Interview with J. Michael Kosterlitz on 6 December 2016, during the Nobel Week in Stockholm, Sweden.

Michael Kosterlitz, welcome to Nobel Week. And you brought some artefacts for the museum, what did you bring?

Michael Kosterlitz: I brought some things representing my two passions in life, or my two passions in life at the time. Which are one rock-climbing guide to big cliff in North Wales, and some old calculations on something, that unfortunately is not what I got the prize for, but one of the few hand read notes that we could find, after I had done a major clear-out. That was, what, 40 years ago or something, so of course, it’s had a few clean-outs since. And old scribbled notes which may be of some value, should I become famous. But at the time, the idea of becoming famous was just ridiculous, so it all went.

And the rock-climbing guide, you used to be a very avid rock climber?

Michael Kosterlitz: Yes, I have two greater passions in life; well, probably in order my passions in life were first rock climbing, second physics and third family.

You are awarded the prize this year for absolute first research that you did, coming into the field that you now work in. Can you tell me a bit about how that came about?

Michael Kosterlitz: I was doing high-energy physics and doing lots of elaborate calculations for no return. Then, I was a post-doc in Italy, and of course I needed another job, so the plan was to go to CERN in Geneva, but I failed to get the paperwork in on time, as is my standard procedure, and ended up at Birmingham university, because that was one of the few places from which I got an offer at the very late stage in the game. Birmingham was actually the last place I wanted to go, but it turned out to be the best move I ever made. Because it was there that I met David Thouless and we started working on this problem. Mind you at the time, as far as I was concerned, it was just an entertaining theoretical problem, no more. I had no conception that this could turn in to something big, no idea at all. I doubt that either of us had. It wasn’t until, probably about the 80ies at the earliest, that I realised that we had done something good.

So, in this time after you had done your research, until the time that you really realised what it had led to, did you think about changing fields again, or moving to other parts within physics?

Michael Kosterlitz: Well, I did change fields; I started working on what is called non-equilibrium problems, in other words, on systems which aren’t in thermal equilibrium. And I was hoping to do something as good, when I realised that the work I had done, David and I had done, was actually good work. And I was trying to do something as good in another field but, never managed.

Have you moved back to this field again, is this what you are working on right now?

Michael Kosterlitz: I haven’t moved back, because I haven’t really thought about the field for a long time. And there’s lots of other people work in the field, and are way ahead, you know, have developed it much further. And so, I am, I guess you could call it, one of the ‘grand old men’ of the field, who has trotted out from time to time to say some deep words about it. But beyond that I don’t really do much in the way of research in that field.

You work with topological changes and phase transitions. When the prize was presented, the Royal Academy brought out some different type of baked goods. Can you try to give us a bit of overview why this would be a useful image?

Michael Kosterlitz: Ok, I’ll try. Let me start by saying that topology is a mathematical subject, which is concerned with the shapes of materials. Not the detailed shapes, because after all, as far as topology is concerned, a plane, you know, a flat surface, is equivalent to a sphere, which is equivalent to any shape you like. All that topology is interested in is the number of holes in the system. It’s a classification of shapes which can be continuously deformed into each other.

Right. You can’t have a half of a hole?

Michael Kosterlitz: Right. I mean, the rules are, you can’t get rid of a hole. Once a hole is there, you can’t get rid of it. Or you can’t make a new hole. Now the connection to what we did is a bit of a stretch, but the idea is that if you take your film of superfluid helium on a nice, flat surface – of course there are no holes in this surface. You say to yourself, what on earth has topology got to do with this? Well, in this context it doesn’t, but there are excitations in films of helium, where the fluid circles round and round a point. These are called vortices. And these excitations do exist, and it turns out they are quite important.

This is where topology comes in; because the surface of the manifold of which the topology is defined, is this layer of superfluid, not the actual thing that it is supported on. And so, if you got a vortex, where the fluid is spinning round and round, near the centre of the vortex, the velocity of the fluid has to divert; go to infinity. Which means that the material can’t be superfluid there, so that is going to hole. So, in other words, if you have a vortex produced, for whatever reason, the topology of the system changes.

Right, so you get these topological changes even in this type of material.

Michael Kosterlitz: Yes.

Was that an intuitive leap, I mean, when you first thought of this idea? Because coming from the outside, it seems as two quite disparate things. Was it intuitive to you that this was a mathematical model that could be used?

Michael Kosterlitz: Not directly. Because to me the physics was all in the various excitations that can occur. So, it is obvious that if you like, well we didn’t know it before we worked on this, that a vortex in superfluid helium, the centre of the vortex, was either empty, nothing there, or it was a normal fluid, not superfluid. So that part of it is simple. And so, I myself came from this point of view; I was only interested in the excitations, topology I didn’t know a thing about. Of course, I had the advantage of working with David Thouless, who seemed to know everything about everything. So, he realised that this was, you know, he used the word topology. And once he explained what topology meant, to me it suddenly became obvious. Call it topology or not, it didn’t really matter, but it sounded like a nice way to talk about it, so we called it ‘topological excitation’.

Are you surprised of how much this field has grown since you’ve worked in it?

