The Nature of Space and Time

by Stephen W. Hawking, Roger Penrose (Afterword)

Contents
Foreword by Sir Michael Francis Atiyah, OM, FRS, FRSE, FMedSci FAA, HonFREng
Lecture 1 - Classical Theory {Hawking}
Lecture 2 - Structure of Spacetime Singularities {Penrose}
Lecture 3 - Quantum Black Holes {Hawking}
Lecture 4 - Quantum Theory and Spacetime {Penrose}
Lecture 5 - Quantum Cosmology {Hawking}
Lecture 6 - The Twistor View of Spacetime {Penrose}
Chapter 7 - The Debate {Hawking and Penrose}

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking ("A Brief History of Time") and Roger Penrose ("The Emperor's New Mind" and "Shadows of the Mind")--disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.

How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?

In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.

Genres: Science, Physics, Nonfiction, Philosophy, Popular Science, Reference, Stem

160 pages, Paperback

First published January 1, 1996

About the author

Stephen William Hawking was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world.
Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD degree in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, paralysed him. After the loss of his speech, he communicated through a speech-generating device initially through use of a handheld switch, and eventually by using a single cheek muscle.
Hawking's scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Initially, Hawking radiation was controversial. By the late 1970s, and following the publication of further research, the discovery was widely accepted as a major breakthrough in theoretical physics. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.
Hawking achieved commercial success with several works of popular science in which he discussed his theories and cosmology in general. His book A Brief History of Time appeared on the Sunday Times bestseller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society, a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He died in 2018 at the age of 76, having lived more than 50 years following his diagnosis of motor neurone disease.

Reviews

[Jenny · Rating 3 out of 5]

Hawking promised that his and Penrose's lectures and debate would be technical, and he delivered on that promise. I liked the book because it's always entertaining to read two great minds bicker a little bit, and I did learn some information about black and white holes, singularities, and the origins of the universe, but I didn't understand most of the book. The jargon is real. There are tons of equations I couldn't possibly understand. What I did appreciate, though, is that Hawking summarized his lectures at the end, and Hawking was a master at making complex ideas seem simple for people like me.
In the debate, I couldn't tell you who won. Penrose seems to say that Hawking wins by comparing their debate to one between Einstein and Bohr, one that people at the time claimed Bohr won. Penrose says he's like Einstein in this debate and Hawking like Bohr, which seems to indicate he felt Hawking won.
Overall, the book is short and a quick read if you're not really trying to understand everything in it. If you want to do that and really make a study of it, you could. But if you just want to get a little out of it and be entertained and challenged, this could work for you too. It helped me, during an off month from work, to keep my brain in motion, at least.

[Tanya · Rating 2 out of 5]

Some of this information is dated, which is to be expected reading it so long after it was written. I could follow most of the math, but was disappointed by the lack of variable definition. Penrose's writing was much more clear than Hawkings and I believe I'll search out some of his writing on the topic the next time I approach this subject.

[Mohamed al-Jamri · Rating 3 out of 5]

قرأت نصف هذا الكتاب فقط لأن النسخة المسموعة لدي لا تحتوي إلا على الأجزاء التي كتبها هوكنج بينما الأجزاء التي كتبها بنروز والجزء المشترك غير موجودة

لفت نظري في الكتاب في هو انتقاد هوكنج لنظرية الأوتار الفائقة وهو أمر أقرؤه له لأول مرة وإن كان نقدًا سريعًا في سطر واحد فإن كان لاذعًا حيث اختار عدم طرح النظرية لسببين الأول هو أنه لا توجد مشاهدات تؤيدها والثاني أنها غير واضحة أو جميلة رياضيًا.

