Nick Huggett
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195379518
- eISBN:
- 9780199776559
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379518.001.0001
- Subject:
- Philosophy, Philosophy of Science
Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are ...
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Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are Zeno's paradoxes? Are there just three dimensions? Are there other universes? What is the shape of space and how do we know? Why does time seem to pass while space does not? What is the difference between the past and future? Is time travel possible? What is spacetime? What is time according to relativity? What is the difference between left and right? What is a quantum particle? Some of these questions are among the oldest humanity has asked about our place in the world, but some are among the most recent: the book both explores their history and the thinkers that have shaped them, and explains the fundamentals of their current understanding. Readers aren't just spectators to the journey, but are engaged in the debates. This book shows that philosophy, by analyzing fundamental concepts and their relationship to the human experience, has a great deal to say about these profound topics. They are not reserved for physics; as the book demonstrates, philosophy can not only address but help advance our view of our deepest questions about the universe, space, and time, and their implications for humanity. It is aimed at inspiring the reader to think philosophically about the universe revealed by physics.Less
Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are Zeno's paradoxes? Are there just three dimensions? Are there other universes? What is the shape of space and how do we know? Why does time seem to pass while space does not? What is the difference between the past and future? Is time travel possible? What is spacetime? What is time according to relativity? What is the difference between left and right? What is a quantum particle? Some of these questions are among the oldest humanity has asked about our place in the world, but some are among the most recent: the book both explores their history and the thinkers that have shaped them, and explains the fundamentals of their current understanding. Readers aren't just spectators to the journey, but are engaged in the debates. This book shows that philosophy, by analyzing fundamental concepts and their relationship to the human experience, has a great deal to say about these profound topics. They are not reserved for physics; as the book demonstrates, philosophy can not only address but help advance our view of our deepest questions about the universe, space, and time, and their implications for humanity. It is aimed at inspiring the reader to think philosophically about the universe revealed by physics.
Frank Arntzenius
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, ...
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Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!Less
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!
Yuri Balashov
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199579921
- eISBN:
- 9780191722899
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579921.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
Material objects persist through time and survive change. How do they manage to do so? What are the underlying facts of persistence? Do objects persist by being ”wholly present” at all moments of ...
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Material objects persist through time and survive change. How do they manage to do so? What are the underlying facts of persistence? Do objects persist by being ”wholly present” at all moments of time at which they exist? Or do they persist by having distinct ”temporal segments” confined to the corresponding times? Are objects three‐dimensional entities extended in space, but not in time? Or are they four‐dimensional spacetime ”worms”? These are matters of intense debate, which is now driven by concerns about two major issues in fundamental ontology: parthood and location. It is in this context that broadly empirical considerations are increasingly brought to bear on the debate about persistence. The book explores this decidedly positive tendency. It begins by stating major rival views of persistence—endurance, perdurance, and exdurance—in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. The overall conclusion—that relativistic considerations favor four‐dimensionalism over three‐dimensionalism—is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four‐dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness.Less
Material objects persist through time and survive change. How do they manage to do so? What are the underlying facts of persistence? Do objects persist by being ”wholly present” at all moments of time at which they exist? Or do they persist by having distinct ”temporal segments” confined to the corresponding times? Are objects three‐dimensional entities extended in space, but not in time? Or are they four‐dimensional spacetime ”worms”? These are matters of intense debate, which is now driven by concerns about two major issues in fundamental ontology: parthood and location. It is in this context that broadly empirical considerations are increasingly brought to bear on the debate about persistence. The book explores this decidedly positive tendency. It begins by stating major rival views of persistence—endurance, perdurance, and exdurance—in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. The overall conclusion—that relativistic considerations favor four‐dimensionalism over three‐dimensionalism—is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four‐dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness.
Dean Rickles, Steven French, and Juha T. Saatsi (eds)
- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780199269693
- eISBN:
- 9780191699436
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269693.001.0001
- Subject:
- Philosophy, Philosophy of Science
Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing ...
