Three Roads To Quantum Gravity (Science Masters) Reprint Edition

Quantum mechanics and general relativity are great, but they are known to be hardly merged into one theory. But if there is a unified theory that describes nature, they should be. Physicists believe in such a unified theory. So there have been a lot of efforts to unify them, and physicists call the unified theory quantum gravity. According to the book, "Three Roads to Quantum Gravity" by Lee Smolin, there are three main approaches to quantum gravity. These are string theory, loop quantum gravity, and theories invented by some original thinkers like Penrose and Connes.

If you are interested in such a topic, you may hear about string theory. I am also a little familiar with string theory by reading articles and books like Brian Green's "Elegant Universe". But unlike with other books about the ultimate physical theory, this book focuses its attention to loop quantum gravity. I also heard the theory and searched wiki, but I could hardly understand it. In the book, although Smolin deals with both of string theory and loop quantum gravity, the focus is laid on loop quantum gravity. One of the reasons would be that loop quantum gravity is his specialty. The book was unlike any other article or book in that the book guided me to loop quantum gravity so easily, interestingly and concretely.

In Prologue, he says,

"I have tried to aim this book at the intelligent layperson, interested in knowing what is going on at the frontiers of physics. I have not assumed any previous knowledge of relativity or quantum theory."

But in my opinion, one would feel comfortable with the book if he has already taken a year-long course of physics and read some books related to this topic like Brian Green's "Elegant Universe", "The Fabric of the Cosmos", and Susskind's "The Black Hole War".

The most important claim of loop quantum gravity is that space-time (the whole history of our universe) is nothing but evolvement of a network of loops. In the theory, there is no space and time independent of matter. And there are limits on the smallest possible sizes of space and time. In the smallest world, they are not continuous, but discrete, that is, there are atoms for space-time. On page 138, the author says, "The spin networks do not live in space; their structure generates space."

According to the book, it is proper that quantum gravity starts with the works of Unruh and Bekenstein on the black hole in 1970s. Bekenstein's work is that the amount of information (here, what information precisely means seems to be an issue) inside a black hole is proportional to the area of the event horizon of the black hole. So if the information inside the black hole increases by some amount, then the area of the event horizon increases by constant times of that amount. This seems to suggest the followings.

1. Information (as we see 0 and 1 in the computer science books) is a discrete quantity, so, according to Bekenstein, the area increases by a discrete amount. If information and area can be regarded being equivalent, then this may imply that the geometric quantity, area, is discrete.

2. The maximal possible information inside a black hole with a fixed horizon area is limited. More generally, the information inside a space of finite volume is finite. This means that space is discrete in a very small scale. To see this, consider a chunk of space. If space is continuous (not discrete), then the chunk can contain an infinite amount of information because to point out the position of an electron in the chunk, we need an infinite length of decimals. Therefore, if there is an upper bound on information, there must be a smallest size of space and so space is discrete.

But the idea of discreteness (quantization) of space and time itself may have been claimed since 1920s. It is because quantum physics established during that period taught people that in very small scales, many fundamental physical quantities including momentum and energy are quantized, and so physicists may very well have thought that space and time also must be quantized.

As I understand the book, string theory and loop quantum gravity have the same origin. In 1950s, there were huge studies on superconductors. People found that, very strangely, the magnetic field lines in a superconductor are quantized. The quantized fields looked like a finite number of strings connecting two poles. But this was really mathematically true. So the Duality Principle was advocated, that is, strings and fields are two ways of looking at the same thing. Among those people, physicists who favoured quantum mechanics developed string theory and physicists who favoured general relativity developed loop quantum gravity. It seems that not until the late 1980s, loop quantum gravity does not have its position as one of the reliable quantum theories of gravity. Among great thinkers of loop quantum gravity in the late 1980s, there are Smolin, Ashtekar, and Rovelli. The book is written in 2001. During 1990s, Thiemann's work seems to be distinguished.

In the book, the author compares loop quantum gravity with string theory. String theory is better in that it seems to succeed in explaining all the four interactions, especially incorporating gravity. Loop quantum gravity does not yet seem to give the whole picture of how we can explain the existing physical world from a network of loops.

