I'm off to Zurich tomorrow for 8th Symposium on Topological Quantum Computing which I'm greatly looking forward to (this will be my first trip to Switzerland.) What I'm not looking forward to is the 15.5 hours it will take me to get from the Seattle airport to the Zurich airport! So, any recommendations for papers I should read, lectures I should listen to, or videos I should watch in order to keep from going insane on during the flight?
Why don't you just take the top 10 papers from scirate? Well, in case you've done that already, here are some recent arXiv papers that I found interesting:
arXiv:0908.3023 - I guess you will have seen this already, but I found that it clarified a lot of the closed-timelike-curves stuff for me.
arXiv:0908.3408 - This paper makes no sense to me, but maybe you could make a stab at understanding what 't Hooft is up to.
arXiv:0907.0372 - An interesting and nontrivial constraint on nonsignaling theories.
arXiv:0908.1867 - I don't know if this is up your street, but I found it to be a useful summary of what we know about various kinds of monogamy of correlations.
If you are feeling foundational you could download some of the talks from the "Reconstructing Quantum Theory" workshop that was held at Perimeter a couple of weeks ago via http://www.pirsa.org/C09016
My top picks from this workshop are: Spekkens, Goyal, Wootters, Fuchs, Rau, Coecke, Hardy, d'Ariano (that's 12 hour's worth) but many of the other talks were good as well. It's interesting to note the convergence of ideas that is happening between Coecke, Hardy and d'Ariano.
If you are anything like me, you will want some non-physics related stuff to do too.
Download some lectures from iTunes U. I just watched this lecture from Steve Jones on Evolution. Wonderful stuff! http://deimos3.apple.com/WebObjects/Core.woa/Browse/ucl.ac.uk.155083788…
Many many more where that came from. ITU is a great resource.
I managed to lose a good chunk of a recent flight from Singapore playing Braid.
For non-physics diversion there is a lot of interesting stuff on TED, this one (about the mind tricks, salesmanship and persuasion) even comes with a free dating advice:
Most long-haul flights have a map display which tells you where you are and how fast you are moving. Refer to this often.
Of course you should try to get some sleep on the flight if you can. If, like me, you don't sleep well on airplanes, at least try to fit in some power naps.
As for papers, I can't make specific recommendations, but I bring "the pile" with me on trips and spend a fair fraction of the flight reading papers.
Spend some time people watching, or walking the concourse, at your connecting airport (wherever that is), especially if it's on the other side of the pond. From the transit time it sounds like either you have some time to kill, or your connection is on this side of the pond. (Please tell me you didn't make the mistake of connecting through JFK. Never book an international flight into JFK unless New York is your final destination.)
I'm currently in transit from St. Louis to Raleigh. The total drive time will be about 15 hours. Whatever you do will be significantly more interesting than trying to find a radio station in the mountains of West Virginia. (yes, my car only has a tape deck and I don't have an ipod type device)
15.5 hours? Hah! Such a short trip! Barely longer than a hop across the Pacific from Auckland to LA.
A long trip like this is perfect for Jonathan Israel's two-volume history of the Enlightenment: Radical Enlightenment and Enlightenment Contested ... I'll drop off our QSE Lab's copy.
The other perfect travel author is Paul Theroux: "You define a good flight by negatives: you didn't get hijacked, you didn't crash, you didn't throw up, you weren't late, you weren't nauseated by the food. So you are grateful." ... "Extensive traveling induces a feeling of encapsulation, and travel, so broadening at first, contracts the mind." ... âThe train passed fruit farms and clean villages and Swiss cycling in kerchiefs, calendar scenes that you admire for a moment before feeling an urge to move on to a new monthâ ... "Tourists don't know where they've been, travelers don't know where they're going." ... "I cannot make my days longer so I strive to make them better."
Oh yeah, I agree with Matt that arXiv:0908.3023 and arXiv:0908.3408 were both very interesting. For me the take-home message of arXiv:0908.3023 is that augmenting the traditional linear dynamics of QM is very risky ... leading to causality violations and/or "computational extravagance" (their nice phrase) ... whereas restricting QM's phase-space dimensionality and/or geometry is much safer. Their reference to J. Polchinski's 1996 article on Poisson/Dirac brackets and Weinberg's nonlinear theory then led me back even further, all the way to Dirac's 1958 article Generalized Hamiltonian dynamics. Unsurprisingly, Dirac's thinking was far ahead of his time in pulling back the symplectic structure of linear quantum mechanics onto (nonlinearly) constrained state-spaces manifolds ... if Dirac had similarly pulled back the (not yet invented in 1958) Lindblad structure of modern quantum measurement theory, then the subsequent development of quantum mechanics might (IMHO) have been very different ... especially in terms of our understanding of quantum dyanamical systems that are definitely not carrying on quantum computations, and hence, might possibly be simulatable with PTIME resources. So all-in-all, arXiv:0908.3023 was (IMHO) a terrific article.
