The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose (PDF)

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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 TimesFrom 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.

User’s Reviews

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. PrologueAm-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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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!

⭐What laws govern our universe? Modern physics doesn’t give a unified answer for this question, but only give partial answers. That is, we have two fundamental theories explaining our universe, relativity and quantum mechanics that conflict in some situations. There are theories like string theory which claims that it might be able to give a unified theory (as physicists say, the final theory). Among them is twistor theory formulated by the author, Roger Penrose in 1950s. As the inventor of twistor theory, he shows to readers how mankind has answered to the question from the ancient times until the present.Several distinguished features of this book include:1. more than 1000 pages with neither typos nor grammatical errors.2. almost all major roads to final theory: string theory, loop variables, twistor theory, non-commutative geometry. For descriptions, the book deals with classical mechanics, relativity, quantum mechanics, and chaos theory from the basics. And also it deals with classical and modern mathematics: irrational numbers, Euclidean geometry, hyperbolic geometry, projective geometry, real number calculus, complex number calculus, Riemann surfaces, Fourier decomposition, generalized functions, Clifford algebra, Grassmann algebra, vector fields on manifolds, Riemannian geometry, exterior derivative, Lie groups, Lie algebras, connections, fibre bundle theory, Cantor’s set theory, Minkowskian geometry, Lorentz geometry, sheaf theory, and tensors. But in spirit, this book is for general audience.What is the most important for a reader? I think it is how much he learned from the reading. In this aspect, I could not give five stars. To finish the book, I spent almost two months. Of course, I learned a quite amount and it was a valuable time. But I think what I gained is just 35 percent of what the book contains. Comparing with Brian Green’s popular books, the book is the next or the next-next level of a book. The difficulty was in concepts relating to relativity, in particular, tensors. In the book, the tensor notation is universal. Even the Maxwell equation is expressed in the tensor notation. I graduated in physics department and have a doctoral degree in mathematics. But I’ve never studied general relativity and its related Lorenz and Minkowskian geometry, and tensor notations. And I’ve never studied quantum field theory and its related tensor formalism as well.If you think that the book is difficult for you also, I would like to give some tips. They are all related to skipping.1. As the author says, skip equations and difficult parts if you don’t want to read it sometimes the whole chapter. If you realize that the part is important to understand the main stream of the book, you can always go back to that part when necessary. At page 74, the author says,My advice to such readers is basically just to read the words and not to bother too much about trying to understand the equations.2. This book is not a textbook. If you want to learn relativity or tensor calculus or quantum physics, then you are referred to standard texts or Youtube lectures. You should not try to learn such subjects from this book. So when you meet some parts dealing with such a sophisticated level physics and think that it’s too difficult, you should skip it without any regret.3. As I said, in spirit, the book is for general audience. But if one can understand more than a half of the book, then I think that he would be at least a graduate student studying quantum field theory and relativity. If you are interested in the question, what laws govern our universe, you are entitled to read the book. But actually, if you are not already familiar with quantum mechanics at least at the level of popular science books, then it would be extremely hard for you to read. You have to make clever choices about what to read if you don’t want to spend time frustrated.4. Its style is informal and narrative, but in some parts, it is very dense. For example, the Newton mechanics is summarized only in three pages. After the section, the author assumes that you have mastered the Newton mechanics!Now I want to share my detailed appreciation.1. If your major is related to science, then among many curriculum subjects, the linear algebra would be the most helpful to read this book, such as, basis, eigenvalue, linear transformations and matrices, basis change, dimension of a vector space. And if you know what a phase space is for a dynamical system, then it would be very helpful (Search the Wiki). And if your major is mathematics, I have something more to say. I’ve read the differential geometry book by O’Neil, Calculus on Manifolds by Spivak and studied one-semester courses of differential topology and Riemannian geometry. So I am familiar with concepts like curvature, 1-form, integration on forms, exterior derivative, Poincare lemma. But that was not so helpful to understand relativity and tensors in the book. Everybody who is interested in the subject knows that they are related, but I think that they live somewhat in different area.2. The book is so concise that sometimes you can’t understand what the author says. For example, I think that the Mach-Zehnder interferometer at page 514 cannot be understood only by the explanations of the book if the reader does not already know it. And for many extremely important experiments including EPR-experiment, the book describes them so briefly that if you are not already familiar with them, you may have difficulty to understand them. And as for quantum entanglement, it is a really amazing phenomenon of quantum mechanics. But if you didn’t already know it, then you may not fully understand it only with this book. As one more example of physics part, while I read the book, I come to know that there is a projective postulate in quantum mechanics that seems to be a very important issue in the book. But I couldn’t understand it even though I tried to read the related parts several times. There are such things on the mathematical part. First of all, although there are explanations about tensors, if you are not already familiar with it, you would have a rare chance of understanding it. As the second instance, at the extremely interesting section on covariant derivative on a fibre bundle (Section 15.8), the explanation is not sufficient for actually calculating the example of A=ik the conjugate of z. As another instance, in the sections on complex numbers, we see some logically vague explanations. I found that the author didn’t explain the fact that if two holomorphic functions on a domain D coincide on a continuous set (in a sense), then they coincide on the domain D.3. There seem to be unsatisfactory explanations. At section 14.3, introducing covariant derivative, the author introduces the concept of parallel transport. But there is some ambiguity whether covariant derivative is derived from the parallel transport or the converse is true (this case is true in mathematical literature). And at section 21.4, it explains the Blackbody radiation. Wien’s formula was already there giving insufficient interpretation of Blackbody radiation and several years after Wien, Planck succeeded in explaining Blackbody radiation with introducing his Planck constant. If so, it is absurd that the Planck constant appears in the Wien’s formula.4. If you are a mathematician, I strongly recommend that you read sections on analytic continuation, hyper-functions, Fourier decomposition, fibre bundles. They are worth reading in the aspect that the book explains to readers the geometric meaning. Once you read them, you will not forget it for a long time. For example, we know that a conformal map is an angle preserving map. The author says that a conformal map preserves shape locally. Maybe this is a common sense to many researchers, but to me it was an astonishing insight. There are many things like that in the book. And there are some differences of point of view to mathematicians like me. For example, in Chapter 5, the author explains complex numbers from the basics, and in Chapter 13, symmetry groups. I thought I knew them. But the way he describes them seems to be strange. As for complex numbers, I skipped some parts and made a decision to retain my understanding. As for symmetry groups, I thought I have to learn more.5. Until the author introduces the generalized function, he asks us what function is. What definition of a function can be satisfactory in theoretical meaning and in practical applications? In fact, I used to ask the same question also, although I was not so explicit. I think anyone who studied mathematics for several years may have conceived the question. His argument is very interesting and really thought-provoking. More than that, he gives an explicit answer about the question.6. Diagrammatic notations and conformal diagrams don’t seem to be helpful for non-specialists.7. While reading through the book, I hoped that I could understand the following sentence…. according to modern physics, all physical interactions are governed by ‘gauge connections’ which, technically, depend crucially on spaces having exact symmetries. (page 289)But even now after finishing the book, I still don’t understand what the above sentence means concretely. My future goal would be to understand it.8. What are the merits of the book? Does the book have a merit that other books do not have? I think it has. The author has no hesitation in expressing his explicit opinion about major current theories.Quantum field theory – mathematically inconsistentInflation cosmology – suspiciousString theory – Doubtful, especially due to its higher-dimensional spacetime. String theory regards spacetime as continuum but the author seems to believe that ultimately, spacetime also should be quantized.Loop variables – At this stage, it is far from being quantum gravity theory.Non-commutative geometry – The model does not incorporate special and general relativity.Quantum group – There is no very clear relation between a quantum group and quantum theory.Topological quantum field theory – It is hard to see them playing direct roles as models of serious physical theories.Another merit of the book is that it gave me a motivation to study relativity, tensors, and quantum field theory by showing a big picture of modern attempts to final theory. I am a group theorist, and I want to meet more various groups in physics. And I am interested in the question: what laws govern our universe? This is the motivation that I chose the book. I hope that I learn more about the area. As remarked above, ultimately, the spacetime also seems that it should have a discrete property at extremely small scale. So some scientists suggested a discrete number system other than real numbers. I thought that’s the right way! But the author suggests that rather than a discrete number system, complex number system would be the right number system. Now I think that it is possible that to describe a discrete object, we may use a continuum like the complex number system.As a whole, the reading was valuable. While I read this book, I received the impression that the author is a very gentle, sincere, honest, kind, careful, and friendly person. Even though I was not totally satisfied with the book, I come to respect his attitude as a scholar.

