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Tuesday, 7 February 2012
Thursday, 2 February 2012
GRAVITATION AND COSMOLOGY: PRINCIPLES AND APPLICATIONS OF THE GENERAL THEORY OF RELATIVITY By STEVEN WEINBERG free download
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PREFACE
N ow that this book is done I can look back, and identify two purposes which
led me to begin writing, and which have guided the work to completion.
One good practical purpose was to bring together and assess the wealth of data
provided over the last decade by new techniques in experimental physics and in
optical, radio, radar, X-ray, and infrared astronomy. Of course, new data will
keep coming in even as the book is being printed, and I cannot hope that this work
will remain up to date forever. I do hope, however, that by giving a comprehensive
picture of the experimental tests of general relativity and observational cosmology,
I will help to prepare the reader (and myself) to understand the nm\' data as they
emerge. I have also tried to look a little way into the future, and to discuss what
may be the next generation of experiments, especially those based on artificial
satellites of the earth and sun.
There was another, more personal reason for my writing this book. In learning
general relativity, and then in teaching it to classes at Berkeley and M.LT., I
became dissatisfied with what seemed to be the usual approach to the subject.
I found that in most textbooks geometric ideas were given a starring role, so that a
student who asked why the gravitational field is represented by a metric tensor, or
why freely falling particles move on geodesics, or why the field equations are
generally covariant would come away with an impression that this had something
to do with the fact that space-time is a Riemannian manifold.
Of course, this was Einstein's point of view, and his preeminent genius
necessarily shapes our understanding of the theory he created. However, I believe
that the geometrical approach has driven a wedge between general relativity
and the theory of elementary particles. As long as it could be hoped, as Einstein
did hope, that matter would eventually be understood in geometrical terms, it
made sense to give Riemannian geometry a primary role in describing the theory
of gravitation. But now the passage of time has taught us not to expect that the
strong, weak, and electromagnf3tic interactions can be understood in geometrical
terms, and too great an emphasis on geometry can only obscure the deep con-
nections between gravitation and the rest of physics. In place of Riemannian geometry, I have based the discussion of general
relativity on a principle derived from experiment: the Principle of the Equivalence
of Gravitation and Inertia. It will be seen that geometric objects, such as the
metric. the affine connection, and the curvature tensor, naturally find their way
into a theory of gravitation based on the Principle of Equivalence and, of course,
one winds up in the end with Einstein's general theory of relativity. However, I
have tried here to put off the introduction of geometric concepts until they are
needed, so that Riemannian geometry appears only as a mathematical tool for
the exploitation of the Principle of Equivalence, and not as a fundamental basis
for the theory of gravitation.
This approach naturally leads us to ask why gravitation should obey the
Principle of Equivalence. In my opinion the answer is not to be found in the realm
of classical physics, and certainly not in Riemannian geometry, but in the con-
straints imposed by the quantum theory of gravitation. It seems to be impossible
to construct any Lorentz-invariant quantum theory of particles of mass zero and
spin two, unless the corresponding classical field theory obeys the Principle of
Equivalence. Thus the Principle of Equivalence appears as the best bridge
between the theories of gravitation and of elementary particles. The quantum
basis for the Principle of Equivalence is briefly touched upon here in a section on
the quantum theory of gravitation, but it was not possible to go far into the
quantum theory in this book.
The nongeometrical approach taken in this book has, to some extent, affected
the choice of the topics to be covered. In particular, I have not discussed in detail
the derivation and classification of complicated exact solutions of the Einstein
field equations, because I did not feel that most of this material was needed for a
fundamental understanding of the theory of gravitation, and hardly any of it
seemed to be relevant to experiments that might be carried out in the foreseeable
future. By this omission, I have left out much of the work done by professional
geI).eral relativists over the past decade, but I have tried to provide an entree
to this work through references and bibliographies. I regret the omission here of a
detailed discussion of the beautiful theorems of Penrose and Hawking on gravi-
tational collapse; these theorems are briefly discussed in Sections 11.9 and 15.11,
but an adequate discussion would have taken up too much time and space.
I have tried to give a comprehensive set of references to the experimental
literature on general relativity and cosmology. I have also given references to
detailed theoretical calculations whenever I have quoted their results. However, I
have not tried to give complete references to all the theoretical material discussed
in the book. Much of this material is now classical, and to search out the original
references would be an exercise in the history of science for which I did not feel
equipped. The mere absence of literature citations should not be interpreted as a
claim that the work presented is original, but some of it is.
It is a pleasure to acknowledge the inestimable help I have received in writing
this book. Students in my classes over the past seven years have, by their questions
and comments, helped to free the calculations of errors and obscurities. I especially thank Jill Punsky for carefully checking many of the derivations. I have drawn
very heavily on the knowledge of many colleagues, including Stanley Deser,
Robert Dicke, George Field, Icko Iben, Jr., Arthur Miller, Philip Morrison, Martin
Rees, Leonard Schiff, Maarten Schmidt, Joseph Weber, Rainier Weiss, and espe-
cially Irwin Shapiro. Finally, I am greatly indebted to Connie Friedman and Lillian
Horton for typing and retyping the manuscript with inexhaustible skill and patience.
STEVEN WEINBERG
Cambridge, Massachusetts
April 1971
N ow that this book is done I can look back, and identify two purposes which
led me to begin writing, and which have guided the work to completion.
One good practical purpose was to bring together and assess the wealth of data
provided over the last decade by new techniques in experimental physics and in
optical, radio, radar, X-ray, and infrared astronomy. Of course, new data will
keep coming in even as the book is being printed, and I cannot hope that this work
will remain up to date forever. I do hope, however, that by giving a comprehensive
picture of the experimental tests of general relativity and observational cosmology,
I will help to prepare the reader (and myself) to understand the nm\' data as they
emerge. I have also tried to look a little way into the future, and to discuss what
may be the next generation of experiments, especially those based on artificial
satellites of the earth and sun.
There was another, more personal reason for my writing this book. In learning
general relativity, and then in teaching it to classes at Berkeley and M.LT., I
became dissatisfied with what seemed to be the usual approach to the subject.
I found that in most textbooks geometric ideas were given a starring role, so that a
student who asked why the gravitational field is represented by a metric tensor, or
why freely falling particles move on geodesics, or why the field equations are
generally covariant would come away with an impression that this had something
to do with the fact that space-time is a Riemannian manifold.
Of course, this was Einstein's point of view, and his preeminent genius
necessarily shapes our understanding of the theory he created. However, I believe
that the geometrical approach has driven a wedge between general relativity
and the theory of elementary particles. As long as it could be hoped, as Einstein
did hope, that matter would eventually be understood in geometrical terms, it
made sense to give Riemannian geometry a primary role in describing the theory
of gravitation. But now the passage of time has taught us not to expect that the
strong, weak, and electromagnf3tic interactions can be understood in geometrical
terms, and too great an emphasis on geometry can only obscure the deep con-
nections between gravitation and the rest of physics. In place of Riemannian geometry, I have based the discussion of general
relativity on a principle derived from experiment: the Principle of the Equivalence
of Gravitation and Inertia. It will be seen that geometric objects, such as the
metric. the affine connection, and the curvature tensor, naturally find their way
into a theory of gravitation based on the Principle of Equivalence and, of course,
one winds up in the end with Einstein's general theory of relativity. However, I
have tried here to put off the introduction of geometric concepts until they are
needed, so that Riemannian geometry appears only as a mathematical tool for
the exploitation of the Principle of Equivalence, and not as a fundamental basis
for the theory of gravitation.
This approach naturally leads us to ask why gravitation should obey the
Principle of Equivalence. In my opinion the answer is not to be found in the realm
of classical physics, and certainly not in Riemannian geometry, but in the con-
straints imposed by the quantum theory of gravitation. It seems to be impossible
to construct any Lorentz-invariant quantum theory of particles of mass zero and
spin two, unless the corresponding classical field theory obeys the Principle of
Equivalence. Thus the Principle of Equivalence appears as the best bridge
between the theories of gravitation and of elementary particles. The quantum
basis for the Principle of Equivalence is briefly touched upon here in a section on
the quantum theory of gravitation, but it was not possible to go far into the
quantum theory in this book.
