Lily Zhao (Yale), Megan Bedell (Flatiron), and I spoke about Zhao's attempt to understand the variations in the data in the EXPRES precision spectrograph. We have the genius (to us, anyway) idea of using the trace positions in the cross-dispersion direction to calibrate the dispersion direction. Sound wrong-headed? It isn't, because the small number of instrument degrees of freedom that affect the wavelength solution will also affect the trace positions. So they will co-vary. We can even show that they do! The big issue we are having—and we are having great trouble diagnosing this—is that the calibration data (laser-frequency comb, in this case) are offset from the science data in strange ways. Which makes no sense, given the incredible stability of the spectrograph. In our call today, we came up with ways to further investigate and visualize what's going on.

This morning Ana Bonaca and I discussed an a apparent remarkable sensitivity of a likelihood function we have (for a photometric light curve) to change in frequency. There are sampling theorems, which say how smooth your likelihood function can be in the frequency direction. But do these apply when you are fitting multiple frequencies simultaneously? I would have thought yes for sure, but either we have a bug, a numerical instability, or a think-o. I don't think the problem is numerical because our condition numbers on all our matrices are reasonable.

I avoid talking politics on this blog. There are a few issues, though, where I feel not just able, but duty-bound, to speak out. Those are issues affecting graduate students.

This is already pretty unreasonable for many undergrads. But think about PhD students.

Suppose you’re a foreign PhD student at a US university. Maybe your school is already planning to have classes online this fall, like Harvard is. Maybe your school is planning to have classes in person, but will change its mind a few weeks in, when so many students and professors are infected that it’s clearly unreasonable to continue. Maybe your school never changes its mind, but your state does, and the school has to lock down anyway.

As a PhD student, you likely don’t live in the dorms. More likely you live in a shared house, or an apartment. You’re an independent adult. Your parents aren’t paying for you to go to school. Your school is itself a full-time job, one that pays (as little as the university thinks it can get away with).

What happens when your school goes online? If you need to leave the country?

You’d have to find some way out of your lease, or keep paying for it. You’d have to find a flight on short notice. You’d have to pack up all your belongings, ship or sell anything you can’t store, or find friends to hold on to it.

You’d have to find somewhere to stay in your “home country”. Some could move in with their parents temporarily, many can’t. Some of those who could in other circumstances, shouldn’t if they’re fleeing from an outbreak: their parents are likely older, and vulnerable to the virus. So you have to find a hotel, eventually perhaps a new apartment, far from what was until recently your home.

Reminder: you’re doing all of this on a shoestring budget, because the university pays you peanuts.

Can you transfer instead? In a word, no.

PhD students are specialists. They’re learning very specific things from very specific people. Academics aren’t the sort of omnidisciplinary scientists you see in movies. Bruce Banner or Tony Stark could pick up a new line of research on a whim, real people can’t. This is why, while international students may be good at the undergraduate level, they’re absolutely necessary for PhDs. When only three people in the world study the thing you want to study, you don’t have the luxury of staying in your birth country. And you can’t just transfer schools when yours goes online.

I hope that this policy gets reversed, or halted, or schools find some way around it. At the moment, anyone starting school in the US this fall is in a very tricky position. And anyone already there is in a worse one.

As usual, I’m going to ask that the comments don’t get too directly political. As a partial measure to tone things down, I’d like to ask you to please avoid mentioning any specific politicians, political parties, or political ideologies. Feel free to talk instead about your own experiences: how this policy is likely to affect you, or your loved ones. Please also feel free to talk more technically on the policy/legal side. I’d like to know what universities can do to work around this, and whether there are plausible paths to change or halt the policy. Please be civil, and be kind to your fellow commenters.

I really enjoyed last week's Zoom edition of the annual Strings conference. Clifford has said many of the things about it that I support wholeheartedly, so I don't have to repeat them here. One of the things I really liked was the active participation in the chat channel that accompanied the talks.

But some of the things I read there gave me the impression that there is some confusion out there about locality and things that can happen in quantum theories that showed up in discussions related to black hole information loss (or the lack thereof). So I though, maybe it's a good idea to sort these out.

Let's start with some basic quantum information: Entanglement is strange, it allows you to do things that maybe at first you did not expect. You can already see this in the easy, finite dimensional situation. Assume our Hilbert space is a tensor product \[H=H_h\otimes H_t\] of stuff here and stuff there. Further, for simplicity, assume both factors have dimension d and we can pick a basis \[(e_\alpha)_{1\le \alpha\le d}\] for both. If we have a maximally entangled state like \[\Omega = \frac 1{\sqrt d} \sum_\alpha e_\alpha\otimes e_\alpha\] the first observation is that instead of acting with an operator A here, you can as well act with the transposed (with respect to our basis) operator there, as you can see when writing out what it means in component: \[(A\otimes id)\Omega = (id\otimes A^T)\Omega = \frac 1{\sqrt d}\sum_{\alpha\beta} a_{\alpha\beta} e_\beta\otimes e_\alpha.\] That is, with the entangled state, everything, I can do here creates a state that can also be gotten by doing stuff there. And the converse is true as well: Take any state $\psi \in H$. Then I can find an operator $A$ that acts only here that creates this state from the entangled state: \[ \psi = (A\otimes id)\Omega.\] How can we find $A$? First use Schmidt decomposition to write \[\psi = \sum_j c_j f_j\otimes\tilde f_j\] where the $c$'s are non-negative numbers and both the $f$'s and the $\tilde f$'s are an ortho-normal basis. Define $V$ to be the unitary matrix that does the change of basis from the $e$'s to the $f$'s. Then \[ A = \sqrt{d\rho_h}V\] where we used the density matrix $\rho_h$ that is obtained from $\psi$ as a partial trace over the Hilbert space there (i.e. the state that we see here): \[\rho_h = tr_{H_t}|\Omega\rangle\langle \Omega| = \sum_j c_j |f_j\rangle\langle f_j|.\] It's a simple calculation that shows that this $A$ does the job.

In other words, you can create any state of the combined here-there system from an entangled state just by acting locally here.

But what is important is that as still operators here and there commute \[ [A\otimes id, id\otimes B] =0 \] you cannot influence measurements there by acting here. If you only measure there you cannot tell if the global state is still $\Omega$ or if I decided to act here with a non-trivial unitary operator (which would be the time evolution for my local Hamiltonian $A$).

It is easy to see, that you don't really need a maximally entangled state $\Omega$ to start with, you just need enough entanglement such that $\rho_h$ is invertible (i..e that there are no 0 coefficients in the Schmidt decomposition of the state you start with).

And from this we can leave the finite dimensional realm and go to QFT, where you have the Reeh-Schlieder theorem which tells you essentially that the quantum vacuum of a QFT has this entanglement property: In that setting, here corrensponds to any local neighbourhood (some causal diamond for example) while there is everything space-like localised from here (for a nice introduction see Witten's lecture notes on quantum information).

But still, this does not mean that by acting locally here in your room you can suddenly make some particle appear on the moon that somebody there could measure (or not). QFT is still local, operators with space-like separation cannot influence each other. The observer on the moon cannot tell if the particle observed there is just a vacuum fluctuation or if you created it in your armchair even though RS holds and you can create state with a particle on the moon. If you don't believe it, go back to the finite dimensional explicit example above. RS is really the same thing pimped to infinite dimensions.

And there is another thing that complicates these matters (and which I learned only recently): Localization in gauge theories is more complicated that you might think at first: Take QED. Thanks to Gauß' law, you can write an expression for the total charge $Q$ as an integral over the field-strength over a sphere at infinity. This seems to suggest that $Q$ has to commute with every operator localised in a finite region as $Q$ is localised in a region space-like to your finite reason. But what if that localised operator is a field operator, for example the electron field $\psi(x)$? Does this mean $Q, \psi(x)]=0$? Of course not, since the electron is charge, it should have \[ [Q,\psi(x)] = e \psi(x).\] But does that mean that an observer at spatial infinity can know if I apply $\psi(x)$ right here right now? That would be acausal, I could use this to send messages faster than light.

How is this paradox resolved? You have to be careful about the gauge freedom. You can either say that a gauge fixing term you add in the process of quantisation destroys Gauß' law. Alternatively, you can see that acting with a naked $\psi(x)$ destroys the gauge you have chosen. You can repair this but the consequence is that the "dressed" operator is no longer localised at $x$ but in fact is smeared all over the place (as you have to repair the gauge everywhere). More details can be found in Wojciech Dybalski's lecture notes in the very end (who explained this solution to me).

The same holds true for arguments where you say that the total (ADM) mass/energy in a space time can be measured at spatial infinity.

So the upshot is: Even though quantum theory is weird, you still have to be careful with locality and causality and when arguing about what you can do here and what that means for the rest of the universe. This also holds true when you try to resolve the black hole information loss paradox. Did I say islands?

You might have come across news about a search engine for faces: https://pimeyes.com/en/ . You can upload your photo and it will tell you where in the interwebs it has seen you before. Of course, I had to try it. Here are my results: OK, that was to be expected. This is the image I use whenever somebody asks me for a short bio with a picture or which I often use as avatar. This is also the first hit when you search for my name on Google Images. This is fine with me, this image is probably my pubic persona when it comes to the information super-highway. But still, if you meet me on the street, you can use PimEyes to figure out who I am. But that was to be expected. Then there come some variants of this picture and an older one that I used for similar purposes.

Next come pictures like these: There seems to be an Armenian politician with some vague resemblance and the internet has a lot of pictures from him. Fine. I can hide behind him (pretty much like my wife whose name is so common in Germany that the mother of one of our daughter's classmates has the same when you only consider first and maiden name as well as a former federal minister).

But then there is this: And yes, that's me. This is some open air concert one or two years ago. And it's not even full frontal like the sample I uploaded. And there probably 50 other people who are as much recognisable as myself in that picture. And even though this search engine seems not to know about them right now, there must be hundreds of pictures of similar Ali Mitgutsch Wimmelbuch quality that show at which mass activities I participated. I have to admit, I am a little bit scared.

It's going to be a summer of student projects for me! I spoke with Winston Harris (Middle Tennessee State) about our summer project to automate the detection of planets in RV data; he is installing software and data now. I spoke with Abby Shaum (NYU) about phase modulation methods for finding planets; we may have found a signal in a star thought to have no signal! I spoke with Abby Williams (NYU) who, with Kate Storey-Fisher (NYU), is looking at measuring not just large-scale structure but in fact spatial gradients in the large-scale structure, with Storey-Fisher's cool new tools. With Jonah Goldfine (NYU) I looked at his solutions to the exercises in Fitting a Model to Data, done in preparation for some attempts on NASA TESS light curves. And I spoke with Anu Raghunathan (NYU) about possibly speeding up her search for planet transits using box least squares. Our project is theoretical: What are the statistical properties of the BLS algorithm? But we still need things to be much much faster.

Applied Category Theory 2020 is coming up soon! After the Tutorial Day on Sunday July 6th, there will be talks from Monday July 7th to Friday July 10th. All talks will be live on Zoom and on YouTube. Recorded versions will appear on YouTube later.

Here is the program—click on it to download a more readable version:

Here are the talks! They come in three kinds: keynotes, regular presentations and short industry presentations. Within each I’ve listed them in alphabetical order by speaker: I believe the first author is the speaker.

This is gonna be fun.

Keynote presentations (35 minutes)

• Henry Adams, Johnathan Bush and Joshua Mirth, Operations on metric thickenings.

• Nicolas Blanco and Noam Zeilberger: Bifibrations of polycategories and classical linear logic.

• Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Román: Profunctor optics, a categorical update.

• Tobias Fritz, Tomáš Gonda, Paolo Perrone and Eigil Rischel: Distribution functors, second-order stochastic dominance and the Blackwell–Sherman–Stein Theorem in categorical probability.

• Micah Halter, Evan Patterson, Andrew Baas and James Fairbanks: Compositional scientific computing with Catlab and SemanticModels.

• Joachim Kock: Whole-grain Petri nets and processes.

• Andre Kornell, Bert Lindenhovius and Michael Mislove: Quantum CPOs.

• Martha Lewis: Towards logical negation in compositional distributional semantics.

• Jade Master and John Baez: Open Petri nets.

• Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni and Gijs Wijnholds, Categorical vector space semantics for Lambek calculus with a relevant modality.

• David Jaz Myers: Double categories of open dynamical systems.

• Toby St Clere Smithe, Cyber Kittens, or first steps towards categorical cybernetics.

Regular presentations (20 minutes)

• Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jeremy Ledent and Fredrik Nordvall Forsberg: Compositional game theory, compositionally.

• John Baez and Kenny Courser: Coarse-graining open Markov processes.

• Georgios Bakirtzis, Christina Vasilakopoulou and Cody Fleming, Compositional cyber-physical systems modeling.

• Marco Benini, Marco Perin, Alexander Alexander Schenkel and Lukas Woike: Categorification of algebraic quantum field theories.

• Daniel Cicala: Rewriting structured cospans.

• Bryce Clarke: A diagrammatic approach to symmetric lenses.

• Bob Coecke, Giovanni de Felice, Konstantinos Meichanetzidis, Alexis Toumi, Stefano Gogioso and Nicolo Chiappori: Quantum natural language processing.

• Geoffrey Cruttwell, Jonathan Gallagher and Dorette Pronk: Categorical semantics of a simple differential programming language.

• Swaraj Dash and Sam Staton: A monad for probabilistic point processes.

• Giovanni de Felice, Elena Di Lavore, Mario Román and Alexis Toumi: Functorial language games for question answering.

• Giovanni de Felice, Alexis Toumi and Bob Coecke: DisCoPy: monoidal categories in Python.

• Brendan Fong, David Jaz Myers and David I. Spivak: Behavioral mereology: a modal logic for passing constraints.

• Rocco Gangle, Gianluca Caterina and Fernando Tohme, A generic figures reconstruction of Peirce’s existential graphs (alpha).

• Jules Hedges and Philipp Zahn: Open games in practice.

• Jules Hedges: Non-compositionality in categorical systems theory.

• Michael Johnson and Robert Rosebrugh, The more legs the merrier: A new composition for symmetric (multi-)lenses.

• Joe Moeller, John Baez and John Foley: Petri nets with catalysts.

• John Nolan and Spencer Breiner, Symmetric monoidal categories with attributes.

• Joseph Razavi and Andrea Schalk: Gandy machines made easy via category theory.

• Callum Reader: Measures and enriched categories.

• Mario Román: Open diagrams via coend calculus.

• Luigi Santocanale, Dualizing sup-preserving endomaps of a complete lattice.

• Dan Shiebler: Categorical stochastic processes and likelihood.

• Richard Statman, Products in a category with only one object.

• David I. Spivak: Poly: An abundant categorical setting for mode-dependent dynamics.

• Christine Tasson and Martin Hyland, The linear-non-linear substitution 2-monad.

• Tarmo Uustalu, Niccolò Veltri and Noam Zeilberger: Proof theory of partially normal skew monoidal categories.

• Dmitry Vagner, David I. Spivak and Evan Patterson: Wiring diagrams as normal forms for computing in symmetric monoidal categories.

• Matthew Wilson, James Hefford, Guillaume Boisseau and Vincent Wang: The safari of update structures: visiting the lens and quantum enclosures.

• Paul Wilson and Fabio Zanasi: Reverse derivative ascent: a categorical approach to learning Boolean circuits.

• Vladimir Zamdzhiev: Computational adequacy for substructural lambda calculi.

• Gioele Zardini, David I. Spivak, Andrea Censi and Emilio Frazzoli: A compositional sheaf-theoretic framework for event-based systems.

It was a very low-research day! But I did get in an hour with Bedell (Flatiron), discussing our plan to automate some aspects of exoplanet detection and discovery. The idea is: If we can operationalize and automate discovery, we can use that to perform experimental design on surveys. Surveys that we want to optimize for exoplanet yield. We discussed frequentist vs Bayesian approaches.

Any group acts as automorphisms of itself, by conjugation. If we differentiate this idea, we get that any Lie algebra acts as derivations of itself. We can then enhance this in various ways: for example a Poisson algebra is both a Lie algebra and a commutative algebra, such that any element acts as derivations of both these structures.

Why do I care?

In my paper on Noether’s theorem I got excited by how physics uses structures where each element acts to generate a one-parameter group of automorphisms of that structure. I proved a super-general version of Noether’s theorem based on this idea. It’s Theorem 8, in case you’re curious.

But the purest expression of the idea of a “structure where each element acts as an automorphism of that structure” is the concept of “rack”.

Even simpler than a rack is a “shelf”.

Alissa Crans defined a shelf to be a set $S$ equipped with a binary operation $\triangleright \colon S \times S \to S$ such that each element $a \in S$ gives a map $a \triangleright - \colon S \to S$ that is a shelf endomorphism.

If you don’t like the circularity of this definition (which is the whole point), what I’m saying is that a shelf is a set $S$ equipped with a binary operation $\triangleright \colon S \times S \to S$ such that

$a \triangleright (b \triangleright c) = (a \triangleright b) \triangleright (a \triangleright c)$

This is called the self-distributive law, since it says the operation $\triangleright$ distributes over itshelf. (Sorry: “itself”.)

Actually this is a left shelf; there is also a thing called a “right shelf”. Any group is both a left shelf and a right shelf in a natural way, via conjugation.

We can similarly define a rack to be a set $S$ equipped with a binary operation $\triangleright \colon S \times S \to S$ such that each element $a \in S$ gives a map $a \triangleright - \colon S \to S$ that is a rack automorphism.

In other words, a rack is a shelf $S$ where each map $a \triangleright - \colon S \to S$ is invertible.

It’s common to write the inverse of the map $a \triangleright -$ as $- \triangleleft a$. Then we can give a completely equational definition of a rack! It’s a set $S$ with two binary operations $\triangleright, \triangleleft \colon S \times S \to S$ obeying these identities:

$(c \triangleright b) \triangleright a = (c \triangleright a) \triangleright (b \triangleright a), \qquad a \triangleleft(b \triangleleft c) = (a \triangleleft b) \triangleleft(a \triangleleft c)$

$(a \triangleleft b) \triangleright a = b , \qquad a \triangleleft(b \triangleright a) = b$

These axioms are slightly redundant, but nicely symmetrical.

If we have a shelf that’s a smooth manifold, and the operation $\triangleright$ is smooth, and an element $e \in S$ obeying $e \triangleright a = a$ for all $a \in S$, then I think we can differentiate the shelf operation at $e$ and get a “Leibniz algebra”.

A Leibniz algebra is a vector space $L$ with a bilinear operation $[-,-] \colon L \times L \to L$ such that each element $a \in L$ gives a map $[a,-] \colon L \to L$ that is a Leibniz algebra derivation. In other words, the Jacobi identity holds:

$[a, [b,c]] = [[a,b], c] + [b, [a,c]]$

Again, this is really a left Leibniz algebra, and we could also consider “right” Leibniz algebras. Any Lie algebra is naturally both a left and a right Leibniz algebra.

I’ve been trying to understand Jordan algebras, and here’s one thing that intrigues me: in a Jordan algebra $A$, any pair of elements $a,b \in A$ acts to give a derivation of the Jordan algebra, say $D_{a,b} \colon A \to A$, as follows:

$D_{a,b} (c) = a \circ (b \circ c) - b \circ (a \circ c)$

If $L_a$ means left multiplication by $a$, this says $D_{a,b} = L_a L_b - L_b L_a$.

This property of Jordan algebras seems nicer to me than the actual definition of Jordan algebra! So we could imagine turning it into a definition. Say a pre-Jordan algebra is a vector space $A$ equipped with a bilinear map $\circ : A \times A \to A$ such that for any $a,b \in A$, the map $D_{a,b} \colon A \to A$ defined above is a derivation, meaning

$D_{a,b}(c \circ d) = D_{a,b} (c) \circ d + c \circ D_{a,b}(d)$

for all $c, d \in A$.

Puzzle. Are there pre-Jordan algebras that aren’t Jordan algebras? Are any of them interesting?

