Towards a Theory of Spacetime Theories

Author: Dennis Lehmkuhl,Gregor Schiemann,Erhard Scholz
Publisher: Birkhäuser
ISBN: 1493932101
Category: Mathematics
Page: 335
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This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally.

CPT Invariance and the Spin-Statistics Connection

Author: Jonathan Bain
Publisher: Oxford University Press
ISBN: 0191044555
Category: Science
Page: 208
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This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.

Beyond Einstein

Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century
Author: David E. Rowe,Tilman Sauer,Scott Walter
Publisher: Birkhäuser
ISBN: 1493977083
Category: Science
Page: 349
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Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

Architectures of Time

Toward a Theory of the Event in Modernist Culture
Author: Sanford Kwinter
Publisher: MIT Press
ISBN: 9780262611817
Category: Architecture
Page: 237
View: 3210

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An exploration of twentieth-century conceptions of time and their relation to artistic form.

Big Bang

The Origin of the Universe
Author: Simon Singh
Publisher: Harper Collins
ISBN: 0007162219
Category: Science
Page: 560
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A half century ago, a shocking Washington Post headline claimed that the world began in five cataclysmic minutes rather than having existed for all time; a skeptical scientist dubbed the maverick theory the Big Bang. In this amazingly comprehensible history of the universe, Simon Singh decodes the mystery behind the Big Bang theory, lading us through the development of one of the most extraordinary, important, and awe-inspiring theories in science.

The Order of Time

Author: Carlo Rovelli
Publisher: Penguin
ISBN: 0735216126
Category: Science
Page: 256
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The perfect graduation gift "Meet the new Stephen Hawking . . . The Order of Time is a dazzling book." --The Sunday Times From the bestselling author of Seven Brief Lessons on Physics, a concise, elegant exploration of time. Why do we remember the past and not the future? What does it mean for time to "flow"? Do we exist in time or does time exist in us? In lyric, accessible prose, Carlo Rovelli invites us to consider questions about the nature of time that continue to puzzle physicists and philosophers alike. For most readers this is unfamiliar terrain. We all experience time, but the more scientists learn about it, the more mysterious it remains. We think of it as uniform and universal, moving steadily from past to future, measured by clocks. Rovelli tears down these assumptions one by one, revealing a strange universe where at the most fundamental level time disappears. He explains how the theory of quantum gravity attempts to understand and give meaning to the resulting extreme landscape of this timeless world. Weaving together ideas from philosophy, science and literature, he suggests that our perception of the flow of time depends on our perspective, better understood starting from the structure of our brain and emotions than from the physical universe. Already a bestseller in Italy, and written with the poetic vitality that made Seven Brief Lessons on Physics so appealing, The Order of Time offers a profoundly intelligent, culturally rich, novel appreciation of the mysteries of time.

The Ascent of Gravity: The Quest to Understand the Force that Explains Everything

Author: Marcus Chown
Publisher: Pegasus Books
ISBN: 1681775948
Category: Science
Page: 256
View: 1823

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Why the force that keeps our feet on the ground holds the key to understanding the nature of time and the origin of the universe. Gravity is the weakest force in the everyday world yet it is the strongest force in the universe. It was the first force to be recognized and described yet it is the least understood. It is a "force" that keeps your feet on the ground yet no such force actually exists. Gravity, to steal the words of Winston Churchill, is "a riddle, wrapped in a mystery, inside an enigma." And penetrating that enigma promises to answer the biggest questions in science: what is space? What is time? What is the universe? And where did it all come from? Award-winning writer Marcus Chown takes us on an unforgettable journey from the recognition of the "force" of gravity in 1666 to the discovery of gravitational waves in 2015. And, as we stand on the brink of a seismic revolution in our worldview, he brings us up to speed on the greatest challenge ever to confront physics.

Einstein Was Right!

Author: Karl Hess
Publisher: CRC Press
ISBN: 9814463701
Category: Mathematics
Page: 220
View: 8530

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All modern books on Einstein emphasize the genius of his relativity theory and the corresponding corrections and extensions of the ancient space–time concept. However, Einstein’s opposition to the use of probability in the laws of nature and particularly in the laws of quantum mechanics is criticized and often portrayed as outdated. The author of Einstein Was Right! takes a unique view and shows that Einstein created a "Trojan horse" ready to unleash forces against the use of probability as a basis for the laws of nature. Einstein warned that the use of probability would, in the final analysis, lead to spooky actions and mysterious instantaneous influences at a distance. John Bell pulled Einstein’s Trojan horse into the castle of physics. He developed a theory that together with experimental results of Aspect, Zeilinger, and others "proves" the existence of quantum nonlocalities, or instantaneous influences. These have indeed the nature of what Einstein labeled spooky. Einstein Was Right! shows that Bell was not aware of the special role that time and space–time play in any rigorous probability theory. As a consequence, his formalism is not general enough to be applied to the Aspect–Zeilinger type of experiments and his conclusions about the existence of instantaneous influences at a distance are incorrect. This fact suggests a worldview that is less optimistic about claims that teleportation and influences at a distance could open new horizons and provide the possibility of quantum computing. On the positive side, however, and as compensation, we are assured that the space–time picture of humankind developed over millions of years and perfected by Einstein is still able to cope with the phenomena that nature presents us on the atomic and sub-atomic level and that the "quantum weirdness" may be explainable and understandable after all.

