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The Road to Reality: A Complete Guide to the Laws of the Universe Paperback – Illustrated, January 9, 2007

by Roger Penrose (Author)

4.6 1,121 ratings

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Nobel Prize-winner Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive—and comprehensible—account of the physics of the universe.

A "guide to physics’ big picture, and to the thoughts of one of the world’s most original thinkers.”—The New York Times

From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space.

Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

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Editorial Reviews

Review

“A comprehensive guide to physics’ big picture, and to the thoughts of one of the world’s most original thinkers.”—The New York Times

“Simply astounding. . . . Gloriously variegated. . . . Pure delight. . . . It is shocking that so much can be explained so well. . . . Penrose gives us something that has been missing from the public discourse on science lately–a reason to live, something to look forward to.” —American Scientist

“A remarkable book . . . teeming with delights.” —Nature

“This is his magnum opus, the culmination of an already stellar career and a comprehensive summary of the current state of physics and cosmology. It should be read by anyone entering the field and referenced by everyone working in it.” —The New York Sun

“Extremely comprehensive. . . . The Road to Reality unscores the fact that Penrose is one of the world’s most original thinkers.” —Tucson Citizen

“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.”
—The Times (London)

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

“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

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 2020 Nobel Prize in Physics for his work on black hole formation, as well as 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 Cycles of Time, The Road to Reality, The Nature of Space and Time, which he wrote with Hawking, and The Emperor’s New Mind. He has lectured extensively at universities throughout America. He lives in Oxford.

Excerpt. © Reprinted by permission. All rights reserved.

Prologue

Am-tep was the King’s chief craftsman, an artist of consummate skills. It was night, and he lay sleeping on his workshop couch, tired after a handsomely productive evening’s work. But his sleep was restless – perhaps from an intangible tension that had seemed to be in the air. Indeed, he was not certain that he was asleep at all when it happened. Daytime had come – quite suddenly – when his bones told him that surely it must still be night.

He stood up abruptly. Something was odd. The dawn’s light could not be in the north; yet the red light shone alarmingly through his broad window that looked out northwards over the sea. He moved to the window and stared out, incredulous in amazement. The Sun had never before risen in the north! In his dazed state, it took him a few moments to realize that this could not possibly be the Sun. It was a distant shaft of a deep fiery red light that beamed vertically upwards from the water into the heavens.

As he stood there, a dark cloud became apparent at the head of the beam, giving the whole structure the appearance of a distant giant parasol, glowing evilly, with a smoky flaming staff. The parasol’s hood began to spread and darken – a daemon from the underworld. The night had been clear, but now the stars disappeared one by one, swallowed up behind this advancing monstrous creature from Hell.

Though terror must have been his natural reaction, he did not move, transfixed for several minutes by the scene’s perfect symmetry and awesome beauty. But then the terrible cloud began to bend slightly to the east, caught up by the prevailing winds. Perhaps he gained some comfort from this and the spell was momentarily broken. But apprehension at once returned to him as he seemed to sense a strange disturbance in the ground beneath, accompanied by ominous-sounding rumblings of a nature quite unfamiliar to him. He began to wonder what it was that could have caused this fury. Never before had he witnessed a God’s anger of such magnitude.

His first reaction was to blame himself for the design on the sacrificial cup that he had just completed – he had worried about it at the time. Had his depiction of the Bull-God not been sufficiently fearsome? Had that god been offended? But the absurdity of this thought soon struck him. The fury he had just witnessed could not have been the result of such a trivial action, and was surely not aimed at him specifically. But he knew that there would be trouble at the Great Palace. The Priest-King would waste no time in attempting to appease this Daemon-God. There would be sacrifices. The traditional offerings of fruits or even animals would not suffice to pacify an anger of this magnitude. The sacrifices would have to be human.

Quite suddenly, and to his utter surprise, he was blown backwards across the room by an impulsive blast of air followed by a violent wind. The noise was so extreme that he was momentarily deafened. Many of his beautifully adorned pots were whisked from their shelves and smashed to pieces against the wall behind. As he lay on the floor in a far corner of the room where he had been swept away by the blast, he began to recover his senses, and saw that the room was in turmoil. He was horrified to see one of his favourite great urns shattered to small pieces, and the wonderfully detailed designs, which he had so carefully crafted, reduced to nothing.

