How quantum is a given state?

One of the puzzles I have been thinking about for a little bit (triggered by trying to explain to Referees that we were definitely seeing a quantum phenomenon) is trying to answer the question: Given a certain quantum state, can you quantify how quantum it is?

I have a sharp senior working on it (whenever he can not manufacture sufficient number of excuses relating to his two comps exercises in Math and Physics, his robotics projects, and general life excitement, sigh) right now. The starting point of our analysis is the idea that you can take the Wigner function corresponding to your quantum state, find out how much ‘negativity’ there is in that Wigner function and call the amount of negativity a measure of the quantum-ness of the state.

This seems fundamentally fair: Classical probability distributions in phase-space are positive-definite, and it is clear that Wigner function negativity comes from interference effects, so quantifying this should be a pretty good measure of quantum-ness. It is, except in a handful of cases, a numerical exercise, which is a bit of a pain, but that’s fine.

However, there is something counter-intuitive about what emerges from this calculation, and my instinct is that this should be a resolvable issue. Our project figuring this out is moving slowly however, and I’m not completely comfortable revealing all of our thinking so far on this particular project. So I’ll leave it as an exercise to the reader — take a look at that paper by Kenfack and Zycskowski (which has since been published in J. Phys. A) and see if you can find what’s weird about the one (semi-)analytic result they have on the harmonic oscillator.

And if you want to talk about it with us — and in particular about resolutions of the weirdness –  that would be great; as I’ve said before, I’m always open to fresh collaborations/conversations.

What I like about this project is that it has all the hallmarks of a classic liberal-arts-college theorist project: Deep enough to be very provocative, but simple enough for an undergrad to make progress. Of course, I could just be completely out of the loop on some critical literature. We shall see.

National Society of Black Physicists/National Society of Hispanic Physicists Joint Annual Meeting 2008

I am at the National Society of Black Physicists/National Society of Hispanic Physicists annual meeting for the 3rd year in a row, this time in Washington, D.C. The first time I went it was because I wanted to find out what was behind the much bemoaned lack of minority Ph.Ds in physics — I was tired of arguing about numbers, and as with everything else in life, wanted to understand the human side of the issue. That visit, to San Jose, was a revelation. To sit in a ballroom-full of physicists listening to great talks is always a great experience for me — I am a physics geek, cool physics ideas turn me on, and it’s like going to a live rock concert to hear and discuss these ideas along with so many other aficionados. But to sit in a ballroom-full of minority physicists was novel, and it affected me in a deep emotional way.

I managed to connect with a member of the board for the conference program, Wendell Hill, and the next year, in Boston, Carleton, Bowdoin, and Morehouse faculty and deans put together a panel on careers at ‘elite’ liberal arts colleges. When I am feeling particularly blunt, I like to contrast places like Carleton and Bowdoin with the HBCUs (the Historically Black Colleges and Universities) by calling Carleton a Historically White College — and in physics it certainly is. So careers at such places honestly don’t appear on the radar for most of the smart young students out there — it would be like teaching in a foreign country for many. And elite colleges and the minority physicists community has so much to gain from that not being the case. Wendell suggested to me this year that it might be time to come back next year for another pitch, and even if we are not in the hiring cycle next year, I think I might give it a whirl.

This year I am here (along with a colleague, who I persuaded at the Boston conference to come to Carleton last year for a short-term gig while postponing her post-doc — we brought along three students, too) with the primary goal to recruit faculty for a visiting position for next year — and since we will be conducting a tenure-track search the year after, this is in some sense for that tenure-track position, but with less pressure on both sides. And I’ve found some great candidates. What I’ve enjoyed greatly in the process is getting to know the younger students, and to talk to them about the future, and how they might think of teaching at one of these colleges.

I know there’s little chance we’ll be hiring when these kids hit the market, so it might look a little unfocused to talk to them, but I see this as being of general benefit to the physics community, and thence of specific benefit to Carleton. It’s in keeping with a broader philosophy I have of focusing on the long term, and on statistics where possible. It takes a damn sight more effort, and is far more chancy, for me to try to attract a specific person to Carleton. But if I keep talking up liberal arts colleges — and it comes easy to me, I love my job — and if every liberal arts college faculty member keeps talking up liberal arts colleges when possible, in the long term we all benefit from the increased talent pool, whether minority or otherwise.

