Time and Consistent Relativity Physical and Mathematical Fundamentals

Time and Consistent Relativity: Physical and Mathematical Fundamentals establishes a new and original theory of time relativity, which is fully consistent. It explains why Einstein?s theory of time relativity is physically meaningless and mathematically based on tacit inacceptable assumptions, and why it represents the singular case from the mathematical point of view. The consistent relativity theory established in the book represents an exit from the situation created by Einstein?s theory of time relativity.

This original book presents novel results on time and its relativity that constitute the consistent relativity theory. The results are free of mistakes, inconsistencies, and paradoxes of Einstein?s time relativity theory. The author?s original discoveries and results constitute the new physical and mathematical fundamentals on time and its relativity. The book presentation is concise, clear, and self-contained. It covers the phenomenon of time and its properties and results in a definition and characterization of time. It enables the great variety of new mathematical results presented in the form of theorems and their corollaries and specifies the necessary and sufficient conditions for the corresponding statements to hold. The proofs are rigorous.

This book:

• Explains the physical nature of time
• Presents the definition and characterization of time
• Explains the physical sense of time relativity
• Rejects Einstein?s time relativity theory as the general one
• Proves that Einstein?s time relativity theory represents a singular case valid under tacit, physically meaningless and mathematically inacceptable, assumptions
• Generalizes and extends the Galilean-Newtonian meaning of time and its relativity
• Introduces various new classes of mathematical transformations related to temporal, spatial, and velocity coordinates and proves the necessary and sufficient conditions for their validity
• Discovers a great specter of new results on the time uniqueness, relativity, and temporal speed
• Discovers and proves a great specter of new results on the velocity and its transformations
• Discovers and proves a great specter of new results on the light speed and its invariance and non-invariance
• Discovers and proves the relationship of the light speed and the upper limiting speed
• Opens new directions for further research in physics and mathematical physics

Preface

Introduction

PART I. TIME

1. Interpretations of Time

1. Introductory comment
2. Time as a topic
3. Arts and time
4. Biology and time
5. Economics and time
6. Human and time
7. Information and time
8. Mathematics and time
9. Philosophy and time
10. Physics and time
11. Psychology and time
12. Religion and time
13. Works on time in general
14. Works on time

2. Newton and Einstein on Time

1. Newton's explanation of time
2. Einstein's interpretation of time
3. Einstein's versus Newton's explanation

3. Nature and Properties of Time

1. Quantities, dimensions and units
2. Definition and properties of time
3. Time scales, units and interval mappings
4. Physical variables and spaces
5. Physical constituents of the existence
6. Time, space and events. Simultaneity
7. Time, velocity and light velocity
8. Clock principles
9. Time and movement
10. Human and time

4. New Fundamentals

1. Physical variables, time and new principles
2. Modeling and relativity principles
3. Time, principles and dynamical systems
4. New fundamental theorems

PART II. TIME FIELDS AND RELATIVITY

5. Time Fields and Transformations

1. Time field: definition and properties
2. Time fields. Generic transformations
3. Compatibility. Consistency
4. Basic mathematical problem
5. General, special and singular case

6. Why not Einstein`s Relativity Theory?

1. Einstein's condition and transformations
2. Time Fields and Lorentz transformations
3. Failure of Einstein`s Relativity Theory
4. Inapplicability of Lorentz transformations
5. Paradoxes of Lorentz transformations
6. Einstein`s paradoxes, mistakes and absurd
7. Concluding rebuttals to Einstein`s postulates
8. Conclusion on Einstein's Theory

7. Non-Einsteinean Approaches to Relativity

1. Galilean - Newtonean approach
2. Dynamical systems approach to relativity
3. Generalized Galilean - Newtonean approach
4. Guideline

8. Conclusion on Time and Time Fields

PART III. PARTIALLY COMPATIBLE BUT CONSISTENT (PCC) RELATIVITY THEORY (RT)

9. Partial Compatibility

1. Origin of partial compatibility
2. Time-invariant nonuniformity
3. Time-invariant uniformity

10. Light Speed of the Arbitrary Point

1. General nonuniformity
2. Nonuniformity
3. Weak nonuniformity
4. Uniformity: general through special
5. Weak uniformity results
6. Relative uniformity results

11. Any Speed of the Arbitrary Point

1. General spatial uniformity
2. General complete uniformity

12. Conclusion on PCC Relativity Theory

PART IV. COMPATIBLE AND CONSISTENT (CC) RELATIVITY THEORY

13. Colinear Motions: Transformations

1. Importance. Time-invariance
2. Nonuniformity: general
3. Nonuniformity: ordinary
4. Nonuniformity: weak
5. General uniformity
6. Uniformity
7. Special uniformity
8. General weak uniformity
9. Weak uniformity
10. Special weak uniformity
11. General relative uniformity
12. Relative uniformity
13. Special relative uniformity
14. Conclusion on colinear motions

14. Noncolinear Motions: Transformations

1. Generic forms
2. General nonuniformity
3. General uniformity
4. General weak uniformity
5. General relative uniformity
6. Conclusion on noncolinear motions

15. Conclusion on CC Relativity Theory

PART V. GENERAL CONCLUSION

PART VI. SUBSIDIARY PARTS

16. Bibliography
17. Notational Details
18. Appendices: Proofs
19. Indexes

Lyubomir T. Gruyitch, DSc, has very rich international academic and research experience. Now retired, he was a professor at the Ecole Nationale d'Ingénieurs, which integrated with the Institut Polytechnique de Sévenans into the University of Technology Belfort–Montbeliard, in France; the AECI professor of control in the Department of Electrical Engineering at the University of Natal, Durban, South Africa; and a professor of automatic control in the Faculty of Mechanical Engineering at the University of Belgrade, Belgrade, Serbia. He has also been a visiting professor at Louisiana State University, Baton Rouge, Louisiana; the University of Notre Dame, Notre Dame, Indiana; and the University of Santa Clara, Santa Clara, California. He continues to teach and participate at conferences on an invited basis. Dr. Gruyitch is the author of several published books and many scientific papers on dynamical systems, on control systems, and on time and its relativity. He has participated at many scientific conferences throughout the world. He has been honored with several awards, including the highest award by the Faculty of Mechanical Engineering, University of Belgrade, for teaching and scientific contributions to the faculty, 1964–1992; and an award from the Yugoslav Air Force Academy for teaching achievements in the undergraduate course foundations of automatic control. Dr. Gruyitch is a Certified Mechanical Engineer (Dipl. M. Eng.), Master of Electrical Engineering Sciences (M. E. E. Sc.), and Doctor of Engineering Sciences (DSc), all from the University of Belgrade, Serbia.