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".

Quantum imaging with entanglement and undetected photons in Vienna

[Update 9/1:  I have been planning (before any comments, incidentally) to write a version of this post which just provides a concise verbal explanation of the experiment, supplemented perhaps with a little formal calculation.  However, I think the discussion below comes to a correct understanding of the experiment, and I will leave it up as an example of how a physicist somewhat conversant with but not usually working in quantum optics reads and quickly comes to a correct understanding of a paper.  Yes, the understanding is correct even if some misleading language was used in places, but I thank commenter Andreas for pointing out the latter.]

Thanks to tweeters @AtheistMissionary and @robertwrighter for bringing to my attention this experiment by a University of Vienna group (Gabriela Barreto Lemos, Victoria Borish, Garrett D. Cole, Sven Ramelo, Radek Lapkiewicz and Anton Zeilinger), published in Nature, on imaging using entangled pairs of photons.  It seems vaguely familiar, perhaps from my visit to the Brukner, Aspelmeyer and Zeilinger groups in Vienna earlier this year;  it may be that one of the group members showed or described it to me when I was touring their labs.  I'll have to look back at my notes.

This New Scientist summary prompts the Atheist and Robert to ask (perhaps tongue-in-cheek?) if it allows faster-than-light signaling.  The answer is of course no. The New Scientist article fails to point out a crucial aspect of the experiment, which is that there are two entangled pairs created, each one at a different nonlinear crystal, labeled NL1 and NL2 in Fig. 1 of the Nature article.  [Update 9/1: As I suggest parenthetically, but in not sufficiently emphatic terms, four sentences below, and as commenter Andreas points out,  there is (eventually) a superposition of an entangled pair having been created at different points in the setup; "two pairs" here is potentially misleading shorthand for that.] To follow along with my explanation, open the Nature article preview, and click on Figure 1 to enlarge it.  Each pair is coherent with the other pair, because the two pairs are created on different arms of an interferometer, fed by the same pump laser.  The initial beamsplitter labeled "BS1" is where these two arms are created (the nonlinear crystals come later). (It might be a bit misleading to say two pairs are created by the nonlinear crystals, since that suggests that in a "single shot" the mean photon number in the system after both nonlinear crystals  have been passed is 4, whereas I'd guess it's actually 2 --- i.e. the system is in a superposition of "photon pair created at NL1" and "photon pair created at NL2".)  Each pair consists of a red and a yellow photon; on one arm of the interferometer, the red photon created at NL1 is passed through the object "O".  Crucially, the second pair is not created until after this beam containing the red photon that has passed through the object is recombined with the other beam from the initial beamsplitter (at D2).  ("D" stands for "dichroic mirror"---this mirror reflects red photons, but is transparent at the original (undownconverted) wavelength.)  Only then is the resulting combination passed through the nonlinear crystal, NL2.  Then the red mode (which is fed not only by the red mode that passed through the object and has been recombined into the beam, but also by the downconversion process from photons of the original wavelength impinging on NL2) is pulled out of the beam by another dichroic mirror.  The yellow mode is then recombined with the yellow mode from NL1 on the other arm of the interferometer, and the resulting interference observed by the detectors at lower right in the figure.

It is easy to see why this experiment does not allow superluminal signaling by altering the imaged object, and thereby altering the image.  For there is an effectively lightlike or timelike (it will be effectively timelike, given the delays introduced by the beamsplitters and mirrors and such) path from the object to the detectors.  It is crucial that the red light passed through the object be recombined, at least for a while, with the light that has not passed through the object, in some spacetime region in the past light cone of the detectors, for it is the recombination here that enables the interference between light not passed through the object, and light passed through the object, that allows the image to show up in the yellow light that has not (on either arm of the interferometer) passed through the object.  Since the object must be in the past lightcone of the recombination region where the red light interferes, which in turn must be in the past lightcone of the final detectors, the object must be in the past lightcone of the final detectors.  So we can signal by changing the object and thereby changing the image at the final detectors, but the signaling is not faster-than-light.

Perhaps the most interesting thing about the experiment, as the authors point out, is that it enables an object to be imaged at a wavelength that may be difficult to efficiently detect, using detectors at a different wavelength, as long as there is a downconversion process that creates a pair of photons with one member of the pair at each wavelength.  By not pointing out the crucial fact that this is an interference experiment between two entangled pairs [Update 9/1: per my parenthetical remark above, and Andreas' comment, this should be taken as shorthand "between a component of the wavefunction in which an entangled pair is created in the upper arm of the interferometer, and one in which one is created in the lower arm"], the description in New Scientist does naturally suggest that the image might be created in one member of an entangled pair, by passing the other member through the object,  without any recombination of the photons that have passed through the object with a beam on a path to the final detectors, which would indeed violate no-signaling.

I haven't done a calculation of what should happen in the experiment, but my rough intuition at the moment   is that the red photons that have come through the object interfere with the red component of the beam created in the downconversion process, and since the photons that came through the object have entangled yellow partners in the upper arm of the interferometer that did not pass through the object, and the red photons that did not pass through the object have yellow partners created along with them in the lower part of the interferometer, the interference pattern between the red photons that did and didn't pass through the object corresponds perfectly to an interference pattern between their yellow partners, neither of which passed through the object.  It is the latter that is observed at the detectors. [Update 8/29: now that I've done the simple calculation, I think this intuitive explanation is not so hot.  The phase shift imparted by the object "to the red photons" actually pertains to the entire red-yellow entangled pair that has come from NL1 even though it can be imparted by just "interacting" with the red beam, so it is not that the red photons interfere with the red photons from NL2, and the yellow with the yellow in the same way independently, so that the pattern could be observed on either color, with the statistical details perfectly correlated. Rather, without recombining the red photons with the beam, no interference could be observed between photons of a single color, be it red or yellow, because the "which-beam" information for each color is recorded in different beams of the other color.  The recombination of the red photons that have passed through the object with the undownconverted photons from the other output of the initial beamsplitter ensures that the red photons, all end up in the same mode after crystal NL2 whether they came into the beam before the crystal or were produced in the crystal by downconversion, thereby ensuring that the red photons contain no record of which beam the yellow photons are in, and allowing the interference due to the phase shift imparted by the object to be observed on the yellow photons alone.]

