quantum field theory

‘No string theorists in non-elite institutions’

Shiraz Naval Minwalla, a professor of theoretical physics at the Tata Institute of Fundamental Research (TIFR), Mumbai, won the New Horizons in Physics Prize for 2013 on November 5. The prize – which recognizes ‘promising researchers’ and comes with a cash prize of $100,000 – is awarded by the Fundamental Physics Prize Foundation, set up by Russian billionaire Yuri Milner in 2012.

Shiraz has been cited for his contributions to the study of string theory and quantum field theory, particularly for improving our understanding of the equations governing fluid dynamics, and using them to verify the predictions of all quantum field theories as opposed to a limited class of theories before.

On November 12, Shiraz was also awarded the Infosys Foundation Prize in the physical sciences category. He was the youngest among this year’s winners.

I interviewed him over Skype for The Hindu (major hat-tip to Akshat Rathi), which is where this interview first appeared (on November 13, 2013). Shiraz had some important things to say, including the now-proverbial ‘the Indian elementary school system sucks’, and that India is anomalously strong in the arena of string theory research, although it doesn’t yet match up to the US’s output qualitatively, but that almost none of it happens in non-elite institutions.

Here we go.

Why do you work with string theory and quantum field theory? Why are you interested in these subjects?

Because it seems like one of the roads to completing one element of the unfinished task of physics. In the last century, there have been two big developments in physic. The quantum revolution, which established the language of quantum mechanics for dealing with physical systems, and the general theory of relativity, which established the dynamic nature of spacetime as reality in the world and realized it was responsible for gravity. These two paradigms have been incredibly successful in their domains of applicability. Quantum theory is ubiquitous in physics, and is also the basis for theories of elementary particle physics. The general relativity way of thinking has been successful with astrophysics and cosmology, i.e. successful at larger scales.

These paradigms have been individually confirmed and individually very successful, yet we have no way of putting them together, no single mathematically consistent framework. This is why I work with string theory and quantum field theory because I think it is the correct path to realize a unified quantum theory of gravity.

What’s the nature of your work that has snagged the New Horizons Prize? Could you describe it in simpler terms?

The context for this discussion is the AdS/CFT correspondence of string theory. AdS/CFT asserts that certain conformal quantum field theories admit a reformulation as higher dimensional theories of gravity under appropriate circumstances. Now it has long been expected that the dynamics of any quantum field theory reduces, under appropriate circumstances, to the equations of hydrodynamics. If you put these two statements together it should follow that Einstein’s equations of gravity reduce, under appropriate circumstances, to the equations of hydrodynamics.

My collaborators and I were able to directly verify this expectation. The equations of hydrodynamics that Einstein’s equations reduce have particular values of transport coefficients. And there was a surprise here. It turns out that the equations charged relativistic hydrodynamics that came out of this procedure were slightly different in form from those listed in textbooks on the subject, like the text of [Lev] Landau and [Evgeny] Lifshitz. The resolution of this apparent paradox was obtained by [Dam] Son and [Piotr] Surowka and in subsequent work, where it was demonstrated that the textbook expectations for the equations of hydrodynamics are incomplete. The correct equations sometimes have more terms, in agreement with our constructions.

The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple – particularly symmetric – theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.

How do you see the Prize helping your research work? Does this make it easier for you to secure grants, etc.?

It pads my CV. [Laughs] So… anything I apply for henceforth becomes a little more likely to work out, but it won’t have a transformative impact on my career nor influence it in any way, frankly. It’s a great honour, of course. It makes me happy, it’s an encouragement. But I’m quite motivated without that. [After being asked about winning the Infosys Foundation Prize] I’m thrilled, but I’m also a little overwhelmed. I hope I live up to all the expectations. About being young – I hope this means that my best work is ahead of me.

What do you think about the Fundamental Physics Prize in general? About what Yuri Milner has done for the world of physics research?

Until last week, I hadn’t thought about it very much at all. The first thing to say is when Milner explained to me his motivations in constituting this prize, I understood it. Let me explain. As you know, Milner was a PhD student in physics before he left the field to invest in the Internet, etc. He said he left because he felt he wasn’t good enough to do important work.