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Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing non-gravitational forces. This book brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This book closes that gap, with chapters written by some of the leading researchers in the field. Individual chapters defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems.Less
Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing non-gravitational forces. This book brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This book closes that gap, with chapters written by some of the leading researchers in the field. Individual chapters defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems.
Stephen Hawking
- Published in print:
- 2007
- Published Online:
- January 2007
- ISBN:
- 9780195310726
- eISBN:
- 9780199785179
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195310726.003.0003
- Subject:
- Religion, Religion and Society
Stephen Hawking is a public intellectual and the best-selling author of A Brief History of Time, The Universe in a Nutshell, The Large Scale Structure of Spacetime with George Ellis, Stephen ...
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Stephen Hawking is a public intellectual and the best-selling author of A Brief History of Time, The Universe in a Nutshell, The Large Scale Structure of Spacetime with George Ellis, Stephen Hawking’s Universe: The Cosmos Explained, and many other books. Hawking is a cosmologist who is well known for his courageous battle with Lou Gehrig’s disease. He first published his no-boundary proposal in 1970, concerning the expansion of the universe and the big bang, and he introduced his rather technical ideas at the Vatican in 1981, where he also was able to meet and speak with Pope John Paul II. Hawking dislikes the label “atheist”, for his views on God are quite mysterious, and he has written of his quest to “know the mind of God”.Less
Stephen Hawking is a public intellectual and the best-selling author of A Brief History of Time, The Universe in a Nutshell, The Large Scale Structure of Spacetime with George Ellis, Stephen Hawking’s Universe: The Cosmos Explained, and many other books. Hawking is a cosmologist who is well known for his courageous battle with Lou Gehrig’s disease. He first published his no-boundary proposal in 1970, concerning the expansion of the universe and the big bang, and he introduced his rather technical ideas at the Vatican in 1981, where he also was able to meet and speak with Pope John Paul II. Hawking dislikes the label “atheist”, for his views on God are quite mysterious, and he has written of his quest to “know the mind of God”.
Thomas Sattig
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199279524
- eISBN:
- 9780191604041
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199279527.003.0002
- Subject:
- Philosophy, Philosophy of Science
This chapter serves as an introduction to the themes of the book. The thesis of temporal supervenience is that all facts about ordinary time, all facts shaped by our ordinary temporal discourse, ...
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This chapter serves as an introduction to the themes of the book. The thesis of temporal supervenience is that all facts about ordinary time, all facts shaped by our ordinary temporal discourse, logically supervene on facts about spacetime; what goes on in spacetime fully determines what goes on in ordinary time. Temporal supervenience has many aspects, corresponding to various kinds of supervenient temporal phenomena. Among the most basic phenomena are persistence and change through ordinary time. The problem of temporal supervenience with respect to these phenomena has two components. The first component is to specify the spatiotemporal supervenience base of persistence and change. How do objects occupy spacetime? And how are properties instantiated across occupied spacetime? The second component is to build an explanatory bridge from the supervenience base to the supervenient phenomena. Such a bridge requires an ‘analysis’ of temporal existence and temporal instantiation, that is, a semantic account of ordinary temporal predications such as ‘a was F’. The problem of temporal supervenience thus connects the metaphysics of time with the semantics of temporal discourse. Before the supervenience of ordinary temporal facts on spacetime facts can be explained, the shape of ordinary time needs to be clarified. This is a further task of Chapter 1. Tenserism and A-time are criticized in the context of temporal supervenience with the aim of promoting detenserism as the correct account of tense and B-time as the true shape of ordinary time.Less
This chapter serves as an introduction to the themes of the book. The thesis of temporal supervenience is that all facts about ordinary time, all facts shaped by our ordinary temporal discourse, logically supervene on facts about spacetime; what goes on in spacetime fully determines what goes on in ordinary time. Temporal supervenience has many aspects, corresponding to various kinds of supervenient temporal phenomena. Among the most basic phenomena are persistence and change through ordinary time. The problem of temporal supervenience with respect to these phenomena has two components. The first component is to specify the spatiotemporal supervenience base of persistence and change. How do objects occupy spacetime? And how are properties instantiated across occupied spacetime? The second component is to build an explanatory bridge from the supervenience base to the supervenient phenomena. Such a bridge requires an ‘analysis’ of temporal existence and temporal instantiation, that is, a semantic account of ordinary temporal predications such as ‘a was F’. The problem of temporal supervenience thus connects the metaphysics of time with the semantics of temporal discourse. Before the supervenience of ordinary temporal facts on spacetime facts can be explained, the shape of ordinary time needs to be clarified. This is a further task of Chapter 1. Tenserism and A-time are criticized in the context of temporal supervenience with the aim of promoting detenserism as the correct account of tense and B-time as the true shape of ordinary time.