Most of us have been staying holed up at home lately. I spent the last month holed up writing a paper that expands on my talk at a conference honoring the centennial of Noether’s 1918 paper on symmetries and conservation laws. This made my confinement a lot more bearable. It was good getting back to this sort of mathematical physics after a long time spent on applied category theory. It turns out I really missed it.

While everyone at the conference kept emphasizing that Noether’s 1918 paper had two big theorems in it, my paper is just about the easy one—the one physicists call Noether’s theorem:

People often summarize this theorem by saying “symmetries give conservation laws”. And that’s right, but it’s only true under some assumptions: for example, that the equations of motion come from a Lagrangian.

This leads to some interesting questions. For which types of physical theories do symmetries give conservation laws? What are we assuming about the world, if we assume it is described by a theories of this type? It’s hard to get to the bottom of these questions, but it’s worth trying.

We can prove versions of Noether’s theorem relating symmetries to conserved quantities in many frameworks. While a differential geometric framework is truer to Noether’s original vision, my paper studies the theorem algebraically, without mentioning Lagrangians.

Now, Atiyah said:

…algebra is to the geometer what you might call the Faustian offer. As you know, Faust in Goethe’s story was offered whatever he wanted (in his case the love of a beautiful woman), by the devil, in return for selling his soul. Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.

While this is sometimes true, algebra is more than a computational tool: it allows us to express concepts in a very clear and distilled way. Furthermore, the geometrical framework developed for classical mechanics is not sufficient for quantum mechanics. An algebraic approach emphasizes the similarity between classical and quantum mechanics, clarifying their differences.

In talking about Noether’s theorem I keep using an interlocking trio of important concepts used to describe physical systems: ‘states’, ‘observables’ and `generators’. A physical system has a convex set of states, where convex linear combinations let us describe probabilistic mixtures of states. An observable is a real-valued quantity whose value depends—perhaps with some randomness—on the state. More precisely: an observable maps each state to a probability measure on the real line. A generator, on the other hand, is something that gives rise to a one-parameter group of transformations of the set of states—or dually, of the set of observables.

It’s easy to mix up observables and generators, but I want to distinguish them. When we say ‘the energy of the system is 7 joules’, we are treating energy as an observable: something you can measure. When we say ‘the Hamiltonian generates time translations’, we are treating the Hamiltonian as a generator.

In both classical mechanics and ordinary complex quantum mechanics we usually say the Hamiltonian is the energy, because we have a way to identify them. But observables and generators play distinct roles—and in some theories, such as real or quaternionic quantum mechanics, they are truly different. In all the theories I consider in my paper the set of observables is a Jordan algebra, while the set of generators is a Lie algebra. (Don’t worry, I explain what those are.)

When we can identify observables with generators, we can state Noether’s theorem as the following equivalence:

$The \; generator \; a \; generates \; transformations \; that \; leave \; the
observable \; b \; fixed\!.$

$\Updownarrow$

$The \; generator \; b \; generates \; transformations \; that \; leave \; the \; observable \; a \; fixed\!.$

In this beautifully symmetrical statement, we switch from thinking of $a$ as the generator and $b$ as the observable in the first part to thinking of $b$ as the generator and $a$ as the observable in the second part. Of course, this statement is true only under some conditions, and the goal of my paper is to better understand these conditions. But the most fundamental condition, I claim, is the ability to identify
observables with generators.

In classical mechanics we treat observables as being the same as generators, by treating them as elements of a Poisson algebra, which is both a Jordan algebra and a Lie algebra. In quantum mechanics observables are not quite the same as generators. They are both elements of something called a ∗-algebra. Observables are self-adjoint, obeying

$a^* = a$

while generators are skew-adjoint, obeying

$a^* = -a$

The self-adjoint elements form a Jordan algebra, while the skew-adjoint elements form a Lie algebra.

In ordinary complex quantum mechanics we use a complex ∗-algebra. This lets us turn any self-adjoint element into a skew-adjoint one by multiplying it by $\sqrt{-1}$. Thus, the complex numbers let us identify observables with generators! In real and quaternionic quantum mechanics this identification is impossible, so the appearance of complex numbers in quantum mechanics is closely connected to Noether’s theorem.

In short, classical mechanics and ordinary complex quantum mechanics fit together in this sort of picture:

To dig deeper, it’s good to examine generators on their own: that is, Lie algebras. Lie algebras arise very naturally from the concept of ‘symmetry’. Any Lie group gives rise to a Lie algebra, and any element of this Lie algebra then generates a one-parameter family of transformations of that very same Lie algebra. This lets us state a version of Noether’s theorem solely in terms of generators:

$The \; generator \; a \; generates \; transformations \; that \; leave \; the \; generator \; b fixed\!.$

$\Updownarrow$

$The \; generator \; b \; generates \; transformations \; that \; leave \; the \; generator \; a \; fixed\!.$

And when we translate these statements into equations, their equivalence follows directly from this elementary property of the Lie bracket:

$[a,b] = 0$

$\Updownarrow$

$[b,a] = 0$

Thus, Noether’s theorem is almost automatic if we forget about observables and work solely with generators. The only questions left are: why should symmetries be described by Lie groups, and what is the meaning of this property of the Lie bracket?

In my paper I tackle both these questions, and point out that the Lie algebra formulation of Noether’s theorem comes from a more primitive group formulation, which says that whenever you have two group elements $g$ and $h$,

$g \; commutes \; with h\!.$

$\Updownarrow$

$h \; commutes \; with \; g\!.$

That is: whenever you’ve got two ways of transforming a physical system, the first transformation is ‘conserved’ by second if and only if the second is conserved by the first!

However, observables are crucial in physics. Working solely with generators in order to make Noether’s theorem a tautology would be another sort of Faustian bargain. So, to really get to the bottom of Noether’s theorem, we need to understand the map from observables to generators. In ordinary quantum mechanics this comes from multiplication by $i$. But this just pushes the mystery back a notch: why should we be using the complex numbers in quantum mechanics?

For this it’s good to spend some time examining observables on their own: that is, Jordan algebras. Those of greatest importance in physics are the unital JB-algebras, which are unfortunately named not after me, but Jordan and Banach. These allow a unified approach to real, complex and quaternionic quantum mechanics, along with some more exotic theories. So, they let us study how the role of complex numbers in quantum mechanics is connected to Noether’s theorem.

Any unital JB-algebra $O$ has a partial ordering: that is, we can talk about one observable being greater than or equal to another. With the help of this we can define states on $O,$ and prove that any observable maps each state to a probability measure on the real line.

More surprisingly, any JB-algebra also gives rise to two Lie algebras. The smaller of these, say $L,$ has elements that generate transformations of $O$ that preserve all the structure of this unital JB-algebra. They also act on the set of states. Thus, elements of $L$ truly deserve to be considered ‘generators’.

In a unital JB-algebra there is not always a way to reinterpret observables as generators. However, Alfsen and Shultz have defined the notion of a ‘dynamical correspondence’ for such an algebra, which is a well-behaved map

$\psi \colon O \to L$

One of the two conditions they impose on this map implies a version of Noether’s theorem. They prove that any JB-algebra with a dynamical correspondence gives a complex ∗-algebra where the observables are self-adjoint elements, the generators are skew-adjoint, and we can convert observables into generators by multiplying them by $i$.

This result is important, because the definition of JB-algebra does not involve the complex numbers, nor does the concept of dynamical correspondence. Rather, the role of the complex numbers in quantum mechanics emerges from a map from observables to generators that obeys conditions including Noether’s theorem!

To be a bit more precise, Alfsen and Shultz’s first condition on the map $\psi \colon O \to L$ says that every observable $a \in O$ generates transformations that leave $a$ itself fixed. I call this the self-conservation principle. It implies Noether’s theorem.

However, in their definition of dynamical correspondence, Alfsen and Shultz also impose a second, more mysterious condition on the map $\psi$. I claim that that this condition is best understood in terms of the larger Lie algebra associated to a unital JB-algebra. As a vector space this is the direct sum

$A = O \oplus L$

but it’s equipped with a Lie bracket such that

$[-,-] \colon L \times L \to L \qquad [-,-] \colon L \times O \to O$

$[-,-] \colon O \times L \to O \qquad [-,-] \colon O \times O \to L$

As I mentioned, elements of $L$ generate transformations of $O$ that preserve all the structure on this unital JB-algebra. Elements of $O$ also generate transformations of $O,$ but these only preserve its vector space structure and partial ordering.

What’s the meaning of these other transformations? I claim they’re connected to statistical mechanics.

For example, consider ordinary quantum mechanics and let $O$ be the unital JB-algebra of all bounded self-adjoint operators on a complex Hilbert space. Then $L$ is the Lie algebra of all bounded skew-adjoint operators on this Hilbert space. There is a dynamical correpondence sending any observable $H \in O$ to the generator $\psi(H) = i H \in L,$ which then generates a one-parameter group of transformations of $O$ like this:

$a \mapsto e^{i t H/\hbar} \, a \, e^{-i t H/\hbar} \qquad \forall t \in \mathbb{R}, a \in O$

where $\hbar$ is Planck’s constant. If $H$ is the Hamiltonian of some system, this is the usual formula for time evolution of observables in the Heisenberg picture. But $H$ also generates a one-parameter group of transformations of $O$ as follows:

$a \mapsto e^{-\beta H/2} \, a \, e^{-\beta H/2} \qquad \forall \beta \in \mathbb{R}, a \in O$

Writing $\beta = 1/k T$ where $T$ is temperature and $k$ is Boltzmann’s constant, I claim that these are ‘thermal transformations’. Acting on a state in thermal equilibrium at some temperature, these transformations produce states in thermal equilibrium at other temperatures (up to normalization).

The analogy between $i t/\hbar$ and $1/k T$ is often summarized by saying “inverse temperature is imaginary time”. The second condition in Alfsen and Shultz’s definition of dynamical correspondence is a way of capturing this principle in a way that does not explicitly mention the complex numbers. Thus, we may very roughly say their result explains the role of complex numbers in quantum mechanics starting from three assumptions:

observables form Jordan algebra of a nice sort (a unital JB-algebra)

the self-conservation principle (and thus Noether’s theorem)

the relation between time and inverse temperature.

I still want to understand all of this more deeply, but the way statistical mechanics entered the game was surprising to me, so I feel I made a little progress.

I hope the paper is half as fun to read as it was to write! There’s a lot more in it than described here.

There is great anxiety and frustration over the latest pronouncement from DHS/ICE about international students in the US. Let me give a little context. For many years there has been a rule that international students studying in the US can take no more than 3 credits (or equivalent) per semester of purely online instruction. The point of that was to prevent many people from applying for F visas and then "studying" at online-only diploma mills while actually working. That is, it was originally a policy meant to encourage that student visas go to legitimate international students and scholars pursuing degrees at accredited universities. In the spring when the pandemic hit and many universities transitioned to online instruction in the middle of the semester, DHS granted a waiver on this requirement. Well, now they are trying to rescind that, and are doing so in a particularly draconian way: As written, if a university goes online-only, either from the start of the semester or even partway through due to public health concerns, the international students would face having to leave the US on short notice. This is a terrible, stupid, short-sighted way to handle this situation, and it doesn't remotely serve the best interests of any constituency (student, university, or country). Unsurprisingly, many many organizations are pushing back against this. Hopefully there will be changes and/or workarounds.

On to science. Quanta has an article about the origins of the rigidity of glass. The discussion there is about whether there is a kind of hidden structural order in the glassy material. Fundamentally (as I've written previously), rigidity in any solid results from a combination of very slow timescales for atomic motion (due to lack of thermal energy available to overcome "barriers") and the Pauli principle giving a hard-core repulsion between atoms. Still, the question of the underlying nature of glassy systems remains fascinating.

The 2D materials experts at Columbia have shown clean fractional quantum Hall physics in a monolayer of WSe<sub>2</sub>. The actual paper is here. I have yet to come up with a really nice, generally accessible write-up of the FQH effect. The super short version: Confine charge carriers in strictly two dimensions, and throw in a large magnetic field perpendicular to the plane (such that the energy associated with cyclotron motion dominates the kinetic energy). At certain ratios of magnetic field to number of charge carriers, the charge carriers can condense into new collective states (generally distinguished by topology rather than broken symmetries like the liquid-gas or nonmagnetic/ferromagnetic phase transitions). The fractional quantum Hall states can have all sorts of unusual properties, but the key point here is that they are fragile. Too much disorder (like missing atoms or charged impurities), and the energy associated with that disorder can swamp out the energy savings of condensing into such a state. It's remarkable that the material quality of the monolayer transition metal dichalcogenide (and its encapsulating boron nitride surroundings) is so high. Seeing how FQH states evolve in this example new material system with rich band structure should be interesting.

I feel bad for only now learning about this great series of talks about the state of the art in spintronics, trying to understand, engineer, and control the motion of spin.

For your animal video needs, get the behind-the-scenes story about Olive and Mabel here.

Abstract. We illustrate some new paradigms in applied category theory with the example of coarse-graining open Markov processes. Coarse-graining is a standard method of extracting a simpler Markov process from a more complicated one by identifying states. Here we extend coarse-graining to ‘open’ Markov processes: that is, those where probability can flow in or out of certain states called ‘inputs’ and ‘outputs’. One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side. These constructions make open Markov processes into the morphisms of a symmetric monoidal category. But we can go further and construct a symmetric monoidal double category where the 2-morphisms include ways of coarse-graining open Markov processes. We can describe the behavior of open Markov processes using double functors out of this double category.

I'm writing a paper on uncertainty estimation—how you put an error bar on your measurement—and at the same time, Kate Storey-Fisher (NYU) and I are working on a new method for estimating the correlation function (of galaxies, say) that improves the precision (the error bar) on measurements.

In the latter project (large-scale structure), we are encountering some interesting conceptual things. For instance, if you make many independent measurements of something (a vector of quantities say) and you want to plot your mean measurement and an uncertainty, what do you plot? Standard practice is to use the square root of the diagonal entries of the covariance matrix. But you could instead plot the inverse square roots of the diagonal entries of the inverse covariance matrix. These two quantities are (in general) very different! Indeed we are taught that the former is conservative and the latter is not, but it really depends what you are trying to show, and what you are trying to learn. The standard practice tells you how well you know the correlation function in one bin, marginalizing out (or profiling) any inferences you have about other bins.

In the end, we don't care about what we measure at any particular radius in the correlation function, we care about the cosmological parameters we constrain! So Storey-Fisher and I discussed today how we might propagate our uncertainties to there, and compare methods there. I hope we find that our method does far better than the standard methods in that context!

Apologies for this rambling, inside-baseball post, but this is my research blog, and it isn't particularly intended to be fun, useful, or artistic!

If there were ever a time for liberals and progressives to put aside their internal squabbles, you’d think it was now. The President of the United States is a racist gangster, who might not leave if he loses the coming election—all the more reason to ensure he loses in a landslide. Due in part to that gangster’s breathtaking incompetence, 130,000 Americans are now dead, and the economy tanked, from a pandemic that the rest of the world has under much better control. The gangster’s latest “response” to the pandemic has been to disrupt the lives of thousands of foreign scientists—including several of my students—by threatening to cancel their visas. (American universities will, of course, do whatever they legally can to work around this act of pure spite.)

So how is the left responding to this historic moment?

This weekend, 536 people did so by … trying to cancel Steven Pinker, stripping him of “distinguished fellow” and “media expert” status (whatever those are) in the Linguistics Society of America for ideological reasons.

Yes, Steven Pinker: the celebrated linguist and cognitive scientist, author of The Language Instinct and How the Mind Works (which had a massive impact on me as a teenager) and many other books, and academic torch-bearer for the Enlightenment in our time. For years, I’d dreaded the day they’d finally come for Steve, even while friends assured me my fears must be inflated since, after all, they hadn’t come for him yet.

I concede that the cancelers’ logic is impeccable. If they can get Pinker, everyone will quickly realize that there’s no longer any limit to who they can get—including me, including any writer or scientist who crosses them. If you’ve ever taken, or aspire to take, any public stand riskier than “waffles are tasty,” then don’t delude yourself that you’ll be magically spared—certainly not by your own progressive credentials.

I don’t know if the “charges” against Pinker merit a considered response (Pinker writes that some people wondered if they were satire). For those who care, though, here’s a detailed and excellent takedown by the biologist and blogger Jerry Coyne, and here’s another by Barbara Partee.

So, it seems Pinker once used the term “urban crime,” which can be a racist dogwhistle—except that in this case, it literally meant “urban crime.” Pinker once referred to Bernie Goetz, whose 1984 shooting of four robbers in the NYC subway polarized the US at the time, as a “mild-mannered engineer,” in a sentence whose purpose was to contrast that description with the ferocity of Goetz’s act. Pinker “appropriated” the work of a Black scholar, Harvard Dean Lawrence Bobo, which apparently meant approvingly citing him in a tweet. Etc. Ironically, it occurred to me that the would-be Red Guards could’ve built a much stronger case against Pinker had they seriously engaged with his decades of writing—writing that really does take direct aim at their whole worldview, they aren’t wrong about that—rather than superficially collecting a few tweets.

What Coyne calls the “Purity Posse” sleazily gaslights its readers as follows:

We want to note here that we have no desire to judge Dr. Pinker’s actions in moral terms, or claim to know what his aims are. Nor do we seek to “cancel” Dr. Pinker, or to bar him from participating in the linguistics and LSA communities (though many of our signatories may well believe that doing so would be the right course of action).

In other words: many of us “may well believe” that Pinker’s scientific career should be ended entirely. But magnanimously, for now, we’ll settle for a display of our power that leaves the condemned heretic still kicking. So don’t accuse us of wanting to “cancel” anyone!

In that same generous spirit:

Though no doubt related, we set aside questions of Dr. Pinker’s tendency to move in the proximity of what The Guardian called a revival of “scientific racism”, his public support for David Brooks (who has been argued to be a proponent of “gender essentialism”), his expert testimonial in favor of Jeffrey Epstein (which Dr. Pinker now regrets), or his dubious past stances on rape and feminism.

See, even while we make these charges, we disclaim all moral responsibility for making them. (For the record, Alan Dershowitz asked Pinker for a linguist’s opinion of a statute, so Pinker provided it; Pinker didn’t know at the time that the request had anything to do with Epstein.)

Again and again, spineless institutions have responded to these sorts of ultimatums by capitulating to them. So I confess that the news about Pinker depressed me all weekend. The more time passed, though, the more it looked like the Purity Posse might have actually overplayed its hand this time. Steven Pinker is not weak prey.

Let’s start with what’s missing from the petition: Noam Chomsky pointedly refused to sign. How that must’ve stung his comrades! For that matter, virtually all of the world’s well-known linguists refused to sign. Ray Jackendoff and Michel DeGraff were originally on the petition, but their names turned out to have been forged (were others?).

But despite the flimsiness of the petition, suppose the Linguistics Society of America caved. OK, I mused, how many people have even heard of the Linguistics Society of America, compared to the number who’ve heard of Pinker or read his books? If the LSA expelled Pinker, wouldn’t they be forever known to the world only as the organization that had done that?

I’m tired of the believers in the Enlightenment being constantly on the defensive. “No, I’m not a racist or a misogynist … on the contrary, I’ve spent decades advocating for … yes, I did say that, but you completely misunderstood my meaning, which in context was … please, I’m begging you, can’t we sit and discuss this like human beings?”

It’s time for more of us to stand up and say: yes, I am a center-left extremist. Yes, I’m an Enlightenment fanatic, a radical for liberal moderation and reason. If liberalism is the vanilla of worldviews, then I aspire to be the most intense vanilla anyone has ever tasted. I’m not a closeted fascist. I’m not a watered-down leftist. I’m something else. I consider myself ferociously anti-racist and anti-sexist and anti-homophobic and pro-downtrodden, but I don’t cede to any ideological faction the right to dictate what those terms mean. The world is too complicated, too full of ironies and surprises, for me to outsource my conscience in that way.