⭐* SynopsisThis book is, in my estimation, is built for Maths, Physics and Cosmology as presently understood. It’s helpful if you’ve encountered these topics previously as these often meshed together.* Target Audience, A-level, H.N.D, Degree, Masters?It’s helpful if you have at least an A-level in these topics; Maths or Physics or Astronomy, prior to starting this book. All the better if have any degree background.* Contents1. the roots of science 2. An ancient theorem and a modern question, 3. Kinds of numbers in the physical world, 4 Magical complex numbers, 5. The geometry of logarithms, powers and roots, 6. Real-number calculus, 7. Complex number calculus, 8. Riemann surfaces and complex mappings, 9, Fourier decomposition and hyperfunctions, 10. Surfaces, 11. Hypercomplex numbers, 12. Manifolds of n dimensions, 13 Symmetry groups, 14. Calculus on manifolds, 15. Fibre bundle and gauge connections, 16 The ladder of infinity, 17 Spacetime, 18. Minkowskian geometry, 19 The classical fields of Maxwell and Einstien, 20. Lagrangians and hamiltonians, 21. The quantum particle, 22, Quantum algebra, geometry and spin, 23 The entangled quantum world, 24. Dirac’s electron and antiparticles, 25 The standard model of particle physics, 26. Quantum field theory, 27 The big bang and its thermodynamic legacy, 28 Speculative theories of the early universe, 29. The measurement paradox, 30. Gravity’s role in quantum state reduction, 31. Supersymmetry, supra-dimensionality and strings, 32 Einsteins narrower path and lop variables, 33. More radical perspectives; twistor theory, 34. Where lies the road to reality?* What’s the book like?The book starts very simply and progressively builds upon Math, Physics and Cosmology. The further you read, the topics become more expanded and detailed. The book often has several lines, single sentences to carry the weight of the argument.It’s definitely better if you’ve read these topics before in other books. Its strength is carrying multi-level, multi-topic arguments along. My limit on previous reading is reading the standard model of particle physics. It’s required on its own. I have this book on my shelf.After later Cosmology parts, I became a bit overwhelmed with my inability to follow it with what it’s trying to explain.* SummaryThis book tries its best to explain these topics. It requires other books beforehand. If you are into Cosmology, it’s right up your alley.

