Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity
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A01=Abraham Albert Ungar
Analytic Hyperbolic Geometry
Author_Abraham Albert Ungar
Category=PHR
Category=PHU
Enriched Special Relativity
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Gyrogroup
Gyrovector Space
Hyperbolic Barycentric Coordinates
Hyperbolic Geometry
Hyperbolic Trigonometry
Hyperbolic Vector Spaces
Relativistic Center of Mass
Relativistic Mass
Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement
Product details
- ISBN 9789811244100
- Publication Date: 21 Mar 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. The premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Gyrovectors turn out to be equivalence classes that add according to the gyroparallelogram law just as vectors are equivalence classes that add according to the parallelogram law. In the gyrolanguage of this book, accordingly, one prefixes a gyro to a classical term to mean the analogous term in hyperbolic geometry. As an example, the relativistic gyrotrigonometry of Einstein's special relativity is developed and employed to the study of the stellar aberration phenomenon in astronomy.Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. It turns out that the invariant mass of the relativistic center of mass of an expanding system (like galaxies) exceeds the sum of the masses of its constituent particles. This excess of mass suggests a viable mechanism for the formation of dark matter in the universe, which has not been detected but is needed to gravitationally "glue" each galaxy in the universe. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying hyperbolic geometry.