The nongeometrical approach taken in this book has, to some extent, affected
the choice of the topics to be covered. In particular, I have not discussed in detail
the derivation and classification of complicated exact solutions of the Einstein
field equations, because I did not feel that most of this material was needed for a
fundamental understanding of the theory of gravitation, and hardly any of it
seemed to be relevant to experiments that might be carried out in the foreseeable
future. By this omission, I have left out much of the work done by professional
geI).eral relativists over the past decade, but I have tried to provide an entree
to this work through references and bibliographies. I regret the omission here of a
detailed discussion of the beautiful theorems of Penrose and Hawking on gravi-
tational collapse; these theorems are briefly discussed in Sections 11.9 and 15.11,
but an adequate discussion would have taken up too much time and space.
I have tried to give a comprehensive set of references to the experimental
literature on general relativity and cosmology. I have also given references to
detailed theoretical calculations whenever I have quoted their results. However, I
have not tried to give complete references to all the theoretical material discussed
in the book. Much of this material is now classical, and to search out the original
references would be an exercise in the history of science for which I did not feel
equipped. The mere absence of literature citations should not be interpreted as a
claim that the work presented is original, but some of it is.
It is a pleasure to acknowledge the inestimable help I have received in writing
this book. Students in my classes over the past seven years have, by their questions
and comments, helped to free the calculations of errors and obscurities. I especially thank Jill Punsky for carefully checking many of the derivations. I have drawn
very heavily on the knowledge of many colleagues, including Stanley Deser,
Robert Dicke, George Field, Icko Iben, Jr., Arthur Miller, Philip Morrison, Martin
Rees, Leonard Schiff, Maarten Schmidt, Joseph Weber, Rainier Weiss, and espe-
cially Irwin Shapiro. Finally, I am greatly indebted to Connie Friedman and Lillian
Horton for typing and retyping the manuscript with inexhaustible skill and patience.
STEVEN WEINBERG
Cambridge, Massachusetts
April 1971
Wednesday, 1 February 2012
The Cosmic Connection By Carl Sagan free download
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How to download from 4shared Click Here To Know
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Part One: COSMIC PERSPECTIVES
1. A Transitional Animal
2. The Unicorn of Cetus
3. A Message from Earth
4. A Message to Earth
5. Experiments in Utopias
6. Chauvinism
7. Space Exploration as a Human Enterprise
I. The Scientific Interest
8. Space Exploration as a Human Enterprise
II. The Public Interest
9. Space Exploration as a Human Enterprise
III. The Historical Interest
Part Two: THE SOLAR SYSTEM
10. On Teaching the First Grade
11. "The Ancient and Legendary Gods of Old"
12. The Venus Detective Story
13. Venus Is Hell
14. Science and "Intelligence"
15. The Moons of Barsoom
16. The Mountains of Mars
I. Observations From Earth
17. The Mountains of Mars
II. Observations From Space
18. The Canals of Mars
19. The Lost Pictures of Mars
20. The Ice Age and the Cauldron
21. Beginnings and Ends of the Earth
22. Terraforming the Planets
23. The Exploration and Utilization of the Solar System
Part Three: BEYOND THE SOLAR SYSTEM
24. Some of My Best Friends Are Dolphins
25. "Hello, Central Casting? Send Me Twenty Extraterrestrials"
26. The Cosmic Connection
27. Extraterrestrial Life: An Idea Whose Time Has Come
28. Has the Earth Been Visited?
29. A Search Strategy for Detecting Extraterrestrial Intelligence
30. If We Succeed
31. Cables, Drums, and Seashells
32. The Night Freight to the Stars
33. Astroengineering
34. Twenty Questions: A Classification of Cosmic Civilizations
35. Galactic Cultural Exchanges
36. A Passage to Elsewhen
37. Starfolk
I. A Fable
38. Starfolk
II. A Future
39. Starfolk
III. The Cosmic Cheshire Cats
Preface
When I was twelve, my grandfather asked me – through a translator (he had
never learned much English) – what I wanted to be when I grew up. I answered,
"An astronomer," which, after a while, was also translated. "Yes," he replied, "but
how will you make a living?"
I had supposed that, like all the adult men I knew, I would be consigned to a
dull, repetitive, and uncreative job, astronomy would be done on weekends. It was
not until my second year in high school that I discovered that some astronomers
were paid to pursue their passion. I was overwhelmed with joy; I could pursue my
interest full-time.
Even today, there are moments when what I do seems to me like an
improbable, if unusually pleasant, dream: To be involved in the exploration of
Venus, Mars, Jupiter, and Saturn; to try to duplicate the steps that led to the
origin of life four billion years ago on an Earth very different from the one we
know; to land instruments on Mars to search there for life; and perhaps to be
engaged in a serious effort to communicate with other intelligent beings, if such
there be, out there in the dark of the night sky.
Had I been born fifty years earlier, I could have pursued none of these
activities. They were then all figments of the speculative imagination. Had I been
born fifty years later, I also could not have been involved in these efforts, except
possibly the last, because fifty years from now the preliminary reconnaissance of
the Solar System, the search for life on Mars, and the study of the origin of life will
have been completed. I think myself extraordinarily fortunate to be alive at the
one moment in the history of mankind when such ventures are being undertaken.
So when Jerome Agel approached me about doing a popular book to try to
communicate my sense of the excitement and importance of these adventures, I
was amenable – even though his suggestion came just before the Mariner 9
mission to Mars, which I knew would occupy most of my waking hours for many
months. At a later time, after discussing communication with extraterrestrial
intelligence, Agel and I had dinner in a Polynesian restaurant in Boston. My fortune
cookie announced, "You will shortly be called upon to decipher an important
message." This seemed a good omen.
After centuries of muddy surmise, unfettered speculation, stodgy conservatism,
and unimaginative disinterest, the subject of extraterrestrial life has finally come of
age. It has now reached a practical stage where it can be pursued by rigorous
scientific techniques, where it has achieved scientific respectability and where its
significance is widely understood. Extraterrestrial life is an idea whose time has
come.
This book is divided into three major sections. In the first part I try in several
ways to convey a sense of cosmic perspective – living out our lives on a tiny hunk
of rock and metal circling one of 250 billion stars that make up our galaxy in a
universe of billions of galaxies. The deflation of some of our more common
7
conceits is one of the practical applications of astronomy. The second part of the
book is concerned with various aspects of our Solar System – mostly with Earth,
Mars, and Venus. Some of the results and implications of Mariner 9 can be found
here. Part Three is devoted to the possibility of communicating with
extraterrestrial intelligence on planets of other stars. Since no such contact has yet
been made – our efforts to date have been feeble – this section is necessarily
speculative. I have not hesitated to speculate within what I perceive to be the
bounds of scientific plausibility. And, although I am not by training a philosopher
or sociologist or historian, I have not hesitated to draw philosophical or social or
historical implications of astronomy and space exploration.
The astronomical discoveries we are in the midst of making are of the broadest
human significance. If this book plays a small role in broadening public
consideration of these exploratory ventures, it will have served its purpose.
As with all ongoing work and especially all speculative subjects, some of the
statements in these pages will elicit vigorous demurrers. There are other books
with other opinions. Reasoned disputation is the lifeblood of science – as is, sadly,
infrequently the case in the intellectually more anemic arena of politics. But I
believe that the more controversial opinions expressed here have, nevertheless, a
significant scientific constituency. I have purposely introduced the same concept
in slightly different contexts in a few places where I felt the discussion required it.
The book is carefully structured, but, for the reader who wishes to browse ahead,
most chapters are self-contained.
There are far too many who helped shape my opinions on these subjects for
me to thank them all here. But in rereading these chapters, I find I owe a special
debt to Joseph Veverka and Frank Drake, both of Cornell University, with whom
over the past few years I have discussed so many aspects of this volume. The book
was composed partly during a very long transcontinental trip in a very short
automobile. I thank Linda and Nicholas for their encouragement and patience. I
am also grateful to Linda for drawing two handsome humans and one elegant
unicorn. And I am grateful to the late Mauritz Escher for permission to reproduce
his "Another World" and to Robert Macintyre for the human figure and star field
in Part Three. Jon Lomberg's paintings and drawings have been a source of
intellectual and aesthetic excitement for me, and I am grateful to him for
producing many of them especially for this book. Hermann Eckleman's careful
photographic reproductions of Lomberg's work have facilitated their appearance
in this book. And I thank Jerome Agel, without whose time and persistence this
book would never have been written.
