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635 of 652 people found the following review helpful
on December 18, 2005
Let me confess at the outset that I have a PhD in theoretical physics that I gained in 1969. The subject matter was quantum electrodynamics. However, I have worked my entire life in the computer industry. Despite this, I have always kept a background interest in physics. I've retained quite a lot of my original mathematical knowledge but have obviously become relatively rusty. Over the years, I've enjoyed reading several of Roger Penrose's books and found all of them provocative. I bought this book because I thought it would quickly explain to me the latest ideas involved in reconciling relativity and quantum mechanics and lead me to the most recent ideas in dealing with gravity waves, for example.

The book started with a disarming claim to be able to teach a non- mathematician sufficient of the maths to be able to follow the arguments being set out. It even invited the reader to skip the detail of the maths where this became an obstacle. With my background, I therefore settled down for an engaging read. Boy, was I in for a surprise!

The alarm bells began to ring when early on, I passed through the explanations of calculus. Although I obviously had no difficulty in understanding Penrose, I could easily see that a neophyte would not be able to pick up the subject with the limited explanations given. Soon, at around 300 pages in, I crashed into a personal lack of knowledge and, sure enough, Roger Penrose's explanations left me floundering. As a result, I had to put the book to one side and fill in the gaps in my knowledge from other sources. Eventually, I was able to return to the book. However, this became a recurring process - I found that, on several occasions, I had to put the book to one side and educate/re-educate myself from the texts of others.

This meant that this book was a real struggle to read. It became clear at many points that the mathematical jargon was so intense, that during the editing process, the author had lost sight of the exact state of knowledge that the reader would have achieved. This meant that the intense bouts of correct mathematical terminology and descriptions frequently formed impenetrable barriers to explanations.

The whole book gave the impression of being an honest attempt to lead the reader up a very long slope indeed (more than a PhD's worth) and into a sufficient state of education that he or she would be able to read and understand the concepts and detail of Twistor Theory, Roger Penrose's speciality in this subject matter. For me this failed. I found the chapter on the latter to be the most incomprehensible part of the book, which I thought was a pity after all the effort that I had put in as a reader and that Penrose had put in as an author. In all fairness, Penrose does make it clear that his Twistor Theory is not in any way mainstream.

What does come out very clearly indeed is that Penrose believes that a whole new breakthrough is needed to reconcile quantum mechanics and relativity - and that what is around today is not up to it, despite the enthusiasts behind the most popular approaches: string theory and loop quantum gravity.

As I read the book, I kept hearing the voice of my old postgraduate supervisor saying, "Where's the physics? You can't just keep churning the mathematical sausage machine. Where's the physics? That's what really matters!" Unfortunately, I felt that this book suffered from just that. And that gave me the impression that today's theoretical physics had left physics behind. If that is true, then this book, for all its problems, has succeeded in making this clear. If it is false, then this book has done physics a disservice.

Roger Penrose is obviously a brilliant mathematician. Equally obviously, he has no real concept of just how little mathematics ordinary mortals know or can even absorb. At the end of my reading of the book, it was abundantly clear how very much I did not know. On the positive side, it did provide a good roadmap of the gaps in my knowledge that I had to be prepared to fill in if I really wanted to be able to understand the subject! This, I felt, was the book's real strength. Perhaps it should have been better titled "The Roadmap To Reality".

This book is not for the casual reader expecting a breeze-through read like Hawkings' "A Brief History of Time".
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692 of 715 people found the following review helpful
on November 16, 2004
The first half of this extremely challenging book takes the reader through huge swathes of mathematical territory - hyperbolic geometry, complex numbers, complex calculus, Riemann surfaces, n-manifolds and many more topics are covered.

These chapters don't just convey a general impression of each subject in laymans English, but make heavy use of formulae and mathematical notation, effectively letting the maths do the talking where a more 'pop' science book would be breaking out the strained analogies.

Although Penrose takes care to provide the reader with all groundwork necessary to understanding these subjects, this is still fundamentally difficult and unintuitive stuff and non-mathematicians will find that each page requires heavy concentration; skipping or skimming any part of these chapters renders later chapters unintelligible. Still, careful reading reaps huge rewards - the ideas these chapters cover are deep and beautiful.

