**The Foundation for Polish Science (FNP) celebrates its 25th anniversary this year. To mark the occasion, we have invited 25 beneficiaries of our programmes to tell us about how they “practise” science. What fascinates them? What is so exciting, compelling and important in their particular field that they have decided to devote a major part of their lives to it? How does one achieve success?**

The interviewees are researchers representing many very different fields, at different stages of their scientific careers, with diverse experience. But they have one thing in common: they practise science of the highest world standard, they have impressive achievements to their credit and different kinds of FNP support in their extensive CVs. We are launching the publication of our cycle; successive interviews will appear regularly on the FNP website.

Pleasant reading!

**The Importance of Physicists Talking**

**Assoc. Prof. Piotr Sułkowski, a theoretical physicist, talks to Patrycja Dołowy and Olaf Szewczyk.**

PATRYCJA DOŁOWY, OLAF SZEWCZYK: **We are in a room of the University of Warsaw’s Faculty of Physics in Pasteur Street, within four walls, with a floor and a ceiling. But how many dimensions are we really in?**

PIOTR SUŁKOWSKI: Some theories I deal with predict that in fact there could be more than four dimensions. According to string theory, there should be ten. It’s worth noting that this number consistently follows from the principles of quantum mechanics forming the foundation of this theory (it’s not an arbitrarily chosen number). Therefore physicists are trying to understand why we only experience four of those ten dimensions and to explain how whatever occurs in the six invisible dimensions translates into what happens in the other four. Because it has to, in one way or another.

**String theory raises many hopes as being a theory that describes the world in the most complete way, but some also say it lacks the elegance and simplicity that we might expect from fundamental rules governing physics.**

String theory itself is simple and its foundations very elegant. What is complicated is some of its problems, for instance those related to the six dimensions we cannot see or experience. It’s true that for some time we have lacked experimental data on the basis of which we could develop the phenomenological aspects of this theory. Among other things, contrary to initial hopes, due to the difference between the scales we are able to study in experiments and those that are supposed to correspond to the lengths of elementary strings, it hasn’t been possible to derive the Standard Model of elementary particles from the assumptions of string theory; the model has been known for several dozen years and was recently confirmed once again by the discovery of the Higgs boson. It’s worth underlining, however, that string theory research has led to significant discoveries in the closely related quantum field theory, which in a sense is a universal language of contemporary physics and the foundation of many other areas of physics, e.g. elementary particle physics, nuclear physics, condensed matter physics or statistical physics.

**The Standard Model is one of the most important theories of contemporary physics. It describes the physics of elementary particles – the fundamental components of matter. How is your field – string theory – related to it?**

There is no strict boundary – at least as far as the development of theoretical ideas and concepts is concerned – between string theory and elementary particle theory as well as many other areas of contemporary physics. As I mentioned, string theory is closely linked to quantum field theory. Ignoring the connection would be artificial and scientifically unfounded. Great physicists studying string theory have made and still make major discoveries in other areas: elementary particle physics, gravity, condensed matter physics. They are open to different directions of research and are interested in anything important and engaging.

*Pictured: **prof. dr. hab. Piotr Sułkowski, photo by One HD*

**Some say that not much that’s new has happened in theoretical physics in the last quarter of a century. The most famous discovery of recent years – the Higgs boson – only confirmed a theory developed fifty years ago. This is an unprecedented situation in over two centuries of the history of modern science.**

I wouldn’t call the present pace of development in physics unprecedented. Today, elementary particle physics notwithstanding, breakthrough discoveries are made in many other areas of physics. Elementary particle physics, as the name indicates, studies the smallest components of matter and, generally speaking, what happens on very small distance scales. Equally interesting and no less fundamental questions apply to what happens at very large distances, in processes occurring on cosmic scales. In this context, the discovery of gravity waves in the past year is extremely important, for example. One of the first people to study their properties, back in the 1950s, was Professor Andrzej Trautman from our faculty, and their detection today undoubtedly marks the start of a new field and opens the way to completely new ways of studying the Universe. The pace of discovery of extrasolar planets has been extraordinary in recent years as well, and also the related development of research on the possibility of life existing on them, which has already given rise to a new field that has been called astrobiology. It’s also fascinating to find how matter organizes itself on intermediate scales – such phenomena are studied within fields including condensed matter physics, atomic and nuclear physics, quantum optics, biophysics. These fields are developing very quickly at present and we can say that mainly the research conducted within them translates into extremely dynamic progress in technology, telecommunications or medicine. Perhaps the aforementioned new research areas will give a new impulse to elementary particle physics. Such hopes are being pinned on another young field in particular, called astroparticle physics, which tries to explain the relationships between the properties of the fundamental building blocks of matter and the things we observe looking at the sky. Meanwhile, it’s true that today we don’t discover as many new particles as we did a few decades ago.