He said one motivation was that people who are doing well needn’t found Internet companies. This is his personal opinion, one should respect that. Second: He felt that 70 or 80 years ago, physicists were celebrities who played a large role in motivating some young people to do science. Nowadays, there are no such people. I think I agree. Milner wants to do what he can to push the clock back on that. Third: Milner is uniquely well-positioned because he understands physics research because of his own background and he understands the world of business. So, he wanted to bridge these worlds. All these are reasonable ways of looking at the world.

If I had a lot of money, this isn’t the way I would have gone about it. There are many more efficient ways. For instance, more smaller prizes for younger people makes more sense than few big prizes for well established people. Some of the money could have gone as grants. I haven’t seriously thought about this, though. The fact is Milner didn’t have to do this but he did. It’s a good thing. This is his gesture, and I’m glad.

Are the Fundamental Physics Prizes in any way bringing “validity” to your areas of research? Are they bringing more favourable attention you wouldn’t have been able to get otherwise?

Well, of late, it has become fashionable sometimes to attack string theory in certain parts of the world of physics. In such an environment, it is nice to see there are other people who think differently.

What are your thoughts on the quality of physics research stemming from India? Are there enough opportunities for researchers at all levels of their careers?

Let me start with string theoretic work, which I’m aware of, and then extrapolate. String theory work done in India is pretty good. If you compared the output from India to the US, the work emerging from the US is way ahead qualitatively. But if you compared it to Japan’s output, I would say it’s clear that India does better. Japan has a large string theory community supported by American-style salaries whereas India runs on a shoestring. Given that and the fact that India is a very poor country, that’s quite remarkable. There’s no other country with a GDP per capita comparable to India’s whose string theoretic output is anywhere as good. In fact, the output is better than any country in the European Union, but at the same time not comparable to the EU’s as a whole. So you get an idea of the scale: reasonably good, not fantastic.

The striking weakness of research in India is that research happens by and large only in a few elite institutions. But in the last five years, it has been broadening out a bit. TIFR and the Harish-Chandra Research Institute [HRI] have good research groups; there are some reasonably good young groups in Indian Institute of Science [IIS], Bengaluru; Institute of Mathematical Sciences, Chennai; some small groups in the Chennai Mathematical Institute, IIT-Madras, IIT-Bombay, IIT-Kanpur, all growing in strength, The Indian Institute of Science Education and Research (IISER), Pune, has also made good hires in string theory.

So, it’s spreading out. The good thing is young people are being hired in many good places. What is striking is we don’t yet have participation from universities; there are no string theorists in non-elite institutions. Delhi University has a few, very few. This is in striking contrast with the US, where there are many groups in many universities, which gives the community great depth of research.

If I were to give Indian research a grade sheet, I’d say not bad but could do much better. There are 1.2 billion people in the country, so we should be producing commensurate output in research. We shouldn’t content ourselves by thinking we’re doing better than [South] Korea. Of course it is an unfair thing to ask for, but that should be the aim. For example, at TIFR, when we interview students for admission, we find that we usually have very few really good candidates. It’s not that they aren’t smart; people are smart everywhere. It’s just one reason: that the elementary school system in the country is abysmal. Most Indians come out of school unable to contribute meaningfully to any intellectual activity. Even Indian colleges have the same quality of output. The obvious thing is to make every school in India a reasonable school [laughs]. Such an obvious thing but we don’t do it.

Is there sufficient institutional and governmental support for researchers?

At the top levels, yes. I feel that places with the kind of rock-solid support that TIFR gives its faculty are few and far between. In the US many such places exist. But if you went to the UK, the only comparable places are perhaps Cambridge and Oxford. Whereas if you went to the second tier Durham University, you’ll see it’s not as good a place to be as TIFR. In fact, this is true for most universities around the world.

Institutions like TIFR, IIS, HRI and the National Centre for the Biological Sciences give good support and scientists should recognize this. There are few comparable places in the Third World. What we’re missing however is the depth. The US research community has got so good because of its depth. Genuine, exciting research is not done just in the Ivy League institutions. Even small places have a Nobel Laureate teaching there. So, India may have lots of universities but they are somehow not able to produce good work.