Thomas Sattig
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199279524
- eISBN:
- 9780191604041
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199279527.003.0003
- Subject:
- Philosophy, Philosophy of Science
Part of the problem of temporal supervenience is the problem of spatiotemporal location: how are objects located in spacetime? This chapter provides a detailed statement of various answers to this ...
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Part of the problem of temporal supervenience is the problem of spatiotemporal location: how are objects located in spacetime? This chapter provides a detailed statement of various answers to this problem. The main answers are three-dimensionalism and four-dimensionalism. The three-dimensionalist holds that an object occupies many temporally unextended regions of spacetime, whereas the four-dimensionalist holds that an object occupies only a single temporally extended region of spacetime. Subsequently to stating these accounts of spatiotemporal location, the chapter discusses the relationship of three-dimensionalism and four-dimensionalism to other theses and theories, including the theory of temporal parts, endurantism, perdurantism, eternalism, and presentism.Less
Part of the problem of temporal supervenience is the problem of spatiotemporal location: how are objects located in spacetime? This chapter provides a detailed statement of various answers to this problem. The main answers are three-dimensionalism and four-dimensionalism. The three-dimensionalist holds that an object occupies many temporally unextended regions of spacetime, whereas the four-dimensionalist holds that an object occupies only a single temporally extended region of spacetime. Subsequently to stating these accounts of spatiotemporal location, the chapter discusses the relationship of three-dimensionalism and four-dimensionalism to other theses and theories, including the theory of temporal parts, endurantism, perdurantism, eternalism, and presentism.
Thomas Sattig
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199279524
- eISBN:
- 9780191604041
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199279527.003.0006
- Subject:
- Philosophy, Philosophy of Science
This chapter develops a three-dimensionalist account of temporal supervenience — the temporal-regions account — and argues that the latter shares the main virtues and avoids the main drawbacks of its ...
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This chapter develops a three-dimensionalist account of temporal supervenience — the temporal-regions account — and argues that the latter shares the main virtues and avoids the main drawbacks of its four-dimensionalist rival. The three-dimensionalist account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of objects, and that the facts of temporal instantiation logically supervene on the atemporal instantiation of properties by temporally unextended spacetime regions occupied by objects. Structural similarities of the temporal-regions account and the temporal-parts account are pointed out, and the temporal-regions account is shown to avoid the problems that threaten the temporal-parts account. The remainder of the chapter deals with various consequences and apparent difficulties of three-dimensionalist supervenience.Less
This chapter develops a three-dimensionalist account of temporal supervenience — the temporal-regions account — and argues that the latter shares the main virtues and avoids the main drawbacks of its four-dimensionalist rival. The three-dimensionalist account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of objects, and that the facts of temporal instantiation logically supervene on the atemporal instantiation of properties by temporally unextended spacetime regions occupied by objects. Structural similarities of the temporal-regions account and the temporal-parts account are pointed out, and the temporal-regions account is shown to avoid the problems that threaten the temporal-parts account. The remainder of the chapter deals with various consequences and apparent difficulties of three-dimensionalist supervenience.