**Why is that?**

We have reached such scales of energy in which new particles do not appear in experiments – it seems that’s just the property of our Universe. Therefore our task is to study it the way it is, and not the way we’d like it to be. Of course various hypotheses exist saying that new particles should appear for even greater energies, but so far we have no access to them. Our equipment, in particular the Large Hadron Collider at CERN thanks to which we found the Higgs boson, has attained such parameters and dimensions that it’s very hard to push the boundary even further. However, research on elementary particles and the funding assigned to it has been and still is worth it. It’s hard to overestimate its impact on the development of contemporary civilization. It’s worth underlining and reminding all sceptics that funding earmarked for the construction and maintenance of research accelerators is only a small fraction of the money spent on the construction and operation of accelerators used for medical purposes (including cancer treatment) and in industry. Besides, it was the need to analyse enormous amounts of data at CERN that led to the birth of the Internet. That only confirms how difficult it is to predict the impact of fundamental research on the development of science and even on everyday life.

**If you were to say something about the research for which you received the prestigious five-year ERC (European Research Council) grant, where would you start?**

My field is theoretical and mathematical physics – including string theory and the quantum field theory I mentioned before – and their relation to mathematics. In particular, in the past few years I have been studying the relation between physics and mathematical knot theory. Mathematicians are trying to classify and somehow describe all knots – configurations that can be tied on an ordinary piece of string. Though it might seem like a mundane problem, knot theory is a very important branch of mathematics, while the problem of knot classification is extremely difficult and closely tied to many other areas of maths. It also turns out that the formalism of contemporary physics provides extremely effective tools and inspiration related to knot theory problems. Using the methods of theoretical physics we are trying to answer questions posed by mathematicians: how to distinguish different knots and classify them, e.g. we are looking for what we call knot invariants, which are simple objects (like numbers or functions) that characterize a given knot and set it apart from others. This is one of the problems in the project financed from the ERC grant that I am implementing.

**What is the effect of this research? For example, what does the problem of knot classification involve?**

The main question that mathematicians are asking might seem simple: how to tell which knots are equivalent, meaning which knots can be made to coincide without cutting them. This turns out to be a very hard question, but one worth answering because it is of key importance for a great many fields involving knots, and even in everyday life. Someone who has to untangle a knot on their shoelace or a sailor who has to tie a rope, in practice is also solving problems related to knot theory. The only difference compared to mathematical knot theory is that in the theory we consider knots on closed curves – those whose ends are fused. If we take a straight piece of string, fuse the ends, the result is an ordinary loop, or what we call a trivial knot. If we first tied a knot on the string, even the simplest one, and then fused the ends, we would have a more complicated configuration that cannot be made to coincide with a trivial knot (i.e. an unknotted loop) in a continuous way – to do that, we would first have to cut the string and untangle it. If you look at two drawings of more complicated knots, or at any two knots, and ask whether one can be transformed into the other in a continuous way, without any cutting and fusing back together, then it turns out to be a very complicated question to which mathematicians are seeking an answer…

**And have been for a very long time?**

Already more than 25 years ago, in 1990, the Fields Medal – considered the mathematical equivalent of a Nobel Prize – was awarded for this kind of work. At about the same time, physicists realised that some results obtained within quantum field theory reproduced and largely generalised the knot invariants known to mathematicians. In physics theories you calculate the probabilities of certain processes – and those mathematical knot invariants turned out to correspond, from a physical viewpoint, to the probability of the movement of particles (described by some peculiar theories) along knotted trajectories. Such a physical interpretation enabled many specific results to be obtained, which mathematicians started to analyse. My research concerns precisely this type of problem. Perhaps it sounds like an abstraction, but as I mentioned, knots and their invariants play a role in many other fields – hence the need to be able to distinguish and characterize knots.

*Pictured: **prof. dr. hab. Piotr Sułkowski, photo by One HD*

**Who might find it useful?**

Lately, biophysicists in particular, who also deal with knots – those forming in DNA and in proteins. Among the researchers studying these problems is my wife Joanna Sułkowska as well as myself (though it’s not the main subject of my research) – as you can see, knots can connect and bind people in different ways (*laughs*). For a long time scientists used to think knots couldn’t form in proteins; however, a great many have been found in recent years. Proteins are long chains that are slightly similar to Christmas tree paper chains, composed of a few dozen to several hundred amino acids. They assume a three-dimensional form in space, and how they work in the body depends on the shape. Therefore one can ask: Can a given shape of protein form a knot, can different kinds of knots form in proteins, what purpose could this serve, is the existence of knots related to a protein’s function and how? In other fields, people study different properties of knots, which are also computer-modelled, e.g. their stretching strength. In all these problems it is essential to use mathematical knot invariants. Therefore we can hope that the results of our research will also become important one day in seemingly distant fields.

**What specifically does your work look like? With experimental physicists it’s obvious, they sit in a lab, set things up, fiddle with things, observe, record. But you calculate, is that right?**

I conduct theoretical research which consists mainly in calculating, or proving certain relationships or theorems. I work with pen and paper, and also with a computer, e.g. when carrying out symbolic computation. I head a research team of almost twenty people, ten of whom work at the University of Warsaw’s Faculty of Physics and the others at various centres abroad. There are many important problems and questions in physics that it would be good to answer but we often don’t know how to go about it. Therefore we try to build simpler models or theories that may not answer the most important question but will bring us closer to it, enable us to understand the essence of a given problem in a simpler example. It’s usually worth understanding something first on a simpler example. For instance, certain physics theories describe our world which is four-dimensional (if we take time as one of those dimensions). They are often hard to solve, so models that are easier to analyse are considered, with a smaller number of dimensions, e.g. two or three, that can help understand the essence of certain phenomena.