[ᛚᚨᚱᚲᚨ × ᚠᛖᚾᚱᛁᚱ (Semi hiatus) · Rating 3 out of 5]

"Io non chiedo che una teoria corrisponda alla realtà perchè non so quale sia questa realtà." Stephen Hawking

I momenti più belli passati leggendo questo dibattito tra Stephen Hawking e Roger Penrose, dibattito avvenuto nel 1994 all'Isaac Newton Institute for Mathematical Sciences dell'Università di Cambridge:
1. ...ma almeno è in italiano?
2. Qualcosa capirò, tra tutte queste formule e leggi date per scontate...
3. Nope.
4. NOPE.
5. Lo rileggerò quando sarò meno capra...
6. *arrivata a pagina 130* "Dovrò introdurre un po' di notazione bispinoriale. È a questo punto, di solito, che ci si comincia a confondere[...]." (Penrose) *risata ad alta voce. Continua. Isterica*
7. Sì, ok, però è da metà libro che trascinate 'sto gatto moribondo di Schrödinger perchè nessuno dei due vuole darla vinta all'altro riguardo ai vostri differenti approcci in merito. Siamo alla penultima pagina. Anche il curatore del libro, nell'ultima sezione dedicata alle domande rivolte ai due fisici, taglia una domanda (indovinate un po' quale) scrivendo "Una domanda confusa ancora sul gatto. Roger Penrose rispiega il problema del gatto." Inutile dire che l'ho letto in tono esasperato. Let it go, Let it goooo~ (e mi sento in dovere di dire che odio Frozen, ma a quel punto il cervello andava per i fatti suoi).

[albin james · Rating 5 out of 5]

Rows and flows of angel hair
And ice cream castles in the air
And feather canyons everywhere
I've looked at clouds that way

But now they only block the sun
They rain and snow on everyone
So many things I would have done
But clouds got in my way

I've looked at clouds from both sides now
From up and down, and still somehow
It's cloud illusions I recall
I really don't know clouds at all

Moons and Junes and Ferris wheels
The dizzy dancing way you feel
As every fairy tale comes real
I've looked at love that way

But now it's just another show
You leave 'em laughing when you go
And if you care, don't let them know
Don't give yourself away

I've looked at love from both sides now
From give and take, and still somehow
It's love's illusions I recall
I really don't know love at all

Tears and fears and feeling proud
To say "I love you" right out loud
Dreams and schemes and circus crowds
I've looked at life that way

But now old friends are acting strange
They shake their heads, they say I've changed
Well something's lost, but something's gained
In living every day

I've looked at life from both sides now
From win and lose and still somehow
It's life's illusions I recall
I really don't know life at all

I've looked at life from both sides now
From up and down and still somehow
It's life's illusions I recall
I really don't know life at all

[Lance Schonberg · Rating 3 out of 5]

Up front: this book is not for everyone. I’m actually not certain it was for me. I haven’t really studied physics since the courses I took in the early 1990s in university. This was originally written a few years later, but assumes more than merely a rough knowledge of Relativity and Quantum mechanics – you actually need something more than just a basic introduction to really grasp what’s going on here.
But, armed with the internet, I persevered, more or less.
The science may be a bit dated, but since the book is 20 years old, that shouldn’t be too surprising. It’s also hard to tell without more physics, and more recent physics, than I have.
As a result, this is going to be a rather shorter review than I often write.
Hawking and Penrose are having a friendly conflict about the nature and structure of the universe. This is not a book for generalists or people with a passing interest in relativity and quantum mechanics. While the authors assume you have a basic familiarity with the relevant mathematics and quantum mechanics, I might suggest that basic familiarity is more along the lines of post-graduate.
Overall rating: 3 stars, but I should probably actually go with 2. What I understood was interesting, but what I understood wasn’t enough of the book. This isn’t a popular science book. Penrose and Hawking are talking much closer to the level the operate at. If you’re close to that level, the book is probably a lot more enjoyable.

[Ryan · Rating 4 out of 5]

Considerably more technical than either Hawking or Penrose's lay material (A Brief History of Time etc.) If you're seeking an introduction to the controversy behind Hawking's quantum gravity speculations (Hawking radiation, the no-hair theorem) then this is a good start. Is quantum information lost in black hole evaporation? There are still no solid answers to the questions posed here.