As I mentioned, not having done the calculation, I don't think I fully understand what is happening.  [Update: Now that I have done a calculation of sorts, the questions raised in this paragraph are  answered in a further Update at the end of this post.  I now think that some of the recombinations of beams considered in this paragraph are not physically possible.]  In particular, I suspect that if the red beam that passes through the object were mixed with the downconverted beam on the lower arm of the interferometer after the downconversion, and then peeled off before detection, instead of having been mixed in before the downconversion and peeled off afterward, the interference pattern would not be observed, but I don't have clear argument why that should be.  [Update 8/29: the process is described ambiguously here.  If we could peel off the red photons that have passed through the object while leaving the ones that came from the downconversion at NL2, we would destroy the interference.  But we obviously can't do that; neither we nor our apparatus can tell these photons apart (and if we could, that would destroy interference anyway).  Peeling off *all* the red photons before detection actually would allow the interference to be seen, if we could have mixed back in the red photons first; the catch is that this mixing-back-in is probaby not physically possible.]  Anyone want to help out with an explanation?  I suspect one could show that this would be the same as peeling off the red photons from NL2 after the beamsplitter but before detection,  and only then recombining them with the red photons from the object, which would be the same as just throwing away the red photons from the object to begin with.  If one could image in this way, then that would allow signaling, so it must not work.  But I'd still prefer a more direct understanding via a comparison of the downconversion process with the red photons recombined before, versus after.  Similarly, I suspect that mixing in and then peeling off the red photons from the object before NL2 would not do the job, though I don't see a no-signaling argument in this case.  But it seems crucial, in order for the yellow photons to bear an imprint of interference between the red ones, that the red ones from the object be present during the downconversion process.

The news piece summarizing the article in Nature is much better than the one at New Scientist, in that it does explain that there are two pairs, and that the one member of one pair is passed through the object and recombined with something from the other pair.  But it does not make it clear that the recombination takes place before the second pair is created---indeed it strongly suggests the opposite:

According to the laws of quantum physics, if no one detects which path a photon took, the particle effectively has taken both routes, and a photon pair is created in each path at once, says Gabriela Barreto Lemos, a physicist at Austrian Academy of Sciences and a co-author on the latest paper.

In the first path, one photon in the pair passes through the object to be imaged, and the other does not. The photon that passed through the object is then recombined with its other ‘possible self’ — which travelled down the second path and not through the object — and is thrown away. The remaining photon from the second path is also reunited with itself from the first path and directed towards a camera, where it is used to build the image, despite having never interacted with the object.

Putting the quote from Barreta Lemos about a pair being created on each path before the description of the recombination suggests that both pair-creation events occur before the recombination, which is wrong. But the description in this article is much better than the New Scientist description---everything else about it seems correct, and it gets the crucial point that there are two pairs, one member of which passes through the object and is recombined with elements of the other pair at some point before detection, right even if it is misleading about exactly where the recombination point is.

[Update 8/28: clearly if we peel the red photons off before NL2, and then peel the red photons created by downconversion at NL2 off after NL2 but before the final beamsplitter and detectors, we don't get interference because the red photons peeled off at different times are in orthogonal modes, each associated with one of the two different beams of yellow photons to be combined at the final beamsplitter, so the interference is destroyed by the recording of "which-beam" information about the yellow photons, in the red photons. But does this mean if we recombine the red photons into the same mode, we restore interference? That must not be so, for it would allow signaling based on a decision to recombine or not in a region which could be arranged to be spacelike separated from the final beamsplitter and detectors.  But how do we see this more directly?  Having now done a highly idealized version of the calculation (based on notation like that in and around Eq. (1) of the paper) I see that if we could do this recombination, we would get interference.  But to do that we would need a nonphysical device, namely a one-way mirror, to do this final recombination.  If we wanted to do the other variant I discussed above, recombining the red photons that have passed the object with the red (and yellow) photons created at NL2 and then peeling all red photons off before the final detector, we would even need a dichroic one-way mirror (transparent to yellow, one-way for red), to recombine the red photons from the object with the beam coming from NL2.  So the only physical way to implement the process is to recombine the red photons that have passed through the object with light of the original wavelength in the lower arm of the interferometer before NL2; this just needs an ordinary dichroic mirror, which is a perfectly physical device.]

Free will and retrocausality at Cambridge II: Conspiracy vs. Retrocausality; Signaling and Fine-Tuning

Expect (with moderate probability) substantial revisions to this post, hopefully including links to relevant talks from the Cambridge conference on retrocausality and free will in quantum theory, but for now I think it's best just to put this out there.

Conspiracy versus Retrocausality

One of the main things I hoped to straighten out for myself at the conference on retrocausality in Cambridge was whether the correlation between measurement settings and "hidden variables" involved in a retrocausal explanation of Bell-inequality-violating quantum correlations are necessarily "conspiratorial", as Bell himself seems to have thought.  The idea seems to be that correlations between measurement settings and hidden variables must be due to some "common cause" in the intersection of the backward light cones of the two.  That is, a kind of "conspiracy" coordinating the relevant hidden variables that can affect the meausrement outcome with all sorts of intricate processes that can affect which measurement is made, such as those affecting your "free" decision as to how to set a polarizer, or, in case you set up a mechanism to control the polarizer setting according to some apparatus reasonably viewed as random ("the Swiss national lottery machine" was the one envisioned by Bell), the functioning of this mechanism.  I left the conference convinced once again (after doubts on this score had been raised in my mind by some discussions at New Directions in the Philosophy of Physics 2013) that the retrocausal type of explanation Price has in mind is different from a conspiratorial one.

