5 comments about The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics).

1. This book of Stephen Hawking is the more elegant one on modern General Relativity and is my favorite book. It covers in brilliant form the gravitational collapse of a star, the theory of black holes, the space-time singularities, the causal structure of space-time, and in its end the initial singularity of the universe, popularly known as the Big Bang. The book is highly mathematical, and is pressuposed that the reader have studied basic abstract algebra and point set topology. But, for the readers highly interested in these subjects(as I am), this is not a obstacle. All theoretical physicists interested in modern General Relativity should have this book, a testimony of the Genius of Stephen Hawking. Definitively, a magnific book.



2. Don't be mislead by Hawking's popular works, this is a book by a mathematician written for mathematicians. Unless you studied mathematics to at least graduate level (you need to understand vector calculus, vector spaces and tensors to get anywhere) you are unlikely to get much from this book. Even then to read it at anything other than the most superficial level is very hard work. However even at the superficial level it gives one insights into some interesting aspects of general relativity.



3. The early seventies saw a revolution in cosmology; for the first time, modern mathematical methods were applied to the discipline, with intriguing results. This book was (along with Penrose's articles) the seminal work in global general relativity. Often overlooked is that the first half of Hawking & Ellis is devoted to traditional GR via the tensor calculus, and the q-form conception. However, trying to learn GR with this volume is not recommended (instead, cf. D'Inverno). The meat-and-potatoes of the book is the discussion of gravitational collapse, and the singularity theorems. They provide us with intuitively good reasons for believing in some very strange phenomenon. If you're interested in the frontiers of modern science, and have the appropriate mathematical background, this book cannot be recommended too highly. The little yellow book stands supreme in the hierarchy of works of modern physics.



4. This book is now a classic and is written by two giants in mathematics and physics. It wil be used for many years to come and is certainly one of the most widely quoted in the subject.

   The authors begin the book by a discussion of the role of gravity in physics and its role as determining the causal structure of the universe. They introduce the idea of a closed trapped surface, setting the stage for the goal of the book, namely the study of the conditions under which a space-time singularity must occur. Black holes and the beginning of the universe are cited as examples of these singularities. The authors also outline briefly the content of each chapter. A neat argument is given for the significance of focal points via the use of Raychaudhari's equation.

   The second chapter is an overview of the background in differential geometry needed in the rest of the book. Although complete from an axiomatic point of view, the approach is much too formal for readers who do not have a knowledge of differential geometry. Such a reader should gain the necessary background elsewhere.

   General relativity as a theory of gravitation is discussed in chapter 3. Spacetime is assumed to be a connected 4-dimensional smooth manifold on which is defined a Lorentz metric. The topology is assumed to be Hausdorff. Some of the more interesting or well-written parts of this chapter include the example of a spacetime that is not inextendible, the determination of the conformal factor for the spacetime metric, and the discussion of alternative field equations.

   The authors discuss the physicial significance of curvature in chapter 4, namely its effect on families of timelike and null curves. The most important part of this chapter is the discussion on certain inequalities tht the energy-momentum tensor should satisfy from a physical viewpoint. These inequalities, called the weak energy condition and the dominant energy condition, allow the authors to prove the existence of singularities in a later chapter. The reader can see clearly the role of the Jacobi equation, and its solution, the Jacobi field, in measuring the separation of nearby geodesics. The existence of conjugate points is proven, and shown to imply the existence of self-intersections in families of geodesics. As a warm-up to showing the non-existence of geodesics of maximal length, the authors employ variational calculus to study how to vary non-spacelike curves connecting points in convex normal neighborhoods in spacetime, and between points and hypersurfaces. In particular, it is shown that a timelike geodesic curve from a hypersurface to a point is maximal iff there is no conjugate point to the hypersurface along the curve. In addition, the authors prove that two points joined by a non-spacelike curve which is not a null geodesic can be joined by a timelike curve.

   The authors consider the exact solutions of the Einstein field equations in chapter 5. Most of the "usual" spacetimes are considered, including Minkowski, De Sitter, Anti-de-Sitter, Robertson-Walker, Schwarzschild, Reissner-Nordstrom, Kerr, Taub-Nut, and Godel. The emphasis in on the global properties of the spacetimes and the existence of singularities in them. The famous Penrose diagrams are used to "compactify" spacetimes in order to study their behavior at infinity and their conformal properties. The authors first introduce the concept of a future (past) Cauchy development here, so important in later developments in the book. The reader can see the tools developed in chapter 4 in play here; for example, the existence of a singularity in a spatially homogeneous cosmology is shown to follow directly from the Raychaudhuri equation. The existence of the singularity is proved to be independent of any acceleration or rotation of matter in such cosmologies.

   In chapter 5, the authors consider the causal structure of spacetime, namely the study of its conformal geometry. The consideration of the set of all metrics conformal to the physical metric allows one to discuss "geodesic completeness" of spacetime, this concept forming the basis of a later definition of a singularity in spacetime. The more interesting topics discussed in this chapter include the causality conditions (there are no closed non-spacelike curves), and the Alexandrov topology and its connection with the strong causality condition (every neighborhood of a point contains a neighborhood of the point no non-separable curve of which intersects it more than once). When strong causality does hold, the Alexandrov topology is equivalent to the usual manifold topology, and thus the topology of spacetime can be determined by the observation of causal relationships. The discussion on the role of global hyperbolicity in showing the existence of a maximal geodesic is also very well-written.

   The next chapter is pretty much independent of the rest, and was put in no doubt for the mathematician who desires to understand the Einstein equations as a set of nonlinear second-order hyperbolic partial differential equations with initial data on a 3-dimensional manifold, the famous Cauchy problem in general relativity.

   Chapter 8 is the most important in the book, for its uses the constructions of earlier chapters to define the notion of a singularity in spacetime. The authors argue that singularities are points where physical laws break down and thus to characterize them one attempts to find out whether any such points have been removed, making spacetime "incomplete" in some sense. Such a notion of incompleteness is very meaningful in topological spaces with a positive definite metric, since in that case one can define completeness in terms of the convergence of Cauchy sequences. In spacetimes with a Lorentz metric, the authors discuss the notion of geodesic completeness for null and timelike geodesics. A very detailed treatment of the now famous singularity theorems is given, these theorems involving an inequality of the Ricci tensor. The last two chapters of the book are more physical in nature wherein the singularity problem is shown to have physical relevance via the occurence of black holes at the endpoint of evolution of massive stars.




5. I think that this book has great depth, and is one of the best Stephen Hawking books I have read. My favourite remains 'A Brief History of Time', but still this book is extremely excellent. My compliments to the chef.

5 comments about Einstein and Religion: Physics and Theology.

1. I think Jammer does us a fine service by writing a book about a subject that is too often neglected. Not that Einstein's religious views were ever unknown, but it is surprising that this seems to be the first book devoted to this subject.
   