[Caitee Nigro · Rating 4 out of 5]

This book was recommended to me by a good friend a while back, who insisted I purchase my own copy because he couldn't stand to part - even temporarily - with his. So I did. Maybe a month later, co-author Sir Roger Penrose spoke at a local university and I was fortunate enough to see him, as well as have my very untouched copy of The Nature of Space and Time signed by him. Only recently did I read it, and I'd be lying if I said I could comprehend more than half on my own.
Reading this book, more a collection of expository scientific essays than anything else, worked itself out into a research project for me; every chapter was organized by subtopics or sub-processes that required a considerable deal of Wikipedia look-ups on my end to keep up with the content (which, by the way, must, must, must be read in order). The back-and-forthness of it, however, did pay off in the end in that if someone asked me, "What the hell is 'spacetime' anyway?" I could explain to them (though not nearly as eloquently as Hawking or Penrose--it's a start, right?) the relationship between theoretical "space," physical space and the effect that they have on time and its perception. The Nature of Space and Time sparked in my interest in reading more on theoretical physics, and I'd quickly recommend the book to anyone with a shared interest who 1) has a PhD or 2) doesn't mind three hours plus of research per fifty lines of text.

[Serdar · Rating 3 out of 5]

Exceedingly specialized discussion but fascinating to watch two of the biggest scientific minds of the past decades go at it.

[UraniaEXLibris · Rating 4 out of 5]

Leggere un saggio di astrofisica, specie dopo aver pescato il suggerimento da un elenco uscito dopo aver scritto su Google “libri sull’astronomia”, può risultare una vera e propria sfida. In particolare se l’ultima volta che hai affrontato un problema su massa, velocità e moto rettilineo uniforme (posto che qui siamo ben oltre) è stata tre anni fa. Al liceo. Sicuramente non scientifico. Ottimo. Insomma, idea grandiosa quella di cimentarsi in una lettura simile ex abrupto, soprattutto quando il magnanimo Google ti aveva anche gentilmente indicato saggi meno tecnici e più divulgativi (come un casuale “Vi racconto l’Astronomia” di Margherita Hack). Ho sbagliato lettura? Sì, no, boh, forse. No. E vi spiego perchè. Chiaramente la quasi totalità delle affermazioni contenute nel saggio l’ho data per buona, e per buona intendo assodata, in quanto, per ovvie ragioni, non avevo altre fonti nel mio archivio con cui confrontare le teorie ivi descritte e dimostrate. Eppure mi è piaciuto leggere questo saggio. In fondo a volte una lettura simile ricorda quanto ancora non si conosce e quanto ancora si ha da imparare. Ridimensiona, ma fornisce anche una spinta per andare avanti. Per andare “verso l’infinito e oltre”. Come soleva affermare Buzz Lightear. Per saperne di più certo, ma anche per superare i nostri limiti (limiti che spesso ci creiamo da soli per rimanere nella “comfort zone”). Non è però stata una lettura del tutto “oscura” e se ho potuto orientarmi è stato grazie non al corso di fisica ma a quello di chimica. Concetti come l’entropia, i principi della termodinamica, lo spin, il paradosso del gatto di Schrödinger, alcune teorie di Einstein, il principio di indeterminazione di Heisenberg, erano argomenti già presenti nella mia memoria e sono contenta di aver aggiunto qualcosa di nuovo per ognuno di essi. Ho anche imparato una cosa nuova: la “teoria dei Twistors”. Qualcuno direbbe che è poca cosa sapere della sua esistenza e non averla capita. È vero. Ma se si considera che prima di questa lettura non ne sospettavo nemmeno l’esistenza, sono contenta perchè le mie conoscenze in qualche modo si sono arricchite. Chissà magari è solo il primo passo che mi porterà un giorno a comprenderla. È pur sempre un inizio. Perciò anche se da un lato mi rincresce di non aver compreso il saggio nella sua interezza, sono comunque contenta di aver trovato qualcosa che mi ha riportato alla mente una disciplina che mi ha sempre affascinata e che al liceo era una delle mie preferite. In generale il saggio, seppur ostico nell’argomento, ha il vantaggio di lasciarsi seguire. Facendo lo sforzo di tenere a mente gli enunciati che vengono spiegati e dimostrati passo dopo passo il lettore riesce, proseguendo nella lettura, a ritrovarsi e trovare un filo conduttore. Unica pecca: averlo letto in digitale. Consiglio vivamente di leggerlo in cartaceo per prendere completa visione delle formule e delle figure (sull’ereader purtroppo risultano microscopiche se non addirittura invisibili). Un’ulteriore e triste conferma del fatto che l’ereader non è ancora pronto nè attrezzato per la saggistica.