The big payoff comes in the second half of the book, where the topics covered in the first half are applied to our current understanding of the nature of our universe.

Classical physics, relativity, various aspects of quantum mechanics, string theory and twistor theory (and more besides) are covered, and the first half of the book is revealed as a primer necessary to fully understanding this material.

It's worth repeating - this is a very, very heavyweight book for non-mathematicians. As someone with only a strong laymans knowledge of maths, I found most of the book very difficult indeed. I often had to read each chapter three or four times with a break in between each reading for the material to sink in. But reading this book was as good a mental workout as I've had in a long time, and the end result was that I feel like I've attained a much deeper understanding of the nature of realiy than any book written in plain English could ever convey. The only reason I'm not giving the book 5 stars is that the difficulty of the subject matter makes it fairly inaccessible, albeit necessarily so in my opinion.

If you do get this book, good luck, and don't give up!
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547 of 584 people found the following review helpful
VINE VOICEon February 26, 2005
It's a delicate balance for book: Encyclopedic vs well focused on a unifying theme!

Penrose succeeds admirably. It's not boring! Books like this are few and far between. Indeed, there are preciously few authors who manage to successfully guide beginning students into serious scientific topics; and even fewer who can see the big picture, and do it all. And then keeping our attention through more than 1000 pages! Penrose's book is inspiring, informative, exciting; and at the same time it's honest about what math and physics are. It is modest when modesty is called for. You are not cheated. You do get the equations (not just hand waving!), but you are gently prepared in advance, so you will want the mathematical formulae. Penrose's book is likely to help high school students getting started in science; and to inspire and inform us all. There is something for everyone: for the beginning student in math or in physics, for the educated layman/woman (perhaps the students' parents), for graduate students, for teachers, for scientists, for researchers; and the list goes on.

It is one of the very few books of this scope that is not intimidating. Not in the least!

I can't begin to do justice to this terrific book. Get it, and judge for yourself. I will also not give away the ending, other than saying that the title of the book is a good hint. And you will be able to form your own take, and your own ideas on the conclusion. Like with all good and subtle endings, they can be understood and appreciated at several levels.

I came across Penrose's book in my bookstore by accident, and I was at first apprehensive: The more than 1000 pages, and the 3.3 pounds are enough to intimidate anyone. But when I started to read, I found myself unable to put it down. And I didn't: Bought it; and I had several days of enjoyable reading. I am not likely to put it away to collect dust either. It is the kind of book you will want to keep using, and to return to.

It will not surprise that one of Penrose's unifying themes is the compelling and pleasing geometric images that underlie both the mathematics (roughly one third of the book: modern geometry, Riemann surfaces, complex functions, Fourier analysis, visions of infinity), and the physics: Cosmology (the big bang, black holes), gravity, thermodynamics, relativity (classical and modern: loop quantum gravity, twisters), and quantum theory (wave-particle duality, atomic spectra, coherence, measurements).

The pictures: In fact, this semester, I was just teaching a graduate course, and I had a hard time presenting of Riemann surfaces in an attractive way. It's a subject that typically comes across as intimidating in many of the classical books: Take Herman Weyl's book, for example. I also found it refreshing to see that Roger Penrose gave the many illustrations his own personal and artistic touch; as opposed to having flashy pictures generated by the latest in color-graphics and special effects. I think readers will relate better to Penrose's own illustrations: They isolate and highlight the core ideas and they are not intimidating: We sense that we ourselves would have been able to make similar pencil sketches. Or at least we are encouraged to try!

The common theme in the pictures serves to bring to life the underlying and fundamental ideas;--- another attractive feature of the book! It is otherwise easy to get lost in some of the equations, and in the encyclopedic panorama of topics. Review by Palle Jorgensen, February 2005.
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65 of 69 people found the following review helpful
on November 12, 2005
I don't make a habit of discussing books I haven't finished reading, let alone reviewing them. I'm breaking with habit because, first, I think I've made a reasonable stab at getting into this book, and second, I'll probably die of old age somewhere around page 800 and want to have my say before then.

