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The Road to Reality : A Complete Guide to the Laws of the Universe Hardcover – February 22, 2005

by Roger Penrose (Author)

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From one of our greatest living scientists, a magnificent book that provides, for the serious lay reader, the most comprehensive and sophisticated account we have yet had of the physical universe and the essentials of its underlying mathematical theory.

Since the earliest efforts of the ancient Greeks to find order amid the chaos around us, there has been continual accelerated progress toward understanding the laws that govern our universe. And the particularly important advances made by means of the revolutionary theories of relativity and quantum mechanics have deeply altered our vision of the cosmos and provided us with models of unprecedented accuracy.

What Roger Penrose so brilliantly accomplishes in this book is threefold. First, he gives us an overall narrative description of our present understanding of the universe and its physical behaviors–from the unseeable, minuscule movement of the subatomic particle to the journeys of the planets and the stars in the vastness of time and space.

Second, he evokes the extraordinary beauty that lies in the mysterious and profound relationships between these physical behaviors and the subtle mathematical ideas that explain and interpret them.

Third, Penrose comes to the arresting conclusion–as he explores the compatibility of the two grand classic theories of modern physics–that Einstein’s general theory of relativity stands firm while quantum theory, as presently constituted, still needs refashioning.

Along the way, he talks about a wealth of issues, controversies, and phenomena; about the roles of various kinds of numbers in physics, ideas of calculus and modern geometry, visions of infinity, the big bang, black holes, the profound challenge of the second law of thermodynamics, string and M theory, loop quantum gravity, twistors, and educated guesses about science in the near future. In The Road to Reality he has given us a work of enormous scope, intention, and achievement–a complete and essential work of science

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1136 pages
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English
Publisher

Knopf
Publication date

February 22, 2005
Dimensions

6.63 x 2.23 x 9.44 inches
ISBN-10

0679454438
ISBN-13

978-0679454434
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Editorial Reviews

Amazon.com Review

If Albert Einstein were alive, he would have a copy of The Road to Reality on his bookshelf. So would Isaac Newton. This may be the most complete mathematical explanation of the universe yet published, and Roger Penrose richly deserves the accolades he will receive for it. That said, let us be perfectly clear: this is not an easy book to read. The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture. Still, math-friendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefully--it's over a thousand pages long and weighs nearly 4 pounds) and start at the beginning, where Penrose sets out his purpose: to describe "the search for the underlying principles that govern the behavior of our universe." Beginning with the deceptively simple geometry of Pythagoras and the Greeks, Penrose guides readers through the fundamentals--the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces, and Clifford bundles, the tour takes us quickly on to the nature of spacetime. The bulk of the book is then devoted to quantum physics, cosmological theories (including Penrose's favored ideas about string theory and universal inflation), and what we know about how the universe is held together. For physicists, mathematicians, and advanced students, The Road to Reality is an essential field guide to the universe. For enthusiastic amateurs, the book is a project to tackle a bit at a time, one with unimaginable intellectual rewards. --Therese Littleton

From Publishers Weekly

At first, this hefty new tome from Oxford physicist Penrose (The Emperor's NewMind) looks suspiciously like a textbook, complete with hundreds of diagrams and pages full of mathematical notation. On a closer reading, however, one discovers that the book is something entirely different and far more remarkable. Unlike a textbook, the purpose of which is purely to impart information, this volume is written to explore the beautiful and elegant connection between mathematics and the physical world. Penrose spends the first third of his book walking us through a seminar in high-level mathematics, but only so he can present modern physics on its own terms, without resorting to analogies or simplifications (as he explains in his preface, "in modern physics, one cannot avoid facing up to the subtleties of much sophisticated mathematics"). Those who work their way through these initial chapters will find themselves rewarded with a deep and sophisticated tour of the past and present of modern physics. Penrose transcends the constraints of the popular science genre with a unique combination of respect for the complexity of the material and respect for the abilities of his readers. This book sometimes begs comparison with Stephen Hawking's A Brief History of Time, and while Penrose's vibrantly challenging volume deserves similar success, it will also likely lie unfinished on as many bookshelves as Hawking's. For those hardy readers willing to invest their time and mental energies, however, there are few books more deserving of the effort. 390 illus. (Feb. 24)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