I am indebted to John Naugle of NASA for showing me his file on public
response to the Pioneer 10 plaque; the Oregon System of Higher Education for
permission to reproduce some ideas from my book Planetary Exploration; the
Forum for Contemporary History, in Santa Barbara, for permission to reproduce a
portion of my letter distributed by the Forum in January 1973; and Cornell
University Press for permission to reprint a fraction of my chapter "The
8
Extraterrestrial and Other Hypotheses" from UFO's: A Scientific Debate, edited by
Carl Sagan and Thornton Page, Cornell University Press, 1972. I am also grateful to
those who have granted me permission to reproduce in Chapter 4 their remarks
on the Pioneer 10 plaque. The evolution of this book through many drafts owes
much to the technical skills of Jo Ann Cowan, and, especially, Mary Szymanski.
– Carl Sagan
never learned much English) – what I wanted to be when I grew up. I answered,
"An astronomer," which, after a while, was also translated. "Yes," he replied, "but
how will you make a living?"
I had supposed that, like all the adult men I knew, I would be consigned to a
dull, repetitive, and uncreative job, astronomy would be done on weekends. It was
not until my second year in high school that I discovered that some astronomers
were paid to pursue their passion. I was overwhelmed with joy; I could pursue my
interest full-time.
Even today, there are moments when what I do seems to me like an
improbable, if unusually pleasant, dream: To be involved in the exploration of
Venus, Mars, Jupiter, and Saturn; to try to duplicate the steps that led to the
origin of life four billion years ago on an Earth very different from the one we
know; to land instruments on Mars to search there for life; and perhaps to be
engaged in a serious effort to communicate with other intelligent beings, if such
there be, out there in the dark of the night sky.
Had I been born fifty years earlier, I could have pursued none of these
activities. They were then all figments of the speculative imagination. Had I been
born fifty years later, I also could not have been involved in these efforts, except
possibly the last, because fifty years from now the preliminary reconnaissance of
the Solar System, the search for life on Mars, and the study of the origin of life will
have been completed. I think myself extraordinarily fortunate to be alive at the
one moment in the history of mankind when such ventures are being undertaken.
So when Jerome Agel approached me about doing a popular book to try to
communicate my sense of the excitement and importance of these adventures, I
was amenable – even though his suggestion came just before the Mariner 9
mission to Mars, which I knew would occupy most of my waking hours for many
months. At a later time, after discussing communication with extraterrestrial
intelligence, Agel and I had dinner in a Polynesian restaurant in Boston. My fortune
cookie announced, "You will shortly be called upon to decipher an important
message." This seemed a good omen.
After centuries of muddy surmise, unfettered speculation, stodgy conservatism,
and unimaginative disinterest, the subject of extraterrestrial life has finally come of
age. It has now reached a practical stage where it can be pursued by rigorous
scientific techniques, where it has achieved scientific respectability and where its
significance is widely understood. Extraterrestrial life is an idea whose time has
come.
This book is divided into three major sections. In the first part I try in several
ways to convey a sense of cosmic perspective – living out our lives on a tiny hunk
of rock and metal circling one of 250 billion stars that make up our galaxy in a
universe of billions of galaxies. The deflation of some of our more common
7
conceits is one of the practical applications of astronomy. The second part of the
book is concerned with various aspects of our Solar System – mostly with Earth,
Mars, and Venus. Some of the results and implications of Mariner 9 can be found
here. Part Three is devoted to the possibility of communicating with
extraterrestrial intelligence on planets of other stars. Since no such contact has yet
been made – our efforts to date have been feeble – this section is necessarily
speculative. I have not hesitated to speculate within what I perceive to be the
bounds of scientific plausibility. And, although I am not by training a philosopher
or sociologist or historian, I have not hesitated to draw philosophical or social or
historical implications of astronomy and space exploration.
The astronomical discoveries we are in the midst of making are of the broadest
human significance. If this book plays a small role in broadening public
consideration of these exploratory ventures, it will have served its purpose.
As with all ongoing work and especially all speculative subjects, some of the
statements in these pages will elicit vigorous demurrers. There are other books
with other opinions. Reasoned disputation is the lifeblood of science – as is, sadly,
infrequently the case in the intellectually more anemic arena of politics. But I
believe that the more controversial opinions expressed here have, nevertheless, a
significant scientific constituency. I have purposely introduced the same concept
in slightly different contexts in a few places where I felt the discussion required it.
The book is carefully structured, but, for the reader who wishes to browse ahead,
most chapters are self-contained.
There are far too many who helped shape my opinions on these subjects for
me to thank them all here. But in rereading these chapters, I find I owe a special
debt to Joseph Veverka and Frank Drake, both of Cornell University, with whom
over the past few years I have discussed so many aspects of this volume. The book
was composed partly during a very long transcontinental trip in a very short
automobile. I thank Linda and Nicholas for their encouragement and patience. I
am also grateful to Linda for drawing two handsome humans and one elegant
unicorn. And I am grateful to the late Mauritz Escher for permission to reproduce
his "Another World" and to Robert Macintyre for the human figure and star field
in Part Three. Jon Lomberg's paintings and drawings have been a source of
intellectual and aesthetic excitement for me, and I am grateful to him for
producing many of them especially for this book. Hermann Eckleman's careful
photographic reproductions of Lomberg's work have facilitated their appearance
in this book. And I thank Jerome Agel, without whose time and persistence this
book would never have been written.
I am indebted to John Naugle of NASA for showing me his file on public
response to the Pioneer 10 plaque; the Oregon System of Higher Education for
permission to reproduce some ideas from my book Planetary Exploration; the
Forum for Contemporary History, in Santa Barbara, for permission to reproduce a
portion of my letter distributed by the Forum in January 1973; and Cornell
University Press for permission to reprint a fraction of my chapter "The
8
Extraterrestrial and Other Hypotheses" from UFO's: A Scientific Debate, edited by
Carl Sagan and Thornton Page, Cornell University Press, 1972. I am also grateful to
those who have granted me permission to reproduce in Chapter 4 their remarks
on the Pioneer 10 plaque. The evolution of this book through many drafts owes
much to the technical skills of Jo Ann Cowan, and, especially, Mary Szymanski.
– Carl Sagan
The Fabric Of The Cosmos By Brian Greene free download
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How to download from 4shared Click Here To Know
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Contents
Parti REALITY'S ARENA
1. Roads to Reality 3
Space, Time, and Why Things Are as They Are
2. The Universe and the Bucket 23
Is Space a Human Abstraction or a Physical Entity?
3. Relativity and the Absolute 39
Is Spacetime an Einstemian Abstraction or a
Physical Entity?
4. Entangling Space 77
What Does It Mean to Be Separate in a
Quantum Universe?
Part II TIME AND EXPERIENCE
5. The Frozen River 127
Does Time Flow?
6. Chance and the Arrow 143
Does Time Have a Direction?
7. Time and the Quantum 177
Insights into Time's Nature from the Quantum Realm
Part III SPACETIMEAND COSMOLOGY
8. Of Snowflakes and Spacetime 219
Symmetry and the Evolution of the Cosmos
9, Vaporizing the Vacuum 251
Heat, Nothingness, and Unification
10. Deconstructing the Bang 272
What Banged?
11. Quanta in the Sky with Diamonds 304
Inflation, Quantum fitters, and the Arrow of Time
Part IV ORIGINS AND UNIFICATION
12. The World on a String 327
The Fabric According to String Theory
13. The Universe on a Brane 376
Speculations on Space and Time in M-Theory
PartV REALITY AND IMAGINATION
14. Up in the Heavens and Down in the Earth 415
Experimenting with Space and Time
15. Teleporters and Time Machines 437
Traveling Through Space and Time
16. The Future of an Allusion 470
Prospects for Space and Time
Notes 495
Glossary 537
Suggestions for Further Reading 543
Index 545
Preface
Space and time capture the imagination like no other scientific subject.