   The exchanges between Einstein and Rabbi Geller are for me an important new piece of information (see pp. 85-86), as is Einstein's denial of free will in his letter to Besso (p. 87). But interestingly, Jammer neglects to mention Einstein's letter to Otto Juliusburger, who in 1946 tried to assess Hitler's responsibility for the Holocaust. Einstein's reply would not now be considered politically correct (at least in Jammer's Israel): "You take a definite stance on Hitler's responsibility... Objectively, there is after all no free will. What need is there for a criterion for responsibility?" Einstein was of course a sworn enemy of Hitler (and so should he be). But this statement is so amazing that I think Jammer was wrong to omit it. He should have quoted this statement, while emphasizing that Einstein blamed Hitler and the Germans for their evil deeds and he never forgave them. (Most of these quotes, especially if from private letters, are kept in the multi-volume "Collected Papers of Albert Einstein" published by Princeton UP and the Hebrew University of Jerusalem.)
   
   In one of the more interesting quotes in this book, Einstein believed quantum mechanics has no practically relevant impact on his deterministic view of life-events. But in this connection Jammer fails to mention how Bohr's complementarity could be applied to Einstein's determinism with satisfactory results - even though Jammer has a third of the book devoted to speculation about how science now affects philosophical and religious matters. (Despite this, there are some important Einstein quotes in this chapter as well.)
   
   It is obvious that Einstein rejected the notion that quantum uncertainty undermines his denial of free will because he rejected quantum mechanics itself. Jammer points out that Einstein was wrong about locality, which was one of his main objections to quantum mechanics. Jammer cites Bell's theorem (p. 226) and the Aspect experiments as proving nonlocality, and claims that Einstein's belief in locality and his determinism are two basic tenets of his philosophy, as they indeed appear to be. But Jammer's implication seems to be that if Einstein got locality wrong, perhaps he was completely wrong about quantum mechanics, hence about quantum uncertainty, thus about determinism, thus about...his denial of free will? In other words, if Einstein was wrong about locality, he might have been wrong about determinism too. If Einstein was mistaken about one basic tenet of his philosophy, what makes us think he was right about the other? What Jammer fails to realize is that it was John Bell himself who said that strict determinism could well be the only way to make nonlocality compatible with all those horrible paradoxes like faster-than-light signals which contradict Special Relativity. In Bell's opinion, Einstein might have been wrong about nature being local, but strict determinism of which Einstein was always convinced might not be wrong after all. This is such an important point that I think Jammer should have discussed it, especially in Chapter 3, where he discusses his (Jammer's) own views on Einstein's philosophy.
   
   On a more trivial note, Jammer is wrong that Einstein picked up his denial of the freedom of the will from Spinoza. The fact is, Einstein got this idea first from Schopenhauer, then from Hume, and only later from Spinoza. I was disappointed how Jammer has throughout this book neglected the importance of Schopenhauer and Hume in Einstein's philosophical and religious development. I would agree though that Einstein's "cosmic religion" came from Spinoza.
   
   Jammer is at pains to emphasize that he doesn't proselytize or paddle any religious or sectarian viewpoints. He succeeds in this regard, in my opinion. What he does clearly try to convey, though, is the impression that religion in general and science are not in conflict, and he quotes Einstein's facetiously ambiguous statement "Science without religion is blind; religion with science is lame" (or something to this effect) to prove this point, almost ad nauseum. I'm not sure Jammer has convinced me. But Einstein's statements about religion are often ambiguous and confusing enough to provide plenty of material for someone with a secret ax to grind to quote from. On the other hand, Einstein was quite adamant and clear in (1) his determinism, (2) his denial of the immortality of the soul (which Einstein did not believe exist apart from the brain), and (3) his denial of a personal God. Jammer does a good job of faithfully reporting these views. This is not as easy a task as it seems, because (1) clearly conflicts with the deeply held beliefs of most people and the basic dogmas of Christian, Catholic, and Jewish religions; because (3) conflicts with all major religions excepting Buddhism; and because (2) conflicts with ALL religions, past and present. So I think Jammer has shown his competence here.
   
   A "B-" effort. I hope someday someone will come up with an even better one. Right now this is the best we have.



2. I think Jammer has not done a thorough enough job on Einstein's denial of free will. I have many books on and about Einstein and I know of many instances in which he made his strict determinism clear. Here is room for improvement.
   
   Jammer is wrong to imply that Einstein's initial belief in a static universe was the result of reading Spinoza. The fact is, many scientists at the time believed in a static universe, and probably most of them had never read Spinoza. Indeed, when Hubble showed that our universe was (and still is) expanding, the scientifc community was taken by surprise. I don't think Spinoza had anything to do with this.
   
   Jammer has said little about the importance of Hume and Schopenhauer to Einstein's philosophical and scientific views. This is a mistake. Hume and Schopenhauer were at least as important to Einstein as Spinoza. The neglect of Schopenhauer may have something to do with the philosopher's antisemitism. But Schopenhauer remained Einstein's favorite philosopher. In his study Einstein had pictures of Newton, Maxwell, Faraday, and Schopenhauer - the sole philosopher of the lot. Einstein quoted from him often on a wide range of subjects. If Schopenhauer was an antisemite, that's because he was such a misanthrope. In fact, he disliked Germans even more (and he was one of them).
   
   I agree that locality and determinism were two of Einstein's fundamental beliefs. Jammer reports with glee that locality has been proven wrong. So therefore determinism may also be wrong, he seems to imply. But according to John Bell, nonlocality may actually prove strict determinism to be right! (I don't believe Einstein was wrong about determinism as an objective fact, even though his interpretation of quantum mechanics may be wrong. The fact is, Heisenberg uncertainty shows up only during measurements; isolated systems are strictly deterministic. Of course, no one knows where this uncertainty comes from - hence the mystery.)
   
   I think that on the whole this book is good. But Jammer places far too much emphasis on Einstein's "Religion without science is blind; science without religion is lame" as though this remark, probably made tongue in cheek, summarized Einstein's religious views. I doubt it. Even if it does, this by no means imply this is an unassailable truth. Steven Weinberg believes that science and religion are antagonistic, one representing knowledge, the other representing ignorance. I agree with Weinberg.



3. Do not be deceived by the welcoming jacket on this book. This is primarily an academic text.
   
   The subtitle is "physics and theology" and not the other way around. This may be deliberate, because although the book actually starts with an emphasis on theology it evolves (or devolves, depending on your perspective) into a treatise on advanced physics.
   
   Despite Jammer's sometimes ackward English and despite the fact that portions read like a master's thesis in philosophy - the book is most accessible on the theological side. The reader gets insight into the spiritual side of Einstein. Jammer shows conclusively that Einstein did believe in God and does a reasonably good job presenting the philisophical underpinnings of Einstein's beliefs.
   
