Author Archives: howard

About howard

Wine, Physics and Song is my blog. Roughly speaking, I'm a quantum physicist, working mostly in the foundations of quantum theory, and in quantum computation and quantum information processing. My main focus recently has been understanding the nature of quantum theory by understanding how the possibilities it gives us for processing information compare to what might have been, by studying information processing in abstract mathematical frameworks, using tools like ordered linear spaces and category theory, in which not only quantum and classical theories, but all sorts of "foil" theories that don't seem to be realized in our physical world, but are illuminating to contrast with quantum theory, can be formulated. Sometimes I like to call this pursuit "mathematical science fiction".

Oxford Kitchen

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I've eaten at least twice---once tonight, and once or twice last June or so... at The Oxford Kitchen on Banbury Road in the heart of Summertown in North Oxford.  Extraordinarily good food.  Nice ambience and décor, stylish but relatively casual.  Exposed brick walls, large silk-screen Campbell's soup can print a nice humorous touch.  Set price menu is extraordinary value.  Hake with Jerusalem artichokes, parsley risotto and some kind of thin (like, microthin) veggie crisps just superb.  Nougatine with quince sorbet, thin (like, microthin) wafers tasting of burnt sugar, toasted almonds, and some crumbly stuff mind-blowingly good.  Pumpkin velouté starter good, not mind-blowing, but set off the wine I had very nicely.  At £18.50 for 2 courses, £15.50 for 2, it's one of the best foodie values I've encountered anywhere.   Wines are carefully chosen and if you have wine in restaurants you know how important that is.  2013 Boschendal Chenin Blanc, coastal region South Africa, £5/175ml is kind of the Chablis of Chenin Blancs---pretty dry, a bit of stereotypical apple flavor but mostly just tastes like really solid white wine a bit flinty-seeming maybe but that's probably just a bit of tannin, really long, flavorful finish no doubt stuck to the palate with a bit of that unobtrusive tannin, a smooth, just the slightest bit unctuous, and not at all hot (overalcoholic) mouthfeel.  To get a chardonnay of this quality, you'd be looking at good village-level white burgundy from the Côtes de Beaune or Nuits, like maybe a St.-Aubin at least (or maybe some particular thing, known to the cognoscenti but not to you unless from a restaurant like this...from a lesser appellation like Mercurey) at least, and 3-4x the price.  Ditto on the red side if you wanted a pinot noir as good as the Claro Reserva 2012 Pinot Noir from Chile ( also £5/175ml)... lush, a bit spicy and earthy, with generous berry flavors too but not a fruit or alcohol bomb, balanced.  These folks have done the work of tasting through dozens of ho-hum reasonably-priced wines to find the ones that deliver an experience that is usually (well, I don't usually spend that kind of money) much more expensive.  Talisker 10 year old, neat in a nice wide rocks glass with a bit of water to splash in, was a perfect finish.  Lively balance between peat and brighter more floral notes, filling the nose with perfume and crackling like fire on your tongue.

I had the tasting menu once last year, it too was superb.  Don't miss Oxford Kitchen if you're in town and can get up to Summertown for a meal.

Des Américains à Paris

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Via Ned Rorem, a really nice photo and audio montage promoting a program of a cappella choral music by some of Nadia Boulanger's American pupils: Ives, Copland, Bernstein, Barber, Stravinsky, Copland, Reich, Glass.   If I were in Luxembourg or deep Southwest France in March, I'd definitely go out of my way to hear this. High-resolution photos; it's worth making the video full-screen.

Viet Cuong, Moth

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For at least a few more days you can stream Moth, by classical composer Viet Cuong, performed, at the Midwest Band Clinic, by the Brooklyn Wind Symphony conducted by Jeff Ball, on Performance Today.  It is also available, probably more permanently, at his website and on his Soundcloud page.  I like the piece a lot.  The performance is excellent, really remarkable for an all-volunteer ensemble.  The style is fairly modern for PT, which is to say it is, roughly, in the idiom of tonal Western classical music from the 1920s and 1930s, with perhaps a smidgin of minimalism.  At first listen I thought it made clear use of the language of Stravinksy, especially Petrouchka and Le Sacre du Printemps, as well as of something resembling the post-Stravinsky and neoclassical phase of the 1930s, say, Milhaud, Poulenc, Constant Lambert, but without descending into pastiche.  On my second listen, with better sound, I was a bit taken aback by what I perceive as strong influence from Le Sacre, both in form and in content.   I am less startled by that after further listens.  Form-wise, it intersperses sections with ostinato, theme repetition (certainly key ingredients of Sacre), and other tension building devices (like modulation, especially stepwise upward modulation, which I don't think are found much in Sacre), with more pensive interludes, often tinged with a minor feel.  Just that kind of alternation is a main structural principal of Sacre.  As my references to neoclassicism and modulation above might suggest, there's somewhat more standard tonal content in Cuong's piece, thought it also has very strong Stravinsky-like "modal" or scalar elements, and occasional vaguely Iberian-sounding moments.  (As an aside, just thinking about harmony in Le Sacre makes me wonder if there is any standard dominant-to-tonic resolution at all in the piece---I think not, or not much.)

