Book Description
It is a widely known but insufficiently appreciated fact that Albert Einstein and Kurt Goedel were best friends for the last decade and a half of Einstein's life. They walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German-Austrian science in which they had grown up. What is not widely known is that in 1949 Goedel made a remarkable discovery: there exist possible worlds described by the theory of relativity in which time, as we ordinarily understand it, does not exist. He added a philosophical argument that demonstrates, by Goedel's lights, that as a consequence, time does not exist in our world either. If Goedel is right, Einstein has not just explained time; he has explained it away.
Without committing himself to Goedel's philosophical interpretation of his discovery, Einstein acknowledged that his friend had made an important contribution to the theory of relativity, a contribution that he admitted raised new and disturbing questions about what remains of time in his own theory. Physicists since Einstein have tried without success to find an error in Goedel's physics or a missing element in relativity itself that would rule out the applicability of Goedel's results. Philosophers, for the most part, have been silent.
_A World Without Time_, addressed to experts and non experts alike, brings to life the sheer intellectual drama of the companionship of Goedel and Einstein, and places their discoveries -- which can only be measured on a millennial scale -- in the context of the great and disturbing intellectual movements of the twentieth century -- in physics, mathematics, logic, philosophy, and the arts. It contains, as well, a poignant and intimate account of the friendship between these two thinkers, each put on the shelf by the scientific fashions of their day -- and ours -- and attempts to rescue from undeserved obscurity the work Goedel did, inspired by Einstein, which made clear for the first time the truly revolutionary nature of the theory of relativity, which to this day is hardly recognized.
Customer Reviews:
more about philosophy than about physics or math.......2007-02-27
A World Without Time is a book about the friendship between Einstein and Godel that occurred toward the end of their lives. The friendship was fruitful in that Godel used Einstein's General Theory of Relativity to prove the existence of what are now called Godel Universes. Godel Universes are universes where time loops back on itself so, if you go sufficiently fast, you would end up back where you started in time. This is interesting but perhaps the most interesting aspect of the book for me was it's philosophical aspect. The author mentions the Vienna Circle and some concepts of philosophy such as positivism and ontology and epistemology which I found very interesting. I found the explanations of Godel's theories hard to follow but got the basic idea. I recommend this book for it's philosophical content. If you want to learn about Godel's Incompleteness theorem I recommend reading Godel, Escher Bach, An Eternal Golden Braid.
Should we dispense with clocks ?.......2007-02-12
The title of the book suggests time does not exist. The justification is a certain solution to Einstein cosmological equation, where the universe is rotating and time travel is possible. A path could reach into the past going around the universe.It is the Godel solution.
Modern cosmology is based on the Robertson Walker metric , or model,where there is a universal time. It fits the obseved universal expansion.The universe was born in a big bang fifteen billions years ago.
Goodel gave too much importance to his solution. After all any equation can allow many mathematical solutions which bear no relation to physical reality or fact.
The book is good reading with old and rare photos.It compelled me to reread "The Godel Solution" in Adler ,Bazin and Schiffer General Relativity.
Early in the century,Kurt Godel had laid a golden egg with his incompleteness theorem, pertaining to pure mathematics, causing some stir among Hilbert and Russell.But his attempt to abolish time, much later in 1949, felt in deaf ears among physicists and cosmologists.This is not about to change any time soon.
Yourgrau does an elegant work in rescuing an old story.It takes us through Europe and the beginnings of the Princeton Advanced Study Institute.
A World Without Time.......2007-01-23
Great book about Godel & Einstein. It tells much about their human side & their friendship. Does good job explaining some of their work.
Very bad book: a waste of your money.......2007-01-17
It is a heap op philosophy, not science. No formula, math, explanation, working examples whatsoever. Just small-talk to fill up the pages. This is NOT a physics book. I was lured into buying it thinking to get a complete textbook on Gödel's explanation of time. Forget it, this book is not worth your money. Go check the internet for PDF's or webpages containing the original publications of Gödel, they are there allright.
A World Without Time.......2007-01-04
I bought this book because I loved the cover. Everyone knows Einstein but it is amazing how few know the equally revolutionary Godel and still fewer know of their freindship. This is an invaluable book for those that (somehow) don't know about Godel's work. I didn't expect much from this book because I know of Godel's revolving universe time paradox. However, I found this book to be extremely interesting. The author's minimalist definition of Godel's theorm (syntax does not equal semantics) was worth the price alone. Unfortunatley the last chapter of the book is muddled in philosophic musings, since I am a Physicist I am less appreciative of pure philosophy.
Average customer rating:
- Schaum's Outline of Quantum Mechanics
- Very useful, needs a rewrite ...
- Best value for money
- Excelente libro de texto sobre Física Cuántica.
- Not great
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Schaum's Outline of Quantum Mechanics (Schaum's)
Eliahu Zaarur , and
Phinik Reuven
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ASIN: 0070540187 |
Book Description
This powerful study guide makes sometimes-daunting material accessible. More than 240 problems solved step-by-step help students gain a firm grasp of proper methods and a solid foundation for further study. All the essentials of this basic course are covered clearly and concisely, cutting study time and making important points memorable. The next-best thing to a private tutor, this study guide helps boost grades and proves ideal for professionals, too, who wish to study solo to master this discipline.