   Unless you have studied advanced quantum physics the second part of this book is very tough going.



4. By some accounts Albert Einstein (1879-1955) was the greatest theoretical physicist of the twentieth century, if not of all time. Max Jammer, Professor of Physics Emeritus and former Rector at Bar-Ilan University in Israel, has written an eminently readable account of Einstein's thoughts on religion, a subject that he insists has been ignored by the over 400 books on Einstein published in the last several decades. Einstein renounced accusations that he was an atheist, and railed against the intolerance of those whom he called "the fanatical atheists." In his three long chapters Jammer portrays Einstein as "undogmatic and yet profoundly religious."
   
   In his first chapter Jammer treats the role of religion in Einstein's private life. Born to what he described as "entirely irreligious Jewish parents," Einstein attended a Catholic primary school where like all students he received religious instruction. From the influences of nature and music he developed pronounced religious feelings quite early, although by age twelve he became estranged from institutional religion (although not from religion as he would define it) through reading some popular scientific books. His first wife, Mileva Maric, was Greek Orthodox, and his last wishes were to be cremated rather than to be buried in any religious tradition. Einstein was decidedly irreligious in the sense that he rejected any and all institutional affiliations, never attended worship services or prayed, rejected all dogmatic theology (eg, miracles, the afterlife or prayer), did not believe that God was in any sense personal, and was a strict determinist. But he found it impossible not to think of himself as religious in the sense of humility and awe at the mystery, rationality and complexity of nature: "the eternal mystery of the world is its comprehensibility." Behind the mystery of nature there seemed to be some superior intelligence: "I believe in Spinoza's God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings."
   
   Chapter two explores what Einstein wrote about religion (he studiously avoided using the word "theology"). As a convinced determinist Einstein did not believe in human free will. He viewed science and religion as complementary rather than as antagonistic, seen in his famous aphorism that "science without religion is lame, religion without science is blind." Science cannot determine ethics or inform us of ultimate purpose or meaning, thought Einstein, for "knowledge of what is does not open the door directly to what should be." Science could never, then, displace or supercede religion. In his final and longest chapter, Jammer examines the possible ramifications of Einstein's theory of relativity and rejection of quantum mechanics ("God," wrote Einstein in 1926, "does not play dice.") for theological ideas like time, eternity, creation ex nihilo, and the Big Bang. Einstein himself rather disingenuously denied that there was any relationship between his physics and theology.
   
   Well-known for his aversion to social convention and defiance of authority, Einstein used a paradox to summarize his personal beliefs and professional thoughts about religion. About a year before he died Einstein wrote in a letter that he understood himself to be a "deeply religious unbeliever." He rejected any and all notions of traditional, institutional religion, but he just as vociferously repudiated atheists who tried to claim him for their cause. Rather, he embraced something like grateful and humble Cosmic Awe at the beauty and complexity of the world he strove so mightily to understand.



5. On page seventy-five Jammer writes "As he once explained to a Japanese scholar, a deep feeling and his belief in a superior mind that reveals itself in the world of expeirence represent his concept of God." That's where I started to really fall for this book. When Jammer quotes Protestant Paul Tillich (passages written in 1940) and Catholic Hans Kung--both prominent Professors of Christian theology--on Einstein's denial of a personal God, I was in love with the book, now better understanding the theological term "a personal God" from the "Jewish-Christain" Tradition. One wonders if Einstein could have read what his friend Max Jammer has written whether Einstein would have softened or even overturned his statements about his denial of a personal God. Also, once Tillich's (with Hans Kung) and Einstein's ideas are laid out together, Einstein's views don't seem to have deserved the public outrage that they received in the 1930's onward by prominent members of the Catholic Church, Protestant Christians, and Orthodox Rabbis. As Max Jammer points out, it's not as if any of Einstein's critics believe that God is a mere person with all our faults and imperfections. In that sense no orthodox Rabbi, Preist, or Preacher would claim to believe in a personal God either.

5 comments about Exploring Black Holes: Introduction to General Relativity.

1. This book sidesteps the hard work needed to motivate and develop the Einstein field equations, and goes directly to one of the most important solutions of the equations, the Schwarzschild solution, which gives rise to the concept of a black hole. By exploring what observers in different parts of space-time would experience along their different trajectories (whether falling into a black hole or watching from a safe spot far away), Taylor and Wheeler manage to convey an intuitive understanding for such typical GR "paradoxes" such as the fact that the same "event" (the crossing over of an object through the event horizon) can be seen to take 15 minutes, or forever, depending on who's watching it.
   
   Because of what it omits, this book is not a complete presentation of GR. It does present the most fun part of GR, however, in a way that is mathematically accessible.
   
   Along the way, a few side questions are adddressed, like "How painful would it be to be squished/torn apart as I fall into a black hole?" A lot of time is also spent explaining how the weird trajectories of light within the event horizon will transmogrify what is seen by the observer.
   
   This is a great book and a lot of fun. I am also left with a greater motivation to go back to a more complete presentation, to be convinced that "this is where you have to end up". Although much longer, this book is a worthy successor to the original output of this dynamic duo, "Spacetime Physics".



2. This book was delivered in immaculate condition and is exactly how I was hoping it would be. Thank you for your product and i hope to do business with you again!
   
   Sincerely,
   
   Travis



3. Einstein's general theory of relativity is perhaps one of the most mathematically intense areas of research any physicist or astronomer could undertake. However this book takes the subject and turns it into a joyous romp through curved spacetime.
   
   By avoiding the field equations and focusing on their solutions the authors impart to the eager student an overview of general relativity and set the stage for a more rigorous approach to be undertaken later. This book is the perfect introduction to the subject.
   
   The book is well suited for advanced undergraduates who have had several hours of physics and mathematics. It is likewise suited to serve as a introductory text for graduate students that are studying astrophysics and astronomy. In the latter case the text serves well as an overview of what general relativity is, many of its findings, its predictions, and its relevance to observational astronomy.
   
   If you have a basic understanding of calculus and have studied the special theory of relativity in some detail then this book is well suited to your needs.



4. This is the best book about General relativity ( GR ) that I have ever read. Instead of trying to explain GR with words the author is using mathematics to to illustrate some of the consequences of GR. This means that some mathematical knowledge is required ( but not knowledge about tensors and dfferential forms ) and that the reader need to spend some time with paper and pencil to truly understand the text. The examples is concentrated on what is happening around black holes but the advance of Mercury's perihelion and the slowing of light around the Sun is also described. A very good book!