Cuong knows how to recombine and play with motives, scales, harmonic tropes and other elements to create interest, unify the piece and move things along in a satisfying way.  He shows this from the outset, with a clever motive consisting of a rising and descending scalar figure, played against a similar but inverted figure (or perhaps they are both fragments of the same extended figure that they evolve into, running up and down on flute, changing direction at different pitches), then relaxing into some Iberian-ish sounds.  At 1:30 we get melodic material very reminiscent of Le Sacre, and around 2:10, I think, the first hint of a four-note figure, which one might notate 3 4 2 1 in minor, also very reminiscent of Sacre (indeed it is very close---and would be identical if the last two notes were interchanged---to the initial four notes of a motive, 3 4 1 2 3 1 in minor with the last two notes twice as long as the preceding four, found in Sacre) that will become increasingly important.  Much of this material is developed and cleverly  combined through what sound to me like various key changes.  Around 3:30 things get more urgent, drums, with ostinato and repetition, especially of the four-note theme, and rising modulation.  (I wonder if there is some influence of John Adams' Harmonielehre here; I am reminded of it, but haven't listened to the Adams piece recently enough to tell.  Or maybe I should just can the speculation about influence.)  Around 4:10, quickly peak tension gives way to a mellow contrapuntal woodwind interlude, and there follows a long stretch with some alternation of faster and more complex passages, building a bit more each time, with pullbacks to this sort of mellowness.  Around 6:30 things seem to get more organized for a final buildup.  The ending, with an upward brass gliss emerging out of the ensemble to a momentarily held note, and then a sudden drop to tympani-punctuated chord, reminds me a little bit of Le Sacre too.

The program for this piece seems to be the gyrating flight of a moth before, and eventual immolation in, a flame, which is also in obvious parallel with Le Sacre's program, of a virgin obliged to dance herself to death in a pagan rite.  So I suspect the structural and idiomatic parallels to Le Sacre are no accident, although the overall tone is much lighter, and at 8'38 in this performance, the piece is of course much shorter.  I interpret these parallels, especially as dextrously integrated with harmonic movement at times quite uncharacteristic of Le Sacre, as a bit of a cheeky and light-hearted tour-de-force of compositional virtuosity.  The thematic material does have interest, but might be a little more on the generic side than ideal in places.  That is not really a problem in this piece.   I enjoyed some of the other pieces on his site but did find some of them a bit lacking in gripping melody.  Sound and Smoke I and II sound tailor-made for something like a fantasy movie soundtrack, and are extremely well done.  Part I sounds just as you might think from the subtitle "feudal castle lights", while Part II I found more distinctive.  I have a feeling that with some even stronger melodic material, perhaps some passages with some longer more sustained lines, Cuong could be really dangerous.  Hopefully Cuong will come up with more gripping melodic material in whatever way is necessary, whether from moments of personal inspiration or by ripping it off with exquisite taste à la Stravinsky if necessary.  (I exaggerate, Stravinsky fans... peace, I am one of you.)  Some of Cuong's other pieces show ability in more contemporary idioms.  He is only 24, a graduate student in composition at Princeton.  He is clearly getting a lot of recognition, as the list of awards, commissions, and performances on his webpage shows.  So he probably has a good career assured.  I hope he has his sights fixed on greatness; I'll be very interested to see what comes next.

Bonus:  On that December 12 PT stream, available for a few more days, the Brahms serenade (end of the 2nd hour) performed by the Sinfonia da Camera, if played on a good stereo, is magic.  (On first hearing through a cheap radio I was unimpressed.  Maybe it is all about the bass, although I think an undistorted treble helps too.)