We’ve had a couple Indians already in what’s going to be three years of the Fundamental Physics Prizes – before you, there was Ashoke Sen. But in the Nobel Prizes in physics, we’ve had a stubborn no-show since Subramanyan Chandrasekhar won it in 1983. Why do you think that is?

There are two immediate responses. First is that, as I mentioned, India has an anomalously strong string theory presence. Why? I don’t know. India is especially strong with string theory. And the Fundamental Physics Prize Foundation has so far had some focus on this. The Nobel Prizes on the other hand require experimental verification of hypotheses. So, for as long as the Foundation has focused on the mathematics in physics, India has done well.

What are you going to do with your $100,000?

I haven’t seriously thought about it.

At the time of my interview, I had no idea he was about to win the Infosys Foundation Prize as well. It seems he’s in great demand! Good luck, Shiraz. 🙂

On meson decay-modes in studying CP violation

In particle physics, CPT symmetry is an attribute of the universe that is held as fundamentally true by quantum field theory (QFT). It states that the laws of physics should not be changed and the opposite of all allowed motions be allowed (T symmetry) if a particle is replaced with its antiparticle (C symmetry) and then left and right are swapped (P symmetry).

What this implies is a uniformity of the particle’s properties across time, charge and orientation, effectively rendering them conjugate perspectives.

(T-symmetry, called so for an implied “time reversal”, defines that if a process moves one way in time, its opposite is signified by its moving the other way in time.)

The more ubiquitously studied version of CPT symmetry is CP symmetry with the assumption that T-symmetry is preserved. This is because CP-violation, when it was first observed by James Cronin and Val Fitch, shocked the world of physics, implying that something was off about the universe. Particles that ought to have remained “neutral” in terms of their properties were taking sides! (Note: CPT-symmetry is considered to be a “weaker symmetry” then CP-symmetry.)

fitch_cronin — Val Logsdon Fitch (L) and James Watson Cronin

In 1964, Oreste Piccioni, who had just migrated to the USA and was working at the Lawrence Berkeley National Laboratory (LBNL), observed that kaons, mesons each composed of a strange quark and an up/down antiquark, had a tendency to regenerate in one form when shot as a beam into matter.

The neutral kaon, denoted as K⁰, has two forms, the short-lived (K_S) and the long-lived (K_L). Piccioni found that kaons decay in flight, so a beam of kaons, over a period of time, becomes pure K_L because the K_S all decay away before them. When such a beam is shot into matter, the K⁰ is scattered by protons and neutrons whereas the K⁰* (i.e., antikaons) contribute to the formation of a class of particles called hyperons.

Because of this asymmetric interaction, (quantum) coherence between the two batches of particles is lost, resulting in the emergent beam being composed of K_S and K_L, where the K_S is regenerated by firing a K⁰-beam into matter.

When the results of Piccioni’s experiment were duplicated by Robert Adair in the same year, regeneration as a physical phenomenon became a new chapter in the study of particle physics. Later that year, that’s what Cronin and Fitch set out to do. However, during the decay process, they observed a strange phenomenon.

According to a theory formulated in the 1950s by Murray Gell-Mann and Kazuo Nishijima, and then by Gell-Mann and Abraham Pais in 1955-1957, the K_S meson was allowed to decay into two pions in order for certain quantum mechanical states to be conserved, and the K_L meson was allowed to decay into three pions.

For instance, the K_L (s*, u) decay happens thus:

s* → u* + W⁺ (weak interaction)
W+ → d* + u
u → g + d + d* (strong interaction)
u → u

Kaon_decay_feynmandiagram — A Feynman diagram depicting the decay of a K_L meson into three pions.

In 1964, in their landmark experiment, Cronin and Fitch observed, however, that the K_L meson was decaying into two pions, albeit at a frequency of 1-in-500 decays. This implied an indirect instance of CP-symmetry violation, and subsequently won the pair the 1980 Nobel Prize for Physics.

An important aspect of the observation of CP-symmetry violation in kaons is that the weak force is involved in the decay process (even as observed above in the decay of the K_L meson). Even though the kaon is composed of a quark and an antiquark, i.e., held together by the strong force, its decay is mediated by the strong and the weak forces.

In all weak interactions, parity is not conserved. The interaction itself acts only on left-handed particles and right-handed anti-particles, and was parametrized in what is called the V-A Lagrangian for weak interactions, developed by Robert Marshak and George Sudarshan in 1957.

