surface violate the Q-algebra multiplication; a condition providing the algebra’s “eternal” stability takes the shape of a continuity-type math unit-less equation com-prising an arbitrary vector. We chose this vector as the oscillation gradient; these pure math ac-tions have amazing results.
The stability condition fractalizes, and when written in the physical micro-world units, it be-comes precisely the Schrodinger equation of QM. The particle’s wave function then is image of oscillating 2D area of the pre-geometric space predicted by Wheeler. Respective 3D physical object is a massive point rotating about an axis. In the “lab” conditions, the fractal equation converts precisely into the Hamilton-Jacobi equation of classical mechanics, the oscillation phase acquiring sense of the action function. Finally, constancy of particle’s rotational velocity leads to the Einstein’s relativistic mechanics.Thus, the math of Q-numbers unites quantum, classical, and relativistic mechanics in one theory
Francis Sgambelluri was born in South Italy and of 77 years old. Although he is not a scientist or a philosopher, he is still inclined towards the scientific research and observation. Being a free thinker, Francis feed himself from the universal table of ideas.
Einstein, in his famous equation E=mc2 (energy equals mass times the speed of light squared), says that mass is energy and energy is mass. This is correct only if we see first the mass and then the energy, not the other way around. Differently said, energy doesn’t exist without mass, but mass without energy does. The existence of energy depends on the mass. No mass, no energy. The equation should have been written M=ec2 (mass equals energy times the speed of light squared) and no viceversa. Now, time, space and energy don’t exist, if so, what is left of Einstein’s special and general relativity?
The questions about space, time, energy and special or general relativity don’t end here. Einstein almost silenced Newton's gravity and in its place placed Maxwell's electromagnetism and his space-time. The Earth no longer revolves around the Sun, like in the old days, but it shoots straight ahead. The theory of general relativity imposes this concept. Let’s suppose now for an instant that the Sun is no longer there, what will happen to the Earth? Will it continue to go around and around even without the Sun or it will start darting into deep space?
Engr. Musa D. Abdullahi was born in Katsina, Nigeria, in 1941. He had his Primary and Secondary education in Nigeria. He obtained BSc degree in physics from the University of Manchester, England, in 1965. He was the first person to obtain a postgraduate degree, in Electronics and Telecommunication, from Ahmadu Bello University, Zaria, Nigeria, in August 1968. He taught at Ahmadu Bello University, Zaria, from 1968 to 1972 and thereafter joined the Nigerian Pubic Service. He retired from the Nigerian Civil Service in August 2000. He was a senior lecturer in electronics and telecommunication at Federal University of Technology, Minna, Nigeria, from 2000 to 2007. He was the Pro-chancellor of Umaru Musa Yar’adua University, Katsina, from 2007 to 20017. He is a member of the Nigerian Institute of Physics, Fellow of the Nigerian Society of Engineers, Fellow of the Academy of Engineering and Member of the Order of Federal Republic of Nigeria (MFR). He is now a Visiting Chief Lecturer in the Department of Electrical and Electronics Engineering, Kaduna Polytechnic, Kaduna, Nigeria. He is a prolific contributor of papers in On-line Journals.
If an electron of charge -e and mass m or positron of charge +e and mass m is to assume any configuration, it is most likely to be an impenetrable spherical shell of radius a with a uniform surface charge. The electric potential is constant and the electric field is zero inside the shell. From outside the shell it is as if the whole charge is concentrated at the centre of the sphere. The radial electric field outside the shell, in accordance with Coulomb’s inverse-square law, pulls the surface charge outwards while the universal space pushes it inwards to maintain a stable structure, like a bubble in the air. Such a configuration should have intrinsic energy En and mass m, where En = ½mc2, c being the speed of light in a vacuum. A positron and an electron join together to form a neutral particle called “unitron” of intrinsic energy 2En, potential energy -En and mass m. The positron, the electron and the “unitron” are proposed as the basic constituent particles of matter. On this premise, two models of the hydrogen atom are developed, a non-nuclear model identified for the gaseous state and a nuclear model for the liquid or solid state, with emission of radiation at frequencies in conformity with the Balmer-Rydberg formula. The hydrogen atom is the building block of atoms of elements and molecules of compounds.
Title: Quantum Spins Of Electrons
Sungwon Yoon has a bachelor degree of International Relations at University of Seoul, Korea and a Master of Law degree from Northwestern University, Chicago/Illinois.
As Michael Faraday came up with electromagnetic field in the 19th century to Maxwell’s equation in 1862 to Max Planck’s blackbody radiation to Albert Einstein’s photoelectric effect in 1905 and Niels Bohr’s bohr model in 1913, electron has been key element that plays core role in formulating physics phenomena.Spintronics, which is the study of spin of electrons in hard solid devices such as semiconductor, is believed to be crucial field regarding engagement of electromagnetic works in spaces at material appliances around us that can promote people’s quality of lives.Therefore, I decided to present my view with combined structures of both QFT and Spintronics that entails electrons movements into practical formula as well as opening possibilities to biophysics that can greatly contribute to our lifecycle and wellbeing.Entire works of mine are based on my self-learning started with a book called ‘Basic Physics’ written by Karl F.Kuhn and self-paced learning online.