For good reason. They form the arena of reality, the very fabric of the cosmos.
Our entire existence —everything we do, think, and experience —
takes place in some region of space during some interval of time. Yet
science is still struggling to understand what space and time actually are.
Are they real physical entities or simply useful ideas? If they're real, are
they fundamental, or do they emerge from more basic constituents? What
does it mean for space to be empty? Does time have a beginning? Does
it have an arrow, flowing inexorably from past to future, as common experience
would indicate? Can we manipulate space and time? In this
book, we follow three hundred years of passionate scientific investigation
seeking answers, or at least glimpses of answers, to such basic but deep
questions about the nature of the universe.
Our journey also brings us repeatedly to another, tightly related question,
as encompassing as it is elusive: What is reality'? We humans only have access to the internal experiences of perception and thought, so how
can we be sure they truly reflect an external world? Philosophers have
long recognized this problem. Filmmakers have popularized it through
story lines involving artificial worlds, generated by finely tuned neurological
stimulation that exist solely within the minds of their protagonists.
And physicists such as myself are acutely aware that the reality we
observe —matter evolving on the stage of space and time —may have little
to do with the reality, if any, that's out there. Nevertheless, because observations
are all we have, we take them seriously. We choose hard data and
the framework of mathematics as our guides, not unrestrained imagination
or unrelenting skepticism, and seek the simplest yet most wide-reaching
theories capable of explaining and predicting the outcome of today's
and future experiments. This severely restricts the theories we pursue. (In
this book, for example, we won't find a hint that I'm floating in a tank, connected to thousands of brain-stimulating wires, making me merely
think that I'm now writing this text.) But during the last hundred years,
discoveries in physics have suggested revisions to our everyday sense of
reality that are as dramatic, as mind-bending, and as paradigm-shaking as
the most imaginative science fiction. These revolutionary upheavals will
frame our passage through the pages that follow.
Many of the questions we explore are the same ones that, in various
guises, furrowed the brows of Aristotle, Galileo, Newton, Einstein, and
countless others through the ages. And because this book seeks to convey
science in the making, we follow these questions as they've been declared
answered by one generation, overturned by their successors, and refined
and reinterpreted by scientists in the centuries that followed.
For example, on the perplexing question of whether completely
empty space is, like a blank canvas, a real entity or merely an abstract
idea, we follow the pendulum of scientific opinion as it swings between
Isaac Newton's seventeenth-century declaration that space is real, Ernst Mach's conclusion in the nineteenth century that it isn't, and Einstein's
twentieth-century dramatic reformulation of the question itself, in which
he merged space and time, and largely refuted Mach. We then encounter
subsequent discoveries that transformed the question once again by
redefining the meaning of "empty," envisioning that space is unavoidably
suffused with what are called quantum fields and possibly a diffuse uniform
energy called a cosmological constant—modern echoes of the old
and discredited notion of a space-filling aether. What's more, we then
describe how upcoming space-based experiments may confirm particular
features of Mach's conclusions that happen to agree with Einstein's general
relativity, illustrating well the fascinating and tangled web of scientific
development.
In our own era we encounter inflationary cosmology's gratifying
insights into time's arrow, string theory's rich assortment of extra spatial
dimensions, M-theory's radical suggestion that the space we inhabit may
be but a sliver floating in a grander cosmos, and the current wild speculation
that the universe we see may be nothing more than a cosmic hologram.
We don't yet know if the more recent of these theoretical proposals
are right. But outrageous as they sound, we take them seriously because
they are where our dogged search for the deepest laws of the universe
leads. Not only can a strange and unfamiliar reality arise from the fertile
imagination of science fiction, but one may also emerge from the cuttingedge
findings of modem physics.
The Cosmic Connection By CARL SAGAN free download
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One: COSMIC PERSPECTIVES
1. A Transitional Animal
2. The Unicorn of Cetus
3. A Message from Earth
4. A Message to Earth
5. Experiments in Utopias
6. Chauvinism
7. Space Exploration as a Human Enterprise
I. The Scientific Interest
8. Space Exploration as a Human Enterprise
II. The Public Interest
9. Space Exploration as a Human Enterprise
III. The Historical Interest
Part Two: THE SOLAR SYSTEM
10. On Teaching the First Grade
11. "The Ancient and Legendary Gods of Old"
12. The Venus Detective Story
13. Venus Is Hell
14. Science and "Intelligence"
15. The Moons of Barsoom
16. The Mountains of Mars
I. Observations From Earth
17. The Mountains of Mars
II. Observations From Space
18. The Canals of Mars
19. The Lost Pictures of Mars
20. The Ice Age and the Cauldron
21. Beginnings and Ends of the Earth
22. Terraforming the Planets
23. The Exploration and Utilization of the Solar System
Part Three: BEYOND THE SOLAR SYSTEM
24. Some of My Best Friends Are Dolphins
25. "Hello, Central Casting? Send Me Twenty Extraterrestrials"
26. The Cosmic Connection
27. Extraterrestrial Life: An Idea Whose Time Has Come
28. Has the Earth Been Visited?
29. A Search Strategy for Detecting Extraterrestrial Intelligence
30. If We Succeed
31. Cables, Drums, and Seashells
32. The Night Freight to the Stars
33. Astroengineering
34. Twenty Questions: A Classification of Cosmic Civilizations
35. Galactic Cultural Exchanges
36. A Passage to Elsewhen
37. Starfolk
I. A Fable
38. Starfolk
II. A Future
39. Starfolk
III. The Cosmic Cheshire Cats
1. A Transitional Animal
2. The Unicorn of Cetus
3. A Message from Earth
4. A Message to Earth
5. Experiments in Utopias
6. Chauvinism
7. Space Exploration as a Human Enterprise
I. The Scientific Interest
8. Space Exploration as a Human Enterprise
II. The Public Interest
9. Space Exploration as a Human Enterprise
III. The Historical Interest
Part Two: THE SOLAR SYSTEM
10. On Teaching the First Grade
11. "The Ancient and Legendary Gods of Old"
12. The Venus Detective Story
13. Venus Is Hell
14. Science and "Intelligence"
15. The Moons of Barsoom
16. The Mountains of Mars
I. Observations From Earth
17. The Mountains of Mars
II. Observations From Space
18. The Canals of Mars
19. The Lost Pictures of Mars
20. The Ice Age and the Cauldron
21. Beginnings and Ends of the Earth
22. Terraforming the Planets
23. The Exploration and Utilization of the Solar System
Part Three: BEYOND THE SOLAR SYSTEM
24. Some of My Best Friends Are Dolphins
25. "Hello, Central Casting? Send Me Twenty Extraterrestrials"
26. The Cosmic Connection
27. Extraterrestrial Life: An Idea Whose Time Has Come
28. Has the Earth Been Visited?
29. A Search Strategy for Detecting Extraterrestrial Intelligence
30. If We Succeed
31. Cables, Drums, and Seashells
32. The Night Freight to the Stars
33. Astroengineering
34. Twenty Questions: A Classification of Cosmic Civilizations
35. Galactic Cultural Exchanges
36. A Passage to Elsewhen
37. Starfolk
I. A Fable
38. Starfolk
II. A Future
39. Starfolk
III. The Cosmic Cheshire Cats
Preface
When I was twelve, my grandfather asked me – through a translator (he had
never learned much English) – what I wanted to be when I grew up. I answered,
"An astronomer," which, after a while, was also translated. "Yes," he replied, "but
how will you make a living?"
I had supposed that, like all the adult men I knew, I would be consigned to a
dull, repetitive, and uncreative job, astronomy would be done on weekends. It was
not until my second year in high school that I discovered that some astronomers
were paid to pursue their passion. I was overwhelmed with joy; I could pursue my
interest full-time.
Even today, there are moments when what I do seems to me like an
improbable, if unusually pleasant, dream: To be involved in the exploration of
Venus, Mars, Jupiter, and Saturn; to try to duplicate the steps that led to the
origin of life four billion years ago on an Earth very different from the one we
know; to land instruments on Mars to search there for life; and perhaps to be
engaged in a serious effort to communicate with other intelligent beings, if such
there be, out there in the dark of the night sky.