Isole e Olena 2005 Chianti Classico

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A half-bottle of the 2005 Isole e Olena Chianti Classico, consumed a few days ago, was superb. Medium-bodied, with a fair bit of fine but fairly grippy tannins, this was elegant, and for a somewhat tannic wine, somewhat velvety and a pleasure to drink. It didn't seem at all tired or oxidized. Flavors predominantly dried cherry or other red fruits and a hint of pine, at least to my nose.  Super tasty.  Nice long finish. Easily my favorite of the Chiantis I've tasted. I don't remember how much I paid but recent vintages seem to go for $13-15 a half bottle, $20-25 a bottle, which although not cheap, is a bargain if they turn out this well. To judge by how youthful and tannic it still was at 9 years old, I'd guess this one needs to be aged to be at its best---at 9 years it was clearly getting there, but could probably go another 5 or more years and possibly get even more.

Isole e Olena don't appear to have a website; there is more information about them at Giuliana Imports, the Boulder-based importer of this bottle.  Since I have been encountering a lot of claims to the effect that a lot of writing about wine is basically just noise and fashion-following and strongly influenced by things other than the pure olfactory sensation of the wine, I'll point out that their description of the 2011 is very close to my description of the 2005, despite my not having read it (as befits a truly serious wine there are no olfactory notes on the label, either) which suggests to me anyway that Isole e Olena make this wine in a consistent style that can be identified by taste.  Of course this is just one observation, and there is definitely a lot of noise and influence from nonolfactory things like price and reputation and label appearance that enters into people's writing about wine.  (Mention of "red fruits"  or "dark berries"  could easily be influenced by the wine's color, for example, although in my opinion there is usually more to it than that.)  My point is that I think there is a genuine olfactory basis for some of this stuff too.

Based on perusing people's notes on the web (after writing mine), it seems that a lot of people liked this wine young, opinions diverged at about 3-7 years after vintage, and the consensus is more clearly positive over the last few years, suggesting it might have gone through a "dumb"  phase as many wines do during aging.  Also, some people seem to object to the relatively lighter-bodied style, which I happen to love when it is combined, as here, with intensity.  This is a serious producer that has been around at least as long as I've been tasting wine, and based on this sample, their Chianti is indeed a classic.  My sense is that if you have the ability to age it to 9-15 years after vintage you can't go wrong buying multiple bottles of this wine in any decent vintage.

What I just wrote is more meaningful than trying to assign some arbitrary number, but I guess on a Parkeresque 100 point scale, I'd give it something like a 92... and not in the inflated sense where anything you like gets 90---to get 90 or above in my book, a wine has to be at least a bit extraordinary.

Iverson/Motian/Grenadier It's Easy To Remember, II: a deeper appreciation

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Since first posting on the topic, I've now played (in my halting way) the solo piano ad lib introduction to the live Ethan Iverson/ Paul Motian/ Larry Grenadier performance of It's Easy to Remember in Guillaume Hazebrouck's transcription, and listened to it several more times.  I'm even more taken by this masterful performance, especially the introduction.  The harmonies in the introduction are often quite dissonant but beautifully limpid, probably due to the very open voicings (wide intervals), and choice of intervals.  The dissonances reminiscent of 20th century classical music combined with untypical but compelling voiceleading remind me a bit of Bill Evans, but the choice of intervals and limpid sonority doesn't so much.  The (incomplete) blow-by-blow that follows is mostly for my own reference, so you might skip down to the next paragraph if harmonic analysis doesn't interest you.  It's far from crucial for appreciating the music, but I really want to know how these sounds are made.  The first part is mostly over an E flat pedal (the piece is in E flat), with couple of excursions to Ab. The first chord is fabulous, with successive intervals of a minor ninth, minor 7th, minor 6th (Eb, E, D, Bb).  Then the two inner voices move inward by a half step for another open, somewhat dissonant chord.  It's perhaps not so important to analyze these harmonically, but the first comes off pretty clearly as an Eb major voicing, with no 3rd which no doubt contributes to the spare, clear sound, and with a major 7th, and as for the E natural (b9 you could say), well it just sounds great, and moves up to a natural 9 on the next chord, while the 7th moves down to the minor 7th of Eb, suggesting perhaps a change in quality to dominant or minor, though not this is not so clear as there's still no 3rd present.  Later in the introduction, the same voicing will indeed function as a dominant leading to an Ab major triad at the end of the first system of the transcription.  But first we get a repeat of the first two chords at a faster pace, except with A natural in place of Bb in the top voice (which is basically paraphrasing the melody).  The tenor voice is going up chromatically, cadencing toward a G as part of the double-whole-note Eb major 7th, the first time we get a 3rd with an Eb chord.  The repose is disturbed with a little tweak up to a B natural in the treble, just to add a little more pretty dissonance to the picture. (Nothing wrong with a touch of the "girlfriend chord" once in a while.)  Then we again get those first two chords, Bb in the treble again, moving in quarters, initiating the same four-quarter-note chromatic ascension in the tenor to G, but the bass moving up to Ab on the last two quarters, over which the harmony sounds first like Ab7, then Ab m7, while the top Bb leads down into a bluesy figure.  The next system finishes out with more chromatic movement in the bass, more intricate melody in the top voice accompanied by good inner voice action especially in the tenor, and a final cadence on Eb major again, with the 3rd but in the same open voicing that marked the first appearance of the G before, except that now the D forms a minor 2nd cluster with that seemingly outrageous, but beautiful, E natural, kind of fusing the initial two dissonant Eb voicings but with the added 3rd for an earthier, more harmonically grounded sound, perfectly capping off the introductory chorus.