Am-tep arose unsteadily from the floor and after a while again approached the window, this time with considerable trepidation, to re-examine that terrible scene across the sea. Now he thought he saw a disturbance, illuminated by that far-off furnace, coming towards him. This appeared to be a vast trough in the water, moving rapidly towards the shore, followed by a cliff-like wall of wave. He again became transfixed, watching the approaching wave begin to acquire gigantic proportions. Eventually the disturbance reached the shore and the sea immediately before him drained away, leaving many ships stranded on the newly formed beach. Then the cliff-wave entered the vacated region and struck with a terrible violence. Without exception the ships were shattered, and many nearby houses instantly destroyed. Though the water rose to great heights in the air before him, his own house was spared, for it sat on high ground a good way from the sea.

The Great Palace too was spared. But Am-tep feared that worse might come, and he was right – though he knew not how right he was. He did know, however, that no ordinary human sacrifice of a slave could now be sufficient. Something more would be needed to pacify the tempestuous anger of this terrible God. His thoughts turned to his sons and daughters, and to his newly born grandson. Even they might not be safe.

Am-tep had been right to fear new human sacrifices. A young girl and a youth of good birth had been soon apprehended and taken to a nearby temple, high on the slopes of a mountain. The ensuing ritual was well under way when yet another catastrophe struck. The ground shook with devastating violence, whence the temple roof fell in, instantly killing all the priests and their intended sacrificial victims. As it happened, they would lie there in mid-ritual – entombed for over three-and-a-half millennia!

The devastation was frightful, but not final. Many on the island where Am-tep and his people lived survived the terrible earthquake, though the Great Palace was itself almost totally destroyed. Much would be rebuilt over the years. Even the Palace would recover much of its original splendour, constructed on the ruins of the old. Yet Am-tep had vowed to leave the island. His world had now changed irreparably.

In the world he knew, there had been a thousand years of peace, prosperity, and culture where the Earth-Goddess had reigned. Wonderful art had been allowed to flourish. There was much trade with neighbouring lands. The magnificent Great Palace was a huge luxurious labyrinth, a virtual city in itself, adorned by superb frescoes of animals and flowers. There was running water, excellent drainage, and flushed sewers. War was almost unknown and defences unnecessary. Now, Am-tep perceived the Earth-Goddess overthrown by a Being with entirely different values.

It was some years before Am-tep actually left the island, accompanied by his surviving family, on a ship rebuilt by his youngest son, who was a skilled carpenter and seaman. Am-tep’s grandson had developed into an alert child, with an interest in everything in the world around. The voyage took some days, but the weather had been supremely calm. One clear night, Am-tep was explaining to his grandson about the patterns in the stars, when an odd thought overtook him: The patterns of stars had been disturbed not one iota from what they were before the Catastrophe of the emergence of the terrible daemon.

Am-tep knew these patterns well, for he had a keen artist’s eye. Surely, he thought, those tiny candles of light in the sky should have been blown at least a little from their positions by the violence of that night, just as his pots had been smashed and his great urn shattered. The Moon also had kept her face, just as before, and her route across the star-filled heavens had changed not one whit, as far as Am-tep could tell. For many moons after the Catastrophe, the skies had appeared different. There had been darkness and strange clouds, and the Moon and Sun had sometimes worn unusual colours. But this had now passed, and their motions seemed utterly undisturbed. The tiny stars, likewise, had been quite unmoved.

If the heavens had shown such little concern for the Catastrophe, having a stature far greater even than that terrible Daemon, Am-tep reasoned, why should the forces controlling the Daemon itself show concern for what the little people on the island had been doing, with their foolish rituals and human sacrifice? He felt embarrassed by his own foolish thoughts at the time, that the daemon might be concerned by the mere patterns on his pots.

Yet Am-tep was still troubled by the question ‘why?’ What deep forces control the behaviour of the world, and why do they sometimes burst forth in violent and seemingly incomprehensible ways? He shared his questions with his grandson, but there were no answers.
. . .

A century passed by, and then a millennium, and still there were no answers.
. . .

Amphos the craftsman had lived all his life in the same small town as his father and his father before him, and his father’s father before that. He made his living constructing beautifully decorated gold bracelets, earrings, ceremonial cups, and other fine products of his artistic skills. Such work had been the family trade for some forty generations – a line unbroken since Am-tep had settled there eleven hundred years before.