Michael Kosterlitz: I am amazed. Because there are so many …  The original papers are referred to so often it’s almost embarrassing. I knew that we both knew very well, that the same ideas could be applied to talking about two-dimensional crystals, at least the melting of two-dimensional crystals. Because the essential excitations that melted the crystal, you can call them dislocations if you wish, which are analogous to vortices in superfluid helium. That is as far as we went with the two-dimensional melting. You can work anything out, at least I did a calculation which didn’t go anywhere, because we made the assumption that the lattice structure didn’t matter. Then we also knew that in principle it could be applied to a superconducting film. So, given an estimate of what the critical temperature should be and so on.

But we never really took it seriously, because our argument was that you couldn’t have true superconductivity in thin films. Which is a correct argument, but we never thought about the question of how, what length scales superconductivity could exist. In turns out that experimentally, if you have a system of, let’s say, a centimetre, you know linear size a centimetre or so, which is big by experimental standards, then, as far as, this system should obey the standard vortex theory, and the cut off that is inherent in superconductivity is irrelevant, because it’s of the order of a centimetre as well.

So, are there any of these, I mean, there a number of proposed practical applications for this work. And sort of, moving on looking into the future, are there any applications that you are especially looking forward to seeing?

Michael Kosterlitz: Oh yes! Oh yes yes yes. Because the hope is that the applications in quantum mechanical systems will eventually lead to this magic quantum computer. And I’ll be waiting for my desktop quantum computer. I hope to get one before I die, but I think that perhaps I shouldn’t hold my breath and wait and expect to get one. But anyway, with the developments in quantum mechanics, related to our ideas, it’s starting to look like a quantum computer may not be such a pie dream as I originally thought.

Looking at your career as a scientist, is there any person that really has inspired you, in your work or in your life?

Michael Kosterlitz: Lots of people. My co-worker David Thouless. I first met him as a London graduate in Cambridge and Oxford around 1961, something like that. And he was teaching us, and it was ‘mathematics for scientists’ or something like that. And as soon as he started lecturing, I realised I am in presence of a mind that operates in a different level to mine, and probably most other people. So, of course, I was incredibly happy to collaborate with David, because collaborating with somebody with a mind like that, is just an amazing experience.

Then there are other people who have certainly influenced me greatly. There is Michael Fischer at Cornell, who taught me, I was a post-doc there, back in, when was it 1973-74, who taught me about phase transitions and critical phenomena and the importance of experimental work and how theories and experiments should collaborate and criticise each other. Then there was John Reppy, also Cornell, also a superb experimentalist, and who is responsible for the experimental verification of our theory. So, I guess there are all sorts of people who influenced my thinking and my career. But the most important ones happened early in my life. And the most important one is of course David Thouless.

A bit more personal question; I know you have been diagnosed with MS some time ago. How did you, what did you do? And how did you sort of overcome, and handle something like that?

Michael Kosterlitz: I didn’t really manage to handle it very well at all, because at the time, as I said earlier, my major obsession, and a big part of my life, was mountain climbing. And that I had to quit because I couldn’t do it anymore. It is not easy to continue when half your life is just cut, you know you have no choice but to cut it out. I had a great deal of difficulty in coming to terms with my disability. However, fortunately, as my neurologist likes to say, I’m his star patient, so I did… My version of MS is at least one of these, going to the big remission where I come back almost to the level that I was before the attack. So eventually I managed to replace my passion for mountaineering with other things, and now I do work a lot and I travel a lot. And fortunately, I’ve got a very valuable wife who supports me whatever I feel like doing. And keeps on insisting ‘Look Michael, you can do it – its not as bad as you think, you can do it’. That is very important to me.

A final question; you’ve said earlier that coming into the field that you were awarded the prize for, one of the crucial things was your total ignorance of the details of that field. What do you mean by that, what do you mean when you say that?

Michael Kosterlitz: Exactly what I said. Because, I was a high-energy physicist. And so, my graduate work at Oxford was all in high-energy physics, and I simply went to the required lectures and so on, and something called statistical mechanics, which I sort of ‘mm’ it was one of these model, rather difficult subjects, where it wasn’t part of my chosen research. I didn’t pay much attention to it. But statistical mechanics is the central tool of condensed-matter physics, so when I went to this problem with David Thouless, changed from high-energy to condensed-matter, then statistical mechanics became very important.

And was it important for you to sort of look at the problem with sort of unconventional eyes, or…?

Michael Kosterlitz: Well sure, oh yes! Because, if you knew too much about it, if you were a normal person like me, you wouldn’t even go into the field because there are plenty of rigorous theorems, which were interpreted, is meaning that in that in systems like thin films of helium, two-dimensional crystals couldn’t exist. And there’s nothing wrong with the theorem, it’s just the interpretation of the theorem that was wrong. So David, who knew about these things, realised that it was just the interpretation that was wrong. Me, I was so stupid and ignorant that I said, I had no idea that this lack of long-range order was a serious problem. And so, I went ahead and basically looked at the problem in a different way, and it worked out.

Thank you so much for your time.  

Michael Kosterlitz: You’re welcome.

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