Deflationary accounts of causality: their impact on retrocausal explanation

Distinguishing "retrocausality" from "conspiratorial causality" is subtle, because it is not clear that causality makes sense as part of a fundamental physical theory.   (This is a point which, in this form, apparently goes back to Bertrand Russell early in this century.  It also reminds me of David Hume, although he was perhaps not limiting his "deflationary" account of causality to causality in physical theories.)  Causality might be a concept that makes sense at the fundamental level for some types of theory, e.g. a version ("interpretation") of quantum theory that takes measurement settings and outcomes as fundamental, taking an "instrumentalist" view of the quantum state as a means of calculating outcome probabilities giving settings, and not as itself real, without giving a further formal theoretical account of what is real.  But in general, a theory may give an account of logical implications between events, or more generally, correlations between them, without specifying which events cause, or exert some (perhaps probabilistic) causal influence on others.  The notion of causality may be something that is emergent, that appears from the perspective of beings like us, that are part of the world, and intervene in it, or model parts of it theoretically.  In our use of a theory to model parts of the world, we end up taking certain events as "exogenous".  Loosely speaking, they might be determined by us agents (using our "free will"), or by factors outside the model.  (And perhaps "determined" is the wrong word.)   If these "exogenous" events are correlated with other things in the model, we may speak of this correlation as causal influence.  This is a useful way of speaking, for example, if we control some of the exogenous variables:  roughly speaking, if we believe a model that describes correlations between these and other variables not taken as exogenous, then we say these variables are causally influenced by the variables we control that are correlated with them.  We find this sort of notion of causality valuable because it helps us decide how to influence those variables we can influence, in order to make it more likely that other variables, that we don't control directly, take values we want them to.  This view of causality, put forward for example in Judea Pearl's book "Causality", has been gaining acceptance over the last 10-15 years, but it has deeper roots.  Phil Dowe's talk at Cambridge was an especially clear exposition of this point of view on causality (emphasizing exogeneity of certain variables over the need for any strong notion of free will), and its relevance to retrocausality.

This makes the discussion of retrocausality more subtle because it raises the possibility that a retrocausal and a conspiratorial account of what's going on with a Bell experiment might describe the same correlations, between the Swiss National lottery machine, or whatever controls my whims in setting a polarizer, all the variables these things are influenced by, and the polarizer settings and outcomes in a Bell experiment, differing only in the causal relations they describe between these variables.  That might be true, if a retrocausalist decided to try to model the process by which the polarizer was set.  But the point of the retrocausal account seems to be that it is not necessary to model this to explain the correlations between measurement results.  The retrocausalist posits a lawlike relation of correlation between measurement settings and some of the hidden variables that are in the past light cone of both measurement outcomes.  As long as this retrocausal influence does not influence observable past events, but only the values of "hidden", although real, variables, there is nothing obviously more paradoxical about imagining this than about imagining----as we do all the time---that macroscopic variables that we exert some control over, such as measurement settings, are correlated with things in the future.   Indeed, as Huw Price has long (I have only recently realized for just how long) been pointing out, if we believe that the fundamental laws of physics are symmetric with respect to time-reversal, then it would be the absence of retrocausality, if we dismiss its possibility, and even if we accept its possibility to the limited extent needed to potentially explain Bell correlations, its relative scarcity, that needs explaining.  Part of the explanation, of course, is likely that causality, as mentioned above, is a notion that is useful for agents situated within the world, rather than one that applies to the "view from nowhere and nowhen" that some (e.g. Price, who I think coined the term "nowhen") think is, or should be,  taken by fundamental physical theories.  Therefore whatever asymmetries---- these could be somewhat local-in-spacetime even if extremely large-scale, or due to "spontaneous" (i.e. explicit, even if due to a small perturbation) symmetry-breaking --- are associated with our apparently symmetry-breaking experience of directionality of time may also be the explanation for why we introduce the causal arrows we do into our description, and therefore why we so rarely introduce retrocausal ones.  At the same time, such an explanation might well leave room for the limited retrocausality Price would like to introduce into our description, for the purpose of explaining Bell correlations, especially because such retrocausality does not allow backwards-in-time signaling.

Signaling (spacelike and backwards-timelike) and fine-tuning. Emergent no-signaling?

A theme that came up repeatedly at the conference was "fine-tuning"---that no-spacelike-signaling, and possibly also no-retrocausal-signaling, seem to require a kind of "fine-tuning" from a hidden variable model that uses them to explain quantum correlations.  Why, in Bohmian theory, if we have spacelike influence of variables we control on physically real (but not necessarily observable) variables, should things be arranged just so that we cannot use this influence to remotely control observable variables, i.e. signal?  Similarly one might ask why, if we have backwards-in-time influence of controllable variables on physically real variables, things are arranged just so that we cannot use this influence to remotely control observable variables at an earlier time?  I think --- and I think this possibility was raised at the conference --- that a possible explanation, suggested by the above discussion of causality, is that for macroscopic agents such as us, with usually-reliable memories, some degree of control over our environment and persistence over time, to arise, it may be necessary that the scope of such macroscopic "observable" influences be limited, in order that there be a coherent macroscopic story at all for us to tell---in order for us even be around to wonder about whether there could be such signalling or not.  (So the term "emergent no-signalling" in the section heading might be slightly misleading: signalling, causality, control, and limitations on signalling might all necessarily emerge together.) Such a story might end up involving thermodynamic arguments, about the sorts of structures that might emerge in a metastable equilibrium, or that might emerge in a dynamically stable state dependent on a temperature gradient, or something of the sort.  Indeed, the distribution of hidden variables (usually, positions and/or momenta) according to the squared modulus of the wavefunction, which is necessary to get agreement of Bohmian theory with quantum theory and also to prevent signaling (and which does seem like "fine-tuning" inasmuch as it requires a precise choice of probability distribution over initial conditions), has on various occasions been justified by arguments that it represents a kind of equilibrium that would be rapidly approached even if it did not initially obtain.  (I have no informed view at present on how good these arguments are, though I have at various times in the past read some of the relevant papers---Bohm himself, and Sheldon Goldstein, are the authors who come to mind.)

I should mention that at the conference the appeal of such statistical/thermodynamic  arguments for "emergent" no-signalling was questioned---I think by Matthew Leifer, who with Rob Spekkens has been one of the main proponents of the idea that no-signaling can appear like a kind of fine-tuning, and that it would be desirable to have a model which gave a satisfying explanation of it---on the grounds that one might expect "fluctuations" away from the equilibria, metastable structures, or steady states, but we don't observe small fluctuations away from no-signalling---the law seems to hold with certainty.  This is an important point, and although I suspect there are  adequate rejoinders, I don't see at the moment what these might be like.