Besides the open voicings and relatively spare use of 3rds (so that they are all the more effective when they are used), movement by half-steps is a major feature of the voice-leading in this introduction, but it doesn't come across with any feeling of slick hepness or angst-ridden compulsion, perhaps because it's not being used heavily as b9 or #11 over dominant chords, or in related diminished or augmented substitutions for dominants.  Maybe there is a relative absence of tritones in the voicings, though I didn't check carefully.  Anyway, the half-step motion is prominent enough to be considered a major musical ingredient, but doesn't really interfere with what sounds to me like a relatively diatonic, if sometimes beautifuly dissonant, feel.  I guess the chromatic motion is not, for the most part, setting up dissonances that cry out for an obvious resolution, nor effecting such resolution.  It reminds me a bit of Stravinksy in that the dissonance is often created by the interaction of natural melodic motions in the voices, and (along with the melodic motion) the actual intervals in the chord seem almost more important than any compulsive "functional" movement in the harmony even though there is some of the latter on occasion.

The other remarkable thing about Iverson's playing on this piece is the strong influence of Monk, assimilated well into Iverson's own style, in the trio portion of the piece.  Monkian upward arpeggios appear as early as measure 16 (the 3rd measure of the first trio chorus), often combined with scalar material that still sounds quite Monkish (as in measure 16), or leading into more original melodic figures (as in measures 25-26).  A classic downward-dropping Monk left-hand figure is used in measure 30, a very bluesy Monkian chorus-ending figure at 44-46, upward arpeggios in 47-48 lead again to more personal Iversonian material in 49-50, and the list could go on.  Often Iverson seems to be extending or filling in Monkish lines with his own material more reminiscent of more standard bop-influenced lines, but never quite the standard bop clichés.  There's lot's of great action in the inner voices too, sometimes Monkian, sometimes not particularly so.  I think Monk's vocabulary and approach, even while it contributed crucially to the lingua franca of bebop and beyond, has probably been underexploited by pianists who are perhaps rightly afraid that it's hard to make something personal this way, something that doesn't sound like copying Monk's licks, but Iverson makes it work to great effect.  (I guess you could argue that a few other pianists have been strongly influenced by Monk's approach while keeping the harmonic and melodic content of their playing further from Monk than Iverson does here.)

In fact, the display of constructive influence by Monk, and the use of Monkian influences in a clear personal style, makes me wonder if the introduction might be more influenced by Monk than I realized.  I haven't listened to Monk's solo piano for a while, and it is probably time to listen to more.

Speaking of more, here's hoping we get to hear more from this set, or others in the same week at the Vanguard.  All About Jazz's review of what was probably the first set on that same Friday (March 11, 2011) is tantalizing, too.  This is some of the most interesting piano playing I've heard in many years---jazz of the highest order.

