## Monday, June 20, 2016 ... /////

### Formal string theory is physics, not mathematics

I was sent a book on string theory by Joseph Conlon and I pretty much hate it. However, it's the concise, frank comments such as his remark at 4gravitons that make it really transparent why I couldn't endorse almost anything that this Gentleman says.

I can’t agree on the sociology. Most of what goes under the name of ‘formal string theory’ (including the majority of what goes under the name of QFT) is far closer in spirit and motivation to what goes on in mathematics departments than in physics departments. While people working here like to call themselves ‘physicists’, in reality what is done has very little in common with what goes on with the rest of the physics department.
What? If you know the amusing quiz "Did Al Gore or Unabomber say it?", these sentences could be similarly used in the quiz "Did Conlon or Sm*lin say it?".

The motivation of formal string theory is to understand the truly fundamental ideas in string theory which is assumed by the practitioners to be the theory explaining or predicting everything in the Universe that may be explained or predicted. How may someone say that the motivation is similar to that of mathematicians? By definition, mathematicians study the truth values of propositions within axiomatic systems they invented, whether or not they have something to do with any real-world phenomena.

In the past, physicists and mathematicians co-existed and almost everyone was both (and my Alma Mater was the Department of Mathematics and Physics – in Prague, people acknowledge the proximity of the subjects). But for more than 100 years, the precise definition of mathematics as something independent of the "facts about Nature" has been carefully obeyed. Although formal string theorists would be mostly OK if they worked in mathematics departments, and some of them do, it would be a wrong classification of the subject.

Formal string theory uses mathematics more intensely, more carefully, and it often uses more advanced mathematics than other parts of physics. But all these differences are purely quantitative – to some extent, all of physics depends on mathematics that has to be done carefully enough and that isn't quite trivial – while the difference between mathematics and physics is qualitative.

Conlon also says that what formal string theorists do has very little in common with the work in the rest of the physics department. One problem with the assertion is that all work in a physics department studies phenomena that in principle follow from the most fundamental laws of Nature – which most of the top formal theorists believe to be the laws of string theory. For this reason, to say that these subdisciplines have nothing in common is laughable.

But they surely focus on very different aspects of the physical objects or reality. However, that's true for basically every other project investigated by people in the physics departments. Lene Hau is playing with some exotic states of materials that allow her to slow down light basically to zero speed. Now, what does it have to do with the work in the rest of her physics department? No classic condensed matter physicists are talking about slow light. For particle physicists, the speed of light is basically always 299,792,458 m/s. Someone else measures the magnetic moment of the electron with the accuracy of one part per quadrillion. It's all about the last digits. What do those have to do with the work in the rest of the physics department?

People are simply doing different things. For Mr Conlon to try to single out formal string theory is absolutely dishonest and totally idiotic.

He seems to be unaware of lots of totally basic facts – such as the fact that his very subfield of string phenomenology is also just a ramification of research in formal string theory. The physicists who first found the heterotic string were doing formal string theory – very analogous activity to what formal string theorists are doing today. People who found its Calabi-Yau compactifications were really doing formal string theory, too. And so on. Conlon's own work is just a minor derivative enterprise extending some previous work that may be mostly classified as formal string theory. How could his detailed work belong to physics if the major insights in his subdiscipline wouldn't belong to physics? It makes absolutely no sense.

Also, formal string theorists are in no way the "first generations of formal theorists". Formal theory has been around for a long time and it's been important at all times. The categorization is sometimes ambiguous. But I think it's right to say that e.g. Sidney Coleman was mostly a formal theorist (in quantum field theory).

The attempted demonization of formal string theory by Mr Conlon makes absolutely no sense. It's at least as irrational and as unjustifiable as the demonization of Jewish physicists in Germany of the 1930s. In both cases, the demonized entities are really responsible for something like 50% of the progress in cutting-edge physics.
From my perspective in string pheno/cosmo/astro, people go into formal topics because they are afraid of real physics – they want to be in areas that are permanently safe, and where their ideas can never be killed by a rude injection of data.
He's so hostile that the quote above could have been said by Peter W*it or the Unabomber, after all. Are you serious, Conlon? And how many papers of yours have interacted with some "rude injection of data"? There have been virtually no data about this kind of questions in your lifetime so what the hell are you talking about?

By definition, formal theorists are indeed people who generally don't want to deal with the daily dirty doses of experimental data. But there's absolutely nothing wrong about it. After all, Albert Einstein could have been classified in the same way, and so could Paul Dirac and others. Formal theorists are focusing on a careful mathematical thinking about known facts which seems a more reliable way for them to find the truth about Nature. And this opinion has been shown precious in so many examples. Perhaps a majority of the important developments in modern physics may be attributed to deeply thinking theorists who didn't want to deal with "rude injections of data".

Another aspect of the quote that is completely wrong is the identification of the "permanent safety" with the "avoidance of rude injections of data". These two things aren't the same. They're not even close. None of them is a subset of the other.

First, even if formal string theory were classified as mathematics, it still wouldn't mean that its papers are permanently safe. If someone writes a wrong paper or makes an invalid conjecture, the error may often be found and a counterexample may be invented. Formal theoretical papers and even mathematical papers run pretty much the same risk of being discredited as papers about raw experimental data. And string theorists often realize that the mathematical investigation of a particular configuration in string theory may be interpreted as a complete analogy of an experiment. Such a calculation may test a "stringy principle" just like regular experiments are testing particular theories.