5. A book I really wouldn't have thought could have been written. There are a lot of books on general relativity at the superficial level, call these books 'mathless.' There are monumental tomes aimed at the graduate student level, call these books 'tensor calculus.' Here is a book exquisitely positioned between these others. The student will need to have had differential calculus, and perhaps a bit of basic physics, and with these he will get a pretty good, introductory understanding of General Relativity.
   
   The real key to this book is that it explains a lot, but then it open up a bunch of other questions, questions that we really haven't answered yet -- things like dark matter, dark energy, accelerating expansion of the universe, and more.
   
   The book ends with: 'How can physics live up to its true greatness except by a new revolution in outlook which dwarfs all past revolutions? And when it comes, will we not say to each other, Oh, how beautiful and simple it all is! How could we ever have missed it so long.'
   
   That's just the awe, the vision, that we want new and budding physicists to have.

2 comments about Albert Einstein, The Human Side.

1. Einstein's longtime secretary (1928-1955) Helen Dukas and Professor Banesh Hoffman who together had written a biography of Einstein here collect some of his correspondance, his very humane replies on a great variety of subjects.
   The work is small but it does reveal Einstein's character. His humor and modesty and wisdom are everywhere in evidence. Einstein's writing often has an aphoristic quality, and there are many memorable sayings in the work.
   A small sample of them follow:
   
   " As for the search for truth ,I know from my own painful searching , with its many blind alleys, how hard it is to take a reliable step, be it ever so small, towards the understanding of that which is truly significant."
   
   "With fame I become more and more stupid, which of course, is a very common phenomenon. There is far too great a disproportion between what one is, and what others think one is, or at least what they say they think one is.But one has to take it all with good humor"
   
   "Where the world ceases to be the scene of our personal hopes and wishes, where we face it as free beings admiring, asking and observing, there we enter the realm of Art and Science. If what is seen and experienced is portrayed in the language of logic, we are engaged in science. If it is communicated through forms whose connections are not accessible to the conscious mind but recognized intuitively as meaningful ,then we are engaged in art.Common to both is the loving devotion to that which transcends personal concern and volition."
   
   This volume touches upon many sides of Einstein, his humanitarianism, devotion to peace, his Zionism, his sense of the beauty that is to be revealed through the objective understanding of the universe."
   
   The book takes the form of the questions his correspondents asked ( Most often given in paraphrased form by the authors of the book) and Einstein's responses to their questions.
   
   If I had one question to ask him it would be, " How is it that it was given to one human being in one relatively short period of time to totally transform Mankind's understanding of nature? Why do you think that you were the one given this miraculous power?



2. It is so good now I want to buy his biography!

5 comments about The Meaning of Relativity, Fifth Edition: Including the Relativistic Theory of the Non-Symmetric Field (Princeton Science Library).

1. The Meaning of Relativity is an advanced book. The title should have made it clear. Einstein delves here into what his theory
   actually MEANS. That is, what must we change (if anything...) in our world conception, in the way we think, as a consequence of his immense discovery. Just think that he meddled with time, a concept static since so long that it is registered deep in our DNA: our concept of time goes back to the epoch where our main purpose was to survive the day
   (sounds familiar? No, no, it was different! It was permanent. What you experience now is transient...)
   So what? Read it! It is a marvellous book. Perhaps you will have to reach for other, more elementary, books, in this enterprise. All right! That almost characterizes a book worth reading. So... go on! It will repay your efforts. It IS doable. You will come out, for instance, with a precise CONSTRUCTION OF SPACE! Your brains will be enriched.You deserve that!



2. There are numerous books on general relativity currently on the market, and these range in difficulty from those written for the beginner or the layman, those written for graduate students in physics, and research monographs covering specialized topics. It is always refreshing to go back to the originator of the subject, and take part in his special insights on the topic. Philosophers and historians of science can definitely benefit from a perusal of this book.

   The author begins this book with a discussion of the origin of the concepts of space-time, the emphasis being partly philosophical and partly psychological, and the reader can see the origin of the author's operationalism in reading this introduction. He is clearly against the philosophers who attempt to remove concepts from experience and put them in his words "in the intangible heights of the a priori". The motion of rigid bodies is used to set up a discussion of Euclidean geometry and linear orthogonal transformations. The author emphasizes the role of the physicist in discerning whether a system of geometry is true or not, contrary to the pure mathematician. Examples of geometrical invariants, such as the Cartesian line element and the volume element are discussed, along with the role of vectors and tensors. Both of these are used as means by which one can give expression to the independence of Cartesian coordinates. Maxwell's equations are put in tensor notation as an example of covariance with respect to Cartesian coordinate transformations. All of this is done to motivate the theories of special and general relativity.

   The theory of spectial relativity is treated in chapter 2, the author introducing his famous principle of special relativity. The author poses the problem of calculating the coordinates and time in an inertial system moving with uniform translation relative to another. He shows how this problem is solved by assuming that time and space are absolute, and if the coordinate axes of the systems are parallel to one another, the Galilean transformations result. Newton's equations of motion are covariant under these transformations, but Maxwell equations are not (but the author chooses not to show this explicitly). He then gives an in-depth discussion of how the Lorentz transformations arise as being those that guarantee the covariance of the Maxwell equations. The author also discusses the signature of the Lorentz metric and how it is related to the light cone. He ends the chapter by developing the energy tensor of the electromagnetic field and matter.

   The author's rejection of inertial frames as being priveleged leads him in the beginning of the next chapter to a short philosophical critique of the principle of inertia. This leads to a discussion of the principle of equivalence and to the origin of the general theory of relativity, a theory which the author developed, amazingly, single-handedly, and which he clearly believes is very much superior to classical mechanics. The intuition to be gained by reading this chapter is invaluable for serious students of general relativity. One can see the simplicity and power of the author's arguments, relying on keen physical intuition and sound use of mathematics. In particular, the author's heuristic derivation of the gravitational field equations from Poisson's equation is briliant. In addition, he is not ashamed to interject philosophical argumentation into his writing, particularly in his discussion of Mach's principle. Such discussions are becoming more rare among physicists at the present time.




