The Intricate Realm of Numbers in Conjunction with the Physical World as Revealed by an Exceptional Numerical Sequence and by Some Outstanding Numerical Conjectures

From Morley's Theorem to Euler-Zeta Function and Beyond

Estudio Científico , 2019 , 367 Páginas

Física - Otros

This work is a simple straightforward investigation of the realm of numbers in conjunction with the physical world, from a perspective capable of encompassing all major findings already known in this field and rediscovered in this paper as for example Schrodinger’s Equation (Sec3) and Lorentz Transforms (both having as origin the main matrix), or for the first time discovered in this paper as for example the “non primes” primes conjectures, Sec12. In this context, some old findings that were not understood (as for example the Vacuum Catastrophe Sec9, or some aspects regarding the zeta function Secs17 to 22 and 28, or Goldbach’s Conjecture and Poncelet’s Drawings Secs26,27,28) receive a meaning, and a few relatively recent findings regarding the Universe are reinterpreted. All these findings, old or new, are inter connecting components of a unique reality that includes (and has as its driving and unifying force) the observer.

The basic constituents of this paper are a few interrelated naturally repeatedly occurring numerical patterns. One of these patterns (that plays a central skeletal role in this paper) is a remarkable infinite double sequence called the main sequence. The components of these numerical patterns in particular the components of the main sequence, which are numbers (in a generalized sense, with undefined ambiguous significance, i.e., capable of taking various concrete meanings in various concrete situations, or remaining just numbers), have not only algorithmic (necessary) number like properties but also non algorithmic (accidental) object like interlocking pattern like properties (see for example Obs1 of Sec4), with the object like interlocking pattern like properties interlocking themselves with the algebraic properties.

Inhaltsverzeichnis (Table of Contents)

• Morley's Theorem Reexamined..
• Morley's Theorem Reformulated (and Proven) for the non Equiangular Case. Coloured Unit...
• Morley's Theorem (for the non Equiangular Case), Continuation. Colours Assigned to the Colour Unit. Their Geometrical and Physical Meaning. Schrodinger's Equation
• The Main Sequence and Some of its Outcomes.
• Morley's Theorem “for the Equiangular Triangle Case\", Singularities, Angle Renormalization, Perpendicularity, Elliptical Planetary Motion...........
• Elementary Particles......
• Lorentz Like Addition Formulas for Velocities, Continued Fractions (CF), Collatz Conjecture, Crossover and Prime Numbers.......
• Random Numbers, Continued Fractions, Crossover, and Prime Numbers..\n
• 4.9 % Ordinary Matter, 26.8 Dark Matter, 68.3 Dark Energy Present in the Universe..........
• Coupling Constants for Elementary Particles......
• Plank's Constant h as Related to the Gravitational Constant G....
• Some Prime Numbers Conjectures and the Main Sequence. The Two “Non Primes” Primes Conjectures......
• The Number Pi Obtained From Fundamental Non Tautological Considerations
• Some Particular Logarithms and their Interconnectedness.......
• Human DNA...
• The Neutrino, the Main Sequence, and the Prime Numbers Conjectures.…….......
• The Main Sequence and the Riemann Hypothesis, Dichotomy: the First Approach.......
• The Main Sequence and the Riemann Hypothesis: the Second Approach...
• The Main Sequence and the Riemann Hypothesis: the Third Approach...........
• The Main Sequence, Schrodinger Equation, and the Riemann Hypothesis: the Fourth Approach...........
• The Zeta Function, its Crossover Continuity Dual, and Riemann Hypothesis: the Fifth Approach
• Riemann Hypothesis, the Main Sequence, and Continued Fractions with Crossover: The Sixth Approach..........\n
• More About the Interrelation Between the Set of Prime Numbers, the Arrow of Time, “Actual Infinity”, Coupling Constants for Elementary Particles, and the Zeta Function. Some Remarkable Numbers and the “Age of the Universe”..\n
• Universe/\"Standard Observer\" Time Scale Discrepancy and the Origin of Mass. The Balanced Universe..........\n
• Goldbach's Conjecture...........
• Goldbach's Conjecture, Poncelet's Drawings, and the Main Sequence: The First Approach
• Goldbach's Conjecture, Poncelet's Drawings, the Double Circle, Prime Numbers: the Second Approach...
• Closing Remarks..........\n

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This work examines the realm of numbers in conjunction with the physical world, encompassing major discoveries and re-discoveries. The paper explores the connection between numbers and the physical world through the lens of various numerical patterns, including a unique infinite double sequence called the main sequence. This sequence serves as the central backbone of the research, demonstrating its role in different aspects of the physical world.

