ITFP, Perimeter: selective guide to talks. #1: Brukner on quantum theory with indefinite causal order

Excellent conference the week before last at Perimeter Institute: Information Theoretic Foundations for Physics.  The talks are online; herewith a selection of some of my favorites, heavily biased towards ideas new and particularly interesting to me (so some excellent ones that might be of more interest to you may be left off the list!).  Some of what would have been possibly of most interest and most novel to me happened on Weds., when the topic was spacetime physics and information, and I had to skip the day to work on a grant proposal.  I'll have to watch those online sometime.  This was going to be one post with thumbnail sketches/reviews of each talk, but as usual I can't help running on, so it may be one post per talk.

All talks available here, so you can pick and choose. Here's #1 (order is roughly temporal, not any kind of ranking...):

Caslav Brukner kicked off with some interesting work on physical theories in with indefinite causal structure.  Normally in formulating theories in an "operational" setting (in which we care primarily about the probabilities of physical processes that occur as part of a complete compatible set of possible processes) we assume a definite causal (partial) ordering, so that one process may happen "before" or "after" another, or "neither before nor after".  The formulation is "operational" in that an experimenter or other agent may decide upon, or at least influence, which set of processes, out of possible compatible sets, the actual process will be drawn, and then nature decides (but with certain probabilities for each possible process, that form part of our theory), which one actually happens.  So for instance, the experimenter decides to perform a Stern-Gerlach experiment with a particular orientation X of the magnets; then the possible processes are, roughly, "the atom was deflected in the X direction by an angle theta," for various angles theta.  Choose a different orientation, Y, for your apparatus, you choose a different set of possible compatible processes.  ("The atom was deflected in the Y direction by an angle theta.")  Then we assume that if one set of compatible processes happens after another, an agent's choice of which complete set of processes is realized later, can't influence the probabilities of processes occuring in an earlier set.  "No signalling from the future", I like to call this; in formalized operational theories it is sometimes called the "Pavia causality axiom".   Signaling from the past to the future is fine, of course.  If two complete  sets of processes are incomparable with respect to causal order ("spacelike-separated"), the no-signalling constraint operates both ways:  neither Alice's choice of which compatible set is realized, nor Bob's, can influence the probabilities of processes occuring at the other agent's site.   (If it could, that would allow nearly-instantaneous signaling between spatially separated sites---a highly implausible phenomenon only possible in preposterous theories such as the Bohmian version of quantum theory with "quantum disequilibrium", and Newtonian gravity. ) Anyway, Brukner looks at theories that are close to quantum, but in which this assumption doesn't necessarily apply: the probabilities exhibit "indeterminate causal structure".  Since the theories are close to quantum, they can be interpreted as allowing "superpositions of different causal structures", which is just the sort of thing you might think you'd run into in, say, theories combining features of quantum physics with features of general relativistic spacetime physics.  As Caslav points out, since in general relativity the causal structure is influenced by the distribution of mass and energy, you might hope to realize such indefinite causal structure by creating a quantum superposition of states in which a mass is in one place, versus being in another.  (There are people who think that at some point---some combinations of spatial scales (separation of the areas in which the mass is located) and mass scales (amount of mass to be separated in "coherent" superposition)) the possibility of such superpositions breaks down.  Experimentalists at Vienna (where Caslav---a theorist, but one who likes to work with experimenters to suggest experiments---is on the faculty) have created what are probably the most significant such superpositions.)

Situations with a superposition of causal orders seem to be exhibit some computational advantages over standard causally-ordered quantum computation, like being able to tell in fewer queries (one?) whether a pair of unitaries commutes or anticommutes.  Not sure whose result that was (Giulio Chiribella and others?), but Caslav presents some more recent results on query complexity in this model, extending the initial results.  I am generally wary about results on computation in theories with causal anomalies.  The stuff on query complexity with closed timelike curves, e.g. by Dave Bacon and by  Scott Aaronson and John Watrous has seemed uncompelling---not the correctness of the mathematical results, but rather the physical relevance of the definition of computation---to me for reasons similar to those given by Bennett, Leung, Smith and Smolin.  But I tend to suspect that Caslav and the others who have done these query results, use a more physically compelling framework because they are well versed in the convex operational or "general probabilistic theories" framework which aims to make the probabilistic behavior of processes consistent under convex combination ("mixture", i.e. roughly speaking letting somebody flip coins to decide which input to present your device with).  Inconsistency with respect to such mixing is part of the Bennett/Leung/Smolin/Smith objection to the CTC complexity classes as originally defined.

[Update:  This article at quotes an interview with Scott Aaronson responding to the Bennett et. al. objections.  Reasonably enough, he doesn't think the question of what a physically relevant definition of CTC computing is has been settled.  When I try to think about this issue sometimes I wonder if the thorny philosophical question of whether we court inconsistency by trying to combine intervention ("free choice of inputs") in a physical theory is rearing its head.  As often with posts here, I'm reminding myself to revisit the issue at some point... and think harder.]

Physics and Song: Perimeter to U2 Tour 360, Rogers Centre, Toronto 9/16/2009, courtesy of Blackberry and/or Mike Lazaridis

Courtesy of Mike Lazaridis (CEO and co-founder of Research in Motion, the company that makes the Blackberry, and founder of Perimeter Institute, where I work), and/or his company (THANKS!!) the staff at Perimeter Institute was bused to Toronto and treated to the first of two U2 shows in the Rogers Centre, downtown next to the CN tower.  The roof was open on the arena, and those on the west side could see changing, glowing colors lighting up the elevator strip all the way up the CN tower, and encircling the observation deck. In my account of the concert below, I'll link to mostly YouTube videos to that give a play-by-play record of most of the concert---be warned that some of these are pretty low quality, though a few are surprisingly good.