3. Einstein's theory seeks to unite time, space and impliedly
   distance and light phenomena into a rational set of equations which are congruent to the Euclidian geometry. In essence,
   the concept of time is meaningless except in relation to
   light . Without light, there would be no reference point
   for measuring distance in space because the whole area would
   be dark and unidentifiable for scientific measurement and
   comparison purposes. The use of the volumetric triple integral
   seeks to make a measurement on 3-planes. i.e. x,y and z
   Later in the work, Einstein explains that the laws of
   configuration of rigid bodies with respect to K' do not agree
   with the laws of configuration of rigid bodies that are
   in accordance with Euclidean geometry. He provides an example
   wherein two similar clocks rotate simultaneously on the
   periphery and the center of a circle, then judged from K- the
   clock on the periphery will go slower than the clock at the
   center. He explains this difference as the result of the
   gravitational field influence as determinants in the metric
   laws of the space and time continuum. What happens when the
   clocks are in a perfect vacuum? In addition, time travel is
   a function of how light travels. Finite differences in the
   radii of the clocks (periphery and center) imply distances with
   slight changes in respect to the time light takes to travel
   from one end of the radii (periphery or center) to the other.
   In the Riemann Tensor, Einstein depicts an amorphous masse
   dependent upon the path of displacement. The outline of the
   masse approximates a square so that the area or volume is
   determinate by approximation to the closest geometric form
   to the amorphous masse i.e. a square
   
   On page 92, Einstein states that the rate of a clock is slower
   the greater is the masse of the ponderable matter in the
   neighborhood. This comports with the theory and computation
   of inertia. As the base and height increases, the inertial
   computation is geometrically greater in accordance with the
   formulas of inertia [ ((b x h^3)/12) ]. In the discussion of
   Mach, Einstein states that the inertia of a body must increase
   when ponderable masses are piled in the neighborhood. This is
   proven by computing inertia utilizing more massive bases and
   heights. As the base and height increases, the inertial
   computation is geometrically greater thereby proving that the
   inertia of a body must increase when ponderable masses are
   piled up in the neighborhood.
   
   Einstein discusses the theory of Mach in relation to inertia
   and the mutual action of bodies. The actual measurement of
   Mach has at least 3 different levels; namely, subsonic,
   sonic and supersonic measurements
   
   Einstein argues that the hypothesis that the universe is
   infinite and Euclidean at infinity is complicated from the
   relativistic point of view. The universe expands and contracts .
   Accordingly, the nature tends to approximate non-Euclidean
   or quasi-Euclidean objects in the evolution toward the
   expansive and infinite state which Einstein postulates as
   potentially Euclidean in order.
   
   Einstein argues against an infinite space by stating:
   
   " 1. From the standpoint of the theory of relativity , to postulate a closed universe is very much simpler than to postulate the corresponding boundary condition at infinity
   of the quasi-Euclidian structure of the universe.
   
   2. The idea that Mach expressed, that inertia depends upon the mutual action of bodies, is contained, to a first approximation,
   in the equations of the theory of relativity; it follows from these equations that inertia depends, at least in part upon
   mutual actions between masses.
   
   3. An infinite universe is possible only if the mean density
   of matter in the universe vanishes. Although such an assumption is logically possible, it is less probable than the assumption that there is a finite mean density of matter in the universe."
   
   Critique:
   
   The idea of a closed universe is simpler. It comports with experience. For instance, why does Haley's Comet return every
   75 years. The idea of an infinite universe would imply the existence of a less dense outer-superstructure. As objects hurled in space, they would be drawn into the less dense regions. The idea of a bounded universe implies a boundary
   to ricochet speeding objects. Otherwise, every speeding object
   would continue into an infinite universe with a denseless
   path of space.
   
   To prove the third postulate, scientists must have better information on the mean density at the outer edges of the universe. Does density remain constant or does it evaporate
   with greater distances toward the universe boundary regions?
   If a boundary exists as postulated in the finite universe,
   what is the boundary? Is the boundary a wall in space?
   If so, what exists beyond the wall? At the corners of the universe, what structures exist to modulate areas of higher
   density and less density or infinitestimal density?
   In addition, there is a theory of an expanding universe.
   How does the universe expand and what outer region accomodates
   this expansion. The idea of an expanding universe admits to
   an expanding boundary. Again, this poses the earlier question.
   i.e. There must be free space to accomodate an expanding
   universe. Is this free space dense or denseless.
   
   This concept is similar to a computer gigobyte superstructure.
   Users can define different regions on the computer disc.
   These regions consist of utilized space and free space.
   Conceptually, the universe may be seen in the same way.
   It consists of both bounded and unbounded space.



4. This book is an excellent collection of 'lectures' by Einstein himself and present the 'eventual' form of the Special & General Theories of Relativity (as in the 1950s). A handy accompaniment to undergraduate study in relativity, the book is a *mathematical* exposition into its broad features - and is NOT by any means a popular/lay account of what the theories mean. The title of the book may be a little dis-orienting in this regard - but the subtitle should lay to rest any doubts!
   
   Einstein starts with pre-relativity physics formulated in the language of tensors and moves on to present the Special Theory using the same apparatus. The next two chapters delve really deep into the philosophy of the General Theory (GR) complete with equations. The Appendices are further advanced topics in GR - and may be of interest only to graduate students.
   
   For a non-physicist like me, with a sufficent background in the requisite mathematics and some prior exposure to the topic, this book was a real treat. It is a classic well worth its place in a personal library. This book is, however, not recommended for those who are looking for something along the lines of Hawkings' A Brief History of Time.



5. Laymen, such as myself, are familiar with the equation e=mc2; yet how many of us non-scientists actually know what this means? Einstein explains this in a series of four lectures. While the explaination is clear, the mathematics behind it (and the implications of relativity theory) are far from easy for the layperson to understand.
   
   The first section on space and time in pre-relativity physics provides the foundation for exactly why his theories are so revolutionary. I was able to digest this without much difficulty. The real challenges (for me at least) began with his explaination of special and general relativity - that space, time and light are dependent on each other, and in fact are (hence the name) all relative ... a real mind-bender. Sadly, I was unable to make it through the second half of the lecture on general relativity - too abstract for one who is not a scientist by training or vocation.
   
   Nonetheless it is a worthwhile (if difficult) read. For those who are weak in mathematics (Euclidian geometry or below) much of the details will be incomprehensable; don't let this dissuade you - part of the genius of Einstein is his ability to explain what the mathematics proves. A seminal work in science, and highly recommended for those with the patience, training or deeply committed interest in the subject.

4 comments about General Relativity from A to B.

1. For anyone who wishes to gain a deep and true understanding the meaning of General Relativity's space-time, this a book to read. And that this understanding is gained with mathematics no more sophisticated than high school geometry and algebra tells you that the author is not only a master, but also a superb expositor, of this subject. A highschooler having a passion for Physics to a Graduate Student struggling to "internalize" the meaning of her complex equations will be delightfully enlightened reading this book.



2. This book is not a college book on relativity. it is written for curious mind who wants to know something about the relativity and author gives a very layman introduction to it.It starts with space-time concept of Aristotelian, Galilean view and than slowly enters into relativistic view. A lot of space has been delegated to definition and explanation of the concept of Iterval and than jumps into physical meaning of the concepts. It is only as the author says from A to B and no more.



3. This still ranks as one of my favorite relativity books. There is virtually no math to speak of. Yet, the author in a very descriptive way, will take you from Aristotelian view to the Galilean view and finally to the relativistic paradigm. Concepts such as events, event horizons, interval etc. are explained quite beautifully. The idea of the interval and the physics and geometry of the same is shown in a most interesting way.