Paul Groves, Joseph Illick at Santa Fe Festival of Song: Duparc, Britten, Liszt, Rachmaninoff

On August 8th, we were treated to singing of transcendent beauty from tenor Paul Groves, with superb accompaniment by pianist Joseph Illick, in deeply felt and well-conceived interpretations of  songs by Henri Duparc, Franz Liszt and Sergei Rachmaninoff, and Benjamin Britten's wonderful and imaginative arrangements of British Isles folksongs.  The recital was part of the Santa Fe Festival of Song, a project of Performance Santa Fe (the organization formerly known as the Santa Fe Concert Association) in which singers who are in town to perform at the Opera give art song recitals.  Groves is Florestan in Santa Fe's Fidelio this year, and after hearing him in this recital, I'm eagerly anticipating his performance in that role.

Groves' voice is sweet and clear, but very powerful when he wants it to be, without losing any clarity or getting ragged at volume.  His control over breath, and dynamic range are amazing and deployed to great interpretive effect.  I don't believe that there is a single ideal way of interpreting most songs (though of course some songs may support a more limited range of workable approaches than others)...but I will say that Groves' performances of almost all of these songs were sheer perfection---while one could imagine a different approach being equally successful if equally well-executed, I mostly couldn't imagine anyone singing these songs better than Groves did here. He used the full range of vocal expression available to one with a top-of-the-line trained operatic voice. While a more subdued approach, with climaxes not quite as operatic in their intensity, could work equally well in many of these songs, and indeed provide a perfect opportunity for superb artistry by those who don't quite have the unbelievable volume and projection required for major-stage opera, I am not one who takes the view that operatic intensity should be banished from art-song interpretation. Groves' performance here was an illustration of how perfect and appropriate an approach informed by operatic experience, and empowered by an operatic technique and voice, can be in the art song.

The concert began with Duparc.  I thought the first song, Le manoir de Rosemonde, came off as perhaps a tad too intense and vocally operatic an interpretation, though flawlessly sung.  This might have been in part a matter of gauging the room sound; the Santa Fe United Methodist Church sanctuary is of modest size, with a relatively live and reflective acoustic.  What followed ranged from superb to sublime.  Extase was languorous and hypnotic, Soupir serene and heartfelt, Phidylé an entrancing mélange of rapture and whatever the right word is to express a slightly wistful, mildly sensual, very french kind of elegant wallowing in wistful nostalgia.

Following this, a definite change of pace with five Benjamin Britten settings of British folksongs. A substantial musical contribution from Britten here, with sometimes humorous, often very pretty and always very original settings that enhance, rather than working at cross-purposes to, the feeling and folk flavor of these songs. The Brisk Young Widow had verve and humour. In Sally in Our Alley, Groves did a superb job of putting across a broadly humorous, multi-verse narrative, with an unexpectedly poignant turn in the end. As pointed and effective an artistic meditation on class division as you will find anywhere, while avoiding dourness and simultaneously celebrating the joy of life.  Early One Morning was quiet and poignant, beautifully shaped by Groves, while in The Lincolnshire Poacher and Ca' the Yowes Groves used the more robust side of his voice to great effect in an earthier vein. At the reception following the concert, Groves remarked these Britten folksong settings are actually the most difficult to sing of the works on the program, because of their choppier, less legato line if I understood correctly. (Speculating, this may in part be a peculiarity of singing in English, at least compared to the more vowel-centered nature of French and even Russian (and of course Italian and even German, although neither of these two languages were used in this program)). Of course, that comparison may be more likely to apply once one has put in the hours and years of work necessary to do long lines with the rock-solid breath support and control, and imperturbable legato where necessary, required by the French and Russian-language works on the program.

Next up was a group of four Victor Hugo poems set by Franz Liszt, ranging through a wide range of moods and emotions, from the flirtatious humor of Comment, disaient-ils, to the over-the-top protestations of love in Enfant, si j'etais roi, to the long-lined, sensual love poetry of Oh! quand je dors  (another case where the adjective "sublime" applies to Groves' rendering).  Very colorful, sometimes dramatic, settings of these poems.  Excellent music that I did not know before this recital, and that I was very glad to be made aware of, especially in interpretations of this caliber.

The recital concluded with three songs of Sergei Rachmaninoff.  In the Silence of the Night (Fet), How Fair this Spot (Galin), and Oh Never Sing to Me Again (Pushkin). Again perfectly sung, with focused and specific portrayal of emotion, startling in their beauty and impact.

For the encore, Groves brought out baritone Kostas Smoriginas for an unexpected treat---the duet "Au Fond du Temple Saint" from Bizet's The Pearl Fishers. They took it perhaps a tad faster than I think optimal, but did a fabulous job---Groves' vocal control, and ability to do high, soft, and sweet as well as powerful and passionate was a key here, as was Smoriginas' incredibly deep, full, and powerful baritone, depth and darkness balanced by plenty of high-in-the-mask, projecting resonance that did not shade at all into brittleness.  Smoriginas is Escamillo in Santa Fe's Carmen this season; I will not hear Carmen until its last performance, but based on this duet, Smoriginas has just the voice this role needs, and should be amazing in it.  In many recordings I have of this aria, the baritone recedes a bit into the mix compared with the tenor (who is a bit more the star of this aria)---so it was great to hear the baritone part so clearly in this classic romance-meets-bromance potboiler. When the tenor and baritone united in singing the melody in sync partway through, the effect was thrilling.

At the reception I overheard Mr. Groves thanking the organizers for the opportunity to give a recital while in Santa Fe, and lamenting that while opera singers love to do recitals, there are not as many opportunities for them as there were even as recently as the 1990s, when he could do lengthy recital tours in Europe and elsewhere. Listen up, agents, impresarios, and program committees because some of us are on the lookout for the kind of intense and transporting experience of aesthetic perfection one gets from hearing a singer of the caliber of Paul Groves up close in recital.