Review

Praise for The Road to Reality by Roger Penrose

“A truly remarkable book...Penrose does much to reveal the beauty and subtlety that connects nature and the human imagination, demonstrating that the quest to understand the reality of our physical world, and the extent and limits of our mental capacities, is an awesome, never-ending journey rather than a one-way cul-de-sac.”
—London Sunday Times

“Penrose’s work is genuinely magnificent, and the most stimulating book I have read in a long time.”
—Scotland on Sunday

“Science needs more people like Penrose, willing and able to point out the flaws in fashionable models from a position of authority and to signpost alternative roads to follow.”
—The Independent

“What a joy it is to read a book that doesn't simplify, doesn't dodge the difficult questions, and doesn't always pretend to have answers...Penrose’s appetite is heroic, his knowledge encyclopedic, his modesty a reminder that not all physicists claim to be able to explain the world in 250 pages.”
—London Times

“For physics fans, the high point of the year will undoubtedly be The Road to Reality.”
—Guardian

About the Author

Roger Penrose is Emeritus Rouse Ball Professor of Mathematics at Oxford University. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics, which he shared with Stephen Hawking for their joint contribution to our understanding of the universe. His books include The Emperor’s New Mind, Shadows of the Mind, and The Nature of Space and Time, which he wrote with Hawking.He has lectured extensively at universities throughout America. He lives in Oxford.

Excerpt. © Reprinted by permission. All rights reserved.

Preface

The purpose of this book is to convey to the reader some feeling for what is surely one of the most important and exciting voyages of discovery that humanity has embarked upon. This is the search for the underlying principles that govern the behaviour of our universe. It is a voyage that has lasted for more than two-and-a-half millennia, so it should not surprise us that substantial progress has at last been made. But this journey has proved to be a profoundly difficult one, and real understanding has, for the most part, come but slowly. This inherent difficulty has led us in many false directions; hence we should learn caution. Yet the 20th century has delivered us extraordinary new insights–some so impressive that many scientists of today have voiced the opinion that we may be close to a basic understanding of all the underlying principles of physics. In my descriptions of the current fundamental theories, the 20th century having now drawn to its close, I shall try to take a more sober view. Not all my opinions may be welcomed by these ‘optimists’, but I expect further changes of direction greater even than those of the last century.

The reader will find that in this book I have not shied away from presenting mathematical formulae, despite dire warnings of the severe reduction in readership that this will entail. I have thought seriously about this question, and have come to the conclusion that what I have to say cannot reasonably be conveyed without a certain amount of mathematical notation and the exploration of genuine mathematical concepts. The understanding that we have of the principles that actually underlie the behaviour of our physical world indeed depends upon some appreciation of its mathematics. Some people might take this as a cause for despair, as they will have formed the belief that they have no capacity for mathematics, no matter at how elementary a level. How could it be possible, they might well argue, for them to comprehend the research going on at the cutting edge of physical theory if they cannot even master the manipulation of fractions? Well, I certainly see the difficulty.

Yet I am an optimist in matters of conveying understanding. Perhaps I am an incurable optimist. I wonder whether those readers who cannot manipulate fractions–or those who claim that they cannot manipulate fractions–are not deluding themselves at least a little, and that a good proportion of them actually have a potential in this direction that they are not aware of. No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can see only the stern face of a parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence–a duty, and a duty alone–and no hint of the magic or beauty of the subject might be allowed to come through. Perhaps for some it is too late; but, as I say, I am an optimist and I believe that there are many out there, even among those who could never master the manipulation of fractions, who have the capacity to catch some glimpse of a wonderful world that I believe must be, to a significant degree, genuinely accessible to them.

One of my mother’s closest friends, when she was a young girl, was among those who could not grasp fractions. This lady once told me so herself after she had retired from a successful career as a ballet dancer. I was still young, not yet fully launched in my activities as a mathematician, but was recognized as someone who enjoyed working in that subject. ‘It’s all that cancelling’, she said to me, ‘I could just never get the hang of cancelling.’ She was an elegant and highly intelligent woman, and there is no doubt in my mind that the mental qualities that are required in comprehending the sophisticated choreography that is central to ballet are in no way inferior to those which must be brought to bear on a mathematical problem. So, grossly overestimating my expositional abilities, I attempted, as others had done before, to explain to her the simplicity and logical nature of the procedure of ‘cancelling’.