   The chapters are organized very well and the writing is very good. To follow the text a certain degree of concentration is required because the diagrams need to be checked as one proceeds.

   This text is quite suitable for junior high and high school students not to mention college graduates who wish to know something beyond the cursory in relativity theory.

   I happened to come across this book at a used bookstore in 1979. Very few of my friends were even aware of this book. It was one of those sleepers so much so that a while back this volume had gone out of publication. However, now it's back, thank God. If you want a non-technical but quite thorough peek into Special Relativity get this book. If you are one of those who would prefer a tad more math and a less wordy introduction go with James A. Smith's An Introduction To Special Relativity, published by Dover.




4. The author presents fundamental ideas of theory of relativity in a non-mathematical form using conversation approach to readers with little science background. The book is highly descriptive and the reader is bound to get bored since this is a discussion of about basic ideas about space and time using two-dimensional space-time diagrams. The first part of the book describes the notion of space and time in terms of Aristotelian and Galilean view points. The second half describes how the idea of spatial distance and elapsed time (interval) are incorporated into space time as geometrical entity. The author uses a general framework in this book for explaining general relativity. This is done by describing an event and assemble them into space-time (in a space-time diagram) and describe what is going-on in the physical world in terms of collection of events, and relationships between events is evaluated using measuring instruments such as light pulses and clocks. The intrinsic relationship between two events is described by interval (measured by physical experiences of observers). From the interval, one determines how light goes and how clock move and tick. The author eventually explains how equating intervals leads to relationship between `real' physical measurements. The interval is a sort of misty thing that stands in the background and integrates into space-time. In the final chapter the author discusses an application of general relativity to understand the properties of blackholes: It is here that the readers appreciate the importance relativity. The reader must have patience to read this book and he/she must be prepared to read chapters 5 and 6 second and perhaps third time to understand the underlying concept. If you do not have patience you will be lost and you will dislike this book

5 comments about Subtle Is the Lord: The Science and the Life of Albert Einstein.

1. This is a beautifully written book. I have been intrigued by the personality of Albert Einstein since my childhood (when I saw a postage stamp with his portrait and the famous equation "E=mc^2"), and I always wanted to know what exactly has made him so famous. During my school years I loved to read books about physics, and always enjoyed lessons of physics in school. By that time I thought that I have really good grasp of physics, but still it seemed strange to me why, when the special theory of relativity was explained well enough in many accessible books, the general theory was only mentioned as "the greatest achievement of human mind", but it was never explained in detail, only some of its consequences, like the precession of Mercury's orbit or starlight bending by the Sun, were described, but nobody explained from where these 43" or 1,75" came from ! When in 1989 I bought this book, I enjoyed reading about the details of Einstein's biography, but I was quite shocked that most of the equations in the part about the general relativity were completely beyond my understanding. This fact had been irritating me for a number of years, until in 2002 I have decided to take the plunge and try to learn the general relativity properly. This has been a tough going and took almost two years, but by the end I could really understand what the terms, like the metric tensor, Christoffel symbols or R^i_jkl do really mean, or why R_ij-(1/2)*g_ij*R=k*T_ij, and I was also absolutely stunned by the beauty of this theory. This prompted me not only to read lots of other books about the relativity (MTW, Weinberg, Wald, Hawking & Ellis and many others), but also to learn the classical electrodynamics, quantum mechanics, and now I'm trying to learn the quantum field theory - all this thanks to this excellent book !



2. I have really enjoyed reading A. Pais' biography of Einstein. The book is a very detailed scientific biography. And I would like to stress this point: if you are looking for anecdotes or gossips this is not your book. The main goal of the author is to expose the ideas and scientific achievements of Einstein, explaining in detail his theories. This is a taugh book for someone without a physics background, because Pais has written a book on the physics of the last century, with a detailed account of the origin and development of relativity and quantum theories. And it uses all the mathematical concepts physicists are familiar with.
   Otherwise, this is the best biography of Einstein I have read.



3. The science...the physics is there for those who really want to know. There are no shortcuts or dumming it down. But the heart and the soul is also there of this truly brilliant mind. Over the years I've read this book several times, in fact, have had to order it three times, because every time I loan it to someone, it is never returned to me (I guess they liked it too.)



4. This is a well-written and entertaining biography of one of the world's greatest and most famous physicists: his life, his times, and especially his science. As other reviewers have correctly emphasized, this book does not shy away from mathematical formulas and details of the physics. While it does contain a lot of "traditional biographical" information, there is a heavy emphasis on the science -- which is great if you love physics and have the background, but I doubt many would enjoy that part.
   
   The author (Pais) was an eminent theoretical physicist who knew Einstein near the end of Einstein's life.
   
   Among the interesting tidbits I learned: Contrary to the lore I had always heard, Einstein was a top-notch student. Also, back in his day it was much harder than today to get a job in physics research, and university positions didn't pay well either. Even Einstein had trouble initially finding an academic job ! Of course, when he (working at a patent office) published a series of ground-breaking papers on theoretical physics, his academic career took off. It was also interesting to learn how little he knew about the scientific literature and how much he invented and re-invented physics on his own, especially when he was in isolation in the patent office. It seems all the great ones work that way, R. Feynman being another example that comes to mind.



5. I had to skip over most of the mathematical formulas in this book other than to note that there was a little fine tuning going on in crunching the numbers that all physicists have to do in the course of their research.
   
   I appreciated Einstein's concept that philosophizing was like *writing in honey: it all turns to mush.* Perhaps modern science has been too Westernized to find a unified field theory without have to revert to a grand unifier such as Spinoza intimated. I was glad to see that Einstein was attracted to Spinoza, who was known as a God-intoxicated atheist.
   
   A good read for those who want to learn more of the Divine Man.

4 comments about Foundations of Modern Cosmology.

1. I got this book from my university library. Pretty easy reading considering I'm an engineering student. But then, this book isn't just for physics/astronomy students, as the authors have mentioned. It starts by giving a brief history of cosmology, continuing to current understanding before going to the current problems. The book is not math intensive as it emphasize on understanding the concepts. That's why it is something like a popular-science book. For those who have an interest in cosmology, consept-wise, I recommend this title. Those requiring intensive math, look elsewhere. The other cosmology book I've read is by Martin Roos.



2. This is a serious yet easy to read book on a facinating and popular subject and its main commendation is its accessibility and rigour. It is an excellent antidote to some of the glossy and expensively packeged books by "pop" writers and TV programmes.