D. Dennis Hudson
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195369229
- eISBN:
- 9780199871162
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195369229.003.0015
- Subject:
- Religion, Hinduism
The designers of the temple mapped the cosmos by means of thirty panels in the bottom floor of the vimana, in a sequence that begins immediately north of the porch's western doorway and proceeds ...
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The designers of the temple mapped the cosmos by means of thirty panels in the bottom floor of the vimana, in a sequence that begins immediately north of the porch's western doorway and proceeds clockwise. The viewer is led from God's gross body to His subtle body. Jambhu, with Meru at its center, is the central one of seven concentric continents separated by different liquids; the outermost is Pushkara, surrounded by the mountainous Lokaloka. Lokaloka is the “all‐encompasing placenta” within which Brahma wakes and sleeps. Dhruva is the apex of the universe. Bharata is one of nine regions of Jambhu, and is the only realm of intentional action, and therefore the only one with the the Chatur Yuga structure of chronology. Panels on the vimana show the forms Vasudeva takes in each region. The panels also represent day‐and‐night, months, and the ages.Less
The designers of the temple mapped the cosmos by means of thirty panels in the bottom floor of the vimana, in a sequence that begins immediately north of the porch's western doorway and proceeds clockwise. The viewer is led from God's gross body to His subtle body. Jambhu, with Meru at its center, is the central one of seven concentric continents separated by different liquids; the outermost is Pushkara, surrounded by the mountainous Lokaloka. Lokaloka is the “all‐encompasing placenta” within which Brahma wakes and sleeps. Dhruva is the apex of the universe. Bharata is one of nine regions of Jambhu, and is the only realm of intentional action, and therefore the only one with the the Chatur Yuga structure of chronology. Panels on the vimana show the forms Vasudeva takes in each region. The panels also represent day‐and‐night, months, and the ages.
Yuri Balashov
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199579921
- eISBN:
- 9780191722899
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579921.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
A simplified overview of the geometrical structure of Newtonian, neo‐Newtonian (Galilean), and special relativistic (Minkowski) spacetime, intended for the non‐specialist. The notions of reference ...
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A simplified overview of the geometrical structure of Newtonian, neo‐Newtonian (Galilean), and special relativistic (Minkowski) spacetime, intended for the non‐specialist. The notions of reference frame, coordinate system and coordinate transformation are briefly introduced, followed by a more extended discussion of kinematic relativistic phenomena, such as relativity of simultaneity, length contraction and time dilation, which are important for the arguments of later chapters. The interplay of important ideas of invariance, perspectivalism and objectivity is of special note.Less
A simplified overview of the geometrical structure of Newtonian, neo‐Newtonian (Galilean), and special relativistic (Minkowski) spacetime, intended for the non‐specialist. The notions of reference frame, coordinate system and coordinate transformation are briefly introduced, followed by a more extended discussion of kinematic relativistic phenomena, such as relativity of simultaneity, length contraction and time dilation, which are important for the arguments of later chapters. The interplay of important ideas of invariance, perspectivalism and objectivity is of special note.
Alexander Bird
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199227013
- eISBN:
- 9780191711121
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227013.003.0007
- Subject:
- Philosophy, Metaphysics/Epistemology
Geometrical and other properties that may be labelled ‘structural’ are held up as examples of properties that are not potencies, but are categorical properties. The debate between Mellor and Prior is ...
