Category: General

Posting will continue to be light-to-non-existent over the next week and a half, as I finish up several big projects. In particular, I’m heading to Amsterdam on Saturday, and expect to be largely out of touch for a week.

What are the different possible phases of matter?

One of the big advances of twentieth century physics was the development of a very general set of ideas – the renormalization group – that let you analyse and understand the properties of different phases of matter, and the phase transitions between them. This development was done by a whole bunch of people, including Landau, Ginzburg, Kadanoff, Michael Fisher, Wilson, and others.

In a recent issue of Science there’s an article by Senthil, Balents, Sachdev, Vishwanath and Matthew Fisher claiming to have found a significant class of phase transitions that can’t be understood within this framework. (Here’s the long (and possibly more comprehensible) version of the paper at a publicly accessible site.)

This would seem to be extremely significant if true, which is why I’m reading the paper. I’m reminded, as I read, however, of the many basic items of background material I don’t understand all that well.

One thing that always bugs me when I read about phase transitions is the question “What is an order parameter?” Landau introduced this concept as the unifying idea behind his theory of phase transitions. Examples include the magnetisation of a ferromagnet, and the phase in a superconductor.

So far as I can tell, the order parameter is usually divined, as opposed to defined. How are we supposed to deduce the order parameter? Is there a freedom in our choice of order parameter? What makes one choice of order parameter a good one? I’d love to fully understand the answers to any of these questions.

In the comments to the previous post, Pyracantha points to a post at Electron Blue. It’s all interesting, but I thought this deserved wider propagation:

In gratitude for his Web curriculum efforts, I dared to write Dr. ‘t Hooft an e-mail explaining what I was doing and inviting him to look at my own Website. To my astonishment, he promptly sent me a reply! He commented positively on my site, and reminded me that his curriculum section was only at the beginning stages. Yes, this busy elite scientist took the time to send a reply back to a beginning student. This is a class act. I would call it nobelprize oblige.

This reminded me of a nice story I heard years ago: Stanford Nobelist Doug Osheroff excused himself from the party Stanford threw in his honour when his Nobel was announced, saying that he had to go and teach his class of first year engineers. That’s class.

How to become a good theoretical physicist, by Gerard ‘t Hooft. If anybody should know, I guess it’s ‘t Hooft.

Two very interesting posts (and discussion threads) at Uncertain Principles: here and here. Here’s the second post in full, with a few comments of my own thrown in.

In the very nice comment thread that’s sprung up around the last post (this is why I envy Teresa Nielsen Hayden), Mary Messall writes about Physics in general:

The thing is stories don’t give you numbers that can be checked by experiment. Equations do. Insofar as we demand that our science be experimentally verifiable, we’re demanding that it consist of equations. In that sense there’s no such thing as “a scientific explanation.” Explanations are inherently unscientific — unpredictive, unfalsifiable.

What’s more, I find (to my dismay) that a great many, perhaps even the majority, of the equations we’re given in class are used *without* interpretation. Sometimes I wander around demanding an interpretation for some specific expression from everyone in the department, and mostly I eventually come up with some story that satisfies me, but it’s amazing how many of the people I ask in the meantime don’t know and *don’t care*.

And they’re better at solving problems than I am.

I’m a little bit bitter about some of the professors who’ve had that attitude. “Interpretation is the same thing as popularization, as speculation. Frivolous. Unrigorous. Beneath us. Shut up and calculate.” They’re right, in a way. It can’t predict anything.

I guess I still think stories (and applications, which are usually disdained by the same people) are the [horse], and the equations are the [cart]. But the equations-for-their-own-sakes people may be better scientists than I am. I’m not sure.

It’s a big enough idea that it deserves a post of its own. I’ve written about something vaguely similar in the area of lecture prep– twice, in fact: one, two– so it should come as no surprise that I tend to think of stories as an integral part of physics.

Contrary to what Mary says, I’ve found that the very best physicists I know (and this includes a couple of Nobel laureates, if I may be permitted a JVP moment) are the ones who have the best grasp of the stories and interpretations.