   As the introduction of the book makes clear, the authors aim for a wide audience for whom Cosmology is not a core discipline. Not only do they do a good job in meeting this goal, but they also present the physical concepts and experimental results in a way that provides new and deep insights to those whose main interest is Physics. For instance, the discussion of the Big Bang and the cosmic models provides an excellent complement to the mathematical presentation of authors like M.V. Berry. Equally, there is a plethora of material that describes experimental results like those for General Relativity: bending of light under the infulence of the sun's gravity, the Eotovos experiment to demonstrate the Equivalence Principle, etc.

   The book covers a broad field: Some historical aspects, Special and General Relativity, the Big Bang and various cosmic models, dark matter, and large scale structure.

   The glossary and the authors' web site provide further information on the subject.




3. I took the class given by Hawley and he makes the book extremely easy to comprehend. Granted, he wrote it, the man is a hilarious comedic genius. He makes the concepts in the book very simple, and easy to understand. I've learned the concepts before in this book, and havent fully comprehended it. This book made it all come together. Get it!



4. I order the book relatively close to the date i needed it for class and got it just in time! Thanks a lot!

5 comments about Simply Einstein: Relativity Demystified.

1. If you want to know more about relativity, at Amazon.com you can purchase lots of books. But where do you start?

   Perhaps you have heard about general relativity [GR]. You might think you first have to learn GR. And then special relativity [SR] treats the special, more difficult cases of GR. That's wrong. Start with the relatively easy SR and then try the far more difficult GR. There are several books that treat SR at a level any intelligent person can handle. Most of them avoid mathematics. That's a pity. Mathematics aren't difficult in SR.

   My introduction to SR was as follows:

   I started with Relativity Visualized [Lewis Carroll Epstein] to acquire some feeling with SR.

   Then I jumped to Space and Time in Special Relativity [N. David Mermin] that introduces lots of logical examples and thought experiments, I liked very much. After reading this book you are able to make your own thought experiments, which makes you more critical when reading 'other' books. Mermin shows you the difference between relativistic effects and non-relativistic effects of light traveling. Most books forget about this.

   The next book was Understanding Relativity [Leo Sartori] who did a very good job on explaining Lorentz transformation and the corresponding spacetime diagrams.

   I also read The Elegant Universe [Brian Greene] which is probably the best science book ever for a non-scientist. After reading about Calabi-Yau spaces you wonder what is the problem with understanding SR. I also read parts of Spacetime Physics [Taylor Wheeler] and I must say, Richard Wolfson explains some details of this book in a better way.

   So Simply Einstein [Richard Wolfson] is a book I think is suitable for the more experienced reader in SR. It might not be the book to start with. Try some other books first. This book provides a very thorough summary of SR when you get lost in the other books. But after reading this book I was sure. Something is missing in educating SR and GR.

   In SR most authors try to avoid mathematics while authors of GR books think you know everything about tensor calculus. At this moment I do not understand GR yet. SR is four dimensional, but spacetime diagrams are mostly two dimensional for easier understanding. Why can't GR books treat the subject two dimensional to start with? If anyone knows a books that fills the gap between SR an GR I would be glad to know.

   Back to Wolfson's book. Wolfson did very well by, e.g. explaining time dilation mathematically and telling you difference between sound waves and electromagnetic waves with respect to relativity. But, as far as I know, no book deals with time dilation in conjunction with length contraction. I developed my own thought experiments. I hope to find in one of the Amazon books the solution to the problem I created.

   Imagine a train, with a length of 180 meter, moving at 0.6c. The train goes forward 180 meter every microsecond. That makes calculations easy. Ground observers measure the length of the train contracted, 144 meters. As far as I know no book deals with the fact how contraction takes place. If contraction happens symmetrically [which I can prove it should] then, an acceleration of the train of 0.2c in 0.2 microseconds will contract the train to 108 meters. The middle of the train will move on with an average speed of 0.7c or 42 meters in 0.2 microseconds. Due to the contraction the back end of the train will be positioned at 54 meter from the middle of the train. This means that the back end of the train has moved 42 meter [during the time of acceleration] plus [72-54 = 18 meter] while contracting = 60 meter in 0.2 microseconds. If this happens the back end of the train moves at the speed of light, as measured by the ground observers. That is not possible. So one way or another time must act differently when the train is accelerating. And that is just the theme of GR.

   Which author handles this theme and can provide a bridge between SR and GR? Where can I find examples on accelerating trains and the warping of time? Maybe in Richard Wolfson's new book? I'm waiting for it.




2. Simply Einstein is the best layman's (people such as me) guide to relativity that I have come across in my attempts to gain some understanding of the subject. I have been a science fiction fan since the early Star Trek days and assumed inter-stellar travel's certainty sometime in the near future. I was quite disappointed when a college friend became the bearer of bad news and told me that faster than light travel is impossible. Nearly as disappointing, as I learned more through the years, is the enormous difficulty of getting anywhere near the speed of light. Since then I have been instantly attracted to any article that discusses ways of getting around relativity. Needless to say Einstein's theories have held a fascination for me despite my educational background lacking even a high school physics course and no math past second year algebra. I have enjoyed numerous PBS specials, which touched on the subject as well as books such as The Idiots Guide to Understanding Einstein and E=MC2. Both are excellent and deserve high reviews. My attempts to understand relativity has been an occasional intellectual exercise for me in the same way that others enjoy puzzles, but the success of my efforts has been limited and elusive as touching a cloud.
   
   I purchased Simply Einstein at an Einstein exhibit that has been touring the country. Don't miss it if it comes to your area! Many of the exhibits seemed to be inspired by this book. The author in over approximately 300 pages builds the case for relativity with the aid of a series of analogies and diagrams. He also periodically sums up the main points needed to understand in a clear and concise manner and repeats himself many times to make it sink in and remind the reader. This eliminates the problem of many similar books in which the critical points are stated once or are in a forest difficult to see because of the trees. Understanding the material in Simply Einstein is not a breeze, but if the reader is willing to put in the time and carefully study the examples, a higher level of understanding will be the reward. I am a long way from true understanding, but the level of mystery has been significantly reduced. The success of this book to me is demonstrated by my having reread it twice since buying it a couple of months ago. Perhaps the most satisfying part is at the end when the author remarks that due to the limitations of the human mind, relativity is something he cannot fully understand and doubts Einstein did either.



3. As this book makes clear, everything is not relative - but I would say that Richard Wolfson's attempt to describe Einstein's theories and their implications is relatively successful. He takes you toward Einsteinian thought one step at a time. First, he gives you a grounding in Newtonian physics, then walks you through Einstein's special theory of relativity, using a number of examples designed to simplify your conceptualization of ideas that tend to go against common sense thinking, and then he attempts to summarize Einstein's general theory of relativity - which, by its nature, is more difficult to expound upon using models and logical examples. Finally, he touches upon some of the implications of the general theory of relativity, giving the reader a quick trek through the notions of black holes, the future of the universe, and other largely astrophysical theories and concepts.
   