In fact, even in the case of the K_S and K_L kaons, their decay into pions can be depicted thus:

K_S → π⁺ + π⁰K_L → π⁺ + π⁺ + π^–

Here, the “+” and “-” indicate a particle’s parity, or handedness. When a K_S decays into two pions, the result is one right-handed (“+”) and one neutral pion (“0”). When a K_L decays into three pions, however, the result is two right-handed pions and one left-handed (“-“) pion.

When kaons were first investigated via their decay modes, the different final parities indicated that there were two kaons that were decaying differently. Over time, however, as increasingly precise measurements indicated that only one kaon (now called K⁺) was behind both decays, physicists concluded that the weak interaction was responsible for resulting in one kind of decay some of the time and in another kind of decay the rest of the time.

To elucidate, in particle physics, the squares of the amplitudes of two transformations, B → f and B* → f*, are denoted thus.

Here,

B = Initial state (or particle); f = Final state (or particle)
B* = Initial antistate (or antiparticle); f* = Final antistate (or antiparticle)
P = Amplitude of transformation B → f; Q = Amplitude of transformation B* → f*
S = Corresponding strong part of amplitude; W = Corresponding weak part of amplitude; both treated as phases of the wave for which the amplitude is being evaluated

Subtracting (and applying some trigonometry):

The presence of the term sin(W_P – W_Q) is a sign that purely, or at least partly, weak interactions can occur in all transformations that can occur in at least two ways, and thus will violate CP-symmetry. (It’s like having the option of having two paths to reach a common destination: #1 is longer and fairly empty; #2 is shorter and congested. If their distances and congestedness are fairly comparable, then facing some congestion becomes inevitable.)

Electromagnetism, strong interactions, and gravitation do not display any features that could give rise to the distinction between right and left, however. This disparity is also called the ‘strong CP problem’ and is one of the unsolved problems of physics. It is especially puzzling because the QCD Lagrangian, which is a function describing the dynamics of the strong interaction, includes terms that could break the CP-symmetry.

[youtube http://www.youtube.com/watch?v=KDkaMuN0DA0?rel=0]

(The best known resolution – one that doesn’t resort to spacetime with two time-dimensions – is the Peccei-Quinn theory put forth by Roberto Peccei and Helen Quinn in 1977. It suggests that the QCD-Lagrangian be extended with a CP-violating parameter whose value is 0 or close to 0.

This way, CP-symmetry is conserved during the strong interactions while CP-symmetry “breakers” in the QCD-Lagrangian have their terms cancelled by an emergent, dynamic field whose flux is encapsulated by massless Goldstone bosons called axions.)

Now, kaons are a class of mesons whose composition includes a strange quark (or antiquark). Another class of mesons, called B-mesons, are identified by their composition including a bottom antiquark, and are also notable for the role they play in studies of CP-symmetry violations in nature. (Note: A B-meson composed of a bottom antiquark and a bottom quark is not called a meson but a bottomonium.)

According to the Standard Model (SM) of particle physics, there are some particles – such as quarks and leptons – that carry a property called flavor. Mesons, which are composed of quarks and antiquarks, have an overall flavor inherited from their composition as a result. The presence of non-zero flavor is significant because SM permits quarks and leptons of one flavor to transmute into the corresponding quarks and leptons of another flavor, a process called oscillating.

And the B-meson is no exception. Herein lies the rub: during oscillations, the B-meson is favored over its antiparticle counterpart. Given the CPT theorem’s assurance of particles and antiparticles being differentiable only by charge and handedness, not mass, etc., the preference of B*-meson for becoming the B-meson more than the B-meson’s preference for becoming the B*-meson indicates a matter-asymmetry. Put another way, the B-meson decays at a slower rate than the B*-meson. Put yet another way, matter made of the B-meson is more stable than antimatter made of the B*-meson.