Einstein's Theory

A Rigorous Introduction for the Mathematically Untrained
Author: Øyvind Grøn,Arne Næss
Publisher: Springer Science & Business Media
ISBN: 9781461407065
Category: Science
Page: 341
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This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.

Einstein's Legacy

The Unity of Space and Time
Author: Julian Schwinger
Publisher: Courier Corporation
ISBN: 048614674X
Category: Science
Page: 160
View: 4044

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A Nobel Laureate relates the fascinating story of Einstein and relativity theory in well-illustrated, nontechnical terms, discussing the meaning of time, gravity and its effect on light, the curving of space-time, more.

A Most Incomprehensible Thing

Notes Towards a Very Gentle Introduction to the Mathematics of Relativity
Author: Peter Collier
Publisher: Incomprehensible Books
ISBN: 0957389469
Category: Science
Page: 274
View: 9445

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A clear and enjoyable guide to the mathematics of relativity To really understand relativity – one of the cornerstones of modern physics – you have to get to grips with the mathematics. This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes. Understand even the basics of Einstein's amazing theory and the world will never seem the same again. March 2017. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

Pseudodifferential Methods in Number Theory

Author: André Unterberger
Publisher: Birkhäuser
ISBN: 3319927078
Category: Mathematics
Page: 173
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Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.

Physical Relativity

Space-time Structure from a Dynamical Perspective
Author: Harvey R. Brown
Publisher: Oxford University Press on Demand
ISBN: 0199275831
Category: Science
Page: 225
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Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein'streatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines andextends these arguments (which support a more 'constructive' approach to relativistic effects in Einstein's terminology), after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with therole this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory withquantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics.

Seven Brief Lessons on Physics

Author: Carlo Rovelli
Publisher: Penguin
ISBN: 0399184430
Category: Science
Page: 96
View: 455

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Look out for Carlo Rovelli's next book, Reality Is Not What It Seems. Instant New York Times Bestseller “One of the year’s most entrancing books about science.”—The Wall Street Journal “Clear, elegant...a whirlwind tour of some of the biggest ideas in physics.”—The New York Times Book Review This playful, entertaining, and mind-bending introduction to modern physics briskly explains Einstein's general relativity, quantum mechanics, elementary particles, gravity, black holes, the complex architecture of the universe, and the role humans play in this weird and wonderful world. Carlo Rovelli, a renowned theoretical physicist, is a delightfully poetic and philosophical scientific guide. He takes us to the frontiers of our knowledge: to the most minute reaches of the fabric of space, back to the origins of the cosmos, and into the workings of our minds. The book celebrates the joy of discovery. “Here, on the edge of what we know, in contact with the ocean of the unknown, shines the mystery and the beauty of the world,” Rovelli writes. “And it’s breathtaking.”

Introduction to Quantum Groups

Author: George Lusztig
Publisher: Springer Science & Business Media
ISBN: 9780817647179
Category: Mathematics
Page: 352
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The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Ripples in Spacetime

Einstein, Gravitational Waves, and the Future of Astronomy
Author: Govert Schilling
Publisher: Harvard University Press
ISBN: 0674971663
Page: 340
View: 730

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The detection of gravitational waves—ripples in spacetime—has already been called the scientific coup of this century. Govert Schilling recounts the struggles that threatened to derail the quest and describes the detector’s astounding precision, weaving far-reaching discoveries about the universe into a gripping story of ambition and perseverance.

Spherical Sampling

Author: Willi Freeden,M. Zuhair Nashed,Michael Schreiner
Publisher: Birkhäuser
ISBN: 3319714589
Category: Mathematics
Page: 596
View: 2959

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This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

Einstein's Theory of Relativity

Author: Max Born
Publisher: Courier Corporation
ISBN: 0486142124
Category: Science
Page: 400
View: 3252

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Semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, more) and of Einstein's theories of relativity.

The Noether Theorems

Invariance and Conservation Laws in the Twentieth Century
Author: Yvette Kosmann-Schwarzbach
Publisher: Springer Science & Business Media
ISBN: 9780387878683
Category: Mathematics
Page: 205
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In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.

Approaches to Quantum Gravity

Toward a New Understanding of Space, Time and Matter
Author: Daniele Oriti
Publisher: Cambridge University Press
ISBN: 0521860458
Category: Science
Page: 583
View: 3659

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Containing contributions from leading researchers in this field, this book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. It introduces the most current approaches to this problem, and reviews their main achievements.