Atjaunināt sīkdatņu piekrišanu

E-grāmata: Subtlety in Relativity [Taylor & Francis e-book]

  • Formāts: 440 pages, 10 Illustrations, color; 18 Illustrations, black and white
  • Izdošanas datums: 13-Dec-2017
  • Izdevniecība: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9781351238328
Citas grāmatas par šo tēmu:
  • Taylor & Francis e-book
  • Cena: 168,97 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standarta cena: 241,39 €
  • Ietaupiet 30%
  • Formāts: 440 pages, 10 Illustrations, color; 18 Illustrations, black and white
  • Izdošanas datums: 13-Dec-2017
  • Izdevniecība: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9781351238328
Citas grāmatas par šo tēmu:

Subtlety in Relativity is the only book that has been written after the author’s discovery of a new way in which wave phenomena occur—the emission origin of waves. This drastically changes most issues of the old debate over the world being either deterministic or probabilistic. The emission origin of waves is not incompatible with the ideas of quantum theory; rather, this new and novel way in which waves can be generated justifies the use of mathematical and probabilistic methods of quantum theory. However, the emission origin of waves shows that quantum theory is statistically incomplete in, precisely, Einstein’s sense. There exists, then, a certain, previously unexplored, conceptual framework underlying the ideas of quantum theory. Whether this is the theory that Einstein and others were looking for then, how this way of thinking is related to the ideas of relativity, and whether this is a relativistic theory in the usual sense of this word are questions this book answers.

The book demonstrates how the Doppler effect with acceleration is essential to interpreting astronomical observations. It also offers a detailed and self-sufficient technical background of mathematical ideas of category theory. The book is divided into two parts. The first is less mathematical and more conceptual in its orientation. The second focuses on mathematical ideas needed to implement physical concepts. The book is a great reference for advanced undergraduate- and graduate-level students of physics and researchers in physics, astronomy, and cosmology, who will gain a deeper understanding of relativity from it.