The dust jacket and various reviews assure us that this book is written for "the serious lay reader." That depends on how we define "serious" and "lay." For "serious" I might say "insanely obsessive," and for "lay," "without a graduate degree in physics." Penrose claims that "you can gain much from this book" while skipping over the formulae. I suppose that depends on what he means by "gain" and "much."

As I see it, this book is for the lay reader who studied and hasn't forgotten all he learned about calculus, linear algebra, and complex variables. Penrose lays out mathematical concepts in a clear and logical way, but I find that this text is detailed enough to remind me of things I once knew, not to teach me math I never had. His serious lay reader might have been trained as an engineer, but probably not as a lit. theorist.

Do I think the lit. theorist can gain much by reading this book? Not if reading means skipping over the formulae. The math in this book couldn't be relegated to an appendix; it's integral to the text. Let me repeat: I don't think this book could be re-written so that the mathematical formulae are in an appendix and remain a coherent explanation of physics. This isn't just Greene's Elegant Universe with a lot of mathematical explanation tacked on. The mathematical material is integral to understanding Penrose's explanations of physical theory and laws. (Okay, I've skipped ahead to later chapters - I wanted to see if I could understand "Quantum field theory" (Ch. 26) just reading the words. Ha!) If you haven't studied the math, this book isn't the place to learn it, and if you can't understand the math, the physics makes no sense.

I did actually study a lot of math in college, but since I rarely use more than basic calculus these days, I've gone aground on the shoals of Chapter 12, "Manifolds of n dimensions" (about page 225). Perhaps when I take a vacation I can pull down my math texts and get up to speed on this. I really am enjoying this book. It's a challenge and it's helping get some of the cobwebs out of the math regions of my brain. I like the illustrations, the notes are interesting and informative, and I think this book really can help a non-physicist understand (or at least have pretty solid delusions of understanding) the intellectual feast of modern physics. But let's be clear that the reader must have some degree of mathematical sophistication. It isn't for the mathematically innocent.
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29 of 29 people found the following review helpful
on February 3, 2007
I've been interested in reading theoretical physics beyond the usual hand-waving popular level for a long time, but it's been difficult to find materials that cater to readers who don't need to be hand-held at least in basic math. I've got a Master's in CS with a math minor, and I'm fairly comfortable with calculus up to the real multivariate level and I've read a lot of popular-level texts on relativity and QM (which have left me theoretically unsatisfied), so tackling Road to Reality seemed like an appropriate challenge.

I really don't know who is in the target audience. This is certainly not something for the non-mathematically inclined layperson. You really, really need to already know math at least to where I am now, and it still requires a lot of absorption of new concepts -- probably from some other sources, too, as you just can't get up to speed with complex analysis and tensors from the 350 pages of math textbook provided. I am pretty much right at the treshold where I'm able to just take a lot of the math on faith and trust that the conclusions really do follow that are presented.

You also really need to already be familiar with the concepts of relativity, curved spacetime and quantum particles, as Penrose does his exposition directly from the mathematics, which you will probably be weak on already. If you weren't, you'd be a Physicist already, or a really competent Mathematician, who would be reading some other book. His formalisms are highly advanced, so it is crucial you at least gain an appreciation of what the mathematical building blocks, on a high level, are. It really is a pity that there isn't more space dedicated to actual mathematical exposition of concepts such as tensors and gauge connections, because you'll need them SO much in what follows. This should have been two books instead of one!

The prior exposure to advanced physics concepts becomes valuable exactly because of the reliance on, say, the tensor-heavy formalism that it is rather difficult to divine the more intuitive meanings of related theories. For example Einstein's special relativity can be derived from MUCH more basic math (see Einstein's own popular book "Relativity") that makes its implications so much more clear than the dense modern-math treatment.