But it was not just artistic skills that had been passed down from generation to generation. Am-tep’s questions troubled Amphos just as they had troubled Am-tep earlier. The great story of the Catastrophe that destroyed an ancient peaceful civilization had been handed down from father to son. Am-tep’s perception of the Catastrophe had also survived with his descendants. Amphos, too, understood that the heavens had a magnitude and stature so great as to be quite unconcerned by that terrible event. Nevertheless, the event had had a catastrophic effect on the little people with their cities and their human sacrifices and insignificant religious rituals. Thus, by comparison, the event itself must have been the result of enormous forces quite unconcerned by those trivial actions of human beings. Yet the nature of those forces was as unknown in Amphos’s day as it was to Am-tep.

Amphos had studied the structure of plants, insects and other small animals, and crystalline rocks. His keen eye for observation had served him well in his decorative designs. He took an interest in agriculture and was fascinated by the growth of wheat and other plants from grain. But none of this told him ‘why?’, and he felt unsatisfied. He believed that there was indeed reason underlying Nature’s patterns, but he was in no way equipped to unravel those reasons.

One clear night, Amphos looked up at the heavens, and tried to make out from the patterns of stars the shapes of those heroes and heroines who formed constellations in the sky. To his humble artist’s eye, those shapes made poor resemblances. He could himself have arranged the stars far more convincingly. He puzzled over why the gods had not organized the stars in a more appropriate way? As they were, the arrangements seemed more like scattered grains randomly sowed by a farmer, rather than the deliberate design of a god. Then an odd thought overtook him: Do not seek for reasons in the specific patterns of stars, or of other scattered arrangements of objects; look, instead, for a deeper universal order in the way that things behave.

Amphos reasoned that we find order, after all, not in the patterns that scattered seeds form when they fall to the ground, but in the miraculous way that each of those seeds develops into a living plant having a superb structure, similar in great detail to one another. We would not try to seek the meaning in the precise arrangement of seeds sprinkled on the soil; yet, there must be meaning in the hidden mystery of the inner forces controlling the growth of each seed individually, so that each one follows essentially the same wonderful course. Nature’s laws must indeed have a superbly organized precision for this to be possible.

Amphos became convinced that without precision in the underlying laws, there could be no order in the world, whereas much order is indeed perceived in the way that things behave. Moreover, there must be precision in our ways of thinking about these matters if we are not to be led seriously astray.

It so happened that word had reached Amphos of a sage who lived in another part of the land, and whose beliefs appeared to be in sympathy with those of Amphos. According to this sage, one could not rely on the teachings and traditions of the past. To be certain of one’s beliefs, it was necessary to form precise conclusions by the use of unchallengeable reason. The nature of this precision had to be mathematical – ultimately dependent on the notion of number and its application to geometric forms. Accordingly, it must be number and geometry, not myth and superstition, that governed the behaviour of the world.

As Am-tep had done a century and a millennium before, Amphos took to the sea. He found his way to the city of Croton, where the sage and his brotherhood of 571 wise men and 28 wise women were in search of truth. After some time, Amphos was accepted into the brotherhood. The name of the sage was Pythagoras.

Product details

Publisher ‏ : ‎ Vintage; Reprint edition (January 9, 2007)
Language ‏ : ‎ English
Paperback ‏ : ‎ 1136 pages
ISBN-10 ‏ : ‎ 0679776311
ISBN-13 ‏ : ‎ 978-0679776314
Item Weight ‏ : ‎ 2.38 pounds
Dimensions ‏ : ‎ 6.2 x 1.9 x 9.2 inches

Best Sellers Rank: #33,521 in Books (See Top 100 in Books)
- #8 in Mathematical Physics (Books)
- #44 in Astrophysics & Space Science (Books)
- #56 in Cosmology (Books)

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H. Martin

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!

65 people found this helpful

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Henry

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!

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An Avid Reader

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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Bernardo Maia

Excelente

Reviewed in Brazil on April 10, 2023

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Estou lendo este livro atualmente, e posso dizer que ele introduz assuntos densos de matemática e física de uma forma leve e inteligente. A leitura é fluida, de tal forma que não vejo o tempo passar enquanto leio. Indico fortemente para qualquer amante de física e matemática que queira ir além da divulgação científica (e que tenha um conhecimento básico sobre ambas as ciências cotadas).

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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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