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E-raamat: Time and Consistent Relativity: Physical and Mathematical Fundamentals [Taylor & Francis e-raamat]

(Retired Professor, University of Technology BelfortMontbeliard, France)
  • Formaat: 602 pages
  • Ilmumisaeg: 08-May-2015
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-13: 9780429156366
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  • Taylor & Francis e-raamat
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Time and Consistent Relativity: Physical and Mathematical FundamentalsSuurem pilt
  • Formaat: 602 pages
  • Ilmumisaeg: 08-May-2015
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-13: 9780429156366
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429156366
Time and Consistent Relativity: Physical and Mathematical Fundamentals establishes a new and original theory of time relativity, which is fully consistent. It explains why Einsteins 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 Einsteins 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 Einsteins time relativity theory. The authors 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 Einsteins time relativity theory as the general one





Proves that Einsteins 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 xv
0.1 Relevant citations
xv
0.2 Why Consistent Time Relativity Theory?
xvi
0.3 Problems to be solved
xvii
0.4 Acknowledgement
xx
1 Introduction
1(6)
1.1 The goals of the book
1(1)
1.2 Book composition
2(3)
1.3 On the notation and proofs
5(2)
I Time 7(162)
2 Interpretations of Time
9(46)
2.1 Introductory comment
9(1)
2.2 Time as a topic
9(2)
2.3 Arts and time
11(1)
2.4 Biology and time
12(5)
2.5 Economics and time
17(1)
2.6 Human and time
18(5)
2.7 Information and time
23(1)
2.8 Mathematics and time
24(3)
2.9 Philosophy and time
27(5)
2.10 Physics and time
32(12)
2.11 Psychology and time
44(3)
2.12 Religion and time
47(2)
2.13 Works on time in general
49(3)
2.14 Works on time: reviews
52(3)
3 Newton and Einstein on Time
55(6)
3.1 Newton's explanation of time
55(2)
3.2 Einstein's interpretation of time
57(2)
3.3 Einstein's versus Newton's explanation
59(2)
4 Nature and Properties of Time
61(84)
4.1 Quantities, dimensions and units
61(3)
4.2 Definition and properties of time
64(20)
4.2.1 Principal Einstein's contradiction
65(1)
4.2.2 Various claims on time
65(1)
4.2.3 Definition of time
65(2)
4.2.4 Time value
67(2)
4.2.5 Time properties and characterization
69(3)
4.2.6 Existence of time
72(1)
4.2.7 Uniqueness of time
73(1)
4.2.8 Name for time
74(1)
4.2.9 Beginning, end, and time
74(1)
4.2.10 Existence, time value counting and measurement
75(1)
4.2.11 Numerical values of time and relativity
76(2)
4.2.12 Time order
78(1)
4.2.13 Time flow direction
78(1)
4.2.14 Speed of the time value evolution (time speed)
79(4)
4.2.15 Continuous-time set and discrete-time set
83(1)
4.3 Time scales, units and interval mappings
84(8)
4.3.1 Dimensions and units of time
85(1)
4.3.2 Time axes
85(1)
4.3.3 Time scaling coefficients: definition
86(3)
4.3.4 Time scaling coefficients: geometrical interpretation
89(1)
4.3.5 Time axis transformation
90(2)
4.4 Physical variables and spaces
92(9)
4.4.1 Physical variables
92(1)
4.4.2 Values of physical variables
93(2)
4.4.3 Representation of a physical variable
95(1)
4.4.4 Time and physical variables
96(2)
4.4.5 Spaces
98(1)
4.4.6 Spaces and physical variables
99(2)
4.5 Physical constituents of the existence
101(6)
4.5.1 Existence and physical constituents
101(3)
4.5.2 Energy, matter, and fundamental laws of physics
104(3)
4.6 Time, space and events. Simultaneity
107(8)
4.6.1 Time axes and space
107(1)
4.6.2 Time, space and coordinate systems
108(1)
4.6.3 Time and space: integral space
109(4)
4.6.4 Simultaneity of events
113(2)
4.7 Time, velocity and light velocity
115(6)
4.7.1 Time, relative velocities and their values
115(1)
4.7.2 Time, light velocity, and light speed
116(1)
4.7.3 Time, light speed, units and coordinate systems
117(3)
4.7.4 Relative light velocities and their values
120(1)
4.8 Clock principles
121(14)
4.8.1 Time value measurement and clock
122(1)
4.8.2 General clock principle
123(4)
4.8.3 Relativity theory based clock principle
127(4)
4.8.4 Time and the cause of the clock operation