Now, this IS a great book, but don't expect it to enlighten you from zero. For those readers who really want to see what the REAL math looks like, this is a nice exposition, but the mathematics part in the beginning could have been written accordingly -- starting from the assumption that the reader already is mathematically capable, but needs some *real* background in complex analysis, weird topologies and the mathematical machinery you operate therein.
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143 of 164 people found the following review helpful
on November 24, 2005
What I write below is my opinion. But on the other hand, you should be also told that most of the theoretical physicists would agree with most of my statements.

First of all, let me mention that Roger Penrose is a great mathematician, a highly influential mathematical physicist, and an original thinker. We mention his name hundreds of times every day in connection with many discoveries. For example, we investigate the Penrose limits of geometries; the Penrose causal diagrams; twistors; many other notions in general relativity (including methods to extract energy from rotating black holes).

Many people know the Penrose triangle or Penrose tilings. Our colleagues outside the mainstream also like the spin networks that he invented decades before "loop quantum gravity" was constructed.

Penrose is also connected with many ideas that we consider to be standard crackpot ideas and we have read about them in his previous books: for example, he proposed that the collapse of the wavefunction is induced by the gravitational force and it is responsible for consciousness. Neither of these conjectured links has ever been given a rational justification. And this book does not justify them either.

Penrose likes simple and important mathematical ideas - such as spinors - and he explains many them in "The Road to Reality" quantitatively. I hope that many physics fans will learn such things - complex calculus, spinors, and some other algebraic methods - from this book. Incidentally, his and Rindler's book was the first one about spinors I encountered at the high school. It was fun but I don't think that it was the most logical way to explain these issues. The book also covers twistor theory, started by Penrose in 1967, but the new exciting developments are ignored.

Sometimes his explanations are too original and idiosyncratic (and maybe inefficient) but his comments are usually entertaining. But much like Einstein, Penrose chooses to reject many other important physical insights and ideas - for example most ideas that have been relevant in theoretical physics in the last 25 or 30 years.

His strange opinions about the interpretation of quantum mechanics were the beginning; his incomprehensible criticism of the black hole thermodynamical calculations were the next step; his dislike for string theory and cosmic inflation (chapter 28, 31, 34) show that he must believe that nothing interesting has happened in physics for 25 years, to say the least.

Concerning inflation, the book proposes some ideas about the likelihood of the initial conditions for the Big Bang; these ideas make no sense to me. Penrose also criticizes string theory - not just using the usual content-free pseudoarguments but also, for example, for having singularities in its moduli spaces. He has obviously not understood that the smoothness of physics of string theory around the points that would be singular in general relativity has been firmly established and became one of the great results of the Second Superstring Revolution and one of the important applications of p-branes. Penrose does not care about any of these ideas and calculations.

Well, most of us strongly disagree with Penrose's opinion that nothing has happened for 30 years. Moreover, most of us feel that Penrose has no alternatives for the theories studied in the last 30 years to offer and he does not even care much about the questions that others are trying to solve.

The book is not a real single road to reality. It should be called "Fifty Sidewalks Around Reality". The book may be described as a piece of art and philosophy with many layers of confusion, feelings, uncertainty, and potentially ingenious speculative ideas that others so far find completely wrong. His ideas about particle physics are often composed of errors and fantasies.

For example, Penrose incorrectly believes that the Cabibbo angle controls the mixing of kaons and their antiparticles into the short-lived and long-lived energy eigenstates. He also speculates about some alternatives to the electroweak symmetry breaking - alternatives that involve a "new kind of disorder" and that apparently cannot work according to the laws of quantum field theory.

It is not just string theory that Penrose cannot swallow. He has similar problems with the Standard Model, semiclassical gravity, inflationary cosmology, and other issues.

Although the book is interesting and most physics fans won't be able to identify these errors anyway, everyone should know that Penrose certainly does not describe the state-of-the-art theoretical physics. He has contributed many precious ideas and he knows many more but certainly not all of them, not even in mathematics. Mathematics, especially its fields connected to string theory, has recently been expanded in amazing ways and Penrose chose to ignore most of these developments.