Maria Stuarda, with Joyce DiDonato and Carmen Gianattasio at the Royal Opera, Covent Garden

July 18th: my first time at Covent Garden, for the Royal Opera production (joint with Barcelona, the Theâtre des Champs-Elysées, and the Polish National Opera) of Donizetti's Maria Stuarda.  The fashion for reviving some of the lesser-known bel canto operas seems as strong as ever these days, especially with singers like Joyce DiDonato available to star in them.  This one was very much worth doing.  The opera is not perfect dramatically, but neither is it devoid of drama.  Of course we know how it's going to end, but the first act generates suspense over whether Elizabeth will meet with Mary, how they will interact, and especially what will happen to Roberto, Mary's lover and apparently one of Elizabeth's favorites too.  (I'm no expert on the history, but the libretto was adapted from a Walter Scott novel or play and is, I think, none too accurate historically.)  The final scene goes on perhaps a bit too long, Mary's final forgiveness of Elizabeth and lengthy exhortations, following her final confession to Talbot, to the assembled crowd and to Roberto to forgive her and enable peace and prosperity in the British dominions strains credulity a bit, seeming a bit corny and overpious.  The music is often strong here, but not uniformly so, Mary's prayer with crowd response seemed weak in comparison with similar scenes in other works of the era, e.g. the transcendent prayer scene in Rossini's Maometto Secundo.

A long first scene features Elizabeth, then others, especially Roberto, in colloquy with her.  Mary doesn't appear until well into the act, after a mini-intermission (lights up for a five-minute scene change) in the first act.  Carmen Gianattasio carried this portion strongly---her coloratura technique seemed quite secure to me, her voice pure and unstrained even at  high volume or high pitch.  Pretty good characterization too---her Elizabeth did seem a bit petulant at times, frayed by the stress of her position, but I guess it's tough to be Queen.  Sometimes she seemed slightly detached from the role, possibly because the attention to superb execution of demanding singing kept her from losing herself in the part.  Ismael Jordi as Roberto also came off well vocally, although to my ears, a bit "sung", sometimes phrasing with ever-so-slightly exaggerated flourishes.  But no vocal roughness, a  tone with good body and clarity, good projection, and pretty good characterization and intensity although again perhaps not inhabiting the role as completely as he could have.  But a singer I hope to hear again, whose presence in a cast I'd consider a definite attraction.

The production made some questionable choices, possibly in trying to keep to a budget... full Elizabethan costume for the women, especially Elizabeth, was a good choice, but it seemed weird to combine it with dark waistcoats and suits on the men, possibly of Edwardian vintage like the massive leather-upholstered couches and wood panelling that furnished the supposed Royal palace.  Elizabeth was portrayed as a bit on the vulgar side, especially when she rips off Roberto's shirt and runs her hands all over him in a jealous fit.  This lead to a long bout of shirtless singing by Roberto, well sung but the tableau unfortunately reminiscent of a Chippendales billboard.  A bit tacky, but perhaps effective in putting over a certain take on Elizabeth and inducing queasiness at her harassment of Roberto.

While the first part of the first act was an example of extremely well-sung, if somewhat oddly staged, opera, the appearance of DiDonato as Maria at the midpoint of the first act was the operatic equivalent of engaging warp drive.  Her first aria was a lament at being imprisoned, but suffused---at least in my recollection of it--- more by a mood of reverie and remembrance of lost pleasures and beauty than a mood of grief.  Stunningly beautiful singing, the more so because not especially showy technically and not exploiting the hotter emotions.  There may well have been technically very difficult things here, too---I don't really recall, but certainly soft high passages may have been in play---but if so they were executed so effortlessly that the focus was on the character and the music.

DiDonata was excellent in Rossini's La Donna del Lago (another bel-canto-era Walter Scott-based opera) last summer in Santa Fe, but she sounded even better here, perhaps in part due to the superb acoustics of Covent Garden, which may well be the best of any major opera house I've been in  this regard.  The open sides at Santa Fe may make it hard for the sound to penetrate with full vibrancy to the cheap seats I usually occupy at the back of the main floor, whereas even in the very moderately-priced Upper Amphiteatre center section (next stop is the roof, but having a straight-ahead view of the stage instead of looking sideways out of a box was a blessing) the orchestral and vocal sound was clear and detailed, with perfectly adequate volume, sweet but with no loss of clarity.

Complete technical control and vocal security enabled her to be totally absorbed in the role...the effect was that she had become the character, rather than consciously acting it---whether or not this effect was achieved in part by conscious real-time effort or whether she was "in the zone" by dint of intense past effort mastering the role being immaterial.  This level of performance continued for the rest of the opera, making it for the most part extremely compelling theatrically and musically, despite the usual uneven level of musical inspiration expected from a less-performed bel canto opera, and some dramatic weakness in the second act.  Occasional stretches of stereotyped and routine bel canto writing were often lent interest by the drama involved, and there were plenty of passages with much more musical interest, inextricably entwined, as is so important in opera, with the drama.

To mention just a few such highlights, beyond Mary's first scene in the prison: the meeting between Mary and Elizabeth is of course classic, both Mary's controlled, but intense, pleading for mercy and then her startlingly intense outburst of anger when she has decided that Elizabeth cannot be moved, and reacts to Elizabeth's insult.  I found out later that censors required these words be cut from the original production, though soprano Maria Malibran sang them anyway in the first performance (leading, after a few more performances, to the production being shut down).    One didn't need to know this history for it to be a visceral thrill and shock when Mary let loose with "Figlia impura di Bolena, parli tu di disonore?  Meretrice indegna e oscena, in te cada il mio rossore. Profanato è il soglio inglese, vil bastarda, dal tuo piè!"  (Impure daughter of Boleyn, you speak of dishonor?  Worthless, obscene whore, I blush for you.  The English throne is profaned, vile bastard, by your foot!).

The scene in which Mary confesses to Talbot (extremely well sung and characterized by Matthew Rose) was another highlight, especially the swift darkening of mood when Mary gives in to Talbot's insistence that she confront her past crimes (alluding, possibly, to collusion in the murder of her first husband).  It's the darker highlights that seem to have stuck in my memory, but there were plenty of moments of more positive passion that were outstanding as well.

All the singers were at least excellent---I didn't feel like the opera was losing out from weakness in any aspect of the musical presentation.  In the scenes with the counselor---probably Guglielmo Cecil---urging Elizabeth against clemency, both Elizabeth and Guglielmo really made palpable and plausible a feeling of being trapped into denying Mary mercy---these ex-monarchs, granted clemency, are all too likely to come back and menace you.

The contemporary, white-tiled hospital-like setting of the execution chamber, while continuing the theme of random anachronism, was effective in one respect---reminding us that the current practice of capital punishment is not all that different from the stump-and-ax execution block of Elizabethan times.  DiDonato's stamina and superb singing carried the long, long final scene well, although not completely compensating for the length of the scene, which somewhat undermined the drama.  Still, it prompted plenty of meditations on politics, religion, personality, history, and the meaning of this drama in the milieu of early 19th century Italy, in which Catholicism and tradition was presumably  confronting Romanticism and republicanism.