I believe that my efforts were as unsuccessful as were those of others. (Incidentally, her father had been a prominent scientist, and a Fellow of the Royal Society, so she must have had a background adequate for the comprehension of scientific matters. Perhaps the ‘stern face’ could have been a factor here, I do not know.) But on reflection, I now wonder whether she, and many others like her, did not have a more rational hang-up–one that with all my mathematical glibness I had not noticed. There is, indeed, a profound issue that one comes up against again and again in mathematics and in mathematical physics, which one first encounters in the seemingly innocent operation of cancelling a common factor from the numerator and denominator of an ordinary numerical fraction.

Those for whom the action of cancelling has become second nature, because of repeated familiarity with such operations, may find themselves insensitive to a difficulty that actually lurks behind this seemingly simple procedure. Perhaps many of those who find cancelling mysterious are seeing a certain profound issue more deeply than those of us who press onwards in a cavalier way, seeming to ignore it. What issue is this? It concerns the very way in which mathematicians can provide an existence to their mathematical entities and how such entities may relate to physical reality.

I recall that when at school, at the age of about 11, I was somewhat taken aback when the teacher asked the class what a fraction (such as 3/8) actually is! Various suggestions came forth concerning the dividing up of pieces of pie and the like, but these were rejected by the teacher on the (valid) grounds that they merely referred to imprecise physical situations to which the precise mathematical notion of a fraction was to be applied; they did not tell us what that clear-cut mathematical notion actually is. Other suggestions came forward, such as 3/8 is ‘something with a 3 at the top and an 8 at the bottom with a horizontal line in between’ and I was distinctly surprised to find that the teacher seemed to be taking these suggestions seriously! I do not clearly recall how the matter was finally resolved, but with the hindsight gained from my much later experiences as a mathematics undergraduate, I guess my schoolteacher was making a brave attempt at telling us the definition of a fraction in terms of the ubiquitous mathematical notion of an equivalence class.

What is this notion? How can it be applied in the case of a fraction and tell us what a fraction actually is? Let us start with my classmate’s ‘something with a 3 at the top and an 8 on the bottom’. Basically, this is suggesting to us that a fraction is specified by an ordered pair of whole numbers, in this case the numbers 3 and 8. But we clearly cannot regard the fraction as being such an ordered pair because, for example, the fraction 6/16 is the same number as the fraction 3/8, whereas the pair (6, 16) is certainly not the same as the pair (3, 8). This is only an issue of cancelling; for we can write 6/16 as 3x2/8x2 and then cancel the 2 from the top and the bottom to get 3/8. Why are we allowed to do this and thereby, in some sense, ‘equate’ the pair (6, 16) with the pair (3, 8)? The mathematician’s answer–which may well sound like a cop-out–has the cancelling rule just built in to the definition of a fraction: a pair of whole numbers (a x n, b x n) is deemed to represent the same fraction as the pair (a, b) whenever n is any non-zero whole number (and where we should not allow b to be zero either).

But even this does not tell us what a fraction is; it merely tells us something about the way in which we represent fractions. What is a fraction, then? According to the mathematician’s ‘‘equivalence class’’ notion, the fraction 3/8, for example, simply is the infinite collection of all
pairs

(3, 8), ( – 3, – 8), (6, 16), ( – 6, – 16), (9, 24), ( – 9, – 24), (12, 32), . . . ,

where each pair can be obtained from each of the other pairs in the list by repeated application of the above cancellation rule.* [ * This is called an ‘equivalence class’ because it actually is a class of entities (the entities, in this particular case, being pairs of whole numbers), each member of which is deemed to be equivalent, in a specified sense, to each of the other members.] We also need definitions telling us how to add, subtract, and multiply such infinite collections of pairs of whole numbers, where the normal rules of algebra hold, and how to identify the whole numbers themselves as particular types of
fraction.

This definition covers all that we mathematically need of fractions (such as 1/2 being a number that, when added to itself, gives the number 1, etc.), and the operation of cancelling is, as we have seen, built into the definition. Yet it seems all very formal and we may indeed wonder whether it really captures the intuitive notion of what a fraction is. Although this ubiquitous equivalence class procedure, of which the above illustration is just a particular instance, is very powerful as a pure-mathematical tool for establishing consistency and mathematical existence, it can provide us with very topheavy-looking entities. It hardly conveys to us the intuitive notion of what 3/8 is, for example! No wonder my mother’s friend was confused.