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Geometrical and other properties that may be labelled ‘structural’ are held up as examples of properties that are not potencies, but are categorical properties. The debate between Mellor and Prior is examined in order to shed light on this question. The problem is then related to the question of whether a true physical theory should be background-free, on the grounds that it is the presence of spacetime as a background in intuitive physical theories that is responsible for the appearance that spatial properties are categorical, whereas advanced physical theories tend to be background-free.Less
Geometrical and other properties that may be labelled ‘structural’ are held up as examples of properties that are not potencies, but are categorical properties. The debate between Mellor and Prior is examined in order to shed light on this question. The problem is then related to the question of whether a true physical theory should be background-free, on the grounds that it is the presence of spacetime as a background in intuitive physical theories that is responsible for the appearance that spatial properties are categorical, whereas advanced physical theories tend to be background-free.
Nick Huggett
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195379518
- eISBN:
- 9780199776559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379518.003.0001
- Subject:
- Philosophy, Philosophy of Science
This chapter orients the reader to the material of the book by illustrating the interaction between physics and philosophy since their investigations by the ancient Greeks, and by explaining, in ...
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This chapter orients the reader to the material of the book by illustrating the interaction between physics and philosophy since their investigations by the ancient Greeks, and by explaining, in elementary terms, some basic philosophical and physical concepts. The example used is the question of change: what is change such that something can change and yet remain the same thing? The question is one of the oldest in philosophy (dating at least to the fifth century BC), but fundamental to physics: physics describes change, but how is to be described? The chapter explains what great philosopher‐physicists – Aristotle, Descartes and Newton – said as they developed physics in the form we recognize today. It goes on to explicate the idea of a ‘law of physics’, something that regulates physical change, using examples drawn on in the rest of the book. Finally contemporary ideas of ‘spacetime physics’ are introduced.Less
This chapter orients the reader to the material of the book by illustrating the interaction between physics and philosophy since their investigations by the ancient Greeks, and by explaining, in elementary terms, some basic philosophical and physical concepts. The example used is the question of change: what is change such that something can change and yet remain the same thing? The question is one of the oldest in philosophy (dating at least to the fifth century BC), but fundamental to physics: physics describes change, but how is to be described? The chapter explains what great philosopher‐physicists – Aristotle, Descartes and Newton – said as they developed physics in the form we recognize today. It goes on to explicate the idea of a ‘law of physics’, something that regulates physical change, using examples drawn on in the rest of the book. Finally contemporary ideas of ‘spacetime physics’ are introduced.
Nick Huggett
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195379518
- eISBN:
- 9780199776559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379518.003.0014
- Subject:
- Philosophy, Philosophy of Science
These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers ...
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These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers with no prior background, and illuminates the conceptual foundations well. Chapter 14 first shows how Einstein used the extraordinary physical fact that light has the same speed relative to any standard of rest, to conclude that whether two things happen simultaneously is relative: there is no answer to the question whether they are separated in time or only space, they are just in ‘spacetime’. Relativity of simultaneity is represented geometrically, and it is simply shown that moving objects shrink and moving clocks slow down. Chapter 15 addresses the twins ‘paradox’, and the implications of relativity for time, especially whether it abolishes the ‘present’; Gödel's spacetime, in which there are paths leading back in time is explained.Less
These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers with no prior background, and illuminates the conceptual foundations well. Chapter 14 first shows how Einstein used the extraordinary physical fact that light has the same speed relative to any standard of rest, to conclude that whether two things happen simultaneously is relative: there is no answer to the question whether they are separated in time or only space, they are just in ‘spacetime’. Relativity of simultaneity is represented geometrically, and it is simply shown that moving objects shrink and moving clocks slow down. Chapter 15 addresses the twins ‘paradox’, and the implications of relativity for time, especially whether it abolishes the ‘present’; Gödel's spacetime, in which there are paths leading back in time is explained.
Nick Huggett
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195379518
- eISBN:
- 9780199776559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379518.003.0015
- Subject:
- Philosophy, Philosophy of Science
These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers ...