I’ve also heard some great talks here: For example, one from an undergrad, Cacey Stevens, who worked during an REU with Sid Nagel at Chicago studying the physics of splashing. Totally fundamental, beautiful experiments, puzzling, very cool. John Mathers (Nobel 2006) gave a plenary talk on the state of our understanding of the Universe, and the next generation of telescopes, and I got to puzzle some more about dark energy, the notion that everything we think of as matter is essentially ‘noise’ on the scale of ’stuff’ in the Universe. I really enjoyed the atomic physics talks, including a very gracefully pedagogical one from Luiz Orozco about Francium, and a sweet description of some beautiful cold-atom Bose condensate and degenerate Fermi gas work by Marcius Extavour of Joe Thywissen’s lab in Toronto. Jun Kono’s lab from Rice University was well represented by a couple of excellent poster presentation on device physics — one student working with quantum dots and another with carbon nanotubes.

There were also intriguing talks from physics education researchers, including one from a friend of mine, Chandralekha Singh (I hadn’t met her in about 10 years, so it was great to reconnect) about the connection between cognitive science theory and teaching techniques. I sat with Chandralekha at a couple of meals and got to argue furiously with her about the benefits of teaching students quantum mechanics from the Stern-Gerlach experiments, a finite dimensional Hilbert space, and Dirac notation perspective first (I do this, and love it!) versus the traditional Schrodinger equation and partial differential equation method, which I have to say frustrates me tremendously. Given Chandralekha’s background, the conversation was appropriately meta, and hence very valuable.

I also got to make some new friends and reconnect with old friends, including the always remarkable Philip Phillips. My first memory of Philip is from when I was a young grad student at a conference in Los Alamos. I walked by him arguing with someone in a corner, and I heard him saying with what I now know is his characteristic forthrightness: ‘It’s so much better to solve the exact problem approximately than the approximate problem exactly.’ I was very struck by that and have repeated it to myself as a mantra for a guiding principle for my work (of course my math colleague told me that it exactly the opposite in math, but hey, that’s how you can tell us apart). I reminded Philip of that phrase when I saw him next, and he said: ‘Hmm, I don’t remember saying that, but it sounds like me.’

As always, when I travel during the teaching year, I landed up at this conference edgy from the stress of getting things organized enough to get away for a few days, and unclear about the benefits of doing this. And as always, I am going to leave happy I came.

Advising, advising, advising

This is advising week — because of travel plans later this week, it is advising 1/2 week for me, so there is a flood of students in here walking in and out. As with everything else I do at Carleton (perhaps grading excepted), I value these conversations, and enjoy them — but the number can get a little overwhelming.

I taught a Cross-Cultural Studies Seminar last term, and incoming students often get assigned to Profs from their first term seminar. So for a change I have many kids with interests clearly on the other side of campus. Not that all my advisees land up in the sciences typically, but since I’ve usually met them through a physics course, I know they aren’t antipathetic to science. Not this year!

Some conversations with first-years are interesting, about why one might choose an Asian Studies major, for example, and how to make choices within the broad range that Carleton offers, with the minimal constraints it imposes.

There’s one student who wants to spend a long time away from campus, and I’ve asked him to convince me that he can do this by mapping out a course of study over the next few years. I tell him that he can argue all he likes that it should be possible to do this, but one example, which would take him a couple of hours at most, would make me happy, and constitute empirical proof that it is possible to do the major he wants even with all that time away from Carleton. It would make sure that there are no ‘oops’-es to address later. But there’s something about this exercise that he simply doesn’t want to do — not a particularly empirical thinker, perhaps?