For example, as loop quantum gravity claims, if space-time is just a network of loops, then we should be able to explain how to construct the network so that its collective chunk is smooth and has the three dimensional Euclidean geometry. To do that, physicists tried to get ideas from material physics. There are many crystal structures by that metals form Euclidean shapes. We may be able to mimic the crystal structure if we are to explain the case of the networks of loops. But in the case, we also have to explain why nature chose the structure of the networks among other possibilities.

Loop quantum gravity is better in that it is background independent as general relativity is, that is, matter does not move on the fixed, unchanging stage of space-time, but matter and space-time are all changing together. In string theory, strings move on a fixed, unchanging stage of continuous space-time. But according to the book, the ultimate quantum gravity must be background independent, so string theory is at most an approximation of the ultimate quantum gravity.

There are many other interesting stories about string theory and loop quantum gravity. For example, the book says that there goes a programme of research under work to unify them. Their point of view is that loop quantum gravity describes the smallest scale of the world and string theory describes the world of the next smallest scale, so string theory can be explained from loop quantum gravity.

Reading the book, at a few places, I felt the difficulty in understanding what the book was saying.

1. At the beginning of Chapter 3, it poses an important problem. "The root of the apparent paradox is that my own experience is of one thing or the other, but the description of me that would be given in quantum theory by another observer has me most often in a superposition which is none of the things I actually experience. There are a few possible resolutions of this mystery." (page 39)

But I was totally not able to understand the following possible resolutions in the book. For me, Chapter 3 has its meaning only in raising the paradox.

2. At the end of Chapter 5, it says that if we can observe light from near the horizon of a black hole, we may get a clue about the structure of space and time at the Planck scale. Following that, it says, "Unfortunately, it has so far proved impractical to make a black hole, so no one has been able to do this experiment." But I cannot understand why we need to make a black hole in a laboratory. As far as I know, there are plenty of candidates of black holes in the sky. It would be done if we observe the candidates.

3. In Chapter 6, it introduces the work of Bill Unruh in the 1970s;

"Accelerating observers (in vacuum) see themselves as embedded in a gas of hot photons at a temperature proportional to their acceleration."

Temperature is related to the random motion of particles in the vacuum. The book explains where the randomness comes from. To do that, introducing the EPR experiment, it gives an example of two photons that are created together. When two photons are created together, they are found to have to following property.

"... when they are measured... their properties are correlated in such a way that a complete description of either one of them involves the other." (page84)

This is the basic argument for the next discussions of the book. I could not understand the sentence. Suppose I have two things A and B. The sentence seems to imply that if I want to completely know A, I must know B. But this is absurd. Even in quantum mechanics, if I want to know just one property of A at a time, then I can definitely know it. The cases that are inhibited in quantum mechanics are when we try to know some two properties of an object simultaneously.

I listed these for the readers who are not so skillful in English or Physics. They may feel ashamed when it happens that they cannot understand some parts of the book. I think that they don't need to feel that way. Such parts are either mistakes of the author or not important now to the readers, so they can be skipped without worry.

I was extremely thrilled while reading the book. I read the book twice. The second reading was far beneficial and exciting than the first reading. I'd like to appreciate the author for the nice experience.

Considering the experimental status of theories of quantum gravity, it is remarkable that research in this area has progressed to the level in which it has in the last few decades. If one examines the history of science it is readily apparent that laboratory and observational data drove the most successful scientific theories. By reading this book and by perusing some of the extensive literature on quantum gravity, it seems justified to view research in quantum gravity as being driven more by internal consistency requirements and reasons of aesthetics. The author gives an interesting overview of this research, and targets the "popular audience" for its readership. The author expresses great optimism that a successful theory of quantum gravity will be attained within the next decade. Considering the current difficulties in this research, this is indeed a refreshing attitude.