If this show comes to your town---as it I believe it will to Barcelona, beginning in December ---it's not to be missed.  Strong singing all around, a fairly dramatically effective and psychologically interesting work, with attractive and often striking music throughout, and an unbelievably charismatic and inspired dramatic and vocal performance by Joyce DiDonato---a chance to see and hear a true operatic superstar, and to understand why she's in that category, for how profoundly she deepens the dramatic, psychological, and musical impact of the work.





Free will and retrocausality in the quantum world, at Cambridge. I: Bell inequalities and retrocausality

I'm in Cambridge, where the conference on Free Will and Retrocausality in the Quantum World, organized (or rather, organised) by Huw Price and Matt Farr will begin in a few hours.  (My room at St. Catherine's is across from the chapel, and I'm being serenaded by a choir singing beautifully at a professional level of perfection and musicality---I saw them leaving the chapel yesterday and they looked, amazingly, to be mostly junior high school age.)  I'm hoping to understand more about how "retrocausality", in which effects occur before their causes, might help resolve some apparent problems with quantum theory, perhaps in ways that point to potentially deeper underlying theories such as a "quantum gravity". So, as much for my own use as anyone else's, I thought perhaps I should post about my current understanding of this possibility.

One of the main problems or puzzles with quantum theory that Huw and others (such as Matthew Leifer, who will be speaking) think retrocausality may be able to help with, is the existence of Bell-type inequality violations. At their simplest, these involve two spacelike-separated regions of spacetime, usually referred to as "Alice's laboratory" and "Bob's laboratory", at each of which different possible experiments can be done. The results of these experiments can be correlated, for example if they are done on a pair of particles, one of which has reached Alice's lab and the other Bob's, that have previously interacted, or were perhaps created simultaneously in the same event. Typically in actual experiments, these are a pair of photons created in a "downconversion" event in a nonlinear crystal.  In a "nonlinear"  optical process photon number is not conserved (so one can get a "nonlinearity" at the level of a Maxwell's equation where the intensity of the field is proportional to photon number; "nonlinearity" refers to the fact that the sum of two solutions is not required to be a solution).  In parametric downconversion, a photon is absorbed by the crystal which emits a pair of photons in its place, whose energy-momentum four-vectors add up to that of the absorbed photon (the process does conserve energy-momentum).   Conservation of angular momentum imposes correlations between the results of measurements made by "Alice" and "Bob" on the emitted photons. These are correlated even if the measurements are made sometime after the photons have separated far enough that the changes in the measurement apparatus that determine which component of polarization it measures (which we'll henceforth call the "polarization setting"), on one of the photons, are space-like separated from the measurement process on the other photon, so that effects of the polarization setting in Alice's laboratory, which one typically assumes can propagate only forward in time, i.e. in their forward light-cone, can't affect the setting or results in Bob's laboratory which is outside of this forward light-cone.  (And vice versa, interchanging Alice and Bob.)

Knowledge of how their pair of photons were prepared (via parametric downconversion and propagation to Alice and Bob's measurement sites) is encoded in a "quantum state" of the polarizations of the photon pair.  It gives us, for any pair of polarization settings that could be chosen by Alice and Bob, an ordinary classical joint probability distribution over the pair of random variables that are the outcomes of the given measurements.  We have different classical joint distributions, referring to different pairs of random variables, when different pairs of polarization settings are chosen.   The Bell "paradox" is that there is no way of introducing further random variables that are independent of these polarization settings, such that for each pair of polarization settings, and each assignment of values to the further random variables, Alice and Bob's measurement outcomes are independent of each other, but when the further random variables are averaged over, the experimentally observed correlations, for each pair of settings, are reproduced. In other words, the outcomes of the polarization measurements, and in particular the fact that they are correlated, can't be "explained" by variables uncorrelated with the settings. The nonexistence of such an explanation is implied by the violation of a type of inequality called a "Bell inequality". (It's equivalent to to such a violation, if "Bell inequality" is defined generally enough.)

How I stopped worrying and learned to love quantum correlations

One might have hoped to explain the correlations by having some physical quantities (sometimes referred to as "hidden variables") in the intersection of Alice and Bob's backward light-cone, whose effects, propagating forward in their light-cone to Alice and Bob's laboratories, interact their with the physical quantities describing the polarization settings to produce---whether deterministically or stochastically---the measurement outcomes at each sites, with their observed probabilities and correlations. The above "paradox" implies that this kind of "explanation" is not possible.

Some people, such as Tim Maudlin, seem to think that this implies that quantum theory is "nonlocal" in the sense of exhibiting some faster-than-light influence. I think this is wrong. If one wants to "explain" correlations by finding---or hypothesizing, as "hidden variables"---quantities conditional on which the probabilities of outcomes, for all possible measurement settings, factorize, then these cannot be independent of measurement settings. If one further requires that all such quantities must be localized in spacetime, and that their influence propagates (in some sense that I'm not too clear about at the moment, but that can probably be described in terms of differential equations---something like a conserved probability current might be involved) locally and forward in time, perhaps one gets into inconsistencies. But one can also just say that these correlations are a fact. We can have explanations of these sorts of fact---for example, for correlations in photon polarization measurements, the one alluded to above in terms of energy-momentum conservation and previous interaction or simultaneous creation---just not the sort of ultra-classical one some people wish for.


It seems to me that what the retrocausality advocates bring to this issue is the possibility of something that is close to this type of classical explanation. It may allow for the removal of these types of correlation by conditioning on physical quantities. [Added July 31: this does not conflict with Bell's theorem, for the physical quantities are not required to be uncorrelated with measurement settings---indeed, being correlated with the measurement settings is to be expected if there is retrocausal influence from a measurement setting to physical quantities in the backwards light-cone of the measurement setting.] And unlike the Bohmian hidden variable theories, it hopes to avoid superluminal propagation of the influence of measurement settings to physical quantities, even unobservable ones.  It does this, however, by having the influence of measurement settings pursue a "zig-zag" path from Alice to Bob: in Alice's backward light-cone back to the region where Alice and Bob's backward light-cones intersect, then forward to Bob's laboratory. What advantages might this have over superluminal propagation? It probably satisfies some kind of spacetime continuity postulate, and seems more likely to be able to be Lorentz-invariant. (However, the relation between formal Lorentz invariance and lack of superluminal propagation is subtle, as Rafael Sorkin reminded me at breakfast today.)

