“I have absolutely no doubt that it's not our universe”: Henry's review of Conversations on Quantum Gravity by Jay Armas
This review also appears on Goodreads.
It is by now a well-worn slogan that there is something called the unreasonable effectiveness of mathematics in the natural sciences. What is called ‘mathematical physics’ is considered to be the part of mathematics – the purely abstract world of definitions, theorems and proofs – where any purported connection to experimental physics and the nebulous concept of ‘evidence’ is merely possible and not strictly necessary. Mathematical physicists are mathematicians; it is someone else’s job to think about collecting the data. Large experiments such as the LHC have done an amazing job at revealing new entities such as the Higgs boson but have not yet revealed supersymmetry, a key part of the proposed theoretical physics underlying string theory.
String theory, the principal subject of this recent book on quantum gravity, is perhaps the most famous example of this kind of research work. String theory is nowadays extremely mathematical in its approach – completely unintelligible to the general reader. Along with one of the oldest areas of mathematics known as number theory, it perhaps tests the limits of what is comprehensible to the human brain. And yet string theory is a successful research programme that continues to attract funding long after its critics have attacked it for not generating any experimental evidence that might confirm or disconfirm the ‘theory’. Although, as the book under review reveals, string theorists don’t consider string theory to be a theory that makes predictions at all, but rather a ‘framework’ (just like quantum field theory, we are told). Not only that, but apparently string theory isn’t really about strings either.
Conversations on Quantum Gravity, according to physicist Astrid Eichhorn, is “an unconventional ‘long-exposure photograph’ of the evolving research field of quantum gravity”. The various research programmes include string theory, loop quantum gravity (LQG), asymptotic safety, causal dynamical triangulations (CDT), causal sets, non-commutative geometry, Hořava-Lifshitz gravity, and a few other approaches. The relative sizes of these programmes vary quite significantly. The largest, string theory, claims hundreds of thousands of published research papers over several decades, whereas many smaller areas may have just tens or hundreds of papers to date. But a continuing theme throughout the book is that the sociology and history of scientific research is not a guide to its truth. A range of experts from across mathematical and theoretical physics are consulted and one rarely has the feeling that a theoretical perspective is missing.
I consider the book to be a serious achievement. Readers are treated to engaging conversations which reveal the true nature of modern science. The level of each interview varies in technical detail such that even if one were to come to the book with no more than (say) high school calculus they should still gain something from the honesty and personality of each interviewee. Careful editing and planning have ensured that a consistent set of questions appears throughout many of the interviews, letting the material connect thematically from one interviewee to the next.
While not all of my favourite passages could be quoted and still keep this review of a reasonable length, here is a selection of quotes to provide some sort of flavour of the book.
Nima Arkani-Hamed on the role of the theoretical physicist in modern society:
“Theoretical physicists are human beings with emotions, jealousies, envies, hatreds, loves as everyone else but I think that [...] theoretical physicists also have a deep kind of humility. This kind of humility is such that you believe in your smallness relative to the kind of questions that you are asking. This is the idea that there is something greater than yourself and that not only you are devoting your life to it but also that entire groups of people devoted generations of their lives to explore these questions and push the limits of knowledge further. It’s as noble and pure a quest as human beings have ever embarked on. So, I think it’s really important for us to keep showing people that truth matters, it exists, it’s worth pursuing and that it’s bigger than all of us.”
Alain Connes on the role of the mathematician in modern society:
“There is a very simple answer. The role of the mathematician is to create concepts. Let me take one instance, the notion of truth, in order to illustrate what I mean. We all have in mind that something is either true or false. If we attend a debate on politics or another controversial topic, we are prone to say that this guy is right and that guy is wrong and that’s our way of making a judgement. Now, it turns out that probably we should be more advanced at the level of the formalisation of the idea of truth. In fact, there is a mathematical concept which has been created by A. Grothendieck which is the concept of topos and which has, thanks to contributions of F. W. Lawvere, a far more sophisticated notion of truth. Technically the “truth values” form an object of the topos and this object classifies sub-objects exactly like the characteristic function (which takes values in the two point set “True, False”) of a subset does in the case of the topos of sets. Thus for this simplest topos something is true or false. But as soon as you take a slightly more involved topos, such as the topos of quivers, you get a much more refined notion of truth values and in the case of quivers it involves "making mistakes, corrections, checking" as fundamental parts of the structure. From this example, you witness that mathematics is a factory of concepts which are extremely rich, which are subtle and which of course are hard to grasp by the public in general due to their mathematical precise and involved formulation. This lack of grasp by the public holds at a certain time in the history of civilisation but I believe that in later years these concepts will become common. This sophisticated notion of truth has, by the way, nothing to do with probabilities. It’s a very beautiful and precise notion developed by a great genius of mathematics. So, to me, this is the role of mathematics: fabricate concepts and facilitate the process by which the public acquires them. That’s it.”