Had I been born fifty years earlier, I could have pursued none of these
activities. They were then all figments of the speculative imagination. Had I been
born fifty years later, I also could not have been involved in these efforts, except
possibly the last, because fifty years from now the preliminary reconnaissance of
the Solar System, the search for life on Mars, and the study of the origin of life will
have been completed. I think myself extraordinarily fortunate to be alive at the
one moment in the history of mankind when such ventures are being undertaken.
So when Jerome Agel approached me about doing a popular book to try to
communicate my sense of the excitement and importance of these adventures, I
was amenable – even though his suggestion came just before the Mariner 9
mission to Mars, which I knew would occupy most of my waking hours for many
months. At a later time, after discussing communication with extraterrestrial
intelligence, Agel and I had dinner in a Polynesian restaurant in Boston. My fortune
cookie announced, "You will shortly be called upon to decipher an important
message." This seemed a good omen.
After centuries of muddy surmise, unfettered speculation, stodgy conservatism,
and unimaginative disinterest, the subject of extraterrestrial life has finally come of
age. It has now reached a practical stage where it can be pursued by rigorous
scientific techniques, where it has achieved scientific respectability and where its
significance is widely understood. Extraterrestrial life is an idea whose time has
come.
This book is divided into three major sections. In the first part I try in several
ways to convey a sense of cosmic perspective – living out our lives on a tiny hunk
of rock and metal circling one of 250 billion stars that make up our galaxy in a
universe of billions of galaxies. The deflation of some of our more common
7
conceits is one of the practical applications of astronomy. The second part of the
book is concerned with various aspects of our Solar System – mostly with Earth,
Mars, and Venus. Some of the results and implications of Mariner 9 can be found
here. Part Three is devoted to the possibility of communicating with
extraterrestrial intelligence on planets of other stars. Since no such contact has yet
been made – our efforts to date have been feeble – this section is necessarily
speculative. I have not hesitated to speculate within what I perceive to be the
bounds of scientific plausibility. And, although I am not by training a philosopher
or sociologist or historian, I have not hesitated to draw philosophical or social or
historical implications of astronomy and space exploration.
The astronomical discoveries we are in the midst of making are of the broadest
human significance. If this book plays a small role in broadening public
consideration of these exploratory ventures, it will have served its purpose.
As with all ongoing work and especially all speculative subjects, some of the
statements in these pages will elicit vigorous demurrers. There are other books
with other opinions. Reasoned disputation is the lifeblood of science – as is, sadly,
infrequently the case in the intellectually more anemic arena of politics. But I
believe that the more controversial opinions expressed here have, nevertheless, a
significant scientific constituency. I have purposely introduced the same concept
in slightly different contexts in a few places where I felt the discussion required it.
The book is carefully structured, but, for the reader who wishes to browse ahead,
most chapters are self-contained.
There are far too many who helped shape my opinions on these subjects for
me to thank them all here. But in rereading these chapters, I find I owe a special
debt to Joseph Veverka and Frank Drake, both of Cornell University, with whom
over the past few years I have discussed so many aspects of this volume. The book
was composed partly during a very long transcontinental trip in a very short
automobile. I thank Linda and Nicholas for their encouragement and patience. I
am also grateful to Linda for drawing two handsome humans and one elegant
unicorn. And I am grateful to the late Mauritz Escher for permission to reproduce
his "Another World" and to Robert Macintyre for the human figure and star field
in Part Three. Jon Lomberg's paintings and drawings have been a source of
intellectual and aesthetic excitement for me, and I am grateful to him for
producing many of them especially for this book. Hermann Eckleman's careful
photographic reproductions of Lomberg's work have facilitated their appearance
in this book. And I thank Jerome Agel, without whose time and persistence this
book would never have been written.
I am indebted to John Naugle of NASA for showing me his file on public
response to the Pioneer 10 plaque; the Oregon System of Higher Education for
permission to reproduce some ideas from my book Planetary Exploration; the
Forum for Contemporary History, in Santa Barbara, for permission to reproduce a
portion of my letter distributed by the Forum in January 1973; and Cornell
University Press for permission to reprint a fraction of my chapter "The
8
Extraterrestrial and Other Hypotheses" from UFO's: A Scientific Debate, edited by
Carl Sagan and Thornton Page, Cornell University Press, 1972. I am also grateful to
those who have granted me permission to reproduce in Chapter 4 their remarks
on the Pioneer 10 plaque. The evolution of this book through many drafts owes
much to the technical skills of Jo Ann Cowan, and, especially, Mary Szymanski.
– Carl Sagan
When I was twelve, my grandfather asked me – through a translator (he had
never learned much English) – what I wanted to be when I grew up. I answered,
"An astronomer," which, after a while, was also translated. "Yes," he replied, "but
how will you make a living?"
I had supposed that, like all the adult men I knew, I would be consigned to a
dull, repetitive, and uncreative job, astronomy would be done on weekends. It was
not until my second year in high school that I discovered that some astronomers
were paid to pursue their passion. I was overwhelmed with joy; I could pursue my
interest full-time.
Even today, there are moments when what I do seems to me like an
improbable, if unusually pleasant, dream: To be involved in the exploration of
Venus, Mars, Jupiter, and Saturn; to try to duplicate the steps that led to the
origin of life four billion years ago on an Earth very different from the one we
know; to land instruments on Mars to search there for life; and perhaps to be
engaged in a serious effort to communicate with other intelligent beings, if such
there be, out there in the dark of the night sky.
Had I been born fifty years earlier, I could have pursued none of these
activities. They were then all figments of the speculative imagination. Had I been
born fifty years later, I also could not have been involved in these efforts, except
possibly the last, because fifty years from now the preliminary reconnaissance of
the Solar System, the search for life on Mars, and the study of the origin of life will
have been completed. I think myself extraordinarily fortunate to be alive at the
one moment in the history of mankind when such ventures are being undertaken.
So when Jerome Agel approached me about doing a popular book to try to
communicate my sense of the excitement and importance of these adventures, I
was amenable – even though his suggestion came just before the Mariner 9
mission to Mars, which I knew would occupy most of my waking hours for many
months. At a later time, after discussing communication with extraterrestrial
intelligence, Agel and I had dinner in a Polynesian restaurant in Boston. My fortune
cookie announced, "You will shortly be called upon to decipher an important
message." This seemed a good omen.
After centuries of muddy surmise, unfettered speculation, stodgy conservatism,
and unimaginative disinterest, the subject of extraterrestrial life has finally come of
age. It has now reached a practical stage where it can be pursued by rigorous
scientific techniques, where it has achieved scientific respectability and where its
significance is widely understood. Extraterrestrial life is an idea whose time has
come.
This book is divided into three major sections. In the first part I try in several
ways to convey a sense of cosmic perspective – living out our lives on a tiny hunk
of rock and metal circling one of 250 billion stars that make up our galaxy in a
universe of billions of galaxies. The deflation of some of our more common
7
conceits is one of the practical applications of astronomy. The second part of the
book is concerned with various aspects of our Solar System – mostly with Earth,
Mars, and Venus. Some of the results and implications of Mariner 9 can be found
here. Part Three is devoted to the possibility of communicating with
extraterrestrial intelligence on planets of other stars. Since no such contact has yet
been made – our efforts to date have been feeble – this section is necessarily
speculative. I have not hesitated to speculate within what I perceive to be the
bounds of scientific plausibility. And, although I am not by training a philosopher
or sociologist or historian, I have not hesitated to draw philosophical or social or
historical implications of astronomy and space exploration.
The astronomical discoveries we are in the midst of making are of the broadest
human significance. If this book plays a small role in broadening public
consideration of these exploratory ventures, it will have served its purpose.
As with all ongoing work and especially all speculative subjects, some of the
statements in these pages will elicit vigorous demurrers. There are other books
with other opinions. Reasoned disputation is the lifeblood of science – as is, sadly,
infrequently the case in the intellectually more anemic arena of politics. But I
believe that the more controversial opinions expressed here have, nevertheless, a
significant scientific constituency. I have purposely introduced the same concept
in slightly different contexts in a few places where I felt the discussion required it.
The book is carefully structured, but, for the reader who wishes to browse ahead,
most chapters are self-contained.
