1 comments about Newton to Einstein: The Trail of Light: An Excursion to the Wave-Particle Duality and the Special Theory of Relativity.

1. This book is clear and very interesting. It teaches the general idea of light and modern physics. It can be too simplistic at times for technically minded people.

5 comments about Einstein's Theory of Relativity.

1. At times notation can be a distraction, at other times notation can cause confusion, as in E&M most notably. Max Born's book is a gem and if you can get around the mild distractions and focus on the ideas then you may even get around the paradoxes in Relatively, where "common sense" is a distraction.
   Some gifted people can write and explain well the most complex ideas some cannot. Max Born succeeds one of the best popular books on Relativity.



2. The book starts with an interesting and simple overview on Mechanics and Electromagnetism. The basic concepts of SR are presented, like Lorentz Transformations, space contraction, time dilatation, velocities addiction and the well known "E = mc2". It ends with a small introduction to GR.

   The notation is not quite usual, so don't be surprised to read "K = mb" for the usual "F = ma". Anyway, read it if you are young (I read it right after my "Sweet Sixteen") or if you want reduced knowledge of the matter.




3. This little book is a complete delight; if you can only take one physics book to bed with you at night, this might be it. Born reviews much of classical mechanics and E&M, and gives a great introduction to special relativity. There is a bit more on the history of ether than I really wanted to see, but that aside, this a wonderful, comprehensive, handy (not big and heavy) and inexpensive book. I highly recommend it.



4. Dr. Einstein oft lamented that so few really understood his theories. He said that perhaps there was one or maybe two people that understood. It seems to me Max Born must be one of them. His work simplifies as much as possible without sacrificing the level of knowledge needed to grasp the topic and begin to see its implications. It is a complex topic but Max Born rises to the occasion to give us at least a glimpse into this important subject.



5. This is perhaps the best of the non-technical treatments out there of RT that require some mathematical literacy but no higher math like calculus. I read an earlier edition of this book almost 30 years ago when first in college, after reading one of the non-mathematical books, and it really opened my eyes to some of more advanced and technical aspects of the theory. Yes, there is considerable math in the book, but it's all algebra, no calculus is needed. Born covers all the important facets and aspects of the theory, without skipping over the more difficult concepts.
   
   Years later, when my mathematical skills were more developed (I was up thru advanced calc and a year of differential equations), I went to the trouble (although I was just a biology major), of reading one of Born's books on Optics, which was quite fascinating. It brought back memories of the earlier, more readable relativity book, since I wasn't quite up to the level of his book on Optics, but then it's always good to try to stretch your mind a bit. But Born was such a great presenter that I struggled through the book despite the overall level of technical difficulty. I find optics for some reason the most interesting of all the areas of physics that I have tried to learn something about, perhaps because of my graduate work in the neurophysiology and biophysics of visual perception, to which it has some relevance.
   
   But getting back to this book, you won't find the math too daunting if you just remember some high school algebra. I learned more from this book than any other popular treatment, of which I've probably read half a dozen. Overall, a great intro to the subject and probably the most unstintingly detailed in coverage of the more difficult ideas.

5 comments about Introducing Relativity, New Edition (Introducing... S.).

1. A simply silly collection of kiddy drawings. Look elsewhere for genuine content.



2. ... came out dumb too.
   I'm usually the first in line when there's Weighty Knowledge to be had on the cheap, and there ain't much that's toting a heavier load than Einstein's Theory of Relativity. So, skinny book + cartoons on every page + minimal text = Smart Me. Oh, happy day.
   I was doing okay up until the two crows that looked kind of like Heckle and Jeckle showed up. Look, you can throw all the cute pictures you got but they aren't going to get me any closer to understanding geodesics and metrics. And that was just the crows! The chimp with the egg beater was pushing tensors and the gorillas with the pointy sticks were trying to explain vectors. Sorry. From the birds on I was absorbing what the authors were throwing at me about as well as a concrete wall absorbs tennis balls.
   I like the idea of presenting complex topics in a graphic-text format. Unfortunately, I think this topic needs quite a bit more text and (gulp) an in-depth explanation of the math behind it all.



3. I definately agree with the reviewers who say it's difficult, but this was the first and only introducing book I have ready perhaps 8 times. Each time, I walk away with a little bit more. Now I feel ready to actually tackle the real deal and research relatively from the horse's mouth. I highly recommend this book, but if you do read it, be prepared to read it several times before it all sinks in.