Fingering a fragment of Silver

The great jazz pianist and composer Horace Silver died yesterday.  Ethan Iverson has posted, at his blog Do the Math, an excellent transcription of Silver's piano playing in a trio with Percy Heath and Art Blakey, on Silver's composition "Opus de Funk".  I've been working on playing it, and thought I would post the fingerings (see below or click here for pdf) I've worked out for the eight-measure introductory line Horace plays to start the performance, and repeats at the end, and (added on June 24) the first sixteen bars of the main strain. I'll continue to update this as I do more of the piece, but it may be awhile.

Where the fingerings stop in the middle of a continuous line, the implication is to continue with an ascending or descending sequence, or where that doesn't make sense, "do the obvious thing" (usually use whatever finger was most recently used for a given note). I have put some possible alternate fingerings in parentheses, usually above the staff.

As a pianist, I'm self-taught and none too fluent so far, and one main point of posting these fingerings is to get feedback, so if experienced pianists want to give some, that's welcome.  The other point is to provide a little bit of encouragement for people to dive into playing Ethan's transcription of this piece, and otherwise to explore Silver's music.

Morning listening: Tchaikowsky and Piazzola on APM's Performance Today

I take Astor Piazzola's work very much on a composition by composition basis.... some of it leaves me relatively unmoved, other pieces I really enjoy.  I really enjoyed the Tangata for saxophone quartet, played by the Ancia Saxophone Quartet at Bethlehem Lutheran Church in Minneapolis, Minnesota.  21'30 in this feed from Performance Today (you'll need to click on Hour 2 on the RHS of the page; stream should be available for at least a week).  I thought it might be Poulenc, then changed my mind to Piazzola, which turned out to be right.  It's probably the Poulencian playfulness and part-writing that grabbed me, as well as the superb playing by the quartet.  Following it (at 34:47  in the same feed) Tschaikowsky's dramatic overture-fantasia on Hamlet, Opus 67, is also extraordinarily well-played and recorded from a concert in Hamburg, by the North German Radio Symphony Orchestra, under Christoph Eschenbach.  Excellent, dramatic stuff.

Restaurant Zur Herrenmuehle, Heidelberg

While visiting Markus Müller at the Institute for Theoretical Physics at the University of Heidelberg to work on on our paper with Cozmin Ududec, I strolled all the way through the old town from my hotel on Bismarckplatz, past the Holy Ghost church on the market square, throught the Karslplatz with the illuminated castle ruins looming on the hillside above, and on down the less frequented end of the Hauptstrasse to the Restaurant Zur Herrenmuehle.  It was well worth the walk.  In a former mill, from the 17th century (hence the name "at the old mill", or maybe "at Old Man Mill").  I had the four course version of the Landhausmenu.  I tend toward vegetarianism with some fish, but am not completely strict about it, and suspended it here:  there was a little bit of salted beef in the soup course, and the main course was venison.  I suppose I rationalized it a bit by thinking that the deer at least run around free for most of their lives, rather than being cooped up in feedlots for a good chunk of them.  The first course, if I recall correctly, was marinated salmon (essentially lox) with anise and pepper, pickled mango, and asparagus; the second was a smooth foamed pearl-onion soup with whole pearl onions and a few salt-cured beef slices; excellent, concentrated flavor (would have been excellent even without the beef).  These went very well with a "Trocken" Riesling, Kabinett I believe, but I've forgotten the producer.  (One of the Rhine regions, I think.)   "Trocken" means dry, and refers to a more typically international method of winemaking that foregoes the traditional German süssreserve (sweet reserve) of unfermented wine added to end fermentation.  This wine, however, tasted closer to a traditional German style than your usual West Coast US or Alsatian Riesling.  The main course involved rare roasted or grilled venison and brussels sprouts flavored with real vanilla bean (a stroke of genius), as well as other delicious stuff.  The final course was semolina pudding slices with pistachios, etc...  When I ordered a glass of red wine to go with the venison, I mentioned two of the wines by the glass--neither German---that I was considering.  The one I didn't mention was a Spätburgunder, a German pinot noir.  The waiter recommended I have the Spätburgunder with the venison, and he was absolutely right.  While still recognizably a little bit sweet and fruity (a style that can be annoying in Spätburgunder if done clumsily, which is why I was not considering it initially), it was balanced, rather velvety and refined, with a kind of graham-cracker-like texture to the somewhat softened tannins, and a little bit of minerality and complexity in addition to beautiful strawberry-ish fruit.  Perfect complement, in the echoing-with-subtle-differences mode, to the venison.  I love it when a restaurant knows what wines go with their dishes, and isn't afraid to tell you.  I asked about the producer, and recall that it was fairly local, somewhat to the south of Heidelberg, I believe.  But I didn't jot down the name, unfortunately.  Probably one of those superb small local producers whose output is all spoken for by the local restaurants, wineshops, and customers, and not to be found in the US anyway (plus Spätburgunder may not be the best-traveling wine, freshness being a big part of its appeal).  I ordered a brandy rather than a coffee as an after-dinner-drink, and ended up with a surprise, a Spanish brandy (wish I could recall the producer!) that was a glorious end to the meal, and turned out to be complimentary.  The interior, as you can see by some of the pictures on the website, is elegant but still retains some of the rusticity of the old mill, for instance the wooden beams, and the bench seating around the edge of the room, even if not part of the original mill, lends a slightly rustic touch too.  Service was perfect, friendly and not obtrusive, and everyone there obviously loves good food and is happy to be providing it at a really high level.  I don't know if this restaurant has a Michelin star but I would definitely give it one (at least).  This is one of those places that should be known to all in the international fraternity (sorority, egalité) of lovers of fine food matched with equally fine wines... it is obviously owned, run, and staffed by members of the same.

Probable signature of gravitational waves from early-universe inflation found in cosmic microwave background by BICEP2 collaboration.