Customer Reviews:
Schaum's Outline of Quantum Mechanics.......2007-01-21
Basic information, and lots of problems (many worked out, others with answers). Makes for good practice and review.
Very useful, needs a rewrite ..........2006-11-19
This book is useful. There is a variety of problems from fairly easy to difficult, but in general, the problems are similar (and often the same) as problems in graduate texts such as Merzbacher, Cohen, etc.. My complaint with this book is not necessarily the typos (although they should be fixed given the popularity of this book). My complaint is that that the authors sometimes skip steps in the solutions that are so critical, that is is nearly impossible to understand them. A useful solution can leave out mathematical drudgery, and calculations, but it shouldn't leave out critical steps that have been covered earlier in the book, because a solutions manual like this is not usually used as a textbook, it is used as a reference.
For instance I may want to try a practice problem on the Variational Method, and the problem leaves out steps that may have been covered in earlier chapters. So I spend hours playing with the problem until I find the solution. This is not useful, and not what a problems and solutions book should do. I understand that not every step can be included, but I would rather see more complete solutions, which might sacrifice the unsolved problems and the blank pages at the end of the book.
This book seems to have been typewritten from the authors' handwritten notes, because many of the typos are consistent with penmanship. But one of the authors should go over all of the solutions, flesh out the missing steps, and correct the errors. Without doing this, the physics student can't rely on this book as a trusted source, since they never know if the error they encounter is a typo or their own mistake.
Regardless, this is a useful book, and I have learned a lot from it.
Best value for money.......2006-08-25
This book is a complete introductory course that presents the basic concepts of Quantum Mechanics.
As a newcomer to this subject, I was puzzled by the separate definitions of the similar notions of inner product (denoted
< , >), scalar product (denoted ( , )), scalar product (denoted
< | >) and Dirac bracket (also denoted
< | >). It would be most helpful if, in a future edition, the authors could define these four notions in one place, along with an explanation of the differences (if any) between them.
Apart from this minor annoyance, for which I deducted one star, this book succesfully tackles a most important and difficult subject. The writing and presentation are up to the usually high standards of Schaum's Outline series. There are plenty of exercises, both solved and unsolved. And it's excellent value for money. For the price, there's no serious competition.
A better mathematical treatment, based on linear vector spaces, may be found in "Principles of Quantum Mechanics" by Shankar.
Excelente libro de texto sobre Física Cuántica........2006-01-30
La mayoría de los textos de Física Cuántica que he leído, son inabordables en algunos momentos por la complejidad de la misma notación, falta de ejemplos directos de aplicación, y deficientes estructuraciones del contenido. El resultado es que finalmente te ves rodeado de una gran cantidad de libros de texto, para cubrir diferentes capítulos.
En cambio este libro, sobresale con holgura, cubriendo todas esas carencias.
* La estructura del libro es correcta.
* El número de ejemplos es muy amplio (como si no en un Schaum's).
* La notación es la que normalmente se utiliza en este campo.
¡ Qué más se puede pedir, en un libro de texto !.
Carlos Ortega
2006-01-30
Not great.......2006-01-28
I bought this book as I was taking undergraduate-level Quantum Mechanics. While it has a better review and analysis of bra and ket notation than, say, the Griffiths text, and has excellent applications (square well, energy levels, Landau Levels, etc.), it was practically useless until I finished the course. Additionally, as others have pointed out, the outline is riddled with errors. It is not as well-written as Murray Spiegel's Vector Analysis or Fourier Series books. If you're a graduate student or want a refresher course, I'd consider it. Otherwise, this is not the ideal choice.
Book Description
Why is the future so different from the past? Why does the past affect the future and not the other way around? What does quantum mechanics really tell us about the world? In this important and accessible book, Huw Price throws fascinating new light on some of the great mysteries of modern physics, and connects them in a wholly original way. Price begins with the mystery of the arrow of time. Why, for example, does disorder always increase, as required by the second law of thermodynamics? Price shows that, for over a century, most physicists have thought about these problems the wrong way. Misled by the human perspective from within time, which distorts and exaggerates the differences between past and future, they have fallen victim to what Price calls the "double standard fallacy": proposed explanations of the difference between the past and the future turn out to rely on a difference which has been slipped in at the beginning, when the physicists themselves treat the past and future in different ways. To avoid this fallacy, Price argues, we need to overcome our natural tendency to think about the past and the future differently. We need to imagine a point outside time -- an Archimedean "view from nowhen" -- from which to observe time in an unbiased way. Offering a lively criticism of many major modern physicists, including Richard Feynman and Stephen Hawking, Price shows that this fallacy remains common in physics today -- for example, when contemporary cosmologists theorize about the eventual fate of the universe. The "big bang" theory normally assumes that the beginning and end of the universe will be very different. But if we are to avoid the double standard fallacy, we need to consider time symmetrically, and take seriously the possibility that the arrow of time may reverse when the universe recollapses into a "big crunch." Price then turns to the greatest mystery of modern physics, the meaning of quantum theory. He argues that in missing the Archimedean viewpoint, modern physics has missed a radical and attractive solution to many of the apparent paradoxes of quantum physics. Many consequences of quantum theory appear counterintuitive, such as Schrodinger's Cat, whose condition seems undetermined until observed, and Bell's Theorem, which suggests a spooky "nonlocality," where events happening simultaneously in different places seem to affect each other directly. Price shows that these paradoxes can be avoided by allowing that at the quantum level the future does, indeed, affect the past. This demystifies nonlocality, and supports Einstein's unpopular intuition that quantum theory describes an objective world, existing independently of human observers: the Cat is alive or dead, even when nobody looks. So interpreted, Price argues, quantum mechanics is simply the kind of theory we ought to have expected in microphysics -- from the symmetric standpoint. Time's Arrow and Archimedes' Point presents an innovative and controversial view of time and contemporary physics. In this exciting book, Price urges physicists, philosophers, and anyone who has ever pondered the mysteries of time to look at the world from the fresh perspective of Archimedes' Point and gain a deeper understanding of ourselves, the universe around us, and our own place in time.