Preface xi
PART I DEVELOPMENT OF PHYSICAL CONCEPTS
1 The Light Quantum
3(86)
1.1 Wave Theory of Light
3(15)
1.2 Electromagnetism and Light
18(17)
1.3 Atomic Theory of Matter
35(16)
1.4 Radiation and Thermodynamics
51(14)
1.5 What Is a Quantum?
65(14)
1.6 The Mysterious Quantum
79(3)
1.7 Emission Origin for a Wave of Quanta
82(7)
2 The Idea of Relativity
89(34)
2.1 Galileo and Newton
89(8)
2.2 What Is Relativity?
97(5)
2.3 Problem of the Constancy of the Speed of Light
102(1)
2.4 Einstein's Relative Time
103(1)
2.5 Measuring the Speed of Light
103(2)
2.6 Time Is Absolute
105(1)
2.7 General Principle of Relativity
106(5)
2.8 Universal Principle of Relativity
111(5)
2.9 A Light Quantum in Universal Relativity
116(7)
3 Doppler Effect
123(12)
3.1 Doppler Effect in Light
123(1)
3.2 Derivation of the Doppler Shift
124(2)
3.3 Difficulty with Special Relativity
126(1)
3.4 Doppler Shift Formulas with Acceleration
127(4)
3.5 Doppler Analysis with Acceleration
131(4)
PART II CATEGORY THEORY AND UNIVERSAL RELATIVITY
4 What Is a Category?
135(32)
4.1 Introduction
135(1)
4.2 An Arrow
136(2)
4.3 Partial Binary Algebra of Arrows
138(1)
4.4 Definitions of a Category
139(6)
4.5 Some Standard Nomenclature about Categories
145(2)
4.6 Some Examples of Categories
147(6)
4.7 Duality Principle
153(3)
4.8 Subcategory
156(1)
4.9 Generating New Categories from Those Existing
157(7)
4.9.1 Quotient Category
158(1)
4.9.2 Slice or Comma Category
159(1)
4.9.3 Arrow Category
160(1)
4.9.4 Triangle Category
161(1)
4.9.5 Product and Sum Categories
162(1)
4.9.6 Category of Families of Objects of a Category
163(1)
4.10 Categories Presented as Diagrams
164(1)
4.11 Summary
165(2)
5 Properties of Arrows and Objects
167(70)
5.1 Introduction
167(1)
5.2 Diagram and Commuting Diagram
168(1)
5.3 Section and Retraction Arrows
169(2)
5.4 Isoarrow and Related Topics
171(4)
5.4.1 Isomorphic Objects
173(1)
5.4.2 Isomorphism-Dense Subcategory
173(1)
5.4.3 Isomorphism-Closed Subcategory
174(1)
5.5 Monoarrow and Related Topics
175(8)
5.5.1 Monoarrow
175(2)
5.5.2 Subobject
177(2)
5.5.3 Epiarrow
179(2)
5.5.4 Quotient Object
181(1)
5.5.5 Bidirectional Arrow
182(1)
5.6 Intersection and Co-intersection
183(1)
5.7 Factorization
184(1)
5.8 Separator, Separating Set, and Coseparator
185(1)
5.9 Equalizer, Has Equalizer, and Coequalizer
185(8)
5.9.1 Equalizer Arrow
186(2)
5.9.2 Multiple Equalizers
188(1)
5.9.3 Regular Monoarrow
188(2)
5.9.4 Extremal Monoarrow
190(1)
5.9.5 Strict Monoarrow
191(1)
5.9.6 Coequalizer
192(1)
5.10 Constant and Co-constant Arrows
193(1)
5.11 Initial and Terminal Objects
193(1)
5.12 Zero Object
194(1)
5.13 Zero Arrow
194(5)
5.13.1 Pointed Category
198(1)
5.14 Kernel Arrow
199(2)
5.14.1 Normal Monoarrow
201(1)
5.15 Reflection Arrow and Co-reflection Arrow
201(5)
5.16 Source and Sink
206(4)
5.16.1 Sources
206(1)
5.16.2 Monosources
207(3)
5.16.3 Sinks
210(1)
5.17 Product, Coproduct, and Biproduct
210(11)
5.18 Pullback and Push-Out
221(12)
5.18.1 Congruences and Pullbacks
230(2)
5.18.2 Push-Out
232(1)
5.18.3 Pullation Square
232(1)
5.19 Subobject Classifier
233(2)
5.20 Summary
235(2)
6 Functors
237(58)
6.1 Introduction
237(3)
6.1.1 Arrows Connecting Categories
237(2)
6.1.2 Dual Role of a Functor
239(1)
6.2 Some Examples of Functors
240(2)
6.3 Important Nomenclature about Functors
242(1)
6.4 Properties of Functors
243(6)
6.4.1 Preservation of Categorical Property by Functors
243(2)
6.4.2 Reflection of Categorical Property by Functors
245(2)
6.4.3 Isofunctor and Isomorphism of Categories
247(1)
6.4.4 Equivalence Functor
248(1)
6.5 Equivalence of Categories
249(4)
6.6 Functors and Subcategories
253(4)
6.6.1 Inclusion of a Subcategory
254(1)
6.6.2 Full Embedding of a Subcategory
255(1)
6.6.3 Subcategories of Subcategories
256(1)
6.6.4 Skeleton of a Category
256(1)
6.7 Some Relevant Conceptions
257(2)
6.7.1 Graph of a Category
257(1)
6.7.2 Internal and External Characterization
258(1)
6.8 Category of All Categories?
259(1)
6.9 Functors and Natural Transformations
259(6)
6.9.1 Natural Transformation and Natural Isomorphism
259(1)
6.9.2 Usual Product of Natural Transformations
260(1)
6.9.3 Star Product of Natural Transformations
261(2)
6.9.4 Law for the Interchange of the Usual Product and the Star Product of Natural Transformations
263(1)
6.9.5 Godement's Rules
264(1)
6.10 Functor Categories
265(4)
6.11 Evaluation Functor
269(1)
6.12 "Constant Functor" Functor, or CF-Functor
270(1)
6.13 Limits and Colimits
271(9)
6.14 Functors Preserving and Reflecting Limits
280(5)
6.15 Representable Functors
285(1)
6.16 Elements and Yoneda's Results
286(9)
7 Universal Associations by Functors
295(14)
7.1 Introduction
295(1)
7.2 Objects and Arrows: Properties vis-a-vis Functors
295(14)
7.2.1 Universal Associate and Universal Arrow
295(1)
7.2.2 Universal Coassociate and Universal Coarrow
296(1)
7.2.3 Functor-Generation of Objects
297(12)
8 Adjoint Functors and Adjoint Situations
309(10)
8.1 Introduction
309(1)
8.2 Adjoint and Coadjoint Functors
310(1)
8.3 Adjoint Situations
310(5)
8.4 Describing Adjunction
315(4)
9 Categorical Measures
319(20)
9.1 Introduction
319(2)
9.2 Preliminaries
321(3)
9.3 Additivity
324(6)
9.4 Category: Family (C)
330(2)
9.5 Category: pFamily(C)
332(3)
9.6 Additivity and Measures
335(2)
9.7 Summary
337(2)
10 The Meaning of Universal Relativity
339(38)
10.1 Introduction
339(2)
10.2 Categorical Basis
341(4)
10.2.1 Categorical Measures
342(2)
10.2.2 Additive Categories of Real Numbers
344(1)
10.3 Quantifiers of Motion
345(1)
10.3.1 Distance and Changes to Distance
345(1)
10.4 Physical Space Is 3D, Always!
346(6)
10.4.1 Geometry Is a Free Choice
347(1)
10.4.2 Vectors and Changes to Vectors
348(1)
10.4.3 Motion and Time
349(3)
10.5 Physical Coordinate System
352(2)
10.6 Characteristics of "Individuality" of Objects
354(5)
10.7 Categorical Dynamics
359(4)
10.8 Inertialess Objects
363(3)
10.9 Emission Origin for the Wave of Quanta
366(8)
10.9.1 Statistical Considerations
368(2)
10.9.2 Emission and Formation of Wave of Quanta
370(2)
10.9.3 Remarks
372(2)
10.10 Concluding Remarks
374(3)
Epilogue 377(6)
Appendix A Set Theoretical Foundations 383(8)
Appendix B Propositional Calculus 391(8)
Bibliography 399(6)
Index 405
Moreshwar Wagh, Sanjay