Enlightenment liberalism at least has the virtue that it’s not some utopian dream: on the contrary, it’s already led to most of the peace and prosperity that this sorry world has ever known, wherever and whenever it’s been allowed to operate. And while “the death of the Enlightenment” gets proclaimed every other day, liberal ideals have by now endured for centuries. They’ve outlasted kings and dictators, the Holocaust and the gulag. They certainly have it within them to outlast some online sneerers.

Yes, sometimes martyrdom (or at least career martyrdom) is the only honorable course, and yes, the childhood bullies did gift me with a sizeable persecution complex—I’ll grant the sneerers that. But on reflection, no, I don’t want to be a martyr for Enlightenment values. I want Enlightenment values to win, and not by vanquishing their opponents but by persuading them. As Pinker writes:

A final comment: I feel sorry for the signatories. Moralistic dudgeon is a shallow and corrosive indulgence, & policing the norms of your peer group a stunting of the intellect. Learning new ideas & rethinking conventional wisdom are deeper pleasures … and ultimately better for the world. Our natural state is ignorance, fallibility, & self-deception. Progress comes only from broaching & evaluating ideas, including those that feel unfamiliar and uncomfortable.

Spend a lot of time on Twitter and Reddit and news sites, and it feels like the believers in the above sentiment are wildly outnumbered by the self-certain ideologues of all sides. But just like the vanilla in a cake can be hard to taste, so there are more Enlightenment liberals than it seems, even in academia—especially if we include all those who never explicitly identified that way, because they were too busy building or fixing or discovering or teaching, and because they mistakenly imagined that if they just left the Purity Posse alone then the Posse would do likewise. If that’s you, then please ask yourself now: what is my personal break-point for speaking up?

Gravity! This one’s sure to be a crowd-pleaser. We take advantage of some of our previous discussion of curvature and spacetime, but we also talk about Einstein’s physical motivations for inventing general relativity, and the origin of gravitational time dilation and the like.

Most of us have been staying holed up at home lately. I spent the last month holed up writing a paper that expands on my talk at a conference honoring the centennial of Noether’s 1918 paper on symmetries and conservation laws. This made my confinement a lot more bearable. It was good getting back to this sort of mathematical physics after a long time spent on applied category theory. It turns out I really missed it.

While everyone at the conference kept emphasizing that Noether’s 1918 paper had two big theorems in it, my paper is just about the easy one—the one physicists call Noether’s theorem:

People often summarize this theorem by saying “symmetries give conservation laws”. And that’s right, but it’s only true under some assumptions: for example, that the equations of motion come from a Lagrangian.

This leads to some interesting questions. For which types of physical theories do symmetries give conservation laws? What are we assuming about the world, if we assume it is described by a theories of this type? It’s hard to get to the bottom of these questions, but it’s worth trying.

We can prove versions of Noether’s theorem relating symmetries to conserved quantities in many frameworks. While a differential geometric framework is truer to Noether’s original vision, my paper studies the theorem algebraically, without mentioning Lagrangians.

Now, Atiyah said:

…algebra is to the geometer what you might call the Faustian offer. As you know, Faust in Goethe’s story was offered whatever he wanted (in his case the love of a beautiful woman), by the devil, in return for selling his soul. Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.

While this is sometimes true, algebra is more than a computational tool: it allows us to express concepts in a very clear and distilled way. Furthermore, the geometrical framework developed for classical mechanics is not sufficient for quantum mechanics. An algebraic approach emphasizes the similarity between classical and quantum mechanics, clarifying their differences.

In talking about Noether’s theorem I keep using an interlocking trio of important concepts used to describe physical systems: ‘states’, ‘observables’ and `generators’. A physical system has a convex set of states, where convex linear combinations let us describe probabilistic mixtures of states. An observable is a real-valued quantity whose value depends—perhaps with some randomness—on the state. More precisely: an observable maps each state to a probability measure on the real line. A generator, on the other hand, is something that gives rise to a one-parameter group of transformations of the set of states—or dually, of the set of observables.

It’s easy to mix up observables and generators, but I want to distinguish them. When we say ‘the energy of the system is 7 joules’, we are treating energy as an observable: something you can measure. When we say ‘the Hamiltonian generates time translations’, we are treating the Hamiltonian as a generator.

In both classical mechanics and ordinary complex quantum mechanics we usually say the Hamiltonian is the energy, because we have a way to identify them. But observables and generators play distinct roles—and in some theories, such as real or quaternionic quantum mechanics, they are truly different. In all the theories I consider in my paper the set of observables is a Jordan algebra, while the set of generators is a Lie algebra. (Don’t worry, I explain what those are.)

When we can identify observables with generators, we can state Noether’s theorem as the following equivalence:

The generator a generates transformations that leave the
observable b fixed.

The generator b generates transformations that leave the observable a fixed.

In this beautifully symmetrical statement, we switch from thinking of a as the generator and b as the observable in the first part to thinking of b as the generator and a as the observable in the second part. Of course, this statement is true only under some conditions, and the goal of my paper is to better understand these conditions. But the most fundamental condition, I claim, is the ability to identify observables with generators.

In classical mechanics we treat observables as being the same as generators, by treating them as elements of a Poisson algebra, which is both a Jordan algebra and a Lie algebra. In quantum mechanics observables are not quite the same as generators. They are both elements of something called a ∗-algebra. Observables are self-adjoint, obeying

while generators are skew-adjoint, obeying

The self-adjoint elements form a Jordan algebra, while the skew-adjoint elements form a Lie algebra.

In ordinary complex quantum mechanics we use a complex ∗-algebra. This lets us turn any self-adjoint element into a skew-adjoint one by multiplying it by . Thus, the complex numbers let us identify observables with generators! In real and quaternionic quantum mechanics this identification is impossible, so the appearance of complex numbers in quantum mechanics is closely connected to Noether’s theorem.

In short, classical mechanics and ordinary complex quantum mechanics fit together in this sort of picture:

To dig deeper, it’s good to examine generators on their own: that is, Lie algebras. Lie algebras arise very naturally from the concept of ‘symmetry’. Any Lie group gives rise to a Lie algebra, and any element of this Lie algebra then generates a one-parameter family of transformations of that very same Lie algebra. This lets us state a version of Noether’s theorem solely in terms of generators:

The generator a generates transformations that leave the generator b fixed.

The generator b generates transformations that leave the generator a fixed.

And when we translate these statements into equations, their equivalence follows directly from this elementary property of the Lie bracket:

[a,b] = 0

[b,a] = 0

Thus, Noether’s theorem is almost automatic if we forget about observables and work solely with generators. The only questions left are: why should symmetries be described by Lie groups, and what is the meaning of this property of the Lie bracket?

In my paper I tackle both these questions, and point out that the Lie algebra formulation of Noether’s theorem comes from a more primitive group formulation, which says that whenever you have two group elements g and h,

g commutes with h.

h commutes with g.

That is: whenever you’ve got two ways of transforming a physical system, the first transformation is ‘conserved’ by second if and only if the second is conserved by the first!

However, observables are crucial in physics. Working solely with generators in order to make Noether’s theorem a tautology would be another sort of Faustian bargain. So, to really get to the bottom of Noether’s theorem, we need to understand the map from observables to generators. In ordinary quantum mechanics this comes from multiplication by . But this just pushes the mystery back a notch: why should we be using the complex numbers in quantum mechanics?

For this it’s good to spend some time examining observables on their own: that is, Jordan algebras. Those of greatest importance in physics are the unital JB-algebras, which are unfortunately named not after me, but Jordan and Banach. These allow a unified approach to real, complex and quaternionic quantum mechanics, along with some more exotic theories. So, they let us study how the role of complex numbers in quantum mechanics is connected to Noether’s theorem.

Any unital JB-algebra has a partial ordering: that is, we can talk about one observable being greater than or equal to another. With the help of this we can define states on and prove that any observable maps each state to a probability measure on the real line.

More surprisingly, any JB-algebra also gives rise to two Lie algebras. The smaller of these, say has elements that generate transformations of that preserve all the structure of this unital JB-algebra. They also act on the set of states. Thus, elements of truly deserve to be considered ‘generators’.

In a unital JB-algebra there is not always a way to reinterpret observables as generators. However, Alfsen and Shultz have defined the notion of a ‘dynamical correspondence’ for such an algebra, which is a well-behaved map

One of the two conditions they impose on this map implies a version of Noether’s theorem. They prove that any JB-algebra with a dynamical correspondence gives a complex ∗-algebra where the observables are self-adjoint elements, the generators are skew-adjoint, and we can convert observables into generators by multiplying them by

This result is important, because the definition of JB-algebra does not involve the complex numbers, nor does the concept of dynamical correspondence. Rather, the role of the complex numbers in quantum mechanics emerges from a map from observables to generators that obeys conditions including Noether’s theorem!

To be a bit more precise, Alfsen and Shultz’s first condition on the map says that every observable generates transformations that leave a itself fixed. I call this the self-conservation principle. It implies Noether’s theorem.

However, in their definition of dynamical correspondence, Alfsen and Shultz also impose a second, more mysterious condition on the map I claim that that this condition is best understood in terms of the larger Lie algebra associated to a unital JB-algebra. As a vector space this is the direct sum

but it’s equipped with a Lie bracket such that

As I mentioned, elements of generate transformations of that preserve all the structure on this unital JB-algebra. Elements of also generate transformations of but these only preserve its vector space structure and partial ordering.

What’s the meaning of these other transformations? I claim they’re connected to statistical mechanics.

For example, consider ordinary quantum mechanics and let be the unital JB-algebra of all bounded self-adjoint operators on a complex Hilbert space. Then is the Lie algebra of all bounded skew-adjoint operators on this Hilbert space. There is a dynamical correpondence sending any observable to the generator which then generates a one-parameter group of transformations of like this:

where is Planck’s constant. If is the Hamiltonian of some system, this is the usual formula for time evolution of observables in the Heisenberg picture. But also generates a one-parameter group of transformations of as follows:

Writing where is temperature and is Boltzmann’s constant, I claim that these are ‘thermal transformations’. Acting on a state in thermal equilibrium at some temperature, these transformations produce states in thermal equilibrium at other temperatures (up to normalization).

The analogy between and is often summarized by saying “inverse temperature is imaginary time”. The second condition in Alfsen and Shultz’s definition of dynamical correspondence is a way of capturing this principle in a way that does not explicitly mention the complex numbers. Thus, we may very roughly say their result explains the role of complex numbers in quantum mechanics starting from three assumptions:

• observables form Jordan algebra of a nice sort (a unital JB-algebra)

• the self-conservation principle (and thus Noether’s theorem)

• the relation between time and inverse temperature.

I still want to understand all of this more deeply, but the way statistical mechanics entered the game was surprising to me, so I feel I made a little progress.

I hope the paper is half as fun to read as it was to write! There’s a lot more in it than described here.

A bunch of people have been sending me links to a particularly sloppy article that (mis)uses linear regression to draw an incorrect conclusion from some data. So I guess I’ve got to got back to good-old linear regression, and talk about it a bit.

Let’s start with the basics. What is linear regression?

If you have a collection of data – typically data with one independent variable, and one dependent variable (that is, the first variable can vary any way it wants; changing it will change the second variable), then you’re probably interested in how the dependent variable relates to the independent. If you have reason to believe that they should have a linear relationship, then you’d like to know just what that linear relationship is.

If your data were perfect, then you’d just need to plot all of the data points on a graph, with the independent variable on the X axis, and the dependent on the Y, and then your graph would be a line, and you could get its slope and Y intercept, and thus completely capture the relationship.

But data is never perfect. There’s a lot of reasons for that, but no real set of collected data is ever perfect. No matter how perfect the real underlying linear relationship is, real measured data will always show some scatter. And that means that you can draw a lot of possible lines through the collected data. Which one of them represents the best fit?

Since that’s pretty abstract, I’m going to talk a bit about an example – the very example that was used to ignite my interest in math!

Back in 1974 or so, when I was a little kid in second grade, my father was working for RCA, as a physicist involved in manufacturing electronics for satellite systems. One of the important requirements for the products they were manufacturing was that they be radiation hard – meaning that they could be exposed to quite a bit of radiation before they would be damaged enough to stop working.

Their customers – NASA, JPL, and various groups from the U. S. Military, had very strong requirements. They had to show, for a manufacturing setup of a particular component, what the failure profile was.

The primary failure mode of these chips they were making was circuit trace failure. If a sufficiently energetic gamma ray hit one of the circuit traces, it was possible that the trace would burn out – breaking the circuit, and causing the chip to fail.

The test setup that that they used had a gamma ray emitter. So they’d make a manufacturing run to produce a batch of chips from the setup. Then they’d take those, and they’d expose them to increasing doses of radiation from the gamma emitter, and detect when they failed.

For trace failure, the probability of failure is linear in the size of the radiation dose that the chip is exposed to. So to satisfy the customer, they had to show them what the slope of the failure curve was. “Radiation hard” was defined as being able to sustain exposure to some dose of radiation with a specified probability of failure.

So, my dad had done a batch of tests, and he had a ton of little paper slips that described the test results, and he needed to computer the slop of that line – which would give the probability of failure as a multiple of the radiation dose.

I walked into the dining room, where he was set up doing this, and asked what he was doing. So he explained it to me. A lot like I just explained above – except that my dad was a much better teacher than me. I couldn’t explain this to a second or third grader the way that he did!

Anyway… The method that we use to compute the best line is called least squares. The intuition behind it is that you’re trying to find the line where the average distance of all of the datapoints from that line is the smallest. But a simple average doesn’t work well – because some of the data points are above the line, and some are below. Just because one point is, say, above a possible fit by 100, and another is below by 100 doesn’t mean that the two should cancel. So you take the distance between the data points and the line, and you square them – making them all positive. Then you find the line where that total is the smallest – and that’s the best fit.

So let’s look at a real-ish example.

For example, here’s a graph that I generated semi-randomly of data points. The distribution of the points isn’t really what you’d get from real observations, but it’s good enough for demonstration.

The way that we do that is: first we compute the means of and , which we’ll call and . Then using those, we compute the slope as:

Then for the y intercept: .

In the case of this data: I set up the script so that the slope would be about 2.2 +/- 0.5. The slope in the figure is 2.54, and the y-intercept is 18.4.

Now, we want to check how good the linear relationship is. There’s several different ways of doing that. The simplest is called the correlation coefficient, or .

If you look at this, it’s really a check of how well the variation between the measured values and the expected values (according to the regression) match. On the top, you’ve got a set of products; on the bottom, you’ve got the square root of the same thing squared. The bottom is, essentially, just stripping the signs away. The end result is that if the correlation is perfect – that is, if the dependent variable increases linearly with the independent, then the correlation will be 1. If the dependency variable decreases linearly in opposition to the dependent, then the correlation will be -1. If there’s no relationship, then the correlation will be 0.

For this particular set of data, I generated it with a linear equation with a little bit of random noise. The correlation coefficient is slighly greater than 0.95, which is exctly what you’d expect.

Ok, so that’s the basics of linear regression. Let’s get back to the bozo-brained article that started this.

They featured this graph:

You can see the scatter-plot of the points, and you can see the line that was fit to the points by linear regression. How does that fit look to you? I don’t have access to the original dataset, so I can’t check it, but I’m guessing that the correlation there is somewhere around 0.1 or 0.2 – also known as “no correlation”.

You see, the author fell into one of the classic traps of linear regression. Look back at the top of this article, where I started explaining it. I said that if you had reason to believe in a linear relationship, then you could try to find it. That’s the huge catch to linear regression: no matter what data you put in, you’ll always get a “best match” line out. If the dependent and independent variables don’t have a linear relation – or don’t have any actual relation at all – then the “best match” fit that you get back as a result is garbage.

That’s what the graph above shows: you’ve got a collection of data points that to all appearances has no linear relationship – and probably no direct relationship at all. The author is interpreting the fact that linear regression gave him an answer with a positive slope as if that positive slope is meaningful. But it’s only meaningful if there’s actually a relationship present.

But when you look at the data, you don’t see a linear relationship. You see what looks like a pretty random scatterplot. Without knowing the correlation coefficient, we don’t know for sure, but that line doesn’t look to me like a particularly good fit. And since the author doesn’t give us any evidence beyond the existence of that line to believe in the relationship that they’re arguing for, we really have no reason to believe them. All they’ve done is demonstrate that they don’t understand the math that they’re using.

This year's big annual flagship conference in String theory, Strings 2020, ended two days ago. It was a massive success, and it was held entirely online. There were more than 2000 registered participants from all around the world, with sessions where a large portion of that number were engaged simultaneously! This conference's attendance more usually ranges at around 300 - 400, as far as I remember, so this was a spectacular change. The success was made possible by -most importantly- the willingness of many people to take part and engage with each other to a degree that was foreign to most participants, combined with smart and tireless effort by the team of organizers in Cape Town, where the conference was originally going to be held physically. There were excellent talks (selected by the programme committee) and many illuminating discussions.

Due to the pandemic, the conference was originally going to be cancelled (or at least postponed to much later in the year), but organizer Jeff Murugan announced at relatively short notice that they were instead going to attempt to do it online on the original dates, and it is wonderful that so many people around the world engaged, instead of just shrinking away into the Covid-19 gloom.

The other major component of the success is what I want to discuss here. It was the use, sometimes in concert, of tools such as Zoom [...] Click to continue reading this post →

Finally a reward for the hard work we did in the last few videos! (Not that hard work isn’t its own reward.) This week we talk about Gauge Theory, explaining how the forces of nature arise because of local symmetries in quantum fields.

And here is the Q&A video, where we go into more specifics about the Higgs mechanism, how it gives mass to particles, and how that plays out in the Standard Model of particle physics.

Our own John Baez is famous
for inspiring people all around the world through the magic of the
internet, but what’s it like to actually be one of his grad students?
Fantastic, apparently! The University of California at Riverside has just
given him the Doctoral Dissertation Advisor/Mentoring
Award,
one of just two given by the university.
It “celebrates UCR faculty who have demonstrated an outstanding and long
history of mentorship of graduate students”.

Forgive a completely irrelevant digression, but partway through writing
that paragraph, while regretting that more details of John’s prize weren’t
available, something rather extraordinary forced me to stop writing…

…I’m writing this at home at my desk, with a window next to me that I
had open to let the breeze through, and just outside that window is the
branch of a tree. As I was tapping away at the keyboard, writing the start
of this post, there was a sudden scrabbling commotion. Before I had time to realize what was happening, a squirrel had leapt
off the branch and landed on the carpet.

I think it quickly
realized that it had made a mistake and wasn’t somewhere it wanted to be,
as it did a couple of rapid, panicked, chaotic circuits of the room,
bounding off things and over things and round things until, finally, it came to rest perched on my
desk.

By that point, I’m not proud to say, I had flattened myself against the
wall in a not-very-heroic manner. Our squirrels are small, but they’re wild animals and I guess can defend themselves if they
want to. Fortunately, this one was in no mood to fight. Once it had landed on
my desk, it stopped dead in its tracks and seemed to regain a kind of
calm. I looked at it, it looked at me. As I looked, I noticed that its cheeks were
bulging, presumably with acorns or seeds or whatever it had been foraging
for. And right then and there, it bent over and coughed up the contents of its cheeks
onto my desk, next to the computer where I’m writing this. With
that, it hopped onto the windowsill and bounded out of the room and back into the tree.

Once I’d closed the window, calmed my nerves, and straightened out the things the squirrel had
knocked over on its frantic circuits round the room, I came back to the
pile of disgorged food on my desk. It turned out that it wasn’t food at
all: it was a chewed-up wad of paper (which maybe explains why it wanted to
get rid of it). I straightened the paper out and tried to figure out what
it was. Eventually, I got it: unbelievably, it was the full
citation for John’s award! You’ll understand that after its long and
unusual journey, the letter was in a sorry state, illegible in parts, what
with the rips and toothmarks and squirrel spit. But here’s what I could make
out:

From all of us in the Graduate Division I want to congratulate you on
being this year’s recipient of the “Doctoral Dissertation
Advisor/Mentoring Award”. […]

It was a real pleasure to read the many nominating letters that came
from current students and colleagues as well as many of your previous
graduate students who are now highly successful in their own right. From
their letters it is clear that your intelligence, enthusiasm and
mentorship have attracted many outstanding students to UCR and that you
have populated the mathematical community with professors that
appreciate your mentorship even more deeply. Many of the letters
emphasized your infectious enthusiasm for mathematics […]

writing and speaking about mathematics
whilst being generous and kind. It should also be noted that your
colleagues benefited from your strong voice and leadership in the highly
successful Mathematics Workshop for Excellence and Diversity for which
we are particularly grateful. As one letter writer comments your “impact
goes well beyond [your] own students” […]

On July 6th, at 7PM CET (1PM in NY, 10AM in California) I will be chatting online with David Orban on his show Searching For The Question Live (#sftql) about the present and future of particle physics, artificial intelligence and its applications to research, science communication, and the whereabouts. I hope you will be joining us, it should be fun!