There are far too many who helped shape my opinions on these subjects for
me to thank them all here. But in rereading these chapters, I find I owe a special
debt to Joseph Veverka and Frank Drake, both of Cornell University, with whom
over the past few years I have discussed so many aspects of this volume. The book
was composed partly during a very long transcontinental trip in a very short
automobile. I thank Linda and Nicholas for their encouragement and patience. I
am also grateful to Linda for drawing two handsome humans and one elegant
unicorn. And I am grateful to the late Mauritz Escher for permission to reproduce
his "Another World" and to Robert Macintyre for the human figure and star field
in Part Three. Jon Lomberg's paintings and drawings have been a source of
intellectual and aesthetic excitement for me, and I am grateful to him for
producing many of them especially for this book. Hermann Eckleman's careful
photographic reproductions of Lomberg's work have facilitated their appearance
in this book. And I thank Jerome Agel, without whose time and persistence this
book would never have been written.
I am indebted to John Naugle of NASA for showing me his file on public
response to the Pioneer 10 plaque; the Oregon System of Higher Education for
permission to reproduce some ideas from my book Planetary Exploration; the
Forum for Contemporary History, in Santa Barbara, for permission to reproduce a
portion of my letter distributed by the Forum in January 1973; and Cornell
University Press for permission to reprint a fraction of my chapter "The
8
Extraterrestrial and Other Hypotheses" from UFO's: A Scientific Debate, edited by
Carl Sagan and Thornton Page, Cornell University Press, 1972. I am also grateful to
those who have granted me permission to reproduce in Chapter 4 their remarks
on the Pioneer 10 plaque. The evolution of this book through many drafts owes
much to the technical skills of Jo Ann Cowan, and, especially, Mary Szymanski.
– Carl Sagan
GENERAL RELATIVITY & COSMOLOGY for Undergraduates By Professor John W. Norbury
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Contents
1 NEWTONIAN COSMOLOGY 5
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Velocity and Acceleration Equations . . . . . . . . . . . . . . 7
1.4 Cosmological Constant . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Einstein Static Universe . . . . . . . . . . . . . . . . . 11
2 APPLICATIONS 13
2.1 Conservation laws . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 In°ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Quantum Cosmology . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Derivation of the SchrÄodinger equation . . . . . . . . . 16
2.4.2 Wheeler-DeWitt equation . . . . . . . . . . . . . . . . 17
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.8 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 TENSORS 23
3.1 Contravariant and Covariant Vectors . . . . . . . . . . . . . . 23
3.2 Higher Rank Tensors . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Review of Cartesian Tensors . . . . . . . . . . . . . . . . . . . 27
3.4 Metric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.1 Special Relativity . . . . . . . . . . . . . . . . . . . . . 30
3.5 Christo®el Symbols . . . . . . . . . . . . . . . . . . . . . . . . 31
1
2 CONTENTS
3.6 Christo®el Symbols and Metric Tensor . . . . . . . . . . . . . 36
3.7 Riemann Curvature Tensor . . . . . . . . . . . . . . . . . . . 38
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.10 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.11 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 ENERGY-MOMENTUM TENSOR 45
4.1 Euler-Lagrange and Hamilton's Equations . . . . . . . . . . . 45
4.2 Classical Field Theory . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Classical Klein-Gordon Field . . . . . . . . . . . . . . 48
4.3 Principle of Least Action . . . . . . . . . . . . . . . . . . . . 49
4.4 Energy-Momentum Tensor for Perfect Fluid . . . . . . . . . . 49
4.5 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Interacting Scalar Field . . . . . . . . . . . . . . . . . . . . . 51
4.7 Cosmology with the Scalar Field . . . . . . . . . . . . . . . . 53
4.7.1 Alternative derivation . . . . . . . . . . . . . . . . . . 55
4.7.2 Limiting solutions . . . . . . . . . . . . . . . . . . . . 56
4.7.3 Exactly Solvable Model of In°ation . . . . . . . . . . . 59
4.7.4 Variable Cosmological Constant . . . . . . . . . . . . . 61
4.7.5 Cosmological constant and Scalar Fields . . . . . . . . 63
4.7.6 Clari¯cation . . . . . . . . . . . . . . . . . . . . . . . . 64
4.7.7 Generic In°ation and Slow-Roll Approximation . . . . 65
4.7.8 Chaotic In°ation in Slow-Roll Approximation . . . . . 67
4.7.9 Density Fluctuations . . . . . . . . . . . . . . . . . . . 72
4.7.10 Equation of State for Variable Cosmological Constant 73
4.7.11 Quantization . . . . . . . . . . . . . . . . . . . . . . . 77
4.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 EINSTEIN FIELD EQUATIONS 83
5.1 Preview of Riemannian Geometry . . . . . . . . . . . . . . . . 84
5.1.1 Polar Coordinate . . . . . . . . . . . . . . . . . . . . . 84
5.1.2 Volumes and Change of Coordinates . . . . . . . . . . 85
5.1.3 Di®erential Geometry . . . . . . . . . . . . . . . . . . 88
5.1.4 1-dimesional Curve . . . . . . . . . . . . . . . . . . . . 89
5.1.5 2-dimensional Surface . . . . . . . . . . . . . . . . . . 92
5.1.6 3-dimensional Hypersurface . . . . . . . . . . . . . . . 96
5.2 Friedmann-Robertson-Walker Metric . . . . . . . . . . . . . . 99
5.2.1 Christo®el Symbols . . . . . . . . . . . . . . . . . . . . 101
CONTENTS 3
5.2.2 Ricci Tensor . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.3 Riemann Scalar and Einstein Tensor . . . . . . . . . . 103
5.2.4 Energy-Momentum Tensor . . . . . . . . . . . . . . . 104
5.2.5 Friedmann Equations . . . . . . . . . . . . . . . . . . 104
5.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 Einstein Field Equations 107
7 Weak Field Limit 109
8 Lagrangian Methods 111
1 NEWTONIAN COSMOLOGY 5
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Velocity and Acceleration Equations . . . . . . . . . . . . . . 7
1.4 Cosmological Constant . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Einstein Static Universe . . . . . . . . . . . . . . . . . 11
2 APPLICATIONS 13
2.1 Conservation laws . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 In°ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Quantum Cosmology . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Derivation of the SchrÄodinger equation . . . . . . . . . 16
2.4.2 Wheeler-DeWitt equation . . . . . . . . . . . . . . . . 17
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.8 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 TENSORS 23
3.1 Contravariant and Covariant Vectors . . . . . . . . . . . . . . 23
3.2 Higher Rank Tensors . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Review of Cartesian Tensors . . . . . . . . . . . . . . . . . . . 27
3.4 Metric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.1 Special Relativity . . . . . . . . . . . . . . . . . . . . . 30
3.5 Christo®el Symbols . . . . . . . . . . . . . . . . . . . . . . . . 31
1
2 CONTENTS
3.6 Christo®el Symbols and Metric Tensor . . . . . . . . . . . . . 36
3.7 Riemann Curvature Tensor . . . . . . . . . . . . . . . . . . . 38
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.10 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.11 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 ENERGY-MOMENTUM TENSOR 45
4.1 Euler-Lagrange and Hamilton's Equations . . . . . . . . . . . 45
4.2 Classical Field Theory . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Classical Klein-Gordon Field . . . . . . . . . . . . . . 48
4.3 Principle of Least Action . . . . . . . . . . . . . . . . . . . . 49
4.4 Energy-Momentum Tensor for Perfect Fluid . . . . . . . . . . 49
4.5 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Interacting Scalar Field . . . . . . . . . . . . . . . . . . . . . 51
4.7 Cosmology with the Scalar Field . . . . . . . . . . . . . . . . 53
4.7.1 Alternative derivation . . . . . . . . . . . . . . . . . . 55
4.7.2 Limiting solutions . . . . . . . . . . . . . . . . . . . . 56
4.7.3 Exactly Solvable Model of In°ation . . . . . . . . . . . 59
4.7.4 Variable Cosmological Constant . . . . . . . . . . . . . 61
4.7.5 Cosmological constant and Scalar Fields . . . . . . . . 63
4.7.6 Clari¯cation . . . . . . . . . . . . . . . . . . . . . . . . 64
4.7.7 Generic In°ation and Slow-Roll Approximation . . . . 65
4.7.8 Chaotic In°ation in Slow-Roll Approximation . . . . . 67
4.7.9 Density Fluctuations . . . . . . . . . . . . . . . . . . . 72
4.7.10 Equation of State for Variable Cosmological Constant 73
4.7.11 Quantization . . . . . . . . . . . . . . . . . . . . . . . 77
4.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 EINSTEIN FIELD EQUATIONS 83
5.1 Preview of Riemannian Geometry . . . . . . . . . . . . . . . . 84
5.1.1 Polar Coordinate . . . . . . . . . . . . . . . . . . . . . 84
5.1.2 Volumes and Change of Coordinates . . . . . . . . . . 85
5.1.3 Di®erential Geometry . . . . . . . . . . . . . . . . . . 88
5.1.4 1-dimesional Curve . . . . . . . . . . . . . . . . . . . . 89
5.1.5 2-dimensional Surface . . . . . . . . . . . . . . . . . . 92
5.1.6 3-dimensional Hypersurface . . . . . . . . . . . . . . . 96
5.2 Friedmann-Robertson-Walker Metric . . . . . . . . . . . . . . 99
5.2.1 Christo®el Symbols . . . . . . . . . . . . . . . . . . . . 101
CONTENTS 3
5.2.2 Ricci Tensor . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.3 Riemann Scalar and Einstein Tensor . . . . . . . . . . 103
5.2.4 Energy-Momentum Tensor . . . . . . . . . . . . . . . 104
5.2.5 Friedmann Equations . . . . . . . . . . . . . . . . . . 104
5.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 Einstein Field Equations 107
7 Weak Field Limit 109
8 Lagrangian Methods 111
A GUIDE TO PHYSICS PROBLEMS part 2 Thermodynamics, Statistical Physics, and Quantum Mechanics By Sidney B. Cahn free download
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Foreword
It is only rarely realized how important the design of suitable, interesting
problems is in the educational process. This is true for the professor — who
periodically makes up exams and problem sets which test the effectiveness
of his teaching — and also for the student — who must match his skills
and acquired knowledge against these same problems. There is a great need
for challenging problems in all scientific fields, but especially so in physics.