Customer Reviews:
What if?.......2007-05-15
"What if" is perhaps the most significant of all scientific questions because the speculation it causes can lead to remarkable insights.
Likewise, "what if" can also be the inspiration for great fiction as here where the author takes us on many a wild goose chase. While the goose chases aren't necessarily a waste of time, readers should be aware of them nonetheless.
First things first: to understand the physical basis for the arrow of time, we need to understand the basis of reality in which the arrow of time is housed. As currently understood, reality is a confluence of four physical forces:
1) Gravity -- exerted at the macroscopic level and greater consistent with the increasing size of the object in question;
2) Electromagnatism -- exerted macroscopically, it concerns the relationship between electricity and magnatism;
3) The srong nuclear force -- exerted microscopically at the subatomic level, it concerns the relationship between the constituent particles of the nucleus;
SO FAR ALL THE FORCES DESCRIBED ARE TIME SYMMETRICAL, IN OTHER WORDS, THEY OPERATE THE SAME WAY WHETHER ONE IS SEEKING TO UNDERSTAND THE NORMAL SEQUENTIAL PASSAGE OF TIME -- SO CALLED RETARDED TIME -- OR REVERSED TIME SO CALLED ADVANCED TIME.
4) The fourth currently understood fundamental force of nature -- the weak nuclear force -- which also operates microscopically at the subatomic level but relates to proton decay. Since 1957, we have been aware that this force is time asymmetric in that so called K particle decay (so called because the decay pattern in a bubble chamber resembles the letter K) operates in a fashion consistent with retarded time.
While one might think that a fundamental force of nature showing a selective prejudice for the type of time that we physically observe might merit some serious reflection, Price's response is to simply disregard the matter as being physically insignificant because the interactions happen on such a minute scale (viz. the subatomic realm).
In other words, by Price's reasoning the fact that after the Big Bang, matter only outnumbered antimatter by a measure of one billion and one particles to one billion would enable him to say that we live in an antimatter universe because the enumerated differences between the number of particles was so small.
While his discussion of quantum entanglement is fascinating, his insights invariably serve as yet another wild goose chase. Disdained by Albert Einstein as "spooky action at a distance" quantum entanglement is the phenomenon that exists wherein two particles become entangled with a similar subatomic signature. Amazingly, research has shown that regardless of the seeming physical distance between the particles, a change in the signature to one of them can cause a similtaneous change in the signature of the other.
While fascinating, follow up research has failed to show that any useful information can be communicated through this immediate process and therefore -- though interesting -- it doesn't defeat Einsteinian causality.
Indeed, properly understood, it best inspires us to better understand what locality really is when we discuss the quantum level...a discussion not significantly fostered by Price's speculations.
Probabaly a better -- though harder -- read on this topic is Deiter Zeh's Physical Basis for the Direction of Time.
Groundbreaking Evidence for Bicausality.......2006-09-06
TIME'S ARROW is a remarkably well-conceived exploration of the matter of bicausality. Author Huw Price applies a philosopher's logical approach to the physics of time, as he builds such a solid case for reverse time causality that he is influencing many of today's top physicists with his lucid exploration of the subject. TIME'S ARROW methodically presents information about time in a manner that will delight mathematicians, philosophers and physicists alike, in a book that is best read sequentially from beginning to end, in order to ensure full comprehension. This book is obligatory reading for anyone fascinated by time, or who is intrigued to discover what inspired Stephen Hawking in 2006 to write a physics paper on the subject of top-down cosmology... with the notion that the present is affecting the past.
On Price's "Time's Arrow and the Archimededs' Point".......2003-12-20
On page 13 of "Time's Arrow and the Archimededs' Point", Huw Price writes:
".... If time flowed - then as with any flow - it would only make sense to assign that flow a direction with respect to a CHOICE (my emphasis) as to what is to count as the positive direction of time. .... The problem is that until we have such an objective basis we don't have an objective sense in which time is flowing one way rather than the other. In other words, not only does it not seem to make sense to speak of an objective rate of flow of time; it also doesn't make sense to speak of an objective rate of time; it also doesn't make sense to speak of an objective direction of time."