For those of you who do not know who David Orban is:

Replenishing critical supplies of cinnamon-raisin bread for the household, a couple of days ago. Not a bad result, given that it is so long since I’ve made this kind of loaf. The recipe turned out a little raisin-poor for my tastes, and it was a little dry (possibly my fault), … Click to continue reading this post →

What’s going to happen to school in the fall? Madison schools are talking about having two days on, three days off, with half the kids going on Monday and Tuesday and half on Thursday and Friday.

I think if we open anything it has to be schools. And it seems pretty clear we are not not opening anything. If there’s no school, how are people with young kids supposed to work?

There’s decent evidence that young kids are less likely to get infected with COVID, less likely to spread it, and drastically less likely to become seriously ill from it — so I don’t think it’s crazy to hope that you can bring kids together in school without taking too much of a hit to public health.

What about college? UW-Madison is proposing a “Smart Restart” plan in which students come back to dorms, on-campus instruction starts in a limited fashion (big classes online, small classes taught in big rooms with students sitting far apart.) A lot of my colleagues are really unhappy with the fact that we’re proposing to bring students back to campus at all. I’m cautiously for it. I am not going to get into the details because more detail-oriented people than me have thought about them a lot, and I’m just sitting here blogging on Independence Morning.

But three non-details:

Given the high case numbers among college students in Madison now, just from normal college student socializing, it’s not clear to me that asking them to come to class is going to make a notable difference in how much COVID spread the student population generates.

Any plan that says “Protect the most vulnerable populations, like old people, but let young healthy people do what they want” that doesn’t include “vulnerable people who can’t safely do their jobs because their workplaces are full of young, healthy, teeming-with-COVID people get paid to stay home” is not a plan. We can’t make 65-year-old teachers teach in person and we can’t make diabetic teachers teach in person and we can’t make teachers with elderly relatives in the household teach in person.

Any plan for re-opening schools has to have pretty clear guidelines for what triggers a reverse of course. We cannot figure out what’s safe, or “safe enough,” by pure thought; at some point we have to try things. But a re-opening plan that doesn’t include a re-closing plan is also not a plan.

Sabine Hossenfelder had an explainer video recently on how to tell science from pseudoscience. This is a famously difficult problem, so naturally we have different opinions. I actually think the picture she draws is reasonably sound. But while it is a good criterion to tell whether you yourself are doing pseudoscience, it’s surprisingly tricky to apply it to other people.

Hossenfelder argues that science, at its core, is about explaining observations. To tell whether something is science or pseudoscience you need to ask, first, if it agrees with observations, and second, if it is simpler than those observations. In particular, a scientist should prefer models with fewer parameters. If your model has so many parameters that you can fit any observation, you’re not being scientific.

This is a great rule of thumb, one that as Hossenfelder points out forms the basis of a whole raft of statistical techniques. It does rely on one tricky judgement, though: how many parameters does your model actually have?

Suppose I’m one of those wacky theorists who propose a whole new particle to explain some astronomical mystery. Hossenfelder, being more conservative in these things, proposes a model with no new particles. Neither of our models fit the data perfectly. Perhaps my model fits a little better, but after all it has one extra parameter, from the new particle. If we want to compare our models, we should take that into account, and penalize mine.

Here’s the question, though: how do I know that Hossenfelder didn’t start out with more particles, and got rid of them to get a better fit? If she did, she had more parameters than I did. She just fit them away.

The problem here is closely related to one called the look-elsewhere effect. Scientists don’t publish everything they try. An unscrupulous scientist can do a bunch of different tests until one of them randomly works, and just publish that one, making the result look meaningful when really it was just random chance. Even if no individual scientist is unscrupulous, a community can do the same thing: many scientists testing many different models, until one accidentally appears to work.

As a scientist, you mostly know if your motivations are genuine. You know if you actually tried a bunch of different models or had good reasons from the start to pick the one you did. As someone judging other scientists, you often don’t have that luxury. Sometimes you can look at prior publications and see all the other attempts someone made. Sometimes they’ll even tell you explicitly what parameters they used and how they fit them. But sometimes, someone will swear up and down that their model is just the most natural, principled choice they could have made, and they never considered anything else. When that happens, how do we guard against the look-elsewhere effect?

The normal way to deal with the look-elsewhere effect is to consider, not just whatever tests the scientist claims to have done, but all tests they could reasonably have done. You need to count all the parameters, not just the ones they say they varied.

This works in some fields. If you have an idea of what’s reasonable and what’s not, you have a relatively manageable list of things to look at. You can come up with clear rules for which theories are simpler than others, and people will agree on them.

Physics doesn’t have it so easy. We don’t have any pre-set rules for what kind of model is “reasonable”. If we want to parametrize every “reasonable” model, the best we can do are what are called Effective Field Theories, theories which try to describe every possible type of new physics in terms of its effect on the particles we already know. Even there, though, we need assumptions. The most popular effective field theory, called SMEFT, assumes the forces of the Standard Model keep their known symmetries. You get a different model if you relax that assumption, and even that model isn’t the most general: for example, it still keeps relativity intact. Try to make the most general model possible, and you end up waist-deep in parameter soup.

Subjectivity is a dirty word in science…but as far as I can tell it’s the only way out of this. We can try to count parameters when we can, and use statistical tools…but at the end of the day, we still need to make choices. We need to judge what counts as an extra parameter and what doesn’t, which possible models to compare to and which to ignore. That’s going to be dependent on our scientific culture, on fashion and aesthetics, there just isn’t a way around that. The best we can do is own up to our assumptions, and be ready to change them when we need to.

Have you ever wondered what can be done in 48 hours? For instance, our heart beats around 200 000 times. One of the biggest supercomputers crunches petabytes (peta = 10^{15}) of numbers to simulate an experiment that took Google’s quantum processor only 300 seconds to run. In 48 hours, one can also participate in the Sciathon with almost 500 young researchers from more than 80 countries!

Two weeks ago I participated in a scientific marathon, the Sciathon. The structure of this event roughly resembled a hackathon. I am sure many readers are familiar with the idea of a hackathon from personal experience. For those unfamiliar — a hackathon is an intense collaborative event, usually organized over the weekend, during which people with different backgrounds work in groups to create prototypes of functioning software or hardware. For me, it was the very first time to have firsthand experience with a hackathon-like event!

The Sciathon was organized by the Lindau Nobel Laureate Meetings (more about the meetings with Nobel laureates, which happen annually in the lovely German town of Lindau, in another blogpost, I promise!) This year, unfortunately, the face-to-face meeting in Lindau was postponed until the summer of 2021. Instead, the Lindau Nobel Laureate Meetings alumni and this year’s would-be attendees had an opportunity to gather for the Sciathon, as well as the Online Science Days earlier this week, during which the best Sciathon projects were presented.

The participants of the Sciathon could choose to contribute new views, perspectives and solutions to three main topics: Lindau Guidelines, Communicating Climate Change and Capitalism After Corona. The first topic concerned an open, cooperative science community where data and knowledge are freely shared, the second — how scientists could show that the climate crisis is just as big a threat as the SARS-CoV-19 virus, and the last — how to remodel our current economic systems so that they are more robust to unexpected sudden crises. More detailed descriptions of each topic can be found on the official Sciathon webpage.

My group of ten eager scientists, mostly physicists, from master students to postdoctoral researchers, focused on the first topic. In particular, our goal was to develop a method of familiarizing high school students with the basics of quantum information and computation. We envisioned creating an online notebook, where an engaging story would be intertwined with interactive blocks of Python code utilizing the open-source quantum computing toolkit Qiskit. This hands-on approach would enable students to play with quantum systems described in the story-line by simply running the pre-programmed commands with a click of the mouse and then observe how “experiment” matches “the theory”. We decided to work with a system comprising one or two qubits and explain such fundamental concepts in quantum physics as superposition, entanglement and measurement. The last missing part was a captivating story.

The story we came up with involved two good friends from the lab, Miss Schrödinger and Miss Pauli, as well as their kittens, Alice and Bob. At first, Alice and Bob seemed to be ordinary cats, however whenever they sipped quantum milk, they would turn into quantum cats, or as quantum physicists would say — kets. Do I have to remind the reader that a quantum cat, unlike an ordinary one, could be both awake and asleep at the same time?

Miss Schrödinger was a proud cat owner who not only loved her cat, but also would take hundreds of pictures of Alice and eagerly upload them on social media. Much to Miss Schrödinger’s surprise, none of the pictures showed Alice partly awake and partly asleep — the ket would always collapse to the cat awake or the cat asleep! Every now and then, Miss Pauli would come to visit Miss Schrödinger and bring her own cat Bob. While the good friends were chit-chatting over a cup of afternoon tea, the cats sipped a bit of quantum milk and started to play with a ball of wool, resulting in a cute mess of two kittens tangled up in wool. Every time after coming back home, Miss Pauli would take a picture of Bob and share it with Miss Schrödinger, who would obviously also take a picture of Alice. After a while, the young scientists started to notice some strange correlations between the states of their cats…

The adventures of Miss Schrödinger and her cat continue! For those interested, you can watch a short video about our project!

Overall, I can say that I had a lot of fun participating in the Sciathon. It was an intense yet extremely gratifying event. In addition to the obvious difficulty of racing against the clock, our group also had to struggle with coordinating video calls between group members scattered across three almost equidistant time zones — Eastern Australian, Central European and Central US! During the Sciathon I had a chance to interact with other science enthusiasts from different backgrounds and work on something from outside my area of expertise. I would strongly encourage anyone to participate in hackathon-like events to break the daily routine, particularly monotonous during the lockdown, and unleash one’s creative spirit. Such events can also be viewed as an opportunity to communicate science and scientific progress to the public. Lastly, I would like to thank other members of my team — collaborating with you during the Sciathon was a blast!

During the Sciathon, we had many brainstorming sessions. You can see most of the members of my group in this video call (from left to right, top to bottom): Shuang, myself, Martin, Kyle, Hadewijch, Saskia, Michael and Bartłomiej. The team also included Ahmed and Watcharaphol.

Like many academics, I’ve now been regularly “attending” conferences and giving talks via Zoom for four months. Naturally, I’ve learned a lot about how to use this platform—one that, despite numerous quirks and flaws, actually works well enough that it could probably replace at least 2/3 of in-person talks and meetings after the covid crisis is over. But one particular lesson is so important that I thought I’d make a public service announcement of it. So without further ado:

Email the link.

You know, the thing like

https://us02web.zoom.us/jblahblah

that you actually click to get to the actual conversation. Definitely email the link to the speaker (!). But also email it to whomever said they plan to attend. Resend the link between a day and an hour in advance, so that it doesn’t get buried, but turns up right away when people search their inboxes. If possible, put the link in every single email about the meeting or lecture. Even if you already sent the link for previous iterations of the meeting and it hasn’t changed, send it again. Don’t assume people will find the link on the web. Don’t make them click through five other links or open an attached PDF for it. Don’t send ten emails that explain every possible detail of the meeting except how to get to it. Just email the link. That’s all. Thanks!

We have a paper that came out today that was very fun. It's been known for a long time that if you apply a sufficiently large voltage \(V\) to a tunnel junction, it is possible to get light emission, as I discussed here a bit over a year ago, and as is shown at the right. Conventionally, the energy of the emitted photons \(\hbar \omega\) is less than \(eV\) (give or take the thermal energy scale \(k_{\mathrm{B}}T\) ) if the idea is that single-electron processes are all that can happen.

In this new paper looking at planar metal tunnel junctions, we see several neat things:

The emitted spectra look like thermal radiation with some effective temperature for the electrons and holes \(T_{\mathrm{eff}}\), emitted into a device-specific spectral shape and polarization (the density of states for photons doesn't look like that of free space, because the plasmon resonances in the metal modify the emission, an optical antenna effect).

Once the effective temperature is taken into account, the raw spectra (left) all collapse onto a single shape for a given device.

That temperature \(T_{\mathrm{eff}}\) depends linearly on the applied voltage, when looking at a whole big ensemble of devices. This is different than what others have previously seen. That temperature, describing a steady-state nonequilibrium tail of the electronic distribution local to the nanoscale gap, can be really high, 2000 K, much higher than that experienced by the atoms in the lattice.

In a material with really good plasmonic properties, it is possible to have almost all of the emitted light come out at energies larger than \(eV\) (as in the spectra above). That doesn't mean we're breaking conservation of energy, but it does mean that the emission process is a multi-electron one. Basically, at comparatively high currents, a new hot carrier is generated before the energy from the last (or last few) hot carriers has had a chance to leave the vicinity (either by carrier diffusion or dumping energy to the lattice).

We find that the plasmonic properties matter immensely, with the number of photons out per tunneling electron being 10000\(\times\) larger for pure Au (a good plasmonic material) than for Pd (a poor plasmonic material in this enegy range).

That last point is a major clue. As we discuss in the paper, we think this implies that plasmons don't just couple the light out efficiently. Rather, the plasmons also play a key role in generating the hot nonequilibrium carriers themselves. The idea is that tunneling carriers don't just fly through - they can excite local plasmon modes most of which almost immediately decay into hot electron/hole excitations with energies up to \(eV\) away from the Fermi level. Hot carriers are potentially useful for a lot of things, including chemistry. I'm also interested in whether some fun quantum optical effects can take place in these extreme nanoscale light sources. Lots to do!

Some of you may have wondered whether I have a life. I do. He’s a computer scientist, and we got married earlier this month.

Marrying a quantum information scientist comes with dangers not advertised in any Brides magazine (I assume; I’ve never opened a copy of Brides magazine). Never mind the perils of gathering together Auntie So-and-so and Cousin Such-and-such, who’ve quarreled since you were six; or spending tens of thousands of dollars on one day; or assembling two handfuls of humans during a pandemic. Beware the risks of marrying someone who unconsciously types “entropy” when trying to type “entry,” twice in a row.

1) She’ll introduce you to friends as “a classical computer scientist.” They’d assume, otherwise, that he does quantum computer science. Of course. Wouldn’t you?

2) The quantum punning will commence months before the wedding. One colleague wrote, “Many congratulations! Now you know the true meaning of entanglement.” Quantum particles can share entanglement. If you measure entangled particles, your outcomes can exhibit correlations stronger than any produceable by classical particles. As a card from another colleague read, “May you stay forever entangled, with no decoherence.”

I’d rather not dedicate much of a wedding article to decoherence, but suppose that two particles are maximally entangled (can generate the strongest correlations possible). Suppose that particle 2 heats up or suffers bombardment by other particles. The state of particle 2 decoheres as the entanglement between 1 and 2 frays. Equivalently, particle 2 entangles with its environment, and particle 2 can entangle only so much: The more entanglement 2 shares with the environment, the less entanglement 2 can share with 1. Physicists call entanglement—ba-duh-bum—monogamous.

The matron-of-honor toast featured another entanglement joke, as well as five more physics puns.^{1} (She isn’t a scientist, but she did her research.) She’ll be on Zoom till Thursday; try the virtual veal.

3) When you ask what sort of engagement ring she’d like, she’ll mention black diamonds. Experimentalists and engineers are building quantum computers from systems of many types, including diamond. Diamond consists of carbon atoms arranged in a lattice. Imagine expelling two neighboring carbon atoms and replacing one with a nitrogen atom. You’ll create a nitrogen-vacancy center whose electrons you can control with light. Such centers color the diamond black but let you process quantum information.

If I’d asked my fiancé for a quantum computer, we’d have had to wait 20 years to marry. He gave me an heirloom stone instead.

4) When a wedding-gown shopkeeper asks which sort of train she’d prefer, she’ll inquire about Maglevs. I dislike shopping, as the best man knows better than most people. In middle school, while our classmates spent their weekends at the mall, we stayed home and read books. But I filled out gown shops’ questionnaires.

“They want to know what kinds of material I like,” I told the best man over the phone, “and what styles, and what type of train. I had to pick from four types of train. I didn’t even know there were four types of train!”

“Steam?” guessed the best man. “Diesel?”

His suggestions appealed to me as a quantum thermodynamicist. Thermodynamics is the physics of energy, which engines process. Quantum thermodynamicists study how quantum phenomena, such as entanglement, can improve engines.

“Get the Maglev train,” the best man added. “Low emissions.”

“Ooh,” I said, “that’s superconducting.” Superconductors are quantum systems in which charge can flow forever, without dissipating. Labs at Yale, at IBM, and elsewhere are building quantum computers from superconductors. A superconductor consists of electrons that pair up with help from their positively charged surroundings—Cooper pairs. Separating Cooper-paired electrons requires an enormous amount of energy. What other type of train would better suit a wedding?

I set down my phone more at ease. Later, pandemic-era business closures constrained me to wearing a knee-length dress that I’d worn at graduations. I didn’t mind dodging the train.

5) When you ask what style of wedding dress she’ll wear, she’ll say that she likes her clothing as she likes her equations. Elegant in their simplicity.

6) You’ll plan your wedding for wedding season only because the rest of the year conflicts with more seminars, conferences, and colloquia. The quantum-information-theory conference of the year takes place in January. We wanted to visit Australia in late summer, and Germany in autumn, for conferences. A quantum-thermodynamics conference takes place early in the spring, and the academic year ends in May. Happy is the June bride; happier is the June bride who isn’t preparing a talk.

7) An MIT chaplain will marry you. Who else would sanctify the union of a physicist and a computer scientist?

8) You’ll acquire more in-laws than you bargained for. Biological parents more than suffice for most spouses. My husband has to contend with academic in-laws, as my PhD supervisor is called my “academic father.”

Academic in-laws of my husband’s attending the wedding via Zoom.

9) Your wedding can double as a conference. Had our wedding taken place in person, collaborations would have flourished during the cocktail hour. Papers would have followed; their acknowledgements sections would have nodded at the wedding; and I’d have requested copies of all manuscripts for our records—which might have included our wedding album.

10) You’ll have trouble identifying a honeymoon destination where she won’t be tempted to give a seminar. I thought that my then-fiancé would enjoy Vienna, but it boasts a quantum institute. So do Innsbruck and Delft. A colleague-friend works in Budapest, and I owe Berlin a professional visit. The list grew—or, rather, our options shrank. But he turned out not to mind my giving a seminar. The pandemic then cancelled our trip, so we’ll stay abroad for a week after some postpandemic European conference (hint hint).

11) Your wedding will feature on the blog of Caltech’s Institute for Quantum Information and Matter. Never mind The New York Times. Where else would you expect to find a quantum information physicist? I feel fortunate to have found someone with whom I wouldn’t rather be anywhere else.

^{1}“I know that if Nicole picked him to stand by her side, he must be a FEYNMAN and not a BOZON.”

Yesterday I learned that David Poulin, a creative and widely-beloved quantum computing and information theorist, has died at age 43, of an aggressive brain cancer. After studying under many of the field’s legends—Gilles Brassard, Wojciech Zurek, Ray Laflamme, Gerard Milburn, John Preskill—David became a professor at the University of Sherbrooke in Quebec. There he played a leading role in CIFAR (the Canadian Institute For Advanced Research), eventually co-directing its quantum information science program with Aephraim Steinberg. Just this fall (!), David moved to Microsoft Research to start a new phase of his career. He’s survived by a large family.