• The Main Sequence and its Implications for the Physical World
• The Interrelation between Algorithmic and Non-Algorithmic Properties of Numbers
• The Role of the Observer in Shaping and Understanding Reality
• The Exploration and Reinterpretation of Fundamental Concepts in Physics and Mathematics
• The Application of Numerical Patterns to Understanding the Universe and its Components

Zusammenfassung der Kapitel (Chapter Summaries)

• Chapter 1: Morley's Theorem Reexamined: This chapter introduces the concept of Morley's Theorem and begins to reexamine its implications. The chapter sets the stage for further investigation into the theorem's connections to other areas of physics and mathematics.
• Chapter 2: Morley's Theorem Reformulated (and Proven) for the non Equiangular Case. Coloured Unit...: Chapter 2 continues the examination of Morley's Theorem, focusing on the non-equiangular case. This chapter introduces the concept of a colored unit and sets the stage for the exploration of the geometrical and physical meaning of these colors.
• Chapter 3: Morley's Theorem (for the non Equiangular Case), Continuation. Colours Assigned to the Colour Unit. Their Geometrical and Physical Meaning. Schrodinger's Equation: This chapter delves deeper into the concept of colors as introduced in the previous chapter, connecting them to both geometrical and physical meanings. It also introduces Schrodinger's equation within the context of the ongoing examination of Morley's Theorem.
• Chapter 4: The Main Sequence and Some of its Outcomes.: This chapter focuses on the introduction of the main sequence and its significance. It explores the various properties and outcomes of this sequence, setting the stage for further investigations into its role in the physical world.
• Chapter 5: Morley's Theorem “for the Equiangular Triangle Case\", Singularities, Angle Renormalization, Perpendicularity, Elliptical Planetary Motion...........: This chapter examines Morley's Theorem in the context of the equiangular triangle case. It explores concepts such as singularities, angle renormalization, perpendicularity, and elliptical planetary motion, demonstrating the interconnectedness of various aspects of the physical world through the lens of Morley's Theorem.
• Chapter 6: Elementary Particles......: This chapter delves into the realm of elementary particles, exploring their connection to the main sequence and other numerical patterns discussed in the paper.
• Chapter 7: Lorentz Like Addition Formulas for Velocities, Continued Fractions (CF), Collatz Conjecture, Crossover and Prime Numbers.......: This chapter investigates the relationship between Lorentz-like addition formulas for velocities, continued fractions, the Collatz conjecture, crossover, and prime numbers. The chapter explores these concepts through the lens of the main sequence and its properties, demonstrating their interconnection and relevance to the physical world.
• Chapter 8: Random Numbers, Continued Fractions, Crossover, and Prime Numbers..\n: This chapter further examines the connection between random numbers, continued fractions, crossover, and prime numbers. It explores the implications of these concepts in relation to the main sequence and its properties.
• Chapter 9: 4.9 % Ordinary Matter, 26.8 Dark Matter, 68.3 Dark Energy Present in the Universe..........: This chapter analyzes the proportions of ordinary matter, dark matter, and dark energy in the Universe, using the main sequence and its properties to reinterpret these findings and offer new insights into the nature of the Universe.
• Chapter 10: Coupling Constants for Elementary Particles......: This chapter examines the coupling constants for elementary particles in the context of the main sequence, uncovering potential connections and offering new perspectives on the underlying unity of these constants.
• Chapter 11: Plank's Constant h as Related to the Gravitational Constant G....: This chapter investigates the relationship between Plank's constant and the gravitational constant through the lens of the main sequence and its properties, offering insights into the fundamental connection between these constants.
• Chapter 12: Some Prime Numbers Conjectures and the Main Sequence. The Two “Non Primes” Primes Conjectures......: This chapter explores the connection between prime numbers and the main sequence. It delves into prime number conjectures and introduces the intriguing concept of "non primes" primes, offering a unique perspective on the nature of prime numbers and their relationship to the main sequence.
• Chapter 13: The Number Pi Obtained From Fundamental Non Tautological Considerations: This chapter explores the derivation of the number Pi from fundamental non-tautological considerations, offering a unique perspective on the nature of this fundamental mathematical constant.
• Chapter 14: Some Particular Logarithms and their Interconnectedness.......: This chapter examines the interconnections between specific logarithms, exploring their connection to the main sequence and their implications for understanding the mathematical and physical world.
• Chapter 15: Human DNA...: This chapter delves into the realm of human DNA, exploring its connection to the main sequence and its potential implications for understanding the biological world.
• Chapter 16: The Neutrino, the Main Sequence, and the Prime Numbers Conjectures.…….......: This chapter examines the connection between neutrinos, the main sequence, and prime number conjectures, offering insights into the nature of these fundamental particles and their relationship to the broader mathematical and physical world.
• Chapter 17: The Main Sequence and the Riemann Hypothesis, Dichotomy: the First Approach.......: This chapter begins the exploration of the connection between the main sequence and the Riemann Hypothesis. It presents the first approach to understanding this connection, highlighting the interplay between these concepts.
• Chapter 18: The Main Sequence and the Riemann Hypothesis: the Second Approach...: This chapter continues the exploration of the connection between the main sequence and the Riemann Hypothesis, presenting the second approach to understanding this connection and further illuminating their intricate relationship.
• Chapter 19: The Main Sequence and the Riemann Hypothesis: the Third Approach...........: This chapter presents the third approach to understanding the connection between the main sequence and the Riemann Hypothesis, deepening our comprehension of this complex relationship.
• Chapter 20: The Main Sequence, Schrodinger Equation, and the Riemann Hypothesis: the Fourth Approach...........: This chapter examines the connection between the main sequence, Schrodinger's equation, and the Riemann Hypothesis, offering a fourth perspective on their intricate relationship and highlighting the unifying role of the main sequence.
• Chapter 21: The Zeta Function, its Crossover Continuity Dual, and Riemann Hypothesis: the Fifth Approach: This chapter explores the connection between the zeta function, its crossover continuity dual, and the Riemann Hypothesis, offering a fifth perspective on their relationship and highlighting the importance of crossover and continuity in understanding these concepts.
• Chapter 22: Riemann Hypothesis, the Main Sequence, and Continued Fractions with Crossover: The Sixth Approach..........\n: This chapter presents the sixth approach to understanding the connection between the Riemann Hypothesis, the main sequence, and continued fractions with crossover, deepening our understanding of this complex relationship.
• Chapter 23: More About the Interrelation Between the Set of Prime Numbers, the Arrow of Time, “Actual Infinity”, Coupling Constants for Elementary Particles, and the Zeta Function. Some Remarkable Numbers and the “Age of the Universe”..\n: This chapter explores the intricate interrelation between the set of prime numbers, the arrow of time, "actual infinity," coupling constants for elementary particles, and the zeta function. It also highlights remarkable numbers and their connection to the "age of the universe," offering new insights into the nature of these concepts and their interconnectedness.
• Chapter 24: Universe/\"Standard Observer\" Time Scale Discrepancy and the Origin of Mass. The Balanced Universe..........\n: This chapter examines the time scale discrepancy between the Universe and the "standard observer," exploring the origin of mass and the concept of a balanced Universe. The chapter uses the main sequence and its properties to shed new light on these fundamental concepts.
• Chapter 25: Goldbach's Conjecture...........: This chapter delves into Goldbach's Conjecture, exploring its connection to the main sequence and other numerical patterns. It provides insights into the nature of this conjecture and its potential implications for understanding the world of numbers.
• Chapter 26: Goldbach's Conjecture, Poncelet's Drawings, and the Main Sequence: The First Approach: This chapter explores the connection between Goldbach's Conjecture, Poncelet's Drawings, and the main sequence. It presents the first approach to understanding this intricate relationship, offering new perspectives on the nature of these concepts and their interplay.
• Chapter 27: Goldbach's Conjecture, Poncelet's Drawings, the Double Circle, Prime Numbers: the Second Approach...: This chapter continues the exploration of the connection between Goldbach's Conjecture, Poncelet's Drawings, the double circle, and prime numbers, offering a second approach to understanding this intricate relationship and further illuminating its significance.
• Chapter 28: Closing Remarks..........\n: This chapter concludes the paper, summarizing the key findings and offering a final reflection on the significance of the main sequence and its role in connecting the realm of numbers to the physical world. It provides a sense of closure to the exploration undertaken throughout the work.