Sophomores are facing a more dramatic moment: Choosing a major. For them, the world is seemingly narrowing suddenly and I see some students thrash around at this point of decision. How does one choose with confidence that one path through life and expect it to bring happiness? How can one minimize regret? I look back on my choices, and boy did I make it early. I knew when I was a very young kid that I wanted to be a physicist, and the way the Indian system works, my early choice committed me kind of definitively. Given that I hung out with economists all my college life, I am sure I would’ve landed up drifting towards economics if it hadn’t been for that early commitment. Some of my sophomores are still drifting, but most are trying to choose carefully between related fields, or trying to figure out how to double-major, and so on. These conversations end on a slightly nostalgic note, since this is our last advising meeting. After this, they get advisers in their major.

Talking to the seniors, some of their excitement rubs off — they’re getting the grad school acceptances back and the future looks so inviting. There’s a certain amount of reeling back in shock, I have to say, at the fellowships schools are offering nowadays ($25K, wow!) and I am thrilled for them. But they do have to choose. Somewhere in the mists of memory is lost a description of the feeling of choosing a grad adviser at the end of your first year. As a a physicist, one minute you had all the options in the Universe, literally — from studying the cosmos to studying tiny particles, to everything in between. The next, you have committed to one area, and a few months later, to one problem, and very soon after that, you have an incredibly narrow focus. You are the only person in the world who knows your particular research problem as well as you do, and cares about that minus sign with the same intensity that you do.

Boy these kids have a lot of trust in me, asking me to hold their hands through some of this process! The trick of advising, or choosing in general is, as I said in an earlier post, the dichotomy between global statistics and individual chaos: We can reason statistically, make educated guesses about what’s typical or not, but to know what the future will be like for the one contingent case about which we care (that is, ourselves) is impossible. You never can tell the consequences of your choices. And if you did, it would be boring.

The things you learn

Yesterday was exciting: The first physics comps of the season for me (I don’t go unless I am invited or am on the committee) and the unveiling of the new curricular proposals.

So this was definitely one of those kick-ass comps presentations I was talking about earlier. She talked about biomimetic adhesives, that is, the attempt to reproduce the ’stickiness’ of gecko feet.

The facts are amazing: a Tokay gecko can theoretically hold up 2 human beings with the adhesive forces of its feet, with a surface area slightly less than two dimes. And geckos do it without suction, and without exuding any sticky substance whatsoever, with the ability to go from adhesion to ‘running’ on demand. Move over Spiderman, I want to see Geckoman in action!

And the physics (at least, as understood so far) is that it involves van der Waals forces (for the non-physicists, the fact that neutral atoms can separate into positive and negative parts, induce neighboring atoms to separate as well, and therefore attract each other) and some interesting geometry. van der Waals forces only act at the nanometer scale and it turns out that the feet of the gecko are very very branched, such that it can offer this kind of close contact (and facilitate other good properties as well).

It was a great talk, everyone learned a lot, and she even finished with a report on results that came out 2 weeks ago, where a Stanford group has managed to get to approximately half the strength of gecko feet. Man. I can’t wait to read her paper — she promises, in addition, an equivalent discussion of certain butterfly wings that are structured so that they only let certain kinds of light through, so that the color comes from the structure, rather than the ingredients of the wings. Cool.

Right after this talk was the college-wide Faculty meeting, starring the unveiling of new curricular proposals — for graduation requirements, not fiddling with the major — from the team-leads. Things were a little more firmed up than the last look we had at the ECC, and despite the nervousness, all three did a good job (they were standing up there, telling us what *our* vision of liberal education was, and how to implement it. Tough audience!).

Gut reaction(s):

(1) Some of the new requirements are very prescriptive (as are some current ones) ; these will meet with the most resistance or alternatively will be hardest to implement.

(2) All the proposals shift resources around. For example, more first-year seminars might have to be offered, or different kinds of ‘distribution courses’ will be imagined by each Department and so on.

(3) All the proposals ease the weight on physics — yay (assuming we actually accept some version of these proposals)! That is, our Department is the only science that offers 3 or 4 large-enrollment courses a year that people typically take for distribution requirements. The science requirement in all three proposals is definitely decreased, whence …

(4) The pressure on the Arts and some other department is going to increase.

(5) As a member of the ECC, I will be consulted — that is, we get to do some slight nudging and questioning as the next stage evolves (discussion, modification, etc, until we have proposals that can be subjected to an up-or-down vote). But at this point, any faculty member has just as much of a say as any other. Let the discussions begin!