In my descriptions of mathematical notions, I shall try to avoid, as far as I can, the kind of mathematical pedantry that leads us to define a fraction in terms of an ‘infinite class of pairs’ even though it certainly has its value in mathematical rigour and precision. In my descriptions here I shall be more concerned with conveying the id...

Product details

Publisher ‏ : ‎ Knopf (February 22, 2005)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 1136 pages
ISBN-10 ‏ : ‎ 0679454438
ISBN-13 ‏ : ‎ 978-0679454434
Item Weight ‏ : ‎ 3.3 pounds
Dimensions ‏ : ‎ 6.63 x 2.23 x 9.44 inches

Best Sellers Rank: #117,819 in Books (See Top 100 in Books)
- #172 in Cosmology (Books)
- #195 in Astrophysics & Space Science (Books)
- #740 in Mathematics (Books)

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Likely will become one of the Great Books: Buy it!

Reviewed in the United States on May 19, 2006

Verified Purchase

The short version: If you are reading reviews in consideration of purchasing this book then just BUY IT.

It has long been my wish for someone to a write a popular treatment of modern physics, one which includes the math, starts at the beginning, and then covers whatever is needed so that the reader can understand the theories described.

For me, reading physics is fun; it is not a path to "becoming a physicist", but I want something beyond the popular science level. My goal is to become a READER of real physics, and I am willing to work to reach this goal.

This wish describes "The Road to Reality" almost perfectly.

Penrose literally intends to take the reader from basic math through calculus, and on to field theory, Lie Groups/Algebras, calculus of variations (Lagrangians & Hamiltonians), differential geometry with fiber bundles, and tensor analysis. He plans and prepares to explain both quantum physics and general relativity (gravity.)

This book is both a popular science guide and introductory mathematics text (including introductions to advance subjects) at the same time.

The book is a wondrous delight, while simultaneously being maddening for its flaws.

If there were there a thousand similar books, it would be easy to criticise the flaws. The writing is at times simply awful (the worst and most common offense is 'pre-shadowing' for no useful purpose -- and without clearly warning the perhaps already struggling reader). Much of the math details are simple skipped or hand-waved, but the outline and structure provided for mathematical physics is both useful and significant With great persistence by the reader it is understandable. One reads this book both for what it contains, and also for the gateways it will open to other books.

The book likely deserves only four stars, but due to it's unique nature I awarded the fifth as a reward for attempting and coming very close to what most would consider impossible.

On the other hand, any criticism that it is "incomplete" (the subtitle says the "complete guide to the laws of the universe") is unrealistic and similar to criticizing a "complete guide to Europe" or "a complete guide to fishing" for not listing every hotel or restaurant, or for not including a picture of every fish and a map of every body of water.

'Complete' here means comprehensive and full in coverage and scope, not that every detail is specified.

As to criticisms concerning Penrose's idiosyncratic views on physics, he is ABSOLUTELY clear when stating a personal opinion, or covering topics from his own point of view. His own less popular ideas for final theories in physics are a very small portion of the entire book. Pensore clearly delineates his own ideas whenever he mentions them in other sections.

[A little about me, but only as a point of reference, might help you evaluate this review since those with significant college math and physics or those with no background in these subjects will approach this book differently: My prior background only includes high school calculus and physics, though I've read many popular physics titles. At the start, I was mathematically naive at the university level, but I was also completely undaunted by the prospect of learning the math and physics.]

If you buy this book [highly recommend you do] just read it.

Promise yourself that you will keep reading; determine to force your way through no matter what obstacles you encounter. If you have an interest in physics the rewards are immense.

Using the book as a tour guide, outline, overview, and foundation you can find resources freely available on the Internet, or available for sale here on Amazon, to actually LEARN to READ physics.

You should not expect to "become a physicist" without much more study, but you can develop a reading knowledge of the subject beyond the popular treatments, including the mathematics of tensor analysis, differential geometry, and group theory.

An encouragement and warning to young people interested in Physics and Math (as well as those who might buy this book for them) is warranted: If you really want to read this book and work very hard it is possible, but forcing yourself (or being forced) to read it before you have either significant mathematicsal knownlodge and/or the ability to study and develope such know on your own is not a good idea.