As for t'Hooft's article ... it sure was interesting ... so interesting that it's already been Slashdotted! ... but as for what it might mean ... please count me among those who have no immediate clue.
Dave, my suggestion is cheating because you can't really take it with you. But watch the following before you even take off, and you will be so insane you won't care what happens on the flight. ("If you can't beat it, ..." Like quantum mechanics, I don't think anyone understands it, it "just is":
John, anyone: do you think the IMHO travesty known as the decoherence [pseudo?-]"explanation" of collapse, or at least "why we don't see macroscopic superpositions" would have been possible if what you speculate had happened? I can't judge that very well directly, but surely you can appreciate that the way phase changes between one instance and another, is no excuse to pretend that in any one instance we can just sweep one of two or more superpositions under the rug (see handle link.)
Neil B, when it comes to the "travesty known as the decoherence theory of collapse" my (working) opinion is pretty straightforward:
(1) For open quantum systems the decoherence models just plain work. E.g., in designing technologies like quantum spin microscopes, the decoherence models are the best-and-only theoretical framework that we need to generate sensible predictions.
(2) Similarly, for closed quantum systems the symplectic models (i.e., Hamiltonian dynamics) of quantum mechanics just plain work. E.g., for algorithms like Shor's factoring algorithm, symplectic dynamics is the best-and-only theoretical framework that we have.
(3) Decoherent/symplectic frameworks for QM work are equally viable on (linear) Hilbert state-spaces, and on (nonlinear) KÃ¤hler state-spaces ... because in both cases the "compatible triple" of symplectic (Hamiltonian), metric (Rienmannian), and complex structures are present ... and this is all you need.
(4) Why is QM is usually taught as a vector space theory? AFAICT, this is not a mathematical necessity, but instead mainly a historical accident that can be traced to the influence of Dirac's 1930 textbook Principles of Quantum Mechanics. Vector spaces are the simplest state-spaces that are endowed with a compatible triple---that's why Dirac's 1930 book emphasized them----but they are not the only state-spaces having this property (even today, many students are confused on this point). Many QM researchers have emphasized this point (Dirac 1958, Berezin, Ashtekar, Schilling). It is surprising (IMHO) that no one has yet written a QM textbook from the compatible triple point of view; certainly plenty of material is available!
(5) Nowadays, pretty much every large-scale quantum simulation codes has adopted the compatible-triple framework ... although the documentation is only now catching up. The compatible-triple equations fit on a single page. However to teach these equations (at the undergraduate level) requires about two quarters of mathematical prerequisites over-and-beyond the usual tool of vector-space QM (in essence, learning what the compatible triple of Kahlerian geometry is, learning what a Markovian process is, and learning how to join them together). The pragmatic reality is that undergraduate curricula are so crowded (today as in the 1930s) that providing this extra mathematical grounding to QM students is infeasible.
(6) When it comes to the foundations of QM, then (IMHO) the questions that are toughest even to frame sensibly are in the same class as: "Is the universe itself an open quantum system, or a closed quantum system?" For me, one of the lessons of arXiv:0908.3023 is that we haven't yet found a way to frame this class of questions within a mathematically satisfactory context. My own opinion (not too firmly held) is that the vector-space QM may perhaps be too narrow and too rigid a framework to allow good answers --- the more flexible framework of compatible triple QM may perhaps offer a broader scope.
John, thanks for the meaty reply which I can't digest any time soon. Meanwhile, I suggest that decoherence "works" simply because whatever makes the wave function collapse does so by the time we look at it (of course), so it will always be found that way. REM that the way the decoherence argument is presented, they compare one statistical pattern with another to get a presumed equivalency. But without a collapse introduced "by hand" to both localize the WF and eliminate the alternatives (both must happen), there isn't anything to pull in the WF from its extended state. It's a classic circular argument.
One problem is, the superpositions are supposed to keep on evolving regardless of what their phases are (do you still believe in unitary evolution?), and so they should stay that way - evolving as per the Schrodinger equations or equivalents. The fact that phase differs from one case to another is, again, irrelevant to explaining what happens in any one instance. Sure, you can choose not to be a realist (general meaning) who thinks about some "real distribution" of whatever flying around and then going poof - but then, what is really out there meanwhile? So what does the Schrodinger equation describe? You will find some good middle-brow dish at my name link.
BTW, if those curious new ways of talking about QM are "equivalent" to the old, then they are like covariant formulations of EM in relativity - not predicting anything different.
Neil B, I think we're basically on the same wavelength ... decoherence models simulate (efficiently!) pretty much any question that engineers might care to ask. On the other hand, when it comes to constructing entire universes ... well ... it does seem (IMHO) that not only are decoherence models too weak, but the whole apparatus of linear QM is too constraining.
Mathematicians and physicists have been in a similar situation before ... looking beyond the (pedagogically comfortable) framework of (globally) Newtonian dynamics on (globally) Euclidean state-spaces was a considerable wrench in the 20th century ... it will be surprising (IMHO) if we get to the end of the 21st century without similarly looking beyond the comfortable framework of (globally) linear quantum mechanics.