   Simply Einstein is written for a layman audience, but it is by no means an easy read. I really believe you have to have at least some affinity with mathematics and logic in order to really grasp what Wolfson is saying. Of course, those with no such affinity will - I feel safe to say - never even think about reading a book such as this. Wolfson works very hard to provide numerous examples of the theories and concepts of Einsteinian thought, but you can't just breeze through these things and expect to have everything click into place automatically; oftentimes, you have to stop, review, and ponder what you have just read in order to truly get a handle on things. Wolfson's examples are, it seems to me, two-edged swords of a kind. If you know absolutely nothing about relativity, they are quite good and certainly helpful. If, however, you already have some familiarity with the space-time paradoxes of Einsteinian thought (the twin paradox, for example, or the space and time "distortions" of near-light speed travel), a few of Wolfson's examples muck up the water, at least temporarily - you basically have to forget what relativity theory you already know and start again from scratch in order to fully grasp what the author is attempting to show with each example.
   
   Wolfson does do a great job demonstrating the significant differences between Newtonian physics and Einsteinian physics (as well as clearing up popular misconceptions about both subjects), and his information on gravity is enlightening and informative. By the time he gets around to stating that gravity is not a force per se, he has built the foundation upon which he can prove why this is the case. Going further, this allows him to offer an excellent explanation of the curvature of space-time owing to the presence of matter or energy throughout the universe.
   
   If you just want to read about black holes and other fascinating aspects of the universe, this isn't the book for you. That kind of discussion is rather protracted here and comes only after a lot of theory has been introduced and described in some detail. Of course, to truly understand the strangest and most fascinating aspects of our universe, you really do need to have a decent grasp on the general theory of relativity, and this book makes for an excellent introduction to that very subject.



4. I bought this book with the hope that the reviews were true. Oops. Wolfson has a problem with two things: punctuation and clarity. The punctuation can be forgiven as the overexuberance of the non-professional writer. (His use of exclamation points reminds me of a bad paper in a freshman lit. course.) The main problem here is his clarity. He's just not good at explaining things. Further, he has a tendency to meander away from the point and toward minutiae. The result is that the reader is left muttering, 'Hey wait a minute...Go Back. WHY is it that way?' The book promises to clarify relativity - and while it's clear that the author is just having a wonderful time - the book fails. Keep looking.



5. Within just 244 pages, Richard Wolfson takes us on an incredible journey from the ancient pillars of physics -Aristotelian oxcart forces and earth-centered science- to that of modern physics - general relativity and quantum mechanics. This book will change the way you perceive the universe as well as your everyday surroundings. Time dialation, black holes, string theory....all buzz words? Not after this book. Truly a seemingly impossible undertaking......but Wolfson shows his incredible ability to relate difficult to near-impossible concepts to the common non-scientific audience.
   
   But a warning.....do not start this book unless you have the time to finish it. Each page opens a new interesting perspective on not only the history of where we are today, but also what the future holds.
   
   Written for the non-scientist, this book parallels Wolfson's now-legendary, highly recommended, audio course "Einstein's Relativity and the Quantum Revolution", The Teaching Company.
   
   If you have ever wondered about relativity but were afraid to ask while you suffered through countless high school and college science courses, this book is a true revolution. What is remarkable about this book is not only the genius of Einstein and his remarkable discoveries, but the historical path of what led Einstein and the scientific community to realize that their classical physics was "simply" wrong.
   
   Wolson introduces us to the other giants of physics and their work, their risks, and their place in history. He relates the courage of Copernicus and Galileo having to battle both church and misunderstanding. He also brings together the works of Newton to Hawking. Wolson also paints a devasting blow to the scientific community with the failures of the Michelson-Morley experiments and how the true-genius of Einstein rose to change our understanding of the universe.
   
   It is truly unfortunate that we reviewers can only bestow 5 stars to this book. This work is in a class by itself and worthy of our deep appreciation to Richard Wolfson for his gift to our basic understanding of the world we live in.

5 comments about The Principle of Relativity (Dover Books on Physics).

1. Reading the original papers would be best, but if you don't read German then the Dover collection is the next best thing. In the paper on special relativity, the Lorentz transformations are derived via formulating and solving a first order pde, a treatment that no textbook presents (first order pdes aren't taught in math physics, in spite of the fact that every set of first order autonomous odes generates a first order pde). It took my teaching the subject to advanced undergrads in later years to realize what many others have by now noticed, namely, you don't need two postulates for special relativity. "Galilean invariance" is enough. The constancy of the speed of light follows from the requirement that there is no special reference frame.

   Einstein's presentation of GR is unsurpassed for conciseness and clarity, is a model for other researchers to follow when writing papers. Here, he introduces the famous misconception (corrected today in the better texts like Misner, Thorne, and Wheeler) that general covariance is a physical principle. Well, even the greatest minds make mistakes.

   Feynman wrote well, but no scientist to date has written better than Einstein.




2. One of the truly amazing things about the Special Theory is that you only need a decent grasp of high school mathematics and science to fully understand the two original papers. (Depending on your high school you may need to brush up on partial derivatives, but that's all.)
   
   The General Theory is something else again, but by reading around the equations and accepting the descriptions of what is being solved you can still gain some incredible insights into a great intellectual achievement.



3. Dover must be commended for re-printing this collection of 'seminal' papers which cover the development of Relativity. This collection includes Lorentz's papers "Michelson's Interference Experiment" & "Electromagnetic Phenomena ..." and Minkowski's "Space and Time". The latter was instrumental in forging the notion of Minkowski 'space' - and forever altered our conception of how we view time vis-a-vis space. Additional notes by Sommerfield are present as an appendix to Minkowski's paper.
   
   All this is in addition to the famous papers by Einstein which gave birth to Special & General Relativity. In particular, "The Foundation of the General Theory of Relativity" is, of course, a classic - but a tough read. The paper on Special Relativity, "On the Electrodynamics of Moving Bodies", on the other hand, is easily accesible to anyone acquainted with high school mathematics.
   
   Even for the non-physicist, with a suitable grounding in the requisite mathematics, this book is a real gem. In general, it serves an excellent companion to Einstein's The Meaning of Relativity, Fifth Edition: Including the Relativistic Theory of the Non-Symmetric Field (Princeton Science Library) and makes for a priceless addition to a personal library.



4. This book presents Einstein's orginal papers on relativity along with many other "classics" on the subject. A good understanding of college math and physics is a must.



5. I'm not happy with this book at all. I'm not a scientist outside of the field of information technology and I want something to explain Einstein's theories that I could read. I read such a book when I was young. It's out of print, but you can purchase it on Amazon used. It's entitled "Relativity: The Special and the General Theory--A Clear Explanation that Anyone Can Understand" by Albert Einstein.
   
   That did it for me, this book put me to sleep.