Sette capitoli. Sette conferenze. Sette interventi. Due giganti a confronto. In questo saggio Stephen Hawking e il collega Roger Penrose si sfidano a colpi di teorie e dimostrazioni sul tempo, sullo spazio e sui buchi neri, punzecchiandosi a vicenda ma anche unendo le forze. I capitoli sono esattamente alternati: un intervento di Hawking, un intervento di Penrose, fino al settimo che vede entrambi rispondere alle domande e agli interventi. Le “lezioni” di Penrose sono quelle più discorsive e più improntate ad una riflessione filosofica (del resto lui stesso è un filosofo), mentre quelle di Hawking sono decisamente più fiscali e rigide, impostate sulla fisica pura e sul contraddire Einstein (!). Ho apprezzato il fatto che nei saggi a volte venissero riportati i commenti dell’altro interlocutore, anche se questo non era il suo spazio, creando una dimensione non divisa e unidirezionale, ma di dialogo e di inclusività. Ho apprezzato di più i “mini saggi” di Roger Penrose, in quanto sono stati anche occasioni che hanno fatto scaturire riflessioni filosofiche sul tempo, riportando anche qualche breve aneddoto della storia della fisica e della cosmologia. Non posso negare che la parte di Hawking sia stata penalizzata per il semplice fatto di non essere riuscita a vedere il novanta percento delle formule dimostrate e dunque di averla letta in modo frammentario e lacunoso, un’ottima occasione per riprenderlo in cartaceo e perchè no? Magari con qualche nozione in più.

[the_deepest_black]

Hawking: "Uznaje pozytywistyczny pogląd, że fizyczna teoria jest tylko matematycznym modelem i że nie ma sensu pytać, czy odpowiada rzeczywistości. Jedynie, czego można rządać, to by przewidywania teorii zgadzały się z obserwacjami" (14).

Hawking: "Nie wymagam, aby teoria odpowiadała rzeczywistości, ponieważ nie wiem, jak jest rzeczywistość. Rzeczywistość to nie cecha, którą można wykryć papierkiem lakmusowym. Mnie chodzi tylko o to, żeby teoria pozwalała przewidywać wyniki pomiarów" (167).

[Sarah Khalida · Rating 3 out of 5]

And all those mathematical equations and terms like Lagrangian and Eulers numbers which I learned in calculus back in undergrad emerged. A very technical read - I skimmed through most of it and highlighted the 'absorbable parts'. More Stephen Hawking in the future for me!

[Sofana Al-Bahi · Rating 4 out of 5]

Penrose, known for his philosophical ideas and artistic approach, was much more convincing to me than Hawking's math.

The book is too jargon-y for non-academics, but a very interesting debate nevertheless, for anyone wanting to get deeper into the subject. It did well in exposing the gap between the 2 scientists way of thinking and approach.
Hawking's lectures are too wordy yet difficult to understand, despite his known simplified pop-science writings. On the other hand, Penrose's lectures are short and too dense, but more factual and structured.
The diagrams are very helpful in visualizing the ideas, so if you're intending to read it, keep checking the diagrams as you go!

One of the most mesmerizing ideas I concluded from the debate is the fact that information might not be completely lost into black holes, but rather "dispersed" on the holes' boundaries in a way that's similar to holograms. This concept implies that information might in fact be recollected and brought back into shape.
This idea, together with the conclusion that the black holes we currently find withhold a previous universe that kept expanding untill it broke up into a black hole, in the same pattern that the expansion of our universe might lead to its explosion into another black hole in the future, followed by the creation of another new universe yet to come... this idea, together with the hologram-inspired one, imply that we can actually one day be able to "see" what the previous universe had looked like, by recollecting the "lost" information. It also implies that the next universe might be a new one where we can see all the previous universes... the afterlife maybe?

Who knows.

[Aykut Karabay · Rating 3 out of 5]

Zorlayıcı fizik kavramlarıyla, yer yer matematiksel formüllerle uzay ve zaman problemini ele alan bir kitap. Bu nedenle popüler bilim okurlarına hitap edeceğini zannetmiyorum.

