Ebook: The Geometry of Spacetime: An Introduction to Special and General Relativity

In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

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In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

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In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
Content:
Front Matter....Pages i-xvi
Relativity Before 1905....Pages 1-29
Special Relativity — Kinematics....Pages 31-86
Special Relativity — Kinetics....Pages 87-141
Arbitrary Frames....Pages 143-201
Surfaces and Curvature....Pages 203-256
Intrinsic Geometry....Pages 257-328
General Relativity....Pages 329-384
Consequences....Pages 385-434
Erratum to: Relativity Before 1905....Pages 455-455
Erratum to: Special Relativity — Kinematics....Pages 455-455
Erratum to: Special Relativity — Kinetics....Pages 456-457
Erratum to: Arbitrary Frames....Pages 457-458
Erratum to: Surfaces and Curvature....Pages 458-458
Erratum to: Intrinsic Geometry....Pages 458-459
Erratum to: General Relativity....Pages 459-460
Erratum to: Consequences....Pages 460-461
Erratum....Pages 461-463
Back Matter....Pages 435-454

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In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
Content:
Front Matter....Pages i-xvi
Relativity Before 1905....Pages 1-29
Special Relativity — Kinematics....Pages 31-86
Special Relativity — Kinetics....Pages 87-141
Arbitrary Frames....Pages 143-201
Surfaces and Curvature....Pages 203-256
Intrinsic Geometry....Pages 257-328
General Relativity....Pages 329-384
Consequences....Pages 385-434
Erratum to: Relativity Before 1905....Pages 455-455
Erratum to: Special Relativity — Kinematics....Pages 455-455
Erratum to: Special Relativity — Kinetics....Pages 456-457
Erratum to: Arbitrary Frames....Pages 457-458
Erratum to: Surfaces and Curvature....Pages 458-458
Erratum to: Intrinsic Geometry....Pages 458-459
Erratum to: General Relativity....Pages 459-460
Erratum to: Consequences....Pages 460-461
Erratum....Pages 461-463
Back Matter....Pages 435-454
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