Many of his unusual opinions about particle physics, modern cosmology, and string theory seem to be simply erroneous rather than deep. As a famous particle physicist and a 2004 physics Nobel prize winner wrote in the "Science" magazine, there's much to admire and profit from in this book, but judged by the highest standards, "The Road to Reality" is deeply flawed.
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32 of 34 people found the following review helpful
on June 14, 2005
A version of my review was published in the Huntsville (AL) Times.

For a book ostensibly about reality, this one talks a lot about "magic", "mystery", occasional "miracles", and especially the Platonic world of mathematics (or more generally, of "truth"), which Penrose forcefully argues has a reality all its own. Those who fear arithmetic may be lulled by Penrose's gentle preface, which goes into some detail on fractions. This introduces the important mathematical principle of equivalence classes; in the case of fractions, pairs of integers are declared equivalent in a simple way that leads to the normal rules of rational numbers.

But Penrose goes far beyond the simple in his discussion of the mathematical concepts underlying modern physics theories. Penrose's perspective on the mathematics relevant to reality is highly geometrical and visual, and even experts in the field might find new insights in his discussion of hyperbolic geometries, complex numbers (where lies much of the "magic"), and tensors and symmetry groups. Visual insight is difficult when one is talking about higher dimensional spaces, and the lack of visual geometric insight is one of Penrose's complaints about the 10 or more dimensions of typical string theories. Penrose provides startling new ways to look at the four dimensions most relevant to our spacetime, although occasionally his descriptions are marred by poor diagrams. Some of the sections also seem to be missing his unique touch, relying on more pedantic and traditional approaches to the math.

For the very reasonable list price this is really three books in one, and oddly organized for a book ostensibly directed at a lay audience. First is a textbook on the mathematics used by physical theories, complete with exercises. Penrose is careful to define almost everything so an intelligent lay reader could, in principle, follow, but the definitions are brief and not entirely self-contained, and many readers will lose hope fairly quickly. Second Penrose gives a semi-rigorous introduction to the fundamental theories of modern physics, including the remarkable successes of both General Relativity and the quantum field theor of the standard model of particle physics. The real payoff is in the final portion of the book, chapters 27-34, which describes the vast gap that still remains between nature and our theories.

None of the other recent books along these lines - Hawking's

"Brief History of Time", Brian Greene's books, and other recent works by physicists touting our nearness to a "theory of everything" have approached anything like this level of detail. In Penrose's view those other books are all at least partially wrong, and he believes the mathematics needs to be taken seriously to see why.

Penrose dives into this with an attack on inflationary (and other) theories of the big bang, linking the thermodynamic concept of "entropy" to the geometrical structure of the universe, where he is a renowned expert. The fundamental issue, also discussed in Hawking's book, is why the universe has a definite "arrow of time", given that all our accepted physical theories are symmetrical when time is reversed. Somehow the universe started in a highly unusual low-entropy state; Penrose dismisses all the usual arguments about how this could have happened with a statistical analysis from his understanding of spacetime geometries. Did the universe really require a creator to specially select the astronomically low probability universe we started with, or are there physical processes we don't yet understand that introduce this sort of radical time-asymmetry in a natural way? Penrose favors the latter, but makes clear nobody has a good explanation.

The most substantive chapter in the book is Penrose's discussion of superstrings and related ideas. Some highly interesting mathematics has come out of these studies, but they may have little or no relation to the real world. Superstring theories have so far predicted essentially nothing that can be confirmed by experiment - Penrose explains why some often-touted cases of prediction (such as black hole entropy) are in fact rather dubious. Another part of Penrose's problem with them, as with the inflationary theories of the big bang, is that they are undergoing continual rapid evolution so that the superstrings of this year are very different from those of ten years back. Penrose gives a reasonably unbiased presentation of the theories and why people are interested in them, but he does not approve of the bandwagon status they have acquired.

Penrose admits at various points that his views on modern physical theories are somewhat out of the mainstream. His major contributions to physics have ranged widely, but predominantly within the realm of Einstein's "General Relativity", the theory of gravitation. Two of his unique contributions that have not been widely taken up by other physicists are mentioned repeatedly: his view that gravitation is more fundamental than quantum mechanics, and his "twistor" approach to spacetime geometry. The first of these implies that the basic notions of quantum physics may need to be modified with nonlinear terms arising from gravitational interactions within quantum superpositions. For both he identifies new experiments and theoretical work needed to make further progress, including a space-based "Schrodinger's Cat" experiment dubbed FELIX.