4. 2nd edit
   "Introducing Relativity" is explained well enough to be able to get it almost on the first read. Revision always reveals more (this is inherent in what it predicts and is the reason why I edited this review) but relativity is here for anyone who wants to know it.
   
   In terms of the "Introducing..." science series this book complements "Introducing the Universe" and is an extension of "Introducing Newton and classical physics" but it turns out to be the easiest of the three to understand. It also harmonizes Hawking's "A brief history of time" who gives relativity a chapter but this book brings it out more.
   
   Einstein became a household name with his formula E=MC2 meaning energy is mass. As a consequence he established that nothing can travel faster than the speed of light because the energy required to accelerate mass to this speed would be infinite because acceleration also produces an increase in mass.
   
   Einstein understood Newton. Newton showed with his laws of motion how matter moves with and without force and established gravitational effects while Maxwell unified magnetism and electricity by showing that shifts in either electricity or magnetism produces a shift in the other. Newton however also implied that there was no absolute standard of rest because everything is moving. There was no such thing as absolute position or space in his mind. Newton did not believe that time was part of space but separate and could be measured with a good enough clock.
   
   Reality without time is actually like saying that everything is flat and we now know this is an error. This flatness can be imagined by saying that when all questions about matter (sun, moon, planets and forces) was connected through Newton's mechanics of explaining nature it was explained `linked' in a flat sort of way.
   
   Einstein discovered because of the properties of observing light that these `links' have an underlying nature that would change the Newtonian model with his special relativity (SR).
   
   In SR Einstein showed time dilation at near light speeds. A simple theoretical model for this is a ball bouncing between the floor and ceiling. Our concern is just the distance up and down. If we put the room on a train and watch this as the train goes by, the ball also travels the distance the train moved so in one bounce it doesn't just travel up and down, it travels diagonally for us. The diagonal up and down is longer than just up and down. This means that for the observer on the ground the distance traveled was more than what the observer saw while in the room. There is a difference and so time can dilate.
   
   Newton's flat model was not in agreement with SP. Time could change relative to the observer. Only the speed of light remained constant and the law that it could not be broken.
   
   Now that Einstein had changed some of Newton's laws he sought to find how it extended to the rest of Newton's laws. Einstein needed to include velocity in SR in order to solve the simultaneity problem where a force like gravity and velocity can be confused if we don't have a window to observe from while inside the box being pulled by a planet or towed by a rocket.
   
   Einstein eventually realized that gravitational mass and inertial mass are the same which explains this. Linking gravity with inertial mass meant Einstein could under more about this strange force of gravity. This resulted in GR, showing the shape and function of spacetime in the light cone event sliced into four dimensional space with curves called geodesics that matter naturally follows when others forces don't change act on the matter.
   
   Imagine a trampoline made from very flexible material. When you role balls onto the material it creates dips in the plane creating a terrain. For Einstein this created natural curves for things to follow. That is it, GR!... okay so Einstein went more to show that features of this terrain cause affects on what we observe relatively in SR. The biggest feature is how it influences light (it can bend it) and of course the `dragon eating tail' mystery of GR whereby matter cause geometry to curve and geometry tells matter how to move.
   
   There is whole new level of thought with GR. Its discovery meant GR needed to be calculated back into what physicists knew. The mathematics had to adapt and change to include Einstein's new equations and tensors.
   
   Einstein discovered with GR that gravity travels in waves (is not just a strange mystery force, although it is unusual in that it is very weak) and these waves travel at the speed of light and that waves and curves in spacetime are subject to stretching. These gravity waves that are stretched by matter travelling in spacetime are called gravitational waves and were predicted by GR.
   
   GR is summed up by John Wheeler who said "mass grips space by telling it how to curve, space grips mass by telling it how to move."
   
   Core material:
   Space and time
   Newton and gravity
   Maxwell
   Spacetime
   Special relativity
   Time dilation
   Muons
   E=MC2
   Anti-matter
   Simultaneity problem and general relativity
   Slicing spacetime
   General relativity
   Equivalence principle
   Gravitational mass and inertial mass are the same
   Matter follows geodesics unless acted on by a force
   Spacelike, null, timelike
   Metrics
   Spacetime geodesics
   Tensors and field equations
   Positive and negative curved space
   Intrinsic curvature
   Extrinsic curvature
   Vectors
   Light bends
   Black holes
   Gravitational waves and stretching space
   Interference
   
   The book's technical value finishes at around this chapter on Interference. After that we get 50 pages on the standard model of the universe, Hawking and superstring. It really isn't much to do with relativity and you get better information on these topics on more specialized books. I would have preferred the 50 pages to be more about relativity explanations although I understand a need for closure somehow.
   