This book could convince the beginning student of physics or math that these subjects are more difficult than they actually are. Instead they are rather more like any significant skills: they takes some ability, some time to develop, and above all they require careful and persistent work on your part.

Currently (three months after starting), I have finished the book (took two months for this) and also reached a rough, reading competence with advanced calculus, differential equations, lie groups/algebras, complex analysis, Lagrangians & Hamiltonians, and can now read introductory quantum mechanics texts and papers.

Since reading this book, I have made a good start on Tensor Analysis and Differential Geometry. My estimate is about one year for me to fully understand the book and its topics, but the effort is well worth the results already.

Even though, I have sought and used many other sources to improve my understanding, my successes are directly due to the incredible foundation provided by Penrose.

In addition, I highly recommend "Deep Down Things" by Schumm, who is much more clear, but less mathematical, on Lie Groups and Gauge Theory. Schumm relates Lie theory directly to Gauge Symmetries, going beyond mere hand-waving while still remaining mathematically simple and clear.

I further recommend "Understanding Quantum Physics" by Morrison which offers a much better guided, and step-by-step, introduction to the mathematics and postulates of Quantum Mechanics. (Only real criticism of Morrison is that there are NO solutions for exercise, but he does work many other problems in detail.)

Although I bought Morrison's book several years ago and was unable/unwilling to read it, I can now read this one comfortably -- it's not a novel, but it is no longer a fight to read.

Neither of these excellent books offers the scope of Penrose however, so read "The Road to Reality" first. (I might have missed the beauty of Schumm's treatment of Lie groups and Gauge theory had I encounted it first.)

I am also working through "Quantum Mechanics Demystified" and "Relativity Demystified" both by David McMahon, and "A First Course in General Relativity" by Bernard F. Schutz.

[Five months after starting Penrose's book, I now feel comfortable in reading the very imposing "Gravitation" by Misner, Thorne, Wheeler (MTW).]

When I have finished these, my plan is to read "Quantum Field Theory in a Nutshell" by A. Zee and move on to Zwiebach's String Theory book.

Notice that if you don't have the background in math or physics then this book is going to lead you to reading many others and learning many new topics. This truly great book doesn't end the journey but rather opens new worlds and capabilities for the interested reader.

If you are asking "Should I buy it?", then: Yes, JUST BUY IT.

If you do buy it, then JUST READ IT. No matter how long it takes you or how difficult it seems at time just keep reading....

You will be delighted to finish this book, and disappointed that it ends -- expect both emotions at the same time.

Thank you Roger Penrose!

62 people found this helpful

A stupendous piece of work for understanding both the physical world and the stock market!!!

Reviewed in the United States on February 23, 2021

Verified Purchase

I spent about 4 months, on and off, and finally finished reading this great book. I have a dual purpose: (a) I wanted to quickly recover my knowledge in math and physics I acquired during my prior physicist career, and (b) I wanted to see if I could apply anything I learnt from here to the machine trading models as introduced in the book "Forecasting and Timing Markets: A Quantitative Approach." I really enjoyed this book and indeed found a lot of similarities and dissimilarities between building mathematical models for interpreting the real physical world and building models for forecasting market.

Here is a summary of what I have found out to be very applicable and useful:

(1) p.7: What laws govern our universe? How shall we know them? How may this knowledge help us to comprehend the world any hence guide its actions to our advantage? ... Eventually, even the much more complicated apparent motions of the planets began to yield up their secrets, revealing an immerse underlying precision and regularity.
(2) p.18: Fig. 1.3 Three 'worlds' - the Platonic mathematical, the physical, and the mental - and the three profound mysteries in the connections between them. ... everything in the physical universe is indeed governed in completely precise detail by mathematical principles. ... all actions in the universe could be entirely subject to mathematical laws.
(3) p.28: Euclid's first postulate effectively asserts that there is a (unique) straight line segment connecting any two points. His second postulate asserts the unlimited (continuous) extendibility of any straight line segment. His third postulate asserts the existence of a circle with any centre and with any value for its radius. Finally, his fourth postulate asserts the equality of all right angles.
(4) p.45: We are to think of a light, straight, stiff rod, at one end P of which is attached a heavy point-like weight, and the other end R moves along the asymptote.
(5) p.67: The system of complex numbers is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universe.
(6) p. 109: What about the places where the second derivative f''(x) meets the x-axis? These occur where the curvature of f(x) vanishes. In general, these points are where the direction in which the curve y = f(x) 'bends' changes from one side to the other, at a place called a point of inflection.
(7) p. 115: Armed with these few rules (and loads and loads of practice), one can become an 'expert' at differentiation without needing to have much in the way of actual understanding of why the rules work! This is the power of a good calculus.
(8) p.151: Air, of course, consists of enormous numbers of individual fundamental particles (in fact, about 10^20 of them in a cubic centimeter), so airflow is something whose macroscopic description involves a considerable amount of averaging and approximation. There is no reason to expect that the mathematical equations of aerodynamics should reflect a great deal of the mathematics that is deeply involved in the physical laws that govern those individual particles.
(9) p. 211: It seems that Nature assigns a different role to each of these two reduced spin-spaces, and it is through this fact physical processes that are reflection non-invariant can emerge. It was, indeed, one of the most striking unprecedented discoveries of 20th-century physics (theoretically predicted by Chen Ning Yang and Tsung Dao Lee, and experimentally confirmed by Chien-Shiung Wu and her group, in 1957) that there are actually fundamental processes in Nature which do not occur in their mirror-reflected form.
(10) p. 217: For example, the configuration space of an ordinary rigid body in Euclidean 3-space is a non-Euclidean 6-manifold.
(11) p.223: As in Sec 10.2, we have the notion of a smooth function (Phi), defined on manifold M.
(12) p.388: He (Newton) had originally proposed five (or six) laws, law 4 of which was indeed the Galilean principle, but later he simplified them, in his published Principia, to the three 'Newton's laws that we are now familiar with.
(13) p. 390: It is remarkable that, from just these simple ingredients (Newton's formula GmM/r^2), a theory of extraordinary power and versatility arises, which can be used with great accuracy to describe the behavior of macroscopic bodies (and, for most basic considerations, submicroscopic particles also), so long as their speeds are significantly less than that of light.,
(14) p. 392: Galileo's insight does not apply to electric forces; it is a particular feature of gravity alone.
(15) p. 410: We shall also begin to witness the extraordinary power, beauty, and accuracy of Einstein's revolutionary theory.
(16) p. 412: The geometries of Euclidean 2-space and 3-space are very familiar to us. Moreover, the generalization to a 4-dimensional Euclidean geometry E^4 is not difficult to make in principle, although it is not something for which 'visual intuition' can be appealed to.
(17) p. 455: Einstein's famous equation E = mc^2 tells us that mass and energy are basically the same thing and, as Newton had already informed us, it is mass that is the source of gravitation.
(18) p. 462: Einstein originally introduced this extra term, in order to have the possibility of a static spatially closed universe on the cosmological scale. But when it became clear, from Edwin Hubble's observations in 1929, that the universe is expanding, and therefore not static, Einstein withdrew his support for this cosmological constant, asserting that it had been 'his greatest mistake' (perhaps because he might otherwise have predicted the expansion of the universe!). Nevertheless, ideas once put forward do not necessarily go away easily. The cosmological constant has hovered in the background of cosmological theory ever since Einstein first put it forward, causing worry to some and solace to others. Very recently, observations of distant supernovae have had most theorists to re-introduce /\ (greek lambda), or something similar, referred to as 'dark energy', as a way of making these observations consistent with other perceived requirements.
(19) p. 466: The timing of these signals is so precise, and the system itself so 'clean', that comparison between observation and theoretical expectation provides a confirmation of Einstein's general relativity to about one part in 10^14, an accuracy unprecedented in the scientific comparison between the observation of a particular system and theory.
(20) p.490: He (Hilbert) appears to have believed that his total Lagrangian gives us what we would now refer to as a 'theory of everything'.
(21) p. 503: ... it took many years for Einstein's original lonely insights to become accepted.
(22) p. 523: Heisenberg's uncertainty relation tells us that the product of these two spreads cannot be smaller than the order of Planck's constant, and we have Delta-p Delat-x >= h_bar / 2.
(23) p. 528: I denote Schrodinger evolution by U and state reduction by R. This alternation between these two completely different-looking procedures would appear to be a distinctly odd type of way for a universe to behave!
(24) p. 541: As the state of the arts stands, one can either be decidedly sloppy about such mathematical niceties and even pretend that position states and momentum states are actually states, or else spend the whole time insisting on getting the mathematics right, in which case there is a contrasting danger of getting trapped in a 'rigour mortis.'
(25) p.686 (Chapter 27 The Big Bang and its Thermodynamic Legacy): What sorts of laws shape the universe with all its contents? The answer provided by practically all successful physical theories, from the time of Galileo onwards, would be given in the form of a dynamics - that is, a specification of how a physical system will develop with time, given the physical state of of the system at one particular time. These theories do not tell us what the world is like; they say, instead: 'if the world was like such-and-such at one time, then it will be like so-and-so at some later time'.
(26) p.687: The usual way of thinking about how these dynamical laws act is that it is the choice of initial conditions that determines which particular realization of the dynamics happens to occur. Normally, one thinks in terms of systems evolving into the future, from data specified in the last, where the particular evolution that takes place is determined by differential equations.
(27) p.689: What about evolution into the past, rather than the future? It would be a fair comment that such 'chaotic unpredictability" is normally much worse for the 'retrodiction' that is involved in past-directed evolution than for the 'prediction' of the normal future-directed evolution. This has to do with the Second Law of thermodynamics, which in its simplest form basically asserts: Heat flows from a hotter to a cooler body. ... This procedure of dynamic retrodiction is clearly a hopeless prospect in physics. ... For this kind of reason, physics is normally concerned with prediction, rather than retrodiction.
(28) p. 760: Of course, it might indeed ultimately turn out that there is simply no mathematical way of fixing certain parameters in the 'true theory', and that the choice of these parameters is indeed such that the universe in which we find ourselves must be so as to allow sentient life. But I have to confess that I do not much like that idea!
(29) p. 850: But to take this position is to part company with one of the basic principles of Einstein's theory, namely the principle of general covariance.
(30) p. 935: ... A lot of these stem from the fact Einstein's theory is 'generally covariant' (Sec 19.6).