More
These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers with no prior background, and illuminates the conceptual foundations well. Chapter 14 first shows how Einstein used the extraordinary physical fact that light has the same speed relative to any standard of rest, to conclude that whether two things happen simultaneously is relative: there is no answer to the question whether they are separated in time or only space, they are just in ‘spacetime’. Relativity of simultaneity is represented geometrically, and it is simply shown that moving objects shrink and moving clocks slow down. Chapter 15 addresses the twins ‘paradox’, and the implications of relativity for time, especially whether it abolishes the ‘present’; Gödel's spacetime, in which there are paths leading back in time is explained.Less
These chapters explain Einstein's theory of relativity accurately but without mathematics, using a simple geometric operation: drawing the reflection of a line. This approach is accessible to readers with no prior background, and illuminates the conceptual foundations well. Chapter 14 first shows how Einstein used the extraordinary physical fact that light has the same speed relative to any standard of rest, to conclude that whether two things happen simultaneously is relative: there is no answer to the question whether they are separated in time or only space, they are just in ‘spacetime’. Relativity of simultaneity is represented geometrically, and it is simply shown that moving objects shrink and moving clocks slow down. Chapter 15 addresses the twins ‘paradox’, and the implications of relativity for time, especially whether it abolishes the ‘present’; Gödel's spacetime, in which there are paths leading back in time is explained.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0002
- Subject:
- Mathematics, Applied Mathematics
This chapter begins with a discussion of Newton's mechanics. It then covers Maxwell's equations, Minkowski spacetime, Poincaré group, Lorentz group, special relativity, Newtonian law, relativistic ...
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This chapter begins with a discussion of Newton's mechanics. It then covers Maxwell's equations, Minkowski spacetime, Poincaré group, Lorentz group, special relativity, Newtonian law, relativistic law, equivalence of mass and energy, and continuous matter.Less
This chapter begins with a discussion of Newton's mechanics. It then covers Maxwell's equations, Minkowski spacetime, Poincaré group, Lorentz group, special relativity, Newtonian law, relativistic law, equivalence of mass and energy, and continuous matter.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0004
- Subject:
- Mathematics, Applied Mathematics
This chapter begins with a discussion of spherically symmetric spacetimes, the Schwarzschild metric, and other coordinates. It then covers Schwarzschild spacetime, the motion of the planets and ...
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This chapter begins with a discussion of spherically symmetric spacetimes, the Schwarzschild metric, and other coordinates. It then covers Schwarzschild spacetime, the motion of the planets and perihelion precession, stability of circular orbits, deflection of light rays, red shift and time delay, spherically symmetric interior solutions, the Schwarzschild black hole, spherically symmetric gravitational collapse, the Reissner–Nordström solution, and Schwarzschild spacetime in dimension n + 1.Less
This chapter begins with a discussion of spherically symmetric spacetimes, the Schwarzschild metric, and other coordinates. It then covers Schwarzschild spacetime, the motion of the planets and perihelion precession, stability of circular orbits, deflection of light rays, red shift and time delay, spherically symmetric interior solutions, the Schwarzschild black hole, spherically symmetric gravitational collapse, the Reissner–Nordström solution, and Schwarzschild spacetime in dimension n + 1.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0005
- Subject:
- Mathematics, Applied Mathematics
This chapter begins with a discussion of the cosmological principle. It then covers isotropic and homogeneous Riemannian manifolds, Robertson–Walker spacetimes, Friedmann–Lemaître models, homogeneous ...
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This chapter begins with a discussion of the cosmological principle. It then covers isotropic and homogeneous Riemannian manifolds, Robertson–Walker spacetimes, Friedmann–Lemaître models, homogeneous non-isotropic cosmologies, Bianchi class I universes, Bianchi type IX, the Kantowski–Sachs models, Taub and Taub NUT spacetimes, locally homogeneous models, and recent observations and conjectures.Less
This chapter begins with a discussion of the cosmological principle. It then covers isotropic and homogeneous Riemannian manifolds, Robertson–Walker spacetimes, Friedmann–Lemaître models, homogeneous non-isotropic cosmologies, Bianchi class I universes, Bianchi type IX, the Kantowski–Sachs models, Taub and Taub NUT spacetimes, locally homogeneous models, and recent observations and conjectures.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0011
- Subject:
- Mathematics, Applied Mathematics
This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac ...