Further, if the early universe started off as a perfect symmetry (in every way), then the asymmetric formation of B-mesons would have paved the way for matter to take precedence over anti-matter. This is one of the first instances of the weak interaction possibly interfering with the composition of the universe. How? By promising never to preserve parity, and by participating in flavor-changing oscillations (in the form of the W/Z boson).

antimatter_matter — In this composite image of the Crab Nebula, matter and antimatter are propelled nearly to the speed of light by the Crab pulsar. The images came from NASA’s Chandra X-ray Observatory and the Hubble Space Telescope. (Photo by NASA; Caption from Howstuffworks.com)

The prevalence of matter over antimatter in our universe is credited to a hypothetical process called baryogenesis. In 1967, Andrei Sakharov, a Soviet nuclear physicist, proposed three conditions for asymmetric baryogenesis to have occurred.

Baryon-number violation
Departure from thermal equilibrium
C- and CP-symmetry violation

The baryon-number of a particle is defined as one-third of the difference between the number of quarks and number of antiquarks that make up the particle. For a B-meson composed of a bottom antiquark and a quark, the value’s 0; of a bottom antiquark and another antiquark, the value’s 1. Baryon-number violation, while theoretically possible, isn’t considered in isolation of what is called “B – L” conservation (“L” is the lepton number, and is equal to the number of leptons minus the number of antileptons).

Now, say a proton decays into a pion and a position. A proton’s baryon-number is 1, L-number is 0; a pion has both baryon- and L-numbers as 0; a positron has baryon-number 0 and L-number -1. Thus, neither the baryon-number nor the lepton-number are conserved, but their difference (1) definitely is. If this hypothetical process were ever to be observed, then baryogenesis would make the transition from hypothesis to reality (and the question of matter-asymmetry become conclusively answered).

Quark_structure_proton — The quark-structure of a proton (notice that the two up-quarks have different flavors)

Therefore, in recognition of the role of B-mesons (in being able to present direct evidence of CP-symmetry violation through asymmetric B-B* oscillations involving the mediation of the weak-force) and their ability to confirm or deny an “SM-approved” baryogenesis in the early universe, what are called the B-factories were built: a collider-based machine whose only purpose is to spew out B-mesons so they can be studied in detail by high-precision detectors.

The earliest, and possibly most well-known, B-factories were constructed in the 1990s and shut down in the 2000s: the BaBar experiment at SLAC (2008), Stanford, and the Belle experiment at the KEKB collider (2010) in Japan. In fact, a Belle II plant is under construction and upon completion will boast the world’s highest-luminosity experiment.

Belledetector_Belle2 — The Belle detector (L) and the logo for Belle II under construction

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Equations generated thanks to the Daum equations editor.

Assuming this universe…

Accomplished physicists I have met or spoken with in the last four months professed little agreement over which parts of physics were set-in-stone and which parts simply largely-corroborated hypotheses. Here are some of them, with a short description of the dispute.

Bosons – Could be an emergent phenomenon arising out of fermion-fermion interaction; current definition could be a local encapsulation of special fermionic properties
Colour-confinement – ‘Tis held that gluons, mediators of the colour force, cannot exist in isolation nor outside the hadrons (that are composed of quarks held together by gluons); while experimental proof of the energy required to pull a quark free being much greater than the energy to pull a quark-antiquark pair out of vacuum exists, denial of confinement hasn’t yet been conclusively refuted (ref: lattice formulation of string theory)
Massive gluons – A Millennium Prize problem
Gravity – Again, could be an emergent phenomenon arising out of energy-corrections of hidden, underlying quantum fields
Compactified extra-dimensions & string theory – There are still many who dispute the “magical” mathematical framework that string theory provides because it is a perturbative theory (i.e., background-dependent); a non-perturbative definition would make its currently divergent approximations convergent

If you ever get the opportunity to listen to a physicist ruminate on the philosophy of nature, don’t miss it. What lay-people would daily dispute is the macro-physical implications of a quantum world; the result is the all-important subjective clarification that lets us think better. What physicists dispute is the constitution of the quantum world itself; the result is the more objective phenomenological implications for everyone everywhere. We could use both debates.

The philosophies in physics

As a big week for physics comes up–a July 4 update by CERN on the search for the Higgs boson followed by ICHEP ’12 at Melbourne–I feel really anxious as a small-time proto-journalist and particle-physics-enthusiast. If CERN announces the discovery of evidence that rules out the existence of such a thing as the Higgs particle, not much will be lost apart from years of theoretical groundwork set in place for the post-Higgs universe. Physicists obeying the Standard Model will, to think the snowclone, scramble to their boards and come up with another hypothesis that explains mass-formation in quantum-mechanical terms.