All of the approaches to the quantization of gravity rely on mathematical tools that are quite sophisticated, and competence in the use of these tools requires years of study and concentration. Due to the targeted audience, the author does not discuss these in detail, but he does give interesting and intuitive insights into the nature of the mathematical constructions that are used in quantum gravity. One of these, `noncommutative geometry', is quite recent, while the other, `topos theory', has been around for quite some time, albeit in several disguises. If one is to reconcile the two main approaches to quantum gravity, namely the loop approach and string theory, one will need to understand in detail the mathematics behind both of these theories. This will be a formidable undertaking, and it will take disciplined and focused individuals to carry it out. Unfortunately, and the author addresses this in the book, academic and funding pressures discourage such undertakings. This is either an argument for changing the nature of the academy (which will be very difficult) or doing this research outside the academy. But doing research outside the academy runs the risk of it being viewed as low quality, especially by those in the academy, and so this alternative carries high risk also. In either case, research in quantum gravity is difficult not only because of the nature of the subject matter, but also because of the societal and political pressures that make it a very risky endeavor.

The author, and a few others, came to quantum gravity when it was still a relatively young field, and, as he describes in the book, managed to survive in the academic environment. Their zeal is admirable, considering the roller-coast ride of confidence and depression they no doubt felt during their research efforts. There is no doubt now that quantum gravity is considered to be a respectable field of physics, and has attracted some of the best minds that have ever existed on this planet.

The manner in which the author presents the ideas on quantum gravity will no doubt motivate a few bright young people to take up the gauntlet and enter the field. He definitely prefers the loop approach to quantum gravity, being one of the individuals responsible for its development, but he is fair in giving string theory its due. Even professional physicists or mathematicians though who are curious about quantum gravity could gain a lot from a perusal of the book. There are some surprises in store for those who are used to thinking about space and time from a global point of view. This is especially true in the discussion of topos theory and the manner in which it is used in some approaches to quantum gravity. These approaches require that observers always view their place in the world as being one where they must reason using incomplete information. Two or more individuals though who have enough information to decide whether something is true or false will always make the same decision. This `local' view of descriptions, decision-making, and information gathering will be immediately appreciated by the mathematician reader who is acquainted with the concept of a `sheaf'.

The only possible irritation in the book (depending on the reader's theological views) is the discussion on the `weak' and `strong' anthropic principle and its play on very large (and very small) numbers. Those readers (such as this reviewer) who are not troubled by the magnitudes of these numbers will find the discussion somewhat superfluous. Some theologians have been delighted with the ramifications of some of the discussion on the anthropic principle and fine-tuning in recent years, particularly in the use of the "God of The Gap" arguments in cosmology. This will be no doubt continue, due to the need of these theologians to grab at every straw to establish their positions on origins, extremely fragile as they are.

Another one of the virtues of the book is the author's willingness to discuss the social and political context in which research in quantum gravity is done. He describes the string and loop-gravity theorists as effectively being at war with other, but that the degree of cooperation between them has (thankfully) increased in recent years. The contention between these two groups is no doubt partly due to financial pressures from funding agencies and also personal insecurities among the researchers themselves, the latter resulting in sometimes maniacal obsessions for recognition among peers as being the first to arrive at a particular result. Some say this contention is healthy for science, while others say it is a complete waste of time and has no constructive purpose. It is the opinion of this reviewer that the second holds.

As a layperson (and closet science geek), I really appreciated the author's straightforward and mostly non-mathematical approach to a difficult and incomplete new theory about quantum gravity. It covers three approaches which include super strings and M theory and black hole thermodynamics, both of which I hadn't really looked into before. It was great fun and I really enjoyed reading this book!

I found this work to be brilliant and very thought-provoking and would highly recommend it to anyone who may not be a physicist, but has some basic knowledge of science and would like to learn more about a fascinating subject!

Excellent account of recent development in quantum gravity, accessible to the informed non-physicist.

Nice job, Lee.

Smolin's presentation of the three theories was so thought provoking for me that I realized that I wanted to learn more. I had majored in Physics 35 years ago so I had QM and SR under my belt but nothing more modern. One thing that I particualry liked about Smolin's presentation of the three theories currently being worked on - superstring theory, quantum loop theory and blackhole thermodynamics - was the balanced way he kept saying how all three undoubtedly would contribute to the ongoing progress rather than trying to say one has to be right to the exclusion of the other two - it's simply too early to tell. I've spent 2 years (with a tutor) studying QFT in order, hopefully, to be able to at least approach the mathematics behind these theories. I've just ordered a "First Course in String Theory" and realized that I had never written a review of Smolen's book to so-to-speak thank him so I now fill that gap.