**How does the typical grant system relate to this specific kind of research?**

Of course there are many ongoing discussions on how a grant system should work. Systems for financing science are different in different countries and probably none are perfect – the problem is a complicated one. The system in Poland has pros and cons. One of its drawbacks is the temporary nature of grants. Funding is usually granted for two, three years, which can be hard for experimental physicists, for example. They purchase expensive equipment with their grant money and once the funding period is over, they have to consider how to ensure that it is used effectively. There is some pressure stemming from the fact that scientists are regularly, and very often, held accountable for the effects of their work. The emphasis is sometimes on making sure they obtain and present new results quickly. In reality, important discoveries are seldom made within any defined time frame; it often takes quite a lot of time, it can depend on accident or good luck. On the one hand, it would be best to leave scientists to themselves; if they have talent and motivation they are sure to arrive at something important with time – not necessarily every individual separately, but as a community holding discussions and sharing knowledge – regardless of the number of publications written in the meantime, or the number of citations. However, of course given the increasingly mass nature of scientific research, it’s understandable that there has to be some form of checking it, and research is an investment that has to be accounted for somehow. A good grant system should definitely promote scientific excellence in a systemic way: there should be open competitions with transparent and merit-based criteria; risky research should be appreciated, as it can lead to breakthrough discoveries, though it can also turn out to be a blind alley.

**What kind of support is the most important and the best investment in your field?**

The main thing is to find an important subject. Many ideas emerge during scientific meetings with other people – the exchange of thoughts is very important in my field. When scientists talk to one another it often turns out that one person knows one thing, another knows something else, and something new and significant arises from the meeting. Grants enable us to exchange ideas in this way – in my field, they serve mainly to finance travel, conferences and meetings with associates. It is exactly support for contacts among scientists and the development of collaboration that is provided, for example, by various programmes of the Foundation for Polish Science that I had the pleasure of benefiting from: START, HOMING PLUS, as well as INTER which combines interdisciplinary research with the popularization of science.

**Exactly. But how do you popularize mathematics? Or theoretical physics? It must be very hard!**

I run an initiative called *Ask a Physicist *(*http://zapytajfizyka.fuw.edu.pl/*), which thanks to a grant from another FNP programme – eNgage – I’ve been able to expand to include lectures popularizing physics, delivered in our faculty by leading scientists. So far the lecturers have included professors Andrzej Kajetan Wróblewski, Michał Heller, Aleksander Wolszczan, Magdalena Fikus. In December (2016) an *Ask a Physicist* lecture will be given by Prof. Roger Penrose – I encourage everyone to attend! The lectures are about one hour long and afterwards you can ask questions, of which there are always many. It turns out that lots of people are interested in the lectures – people of various ages attend: pupils, students, senior citizens, parents with children. It’s been a great and very pleasant surprise. Sometimes the audience is so large that some have to sit in another lecture hall and watch a broadcast from a camera. I think this kind of activity is worth developing at many universities, also in smaller towns. If it is properly publicized and promoted, there are sure to be many attendees. That’s why other science popularization initiatives are also very valuable, e.g. science festivals. I think it’s very important that we invite people to come here, to our faculties, to the university. It makes them feel they are being treated with respect and they can have genuine contact with things that usually go on behind the closed doors of offices and laboratories.

**You also talk about science to people who aren’t scientists.**

Yes. I take part in meetings with people interested in physics and in radio programmes, I write texts, I answer questions from internet users on the *Ask a Physicist* website.

**What do people ask about?**

We get a lot of questions, some are very surprising. They concern the latest discoveries reported by the media, topics as mysterious as the theory of relativity and quantum mechanics, mathematical and philosophical issues, and also daily life – how telephones and cars work, natural phenomena. These questions are answered by a team of specialists, which I coordinate, from different fields of physics.

**What do you think fascinates people so much in maths or physics?**

A fascination with physics is nothing more than a fascination with the world around us. Mathematics is essential for an accurate description of that world. Once we satisfy our basics needs – we get our sleep and are properly fed – we start wondering about the things going on around us.

**In our post-Enlightenment times, scientists in a way fulfil the ancient role of priests or shamans explaining the world…**

I don’t see myself that way and I wouldn’t call scientists priests; but it is true that our civilization is technical. It’s hard to say what would happen to this civilization if scientists were to suddenly disappear, and with them all the knowledge they have gathered and passed on to successive generations. Yes, you can say that scientists keep the mechanisms of civilizational progress in motion.

**Associate Professor PIOTR SUŁKOWSKI (born 1978 in Warsaw), works at the Faculty of Physics at the University of Warsaw, heading a research group carrying out the “Quantum Fields and Knot Homologies” research project financed with a grant from the ERC. A beneficiary of FNP programmes: START (2009), HOMING Plus (2011), INTER (2012), Ideas for Poland (2014), eNgage (2014).**