I talked once with a distinguished colleague who’d had the chance to see many great scientists speak – people like Feynman, Weinberg, Gell-Mann, Yang, Wilczek, and others. He made a comment about Feynman that struck me very much. The comment was that whatever subject Feynman was talking about, it was obvious that he had thought about it deeply from every conceivable angle, and so had arrived at extremely simple conceptions of many things that were often thought to be rather difficult. As a result it simply appeared that he could see through to the core of things in a way that most of us usually don’t.

This isn’t quite the same as what Chad is saying, but I think it’s closely related. Almost without exception, the most outstanding scientists I’ve met have this common property of trying to see through to the core of things, arriving at an extremely simple conceptual understanding.

At least for the sort of physics that I do, it’s essential to ground your understanding of the physics in terms of the real motions of real atoms that are the basis of everything. If you can understand what’s going on in simple terms, and more importantly explain it that way to other people, that’s a big step toward being able to push experiments in new directions, and explore new phenomena.

I used to think that one of the big sources of differences in ability between different researchers is that some people are much better than others at keeping track of complex ideas.

I now think that’s a cuckoo way of looking at things, and that a more accurate picture is that some people take much more care than others to reduce things to very simple terms all the time. Such people, because they understand things in simple ways (often, in multiple simple ways), can cope with much greater apparent complexity.

To some degree, this is an issue of sub-fields. I work in atomic, molecular, and optical physics, where the problems we study generally involve a smallish number of atoms doing comprehensible things. Other fields rely much more heavily on sophisticated mathematical tricks to make their problems tractable, which makes it harder to tell stories about what’s going on. I took one class on Solid State, and after the first couple of weeks, I no longer had the foggiest idea what was going on in terms of actual electrons moving through solid materials– it was all “reciprocal lattice vectors,” which I still don’t understand– which made it a deeply unpleasant class all told.

I think this desire for simple conceptual pictures is not an issue of subfields. The mathematician Doron Zeilberger describes the great mathematician Gelfand – who worked in some exceedingly technical areas – as having a “unique approach to learning and teaching” that revolves around “giving the simplest possible example, and that Gelfand enforces in his famous seminar, by constantly interrupting speakers and making them explain clearly and simply”.

(The reciprocal lattice vector stuff simply sounds like it was badly taught.)

On the other hand, though, I think the link between success in physics and a good grasp of stories could be extended to many of the best and brightest regardless of research topic. Einstein’s real breakthrough with Special Relativity was a matter of storytelling– people knew before Einstein that Lorentz transformations would solve the problems with Maxwell’s Equations, but thought it was too weird. Einstein showed that not only was it the right solution, but it had to be that way, and he did it by providing stories to make it all make sense (again, see some earlier posts: one, two). Schroedinger’s equation is in some sense a story that makes Heisenberg’s matrix mechanics palatable (the theories are mathematically equivalent, but as I understand it, nobody could make heads or tails of Heisenberg’s stuff). And when you get down to it, what are Feynman diagrams but little stories about what happens to an electron as it moves from point A to point B?

Yes, in some sense, the equations are the main thing. But when you look at the history of physics, you find again and again that the real giants of the field are the people who matched an interpretation to the equations, who came up with stories to explain it all. Any fool with a computer can manipulate equations, but it takes real genius to explain what’s going on in a way that makes it make sense.

I don’t have a good answer to “What’s a photon?”, but at least I can say this: If you feel that interpretations and stories are an important part of physics, you’re in good company.

An anonymous commenter makes some insightful remarks in the comments section on an earlier post about doing worthwhile research:

how about: most people don’t fail because they simply don’t work on important
problems, but they don’t RECOGNIZE an important problem when they see one? Most scientists aren’t taught by anyone how to recognize it, either.

I agree wholeheartedly. The stereotype, of course, is that scientists win kudos by solving well-known problems that are agreed to be important. (I’m thinking, e.g., of Andrew Wiles.) But a substantial amount of great science is done by people who recognize important problems that no one else yet fully recognizes.

This process of recognition is very different skill than problem-solving per se. It’s not taught in any systematic way, at either the graduate or undergraduate level. I have some thoughts about teaching it, but they’re not fully formed, and would take some time to unravel.