The fundamental thread through this book is this relationship between mathematical theories and the reality of nature. The Platonic world provides us with considerable "magic" to explore and be fascinated by, but do the magic and occasional miracles lead us to the truth about reality, or away from it? The reason mathematical truth is not quite the useless tautology Wittgenstein once argued is the linkage it provides between things we might have thought were distinct, but are in fact the same from a certain perspective, just as 3/6 and 1/2 are equivalent as fractions. Penrose illustrates numerous examples of the way mathematical equivalences can change one's perspective on the nature of the world around us - his "twistors" are yet another way of looking at the world, beautiful but quite different from our usual concepts of space and time. Sometimes in the past a beautiful mathematical scheme, like that of the quaternions, has turned out to have little practical use at all, despite much initial promise. Yet Einstein, Dirac, Feynman and others were led by mathematical considerations to theories that had real explanatory and predictive power. Penrose emphasizes the importance of real experiments to guide physical theories.

It seems we simply don't yet have enough experimental capability or mathematical understanding to find the true "theory of everything". It's possible we're close; if we are this book may help to make that happen. But even if we still have a long and winding road to follow, from Penrose's perspective there will be much that is fascinating and beautiful to observe along the way.
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41 of 45 people found the following review helpful
It is clear that I love books, learning, and just the simple act of reading. While there are whole sections of the bookstore I will never enter, I do read rather broadly. Even so, there are some books that I find so stunning that I marvel to even hold them in my hands. This book, "The Road to Reality" by Roger Penrose is one of those books. It is a wonderful achievement and a gift to every one of us.

It has a breadth to it that is quite unique. No matter how specialized you are, even if you have a Ph.D. in mathematics, this book covers so many topics that you will find yourself reading as a generalist saying to yourself, "Yeah, that's neat, I always wanted to learn a bit more about that." And while there is much there for the advanced specialist, it is written in such a way that a person with just an ordinary exposure to mathematics can ignore the math notation (equations) and still get a huge value from reading the text.

This book allows you to dip into it here and there without having to read it front to back. If the ordinary book on cosmology is like taking a trip across an inland lake in a boat, this magnificent volume is like having an ocean to explore. There is a wonderful primer on the roots of science, an exploration of the mathematics based on the Greeks, number theory, logarithms, various forms of calculus, Fourier hyperfunctions, hypercomplex numbers, symmetry groups, and then on to physics.

Penrose gives us the basics of spacetime, 4 space geometry, Lagrangians and Hamiltonians, quantum particles, quantum algebra, the standard model of particle physics, quantum field theory, an examination of the Big Bang and other speculative theories of the early universe, gravity, and much more. He ends with a wonderful section on "Where lies the road to reality". I particularly admire his modesty in stating his feeling that we are not "just about there" in wrapping up physics and that our current best lines of thinking may all indeed be dead ends. Nevertheless even the dropping of a theory represents an advance in knowledge.

You can spend years with this book and should. There are probably four audiences for this book. The advanced specialist who wants to read in areas connected to but other than his expertise, the student (or teacher) who wants to get some context for and supplement to their studies, the generalist (like me) who loves the challenge of learning new things and exploring challenging thought, and someone who simply values having something marvelous on their bookshelf in the odd chance that having all this wonder in one volume might prove valuable one day.

While I could only give "The Road to Reality" five stars, I really view it as a six star event. I recognize that this book is not for everyone, but if you enjoy intellectual mountaineering this is a wonderful peak to climb.
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30 of 32 people found the following review helpful
on October 4, 2004
This is a terrific book. It can take a bright reader who has no more than an undergraduate college degree in a technical field and bring that person to a point where they can read and understand technical papers about fundamental physics and cosmology. It discusses these topics in a way not open to many books for the layman, since it has brought the reader up to speed on the necessary mathematics. Some of the math can be skipped, of course, but it is there to bring the material to life.