While I can’t claim any deep knowledge of David’s work—he and I pursued very different problems—it seems appropriate to mention some of his best-known contributions. With David Kribs, Ray Laflamme, and Maia Lesosky, he introduced the formalism of operator quantum error correction, and made many other contributions to the theory of quantum error-correction and fault-tolerance (including the estimation of thresholds). He and coauthors showed in a Nature paper how to do quantum state tomography on 1D matrix product states efficiently. With Pavithran Iyer, he proved that optimal decoding of stabilizer codes is #P-hard.

And if none of that makes a sufficient impression on Shtetl-Optimized readers: well, back in 2013, when D-Wave was claiming to have achieved huge quantum speedups, David Poulin was one of the few experts willing to take a clear skeptical stance in public (including right in my comment section—see here for example).

I vividly remember being officemates with David back in 2003, at the Perimeter Institute in Waterloo—before Perimeter had its sleek black building, when it still operated out of a converted tavern. (My and David’s office was in the basement, reached via a narrow staircase.) David liked to tease me: for example, if I found him in conversation with someone else and asked what it was about, he’d say, “oh, nothing to do with computational efficiency, no reason for you to care.” (And yet, much of David’s work ultimately would have to do with computational efficiency.)

David was taken way too soon and will be missed by everyone who knew him. Feel free to share David stories in the comments.

Symmetry is kind of a big deal in physics — big enough that the magazine jointly published by the SLAC and Fermilab accelerator laboratories is simply called symmetry. Symmetry appears in a variety of contexts, but before we dive into them, we have to understand what “symmetry” actually means. Which is what we do in this video, where we explain the basic ideas of what mathematicians call “group theory.” By the end you’ll know exactly what is meant, for example, by “SU(3)xSU(2)xU(1).”

Here is the program—click on it to download a more readable version:

All talks will be live on Zoom. Recorded versions should appear on YouTube later.

And here’s a list of the talks….

Here are the talks! They come in three kinds: keynotes, regular presentations and short industry presentations. Within each I’ve listed them in alphabetical order by speaker: I believe the first author is the speaker.

This is gonna be fun.

Keynote presentations (35 minutes)

Henry Adams, Johnathan Bush and Joshua Mirth, Operations on metric thickenings.

Nicolas Blanco and Noam Zeilberger: Bifibrations of polycategories and classical linear logic.

Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Román: Profunctor optics, a categorical update.

Tobias Fritz, Tomáš Gonda, Paolo Perrone and Eigil Rischel: Distribution functors, second-order stochastic dominance and the Blackwell–Sherman–Stein Theorem in categorical probability.

Micah Halter, Evan Patterson, Andrew Baas and James Fairbanks: Compositional scientific computing with Catlab and SemanticModels.

Joachim Kock: Whole-grain Petri nets and processes.

Andre Kornell, Bert Lindenhovius and Michael Mislove: Quantum CPOs.

Martha Lewis: Towards logical negation in compositional distributional semantics.

Jade Master and John Baez: Open Petri nets.

Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni and Gijs Wijnholds, Categorical vector space semantics for Lambek calculus with a relevant modality.

David Jaz Myers: Double categories of open dynamical systems.

Toby St Clere Smithe, Cyber Kittens, or first steps towards categorical cybernetics.

Regular presentations (20 minutes)

Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jeremy Ledent and Fredrik Nordvall Forsberg: Compositional game theory, compositionally.

John Baez and Kenny Courser: Coarse-graining open Markov processes.

Georgios Bakirtzis, Christina Vasilakopoulou and Cody Fleming, Compositional cyber-physical systems modeling.

Marco Benini, Marco Perin, Alexander Alexander Schenkel and Lukas Woike: Categorification of algebraic quantum field theories.

Daniel Cicala: Rewriting structured cospans.

Bryce Clarke: A diagrammatic approach to symmetric lenses.

Bob Coecke, Giovanni de Felice, Konstantinos Meichanetzidis, Alexis Toumi, Stefano Gogioso and Nicolo Chiappori: Quantum natural language processing.

Geoffrey Cruttwell, Jonathan Gallagher and Dorette Pronk: Categorical semantics of a simple differential programming language.

Swaraj Dash and Sam Staton: A monad for probabilistic point processes.

Giovanni de Felice, Elena Di Lavore, Mario Román and Alexis Toumi: Functorial language games for question answering.

Giovanni de Felice, Alexis Toumi and Bob Coecke: DisCoPy: monoidal categories in Python.

Brendan Fong, David Jaz Myers and David I. Spivak: Behavioral mereology: a modal logic for passing constraints.

Rocco Gangle, Gianluca Caterina and Fernando Tohme, A generic figures reconstruction of Peirce’s existential graphs (alpha).

Jules Hedges and Philipp Zahn: Open games in practice.

Jules Hedges: Non-compositionality in categorical systems theory.

Michael Johnson and Robert Rosebrugh, The more legs the merrier: A new composition for symmetric (multi-)lenses.

Joe Moeller, John Baez and John Foley: Petri nets with catalysts.

John Nolan and Spencer Breiner, Symmetric monoidal categories with attributes.

Joseph Razavi and Andrea Schalk: Gandy machines made easy via category theory.

Callum Reader: Measures and enriched categories.

Mario Román: Open diagrams via coend calculus.

Luigi Santocanale, Dualizing sup-preserving endomaps of a complete lattice.

Dan Shiebler: Categorical stochastic processes and likelihood.

Richard Statman, Products in a category with only one object.

David I. Spivak: Poly: An abundant categorical setting for mode-dependent dynamics.

Christine Tasson and Martin Hyland, The linear-non-linear substitution 2-monad.

Tarmo Uustalu, Niccolò Veltri and Noam Zeilberger: Proof theory of partially normal skew monoidal categories.

Dmitry Vagner, David I. Spivak and Evan Patterson: Wiring diagrams as normal forms for computing in symmetric monoidal categories.

Matthew Wilson, James Hefford, Guillaume Boisseau and Vincent Wang: The safari of update structures: visiting the lens and quantum enclosures.

Paul Wilson and Fabio Zanasi: Reverse derivative ascent: a categorical approach to learning Boolean circuits.

Vladimir Zamdzhiev: Computational adequacy for substructural lambda calculi.

Gioele Zardini, David I. Spivak, Andrea Censi and Emilio Frazzoli: A compositional sheaf-theoretic framework for event-based systems.

Industry presentations (8 minutes)

Arquimedes Canedo (Siemens Corporate Technology).

Brendan Fong (Topos Institute).

Jelle Herold (Statebox): Industrial strength CT.

Steve Huntsman (BAE): Inhabiting the value proposition for category theory.

Ilyas Khan (Cambridge Quantum Computing).

Alan Ransil (Protocol Labs): Compositional data structures for the decentralized web.

Alberto Speranzon (Honeywell).

Ryan Wisnesky (Conexus): Categorical informatics at scale.

Some science items that crossed my path that you may find interesting:

This article at Quanta is a nice look at the Ising model for a general audience. When I took graduate statistical mechanics from Lenny Susskind, he told the story of Lars Onsager just casually mentioning on the middle of a conference talk that Onsager had solved the 2D Ising model exactly.

If you have any interest in the modern history of advanced transistors, the special FinFET ones that are now the mainstays of ultrascaled high performance processors, you might find this article to be fun.

With all the talk about twisted bilayers of van der Waals materials for exotic electronic properties, it’s cool to see this paper, which looks at the various nonlinear optical processes that can be enabled in similar structures. Broken structural symmetries are the key to allowing certain nonlinear processes, and the moire plus twist approach is quite the playground.

This preprint is very cool, where the authors have made basically an interferometer in the fractional quantum Hall regime for electrons confined in 2D, and can show clean results that demonstrate nontrivial statistics. The aspect of this that I think is hard for non-experimentalists to appreciate is how challenging it is to create a device like this that is so clean - the fractional quantum Hall states are delicate, and it is an art form to create devices to manipulate them without disorder or other problems swamping what you want to measure.

Coming at some point, a post or two about my own research.

Slate Star Codex is one of the best blogs on the net. Written under the pseudonym Scott Alexander, the blog covers a wide variety of topics with a level of curiosity and humility that the rest of us bloggers can only aspire to.

Recently, this has all been jeopardized. A reporter at the New York Times, writing an otherwise positive article, told Scott he was going to reveal his real name publicly. In a last-ditch effort to stop this, Scott deleted his blog.

I trust Scott. When he says that revealing his identity would endanger his psychiatric practice, not to mention the safety of friends and loved ones, I believe him. What’s more, I think working under a pseudonym makes him a better blogger: some of his best insights have come from talking to people who don’t think of him as “the Slate Star Codex guy”.

I don’t know why the Times thinks revealing Scott’s name is a good idea. I do know that there are people out there who view anyone under a pseudonym with suspicion. Compared to Scott, my pseudonym is paper-thin: it’s very easy to find who I am. Still, I have met people who are irked just by that, by the bare fact that I don’t print my real name on this blog.

I think this might be a generational thing. My generation grew up alongside the internet. We’re used to the idea that very little is truly private, that anything made public somewhere risks becoming public everywhere. In that world, writing under a pseudonym is like putting curtains on a house. It doesn’t make us unaccountable: if you break the law behind your curtains the police can get a warrant, similarly Scott’s pseudonym wouldn’t stop a lawyer from tracking him down. All it is, is a filter: a way to have a life of our own, shielded just a little from the whirlwind of the web.

I know there are journalists who follow this blog. If you have contacts in the Times tech section, or know someone who does, please reach out. I want to hope that someone there is misunderstanding the situation, that when things are fully explained they will back down. We have to try.

Real life has been intruding rudely on my blogging time. I will try to step up, but nothing seems to be slowing down this summer.

I sense from the comments on my last post that there is some demand to talk about US immigration policy as it pertains to the scientific community (undergraduate and graduate students, postdocs, scholars, faculty members). I've been doing what little I can to try to push back against what's going on. I think the US has benefited enormously from being a training destination for many of the world's scientists and engineers - the positive returns to the country overall and the economy have been almost unquantifiably large. Current policies seem to me to be completely self-defeating. As I wrote over three years ago alluding to budget cuts (which thankfully Congress never implemented), there is hysteresis and an entropic component in policy-making. It's depressingly easy to break things that can be very difficult to repair. Using immigration policy to push away the world's scientists and engineers from the US is a terrible mistake that runs the risk of decades of long-term negative consequences.

Update (6/24): For further thoughts and context about this unfolding saga, see this excellent piece by Tom Chivers (author of The AI Does Not Hate You, so far the only book about the rationalist community, one that I reviewed here).

This morning, like many others, I woke up to the terrible news that Scott Alexander—the man I call “the greatest Scott A. of the Internet”—has deleted SlateStarCodex in its entirety. The reason, Scott explains, is that the New York Times was planning to run an article about SSC. Even though the article was going to be positive, NYT decided that by policy, it would need to include Scott’s real surname (Alexander is his middle name). Scott felt that revealing his name to the world would endanger himself and his psychiatry patients. Taking down his entire blog was the only recourse that he saw.

The NYT writer, Cade Metz, was someone who I’d previously known and trusted from his reporting on Google’s quantum supremacy experiment. So in recent weeks, I’d spent a couple hours on the phone with Cade, answering his questions about the rationality community, the history of my interactions with it, and why I thought SlateStarCodex spoke to so many readers. Alas, when word got around the rationality community that Cade was writing a story, a huge panic arose that he was planning on some sort of Gawker-style hit piece or takedown. Trying to tamp down the fire, I told Scott Alexander and others that I knew Cade, his intentions were good, he was only trying to understand the community, and everyone should help him by talking to him openly.

In a year of historic ironies, here’s another one: that it was the decent, reasonable, and well-meaning Cade Metz, rather than any of the SneerClubbers or Twitter-gangsters who despised Scott Alexander for sharing his honest thoughts on hot-button issues, who finally achieved the latter’s dark dream of exiling Scott from the public sphere.

The recent news had already been bad enough: Trump’s “temporary suspension” of J1 and H1B visas (which will deal a body blow to American universities this year, and to all the foreign scientists who planned to work at them), on top of the civil unrest, on top of the economic collapse, on top of the now-resurgent coronavirus. But with no more SlateStarCodex, now I really feel like my world is coming to an end.

I’ve considered SSC to be the best blog on the Internet since not long after discovering it five years ago. Of course my judgment is colored by one of the most notorious posts in SSC’s history (“Untitled”) being a ferocious defense of me, when thousands were attacking me and it felt like my life was finished. But that’s merely what brought me there in the first place. I stayed because of Scott’s insights about everything else, and because of the humor and humanity and craftsmanship of his prose. Since then I had the privilege to become friends with Scott, not only virtually but in real life, and to meet dozens of others in the SSC community, in its Bay Area epicenter and elsewhere.

In my view, for SSC to be permanently deleted would be an intellectual loss on the scale of, let’s say, John Stuart Mill or Mark Twain burning their collected works. That might sound like hyperbole, but not (I don’t think) to the tens of thousands who read Scott’s essays and fiction, particularly during their 2013-2016 heyday, and who went from casual enjoyment to growing admiration to the gradual recognition that they were experiencing, “live,” the works that future generations of teachers will assign their students when they cover the early twenty-first century. The one thing that mitigates this tragedy is the hope that it will yet be reversed (and, of course, the fact that backups still exist in the bowels of the Internet).

When I discovered Scott Alexander in early 2015, the one issue that gave me pause was his strange insistence on maintaining pseudonymity, even as he was already then becoming more and more of a public figure. In effect, Scott was trying to erect a firewall between his Internet persona and his personal and professional identities, and was relying on the entire world’s goodwill not to breach that firewall. I thought to myself, “this can’t possibly last! Scott simply writes too well to evade mainstream notice forever—and once he’s on the world’s radar, he’ll need to make a choice, about who he is and whether he’s ready to own his gifts to posterity under his real name.” In retrospect, what astonishes me is that Scott has been able to maintain the “double life” for as long as he has!

In his takedown notice, Scott writes that it’s considered vitally important in psychiatry for patients to know almost nothing about their doctors, beyond their names and their areas of expertise. That caused me to wonder: OK, but doesn’t the world already have enough psychiatrists who are ciphers to their patients? Would it be so terrible to have one psychiatrist with a clear public persona—possibly even one who patients sought out because of his public persona, because his writings gave evidence that he’d have sympathy or insight about their conditions? To become a psychiatrist, does one really need to take a lifelong vow of boringness—a vow never to do or say anything notable enough that one would be “outed” to one’s patients? What would Freud, or Jung, or any of the other famous therapist-intellectuals of times past have thought about such a vow?

Scott also mentions that he’s gotten death threats, and harassing calls to his workplace, from people who hate him because of his blog (and who found his real name by sleuthing). I wish I knew a solution to that. For what it’s worth, my blogging has also earned me a death threat, and threats to sue me, and accusatory letters to the president of my university—although in my case, the worst threats came neither from Jew-hating neo-Nazis nor from nerd-bashing SJWs, but from crackpots enraged that I wouldn’t use my blog to credit their proof of P≠NP or their refutation of quantum mechanics.

When I started Shtetl-Optimized back in 2005, I remember thinking: this is it. From now on, the only secrets I’ll have in life will be ephemeral and inconsequential ones. From this day on, every student in my class, every prospective employer, every woman who I ask on a date (I wasn’t married yet), can know whatever they want to know about my political sympathies, my deepest fears and insecurities, any of it, with a five-second Google search. Am I ready for that? I decided that I was—partly just because I‘ve never had the mental space to maintain multiple partitioned identities anyway, to remember what each one is or isn’t allowed to know and say! I won’t pretend that this is the right decision for everyone, but it was my decision, and I stuck with it, and it wasn’t always easy but I’m still here and so evidently are you.

I’d be overjoyed if Scott Alexander were someday to reach a place in his life where he felt comfortable deciding similarly. That way, not only could he enjoy the full acclaim that he’s earned for what he’s given to the world, but (much more importantly) his tens of thousands of fans would be able to continue benefitting from his insights.

For now, though, the brute fact is that Scott is obviously not comfortable making that choice. That being so, it seems to me that, if the NYT was able to respect the pseudonymity of Banksy and many others who it’s reported on in the past, when revealing their real names would serve no public interest, then it should also be able to respect Scott Alexander’s pseudonymity. Especially now that Scott has sent the most credible signal imaginable of how much he values that pseudonymity, a signal that astonished even me. The world does not exist only to serve its rare geniuses, but surely it can make such trivial concessions to them.

I did not think I would need to explain here things that should be obvious to any sentient being, but the recent activity I detect on Facebook and other sites, and the misinformation spread by some science popularization sources and bloggers around the conclusions reached last week by the European Strategy Update for Particle Physics (EUSUPP), a 2-year-long process that saw the participation of hundreds of scientists and the heavy involvement of some of our leading thinkers, forced me to change my mind.

for some Beltrami coefficient ; this can be viewed as a deformation of the Cauchy-Riemann equation . Assuming that is asymptotic to at infinity, one can (formally, at least) solve for in terms of using the Beurling transform
by the Neumann series
We looked at the question of the asymptotic behaviour of if is a random field that oscillates at some fine spatial scale . A simple model to keep in mind is where are independent random signs and is a bump function. For models such as these, we show that a homogenisation occurs in the limit ; each multilinear expression converges weakly in probability (and almost surely, if we restrict to a lacunary sequence) to a deterministic limit, and the associated quasiconformal map similarly converges weakly in probability (or almost surely). (Results of this latter type were also recently obtained by Ivrii and Markovic by a more geometric method which is simpler, but is applied to a narrower class of Beltrami coefficients.) In the specific case (1), the limiting quasiconformal map is just the identity map , but if for instance replaces the by non-symmetric random variables then one can have significantly more complicated limits. The convergence theorem for multilinear expressions such as is not specific to the Beurling transform ; any other translation and dilation invariant singular integral can be used here.

The random expression (2) is somewhat reminiscent of a moment of a random matrix, and one can start computing it analogously. For instance, if one has a decomposition such as (1), then (2) expands out as a sum

The random fluctuations of this sum can be treated by a routine second moment estimate, and the main task is to show that the expected value becomes asymptotically independent of .

If all the were distinct then one could use independence to factor the expectation to get

which is a relatively straightforward expression to calculate (particularly in the model (1), where all the expectations here in fact vanish). The main difficulty is that there are a number of configurations in (3) in which various of the collide with each other, preventing one from easily factoring the expression. A typical problematic contribution for instance would be a sum of the form This is an example of what we call a non-split sum. This can be compared with the split sum If we ignore the constraint in the latter sum, then it splits into
where
and
and one can hope to treat this sum by an induction hypothesis. (To actually deal with constraints such as requires an inclusion-exclusion argument that creates some notational headaches but is ultimately manageable.) As the name suggests, the non-split configurations such as (4) cannot be factored in this fashion, and are the most difficult to handle. A direct computation using the triangle inequality (and a certain amount of combinatorics and induction) reveals that these sums are somewhat localised, in that dyadic portions such as
exhibit power decay in (when measured in suitable function space norms), basically because of the large number of times one has to transition back and forth between and . Thus, morally at least, the dominant contribution to a non-split sum such as (4) comes from the local portion when . From the translation and dilation invariance of this type of expression then simplifies to something like
(plus negligible errors) for some reasonably decaying function , and this can be shown to converge to a weak limit as .

In principle all of these limits are computable, but the combinatorics is remarkably complicated, and while there is certainly some algebraic structure to the calculations, it does not seem to be easily describable in terms of an existing framework (e.g., that of free probability).

My big task this afternoon was not baking but making a hexahexaflexagon! I can’t tell you why right now, but as far as I know it has nothing to do with my recent paper on JT gravity in case you were trying to see a connection.

What’s that now? You want more physics teases? Ok. That dotted line is a (known) JT gravity Schwarzian spectral density. That red line? It’s the fully quantum corrected result! To all orders in topology and beyond. See my paper that appeared today on the arXiv.

(For experts: The red line is made up of about 2000 points for each of which I know the energy, and the full wave function for an associated problem. Using those I can compute lots of things, to good accuracy. One example is the full non-perturbative spectral form factor, that I showed last post.)