Schlüsselwörter (Keywords)

The key concepts explored in this work include the main sequence, Morley's Theorem, Schrodinger's equation, the Riemann Hypothesis, Goldbach's Conjecture, prime numbers, continued fractions, coupling constants, elementary particles, the Universe, and the observer. These keywords represent the core focus areas of the research, highlighting the interrelation between mathematics, physics, and the fundamental nature of reality.

• Autor: PhD Ovidiu Mitran (Autor)
• Año de publicación: 2019
• Páginas: 367
• No. de catálogo: V489553
• ISBN (Ebook): 9783668990685
• ISBN (Libro): 9783668990692
• Idioma: Inglés
• Etiqueta: Morley's Theorem, colour, Schrodinger's Equation, the main sequence, the main matrice, elementary particles, Lorenz like addition formula, continued fraction (CF), Collatz conjecture, ordinary matter..., "non primes" primes conjectures, the numbers Pi and e, human DNA, the neutrino, the Euler-Zeta function, the Riemann Hypothesis, the origin of mass, the Balanced Universe, Goldbach's Conjecture, Poncelet's drawings, the double circle, discrete differentiation, Heegner's Numbers, Fermat's Theorem, Age and Size of the Universe, the N NP problem, quantum entanglement, arrow of time, no arrow of time, four colours needed to paint (such) an infinite map, the logarithmic spiral, Cantor's actual infinity, singular sub sequence