Of course, that means starting the book with over 350 pages of math, taught in impressive style by the author, including Euclidean and hyperbolic geometry, number theory, complex numbers, logarithms, complex powers, real and complex calculus, Riemann surfaces, Fourier series, Vector fields, Quaternions, Manifolds, Symmetry groups, and Fibre bundles! That allows him to proceed to discuss quantum mechanics and the rest of fundamental physics.

It is true that Penrose does mention his views about inflation and string theory. But the fact that he has views about these theories does not in any way stop him from being a great teacher. He covers the field of fundamental physics very well indeed.

Penrose does impart a very important viewpoint that I think is valuable for us all. Most scientists are basically positivists: that is, they search for theories that will correspond to measurements (pass experimental tests and provide accurate predictions). It is secondary to them what reality happens to be. But there is something to be said for asking what the reality behind the physics actually is.

If you are a very bright high school graduate about to go to some top notch university to try to become a theoretical physicist, read this book now!
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66 of 76 people found the following review helpful
on February 26, 2005
The stunningly ambitious subtitle to Penrose's latest gift to the world, "A Complete Guide to the Laws of the Universe", is at one and the same time tongue in cheek, since Penrose is cheerfully aware of how far we are yet from knowing the deepest laws of the universe, and perfectly serious, since Penrose wants to equip the diligent reader with the tools to understand all the central issues at the frontiers of 21st century physics.

The key word here is "diligent". How tough is this book? For anyone with three or four years of university math under their belt, it will be pretty straightforward going, with tons of beauties and "ah-hahs" along the way. Penrose aims to provide the central intuitions, and not get bogged down in petty details. As one of a handful of the world's premiere mathematical physicists, he has a firm (and all the more valuable for being slightly idiosyncratic) grasp on what is truly central, and that lets him condense his enormous subject into a mere 1040 pages.

He provides just enough in the way of exercises, unobtrusively tucked into footnotes and handily classified as easy, medium, and hard, to let you check that you are really following along. When dealing with tensors and bundles, which are the language of general relativity and of all the unified theories, he takes care to say most things three times: in the coordinate free language preferred by mathematicians, in the "Einstein summation convention" language preferred by physicists, and in his own diagrammatic notation; so he gives you three chances to get it.

His intent is to be accessible to anyone who isn't mathphobic. A determined reader with a rough grasp of basic calculus concepts is likely to find he has achieved that intent. The learning curve is steep, but all the steps are in place. If you've read any two of Penrose's "Emperor's New Mind", Green's "Elegant Universe", and Hawking's "Brief History of Time", and found them stimulating rather than daunting, then you're ready to tackle this one.

The book deals with all the mathematical machinery it will need in the first 300-odd pages. Relativity follows, then quantum theory, then particle physics and quantum field theory, then cosmology. Penrose always has a fresh perspective, spending a few paragraphs to take a step or two back for a broader, more philosophical view of the territory than the textbooks offer; but all this material, up to page 780, has become standard physics.

Then the pure fun begins. Roger Penrose has never allowed his considerable stature to get in the way of the pleasure of contrarianism, and his take on the Big Kabloona Question, how to reconcile quantum mechanics with general relativity, is as well defended as it is unusual. His longest chapter respectfully spells out the details of the most popular approach to a unified theory, that of strings and branes. But he has always been skeptical of string theory, not just on grounds of verifiability, but also because he feels it fails to involve complex numbers at its foundation. So Road To Reality provides extensive summaries of two leading rival theories: loop quantum gravity, and the twistor theory which Sir Roger and his students have developed over the last several decades. He also discusses at length the notion he originally proposed in "Shadows of the Mind", that gravitational fields may be responsible for the collapse of Schroedinger wave packets.

No volume with the ambitions of this one has existed until now, and no one is better equipped than Penrose to achieve those ambitions, nor could one ask for a more congenial companion or a livelier guide. It belongs on the shelf of every one who aspires to know the real skinny on where physics is, and where it is likely to go in the near future.
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