Ethan Iverson, Paul Motian, Larry Grenadier: It's Easy To Remember, live at the Vanguard

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Excellent piece from 2011 by Ethan Iverson on the late Paul Motian.  Discusses a lot of music I need to check out, and unexpectedly includes a superb live version of Rodgers and Hart's It's Easy to Remember featuring some of the best jazz piano I've heard from Iverson, which means some of the best jazz piano I've heard in recent years. Plus there's a downloadable transcription of his playing, provided by Guillaume Hazebrouck. The harmonies in the piano introduction sound unusual to me, but totally natural.  I really love the intro.  There's a fair bit of Monkishness, especially later in the solo, but well integrated with Iverson's own conception.  Some nice interaction of multiple voices in the piano at times, not in a showy way, adds a lot.  I found this post linked  from Ethan's recent post on Motian's compositions, which Motian's niece and heir Cynthia McGuirl is considering publishing.

Domaine La Millière 2006 Châteauneuf-du-Pape Rouge Vielles Vignes

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Not much on wine recently, so here's a quick one on a wine I had with my parents recently:  the 2006 Domaine La Millière Châteauneuf-du-Pape (Old Vines, Red).    Simply put, this is delicious wine with no flaws; perfection, essentially.    Scent, flavor, and finish are all strongly present and are pretty much of a piece, with a pronounced note of chocolate that reminds me of many Vacqueyras I've tasted, but with a more balanced, elegant character, and definitely not the glyceriney mouthfeel that some of these Vacqueyras have had.  Noticeable tannin, but not at all closed or hard, just helping give the wine some backbone and probably help stick the flavor to the tongue for the strong finish.  Aside from the chocolate, perhaps red fruits, raspberry and maybe cherry, maybe a bit less herbal or spicy than some Châteauneufs I've tasted but that's not a criticism.  Reminiscent a bit of a great Pauillac in some ways (OK, I've only ever tasted one first-growth Pauillac, a free taste of the1984 Lafite-Rothschild, but this does remind me of it in terms of elegance, delicious forward flavors of fruit and sweets, though there was maybe a bit more vanilla than chocolate in the Lafite).  Nothing at all funky or off.  Somewhat silky or velvety... really delicious and refined.  This is a smashing success, I'd say pretty much a great wine.  If I had to give it a Parkeresque rating, something in the 91-93 range (as of the time I first paid any attention to his ratings, which is probably around 1985) would probably do.  Various other vintages of this are in the 19 to 23 euro range at La Millière's website---seems like a bargain to me if they are anything like this quality.  Available in the US for sure...I notice that North Berkeley Imports has them, and I have seen them in Santa Fe at the Casa Sena wine store.  I would, though, age them for 7-10 years or so... at 8 years old this seemed definitely ready to drink but whether it's at its peak or has 5 more years of interesting development I wouldn't pretend to know.  About 60% Grenache and 10% each Syrah, Mourvèdre, Cinsault and Counoise.  The dominant chocolate and red fruits notes likely have a lot to do with the Grenache, with Syrah and Mourvèdre perhaps adding some complexity and depth and maybe, along with the Cinsault, tannin and body.  (I don't know what Counoise is, but perhaps I should find out.)   If this is in your price range, and you're able to keep it till at least 6-7 years from the vintage, I'd say snap up a few bottles or more.  (Might be good younger, for all I know... but I suspect that would be a waste of its potential.)

Carolina Chocolate Drops rock the Rialto, Tucson

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On a visit to Tucson I tore myself away from the U of Arizona --- USC game to go hear the Carolina Chocolate Drops at the Rialto downtown.  Incredibly high-energy show---you can get an idea of the band's sound from Youtube, but it doesn't really convey the impact of a live show.  They are still on tour until October 24th, and the main point of this post is just to say if you have a chance, go.  CCD got their start playing traditional or "old-time" African-American string band music. and that is still a large part of their repertoire.  The lineup has changed over the years, and I'm no expert on the changes since I'm new to the band.  Rhiannon Giddens, the lead singer (who majored in opera as an undergraduate at the Oberlin conservatory), is the only founding member of the band left in the lineup.  (I was amused that she felt she had to explain how her name is pronounced---anyone who doesn't know obviously missed the 70s, but I guess that applies to a good chunk of the audience.) The band is extremely tight, everybody is topnotch, and the numbers featuring the other members are just as strong as those (perhaps a majority) featuring Giddens as primary vocalist, but Giddens is clearly the powerhouse.  Though her manner when singing is not at all stagey or acted, when she starts making music the star power and charisma are immediately apparent.  CCD are currently doing a very wide range of music, much of which will sound familiar but not exactly like anything you've heard before.  This is African-American music that is part of the roots of bluegrass and country, coming out of folk traditions that are perhaps not so well known nowadays, but in CCD's hands it's not at all an exercise in scholarly dusting off of "hmm, interesting" musical curios---it's alive for the performers and audience, sometimes with an impact and energy that reminds me of a solid punk rock show---indeed some of the audience were definitely pogoing.  Much of the music is full of fiddle and banjo, with Malcolm Parson on cello (and sometimes bones), and Rowan Corbett on a variety of instruments, including bones, guitar, banjo, and I think perhaps fiddle on occasion.  Jenkins played guitar, mandolin, and banjo.  Parson's cello playing really added a lot to the ensemble sound, and I liked his rare solos a lot too. If I'm not mistaken, Parson, Jenkins, and Corbett all played bones to great effect, with Corbett especially virtuosic. Jenkins did some excellent vocal work, too, and his solo country blues original was superb.