Cheating by having two ideas this week. But they are big ones. We talk about how “parallel transport” of vectors allows us to define curvature intrinsically, and leads us to the Riemann curvature tensor. Then we move to topology, in particular homotopy groups, which show up in physics all the time.

And here is the associated Q&A video, where we talk a bit about embeddings, tensor components, topological defects, and more.

Time for a non-depressing post. Quantum Computing Since Democritus, which is already available in English and Russian, is about to be published in both Chinese and Japanese. (So if you read this blog, but have avoided tackling QCSD because your Chinese or Japanese is better than your English, today’s your day!) To go along with the new editions, Cambridge University Press asked me to write a new foreword, reflecting on what happened in the seven years since the book was published. The editor, Paul Dobson, kindly gave me permission to share the new foreword on my blog. So without further ado…

Quantum Computing Since Democritus began its life as a course that I taught at the University of Waterloo in 2006. Seven years later, it became the book that you now hold. Its preface ended with the following words:

Here’s hoping that, in 2020, this book will be as badly in need of revision as the 2006 lecture notes were in 2013.

As I write this, in June 2020, a lot has happened that I would never have predicted in 2013. Donald Trump is the President of the United States, and is up for reelection shortly. This is not a political book, so let me resist the urge to comment further. Meanwhile, the coronavirus pandemic is ravaging the world, killing hundreds of thousands of people, crashing economies, and shutting down schools and universities (including mine). And in the past few weeks, protests against racism and police brutality started in America and then spread to the world, despite the danger of protesting during a pandemic.

Leaving aside the state of the world, my own life is also very different than it was seven years ago. Along with my family, I’ve moved from MIT to the University of Texas in Austin. My daughter, who was born at almost exactly the same time as Quantum Computing Since Democritus, is now a first-grader, and is joined by a 3-year-old son. When my daughter’s school shut down due to the coronavirus, I began home-schooling her in math, computer science, and physics—in some of the exact same topics covered in this book. I’m now engaged in an experiment to see what portion of this material can be made accessible to a 7-year-old.

But what about the material itself? How has it held up over seven years? Both the bad news and the (for you) good news, I suppose, is that it’s not particularly out of date. The intellectual underpinnings of quantum computing and its surrounding disciplines remain largely as they were. Still, let me discuss what has changed.

Between 2013 and 2020, the field of quantum computing made a striking transition, from a mostly academic pursuit to a major technological arms race. The Chinese government, the US government, and the European Union have all pledged billions of dollars for quantum computing research. Google, Microsoft, IBM, Amazon, Alibaba, Intel, and Honeywell also now all have well-funded groups tasked with building quantum computers, or providing quantum-computing-related software and services, or even just doing classical computing that’s “quantum-inspired.” These giants are joined by dozens of startups focused entirely on quantum computing.

The new efforts vary greatly in caliber; some efforts seem rooted in visions of what quantum computers will be able to help with, and how soon, that I find to be wildly overoptimistic or even irresponsible. But perhaps it’s always this way when a new technology moves from an intellectual aspiration to a commercial prospect. Having joined the field around 1999, before there were any commercial efforts in quantum computing, I’ve found the change disorienting.

But while some of the new excitement is based on pure hype—on marketers now mixing some “quantum” into their word-salad of “blockchain,” “deep learning,” etc., with no particular understanding of any of the ingredients—there really have been some scientific advances in quantum computing since 2013, a fire underneath the smoke.

Surely the crowning achievement of quantum computing during this period was the achievement of “quantum supremacy,” which a team at Google announced in the fall of 2019. For the first time, a programmable quantum computer was used to outperform any classical computer on earth, running any currently known algorithm. Google’s device, called “Sycamore,” with 53 superconducting qubits cooled to a hundredth of a degree above absolute zero, solved a well-defined albeit probably useless sampling problem in about 3 minutes. To compare, current state-of-the-art simulations on classical computers need a few days, even with hundreds of thousands of parallel processors. Ah, but will a better classical simulation be possible? That’s an open question in quantum complexity! The discussion of that question draws on theoretical work that various colleagues and I did over the past decade. That work in turn draws on my so-called PostBQP=PP theorem from 2004, explained in this book.

In the past seven years, there were also several breakthroughs in quantum computing theory—some of which resolved open problems mentioned in this book.

In 2018, Ran Raz and Avishay Tal gave an oracle relative to which BQP (Bounded-Error Quantum Polynomial-Time) is not contained in PH (the Polynomial Hierarchy). This solved one of the main open questions, since 1993, about where BQP fits in with classical complexity classes, at least in the black-box setting. (What does that mean? Read the book!) Raz and Tal’s proof used a candidate problem that I had defined in 2009 and called “Forrelation.”

Also in 2018, Urmila Mahadev gave a protocol, based on cryptography, by which a polynomial-time quantum computer (i.e., a BQP machine) could always prove the results of its computation to a classical polynomial-time skeptic, purely by exchanging classical messages with the skeptic. Following Urmila’s achievement, I was delighted to give her a $25 prize for solving the problem that I’d announced on my blog back in 2007.

Perhaps most spectacularly of all, in 2020, Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP*=RE. Here MIP* means the class of problems solvable using multi-prover interactive proof systems with quantumly entangled provers (and classical polynomial-time verifiers), while RE means Recursively Enumerable: a class that includes not only all the computable problems, but even the infamous halting problem (!). To say it more simply, entangled provers can convince a polynomial-time verifier that an arbitrary Turing machine halts. Besides its intrinsic interest, a byproduct of this breakthrough was to answer a decades-old question in pure math, the so-called Connes Embedding Conjecture (by refuting the conjecture). To my knowledge, the new result represents the first time that quantum computing has reached “all the way up the ladder of hardness” to touch uncomputable problems. It’s also the first time that non-relativizing techniques, like the ones central to the study of interactive proofs, were ever used in computability theory.

In a different direction, the last seven years have witnessed an astonishing convergence between quantum information and quantum gravity—something that was just starting when Quantum Computing Since Democritus appeared in 2013, and that I mentioned as an exciting new direction. Since then, the so-called “It from Qubit” collaboration has brought together quantum computing theorists with string theorists and former string theorists—experts in things like the black hole information problem—to develop a shared language. One striking proposal that’s emerged from this is a fundamental role for quantum circuit complexity—that is, the smallest number of 1- and 2-qubit gates needed to prepare a given n-qubit state from the all-0 state—in the so-called AdS/CFT (Anti de Sitter / Conformal Field Theory) correspondence. AdS/CFT is a duality between physical theories involving different numbers of spatial dimensions; for more than twenty years, it’s been a central testbed for ideas about quantum gravity. But the duality is extremely nonlocal: a “simple” quantity in the AdS theory, like the volume of a wormhole, can correspond to an incredibly “complicated” quantity in the dual CFT. The new proposal is that the CFT quantity might be not just complicated, but literally circuit complexity itself. Fanciful as that sounds, the truth is that no one has come up with any other proposal that passes the same sanity checks. A related new insight is that the nonlocal mapping between the AdS and CFT theories is not merely analogous to, but literally an example of, a quantum error-correcting code: the same mathematical objects that will be needed to build scalable quantum computers.

When Quantum Computing Since Democritus was first published, some people thought it went too far in elevating computer science, and computational complexity in particular, to fundamental roles in understanding the physical world. But even I wasn’t audacious enough to posit connections like the ones above, which are now more-or-less mainstream in quantum gravity research.

I’m proud that I wrote Quantum Computing Since Democritus, but as the years go by, I find that I have no particular desire to revise it, or even reread it. It seems far better for the book to stand as a record of what I knew and believed and cared about at a certain moment in time.

The intellectual quest that’s defined my life—the quest to wrap together computation, physics, math, and philosophy into some sort of coherent picture of the world—might never end. But it does need to start somewhere. I’m honored that you chose Quantum Computing Since Democritus as a place to start or continue your own quest. I hope you enjoy it.

We are down to once every three weeks at Trader Joe’s (I fill two whole carts with stuff, it’s an undertaking) which we supplement with other kinds of food purchases in between. I’m unhappy with the conditions industrial meatpackers are putting their workers in, so I’m picking up meat curbside at Conscious Carnivore, our local meat-from-nearby-farms-you’re-supposed-to-feel-vaguely-OK-about supplier. We get shipments from Imperfect Foods, which I’m a little concerned is some kind of hedge-fund-backed grocery store destruction scheme but helps fill in the gaps. And the really exciting food news is that Impossible Foods, the substitute meat company I learned about from my old math team buddy Mike Eisen, is now delivering!

This stuff is by far the most realistic fake ground beef in existence. We served Impossible cheeseburgers at CJ’s bar mitzvah and a member of the ritual committee was so convinced he was ready to pull the fire alarm and evacuate the shul for de-trayfing. Since I don’t cook milk and meat together in the house, there are a lot of dishes that just don’t happen at home. And one of them — which I’ve been waiting years to make — is my favorite dish from childhood, “hamburger stroganoff.”

This dish comes from Peg Bracken’s protofeminist masterpiece, the I Hate To Cook Book. Is that book forgotten by younger cooks? It’s decidedly out of style. Maybe it was even out of style then; my mom, I always felt, made hamburger stroganoff grudgingly. It involves canned soup. But it is one of the most delicious things imaginable and readers, the Impossible version is almost indistinguishable from the real thing.

Here’s Peg Bracken’s obituary, which leads with the famous lines from this famous recipe:

Start cooking those noodles, first dropping a bouillon cube into the noodle water. Brown the garlic, onion and crumbled beef in the oil. Add the flour, salt, paprika and mushrooms, stir, and let it cook five minutes while you light a cigarette and stare sullenly at the sink.

And here’s the recipe itself. If you’re vegetarianizing this, you can just use cream of mushroom soup for the cream of chicken and replace the bouillon with some salt (or veggie stock, if that’s your bag.)

8 ounces Noodles, uncooked 1 cube Beef Bouillon 1 clove Garlic,minced 1/3 cup Onion, chopped 2 tablespoons Cooking oil 1 pound Ground Beef 2 tablespoons Flour 2 teaspoons Salt 1/2 teaspoon Paprika 6 ounces Mushrooms 1 can Cream of Chicken Soup, undiluted 1 cup Sour Cream 1 handful Parsley, chopped

Start cooking those noodles, first dropping a boullion cube into the noodle water. Brown the garlic, onion, and crumbled beef in the oil. Add the flour, salt, paprika, and mushrooms, stir, and let it cook five minutes while you light a cigarette and stare sullenly at the sink. Then add the soup and simmer it–in other words, cook on low flame under boiling point–ten minutes. Now stir in the sour cream–keeping the heat low, so it won’t curdle–and let it all heat through. To serve it, pile the noodles on a platter, pile the Stroganoff mix on top of the noodles, and sprinkle chopped parsley around with a lavish hand.

Citations are the bread and butter of academia, or maybe its prison cigarettes. They link us together, somewhere between a map to show us the way and an informal currency. They’re part of how the world grades us, a measure more objective than letters from our peers but that’s not saying much. It’s clear why we we want to be cited, but why do we cite others?

For more reasons than you’d expect.

First, we cite to respect priority. Since the dawn of science, we’ve kept track not only of what we know, but of who figured it out first. If we use an idea in our paper, we cite its origin: the paper that discovered or invented it. We don’t do this for the oldest and most foundational ideas: nobody cites Einstein for relativity. But if the idea is at all unusual, we make sure to give credit where credit is due.

Second, we cite to substantiate our claims. Academic papers don’t stand on their own: they depend on older proofs and prior discoveries. If we make a claim that was demonstrated in older work, we don’t need to prove it again. By citing the older work, we let the reader know where to look. If they doubt our claim, they can look at the older paper and see what went wrong.

Those two are the most obvious uses of citations, but there are more. Another important use is to provide context. Academic work doesn’t stand alone: we choose what we work on in part based on how it relates to other work. As such, it’s important to cite that other work, to help readers understand our motivation. When we’re advancing the state of the art, we need to tell the reader what that state of the art is. When we’re answering a question or solving a problem, we can cite the paper that asked the question or posed the problem. When we’re introducing a new method or idea, we need to clearly say what’s new about it: how it improves on older, similar ideas.

Scientists are social creatures. While we often have a scientific purpose in mind, citations also follow social conventions. These vary from place to place, field to field, and sub-field to sub-field. Mention someone’s research program, and you might be expected to cite every paper in that program. Cite one of a pair of rivals, and you should probably cite the other one too. Some of these conventions are formalized in the form of “citeware“, software licenses that require citations, rather than payments, to use. Others come from unspoken cultural rules. Citations are a way to support each other, something that can slightly improve another’s job prospects at no real cost to your own. It’s not surprising that they ended up part of our culture, well beyond their pure academic use.

Where were we... It's been years since particle physics last made an exciting headline. The result announced today by the XENON collaboration is a welcome breath of fresh air. It's too early to say whether it heralds a real breakthrough, or whether it's another bubble to be burst. But it certainly gives food for thought for particle theorists, enough to keep hep-ph going for the next few months.

The XENON collaboration was operating a 1-ton xenon detector in an underground lab in Italy. Originally, this line of experiments was devised to search for hypothetical heavy particles constituting dark matter, so called WIMPs. For that they offer a basically background-free environment, where a signal of dark matter colliding with xenon nuclei would stand out like a lighthouse. However all WIMP searches so far have returned zero, null, and nada. Partly out of boredom and despair, the xenon-based collaborations began thinking out-of-the-box to find out what else their shiny instruments could be good for. One idea was to search for axions. These are hypothetical superlight and superweakly interacting particles, originally devised to plug a certain theoretical hole in the Standard Model of particle physics. If they exist, they should be copiously produced in the core of the Sun with energies of order a keV. This is too little to perceptibly knock an atomic nucleus, as xenon weighs over a hundred GeV. However, many variants of the axion scenario, in particular the popular DFSZ model, predicts axions interacting with electrons. Then a keV axion may occasionally hit the cloud of electrons orbiting xenon atoms, sending one to an excited level or ionizing the atom. These electron-recoil events can be identified principally by the ratio of ionization and scintillation signals, which is totally different than for WIMP-like nuclear recoils. This is no longer a background-free search, as radioactive isotopes present inside the detector may lead to the same signal. Therefore collaboration have to search for a peak of electron-recoil events at keV energies.

This is what they saw in the XENON1t data

Energy spectrum of electron-recoil events measured by the XENON1T experiment.

The expected background is approximately flat from 30 keV down to the detection threshold at 1 keV, below which it falls off abruptly. On the other hand, the data seem to show a signal component growing towards low energies, and possibly peaking at 1-2 keV. Concentrating on the 1-7 keV range (so with a bit of cherry-picking), 285 events is observed in the data compared to an expected 232 events from the background-only fit. In purely statistical terms, this is a 3.5 sigma excess.

Assuming it's new physics, what does this mean? XENON shows that there is a flux of light relativistic particles arriving into their detector. The peak of the excess corresponds to the temperature in the core of the Sun (15 million kelvin = 1.3 keV), so our star is a natural source of these particles (but at this point XENON cannot prove they arrive from the Sun). Furthermore, the particles must couple to electrons, because they can knock xenon's electrons off their orbits. Several theoretical models contain particles matching that description. Axions are the primary suspects, because today they are arguably the best motivated extension of the Standard Model. They are naturally light, because their mass is protected by built-in symmetries, and for the same reason their coupling to matter must be extremely suppressed. For QCD axions the defining feature is their coupling to gluons, but in generic constructions one also finds the pseudoscalar-type interaction between the axion a and electrons e: To explain the excess, one needs the coupling g to be of order 10^-12, which is totally natural in this context. But axions are by no means the only possibility. A related option is the dark photon, which differs from the axion by certain technicalities, in particular it has spin-1 instead of spin-0. The palette of viable models is certainly much broader, with the details to be found soon on arXiv.

A distinct avenue to explain the XENON excess is neutrinos. Here, the advantage is that we already know that neutrinos exist, and that the Sun emits some 10^38 of them every second. In fact, the background model used by XENON includes 220 neutrino-induced events in the 1-210 keV range. However, in the standard picture, the interactions of neutrinos with electrons are too weak to explain the excess. To that end one has to either increase their flux (so fiddle with the solar model), or to increase their interaction strength with matter (so go beyond the Standard Model). For example, neutrinos could interact with electrons via a photon intermediary. While neutrinos do not have an electric charge, uncharged particles can still couple to photons via dipole or higher-multipole moments. It is possible that new physics (possibly the same that generates the neutrino masses) also pumps up the neutrino magnetic dipole moment. This can be described in a model-independent way by adding a non-renormalizable dimension-7 operator to the Standard Model, e.g.

To explain the XENON excess we need d of order 10^-6. That mean new physics responsible for the dipole moment must be just behind the corner, below 100 TeV or so.

How confident should we be that it's new physics? Experience has shown again and again that anomalies in new physics searches have, with a very large confidence, a mundane origin that does not involve exotic particles or interactions. In this case, possible explanations are, in order of likelihood, 1) small contamination of the detector, 2) some other instrumental effect that the collaboration hasn't thought of, 3) the ghost of Roberto Peccei, 4) a genuine signal of new physics. In fact, the collaboration itself is hedging for the first option, as they cannot exclude the presence of a small amount of tritium in the detector, which would produce a signal similar to the observed excess. Moreover, there are a few orange flags for the new physics interpretation:

Simplest models explaining the excess are excluded by astrophysical observations. If axions can be produced in the Sun at the rate suggested by the XENON result, they can be produced at even larger rates in hotter stars, e.g. in red giants or white dwarfs. This would lead to excessive cooling of these stars, in conflict with observations. The upper limit on the axion-electron coupling g from red giants is 3*10^-13, which is an order of magnitude less than what is needed for the XENON excess. The neutrino magnetic moment explanations faces a similar difficulty. Of course, astrophysical limits reside in a different epistemological reality; it is not unheard of that they are relaxed by an order of magnitude or disappear completely. But certainly this is something to worry about.

At a more psychological level, a small excess over a large background near a detection threshold.... sounds familiar. We've seen that before in the case of the DAMA and CoGeNT dark matter experiments, at it didn't turn out well.

The bump is at 1.5 keV, which is *twice* 750 eV.

So, as usual, more data, time, and patience is needed to verify the new physics hypothesis. On the experimental side, the near future is very optimistic, with the XENONnT, LUX-ZEPLIN, and PandaX-4T experiments all jostling for position to confirm the excess and earn eternal glory. On the theoretical side, the big question is whether the stellar cooling constraints can be avoided, without too many epicycles. It would be also good to know whether the particle responsible for the XENON excess could be related to dark matter and/or to other existing anomalies, in particular to the B-meson ones. For answers, tune in to arXiv, from tomorrow on.

After today's update from the XENON1T experiment, the situation on the front of direct detection of WIMP dark matter is as follows

WIMP can be loosely defined as a dark matter particle with mass in the 1 GeV - 10 TeV range and significant interactions with ordinary matter. Historically, WIMP searches have stimulated enormous interest because this type of dark matter can be easily realized in models with low scale supersymmetry. Now that we are older and wiser, many physicists would rather put their money on other realizations, such as axions, MeV dark matter, or primordial black holes. Nevertheless, WIMPs remain a viable possibility that should be further explored.

To detect WIMPs heavier than a few GeV, currently the most successful strategy is to use huge detectors filled with xenon atoms, hoping one of them is hit by a passing dark matter particle. Xenon1T beats the competition from the LUX and Panda-X experiments because it has a bigger gun tank. Technologically speaking, we have come a long way in the last 30 years. XENON1T is now sensitive to 40 GeV WIMPs interacting with nucleons with the cross section of 40 yoctobarn (1 yb = 10^-12 pb = 10^-48 cm^2). This is 6 orders of magnitude better than what the first direct detection experiment in the Homestake mine could achieve back in the 80s. Compared to the last year, the limit is better by a factor of two at the most sensitive mass point. At high mass the improvement is somewhat smaller than expected due to a small excess of events observed by XENON1T, which is probably just a 1 sigma upward fluctuation of the background.