There are a number of ways that the world we inhabit seems asymmetric in time. Price believes that these perceptions of asymmetry are due to way we see reality, and less how reality actually is. He reminds the reader of how humanity has struggled before with anthropocentrism. Seeing the second law of thermodynamics as an EXPLANATION of time's arrow is just another anthropocentrism.
On page 17, Price writes:
".... The leading candidate for the position (the master arrow) has been the so-called arrow of thermodynamics. This is the asymmetry embodied in the second law of thermodynamics, which says roughly that the entropy of an isolated physical system never decreases.... There is nothing to stop us taking the positive axis to lie in the opposite direction, however, in which case the second law would need to be started as the principle that entropy of an isolated system never increases.... It is not an objective matter whether the gradients really go up or down, for this simply depends on an arbitrary choice of temporal orientation."
On page 20, Price writes:
"... We unwittingly project onto the world some of the idiosyncrasies of our own makeup, seeing the world in the colors of the in-built glass through which we view it. But the distinction between these sources is not always a sharp one, because our constitution is adapted to the peculiarities of our region.... It challenges the image physics holds of itself as an objective enterprise, an enterprise concerned with not with how things seem but with how they actually are. It is always painful for an academic enterprise to have to acknowledge that it might not have been living up to its own professed standards!"
On page 39, Price writes:
"... It seems to me that the problem of explaining why entropy increases has been vastly overrated. The statistical considerations suggest that a future in which entropy reaches its maximum is not in need of explanation; and yet that future, taken together with the low-entropy past, accounts for the general gradient... The puzzle is not about how the universe reaches a state of high entropy, but about how it comes to be starting from a low one. It is not about what appears in our time sense to be the destination of the greater journey on which matter is engaged, but about the point from which - again in our time sense - that journey seems to start."
What Price is describing above is what has been referred to as the ready-state paradox (see Chapter 6 of David Albert's book "Time and Chance"). And Price is right in pointing out that many of our "explanations" seems to fall to our anthropocentrism, given that we start out by assuming what it is that we seek to prove by introducing a time asymmetric ASSUMPTION.
Our low entropy birth at the big bang is a boundary condition, and one does not use statistics and determinism to explain such a boundary condition. Boundary conditions are more generally brute force realizations that are beyond explanation. So if you think that the second law of thermodynamics can explain cosmic evolution, and perhaps even the evolution of life, then think again. Or you may go on a meaningless journey to find the first ready-state.
It is quite plausibly that the early boundary conditions are determined by the present, given that time flowing backward is as plausible as time flowing forward. This brings up the possibility of backward causation, something that Price writes much on. But boundary conditions relate to collective properties, something going against the trend of reductionism. And so backward causation may better apply from the whole to its parts, which mirrors reductionism as forward causation generally goes from parts to whole.
Price writes much on Gold's big bang and big crunch model of the universe, and he writes on alternative views too. Having navigated safely from the time-flow anthropocentrism, Price seems to have gotten himself snagged on a second anthropocentrism that we are isolated from everything else. It is true we may see ourselves as all knowing creatures that are competing for our survival in a lifeless pool of chaos we call our universe. But there is no objective basis for this belief (see Thomas Nagel's "The View from Nowhere"). It is just a possible that we are the forgetful universe reflecting hopelessly into the many egocentric bodies that are said to be all knowing. Are we the inside system or the outside system? The question is symmetrical, and cannot be answered. Then why do we answer it by projecting a Gold's universe onto reality by demanding a separate big crunch future that is just as likely as our big bang past?
A two aspect view of reality does not carry this unwanted anthropocentrism. It is that reality has an all knowing aspect that is perceived to be following the thermodynamic arrow, and the SAME reality holds a sublime shadow aspect where time is reversed from the present. In the sublime aspect the many celebrate as one, whereas in the forward aspect the one fragments into many.
The zone where the two aspects connect is the inexpressible core, where symmetries are broken and manifestation unfolds. It is the core where choices are made, and where creative tensions are released. I believe this two aspect model of the universe provides that best model that answers Price's concerns, and yet it does not demand that the future is locked into a big crunch as the evidence now suggests.
This two-aspect capacity to one reality is consistent with panpsychism, but Price does not mention this either. I mention it in my book, "Trinity":
Trinity: The Scientific Basis of Vitalism and Transcendentalism
OK but not the best.........2003-06-13
The author seems to go out-of-his-way to make this tome more obtuse and forbidding than it needs to be in order to present his theories.
The book is a decent supplement to other books on space/time theory but is indeed a very tedious read, and is more for the serious student than the casual reader who merely enjoys sampling divergent views on cosmologic concepts.
I certainly do not agree with the author on a number of points, but the publication is worth your while if you have the patience to slog through it, and it surely does afford some new perspective on the subject.