As I said, online video doesn't really capture the impact, but this video of them doing Cousin Emmy's Ruby Are You Mad At Your Man from their current tour does a pretty good job.  (I am not sure if this is band-sanctioned, so will remove the link if they request it.)  Music starts around 1:34.

They also cover more recent material, like Dallas Austin's hit for Blu Cantrell, "Hit 'em up Style".  Here's a video from this tour, though I thought the Tucson performance of this song was harder-hitting:

Not all their songs are on the same topic---it's just coincidence that these are two of the best videos on the toob of the current tour.

They don't play many originals, but the song Giddens wrote reflecting her reading of accounts of life under slavery in the 19th century was powerful.

There's a lot more on youtube, including more old-time music, though not so much with the current lineup. They can sing country with the best---I wouldn't be surprised if they hit the country charts one of these days (or perhaps it's already happened); they do a great job with Hank Williams' Please Don't Let Me Love You:

Indeed, Country Girl sounds to me like a straight shot at the contemporary country charts, solid stuff though quite reminscent of a dozen or so other celebrations of down-home-by-the-crick livin' to be encountered over the last decade on mainstream country radio, with an acoustic backing just as rocking and funky as the typical electrified setting for the genre nowadays and just as deserving of a place there.

Definitely a band to get to know, and I plan to delve into their recordings now that I've had the live experience.

Thinking about Robert Wald's take on the loss, or not, of information into black holes

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A warning to readers: As far as physics goes, I tend to use this blog to muse out loud about things I am trying to understand better, rather than to provide lapidary intuitive summaries for the enlightenment of a general audience on matters I am already expert on. Musing out loud is what's going on in this post, for sure. I will try, I'm sure not always successfully, not to mislead, but I'll be unembarassed about admitting what I don't know.

I recently did a first reading (so, skipped and skimmed some, and did not follow all calculations/reasoning) of Robert Wald's book "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics".  I like Wald's style --- not too lengthy, focused on getting the important concepts and points across and not getting bogged down in calculational details, but also aiming for mathematical rigor in the formulation of the important concepts and results.

Wald uses the algebraic approach to quantum field theory (AQFT), and his approach to AQFT involves looking at the space of solutions to the classical equations of motion as a symplectic manifold, and then quantizing from that point of view, in a somewhat Dirac-like manner (the idea is that Poisson brackets, which are natural mathematical objects on a symplectic manifold, should go to commutators  between generalized positions and momenta, but what is actually used is the Weyl form of the commutation relations), doing the Minkowski-space (special relativistic, flat space) version before embarking on the curved-space, (semiclassical general relativistic) one.   He argues that this manner of formulating quantum field theory has great advantages in curved space, where the dependence of the notion of "particle" on the reference frame can make quantization in terms of an expansion in Fourier modes of the field ("particles") problematic.  AQFT gets somewhat short shrift among mainstream quantum field theorists, I sense, in part because (at least when I was learning about it---things may have changed slightly, but I think not that much) no-one has given a rigorous mathematical example of an algebraic quantum field theory of interacting (as opposed to freely propagating) fields in a spacetime with three space dimensions.  (And perhaps the number of AQFT's that have been constructed even in fewer space dimensions is not very large?).  There is also the matter pointed out by Rafael Sorkin, that when AQFT's are formulated, as is often done, in terms of a "net" of local algebras of observables (each algebra associated with an open spacetime region, with compatibility conditions defining what it means to have a "net" of algebras on a spacetime, e.g. the subalgebra corresponding to a subset of region R is a subalgebra of the algebra for region R; if two subsets of a region R are spacelike separated then their corresponding subalgebras commute), the implicit assumption that every Hermitian operator in the algebra associated with a region can be measured "locally"  in that region actually creates difficulties with causal locality---since regions are extended in spacetime, coupling together measurements made in different regions through perfectly timelike classical feedforward of the results of one measurement to the setting of another, can create spacelike causality (and probably even signaling).  See Rafael's paper "Impossible measurements on quantum fields".   (I wonder if that is related to the difficulties in formulating a consistent interacting theory in higher spacetime dimension.)