Anladığım kadarıyla;

1 ) Kütleçekim, uzay-zamanı, bir başlangıcı ve bir de sonu olacak şekilde kıvırıyor, büküyor.

2) Kütleçekim - Termodinamik bağlantısı: kütleçekimin evren üzerindeki etkisini belirliyor.

Uzay-zamanın pozitif eğriliği, klasik genel göreliliğin geçerliliğini kaybettiği tekillikler doğuruyor. Kozmik sansür hipotezi bizi kara deliklerin tekilliklerinden ve evreni yutmasından koruyor. Fakat büyük patlamaya etkisi olamıyor.

Kuantum genel göreliliği, sınır olmaması, gözlemlediğimiz evreni öngörüyor. Hatta mikrodalga Ardalan ışınımında gözlenen dalgalanma spektrumunu da açıklıyor.

Kuantum kuramı, klasik kuramın sağlayamadığı öngörüleri kazandırsa da bunu tam olarak yapamıyor. Çünkü, uzay zamanın tamamını kara delikler ve kozmolojik olay ufukları dolayısıyla göremeyeceğimiz için, gözlemlerimiz, tek bir durum yerine, kuantum durumları bütünü ile belirleniyor. Bu ek bir öngörü getiremese de, evrenin niye klasik göründüğünü de açıklıyor.
Fizikten öngörüyü kaldırıp, onu indirgenmiş şekilde tekrar yerine koyuyor.


Matematik, fizik ve geometri bilgisi, temel astronomi ve fizik kavramlarına hakim olunması gereken okuması zor bir kitap. Popüler bilim kitabı kategorisine girebileceğini hiç zannetmiyorum.

[Pino Sabatelli]

Non posso valutare un libro di cui ho capito davvero pochissimo. A netto del fatto che si tratta del risultato di un dibattito risalente al 1994 e che, pertanto, potrebbe essere in alcuni punti obsoleto, il libro (come peraltro dichiarato in Premessa) richiede una conoscenza tecnica della teoria della relatività generale della teoria quantistica. Che io non ho. Insomma, non è un libro divulgativo. Per nulla.

[Michael Grizer (He-Him) · Rating 3 out of 5]

Interesting book, but way above my head. It should come with a warning that you need a PhD in physics to read it. I understood only a small fraction of it. I recommend A Brief History of Time for an approachable Stephen Hawking book.

[Alessandro Cavallaro · Rating 5 out of 5]

non ho capito una singola frase

[abril :) · Rating 4 out of 5]

penrose moito replica

[Gabriel Palomares Humanes · Rating 4 out of 5]

Un libro que te enseña algo más que solo MC o RG te enseña pensar como haría un científico desde 0 gran lectura que incita a desarrollarte aún más y más y da alas a la bestia de tu curiosidad

[Canberk Celik]

Büyük kısmından pek birşey anlayamadım. Belki lisansüstü bir fizik bilgisi gerekiyor belki de çevirisi kötü. Bölüm sonlarında konuşmacılar fikirlerini bir araya toplamış ve özetlemişler. Bir tek o kısımlar benim düzeyimdeydi.

[Maurizio Codogno · Rating 3 out of 5]

Vent'anni fa Stephen Hawking e Roger Penrose hanno tenuto una serie di conferenze per raccontare come loro pensavano si potessero mettere insieme la teoria della relatività generale e la teoria quantistica dei campi. Non che ci si sia riusciti nemmeno ora a farlo, intendiamoci. Ad ogni modo questo libro raccoglie il testo di queste lezioni. Ve lo dico subito: se non avete studiato fisica a livello universitario non ci capirete molto, o almeno io non sono riuscito a cavarci molto, anche perché la versione epub che ho letto (e che tanto per dire ha un ISBN errato nel colophon...) ha perso dei caratteri una volta letta con Aldiko che è tra i pochi programmi che permettono di leggere un file protetto da DRM; una versione pdf sarebbe stata migliore. Penrose si fa capire un po' di più, Hawking è davvero tosto. Stranamente in un paio di punti mi è parso che Libero Sosio si sia perso: solo che non sono riuscito a copiarmi il testo, sempre per colpa del DRM :-(

[Todd · Rating 2 out of 5]

"Time is the fire in which we burn." Delmore Schwartz

"...time is a companion who goes with us on the journey and reminds us to cherish every moment, because it will never come again." Jean-Luc Picard

I found the information in this set of 3 lectures to be somewhat interesting but because I am not a student (or practitioner) of science I found it to be a bit too specific to the field of physics/quantum mechanics/advanced maths/etc. for my general interest.