   "Introducing time" also has relativity references. Overall this is excellent.



5. Loved it. One of the better books in the series, I think.

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.

5 comments about Introducing Einstein's Relativity.

1. This is without any doubt the best book one can use for starting with GR: it is self contained, well written and moreover it is full of Physical insight. In brief: a great book. Even the introductory mathematical part (about tensor calculus) is great written: not too short and not too long. If one would like to gain an additional point of view about tensor calculus I'd recommend to compare the way followed by R. d'Inverno with that followed by Richtmyer "Principles of advanced mathematical Physics" vol 2 (the last all done in geodesic coordinates: this is a book on maths and not about GR!!). The level of Ray d'Inverno is at advanced undergraduate/1st year graduate: in fact one can find a lot of well discussed topics that are generally left out in other books on the subject. Of course this is not an advanced text like R. Wald or Hawking-Ellis, which are the right books if one wants to get a deeper insight in particular topics. The only fundamental thing R. d'Inverno lacks to treat in a fully way is the form of the Energy of the Gravitational field in GR and its related problems: no specific discussion about it. I think this is an important topic. A valuable (and probably the best) discussion about the latter can be found in L.D.Landau "Field Theory" book, or even in Sean Carroll "Spacetime and Geometry" book (a very good one, my favourite together with Landau and Ray d'Inverno), or you can also have a look about it into P. Dirac or Weinberg.



2. This is an excellent book. But I have seen a 1996 edition of it, not described above.



3. D'Inverno presents all the prerequisite maths needed for GR perfectly. The book is presented perfectly and at the appropriate introductory level for someone who has already done special relativity and wants to jump into GR but doesnt know what a tensor is. There definitly is no better introduction to GR in existence. The exercises at the end of each chapter are brilliant as well. Usually I dont do exercises as they take too long but D'Invernos exercises are a must do. You learn soo much from them and they are more easy than hard. Most books at this level give exercises which are too hard or not that important to understanding the next few chapters. But D'Invernos exercises are perfect especially the ones on the chapters about the maths needed for GR.
   After introducing GR he does stuff on black holes, worm holes, gravitational waves and cosmology.
   
   The only problems with the book are that in the first section of the book he does an introduction to special relativity for those who have never seen it before. It is a very bad intro to special relativity. For the best intro to special rel. one needs to consult "University Physics" by "Young and Fredman".
   But for those who have already done SR, d'invernos intro to SR is new and interesting as a method if a bit too difficult and mathematical.
   Also I would be a bit critical of the fact that after explaining the geometrical structure of GR perfectly he does not even mention how this view of gravity as a force is not exactly "combinable" with the particle physics view of gravity as a force communicated by a graviton. Just a small thought which I think is important. (Weinberg introduces GR by another method which does not use the mathematical geometrical structure throughout as he considers it "overemphasized" and a bit "misleading")
   Wienbergs "General relativity and cosmology" should be the readers next port of call after D'inverno



4. This was one of the books assigned when I took general relativity in college. I found several of the chapters very enjoyable to read. D'Inverno does a great job getting into some of the fascinating physics that lies behind general relativity and its development, like Mach's principles and a great discussion of the equivalence principle. Much of the book is devoted to teaching you the mathematics, and it does so in a good fashion. He has two nice chapters on tensors with homework problems that are doable. One drawback was the book didn't have anything on Cartan's equations or discuss one forms (although he talks about contravariant and covariant vectors). The first half of the book is better than the second half, I found his chapters on special relativity excellent but felt his chapters on black holes and gravity waves were a bit lacking. In any case, I recommend it. Try beefing up your education by reading it along with Schutz so you get some exposure to one forms and all that.



5. This text is well written. It is less well-known than it deserves to be, as it now has many competitors. Needless to say, it deserves attention by the serious student and professors alike.This marvelous resource should not be collecting dust on anyone's bookshelf.

5 comments about A World Without Time: The Forgotten Legacy of Godel and Einstein.

1. 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.



2. ... will be the most appropriate legacy of Kurt Goedel.
   