Philosopher sets the Physicists Straight on Time.......2001-08-24
In this book, Huw Price uses his advantage as a philosopher to show physicists where they're going all wrong on the big "what is time?" issue. I'm teasing, but while making some excellent points, Price does sound a little condescending sometimes. I wondered, while I read, if a physicist would find it merely amusing, or would be growling a bit. This book requires concentration just because he lays out intricate step-by-step explanations and arguments. Because the arguments are built logically, you can't afford to nap. He does indicate several times the chapters that could be skipped without losing his general points. The gist of his argument is this: We exist inside the system (that is, within the space-time continuum),we are deceived by that position into wrong conclusions. The solution he advocates is "Archimedes'point," that is, we should hypothesize a position outside the system,the "view from nowhere," and from there will come up with more accurate explanations of what's going on, in his opinion, that time really is non-directional. He makes some excellent points along the way, and certainly just the exercise of working through his arguments is good for the ol' brain, but some of his arguments and conclusions are invalid. The chief problem I see is; this time-space system has produced directional time perceiving agents like us. (It has produced really cumbersome directional arguments like his!) While our perspective is limited, I don't believe that it can be dismissed. It is a very big deal that beings like us exist in this universe. We can't pretend that the universe exists merely of little bits of matter knocking around. Theoretical physics does drift near the edge of the religious question, and I would have expected a philosopher to at least acknowledge that, while the "God question" is not subject to analysis, physics does at times seem to be working overtime simply to avoid a "prime mover."
Book Description
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth.
This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum field theory, and will be of interest to scientists in general relativity and related fields.
Average customer rating:
- Sweet
- Fascinating, yet complex.
- Requires understanding of physics
- Among the deepest, borderline-philosophical questions in modern physics is that of the origin and formation of the Universe.
- For some guys
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The Nature of Space and Time
Stephen Hawking , and
Roger Penrose
Manufacturer: Princeton University Press
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Amazon.com
Who doesn't love a good argument? When physics heavyweights Stephen W. Hawking and Roger Penrose delivered three sets of back-and-forth lectures capped by a final debate at Cambridge's Isaac Newton Institute, the course of modern cosmological thinking was at stake. As it happens, The Nature of Space and Time, which collects these remarks, suggests that little has changed from the days when Einstein challenged Bohr by refusing to believe that God plays dice. The math is more abstruse, the arguments more refined, but the argument still hinges on whether our physical theories should be expected to model reality or merely predict measurements.
Hawking, clever and playful as usual, sides with Bohr and the Copenhagen interpretation and builds a strong case for quantum gravity. Penrose, inevitably a bit dry in comparison, shares Einstein's horror at such intuition-blasting thought experiments as Schrödinger's long-suffering cat--and scores just as many points for general relativity. The math is tough going for lay readers, but a few leaps of faith will carry them through to some deeply thought-provoking rhetoric. Though no questions find final answers in The Nature of Space and Time, the quality of discourse should be enough to satisfy the scientifically curious. --Rob Lightner
Book Description
Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor's New Mind and Shadows of the Mind)--disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.
How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?
In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.
Customer Reviews:
Sweet.......2007-04-05
The complexity of space and time easily transcribed, though a more laymens terms kind of explaination would have been more interesting.
Fascinating, yet complex........2007-02-23
I found this to be a fascinating overview of some of the major issues in cosmology from both Hawking and Penroses point of view. What is amazing is the actual level of agreement between the two. Perhaps only the real physicists appreciate the nuances of their differences of opinion.
I would recommend this book for anyone who's gone to the trouble of picking up a basic understanding of relativity ( special and/or general ).
The math is not terrbily daunting in most places and you get a real overview for the big picture of the state of relativity and quantum gravity.
Requires understanding of physics.......2007-01-19
To really appreciate this book requires an understanding of physics. Not the superficial stuff where you still believe that Newton was right, but Quantum Mechanics, Topology, and General Relativity.
Among the deepest, borderline-philosophical questions in modern physics is that of the origin and formation of the Universe........2006-08-22
Earlier attempts to formulate an answer that takes into account existing theories and observations have failed because of obstacles posed by gravity. The Nature of Space and Time pitts two heavy weights trying to provide a loop quantum gravitational model that successfully merges current ideas, and which may enable us to overcome such difficulties. Stephen Hawking shot to fame in the world of physics when he provided a mathematical proof for the Big Bang theory. This theory showed that the entire universe exploded from a singularity, an infinitely small point with infinite density and infinite gravity. Hawking was able to come to his proof using mathematical techniques that had been developed by Roger Penrose. These techniques were however developed to deal not with the beginning of the Universe but with black holes.
Science had long predicted that if a sufficiently large star collapsed at the end of its life, all the matter left in the star would be crushed into an infinitely small point with infinite gravity and infinite density...a singularity. Hawking realized that the Universe was, in effect, a black hole in reverse. Instead of matter being crushed into a singularity, the Universe began when a singularity expanded to form everything we see around us today, from stars to planets to people. Hawking realized that to come to a complete understanding of the Universe he would have to unravel the mysteries of the black hole.