That said, one big problem I have with this is that he mentions god several times, and given there is no proof of god, why is he continually referring to a scientific "nothing" in his lectures? Even though I am not a scientist, the fact he mentions god tells me his science is not completely rooted in reality but rather at least in some part is rooted in mythology, and that tells me he lives in a world in which I do not live.

[Wanyoung Kim · Rating 4 out of 5]

Lots of diagrams. Has a lot of loaded philosophical statements that were useful when writing a thesis. Helps to explain singularity, cosmic censorship, etc.

[Stefano · Rating 3 out of 5]

E' difficile definire questo libro un libro di divulgazione. In realt� si tratta di una serie di lezioni (tre a testa pi� una discussione finale) in cui gli autori dimostrano le proprie teorie in merito alla natura dello spaziotempo attraverso lo studio delle singolarit� nell'ambito della meccanica quantistica e della relativit� generale. Per farlo fanno ampio uso di strumenti matematici molto complessi. Per comprendere appieno le dimostrazioni � necessaria una conoscenza specialistica di matematica e fisica (non basta qualche corso di analisi, geometria e fisica generale). Nonostante ci� il libro rimane comunque godibile anche ai non addetti ai lavori, a patto per� di accontentarsi di cogliere solo le idee e i concetti generali.

[Derek · Rating 1 out of 5]

I gave it a good college try, but was immediately swamped by the intense theoretical physics and deep mathematics involved. As a series of lectures between the two physicists as they voice disagreements about the nature of the universe, it was interesting to be a sort of fly on the wall, to see what these big brains talk about when the rest of us aren't around. On the other hand, they're discussing these things at their own level and not the level of a layman, so one might as well be a fly on the wall for the comprehension of the subject is concerned.

I gave up after failing to understand even the nature of the disagreement.

[José Uría · Rating 5 out of 5]

Un libro sólo para especialistas. Repito, sólo para quienes tengan conocimientos de las matemáticas de la relatividad general y los fundamentos de la mecánica cuántica. No hace falta ser experto en gravedad cuántica para seguir las argumentaciones, ni mucho menos. De hecho, cuando Hawking habla para otros físicos es un divulgador de primera, capaz de presentar temas abstrusos de un modo claro y conciso, todo lo contrario que hace en sus nefastos libros de divulgación popular. Y Penrose saca mucho partido a la notación de brakets, por ejemplo. Pero es imprescindible tener conocimientos al nivel de licenciatura de relatividad general y cuántica.

En su campo, un clásico imprescindible.

[Jeff · Rating 3 out of 5]

This is collection of essays is an argument between Hawking and Penrose about the origin and ultimate fate of the universe, plus some entropy notions about black holes. I will say this: Hawking throws equations out there like you flat out know what he's talking about. His disclaimer is that he assumes you know some math and quantum mechanics. The QM arguments were easy enough, and while I've seen some topology before, I wasn't hugely familiar with GR, so his essays were sometimes hard to follow. I thought Penrose's essays were a lot more accessible.

[Hayley · Rating 3 out of 5]

As much as I enjoyed the concepts that were meticulously laid out in this book; it hurt to read. The book required a lot from the reader to understand and keep up with the complex theories, unless of course you brought along your PHD in experimental physics and cosmology, which I did not.

[Hugo Rodrigues · Rating 4 out of 5]

Este livro é um conjunto de ensaios escritos por Roger Penrose e provados (acabados) pelo Stephen Hawking, embora não concordem totalmente um com o outro, provaram que as singularidades(buracos- negros) resultam do colapso de um estrela (sol Gigante), um livro muito interessante...

[Stephen · Rating 2 out of 5]

Not good. Notes from a Cambridge series of lectures. Colloquium level for PhDs in Quantum Gravity and Cosmology. Terms are not explained. Equations are not explained. Familiarity with 4 spheres, deSitter spacetime, Euclideanization of spacetime is assumed.