For me… I don’t know what it means. Sure, I will have to unlearn the Higgs mechanism, which does make a lot of sense, and scour through the outpouring of scientific literature that will definitely follow to keep track of new directions and, more fascinatingly, new thought. The competing supertheories–loop quantum gravity (LQG) and string theory–will have to have their innards adjusted to make up for the change in the mechanism of mass-formation. Even then, their principle bone of contention will remain unchanged: whether there exists an absolute frame of reference. All this while, the universe, however, will have continued to witness the rise and fall of stars, galaxies and matter.

It is easier to consider the non-existence of the Higgs boson than its proven existence: the post-Higgs world is dark, riddled with problems more complex and, unsurprisingly, more philosophical. The two theories that dominated the first half of the previous century, quantum mechanics and special relativity, will still have to be reconciled. While special relativity holds causality and locality close to its heart, quantum mechanics’ tendency to violate the latter made it disagreeable at the philosophical level to A. Einstein (in a humorous and ironical turn, his attempts to illustrate this “anomaly” numerically opened up the field that further made acceptable the implications of quantum mechanics).

The theories’ impudent bickering continues with mathematical terms as well. While one prohibits travel at the speed of light, the other allows for the conclusive demonstration of superluminal communication. While one keeps all objects nailed to one place in space and time, the other allows for the occupation of multiple regions of space at a time. While one operates in a universe wherein gods don’t play with dice, the other can exist at all only if there are unseen powers that gamble on a secondly basis. If you ask me, I’d prefer one with no gods; I also have a strange feeling that that’s not a physics problem.

Speaking of causality, physicists of the Standard Model believe that the four fundamental forces–nuclear, weak, gravitational, and electromagnetic–cause everything that happens in this universe. However, they are at a loss to explain why the weak force is 10³²-times stronger than the gravitational force (even the finding of the Higgs boson won’t fix this–assuming the boson exists). An attempt to explain this anomaly exists in the name of supersymmetry (SUSY) or, together with the Standard Model, MSSM. If an entity in the (hypothetical) likeness of the Higgs boson cannot exist, then MSSM will also fall with it.

Taunting physicists everywhere all the way through this mesh of intense speculation, Werner Heisenberg’s tragic formulation remains indefatigable. In a universe in which the scale at which physics is born is only hypothetical, in which energy in its fundamental form is thought to be a result of probabilistic fluctuations in a quantum field, determinism plays a dominant role in determining the future as well as, in some ways, contradicting it. The quantum field, counter-intuitively, is antecedent to human intervention: Heisenberg postulated that physical quantities such as position and particle spin come in conjugate quantities, and that making a measurement of one quantity makes the other indeterminable. In other words, one cannot simultaneously know the position and momentum of a particle, or the spins of a particle around two different axes.

To me, this seems like a problem of scale: humans are macroscopic in the sense that they can manipulate objects using the laws of classical mechanics and not the laws of quantum mechanics. However, a sense of scale is rendered incontextualizable when it is known that the dynamics of quantum mechanics affect the entire universe through a principle called the collapse postulate (i.e., collapse of the state vector): if I measure an observable physical property of a system that is in a particular state, I subject the entire system to collapse into a state that is described by the observable’s eigenstate. Even further, there exist many eigenstates for collapsing into; which eigenstate is “chosen” depends on its observation (this is an awfully close analogue to the anthropic principle).

That reminds me. The greatest unsolved question in my opinion is whether the universe houses the brain or if the brain houses the universe. To be honest, I started writing this post without knowing how it would end: there were multiple eigenstates it could “collapse” into. That it would collapse into this particular one was unknown to me, too, and, in hindsight, there was no way I could have known about any aspect of its destiny. Having said that, the nature of the universe–and the brain/universe protogenesis problem–with the knowledge of deterministic causality and mensural antecedence, if the universe conceived the brain, the brain must inherit the characteristics of the universe, and therefore must not allow for freewill.

Now, I’m faintly depressed. And yes, this eigenstate did exist in the possibility-space.