Hawking and his fellow physicists embarked on an extraordinary intellectual expedition to tame the black hole. Slowly physicists were coming to understand this most destructive force of nature. But Hawking realized that there was something missing from the emerging picture. All work on black holes to that point used the physics of the large-scale Universe, the physics of gravity first developed by Newton and then refined by Einstein's theories of general and special relativity. Hawking realized that to come to a full understanding of black holes, physicists would also have to use the physics of the small-scale Universe, (the physics that had been developed to explain the movements of atoms and sub-atomic particles, known as quantum mechanics.) The problem was that no one had ever combined these two areas of physics before. But that didn't deter Hawking. He set about developing a new way to force the physics of quantum mechanics to co-exist with Einstein's relativity within the intense gravity of a black hole.
After months of work Hawking came up with a remarkable result. His equations were showing him that something was coming out of the black hole. This was supposed to be impossible. The one thing that everyone thought they knew about black holes was that things went in but nothing, not even light itself, could escape. But the more Hawking checked, the more he was convinced he was right. He could see radiation coming out of the black hole. Hawking then realized that this radiation (Hawking Radiation) would cause the black hole to evaporate and eventually disappear. Although Hawking's theories about black hole evaporation were revolutionary, they soon came to be widely accepted. But Hawking knew that this work had far more fundamental consequences. In 1976 he published a paper called 'The Breakdown of Predictability in Gravitational Collapse'. In it he argued that it wasn't just the black hole that disappeared. All the information about everything that had ever been inside the black hole disappeared too.
There are limits to what science can know. For many years no one took much notice of Hawking's ideas until a fateful meeting in San Francisco. Hawking presented his ideas to some of the world's leading physicists. In the audience were Gerad t'Hooft and Leonard Susskind, two leading particle physicists. They were shocked. Both realized that Hawking's 'breakdown of predictability' applied not only to black holes but to all processes in physics. According to Susskind, if Hawking's ideas were correct then it would infect all physics, there would no longer be any direct link between cause and effect. Physics would become impotent. Since that meeting arguments effectively boiled down into two camps. On the one side were Susskind and those who believed that Hawking was wrong: information could not be lost. On the other were Hawking and those who believed that physics would have to be rewritten to take into account the uncertainty about information that Hawking had uncovered. Until a paper emerged by a young mathematician Juan Maldacena. It claimed to be a rigorous mathematical explanation of what happened to information in black holes. It showed that information was not lost. Hawking, it seemed, was on the losing side. But he was not convinced. Hawking set to work with a young research student, Christophe Galfard, to try to pick apart the Maldacena paper. They thought they could use the same mathematical techniques employed by Maldacena to prove that information was in fact lost. But after two years they still could not prove their thesis.
Hawking was soon back at work, working on a new proof for the information paradox. But he was to defend his long held belief that information was lost in black holes, instead he claimed that he could now prove the opposite. Hawking presented the outline of proof that he hoped would at last solve the problem that he had posed almost 30 years earlier. But despite the bold claims, some physicists remain unconvinced. Over a year has passed and he has still not presented a fully worked mathematical proof to back up his ideas. But Hawking is a stubborn man. If Hawking is going to change his mind on a view he held for almost 30 years then it will be with his own proof, in his own time. In spite of failing health and increasing problems communicating with his colleagues, he is still working on the proof. If he succeeds in completing a proof that convinces his colleagues, he will not only have solved one of the most difficult problems in physics but he will have managed to have produced ground breaking work at the very end of his career. A feat that even his hero Einstein could not accomplish. If not, Hawking will have inspired some future physicist, who will eventually complete the paradox and answer the question 'What happened before The Big Bang?'
--B.D.
For some guys.......2006-08-07
The subject and the contents of this book is very interesting. However, you have to know quite a lot mathematics .....
Far above my level!
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The Quantum Structure of Space and Time: Proceedings of the 23rd Solvay Conference on Physics Brussels, Belgium 1-3 December 2005
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Customer Reviews:
A fascinating and worthy addition to new age and modern-day magic shelves.......2007-07-10
Space/Time Magic is a metaphysical studies guide to taking control of the complex probabilities of one's life. Chapters describe how to use sigils to manifest multiple probabilities; how to use the DNA spiral to explore space/time; writing as a divination practice; how to use technology to enhance space/time workings; and much more. Space/Time Magic literally lives up to its title in its study of mystical practices that affect the four dimensions, and its down-to-earth terminology makes in accessible to readers of all backgrounds. "In magic, particularly results magic, there is a tendency to expect that the result will occur now. This tendency is dangerous, showing as it does that you've fallen into the brainwashing of linear time. No result can be measured as occurring at a specific moment of time, and to try to limit magic in such a manner is ultimately to emasculate your workings. Everything, and this includes magic, happens in its own time." A fascinating and worthy addition to new age and modern-day magic shelves, featuring step-by-step exercises after each chapter.
Excellant!.......2007-04-18
I thoroughly enjoyed this book. The author provides theories from different points of view to explain how the magic works and lots and lots of practical exercises. He details what he has done and how it has turned out, but encourages the reader to take what he has done and build on it. He provided ideas that I would not have thought of; practices that can easily be added to anyone's daily routine. And he can write! I have purchased a few books from other authors in this genre and not all can.