If you write a mathematical paper really carefully and you prove something, it's probably going to be safe. To a lesser extent, that's true in formal theoretical physics, too (the extent is lesser because physics can't ever be quite rigorous because we don't know all the right axioms of Nature). But there's nothing wrong about doing careful work that is likely to withstand the test of time. On the contrary, it's better when the theory papers are of this kind – theorists should try to achieve these adjectives. So Conlon's logic is perverse if he presents this kind of "permanent safety" as a disadvantage. Permanently safe theoretical papers would be those that are done really well. They are an ideal that may and should be approached by the theorists but it can't ever be quite reached.

Second, we must carefully ask what is or isn't "permanently safe". In the previous paragraphs, I wrote that even in the absence of raw experimental data, papers or propositions in theoretical physics (and even mathematics) aren't "permanently safe". They can still be shown wrong. On the other hand, Mr Conlon talks about "areas" that are permanently safe. What is exactly this "area"? If he means the whole subdiscipline of formal theory in high-energy physics, that subdiscipline is indeed permanently safe (assuming that the human civilization won't be exterminated or completely intellectually crippled in some way), and it should be. It is just as permanently safe as condensed matter physics. As physics is making progress, people move to the research of new questions. But they still study solid materials – and similarly, they study the most fundamental and theoretical aspects of the laws of physics.

So what the hell is your problem? People just pick fields. Some people pick formal string theory, other people pick other subdisciplines. No particular paper or project or research direction is permanently safe in any of these subdisciplines. But all sufficiently widely defined subdisciplines are permanently safe and that's a good thing, too. For Mr Conlon to single out formal theory for this assault proves that he lacks the integrity needed to do science. There is absolutely no justification for such singling out.
For those of a certain generation – who did PhDs before or within the 10-15 years following the construction of the Standard Model – this is less true, and they generally have a good knowledge of particle physics. But I would say probably >90% of formal people under the age of 40 have basically zero ability to contribute anything in the pheno/cosmo areas; I have talked to enough to know that most have little real knowledge of how the Standard Model (of either particle physics or cosmology) works, how experiments work, or how ideas to go beyond the SM work.
This is of course a massive attack against a large group of (young) theorists. Tetragraviton objects with a counterexample, Edward Hughes (whom Mr Conlon knows), and I could bring even better examples. The quality and versatility of various people differs, too. I don't want to go into names because a credible grading of all formal theorists below 40 years of age would need a far more careful research.

Instead, let me assume that what Mr Conlon writes is true. He complains that the formal theorists couldn't usefully do phenomenology. Great and what? In the same way, Mr Conlon or other phenomenologists would be unable to do formal theory or most of its subdivisions. What's the difference? Why would he be demanding that people in a different subdiscipline of high-energy physics should be able to do what he does?

Phenomenology and formal theory are overlapping but they have also been "partly segregated" for quite some time. When Paul Ginsparg founded the arXiv.org (originally xxx.lanl.gov) server around 1991, he already established two different archives, hep-ph and hep-th (phenomenology and theory), and invented the clever name "phenomenology" for the first group. This classification reflected a genuine soft split of the community that existed in the early 1990s. In fact, such a split actually existed before string theory was born. It was just a "finer split" that continued the separation into "theory and experiment", something that could have been observed in physics for more than a century.
I have heard the ‘when something exciting happens we will move in and sort it out’ attitude of formal theorists the entire time I have been in the subject – and it’s deluded BS.
Tetragraviton replies that people are far more flexible than Mr Conlon thinks. But I think that the main problem is that Mr Conlon has wrong expectations about what people should be doing. When someone is in love with things like monstrous moonshine, it's rather unlikely that he will immediately join some "dirty" experiment-driven activity. Instead, such a person – just like every other person – may be waiting for interesting events that happen close enough to his specialization. He has a higher probability to join some "uprising" that is closer to his previous work; and a lower probability to join something very different.

But what's obvious, important, and what seems to be completely misunderstood by Mr Conlon is that there must exist (sufficiently many) formal theorists because the evolution of physics without the most theoretical branch would be unavoidably unhealthy. The people who do primarily formal theory may be good at other things – phenomenology, experiments, tennis, or something else. It's good when they are but that's not their primary task. Even if you can't get people who can be like Enrico Fermi and be good at these different enough methodologies or subdisciplines, it's still true that physics – and string theory – simply needs formal theory.

The most effective way to increase the number of "really versatile and smart" formal theorists is to stop the bullying that surely repels a fraction of the greatest young brains from theoretical physics. But whatever is the fraction of the young big shots who choose one subject or another, it's obvious that formal string theory has to be studied.

On the 4gravitons blog, Haelfix posted a sensible comment about the reasons why many people prefer formal string theory over string phenomenology: the search for the right vacuum seems too hard to them because of the large number of solutions, and because of the inability to compute all things "quite exactly" even in a well-defined string compactification (generic quantities are only calculable in various perturbative schemes etc.). For this reason, many people believe that before physicists identify the "precisely correct stringy model" to describe the world around us, some qualitative progress must take place in the foundations of string theory first – and that's why they think that it's a faster route to progress to study formal string theory at this point. Recent decades seem to vindicate them – formal string theory has produced significantly more profound changes than string phenomenology after the mid 1990s. Those victories of formal string theory include D-branes and all the things they helped to spark - dualities, M-theory, AdS/CFT correspondence, advances in black hole information puzzle, the landscape as a sketch of the map of string theory's solutions, and other things. String phenomenology has worked pretty nicely but the changes since the 1980s were relatively incremental in comparison.

Mr Conlon seems to miss all these things – and instead seems to be full of superficial and fundamentally misguided Šmoit-like vitriol that make him attack whole essential subdisciplines of physics.