⭐Having graduated 40+ years ago with a degree in computer science and mathematics, and having read about the first 100 pages so far I can honestly say I have understood about 1/3 of what I have read. I’m sure it’s going to get harder as I progress through Roger Penrose’s Road to Reality, but it is addictive and very thought provoking. The sad thing is I think Roger Penrose is trying to explain many concepts clearly and topologically, and maybe 5+ years ago I would of grasped most of the wonderful concepts. But I do get a ‘flavour’ of what Roger Penrose is explaining. Fascinating!Only 4 stars because I think this book does require degree level mathematics or physics to be able to grasp many of the ideas.

⭐I studied Physics at university some 45 years ago, and started a PhD, hoping to go into theoretical physics, but went into electronic and software engineering instead. Since retiring I have been buying numerous text books to refresh my memory and try and get to grips with the topics in modern theoretical physics.This book covers the various maths topics I’ve been grappling with, e.g manifolds, differential forms, fibre bundles etc, plus fundamentals of quantum field theory, general relativity, string theory and so on.It treats these in a coherent way from a pure mathematics viewpoint, and which I find very interesting.The book is certainly not an easy read, even for people with some maths background, and frequently jumps between straightforward and esoteric new topics. But I’m making progress, currently up to page 200, so only 900 pages to go!It is a good companion for my text books on the various topics it covers, and I would heartily recommend it.

⭐If it’s so good, why have I given it only 3 stars?Simply put, if you don’t already have a reasonable grasp of mathematics up to graduate level, you’re not going to make much sense of the book, at least for the first 17 chapters. After about a month, I’ve only got to chapter 9 and I have to stop to revise some topic or puzzle over the meaning.That said, it’s a fantastic summary of current theoretical and mathematical physics. I’d compare it with Newton’s ‘Principia’. It’s about as comprehensive and equally abstruse.After ch17, it starts to discuss some recognizable physics (at least recognizable to me), Galilean space-time, relativity, electromagnetism, Lagrange, Minkowski, tensors… all that stuff. I haven’t got into it that far yet, I’m just glancing ahead.Anyway, two uses for this book, a mind-blowing trip into the stratosphere of physics – or an impressive coffee table decoration for the middle-class household.

⭐Great, but not an easy read. I am not far through yet, but it seems to get quite tough deeper into the book. It’s fairly ironic as I was reading this hoping to have some easy “popular science” physics with the amazing perspective of Sir Roger Penrose.Having said that, it is for the better that this requires a bit of thought to go through as the insights that Sir Roger Penrose has into the relationships between maths and physics in different areas is great, and definitely gets one pondering!From what I can tell, a lot of the book focuses on maths, before delving more deeply into the physics. In terms of the physics (and maths), I would definitely say that you might get more from the book (and it would be easier to read) if you already have some previous knowledge on the topics so that you can tell the difference between his opinion and ‘generally accepted’ scientific fact.

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