Somewhere near the core of those thoughts is Abel’s advice on mathematics, which I think applies to other fields equally as well: read deeply in the masters, not their followers. This advice, however, needs to be combined with the suggestion made elsewhere in the same comments – don’t just read the masters, but try to solve from scratch the same problems they faced.

Update 03 May 2004: I’ve changed the attributions on the comment. Guessing the identity of an anoynmous commenter is not an especially sensible idea.

Lance Fortnow undercuts John Quiggin, who in turn undercut William Tozier.

See Ebay. Concept due to William Tozier.

Update: I just (re-)computed my Erdos number. Turns out its 3 (via Erdos, Fan Chung, and Richard Cleve). Maybe I ought to get into this auction action? Lance Fortnow (Erdos number 2) ought to be able to do even better.

Dave Bacon asks why his field doesn’t get enough lovin’ among other scientists:

The number one most irritating question I was asked during my faculty interviews was “what will you do if quantum computation doesn’t pan out?” […] And this is what makes the question so irritating: it implies that quantum information science is a fad with no intrinsic intellectual value. Do you ask string theorists whether what they do will be experimentally testable and if not what will they do? Do you ask astrophysicists whether studying cosmology will have any significant impact on society? No. But because these are part of a long tradition of theoretical physics they are acceptable intellectual persuits, whereas quantum information science, being new and getting too much press is most definitely suspect.

I suspect that in the last sentence Dave has put his finger on part, but only a small part, of the problem. I think there’s an another consideration that plays a much bigger role.

String theory, astrophysics, and (to a lesser extent) condensed matter and AMO physics have all done a terrific job of articulating why they matter. They’ve identified deep central questions that are relatively timeless and unarguably important. Furthermore, they’ve communicated those questions clearly and repeatedly, not just within physics, but to other scientists, and, in some instances, to the public at large. Even if the specific approaches they are taking to those questions fail to work – maybe string theory won’t pan out, or gravitational waves won’t be detected, or whatever – the questions will remain important.

Contrast this with quantum information science. Most presentations on quantum information science I’ve seen motivates the field either by saying (a) quantum computing has important practical applications, and so should be pursured, or (b) by making vague allusions to the importance of better understanding quantum mechanics.

In short, the quantum information science community hasn’t fully articulated a sensible narrative containing questions that are big, timeless, and important. And until such a narrative has been articulated, and communicated to the world at large through review articles, overviews, technical and popular books, other scientists will wonder legitimately about the value of the field.

This problem isn’t unique to quantum information science, of course. I’m just using it as an example because Dave used it, and I happen to feel strongly about it. The problem affects many other fields; a good example is complex systems research, which I’m pretty sure has suffered some of the same problems, though in somewhat different ways.

I’m personally convinced that there are big and timeless questions that can be addressed by the techniques of quantum information science. I’ve tried to describe some of these questions here and here and here. (The first article is in Scientific American, and I’m not sure it’s accessible without an institutional subscription.)

This really needs a lengthy post, but in brief I think a big and important problem that can be addressed by quantum information science is to understand the behaviour of complex quantum systems. That is, we want to find general principles governing complex quantum systems, and determine what makes them different from complex classical systems.

This problem is not unrelated to some of the central problems of condensed matter physics, but I think there’s a key difference in approach. Quantum information science starts by taking quantum mechanics very seriously – some would say too seriously – and asking what is possible within the confines of that theory. Condensed matter physics has been much more motivated by experiment, and by the pursuit of some key theoretical models. I think that’s a great thing – condensed matter physics has had fabulous successes beyond number – but I do think the different perspective of quantum information science has something important to contribute.

I’ve said before that I think the so-called “cluster states” are one of the most remarkable recent breakthroughs in quantum computing. One entangled state plus localized measurements is enough to simulate any quantum system! Here’s a link to my journal club notes on the subject. They require a background in quantum mechanics, but should be very easy to read if you’re part of the quantum computing community.

Thanks to Debbie Leung for providing the small pdf file (it was originally 16 meg). I’m posting this in part because Debbie and Panos Aliferis posted a paper yesterday that references these notes.