   READ THIS BOOK for an accessible and entertaining summary of Goedel's important contributions to mathematical logic, his troubled life, and the shamefully defensive response of professional philosophy.
   
   DON'T READ IT for insights into Einstein (a very minor part of the story) or the nature of time.
   
   The title of Palle Yourgau's book A World Without Time: The Forgotten Legacy of Godel And Einstein promises new insights into the physics of time. In fact, Goedel and Yourgrau have nothing significant to say about time. Under Einstein's tutelage (and when both were well into their professional dotage) Goedel found a formal cosmological solution of General Relativity in which non-causal loops can occur. This indeed demonstrates that "time" is not an inherent characteristic of Relativity, but that fact had already been widely recognized ever since Minkowski rewrote Special Relativity with a geometrized time coordinate. By the time Goedel met Einstein, other physicists clearly understood that General Relativity was an incomplete physical theory. So the formal characteristics of the Goedel universe have only mathematical interest.
   
   In the last section of the book, Yourgrau laments that Goedel has been disrespected by professional philosophers. This is like complaining that Mark Spitz wasn't invited to the Special Olympics. The author could better have used those pages to describe Goedel's legacy in modern Category Theory and the powerful intuitionist movement in mathematics.



3. While the book does mostly focus on the lives of Godel and Einstein, it also introduces the ideas and philosophies of many other great early 20th century thinkers. If you don't have a background in logic and the philosophy of science, math, and logics then it will be a difficult read, but well worth it. More people need to learn about Kurt Godel and his amazing insights.



4. During and after their lifetimes, Albert Einstein was considerably more well-known publicly than Kurt Godel. Even today, there are considerably more books on Einstein and his contributions to physics than Godel's contributions to mathematics. But very few have dwelt upon the human and intellectual relationship between the two. Palle Yourgrau has attempted to write precisely such a book within the context of Godel's contributions to the philosophy of time. The key story underlying the book is Godel's discovery of the "disappearance of time" within Einstein's relativity theory. This conclusion is built up slowly throughout the book via brief tours of their friendship at the Institute of Advanced Studies. Contrasts are also drawn on the differences between the outlook of Einstein and Godel. The misunderstanding and neglect of Godel's contribution to the philosophy of time in terms of the disappearance of time within Einstein's relativity framework provides a sad ending to the book. The author also argues (against the views of academic philosophers) that Godel also deserves to be considered to be a philosopher (of time). In fact, one gets the impression that the author wishes to imply that significant and deep intellectual contributions - be it in mathematics, physics, even perhaps in other areas - are only possible when the thinkers are intrinsically philosophers as well. Overall, this is enjoyable book to read even for those who have read other biographies of the two intellectual giants.



5. The argument is that when they define "time" people demand that
   what is in the past is "gone forever", "no longer accessible."
   But since in general relativity it might at least be possible in
   principle to return to ANY arbitrary space-time point the suggestion
   is that WHAT PEOPLE MEAN BY "time" just doesn't exist.
   
   It seems to me, however, that people are constantly changing their
   definitions and concepts. Science is just one thing that may cause
   us to change our concepts and definitions. I would simply take time
   to be an ordering but admit that a cyclic time might be acceptable.
   (Such a view of time was already to be found in some eastern religions.)
   
   A better argument for the nonexistence of time is Barbour's (The End of
   Time).

5 comments about The Universe and Dr. Einstein.

1. This is absolutely the best book on any scientific topic intended for the general reader that I have ever read. It is one of very few books about science I have ever read that I could seriously call a "page turner". Einstein's theories are presented in such a manner that anyone reading the book can understand the concepts without trying. I have read other books that discussed Einstein's theories, but none of them presented the ideas with such lucidity and simplicity, while at the same time not losing the depth and profundity of the concepts.



2. I feel that this book is a must for any home library. If you are experienced in physics, this book is extremely interesting because it delves deaply into the philosophy that brought Dr. Einstein to his great accomplishments. For those that have little knowledge of relativity, the universe, and quantum matters it offers a great introduction with a minimum of complex math. A simple way to understand how Dr. Einstein changed the entire universe. I have studied Albert for years. This is the first time I have read anything that gave me such an insight to his personality and thought processes. HONESTLY, the best book I have ever read.



3. Mr. Barnett, a journalist, crossed over into the arena of science, a subject that he had not studied in college. And to the world's amazement, he captured on paper a clear and easy to read explanation of the genius and elegance of Dr. Einstein's theories concerning the very small (quanta) and the very large (space and time).