131(1)
4.8.5 Energy and movement of clock itself
132(3)
4.9 Time and movement
135(6)
4.10 Human and time
141(4)
4.10.1 Aging, biological state and biological scales of time
141(2)
4.10.2 Psychological feeling of time
143(2)
5 New Fundamentals
145(24)
5.1 Physical variables, time and new principles
145(10)
5.1.1 Introduction
145(1)
5.1.2 Nonlinearities: continuity and discontinuity
146(3)
5.1.3 Physical Continuity Principle (PCP)
149(2)
5.1.4 Physical Uniqueness Principle (PUP)
151(2)
5.1.5 Physical Continuity and Uniqueness Principle (for short: PCUP)
153(2)
5.1.6 Time Continuity and Uniqueness Principle (shortly: TCUP)
)154
5.2 Modelling and relativity principles
155(2)
5.2.1 Modeling principles
155(1)
5.2.2 Principle of relativity of values of variables
156(1)
5.2.3 Principle of mathematical models relativity
157(1)
5.3 Time, principles and dynamical systems
157(4)
5.3.1 Time and motions of dynamical systems
157(2)
5.3.2 Time and dynamical systems with multiple time scales
159(2)
5.4 New fundamental theorems
161(10)
5.4.1 Fundamental theorem on time speed
161(5)
5.4.2 Fundamental theorem on the light speed noninvariance
166(3)
II Time Fields and Relativity 169(84)
6 Time Fields and Transformations
171(28)
6.1 Time field: definition and properties
171(13)
6.1.1 Time axis, temporal environment and space
171(4)
6.1.2 Definition and properties of time fields
175(8)
6.1.3 Temporal environment
183(1)
6.2 Time fields. Generic transformations
184(3)
6.2.1 Speed of a generic point G
184(1)
6.2.2 Time, velocity and generic transformations
185(2)
6.3 Compatibility. Consistency
187(2)
6.3.1 Compatibility of the transformations
187(2)
6.3.2 Consistency of values and of transformations
189(1)
6.4 Basic mathematical problem
189(3)
6.5 General, special and singular case
192(7)
7 Why not Einstein's Relativity Theory?
199(40)
7.1 Einstein's condition and transformations
199(3)
7.2 Time Fields and Lorentz transformations
202(14)
7.2.1 Lorentz transformations
202(8)
7.2.2 Homogenous forms of Lorentz transformations
210(3)
7.2.3 Lorentz transformations and velocity
213(1)
7.2.4 Lorentz transformations and acceleration: paradox
214(1)
7.2.5 Compatibility problem in Einsteinian relativity theory
215(1)
7.3 Failure of Einstein's Relativity Theory
216(21)
7.3.1 Inapplicability of Lorentz transformations
216(2)
7.3.2 Paradoxes of Lorentz transformations
218(7)
7.3.3 Einstein's paradoxes, mistakes and absurd
225(11)
7.3.4 Concluding rebuttals to Einstein's postulates
236(1)
7.4 Conclusion on Einstein's Theory
237(2)
8 Non-Einsteinian Approaches to Relativity
239(12)
8.1 Galilean - Newtonian approach
239(5)
8.2 Dynamical systems approach to relativity
244(2)
8.3 Generalized Galilean - Newtonian approach
246(3)
8.4 Guideline
249(2)
9 Conclusion on Time and Time Fields
251(2)
III Partially Compatible but Consistent Relativity Theory (PCC RT) 253(76)
10 Partial Compatibility
255(22)
10.1 Origin of partial compatibility
255(1)
10.2 Time-invariant nonuniformity
256(5)
10.2.1 On nonuniformity
256(1)
10.2.2 Weak nonuniformity
256(2)
10.2.3 Nonuniformity
258(2)
10.2.4 General nonuniformity
260(1)
10.3 Time-invariant uniformity
261(16)
10.3.1 On uniformity
261(2)
10.3.2 Special relative uniformity
263(2)
10.3.3 Relative uniformity
265(1)
10.3.4 General relative uniformity
266(2)
10.3.5 Special weak uniformity
268(1)
10.3.6 Weak uniformity
269(1)
10.3.7 General weak uniformity
270(2)
10.3.8 Special uniformity
272(1)
10.3.9 Uniformity
273(2)
10.3.10 General uniformity
275(2)
11 Light Speed of the Arbitrary Point
277(32)
11.1 General nonuniformity
277(10)
11.1.1 Transformations of temporal and spatial coordinates
277(7)
11.1.2 Transformations of velocity
284(3)
11.2 Nonuniformity
287(9)
11.2.1 Transformations of temporal and spatial coordinates
287(6)
11.2.2 Transformations of velocity
293(3)
11.3 Weak nonuniformity
296(2)
11.3.1 Transformations of temporal and spatial coordinates
296(2)
11.3.2 Transformations of velocity
298(1)
11.4 Uniformity: general through special
298(8)
11.4.1 Transformations of temporal and spatial coordinates
298(6)
11.4.2 Transformations of velocity
304(2)
11.5 Weak uniformity results
306(1)
11.6 Relative uniformity results
307(2)
12 Any Speed of the Arbitrary Point
309(18)
12.1 General spatial uniformity