That's probably tangential to our concerns here, though, because it appears we can understand the basics of the Hawking effect, of radiation by black holes, leading to black-hole evaporation and the consequent worry about "nonunitarity" or "information loss" in black holes, without needing a quantized interacting field theory.  We treat spacetime, and the matter that is collapsing to form the black hole, in classical general relativistic terms, and the Hawking radiation arises in the free field theory of photons in this background.

I liked Wald's discussion of black hole information loss in the book.  His attitude is that he is not bothered by it, because the spacelike hypersurface on which the state is mixed after the black hole evaporates (even when the states on similar spacelike hypersurfaces before black hole formation are pure) is not a Cauchy surface for the spacetime.  There are non-spacelike, inextensible curves that don't intersect that hypersurface.  The pre-black-hole spacelike hypersurfaces on which the state is pure are, by contrast, Cauchy surfaces---but some of the trajectories crossing such an initial surface go into the black hole and hit the singularity, "destroying" information.  So we should not expect purity of the state on the post-evaporation spacelike hypersurfaces any more than we should expect, say, a pure state on a hyperboloid of revolution contained in a forward light-cone in Minkowski space --- there are trajectories that never intersect that hyperboloid.

Wald's talk at last year's firewall conference is an excellent presentation of these ideas; most of it makes the same points made in the book, but with a few nice extra observations. There are additional sections, for instance on why he thinks black holes do form (i.e. rejects the idea that a "frozen star" could be the whole story), and dealing with anti de sitter / conformal field theory models of black hole evaporation. In the latter he stresses the idea that early and late times in the boundary CFT do not correspond in any clear way to early and late times in the bulk field theory (at least that is how I recall it).

I am not satisfied with a mere statement that the information "is destroyed at the singularity", however.  The singularity is a feature of the classical general relativistic mathematical description, and near it the curvature becomes so great that we expect quantum aspects of spacetime to become relevant.  We don't know what happens to the degrees of freedom inside the horizon with which variables outside the horizon are entangled (giving rise to a mixed state outside the horizon), once they get into this region.  One thing that a priori seems possible is that the spacetime geometry, or maybe some pre-spacetime quantum (or post-quantum) variables that underly the emergence of spacetime in our universe (i.e. our portion of the universe, or multiverse if you like) may go into a superposition (the components of which have different values of these inside-the-horizon degrees of freedom that are still correlated (entangled) with the post-evaporation variables). Perhaps this is a superposition including pieces of spacetime disconnected from ours, perhaps of weirder things still involving pre-spacetime degrees of freedom.  It could also be, as speculated by those who also speculate that the state on the post-evaporation hypersurface in our (portion of the) universe is pure, that these quantum fluctuations in spacetime somehow mediate the transfer of the information back out of the black hole in the evaporation process, despite worries that this process violates constraints of spacetime causality.  I'm not that clear on the various mechanisms proposed for this, but would look again at the work of Susskind, and Susskind and Maldacena ("ER=EPR") to try to recall some of the proposals. (My rough idea of the "ER=EPR" proposals is that they want to view entangled "EPR" ("Einstein-Podolsky-Rosen") pairs of particles, or at least the Hawking radiation quanta and their entangled partners that went into the black hole, as also associated with miniature "wormholes" ("Einstein-Rosen", or ER, bridges) in spacetime connecting the inside to the outside of the black hole; somehow this is supposed to help out with the issue of nonlocality, in a way that I might understand better if I understood why nonlocality threatens to begin with.)