Overall, the concert rocked.  Although I haven't followed U2 closely, I have a couple of their CDs from quite a while back---the excellent Achtung Baby, and a double live one, plus a few LPs kicking around that I haven't listened to recently.  They haven't lost their touch.  I particularly enjoyed some of the songs from their new album: the opening sequence "Breathe",  "Magnificent", and "Get on Your Boots".  My notes call the latter "surrealistic hard rock, with fuzz bass and Nirvana-y guitar riffs".  Its title and tacky-but-tasty riffs (think snarfing a box of Snyder's of Hanover Honey Mustard & Onion Pretzels) remind me of Sonic Youth's "Dirty Boots".   I liked the live "Boots" a bit better than the studio video version you can hear here--- a little grittier and harder-rocking.

Their traveling stage set (apparently one of three---the setup takes long enough that they need to start in one venue before the shows are finished in the next) is a giant pale-green thing, adorned with orange buttons and a tower sticking out the top, that looks like a cross between a giant four-legged beetle and the a lunar lander, and forms a tall canopy over the circular stage.  Under the belly of this thing, there's a huge circular video screen made of elongate hexagonal chunks, which can be interpreted as the thrust nozzle of a rocket engine.  Half-way through the show, the thing elongates vertically to more than twice its size, revealing that the screens are mounted on diagonally criss-crossing metal rods hinged to each other as in a folding set of coat-pegs, or wash-hanging rack.  It's used to show closeups of the performers, and various other graphics integral to the show.

We unfortuately missed the opening act, Snow Patrol, as the bus ride from Waterloo to Toronto is a lengthy proposition when you leave at 4 PM on a weekday.  The show started out with the bug thing towering over the empty stage as Bowie's "Space Oddity" was played on the sound system.  Then some moody, pretty music as the lights went out, the band came on, and the spots came up on them one by one, segueing into the band playing "Breathe" off their new album  (Here's longer, but better, video of the whole initial sequence from the last part of Space Oddity, through the band entrance and "Breathe").   Initially the sound balance left something to be desired---the low bass and kickdrum frequencies that resonate in your chest, and below, were overemphasized for my taste, while the actual low and low-midrange frequencies where the bass melody lives were underemphasized.  And the non-kickdrum parts of the drumset, especially at lower frequencies, were a bit undermixed too (partially remedied by Bono's call for "more drums" early in the set).  But basically the sound was pretty good, especially for an open arena which is probably pretty hard to fill sonically.  Vocals and guitar lines were pretty clear.  The band was able to carry things through Breathe and "No Line on the Horizon" as the sound settled down, or I stopped noticing it, and by Get On Your Boots things were rocking just fine.  (Here's some good video footage, with crummy no-bass sound, of the CN tower ... not sure this is actually "No Line" as claimed by the tuber who posted it, though.)  Here's the beginning of Magnificent (another song I liked from the new album, here's another snippet of it, and here's probably a better video of the whole song, from near the stage.)  This was followed by Get on Your Boots---no acceptable video from Toronto, so here it is from the opening show of the tour, in Barcelona's Olympic Stadium.  "Beautiful Day" from 2000's "All That You Can't Leave Behind" ended with a little snippet from Elvis Costello's "Alison", though with an somewhat altered, and I thought less interesting, melody.  "I Still Haven't Found What I'm Looking For" from Achtung Baby, here beginning with the audience doing a good bit of the singing, was the first of the oldies but goodies for me, followed by a nice version of Elevation (also from "All..."), with the band really getting into a disjointed but rocking groove appropriate to the somewhat "surrealistic" lyrics ("why can't the sun // shoot me from a gun..").  "Your Blue Room" was a classic, lazing-across-inner-space "orbit" song, at a meandering tempo with looping "satellite" motifs and footage shot from the International Space Station, and a little sprechstimme from Commander Frank.  Nice touch (as was the LEM-like stage-set)  in the anniversary year of the moon landing.  (Here it is from Chicago a few days earlier, from farther out so you can see the video display.) [Unknown Caller]  Until the End of the World resumes the sequence from Achtung Baby (begun with "Still Haven't Found...")  An even better video of End. StayUnforgettable Fire (nice sound and video, but cut off after 2:50.  ).  This is when the rocket nozzle video screen got vertically elongated.  More good video of Unforgettable Fire; relatively decent sound for this kind of thing, but bass-challenged.  City of Blinding LightsVertigo / Pump It Up.  Bono announced that Elvis was in the house; this, and the bit of Alison and Oliver's Army, were presumably in his honor.  (Some parts of this sound like Dirty Boots as well.)  I'll Go Crazy if I Don't Go Crazy Tonight (sound issues), a lightweight but hard-rocking pogo-ey, poppy bit of infectious fluff off the new album.  Another version of Crazy with different sound issues and funny audience vocal.  Sunday Bloody Sunday (OK sound, long view; late beginning).  Ends with a snippet of Elvis Costello's "Oliver's Army".  MLK, for Aung San Suu Kyi.  Walk On, and One, for Aung San Suu Kyi (seriously bad audience vocals from near whoever recorded this, but with some redeeming value (humor)).  Amazing Grace.  Where the Streets Have no Name.

Ultraviolet (Light My Way), another oldie but goodie from Achtung Baby.  Bono doesn't slack off when covering old songs...the phrasing is different in different performances, his heart and mind is in it.  With or Without You.  Moment of Surrender.