Reading a physics paper requires familiarity and control of techniques which
can only be obtained by serious practice in solving problems. Confidence
in performing research demands a mastery of detailed technology which
requires training, concentration, and reflection — again, gained only by
working exercises.
In spite of the obvious need, there is very little systematic effort made
to provide balanced, doable problems that do more than gratify the ego of
the professor. Problems often are routine applications of procedures mentioned
in lectures or in books. They do little to force students to reflect
seriously about new situations. Furthermore, the problems are often excruciatingly
dull and test persistence and intellectual stamina more than
insight, technical skill, and originality. Another rather serious shortcoming
is that most exams and problems carry the unmistakable imprint of the
teacher. (In some excellent eastern U.S. universities, problems are catalogued
by instructor, so that a good deal is known about an exam even
before it is written.)
In contrast, A Guide to Physics Problems, Part 2 not only serves an
important function, but is a pleasure to read. By selecting problems from
different universities and even different scientific cultures, the authors have
effectively avoided a one-sided approach to physics. All the problems are
good, some are very interesting, some positively intriguing, a few are crazy;
but all of them stimulate the reader to think about physics, not merely to
train you to pass an exam. I personally received considerable pleasure in
working the problems, and I would guess that anyone who wants to be a
professional physicist would experience similar enjoyment. I must confess
v
vi Foreword
with some embarrassment that some of the problems gave me more trouble
than I had expected. But, of course, this is progress. The coming generation
can do with ease what causes the elder one trouble. This book will be a
great help to students and professors, as well as a source of pleasure and
enjoyment.
Max Dresden
Stanford
It is only rarely realized how important the design of suitable, interesting
problems is in the educational process. This is true for the professor — who
periodically makes up exams and problem sets which test the effectiveness
of his teaching — and also for the student — who must match his skills
and acquired knowledge against these same problems. There is a great need
for challenging problems in all scientific fields, but especially so in physics.
Reading a physics paper requires familiarity and control of techniques which
can only be obtained by serious practice in solving problems. Confidence
in performing research demands a mastery of detailed technology which
requires training, concentration, and reflection — again, gained only by
working exercises.
In spite of the obvious need, there is very little systematic effort made
to provide balanced, doable problems that do more than gratify the ego of
the professor. Problems often are routine applications of procedures mentioned
in lectures or in books. They do little to force students to reflect
seriously about new situations. Furthermore, the problems are often excruciatingly
dull and test persistence and intellectual stamina more than
insight, technical skill, and originality. Another rather serious shortcoming
is that most exams and problems carry the unmistakable imprint of the
teacher. (In some excellent eastern U.S. universities, problems are catalogued
by instructor, so that a good deal is known about an exam even
before it is written.)
In contrast, A Guide to Physics Problems, Part 2 not only serves an
important function, but is a pleasure to read. By selecting problems from
different universities and even different scientific cultures, the authors have
effectively avoided a one-sided approach to physics. All the problems are
good, some are very interesting, some positively intriguing, a few are crazy;
but all of them stimulate the reader to think about physics, not merely to
train you to pass an exam. I personally received considerable pleasure in
working the problems, and I would guess that anyone who wants to be a
professional physicist would experience similar enjoyment. I must confess
v
vi Foreword
with some embarrassment that some of the problems gave me more trouble
than I had expected. But, of course, this is progress. The coming generation
can do with ease what causes the elder one trouble. This book will be a
great help to students and professors, as well as a source of pleasure and
enjoyment.
Max Dresden
Stanford
Preface
Part 2 of A Guide to Physics Problems contains problems from written
graduate qualifying examinations at many universities in the United States
and, for comparison, problems from the Moscow Institute of Physics and
Technology, a leading Russian Physics Department. While Part 1 presented
problems and solutions in Mechanics, Relativity, and Electrodynamics, Part
2 offers problems and solutions in Thermodynamics, Statistical Physics, and
Quantum Mechanics.
The main purpose of the book is to help graduate students prepare for
this important and often very stressful exam (see Figure P.1). The difficulty
and scope of the qualifying exam varies from school to school, but not too
dramatically. Our goal was to present a more or less universal set of problems
that would allow students to feel confident at these exams, regardless of the
graduate school they attended. We also thought that physics majors who are
considering going on to graduate school may be able to test their knowledge
of physics by trying to solve some of the problems, most of which are not
above the undergraduate level. As in Part 1 we have tried to provide as many
details in our solutions as possible, without turning to a trade expression of
an exhausted author who, after struggling with the derivation for a couple of
hours writes, “As it can be easily shown....”
Most of the comments to Part 1 that we have received so far have come not
from the students but from the professors who have to give the exams. The
most typical comment was, “Gee, great, now I can use one of your problems
for our next comprehensive exam.” However, we still hope that this does not
make the book counterproductive and eventually it will help the students to
transform from the state shown in Figure P.1 into a much more comfortable
stationary state as in Figure P.2. This picture can be easily attributed to the
present state of mind of the authors as well, who sincerely hope that Part 3
will not be forthcoming any time soon.
Some of the schools do not have written qualifying exams as part of their
requirements: Brown, Cal-Tech, Cornell, Harvard, UT Austin, University
of Toronto, and Yale. Most of the schools that give such an exam were
vii
viii Preface
happy to trust us with their problems. We wish to thank the Physics Departments
of Boston University (Boston), University of Colorado at Boulder (Colorado),
Columbia University (Columbia), University of Maryland (Maryland),
Massachusetts Institute of Technology (MIT), University ofMichigan
(Michigan), Michigan State University (Michigan State), Michigan Technological
University (Michigan Tech), Princeton University (Princeton),
Rutgers University (Rutgers), Stanford University (Stanford), State University
ofNewYork at Stony Brook (Stony Brook), University of Tennessee at
Knoxville (Tennessee), and University of Wisconsin (Wisconsin-Madison).