Some quick links about the measurement, announced today, by the BICEP2 collaboration using a telescope at the South Pole equipped with transition edge sensors (TESs) read out with superconducting quantum interference devices (SQUIDs), of B-modes (or "curl") in the polarization of the cosmic microwave background (CMB) radiation, considered to be an imprint on the CMB of primordial graviational waves stirred up by the period of rapid expansion of the universe (probably from around 10-35--10-33 sec).  BICEP2 estimates the tensor-to-scalar ratio "r", an important parameter constraining models of inflation, to be 0.2 (+0.7 / -0.5).

Note that I'm not at all expert on any aspect of this!

Caltech press release.

Harvard-Smithsonian Center for Astrophysics press release.

Main paper:  BICEP2 I: Detection of B-mode polarization at degree angular scales.

Instrument paper: BICEP2 II: Experiment and three-year data set

BICEP/Keck homepage with the papers and other materials.

Good background blog post (semi-popular level) from Sean Carroll

Carroll's initial reaction.

Richard Easther on inflation, also anticipating the discover (also fairlybroadly accessible)

Very interesting reaction from a particle physicist at Résonaances.

Reaction from Liam McAllister guesting on Lubos Motl's blog.

Reaction from theoretical cosmology postdoc Sesh Nadathur.

NIST Quantum Sensors project homepage.

Besides a microwave telescope to collect and focus the relevant radiation, the experiment used transition-edge sensors (in which photons can trigger a quantum phase transition) read out by superconducting quantum interference devices (SQUIDs).  I don't know the details of how that works, but TE sensors have lots of applications (including in quantum cryptography), as do SQUIDs;  I'm looking forward to learning more about this one.


Some ideas on food and entertainment for those attending SQUINT 2014 in Santa Fe

I'm missing SQUINT 2014 (bummer...) to give a talk at a workshop on Quantum Contextuality, Nonlocality, and the Foundations of Quantum Mechanics in Bad Honnef, Germany, followed by collaboration with Markus Mueller at Heidelberg, and a visit to Caslav Brukner's group and the IQOQI at Vienna.  Herewith some ideas for food and entertainment for SQUINTers in Santa Fe.

Cris Moore will of course provide good advice too.  For a high-endish foodie place, I like Ristra.  You can also eat in the bar there, more casual (woodtop tables instead of white tablecloths), a moderate amount of space (but won't fit an enormous group), some smaller plates.  Pretty reasonable prices (for the excellent quality).  Poblano relleno is one of the best vegetarian entrees I've had in a high-end restaurant---I think it is vegan.  Flash-fried calamari were also excellent... I've eaten here a lot with very few misses.  One of the maitres d' sings in a group I'm in, and we're working on tenor-baritone duets, so if Ed is there you can tell him Howard sent you but then you have to behave ;-).  The food should be good regardless.  If Jonathan is tending bar you can ask him for a flaming chartreuse after dinner... fun stuff and tasty too.  (I assume you're not driving.)  Wines by the glass are good, you should get good advice on pairing with food.

Next door to Ristra is Raaga... some of the best Indian food I've had in a restaurant, and reasonably priced for the quality.

I enjoyed a couple of lunches (fish tacos, grilled portobello sandwich, weird dessert creations...) at Restaurant Martin, was less thrilled by my one foray into dinner there.  Expensive for dinner, less so for lunch, a bit of a foodie vibe.

Fish and chips are excellent at Zia Café (best in town I think), so is the green chile pie--massive slice of a deep-dish quiche-like entity, sweet and hot at the same time.

I like the tapas at El Mesón, especially the fried eggplant, any fried seafood like oysters with salmorejo, roasted red peppers with goat cheese (more interesting than it sounds).  I've had better luck with their sherries (especially finos) better than their wines by the glass.  (I'd skip the Manchego with guava or whatever, as it's not that many slices and you can get cheese at a market.)  Tonight they will have a pretty solid jazz rhythm section, the Three Faces of Jazz, and there are often guests on various horn.  Straight-ahead standards and classic jazz, mostly bop to hard bop to cool jazz or whatever you want to call it.  "Funky Caribbean-infused jazz" with Ryan Finn on trombone on Sat. might be worth checking out too... I haven't heard him with this group but I've heard a few pretty solid solos from him with a big band.  Sounds fun.  The jazz is popular so you might want to make reservations (to eat in the bar/music space, there is also a restaurant area I've never eaten in) especially if you're more than a few people.

La Boca and Taverna La Boca are also fun for tapas, maybe less classically Spanish.  La Boca used to have half-price on a limited selection of tapas and $1 off on sherry from 3-5 PM.  Not sure if they still do.

Il Piatto is relatively inexpensive Italian, pretty hearty, and they usually have some pretty good deals in fixed-price 3 course meals where you choose from the menu, or early bird specials and such.

Despite a kind of pretentious name Tanti Luci 221, at 221 Shelby, was really excellent the one time I tried it.  There's a bar menu served only in the bar area, where you can also order off the main menu.  They have a happy hour daily, where drinks are half price.  That makes them kinda reasonable.  The Manhattan I had was excellent, though maybe not all that traditional.

If you've got a car and want some down-home Salvadoran food, the Pupuseria y Restaurante Salvadoreño, in front of a motel on Cerillos, is excellent and cheap.

As far as entertainment, get a copy of the free Reporter (or look up their online calendar).  John Rangel and Chris Ishee are two of the best jazz pianists in town;  if either is playing, go.  Chris is also in Pollo Frito, a New Orleans funk outfit that's a lot of fun.  If they're playing at the original 2nd street brewery, it should be a fun time... decent pubby food and brews to eat while you listen.  Saxophonist Arlen Asher is one of the deans of the NM jazz scene, trumpeter and flugelhorn player Bobby Shew is also excellent, both quite straight-ahead.  Dave Anderson also recommended.  The one time I heard JQ Whitcomb on trumpet he was solid, but it's only been once.  I especially liked his compositions.  Faith Amour is a nice singer, last time I heard her was at Pranzo where the acoustics were pretty bad.  (Tiny's was better in that respect.)

For trad New Mexican (food that is) I especially like Tia Sophia's on Washington (I think), and The Shed for red chile enchiladas (and margaritas).

Gotta go.  It's Friday night, when all good grad students, faculty, and postdocs anywhere in the worlkd head for the nearest "Irish pub".