Finally, I have to say that I really like so many drawings in the book, which are simplistic yet stupendously expressive. Thanks Professor Penrose for sharing your knowledge and achievements of many decades, which will benefit many on this planet called Earth!

31 people found this helpful

Great Book a Masterwork - Hardcover

Reviewed in the United States on February 21, 2024

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This book authored by Roger Penrose is amazing! He has a clear writing style with plenty of diagrams covering many interesting aspects of physics. At over a 1000 pages, this book is a must read for anyone with an interest in physics. Impossible to recommend it highly enough!

The publisher Alfred A. Knopf has done a beautiful job of presenting the work. The formatting, fonts and equations are all perfectly readable. The binding on the hardcover is of the highest quality.

(One small thing, which is just my preference and may not to everyone’s liking, is to have the footnotes on the same page and they apply because they are often interesting in their own right. They are at the end of each chapter which is better than being at the back of the book.)

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JULIO CESAR CHIRICHELLA FELICIONI DE SOUZA

Para os interessados em Física Matemática

Reviewed in Brazil on June 26, 2023

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Extenso tratamento das bases matemáticas da Física, com exemplos e aplicações, desde a antiguidade até o início do século XXI. Recomendo ter uma base acadêmica razoável para apreciar melhor a narrativa.

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Dany Provost

Complete.

Reviewed in Canada on August 17, 2021

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Great book. Complete.

Phalguni

Very good. Affordable price.

Reviewed in India on January 27, 2024

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A very good book. The concepts are explained in simple language so that after reading this we can follow it up in other texts covering these topics. Gives a fast overview of the physics of spacetime and gravitation.

antonio coso Balduque

Libro publicado en 2004. Comprado en 2013. Leído en 2021. Un excelente libro que me costó decidirme.