What we are learning about WIMPs is how they can (or cannot) interact with us. Of course, at this point in the game we don't see qualitative progress, but rather incremental quantitative improvements. One possible scenario is that WIMPs experience one of the Standard Model forces, such as the weak or the Higgs force. The former option is strongly constrained by now. If WIMPs had interacted in the same way as our neutrino does, that is by exchanging a Z boson, it would have been found in the Homestake experiment. Xenon1T is probing models where the dark matter coupling to the Z boson is suppressed by a factor cχ ~ 10^-3 - 10^-4 compared to that of an active neutrino. On the other hand, dark matter could be participating in weak interactions only by exchanging W bosons, which can happen for example when it is a part of an SU(2) triplet. In the plot you can see that XENON1T is approaching but not yet excluding this interesting possibility. As for models using the Higgs force, XENON1T is probing the (subjectively) most natural parameter space where WIMPs couple with order one strength to the Higgs field.

And the arms race continues. The search in XENON1T will go on until the end of this year, although at this point a discovery is extremely unlikely. Further progress is expected on a timescale of a few years thanks to the next generation xenon detectors XENONnT and LUX-ZEPLIN, which should achieve yoctobarn sensitivity. DARWIN may be the ultimate experiment along these lines, in the sense that there is no prefix smaller than yocto it will reach the irreducible background from atmospheric neutrinos, after which new detection techniques will be needed. For dark matter mass closer to 1 GeV, several orders of magnitude of pristine parameter space will be covered by the SuperCDMS experiment. Until then we are kept in suspense. Is dark matter made of WIMPs? And if yes, does it stick above the neutrino sea?

The experimental situation in neutrino physics is confusing. One one hand, a host of neutrino experiments has established a consistent picture where the neutrino mass eigenstates are mixtures of the 3 Standard Model neutrino flavors νe, νμ, ντ. The measured mass differences between the eigenstates are Δm12^2 ≈ 7.5*10^-5 eV^2 and Δm13^2 ≈ 2.5*10^-3 eV^2, suggesting that all Standard Model neutrinos have masses below 0.1 eV. That is well in line with cosmological observations which find that the radiation budget of the early universe is consistent with the existence of exactly 3 neutrinos with the sum of the masses less than 0.2 eV. On the other hand, several rogue experiments refuse to conform to the standard 3-flavor picture. The most severe anomaly is the appearance of electron neutrinos in a muon neutrino beam observed by the LSND and MiniBooNE experiments.

This story begins in the previous century with the LSND experiment in Los Alamos, which claimed to observe νμ→νe antineutrino oscillations with 3.8σ significance. This result was considered controversial from the very beginning due to limitations of the experimental set-up. Moreover, it was inconsistent with the standard 3-flavor picture which, given the masses and mixing angles measured by other experiments, predicted that νμ→νe oscillation should be unobservable in short-baseline (L ≼ km) experiments. The MiniBooNE experiment in Fermilab was conceived to conclusively prove or disprove the LSND anomaly. To this end, a beam of mostly muon neutrinos or antineutrinos with energies E~1 GeV is sent to a detector at the distance L~500 meters away. In general, neutrinos can change their flavor with the probability oscillating as P ~ sin^2(Δm^2 L/4E). If the LSND excess is really due to neutrino oscillations, one expects to observe electron neutrino appearance in the MiniBooNE detector given that L/E is similar in the two experiments. Originally, MiniBooNE was hoping to see a smoking gun in the form of an electron neutrino excess oscillating as a function of L/E, that is peaking at intermediate energies and then decreasing towards lower energies (possibly with several wiggles). That didn't happen. Instead, MiniBooNE finds an excess increasing towards low energies with a similar shape as the backgrounds. Thus the confusion lingers on: the LSND anomaly has neither been killed nor robustly confirmed.

In spite of these doubts, the LSND and MiniBooNE anomalies continue to arouse interest. This is understandable: as the results do not fit the 3-flavor framework, if confirmed they would prove the existence of new physics beyond the Standard Model. The simplest fix would be to introduce a sterile neutrino νs with the mass in the eV ballpark, in which case MiniBooNE would be observing the νμ→νs→νe oscillation chain. With the recent MiniBooNE update the evidence for the electron neutrino appearance increased to 4.8σ, which has stirred some commotion on Twitter and in the blogosphere. However, I find the excitement a bit misplaced. The anomaly is not really new: similar results showing a 3.8σ excess of νe-like events were already published in 2012. The increase of the significance is hardly relevant: at this point we know anyway that the excess is not a statistical fluke, while a systematic effect due to underestimated backgrounds would also lead to a growing anomaly. If anything, there are now less reasons than in 2012 to believe in the sterile neutrino origin the MiniBooNE anomaly, as I will argue in the following.

What has changed since 2012? First, there are new constraints on νe appearance from the OPERA experiment (yes, this OPERA) who did not see any excess νe in the CERN-to-Gran-Sasso νμ beam. This excludes a large chunk of the relevant parameter space corresponding to large mixing angles between the active and sterile neutrinos. From this point of view, the MiniBooNE update actually adds more stress on the sterile neutrino interpretation by slightly shifting the preferred region towards larger mixing angles... Nevertheless, a not-too-horrible fit to all appearance experiments can still be achieved in the region with Δm^2~0.5 eV^2 and the mixing angle sin^2(2θ) of order 0.01.

Next, the cosmological constraints have become more stringent. The CMB observations by the Planck satellite do not leave room for an additional neutrino species in the early universe. But for the parameters preferred by LSND and MiniBooNE, the sterile neutrino would be abundantly produced in the hot primordial plasma, thus violating the Planck constraints. To avoid it, theorists need to deploy a battery of tricks (for example, large sterile-neutrino self-interactions), which makes realistic models rather baroque.

But the killer punch is delivered by disappearance analyses. Benjamin Franklin famously said that only two things in this world were certain: death and probability conservation. Thus whenever an electron neutrino appears in a νμ beam, a muon neutrino must disappear. However, the latter process is severely constrained by long-baseline neutrino experiments, and recently the limits have been further strengthened thanks to the MINOS and IceCube collaborations. A recent combination of the existing disappearance results is available in this paper. In the 3+1 flavor scheme, the probability of a muon neutrino transforming into an electron one in a short-baseline experiment is

where U is the 4x4 neutrino mixing matrix. The Uμ4 matrix elements controls also the νμ survival probability

The νμ disappearance data from MINOS and IceCube imply |Uμ4|≼0.1, while |Ue4|≼0.25 from solar neutrino observations. All in all, the disappearance results imply that the effective mixing angle sin^2(2θ) controlling the νμ→νs→νe oscillation must be much smaller than 0.01 required to fit the MiniBooNE anomaly. The disagreement between the appearance and disappearance data had already existed before, but was actually made worse by the MiniBooNE update.

So the hypothesis of a 4th sterile neutrino does not stand scrutiny as an explanation of the MiniBooNE anomaly. It does not mean that there is no other possible explanation (more sterile neutrinos? non-standard interactions? neutrino decays?). However, any realistic model will have to delve deep into the crazy side in order to satisfy the constraints from other neutrino experiments, flavor physics, and cosmology. Fortunately, the current confusing situation should not last forever. The MiniBooNE photon background from π0 decays may be clarified by the ongoing MicroBooNE experiment. On the timescale of a few years the controversy should be closed by the SBN program in Fermilab, which will add one near and one far detector to the MicroBooNE beamline. Until then... years of painful experience have taught us to assign a high prior to the Standard Model hypothesis. Currently, by far the most plausible explanation of the existing data is an experimental error on the part of the MiniBooNE collaboration.

In the particle world the LHC still attracts the most attention, but in parallel there is ongoing progress at the low-energy frontier. A new episode in that story is the Qweak experiment in Jefferson Lab in the US, which just published their final results. Qweak was shooting a beam of 1 GeV electrons on a hydrogen (so basically proton) target to determine how the scattering rate depends on electron's polarization. Electrons and protons interact with each other via the electromagnetic and weak forces. The former is much stronger, but it is parity-invariant, i.e. it does not care about the direction of polarization. On the other hand, since the classic Wu experiment in 1956, the weak force is known to violate parity. Indeed, the Standard Model postulates that the Z boson, who mediates the weak force, couples with different strength to left- and right-handed particles. The resulting asymmetry between the low-energy electron-proton scattering cross sections of left- and right-handed polarized electrons is predicted to be at the 10^-7 level. That has been experimentally observed many times before, but Qweak was able to measure it with the best precision to date (relative 4%), and at a lower momentum transfer than the previous experiments.

What is the point of this exercise? Low-energy parity violation experiments are often sold as precision measurements of the so-called Weinberg angle, which is a function of the electroweak gauge couplings - the fundamental parameters of the Standard Model. I don't like too much that perspective because the electroweak couplings, and thus the Weinberg angle, can be more precisely determined from other observables, and Qweak is far from achieving a competing accuracy. The utility of Qweak is better visible in the effective theory picture. At low energies one can parameterize the relevant parity-violating interactions between protons and electrons by the contact term

where v ≈ 246 GeV, and QW is the so-called weak charge of the proton. Such interactions arise thanks to the Z boson in the Standard Model being exchanged between electrons and quarks that make up the proton. At low energies, the exchange diagram is well approximated by the contact term above with QW = 0.0708 (somewhat smaller than the "natural" value QW ~ 1 due to numerical accidents making the Z boson effectively protophobic). The measured polarization asymmetry in electron-proton scattering can be re-interpreted as a determination of the proton weak charge: QW = 0.0719 ± 0.0045, in perfect agreement with the Standard Model prediction.

New physics may affect the magnitude of the proton weak charge in two distinct ways. One is by altering the strength with which the Z boson couples to matter. This happens for example when light quarks mix with their heavier exotic cousins with different quantum numbers, as is often the case in the models from the Randall-Sundrum family. More generally, modified couplings to the Z boson could be a sign of quark compositeness. Another way is by generating new parity-violating contact interactions between electrons and quarks. This can be a result of yet unknown short-range forces which distinguish left- and right-handed electrons. Note that the observation of lepton flavor violation in B-meson decays can be interpreted as a hint for existence of such forces (although for that purpose the new force carriers do not need to couple to 1st generation quarks). Qweak's measurement puts novel limits on such broad scenarios. Whatever the origin, simple dimensional analysis allows one to estimate the possible change of the proton weak charge as

where M* is the mass scale of new particles beyond the Standard Model, and g* is their coupling strength to matter. Thus, Qweak can constrain new weakly coupled particles with masses up to a few TeV, or even 50 TeV particles if they are strongly coupled to matter (g*～4π).

What is the place of Qweak in the larger landscape of precision experiments? One can illustrate it by considering a simple example where heavy new physics modifies only the vector couplings of the Z boson to up and down quarks. The best existing constraints on such a scenario are displayed in this plot:

From the size of the rotten egg region you see that the Z boson couplings to light quarks are currently known with a per-mille accuracy. Somewhat surprisingly, the LEP collider, which back in the 1990s produced tens of millions of Z boson to precisely study their couplings, is not at all the leader in this field. In fact, better constraints come from precision measurements at very low energies: pion, kaon, and neutron decays, parity-violating transitions in cesium atoms, and the latest Qweak results which make a difference too. The importance of Qweak is even more pronounced in more complex scenarios where the parameter space is multi-dimensional.

Qweak is certainly not the last salvo on the low-energy frontier. Similar but more precise experiments are being prepared as we read (I wish the follow up were called SuperQweak, or SQweak in short). Who knows, maybe quarks are made of more fundamental building blocks at the scale of ~100 TeV, and we'll first find it out thanks to parity violation at very low energies.

Two months ago an experiment in Berkeley announced a new ultra-precise measurement of the fine structure constant α using interferometry techniques. This wasn't much noticed because the paper is not on arXiv, and moreover this kind of research is filed under metrology, which is easily confused with meteorology. So it's worth commenting on why precision measurements of α could be interesting for particle physics. What the Berkeley group really did was to measure the mass of the cesium-133 atom, achieving the relative accuracy of 4*10^-10, that is 0.4 parts par billion (ppb). With that result in hand, α can be determined after a cavalier rewriting of the high-school formula for the Rydberg constant:

Everybody knows the first 3 digits of the Rydberg constant, Ry≈13.6 eV, but actually it is experimentally known with the fantastic accuracy of 0.006 ppb, and the electron-to-atom mass ratio has also been determined precisely. Thus the measurement of the cesium mass can be translated into a 0.2 ppb measurement of the fine structure constant: 1/α=137.035999046(27).

You may think that this kind of result could appeal only to a Pythonesque chartered accountant. But you would be wrong. First of all, the new result excludes α = 1/137 at 1 million sigma, dealing a mortal blow to the field of epistemological numerology. Perhaps more importantly, the result is relevant for testing the Standard Model. One place where precise knowledge of α is essential is in calculation of the magnetic moment of the electron. Recall that the g-factor is defined as the proportionality constant between the magnetic moment and the angular momentum. For the electron we have Experimentally, ge is one of the most precisely determined quantities in physics, with the most recent measurement quoting ae = 0.00115965218073(28), that is 0.0001 ppb accuracy on ge, or 0.2 ppb accuracy on ae. In the Standard Model, ge is calculable as a function of α and other parameters. In the classical approximation ge=2, while the one-loop correction proportional to the first power of α was already known in prehistoric times thanks to Schwinger. The dots above summarize decades of subsequent calculations, which now include O(α^5) terms, that is 5-loop QED contributions! Thanks to these heroic efforts (depicted in the film For a Few Diagrams More - a sequel to Kurosawa's Seven Samurai), the main theoretical uncertainty for the Standard Model prediction of ge is due to the experimental error on the value of α. The Berkeley measurement allows one to reduce the relative theoretical error on ae down to 0.2 ppb: ae = 0.00115965218161(23), which matches in magnitude the experimental error and improves by a factor of 3 the previous prediction based on the α measurement with rubidium atoms.

At the spiritual level, the comparison between the theory and experiment provides an impressive validation of quantum field theory techniques up to the 13th significant digit - an unimaginable theoretical accuracy in other branches of science. More practically, it also provides a powerful test of the Standard Model. New particles coupled to the electron may contribute to the same loop diagrams from which ge is calculated, and could shift the observed value of ae away from the Standard Model predictions. In many models, corrections to the electron and muon magnetic moments are correlated. The latter famously deviates from the Standard Model prediction by 3.5 to 4 sigma, depending on who counts the uncertainties. Actually, if you bother to eye carefully the experimental and theoretical values of ae beyond the 10th significant digit you can see that they are also discrepant, this time at the 2.5 sigma level. So now we have two g-2 anomalies! In a picture, the situation can be summarized as follows:

If you're a member of the Holy Church of Five Sigma you can almost preach an unambiguous discovery of physics beyond the Standard Model. However, for most of us this is not the case yet. First, there is still some debate about the theoretical uncertainties entering the muon g-2 prediction. Second, while it is quite easy to fit each of the two anomalies separately, there seems to be no appealing model to fit both of them at the same time. Take for example the very popular toy model with a new massive spin-1 Z' boson (aka the dark photon) kinetically mixed with the ordinary photon. In this case Z' has, much like the ordinary photon, vector-like and universal couplings to electron and muons. But this leads to a positive contribution to g-2, and it does not fit well the ae measurement which favors a new negative contribution. In fact, the ae measurement provides the most stringent constraint in part of the parameter space of the dark photon model. Conversely, a Z' boson with purely axial couplings to matter does not fit the data as it gives a negative contribution to g-2, thus making the muon g-2 anomaly worse. What might work is a hybrid model with a light Z' boson having lepton-flavor violating interactions: a vector coupling to muons and a somewhat smaller axial coupling to electrons. But constructing a consistent and realistic model along these lines is a challenge because of other experimental constraints (e.g. from the lack of observation of μ→eγ decays). Some food for thought can be found in this paper, but I'm not sure if a sensible model exists at the moment. If you know one you are welcome to drop a comment here or a paper on arXiv.

More excitement on this front is in store. The muon g-2 experiment in Fermilab should soon deliver first results which may confirm or disprove the muon anomaly. Further progress with the electron g-2 and fine-structure constant measurements is also expected in the near future. The biggest worry is that, if the accuracy improves by another two orders of magnitude, we will need to calculate six loop QED corrections...

If you’re wanting to learn some applied category theory, register for the tutorials that are taking place on July 5, 2020 as part of ACT2020!

More details follow….

Applied category theory offers a rigorous mathematical language and toolset for relating different concepts from across math, science, and technology. For example, category theory finds common patterns between geometry (shapes), algebra (equations), numbers, logic, probability, etc. Applied category theory (ACT) looks for how those very same patterns extend outward to data, programs, processes, physics, linguistics, and so on—things we see in the real world. The field is currently growing, as new applications and common patterns are being found all the time. When you understand these ideas, more of your intuitions about the world can be made rigorous and thus be communicated at a larger scale. This in turn gives our community a chance to solve larger and more complex scientific, technological, and maybe even societal problems.

This year’s international applied category theory conference ACT2020 is having a tutorial day, meant to introduce newcomers to applied category theory. Tutorial day will take place on July 5 and will include a few main topics that will be taught semi-traditionally (via presentation, exercises, and discussion) over Zoom, as well as mentors who will be available throughout the day to work with smaller groups and/or individuals. We invite you to sign up here if you’re interested, so we can keep you posted. Hope to see you there!

The four courses will be roughly as follows:

David Spivak: categorical databases for introducing sets, functions, categories, and functors.

Fabrizio Genovese: string diagrams as a graphical language for category theory.

Emily Riehl: the Yoneda lemma in the category of matrices.

If you’re wanting to learn some applied category theory, register for the tutorials that are taking place on July 5, 2020 as part of ACT2020!

Applied category theory offers a rigorous mathematical language and toolset for relating different concepts from across math, science, and technology. For example, category theory finds common patterns between geometry (shapes), algebra (equations), numbers, logic, probability, etc. Applied category theory (ACT) looks for how those very same patterns extend outward to data, programs, processes, physics, linguistics, and so on—things we see in the real world. The field is currently growing, as new applications and common patterns are being found all the time. When you understand these ideas, more of your intuitions about the world can be made rigorous and thus be communicated at a larger scale. This in turn gives our community a chance to solve larger and more complex scientific, technological, and maybe even societal problems.

This year’s international applied category theory conference ACT2020 is having a tutorial day, meant to introduce newcomers to applied category theory. Tutorial day will take place on July 5 and will include a few main topics that will be taught semi-traditionally (via presentation, exercises, and discussion) over Zoom, as well as mentors who will be available throughout the day to work with smaller groups and/or individuals. We invite you to sign up here if you’re interested, so we can keep you posted. Hope to see you there!

The four courses will be roughly as follows:

• David Spivak: categorical databases for introducing sets, functions, categories, and functors.

• Fabrizio Genovese: string diagrams as a graphical language for category theory.

• Emily Riehl: the Yoneda lemma in the context of matrices.

Seit heute gibt es sie, die Corona-Warn-App, und ihr könnt (und solltet, siehe unten) sie herunterladen und installieren.

Das ist die kurze Nachricht. Sie hätte auch in einen Tweet gepasst. Warum noch ein Blogpost? Das liegt daran, dass viele Bedenken gegen diese App kursieren und andererseits niemand (insbesondere nicht der CCC) sagt "Alles Quatsch, die App ist sicher!". Diese Situation würde ich gerne etwas erklären.

Das fängt mit einem Mantra an, dass seit Jahren hergebetet wird: "Sicherheit (im Sinn von Security) ist kein Zustand, sondern ein Prozess". Jede Software, deren Komplexität wesentlich über

10 PRINT "HALLO"

20 GOTO 10

hinaus geht, wird Bugs haben. Ich zitiere gerne eine alte IBM Studie, die besagt, dass es praktisch nicht gelingt, weniger als 1 Bug pro etwa 10.000 Zeilen Code zu haben, weil man, wenn man den Code weiter versucht zu debuggen und testen, dabei mehr Fehler einbaut als man eliminiert. Selbst der NASA, die sich da sehr viel Mühe gibt, fallen regelmässig Raumsonden wegen Softwarefehlern hart auf Planetenoberflächen. Und das sicher nicht, weil die leichtfertig waren.