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Now playing: Nusrat Fateh Ali Khan – Zindagi Jhoom Kar
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Gotta do this

Well, if I don’t post now, I never will, because I feel like I am falling further behind at work (and my body falling apart isn’t helping any).

What’s on my plate? I am going to guess the same as for most people at small colleges. This is what takes time and piles up: Grading and writing letters of recommendation. Mostly grading. ‘Cos things without explicit deadlines don’t get done, is what I’ve found.

In ‘Revolutions’, we’re doing relativity (what I call Act II for my course, Act I being Newtonian physics, and Act III being quantum mechanics). I did a version of the ‘garage paradox’ in class last week involving a centipede and a butcher. For the non-physicists, let’s spell it out: There is an effect in relativity called length contraction so that moving objects shrink along their direction of motion.

In this specific problem, the centipede is of length 10 cm, and traveling at 0.6c. He races by a butcher with a pair of cleavers separated by 9 cm that the butcher slams down simultaneously, in his reference frame, of course, when he sees the centipede between them, which will happen at that speed. The paradox is that in the centipede’s reference frame, the cleavers are traveling at 0.6c, and so the separation between them is what shrinks, down to only 7.2 cm — how can he possibly survive in his reference frame? And yet the reality of his survival or death must be independent of reference frames.

The resolution of the paradox, for those who haven’t played this game before, is that the events — the slamming down of the cleavers — happen at different *times* in the centipede’s reference frame, so the separation between the two isn’t all that relevant.

I teach this paradox by asking students to work through a worksheet which asks very leading questions about the problem, and it’s a pleasure to see comprehension dawning on them as they work it out (it is *remarkable* how many kids used the calculators on their cell-phones). These are humanists, some of whom have never taken a physics class before — and almost all of whom will never see a physics class again — and here they are, figuring out how to deal with space, time, space-time. Later in the term I will ask them to create something based on their personal response to these issues. A few years ago, for that assignment Lisa G created 2 flip books that show the butcher’s and centipede’s perspectives respectively — you can flip through them, and of course, pause to register what is happening. Those flip books are a thing of joy, and I walk around the class, using them as a reward for students once they’ve worked out the paradox’s resolution for themselves. Or sometimes when they throw their hands up in despair at the end of the hour.

Dislocations, a placeholder

Last weekend I went to the 4th HHMI symposium on Diversity in the Sciences, in Chevy Chase, MD. The meeting started with a Sunday evening reception, where I grabbed a beer, had a great conversation with a favorite alum’s dad (a Prof at Kalamazoo), attended the first plenary session, and then headed off to the hotel for a well-deserved rest.  I woke up at 3:30 AM with my right shoulder dislocated. This is the 6th time it has popped out, but in the past, I was at least doing something, even if something as minor as reaching below a hotel-room table to put in a cord for the high-speed connection or something. This time I was only sleeping. Aaargh. 6 excruciating hours of ER waiting later (shoulder dislocations, while painful, are naturally pushed aside by people having heart-attacks) I was somewhat functional and actually learned a fair bit from the conference, and made some new friends or at least acquaintances.

All this to note that I have had a slowed-down week: I can teach (scanned lecture notes, with my marginal scribblings to myself serving to edify my quantum students no end; the ‘Revolutions’ class laughing politely at my ‘at least I am not an economist, unable to say “on the one hand, on the other hand”‘ joke) and can get around, but grading is not moving very fast, nor is typing long blog posts.

This week also saw a visit to Carleton by the remarkable Freeman Hrabowski, president of UMBC. He is one of the most charismatic, focused, blunt, and intense people with whom I have had the privilege to spend time. And he has some very very impressive ideas and results on how to improve student performance in the sciences, particularly for under-represented minorities. My colleagues and I were very struck by him — the best way to summarize this is to note that at some point, one suggested that he’d be an amazing Education Secretary. Every other friend agreed when I told them about this idea. You heard it here first.

So this will have to serve mostly as a placeholder post to say that there’s plenty happening within me without me, but time, and a suitably mobile arm are at a premium.

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Now playing: Radiohead – True Love Waits
via FoxyTunes