Space Time Magic - and then some.......2007-02-20
(Before the review - a disclaimer. I do know the author.)
The book essentially has three themes to it:
1) Magic involving time and space/time such as retroactive magic, time manipulation, divination, and soforth.
2) Concepts and activities that involve our space, time, and space/time ideas, activites, and interpretations.
3) The direct, practacal application of #1 and #2 and how the author did them, often with detailed information.
Therefore Space/Time Magic is probably best thought of as "Space/Time Magic, Space/Time Concepts, and A Whole Lot of Other Stuff." The amount of useful ideas-per-page is extremely high and the repetition of common (or just plain over-repeated information) is extremely low. This is a book that takes difficult concepts, and shows how to apply them, often with direct author's testimony.
However, the book does suffer from times of loosing focus, or introducing techniques that may be useful for space/time work, but aren't as relevant as, say, other elements of the book. This doesn't reduce its usefullness, but it can be distracting.
Space/Time Magic is a book of experimental magic. There's no repetitive correspondence tables or things you've seen before. Though you can apply the work and ideas with surprising ease, its not Magic 101 despite its friendliness.
Magickal applications of quantum mechanics.......2006-11-18
Quantum mechanics is well and truly in the public consciousness these days, largely due to the success of the movie "What the Bleep Do We Know!?" This movie opened the eyes of viewers to the incredible possibilities available. The obvious question those viewers should have asked themselves is how they could go about taking full advantage of the possibilities.
Quantum mechanics provides an explanation for much of what is experienced while practicing magick, in particular that pertaining to the non-linearity of time. Many of the ancients viewed time as circular, while quantum mechanics assigns probabilities to various events.
Taylor takes the reader into a quantum world, where time is non-linear, and retroactive magick is possible. The concept of retroactive magick is fascinating. Taylor deals with the importance of perception defining our reality, and presents this as one of the keys to successful retroactive magick. This to me is probably the most exciting portion of the book as just about everyone has daydreamed about how they would have done things differently with the benefit of hindsight. The possibility of revisiting the past is truly exciting.
As with "Pop Culture Magic," I certainly don't accept everything that Taylor writes in this book. His ideas however, are intriguing, and certainly merit further investigation. Readers will certainly be able to adapt Taylor's ideas into their own paradigms. Taylor's message is an exhortation to leave the confines of the mainstream and experiment, and it is a message well worth sharing.
Space/Time, not for beginners.......2006-05-06
I'm with Lupa, I know Taylor from our many conversations and his posts on his blog.
I've allways been interested in space/time magick since about 2001 and ever since reading Taylor Ellwood's Space/Time magick I think I've found someone who has come to very similar conclusions.
However, I would like to put a side warning that this book is definately not for people who are used to the pop-wicca books that are mostly just regurgitated from some source like Raymond buckland or even Aleister Crowley. These ideas are very advanced, assuming that the person already knows most of the fundimentals of magick, however for some though, these other ideas could be manipulated and 'simplified' for most people.
I think though, the most of what I got out of this was a refreshingin of my own (what I call) reality warping experiments, and made me remember to think nonlinearly when working magick and when working space/time magick.
Definately recomend for others.
Amazon.com
How many dimensions do you live in? Three? Maybe that's all your commonsense sense perception perceives, but there is growing and compelling evidence to suggest that we actually live in a universe of ten real dimensions. Kaku has written an extraordinarily lucid and thought-provoking exploration of the theoretical and empirical bases of a ten-dimensional universe and even goes so far as to discuss possible practical implications--such as being able to escape the collapse of the universe. Yikes. Highly Recommended.
Book Description
Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe.
Customer Reviews:
Really loved this one.......2007-09-23
I'm not a scientist (I'm a classicist) and didn't even enjoy science in school at all. In fact until writers like Michael Behe, Heinz Pagels and Michio Kaku came along science was totally unapproachable for me. For a writer to take such incredibly complex information and present it, not only clearly and understandibly, but also enjoyably, one has to be uniquely gifted. Kaku and Behe can do this and remain my favorites. It's been years since I read this and to this day I can't forget it. So, here's my point. If you, like me, long to understand fascinating ideas that have always seemed incomprehensible, let Michio Kaku help you out. Get this one.
Getting A Handle On the Universe.......2007-08-03
Even though this book is over ten years old, it has paved the way to understanding a little bit more about this universe, prallel universes, ten dimensions and even time warps. Shades of Star Trek and Star Wars!
It's wonderful! Kaku stretches the mind and for a lay person an easy read.
Kaku gives a greater insight into quantum physics without the long equations. I recommend it. Bettye Johnson, award-winning author, Secrets of the Magdalene Scrolls.
Excellent Intro to a Difficult but Fascinating Topic .......2007-06-19
This book has been around for more than a decade now, and while some of the material within is a bit dated, the general principles are very accessible through Kaku's writing style. I'd still highly recommend this book as a good introduction to string theory for the layman.
Once you finish Hyperspace, then I would recommend Brian Greene's The Fabric of the Cosmos: Space, Time, and the Texture of Reality and after that Lisa Randall's Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. Of course, The Elegant Universe is a good intro as well, but your can rent the DVD.