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This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac Einsteinian spacetime. Topics covered include quasilinear systems, quasilinear first-order systems, progressive waves in relativistic fluids, quasilinear quasidiagonal second-order systems, non quasidiagonal second-order systems, fields and equations, and strong gravitational waves.Less
This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac Einsteinian spacetime. Topics covered include quasilinear systems, quasilinear first-order systems, progressive waves in relativistic fluids, quasilinear quasidiagonal second-order systems, non quasidiagonal second-order systems, fields and equations, and strong gravitational waves.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0012
- Subject:
- Mathematics, Applied Mathematics
This chapter presents the general properties of global Lorentzian geometry used in the global in time Einsteinian dynamics. Topics covered include the global existence of Lorentzian metrics, time ...
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This chapter presents the general properties of global Lorentzian geometry used in the global in time Einsteinian dynamics. Topics covered include the global existence of Lorentzian metrics, time orientation, futures and pasts, causal structure of Minkowski spacetime, causal structures on general spacetimes, topology on a space of paths, global hyperbolicity, strong and stable causalities, Cauchy surface, globally hyperbolic Einsteinian spacetimes, and strong cosmic censorship.Less
This chapter presents the general properties of global Lorentzian geometry used in the global in time Einsteinian dynamics. Topics covered include the global existence of Lorentzian metrics, time orientation, futures and pasts, causal structure of Minkowski spacetime, causal structures on general spacetimes, topology on a space of paths, global hyperbolicity, strong and stable causalities, Cauchy surface, globally hyperbolic Einsteinian spacetimes, and strong cosmic censorship.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0013
- Subject:
- Mathematics, Applied Mathematics
This chapter presents a computable sufficient condition for the future causal completeness of a spacetime, and then a sufficient condition for its future or null incompleteness. It gives the ...
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This chapter presents a computable sufficient condition for the future causal completeness of a spacetime, and then a sufficient condition for its future or null incompleteness. It gives the fundamentals of the definitions pertinent to the study of incompleteness of spacetimes by the geometric methods introduced and developed by Penrose, Hawking, and their followers. It provides some elements of black hole theory and comments on Penrose's weak cosmic censorship conjecture, which says essentially that singularities developing from smooth initial data are hidden inside black holes. The conjecture is not easy to make mathematically precise without impoverishing its possible physical content. The chapter analyzes the study by Christodoulou of the singularities in spherically symmetric solutions of the Einstein-scalar equations. An up-to-date survey of results on the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture is presented. Finally, how the Fuchs theorem permits the analysis of some types of initial (Big Bang) singularities occurring in solutions of the Einstein equations, called asymptotically velocity term dominated (AVTD) behavior, is discussed.Less
This chapter presents a computable sufficient condition for the future causal completeness of a spacetime, and then a sufficient condition for its future or null incompleteness. It gives the fundamentals of the definitions pertinent to the study of incompleteness of spacetimes by the geometric methods introduced and developed by Penrose, Hawking, and their followers. It provides some elements of black hole theory and comments on Penrose's weak cosmic censorship conjecture, which says essentially that singularities developing from smooth initial data are hidden inside black holes. The conjecture is not easy to make mathematically precise without impoverishing its possible physical content. The chapter analyzes the study by Christodoulou of the singularities in spherically symmetric solutions of the Einstein-scalar equations. An up-to-date survey of results on the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture is presented. Finally, how the Fuchs theorem permits the analysis of some types of initial (Big Bang) singularities occurring in solutions of the Einstein equations, called asymptotically velocity term dominated (AVTD) behavior, is discussed.