Robbert Dijkgraaf on string theory and whether aesthetic reasoning is a good source of guidance:
“Here the point is what do you exactly mean by “aesthetic” and whom do you ask, right? Perhaps it’s most fair to ask these questions to people outside the field. Mathematicians, for instance, really think that there are beautiful things coming out of string theory. That’s remarkable because actually in general when string theorists say that it’s a beautiful theory, they don’t necessarily see the contact with deep mathematics. I think that the beauty of string theory is its interconnectedness and the deep underlying concepts. [...] So for me, the true beauty of string theory is the way it connects to all these different subjects, even complementary forms of aesthetics. I could give you a list of 100 mathematic subjects which on the surface appear to be completely disjoint and ask for a mathematics textbook where all these 100 mathematical subjects appear. If it’s a mathematician who doesn’t know anything about physics, they would say it doesn’t exist. There’s no such thing that connects automorphic forms, the Langlands program, E8, thermodynamics, differential geometry, all these subjects. But then I say, no, no, no, just start to think about how to quantise wiggling pieces of strings and then you’ll connect all of these subjects. That’s pretty magical! So I think that’s where the real beauty is. [...] We have gone through these transitions in physics where we at first instance seem to have lost beauty. There’s enormous beauty in a Newtonian universe, in classical mechanics. We have lost parts of that because of the indeterminacy of quantum mechanics, where experiments only allow us to state that we have, say, a 57% chance of this outcome happening. You somehow miss some very essential part of what you thought physical theories were all about: determinism. So, in general I think that “coming closer to the truth” also means that you have to give up on certain aspects of conventional beauty and then, if you’re lucky, you get rewarded with something new and exciting in return. In many ways it’s a bit like in arts, where you have various phases in art history. I don’t think that twentieth-century art is intrinsically more beautiful than nineteenth-century or seventeenth-century art. It’s however a different kind of beauty, with more expressive power. In physics the same evolution took place. There were many theories which were very beautiful but which were superseded by something else. In that sense, I think that the fact that “string theory is beautiful and therefore it has to be true” is kind of a silly argument.”
Renate Loll on her view of breakthroughs and progress in theoretical physics:
“If we consider high-energy theoretical breakthroughs, I don’t see any. We have found the Higgs particle but that had been theoretically predicted a long time ago. [...] I think it’s very hard to measure progress, not just in quantum gravity, but in the whole of theoretical high-energy physics. What is progress? If you take some particular approach you can have an objective notion of technical progress within that approach, but that is usually a long shot from understanding more about nature. If I adopt this higher standard, I really think there hasn’t been any theoretical breakthrough in the past 30 years.”
Lee Smolin on philosophy of science and his well-known critique of string theory:
“I have many doubts about whether or not I was the right person to be the author of that book. As a person I am very conflict-adverse and I hated the tone of the controversy. Also my own view of string theory is complicated, with strong pluses and strong minuses, and almost none of the reviews or commentary addressed the subtlety and complexity of the issues – and it was that tension that defined the book for me. I wouldn’t have written the book if I didn’t find a lot to be interested in in string theory and, at the same time, a lot to be disappointed by. Also, very few got the fact that string theory was not the main focus of that book. The book was first of all an essay in the philosophy of science concerned with the question of how science works. It was chiefly addressed to the critique of science made by the philosopher Paul Feyerabend, which had had a huge influence on my view of science, but left me with some unanswered questions, which the book addressed. The main thesis of the book was an elaboration of Feyerabend’s claim that controversy and disagreement within the scientific community play an important role in the progress of science. The key point for me was to propose an answer to Feyerabend’s unanswered questions, which involved a characterisation of science as based in a community bound by a certain code of ethics. [...] String theory was in the book as a case study to illustrate these issues of scientific methodology.”
Andrew Strominger:
“I would say that the one thing we know about string theory is that it’s not a theory of strings.”
Leonard Susskind:
“I don’t think that there’s more than one theory of quantum gravity. There may be more than one solution to its equations. String theory is a theory that has lots of different solutions obeying the basic rules of string theory. There are probably more extensive rules, or rules that are more general and have as their solution a broader class of things, which may include string theory. That’s the way I’m inclined to think about it. But there’s absolutely no doubt in my mind of two things: that string theory is a mathematically consistent theory which contains gravity and quantum mechanics but that is narrow and supersymmetric. I have absolutely no doubt that the mathematical structure of string theory is consistent and I have absolutely no doubt that it’s not our universe.”
This is an essential book for all those interested in the history and philosophy of mathematical physics.