Reviewed in Spain on June 22, 2021

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Orientación> Cómo ya lo indica Penrose en el Prefacio, "El propósito del libro...es la búsqueda de los principios subyacentes que gobiernan el comportamiento de nuestro universo" y algo más adelante "...este libro trata realmente de la relación entre los matemáticos y los físicos..." y "de hecho puede ser utilizado como una guía genuina de las ideas centrales de la física". El libro es estructurado en varias partes sobre matemáticas, física y cosmología. Se recogen varios capítulos que desarrollan diversos conocimientos matemáticos y físicos, entre ellos: Mundo real de Platón; Pitágoras; Euclides. Números reales, complejos, hipercomplejos. Superficies. Geometría de logaritmos, potencias y raíces. Fourier. Simetría. Infinito. Espaciotiempo. Geometría de Minkowsky. Langragianos y hamiltonianos, campos clásicos de Maxwell e Einstein. Modelo Estándar de partículas. Mecánica cuántica (partícula, álgebra, geometría, mundo, QFT, gravedad y su influencia, paradoja de la medida, Copenhague, Schrödinger, etc.). Teoría de cuerdas, teoria de twistores, etc. Llegando a los capítulos de Cosmología (Big Bang, teorías especulativas sobre el universo temprano, agujeros negros, etc. Finalizando con un capítulo de reflexiones sobre las grandes teorías físicas del SXX y ¿Qué es la Realidad?. Entre otras teorías no aceptadas por Penrose, en la época de desarrollo del libro, podemos destacar: GUT, M, F, Universo inflacionario, teoría del BigBang, teorías que se apoyan en más de 4 dimensiones del e-t (Kaluza-Klein, cuerdas), etc. poniendo la esperanza en teorías como la QFT, teoría cuántica de la gravedad, en un profundo entendimiento de los ingredientes del universo más allá del modelo estándar de partículas y una teoría cuántica que englobe las cuatro fuerzas fundamentales. Respecto a donde se invierte el dinero en la Ciencia, deja claro que la moda y los grandes proyectos nublan a los pequeños ."Afortunadamente , los criterios de la ciencia no son los de los gobiernos democráticos".
Opinión> Ante las tres grandes dificultades que entraña esta gran obra de Penrose, "contenido, volumen y densidad" y no siendo yo un especialista en muchos de los temas planteados, decidí iniciar su lectura por aquellos capítulos que podría entender o recordar mejor. Así inicié con el 34 (el último), 28, 17, 26, 27, 25 y 1. Conseguí sobrevivir; así que, pasé a lo "duro" el 8, 5, 6, 7, 9, 10, 11, ... algunos de los cuales conseguí terminar y otros los dejé a medias o a principias. Penrose tardó 8 años en escribir el libro (1996a2004). Los mismos años que yo tardé, desde que lo compré en 2013, hasta empezarlo, 2021. Es decir: Si no eres matemático o físico y no tienes altos conocimientos de estas disciplinas y de cosmología, mejor no intentarlo. 1.100 páginas. Libro bien escrito, con amplia bibliografía (el libro se publicó en 2004), amplio índice alfabético y notas al final de cada capítulo. Han pasado 16 años desde su publicación y 24 desde su inicio de escritura...y la Cosmología avanzó, avanza y avanzará. Es complaciente que Penrose en su prefacio aconseje que "si tienes miedo a las fórmulas, lee las palabras", "o si te encuentras saturado evita los capítulos o parte de ellos" Yo lo hice y aún así..."las palabras se las lleva el viento" y las referencias constantes del autor a capítulos anteriores o posteriores te dificultará su entendimiento, salvo que también los evites... y entonces, para qué compraste el libro.

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Andrea

Richiede attenzione

Reviewed in Italy on October 2, 2020

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E' uno scritto ambizioso: tenta di comprimere secoli di indagine scientifica in un volume da 1000 pagine circa. Per me è un ottimo libro e non vedo come poteva fare di meglio.
Non avendo un background di studi sugli argomenti trattati sono partito alquanto impreparato e ho seguito con molta attenzione ogni parola, rileggendo spesso intere pagine, per poter comprenderne il significato. Sarà un ripasso per chi già conosce il campo, ma per chi lo acquista come un'introduzione è un libro che necessita di un'attenzione continua per ogni frase scritta e sforzo mentale. Non avendo un forte background matematico, ho saltato la maggior parte delle formule, leggendo solo le conclusioni in lingua parlata.
Cercavo un libro del genere, che mi desse una visione d'insieme sulla fisica accademica odierna e sulle sue origini e in modo abbastanza approfondito. Con Penrose l'ho trovato.
Penrose mette in mostra i problemi delle teorie attuali e i paradossi, e spesso offre alternative; anche se mi è mancata tutta la parte dei pionieri dell'elettromagnetismo.

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