Almost certainly, QM will still be locally linear. Just as it was a major challenge in the 20th century to detect deviations from Euclidean geometry on classical state-spaces, it (most likely) will be a major challenge in the 21st century to look for deviations from Hilbert geometry on quantum state-spaces.
And the parallel goes deeper than this. It was hard to confirm GR because, in leading order, the predicted effects of GR look like Newtonian forces on a Euclidean state-space. And it will be hard to confirm (nonlinear) QM because, in leading order, the predicted effects of noise look just like nonlinear QM dynamics.
So if we try to experimentally generate high-order nonclassical correlations (for example, within a 10-100 qubit computer), and we find that the observed correlations become weaker and weaker as their order becomes higher and higher ... is that because the correlations are geometrically quenched by nonlinearities on a KÃ¤hlerian state-space? Or are correlations quenched because of noise in the experiment? Doh! Sections 4.5-6 of our recent NJP Practical Recipes ... article points out that these two cases are mathematically indistinguishable, for the physical reason that (in the proper gauge) noise processes concentrate quantum trajectories onto precisely the low-dimension KÃ¤hlerian state-spaces whose existence we would like to experimentally exclude.
From a quantum systems engineering point-of-view, it's good news either way ... because in practical applications there is always a thermal reservoir lurking nearby ... and if noise from this reservoirs makes quantum systems easy to simulate on low-dimension manifolds ... well ... that just means we can speed the pace, and lower the risks, of the experiments we try, and the practical devices we design.
From a fundamental physics point of view, these issues are much tougher. However, I'm confident that whatever mathematical advances the fundamental math and physics people come up with, these same advances will likely have engineering utility too ... as has been true for centuries :)
Neil asks: Do you still believe in unitary evolution?
I definitely believe in symplectic evolution (which is the natural generalization of unitary evolution on Kählerian state-spaces). And since symplectic structure suffices to ensure that the first and second laws of thermodynamics are respected, that's good enough for engineering purposes!
Well, just to organize my own early-morning thoughts, here is one mathematical approach to answering the question:
Q: Why is quantum mechanics special?
A: Quantum mechanics (QM) is special because three mutually compatible structures associate to it: a symplectic structure, a metric structure, and a complex structure. The symplectic structure endows QM with thermodynamical "goodness" (the first and second laws). The metric structure further endows QM with informatic goodness (a measurement theory having Lindbladian form). The complex structure compatibly reconciles thermodynamic and informatic goodness with causality, by permitting past measurements to determine future dynamics (thus introducing control theory and making information theory "actionable").
Further Reading: Quantum mechanical systems are by definition dynamical systems whose state-spaces are endowed with all three structures as a compatible triple (equivalently these systems are KÃ¤hlerian). Hilbert spaces are the simplest example of a compatible-triple state-space, but they are no means the only such example.
All of these ideas can be found in the "yellow book" mathematical literature. Symplectic stucture is introduced and motivated thermodynamically in Frankel and Smit Understanding Molecular Simulation: from Algorithms to Applications; the mathematics of symplectic structure is covered in Arnol'd's Mathematical Methods of Classical Mechanics. Metric structure in relation to measurement theory is covered (in linear Hilbert state-space) by Nielsen and Chuang Quantum Computation and Quantum Information, chapters 2 and 8; the techniques needed to pull back this theory onto KÃ¤hlerian manifolds are given in Adler's article Derivation of the Lindblad generator structure by use of the Ito stochastic calculus, in on-line notes by Carlton Caves Completely positive maps, positive maps, and the Lindblad form, and in Kloeden and Platen's Numerical Solution of Stochastic Differential Equations. The complex structure induced by these symplectic and metric structures is well-covered in Nakahara's Geometry, Topology and Physics, chapter 8. Ashtekar and Schilling's article Geometrical formulation of quantum mechanics was among the first to unite these threads. And finally, Harris' Algebraic Geometry---a classic of the "yellow book" genre---gives at least some insight into the deeper structure of QM from the "compatible triple" point of view.
The point is, that if we avoid what Bennet et al. recently called the "linearity trap" (arXiv:0908.3023v1), but instead embrace the "compatible triple" framework, then we see that the mathematical framework of QM is sufficiently rich (and sufficiently unexplored) that we not (yet) resort to the desperate expedient of doing philosophy in our attempts to understand it! And conversely, philosophical/foundational analyses that postulate a linear Hilbert space for QM may be building on mathematical foundations that are more confining than nature prefers.
Thank you John for so much attention to my questions and misgivings. Do you think what you've been telling me should be considered a distinct "approach" or solution to QM, like the transactional or MWI, or is it a more clever (you hope) way to envision what we already "know"?
Hmmm ... for me the "compatible triple" framework for QM is an engineering approximation that is so computationally efficient, and so mathematically natural, as to lead us to wonder whether nature herself might embrace it?