The Moscow Institute ofPhysics and Technology (Moscow Phys-Tech) does
not give this type of qualifying exam in graduate school. Some of their problems
came from the final written exam for the physics seniors, some of the
others, mostly introductory problems, are from their oral entrance exams or
Sidney Cahn
New York
Gerald Mahan
Oak Ridge
Boris Nadgorny
Washington, D.C.
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Saturday, 28 January 2012
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Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information free download
Acknowledgements
It is a great pleasure to thank the many people who have contributed to this
dissertation. My deepest thanks go to Dr. Mehdi Golshani, my professor, for
his moral and financial support through the years of my PhD, for his unfailing
positive attitude which remounted my morale more than once, for his understanding
and sympathy for my problems with my hands, and for being my guide
through the maze of quantum world. He has been a valued teacher, and I hope
my seven years at Sharif University have given me even a few of his qualities.
Special thanks go to Ali T. Rezakhani, my close friend, collaborator and
colleague, for his considerable influence on this dissertation. Much of the view
point mentioned here was worked out in valuable conservations with him.
Warm thanks to Dr. Alireza Z. Moshfegh for introducing me to experimental
physics, for our common works which are not part of this thesis, and for his moral
and financial supports through all years of my presence at Sharif University.
Thanks also go to Dr. Vahid Karimipour for his stimulating discussions
on quantum information theory, for reading this thesis and for his illuminating
comments.
I am thankful to Drs. Mohammad Akhavan, Mohammadreza Hedayati and
Majid Rahnama for reading this dissertation and for their valuable comments.
I would like to thank all my teachers, colleagues and friends for many useful
and instructive discussions on physics and life. I am grateful also to those who
are not mentioned by name in the following. In particular let me thank Drs.:
Hesam Arfaie, Farhad Ardalan, Reza Mansouri, Jalal Samimi, and Hamid Salamati
as teachers, and Saman Moghimi, Masoud M. Shafiee, Ahmad Ghodsi, Ali
Talebi, Parviz Kameli, Saeed Parvizi, Husein Sarbolouki, Mohammad Kazemi,
Alireza Noiee, Nima Hamedani, Farhad Shahbazi, Mahdi Saadat, Hamid Molavian,
Mohammad Mardani, Ali A. Shokri, Masoud Borhani, Javad Hashemifar,
Rouhollah Azimirad, Afshin Shafiee, Ali Shojaie, Fatimah Shojaie, Mohammad
M. Khakian, Abolfazl Ramezanpour, Sohrab Rahvar, Parvaneh Sangpour, Ali
Tabeie, Hashem H. Vafa, Ahmad Mashaie, Akbar Jafari, Alireza Bahraminasab,
Akbar Fahmi, Mohammad R. Mohammadizadeh, Sima Ghasemi, Omid Saremi,
Davoud Pourmohammad, Fredric Faure and Ahmad Mohammadi as colleagues
and friends.
I would also like to thank my teachers at Physics Department of Uroumieh
University who encouraged me to continue physics. Particularly, I thank Drs.:
Rasoul Sedghi, Mohammadreza Behforouz, Rasoul Khodabakhsh,Mostafa Poshtkouhi,
Mir Maqsoud Golzan, Jalal Pesteh, Shahriar Afshar, and Mohammad
Talebian.
There are also many people to whom I feel grateful and whom I would like
to thank at this occasion. Each of the following have in one way or another
affected this dissertation, even if only by prompting an explanation or turn of
phrase. I thank Drs.: Partha Ghose, Louis Marchildon, Ward Struyve, Willy
De Baere, Marco Genovese, Adan Cabello, Hrvoje Nikolic, Jean-Francois Van
Huele, Edward R. Floyd, Farhan Saif, Manzoor Ikram, Seth Lloyd, Vladimir E.
v
Kravtsov, Antonio Falci, Ehud Shapiro, Vlatko Vedral, Denis Feinberg, Massimo
Palma, Irinel Chiorescu, Jonathan Friedman, Ignacio Cirac and Paolo Zanardi.
I would like to thank Institute for Studies in Theoretical Physics and Mathematics
(IPM) for financial support of this thesis.
I also appreciate hospitality of the the abdus salam international centre for
theoretical physics (ICTP, Italy) where some part of this work was completed.
Thanks also go to the following people for a lot of beer: Parisa Yaqoubi, Edris
Bagheri, Khosro Orami, Vaseghinia, Yahyavi, Beheshti and Nicoletta Ivanissevich.
dissertation. My deepest thanks go to Dr. Mehdi Golshani, my professor, for
his moral and financial support through the years of my PhD, for his unfailing
positive attitude which remounted my morale more than once, for his understanding
and sympathy for my problems with my hands, and for being my guide
through the maze of quantum world. He has been a valued teacher, and I hope
my seven years at Sharif University have given me even a few of his qualities.
Special thanks go to Ali T. Rezakhani, my close friend, collaborator and
colleague, for his considerable influence on this dissertation. Much of the view
point mentioned here was worked out in valuable conservations with him.
Warm thanks to Dr. Alireza Z. Moshfegh for introducing me to experimental
physics, for our common works which are not part of this thesis, and for his moral
and financial supports through all years of my presence at Sharif University.
Thanks also go to Dr. Vahid Karimipour for his stimulating discussions
on quantum information theory, for reading this thesis and for his illuminating
comments.
I am thankful to Drs. Mohammad Akhavan, Mohammadreza Hedayati and
Majid Rahnama for reading this dissertation and for their valuable comments.
I would like to thank all my teachers, colleagues and friends for many useful
and instructive discussions on physics and life. I am grateful also to those who
are not mentioned by name in the following. In particular let me thank Drs.:
Hesam Arfaie, Farhad Ardalan, Reza Mansouri, Jalal Samimi, and Hamid Salamati
as teachers, and Saman Moghimi, Masoud M. Shafiee, Ahmad Ghodsi, Ali
Talebi, Parviz Kameli, Saeed Parvizi, Husein Sarbolouki, Mohammad Kazemi,
Alireza Noiee, Nima Hamedani, Farhad Shahbazi, Mahdi Saadat, Hamid Molavian,
Mohammad Mardani, Ali A. Shokri, Masoud Borhani, Javad Hashemifar,
Rouhollah Azimirad, Afshin Shafiee, Ali Shojaie, Fatimah Shojaie, Mohammad
M. Khakian, Abolfazl Ramezanpour, Sohrab Rahvar, Parvaneh Sangpour, Ali
Tabeie, Hashem H. Vafa, Ahmad Mashaie, Akbar Jafari, Alireza Bahraminasab,
Akbar Fahmi, Mohammad R. Mohammadizadeh, Sima Ghasemi, Omid Saremi,
Davoud Pourmohammad, Fredric Faure and Ahmad Mohammadi as colleagues
and friends.
I would also like to thank my teachers at Physics Department of Uroumieh
University who encouraged me to continue physics. Particularly, I thank Drs.:
Rasoul Sedghi, Mohammadreza Behforouz, Rasoul Khodabakhsh,Mostafa Poshtkouhi,
Mir Maqsoud Golzan, Jalal Pesteh, Shahriar Afshar, and Mohammad
Talebian.
There are also many people to whom I feel grateful and whom I would like
to thank at this occasion. Each of the following have in one way or another
affected this dissertation, even if only by prompting an explanation or turn of
phrase. I thank Drs.: Partha Ghose, Louis Marchildon, Ward Struyve, Willy
De Baere, Marco Genovese, Adan Cabello, Hrvoje Nikolic, Jean-Francois Van
Huele, Edward R. Floyd, Farhan Saif, Manzoor Ikram, Seth Lloyd, Vladimir E.
v
Kravtsov, Antonio Falci, Ehud Shapiro, Vlatko Vedral, Denis Feinberg, Massimo
Palma, Irinel Chiorescu, Jonathan Friedman, Ignacio Cirac and Paolo Zanardi.
I would like to thank Institute for Studies in Theoretical Physics and Mathematics
(IPM) for financial support of this thesis.
I also appreciate hospitality of the the abdus salam international centre for
theoretical physics (ICTP, Italy) where some part of this work was completed.
Thanks also go to the following people for a lot of beer: Parisa Yaqoubi, Edris
Bagheri, Khosro Orami, Vaseghinia, Yahyavi, Beheshti and Nicoletta Ivanissevich.
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