4. Suppose all matter in the universe is expanding at a uniform rate and that "gravity" doesn't exist. Also imagine standing atop the Leaning Tower of Pisa and releasing two cannon balls. One weighs one ounce and the other ten pounds. Because the earth is rushing up to meet the balls, both seem to fall to the ground at the same rate. A cannon ball fired into the air seems to follow a curved trajectory back to the earth as the ground rushes up to meet it. A comet passing close to the earth seems to be "attracted" to the earth as we are pushed upwards towards it. Einstein says "gravity" is the effect on the path of a moving object caused by distortions in the geometric structure of the space-time continuum caused by mass. But space is "nothing," so how can "nothing" be distorted? Could the earth and all matter be expanding uniformly and unnoticed by us? Could this expansion be the real cause of what we call "gravity" and not the distortion of "nothing"?
   
   This problem, somewhat simplified here, has been bothering me since I first read this book some forty years ago; if anybody can help enlighten me on this, I'd be glad to hear from you!



5. Who would believe that a book on the Theory of Relativity could be written for the masses? Well it was, and this is it. The concepts that the book conveys are mind boggling, yet quite understandable at the same time. You'll never view space, time and the world around you the same again. It's a quick read, but as you'll learn, time is relative.

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.

2 comments about Special Theory of Relativity (Routledge Classics).

1. This is a review of the edition of 1965 which appeared in Russian (1967) in my translation. The book contains a thorough exposition of Einstein's special relativity, with a discussion of historical, philosophical and psychological issues. David Bohm's clear and professional style, as well as many deep and original ideas make this book an outstanding course of this important chapter of theoretical physics, being of great value not only for students, but also for both actively working specialists in physics and philosophy of science, and even for serious laymen. I especially recommend the Chapter 25 (Falsificability of theories) as an excellent food for thought.



2. A thorough but very down-to-earth introduction to the math, physics and philosophy of special relativity, and some of the history leading to its development. Bohm is such a first-rate physicist (well known for his original theorizing about quantum reality) and also a superb teacher who understands where others are coming from. The best quality is his well-rounded understanding of human cognition as it relates to the concepts of the relativity of space and time, matter and energy, etc. A long and really worthwhile appendix discusses Piaget's models of how children form ideas about space, time, permanence, change, etc., and, since we were all children once, the source of many of the metaphors and thought patterns that we bring to our understanding of classical space and time, and also relativity. He argues -- and shows -- that relativity's ideas of flexible space, time, etc., are actually close in structure to a child's notion of the world and therefore not so counter-intuitive as we often think they are. Indeed, his constant message is, "This isn't really so hard, nor is it really as strange as it's made out to be." He shows the errors of the absolutism (and arrogance, really) that grew out of Galileo's and Newton's approaches toward "eternal verities" about the universe, and finds in relativity not only a different approach toward space, time, matter, energy, etc., but toward doing science.
   In the process he does a LOT of math, and relates the formulas to the philosophy and threory he expounds. The math is not hard -- almost no calculus, mostly algebra, a little trigonometry. If you really study this, you can have a very deep understanding of why special relativity concludes what it does. The discussion of Minkowski's geometrical approach is very helpful and complements well the earlier algebraic treatment of the Lorentz transformations.
   I've read quite a few popular books on special relativity and this is definitely among the very best. Bohm converses with the reader, doesn't talk down, and is wise, not cute, about the most surprising aspects of the theory. He clearly has thought deeply about the meaning of special relativity, and I came away feeling fortunate for having one of the great physics minds of our century share his creative insights and many years of experience with me. His thinking has a broad reach -- he refers to Thomas Kuhn several times, and his focus on the physical experience behind our abstract concepts reminded me of Lakoff and Núñez's groundbreaking "Where Mathematics Comes From," and Lakoff and Johnson's "Metaphors We Live By" (both written well after this 1965 book). I feel I understand not only special relativity better, but science in general and its place in our thought.
   
   There are a few small drawbacks. I found myself skipping over some of the tedious derivations of the formulas and picking up without missing anything. The edition I read (Routledge, ppbk 1996) has a few minor math mistakes, which is a pain when you're trying to follow the steps carefully. But all-in-all I found myself eager to come back to the book until I finished it, and I've underlined so much that I'll be going back to it again soon, I think.

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!