The main thing I've taken from Wald's talk is a feeling of not being worried by the possible lack of unitarity in the transformation from a spacelike pre-black-hole hypersurface in our (portion of the) universe to a post-black-hole-evaporation one in our (portion of the) universe. Quantum gravity effects at the singularity either transfer the information into inaccessible regions of spacetime ("other universes"), leaving (if things started in a pure state on the pre-black-hole surface) a mixed state on the post-evaporation surface in our portion of the universe, but still one that is pure in some sense overall, or they funnel it back out into our portion of the universe as the black hole evaporates. It is a challenge, and one that should help stimulate the development of quantum gravity theories, to figure out which, and exactly what is going on, but I don't feel any strong a priori compulsion toward one or the other of a unitary or a nonunitary evolution on from pre-black-hole to post-evaporation spacelike hypersurfaces in our portion of the universe.

 

 

Quantum imaging with entanglement and undetected photons, II: short version

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Here's a short explanation of the experiment reported in "Quantum imaging with undetected photons" by members of Anton Zeilinger's group in Vienna (Barreta Lemos, Borish, Cole, Ramelow, Lapkiewicz and Zeilinger).  The previous post also explains the experiment, but in a way that is closer to my real-time reading of the article; this post is cleaner and more succinct.

It's most easily understood by comparison to an ordinary Mach-Zehnder interferometry experiment. (The most informative part of the wikipedia article is the section "How it works"; Fig. 3 provides a picture.)  In this sort of experiment, photons from a source such as a laser encounter a beamsplitter and go into a superposition of being transmitted and reflected.  One beam goes through an object to be imaged, and acquires a phase factor---a complex number of modulus 1 that depends on the refractive index of the material out of which the object is made, and the thickness of the object at the point at which the beam goes through.  You can think of this complex number as an arrow of length 1 lying in a two-dimensional plane; the arrow rotates as the photon passes through material, with the rate of rotation depending on the refractive index of the material. (If the thickness and/or refractive index varies on a scale smaller than the beamwidth, then the phase shift may vary over the beam cross-section, allowing the creation of an image of how the thickness of the object---or at least, the total phase imparted by the object, since the refractive index may be varying too---varies in the plane transverse to the beam.  Otherwise, to create an image rather than just measure the total phase it imparts at a point, the beam may need to be scanned across the object.)  The phase shift can be detected by recombining the beams at the second beamsplitter, and observing the intensity of light in each of the two output beams, since the relative probability of a photon coming out one way or the other depends on the relative phase of the the two input beams; this dependence is called "interference".

Now open the homepage of the Nature article and click on Figure 1 to enlarge it.  This is a simplified schematic of the experiment done in Vienna.  Just as in ordinary Mach-Zehnder interferometry, a beam of photons is split on a beamsplitter (labeled BS1 in the figure).  One can think of each photon from the source going into a superposition of being reflected and transmitted at the first beamsplitter.  The transmitted part is downconverted by passing through the nonlinear crystal NL1 into an entangled pair consisting of a yellow and a red photon; the red photon is siphoned off by a dichroic (color-dependent) beamsplitter, D1, and passed through the object O to be imaged, acquiring a phase dependent on the refractive index of the object and its thickness.  The phase, as I understand things, is associated with the photon pair even though it is imparted by the passing only the red photon through the object.  In order to observe the phase via interferometry, one needs to involve both the red and yellow photon, coherently.  (If one could observe it as soon as it was imparted to the pair by just interacting with the yellow photon, one could send a signal from the interaction point to the yellow part of the beam instantaneously, violating relativity.)   The red part of the beam is then recombined (at dichroic beamsplitter D2) with the reflected portion of the beam (which is still at the original wavelength), and that portion of the beam is passed through another nonlinear crystal, NL2.  This downconverts the part of the beam that is at the original wavelength into a red-yellow pair, with the resulting red component aligned with --- and indistinguishable from---the red component that has gone through the object.  The phase associated with the photon pair created in the transmitted part of the beam whose red member went through the object is now associated with the yellow photons in the transmitted beam, since the red photons in that beam have been rendered indistinguishable from the ones created in the reflected beam, and so retain no information about the relative phase.  This means that the phase can be observed siphoning out the red photons (at dichroic beamsplitter D3), recombining just the yellow photons with a beamsplitter BS2, and observing the intensitities at the two outputs of this final beamsplitter, precisely as in the last stage of an ordinary Mach-Zehnder experiment.  The potential advantage over ordinary Mach-Zehnder interferometry is that one can image the total phase imparted by the object at a wavelength different from the wavelength of the photons that are interfered and detected at the final stage, which could be an advantage for instance if good detectors are not available at the wavelength one wants to image the object at.