No matter which other books you choose to read, Michio Kaku's Hyperspace is a necessity, because he mentions things you won't hear elsewhere.
Fascinating and challenging.......2007-05-13
Wow, this book was just plain fun to read. Better yet, it was not dumbed down in any way, yet it was completely understandable. This world of cutting-edge physics is not just interesting, but also important. It really makes one wonder what is possible if we can ever solve these last mysteries of physics. I particularly thought he explained higher dimensions well. It's a very difficult idea for us 3 dimensional beings to wrap our heads around, but he manages to give a thorough and convincing explaination. You won't regret buying this book, you'll blow right through it and be telling all your friends about the crazy things you learned about hyperspace.
A Good Book For An Intro To String Theory.......2007-04-27
Once again, Dr Kaku has produced an informative yet accessible book on modern physics. Although this isn't up to date on the latest developments in strings and M theory, the reader isn't likely to be looking for the latest technical findings and conjecture. If what you're seeking is an interesting and absorbing account of this intriguing but untested field, then this is probably the first book you should read on the subject. What makes string theory so fascinating is that it is following the same sequence as previous breakthroughs in physics: a concept is thought out, found to be mathematically consistent, a model is developed, and finally, testing confirms the model. String theory (M theory) has progresssed to the model stage, but we currently lack the technical means to test that model. But the fact that the numbers are in agreement makes it look promising.
Don't be concerned about the math, though. The book mentions some mathematicians and their contributions, but the reader isn't required to get out his pocket calculator to follow along. The book is 99% fact and science, in popular form, and about 1% interesting speculation on what the model implies, if it's accurate. And those implications are stunning: parallel universes, possibly infinite in number, with every conceivable permutation of reality, and many more beyond our comprehension.
Book Description
In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
Customer Reviews:
A great intermediate level book........2007-02-16
We all get an initial taste of relativity in Freshman/Sophomore physics. But where to go next can be a problem. If you like the math accompanying your physics a bit more rigorous than "hand waving", this is a great book. I tried Schutz's book but didn't find the math self contained or rigorous, while trying to jump into Wald's graduate level text on General relativity was way too much to soon. This book strikes a good balance between the physics and the math. Nice coverage of the Lorentz transformation and the invariance of Maxwell's equations under it. Minkowski space time and "hyperbolic" geometry (nice review of hyperbolic functions in analogy with trigonometric functions). And a self contained introduction to differential geometry (as applied to general relativity). I'm finding this great for self study.
Great for learning how to actually use the math behind GR.......2004-07-31
This book is great for teaching the math behind GR using excellent examples from Math and Physics problems (for another great problem solver see also Schaum's Outline of Tensor Calculus, but this has less Physics). It is a bit long winded, spending alot of time on SR and in some place just over the top (for Physicists!), but once through it there should be no problem going to the more advanced texts which deal with more of the uses of GR. At the same level I would also recommend Schutz's First Course in GR, however, Callahan's book goes through and explains the use of the math better, whereas Schutz's is better for uses in GR, surprisingly this is the strength of Callahan's book: you can't really do the Physics properly unless you can do the math! After this it's on to more Physics orientated books like Carroll's excellent Introduction to GR, as a stepping stone to MTW's Gravitation and Wald's GR.
One of the best........2001-08-06
This is one of the best introduction to General Relativity. It is the most accessible introduction to differential geometry. Naturally you have to know calculus, linear algebra, and the basics of special relativity. I bought many books on the subject, and this one belengs to the set I suggest for self-learning.
Disappointing.......2001-04-15
I've only read the first third in detail, but so far this book is frankly disappointing. The treatment is lightweight and padded out with verbiage, some of it oddly off-key. What math or physics student at this level needs (for example) an elementary account of the properties of hyperbolic functions? Spacetime diagrams are drawn with the time axis horizontal, which is something I've never seen in any other relativity text. Okay, it's a minor point, but I found this and similar nonstandard usages a constant irritant. More seriously, the development of relativistic momentum and covariance in chap.3 is quite incoherent, and the definition of 4-velocity is WRONG (at least, by everyone else's standards - it isn't even a 4-vector). There are plenty of exercises, which is good, but no solutions at all - not even outlines - which is not so good.
The book takes over three hundred pages to get to general relativity (where there seems to be no mention of the equivalence principle!), and I doubt if it's worth the effort. You would do better to work through Foster & Nightingale's 'Short Course in General Relativity', which is a first-rate and accessible introduction if you have a little background in special relativity. And it's two-thirds the price.
Conclusion: There may be a good book waiting to be written on these lines, but I'm sorry to say this isn't it. I wouldn't recommend it to anyone as a first course in relativity.
this book.......2001-04-01
At times this book can be confusing, often the author will make something unclear by leaving out a simple sentence or two. I can't really compare it to other texts- although i've looked through many this is the first I tried to actually learn from, but as far as a textbook goes it's not the greatest. In many places once you figure what he's trying to say, you also realize that an added sentence or step or justification would've made it far easier to understand.
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