309(9)
12.1.1 Transformations of temporal and spatial coordinates
309(5)
12.1.2 Transformations of velocity
314(4)
12.2 General complete uniformity
318(13)
12.2.1 Temporal and spatial coordinate transformations
318(4)
12.2.2 Velocity transformations
322(5)
13 Conclusion on PCC Relativity Theory
327(2)
IV Compatible and Consistent Relativity Theory (CC RT) 329(62)
14 Colinear Motions: Transformations
331(28)
14.1 Importance. Time-invariance
331(1)
14.2 Nonuniformity: general
332(12)
14.2.1 Temporal and spatial coordinate transformations
332(9)
14.2.2 Velocity transformations
341(3)
14.3 Nonuniformity: ordinary
344(1)
14.4 Nonuniformity: weak
345(1)
14.4.1 Transformations of temporal and spatial coordinates
345(1)
14.4.2 Transformations of velocity
346(1)
14.5 General uniformity
346(8)
14.5.1 Temporal and spatial coordinate transformations
346(7)
14.5.2 Velocity transformations
353(1)
14.6 Uniformity
354(1)
14.7 Special uniformity
355(1)
14.8 General weak uniformity
355(1)
14.9 Weak uniformity
355(1)
14.10 Special weak uniformity
355(1)
14.11 General relative uniformity
355(1)
14.12 Relative uniformity
356(1)
14.13 Special relative uniformity
356(1)
14.14 Conclusion on colinear motions
356(3)
15 Noncolinear Motions: Transformations
359(30)
15.1 Generic forms
359(5)
15.1.1 Vector variables and time scales
359(1)
15.1.2 Notational preliminaries
359(4)
15.1.3 Generic coordinate transformations
363(1)
15.2 General nonuniformity
364(11)
15.2.1 Transformations of temporal and spatial coordinates
364(7)
15.2.2 Transformations of velocity
371(4)
15.3 General uniformity
375(8)
15.3.1 Transformations of temporal and spatial coordinates
375(6)
15.3.2 Transformations of velocity
381(2)
15.4 General weak uniformity
383(1)
15.5 General relative uniformity
384(1)
15.6 Conclusion on noncolinear motions
385(4)
16 Conclusion on CC Relativity Theory
389(2)
16.1 Common features
389(1)
16.2 On applications of the CC Relativity Theory
390(1)
V General Conclusion 391(16)
17 Problem Solutions
393(12)
18 Summary on time
405(2)
VI Subsidiary Parts 407
19 Notational Details
409(20)
19.1 Introductory comment
409(1)
19.2 Indexes
409(1)
19.2.1 In general
409(1)
19.2.2 Subscripts
410(1)
19.2.3 Superscripts
410(1)
19.3 Letters
410(16)
19.3.1 Caligraphic letters
411(1)
19.3.2 3tattut letters
411(2)
19.3.3 Greek letters
413(2)
19.3.4 Roman letters
415(11)
19.4 Names
426(1)
19.5 Symbols
426(1)
19.6 Units
427(2)
20 Appendices: Proofs for Part 1
429(6)
20.1 Time Uniqueness
429(3)
20.1.1 Einstein's postulate
429(1)
20.1.2 Mathematical expression of Hypothesis 674
429(1)
20.1.3 Direct proof of (20.2) via the light speed
430(1)
20.1.4 Proof of (20.2) by using (7.22)
430(1)
20.1.5 Proof of (20.2) by using (11.54)
431(1)
20.1.6 Termination of the proof via (20.2)
431(1)
20.1.7 Proof via time speed
431(1)
20.2 Proof of Theorem 82
432(3)
21 Appendices: Proofs for Part 2
435(2)
21.1 Proof of Theorem 292
435(1)
21.2 Proof of Theorem 309
436(1)
22 Appendices: Proofs for Part 3
437(32)
22.1 Proof of Theorem 368
437(4)
22.2 Proof of Theorem 376
441(6)
22.3 Proof of Theorem 382
447(1)
22.4 Proof of Theorem 387
448(1)
22.5 Proof of Theorem 389
449(1)
22.6 Proof of Theorem 396
449(2)
22.7 Proof of Theorem 404
451(2)
22.8 Proof of Theorem 412
453(1)
22.9 Proof of Theorem 420
453(4)
22.10 Proof of Theorem 436
457(1)
22.11 Proof of Theorem 456
457(4)
22.12 Proof of Theorem 461
461(4)
22.13 Proof of Theorem 474
465(1)
22.14 Proof of Theorem 482
466(1)
22.15 Proof of Theorem 487
467(2)
23 Appendices: Proofs for Part 4
469(40)
23.1 Proof of Theorem 502
469(3)
23.2 Proof of Claim 509
472(2)
23.3 Proof of Theorem 517
474(6)
23.4 Proof of Theorem 527
480(1)
23.5 Proof of Theorem 564
480(5)
23.6 Proof of Theorem 569
485(9)
23.7 Proof of Theorem 578
494(1)
23.8 Proof of Theorem 582
495(1)
23.9 Proof of Claim 586
496(1)
23.10 Proof of Theorem 592
496(4)
23.11 Proof of Theorem 597
500(7)
23.12 Proof of Theorem 603
507(1)
23.13 Proof of Theorem 606
508(1)
24 Used literature
509(36)
25 Indexes
545
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 BelfortMontbeliard, 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, 19641992; 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.
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