Daher kann es nur darum gehen, möglichst wenig Fehler zu produzieren (mit entsprechenden Tests, Audits, Software-Werkzeugen, die einem helfen etc). Aber niemand, der weiss, was er tut, wird garantieren können, dass man alles gefunden hat. Man kann nur dokumentieren, dass man sich Mühe gegeben hat und dabei nach best practices gehandelt hat. Und vor allem: Wenn dann doch ein Fehler auftaucht, muss man die entsprechende Fehlerkultur haben und ihn schnell und effektiv beseitigen. Besser geht's leider nicht. Die Alternative ist nur, keine Computer bzw keine Software zu benutzen.

Und weil Leute, die wissen, wovon sie reden, genau diesen Umstand kennen, lassen sie sich nicht dazu verleiten "Die App habe ich geprüft, sie ist sicher" öffentlich zu sagen.

Was man aber sehr wohl feststellen kann, ist wenn etwas unsicher ist und man eine Lücke gefunden hat. Und das wird ja auch regelmäßig gemacht und auch der CCC hält sich nicht zurück, über Probleme öffentlich zu reden, wenn man sie denn gefunden hat (responsible disclosure beachtend), wie zB in der jüngsten Vergangenheit beim Telematix-Netzwerk im Gesundheitswesen.

Was man sehr wohl hören sollte, ist dass man genau sowas über die Corona-Warn-App zumindest bisher nicht hört. Es gibt sehr wohl die 10 Prüfsteine für eine solche App und am Anfang sah es nicht so aus, als würden sie eingehalten (zB zentrale Serverstruktur, closed source), aber an dieser Stelle beschwert sich momentan niemand. Vielmehr gibt es viel Lob, dass auf Kritik reagiert wurde: Es werden die Kontaktdaten nur lokal auf den Telefonen gespeichert (auch schon weil Apple und Google dies als sinnvoll eingesehen haben und es nicht wirklich eine App gegen die entsprechenden Betriebsystemhersteller gegeben hätte, schon alleine weil die die Betriebssysteme es aus Securitygründen Apps nicht einfach erlauben, dauerhaft und im Hintergrund Bluetooth zu verwenden) und der Source-Code zusammen mit der Entwicklungsgeschichte wurde öffentlich auf GitHub zur öffentlichen Überprüfung zugänglich gemacht. Und die Öffentlichkeit hat tatsächlich Probleme gefunden. Aber diese wurden nicht ignoriert, sondern behoben.

Und genau das ist der Prozess, von dem ich oben sprach. Den darf man auch gerne mal loben und sagen "so soll's sein, gerne wieder". Und das wird ja auch getan. Man muss dem eben nur zuhören und verstehen (was leider nicht so richtig kommuniziert wird), dass dieses Lob eigentlich die bessere Variante des "Zertifikat: die App ist sicher" ist. Hier ist leider das Schweigen nicht laut genug, das "nicht geschimpft ist genug gelobt" ist leider nicht sehr öffentlichkeitswirksam, bzw bedarf einer Erklärung, wie ich sie hier versuche. Update: Linus Neumann, CCC Sprecher, macht es doch.

"Aber es gibt doch Kritikpunkte" höre ich Euch sagen. Ja, die gibt es. Aber schauen wir sie uns an, ob die von ihnen ausgehende Gefahr den möglichen Nutzen der App übersteigen kann:

"Ich muss Bluetooth anschalten, das hatte schon Lücken in der Vergangenheit." Stimmt. Gilt aber auch für Wifi/Internet. Wenn man sich darum sorgt, empfehle ich das Handy abzuschaffen. Update: Bei Android-Smartphones, die nicht gegen bekannte Probleme gepatched werden können (Android Update nach 1. Februar 2020), ist es vielleicht doch keine gute Idee, Bluetooth einzuschalten. Kann man aber drüber nachdenken, ob das ein Problem der App oder des Smartphones ist.

"Die App ist open source, aber was ist mit der Library von Apple/Google?". Stimmt auch. Gilt aber auch für das Betriebssystem des Handys. Wenn Apple/Google euch überwachen wollen und eure Daten raustragen wollen, können sie das nicht erst seit der App. Sondern seit ihr ein Handy benutzt. Also wieder besser: Handy in den Shredder.

"Wenn nicht viele die App benutzen, nützt sie nichts" (oder auch in der Version "die App ist nicht verpflichtend, so kann sie nicht funktionieren, also benutze ich sie nicht"). Ja. Henne und Ei. Dann benutz sie doch. Ist wieder ein Beispiel des Gefangenendilemmas, kann man ändern indem man selber kooperiert und hofft, dass die anderen zum gleichen Schluss kommen.

Bleibt noch eine Meta-Frage: Ich möchte eigentlich diese ganze Geschichte auch als eine Erfolgsgeschichte des CCC abbuchen, man hat (nehmen wir mal an, es hat tatsächlich einen Einfluss gehabt) echte Verbesserungen erreichen können. Vor allem wenn man sich vor Augen führt, was am Anfang der Geschichte vorgeschlagen wurde, wie GPS-tracking, eine zentrale, staatliche Kontaktdatenbank etc. Der Umstand, dass hier auf die Expertise gehört wird, ist auch ein langfristiger Erfolg, es wurde verstanden, sich über die Jahre als kompetenter und kritischer Beobachter zu etablieren. Die Öffentlichkeit wurde für entsprechende Themen hellhörig gemacht.

Andererseits lese ich auf social media viel Kritik an der App und Erklärungen, warum sie böse ist oder warum man sie sich selber auf keinen Fall installieren will. Die halbwegs rationalen Einwände habe ich eben aufgezählt (auch wenn meine Kosten-Nutzen-Abwegung klar anders ist und ich first thing this morning mir die App installiert habe), es gibt aber auch unendlich viel, was sich im Spektrum Halbwissen bis Aluhuttum bewegt. Es werden viele Bedenken geäussert, die aber eher aus dem Bauch kommen (der Staat will uns Stasi-mässig überwachen) aber aus technischer Sicht nach allem, was man weiss, nicht haltbar sind. Und irgendwie fürchte ich, dass viele von diesen Leuten auch von CCC und Co in ihrer kritischen Sicht mitsozialisiert worden sind und irgendwann falsch abgebogen sind.

Und das ist dann schon ein Wermutstropfen bzw eine Aufgabe für die Zukunft: Wie schafft man es, vor allem auch in seiner Kommunikation, noch deutlicher die begründeten von den unbegründeten Bedenken (die aber so ähnlich klingen) zu trennen? Wie kann man hier offensiver seine Sicht kommunizieren ohne in ein "Wir versprechen Euch, ist alles sicher" verfallen zu müssen? Dieser Text ist jedenfalls ein Versuch in diese Richtung.

Und noch der nötige Disclaimer: Ich bin zwar Mitglied beim CCC (sowohl in München als auch schweigendes im Bundes-CCC). Ich spreche aber nicht für den Club. Dies ist nur meine Meinung (die aber aus meiner Sicht natürlich jedeR teilen sollte, auch alle Clubs der Welt. Haha)

As a spinoff of the workshop Categorical Probability and Statistics, Oliver Shetler has organized a reading group on category theory applied to statistics. The first meeting is Saturday June 27th at 17:00 UTC.

Here is a reading list. I’m sure the group won’t cover all these papers—we’ll start with the first one and see how it goes from there. But it’s certainly helpful to have a list like this.

Fundamental science works by alternating phases of interpretation and refutation. When interpreting the result of experiments, physicists spend their time sweating shirt after shirt in the attempt of formulating economical and coherent explanations of observed phenomena. If the process converges, they formulate a theory which works well, whereby they celebrate for a little while. Then a second phase starts, when hypotheses are formulated on how to refute the shiny new model, finding effects and observatons that do not fit in the formulated framework. And so on.

I was supposed to turn in a manuscript for my new (general-audience book) last week. It’s not finished. But I’ve written a lot of it during the pandemic. Of course it is very hard to be “productive” in the usual way, with the kids here all day. But being in the house all day is somehow the right setup for book-writing, maybe because it so clearly separates life now from my usual life where I am neither staying in the house nor writing a book.

I think the pages I’m putting out are good. As usual, the process of writing is causing me to learn new things faster than I can put them in the book and indeed there is now too much material to actually go in the book, but that means, at any rate, I can be selective and pick just the best.

Pivoting back toward science by way of technology.... Some very large fraction of the microphones out there in electronic gadgets are based on electrets. An electret is an insulating material with a locked-in electrical polarization - for example, take a molten or solvated polymer, embed highly polar molecules in there, and solidify in the presence of a large polarizing electric field. The electrical polarization means that there is an effective surface charge density. You can make that electret into a free-standing foil or a film coating a backing to make a diaphragm. When that film vibrates, it will generate an oscillating voltage on a nearby electrode (which could, say, be the gate electrode of a field-effect transistor). Voila - a microphone that is simple, readily manufacturable, and doesn't need an external power supply.

While electret microphones are losing some marketshare to microelectromechanical ones in things like airpods, they've played a huge part in now ubiquitous phone and acoustic technologies in the late 20th and early 21st centuries. When I was a postdoc I was fortunate one day to meet their coinventor, James West, who was still at Bell Labs, when (if I recall correctly) his summer student gave a presentation on some lead-free ultra-adhesive solder they were working on. He was still patenting inventions within the last two years, in his late 80s - impressive!

After three videos in a row about quantum field theory, we bring things a bit more down to earth by talking about the sizes of things. Mostly about particles and atoms; the sizes of people and planets will have to come later.

Scientific programming was in the news lately, when doubts were raised about a coronavirus simulation by researchers at Imperial College London. While the doubts appear to have been put to rest, doing so involved digging through some seriously messy code. The whole situation seems to have gotten a lot of people worried. If these people are that bad at coding, why should we trust their science?

I don’t know much about coronavirus simulations, my knowledge there begins and ends with a talk I saw last month. But I know a thing or two about bad scientific code, because I write it. My code is atrocious. And I’ve seen published code that’s worse.

Why do scientists write bad code?

In part, it’s a matter of training. Some scientists have formal coding training, but most don’t. I took two CS courses in college and that was it. Despite that lack of training, we’re expected and encouraged to code. Before I took those courses, I spent a summer working in a particle physics lab, where I was expected to pick up the C++-based interface pretty much on the fly. I don’t think there’s another community out there that has as much reason to code as scientists do, and as little training for it.

Would it be useful for scientists to have more of the tools of a trained coder? Sometimes, yeah. Version control is a big one, I’ve collaborated on papers that used Git and papers that didn’t, and there’s a big difference. There are coding habits that would speed up our work and lead to fewer dead ends, and they’re worth picking up when we have the time.

But there’s a reason we don’t prioritize “proper coding”. It’s because the things we’re trying to do, from a coding perspective, are really easy.

What, code-wise, is a coronavirus simulation? A vector of “people”, really just simple labels, all randomly infecting each other and recovering, with a few parameters describing how likely they are to do so and how long it takes. What do I do, code-wise? Mostly, giant piles of linear algebra.

These are not some sort of cutting-edge programming tasks. These are things people have been able to do since the dawn of computers. These are things that, when you screw them up, become quite obvious quite quickly.

Compared to that, the everyday tasks of software developers, like making a reliable interface for users, or efficient graphics, are much more difficult. They’re tasks that really require good coding practices, that just can’t function without them.

For us, the important part is not the coding itself, but what we’re doing with it. Whatever bugs are in a coronavirus simulation, they will have much less impact than, for example, the way in which the simulation includes superspreaders. Bugs in my code give me obviously wrong answers, bad scientific assumptions are much harder for me to root out.

There’s an exception that proves the rule here, and it’s that, when the coding task is actually difficult, scientists step up and write better code. Scientists who want to run efficiently on supercomputers, who are afraid of numerical error or need to simulate on many scales at once, these people learn how to code properly. The code behind the LHC still might be jury-rigged by industry standards, but it’s light-years better than typical scientific code.

I get the furor around the Imperial group’s code. I get that, when a government makes a critical decision, you hope that their every input is as professional as possible. But without getting too political for this blog, let me just say that whatever your politics are, if any of it is based on science, it comes from code like this. Psychology studies, economic modeling, polling…they’re using code, and it’s jury-rigged to hell. Scientists just have more important things to worry about.

Upon coming back online in the midst of camping — wondering which irritating telemarketing firm was pestering me with 27 missed calls and messages — I was completely devastated to learn that one of my closest friends (in our own weird, highly neuro-atypical kinda way), collaborators and mentors — both in academia and in life — Prof Jonathan Dowling, had unexpectedly passed away, whose impact on the world of physics, quantum technology in particular, but most of all upon those with whom he worked — and touched — has been profound. His passing has sent shockwaves through the international scientific community. Jon was, and will remain, one of the most influential people in my life. I know many others can say the same.

Originally I was planning to stay in the camp today, but upon learning this news, instead climbed a nearby peak to erect the most appropriate tribute to Jon I could improvise at the time. Behind the empty bottle of gin (my apologies Jon, the whiskey was still half-full), you will see the Siding Spring Observatory on a nearby mountaintop, which I hope tonight will see a new star in the sky, as he and George Floyd look down from above, both incredibly proud of the American economy*.

*Quick tangent for context: the previous day a woman camping with her son emerged from their tent, saying “My god, did you guys hear that megalomaniac narcissist lunatic wandering around the campsite in pitch black at 5am this morning talking about how good he is, intermittently laughing hysterically? What a complete fucking tool!”. Me: “Oh sorry, that was me and James reading the latest Whitehouse Press interview from CNN. My apologies if you thought you were about to get murdered.” (FYI: she took it pretty well, and saw the humour in it. Not sure about the son.)

The Dowling Tome of the Warrumbungles (geocached at: 31º17’3” S, 148º59’3” E, 760m asl).

Inside the bottle, is a handwritten message, of the most profound and insightful wisdom Jon ever bestowed upon me — of which there is far too much to recall. I geocached the bottle, cunningly hidden away on the summit plateau where it can’t be seen to the naked eye, for someone else to discover (coordinates: 31º17’3” S, 148º59’3” E, 760m asl). I hope one day, one of Dowling’s student-grandchildren — perhaps one of my own — will discover the Dowling Tome of the Warrumbungles, revealing its wisdom for future generations of physicists, and other forms of lunatic, to come. If not, future archeologists will one day uncover it, date it, and ask themselves what primitive species of the distant archeological past would write such incoherent, obviously drunken Irish nonsense.

My friendship and connection with Dowling is a unique one — I think most fond of him can say the same, from their own perspective. Our prisms through which to view the world were so distinct that they provide quite alternate realities within which we respectively live: on one hand highly concentrated from a specific perspective, routine, and way of life, with strict comfort zones and patterns of behaviour; on the other, willy-nilly all over the fucking shop. The fact that such orthogonal lenses through which to view reality, nonetheless demonstrating absolute and respectful recognition for one another — not seeing it as a weakness, but as a strength — is testament to the open-mindedness and inclusivity of both. I think Jon and I would both agree that neuro-diversity is the most important, yet most undervalued form of diversity that exists (it encompasses all the rest).

Jon and I saw the world from opposing ends of the emotional spectrum, yet nonetheless, since the day we met, saw a common underlying sincerity and morality in one another. Every aspect of our world views and life experience were so utterly disparate, yet nonetheless, even at the times of most heightened disagreement, there was always the common thread of utter mutual respect for our differences, the ways in which we viewed the world, and the understanding that an outright difference in opinion should never equate to anger or hate, but rather an opportunity to learn something new. We recognised our differences, of which there were many, not as a basis for exclusion or contempt, rather one most valuable to include for the difference in perspective it has to provide. Jon was one of the few people who has seen me both at my best and at my worst: from hospitalisation to delusion. He never blinked an eye. He accepted it. We would spend all day at the whiteboard, yelling foulmouthed abuse at one another, then switch it off, retire to the pub and piss ourselves laughing about it (unlike the head administrative officer of the host institution at the time, who screamed at us that we were "a bunch of wankers", before storming off in a hissy fit because we stole the $20k digital whiteboard from the common room that'd she'd previously kicked us out of, something Dowling took utmost amusement in, and wore as yet another one of his badges of honour).

It is this anti-commutation (from the emotional perspective), yet commutation (from that of open-mindedness and inclusivity), that brought us together: this is one thing, regardless of the others, that we agreed upon, despite never having said so — the strongest bonds between us are often those we don't express. This is the most valuable lesson I have learnt from Jon (but admittedly not the one written inside the geocached bottle of gin) — that alternate views of reality, despite being potentially orthogonal and incongruent, are the most insightful, and should always be accepted, listened to, and heard: alternate realities underpin the discovery of reality, and our different ones underpinned ours. There is no individual on Earth with the intellectual or emotional capacity to single-handedly provide the unified explanation for everything, although many will pretend to. We both recognised this — the value to include all mindsets, despite the fact that one might not be capable of comprehending the other — I could never quite fully grasp his (in fact hardly at all), and he could never fully grasp mine (I don't think he even tried to, to be honest), yet nonetheless there was an absolute intellectual union between us, at some bizarre level at least. This is the kind of emotio-intellectual union I have had with very few others, and I see it for its value, as should everyone when they encounter it in life. When you lose someone with that level connection, you lose a part of yourself.

To me, Jon was the most inclusive scientist I have ever met, despite being drunk, vulgar and obnoxious much of the time. He never gave a shit about your race, religion, socio-economic class, political orientation, nationality or wealth: his vulgar obnoxiousness was completely and utterly indiscriminate, yet never intended with contempt — all he cared about was whether he believed in you as a person — whether you had the willingness, sincerity and passion to succeed, the only thing that matters, and the one thing we could always agree upon, despite it never being said — in which case you were deserving of more, not less, of his lunacy, which to him was a sign of affection.

Unfortunately his passing means he won’t see our upcoming book, The Quantum Internet, in printed form later this year via Cambridge University Press. He told me it was a pile of crap (referring to it as The Doorstop — because it’s thick and useless), and placed a bet with me (in writing), for a bottle of whiskey of Ryan Mann’s choice (up to a value of $500), that in ten years time it would be my least cited work. He makes these bets with literally everyone, and he always loses. This one was a rookie strategic miscalculation on his part (needles to say, he was completely piss-drunk at the time — not that his reasoning would necessarily be any more coherent if he weren’t), given all I’d need to do to manipulate the outcome of this one is publish a paper gaining no citations at all. “Easy!”, I thought, “I already have plenty of those!”. “You fool, Dowling!”, I smugly boasted to myself at the time, as I went around attempting to win favours from strangers in the form of future contracts by offering them shots of expensive, artisan whiskey, on the tab of one of the world’s most influential physicists, in advance. I was just so proud of myself! On this occasion, however, since he’s a co-author, the book contract is now technically invalidated. I bet the cheeky bastard had it all planned out! God dammit Dowling — was this really necessary, even by our standard of pranksterism (which I acknowledge has significantly devolved to the point of utopia in recent years)? I hope the bottle Ryan had in mind was a bloody good one.

My sense of loss right now is nothing short of catastrophic. But so too is my gratitude for having had a character as unique and impactful as Dowling in my life, which I will continue to despite his passing.

On the last day of his most recent visit here, he made some security arrangements at the last minute, for reasons I can't go into, on the basis of a presumed threat to his life. His characteristically unfiltered way of explaining his reasoning for that decision ("Peter, I'm still worried he's going to turn up at one of my lectures with a gun") triggered a rapid sequence of events that I retrospectively believed saved my own.

Those larger than life never die, of whom Dowling is one, and are certainly never forgotten. And although my heart is bleeding right now, I know he lives on — not in some bullshit metaphysical sense (the kind of thing he overtly despises, see the Deepak Chopra story below; stay out of it, Keith) — but in the sense that he is one of those who in their lives permanently imparts a sense of themselves onto everyone they touch. This is not something that dies with him, or will ever be lost, rather passed on from one generation of physicists to the next. I’m grateful to have been a recipient of what he had to give, and to use Dowling’s exact words,

“There’s no need to pay it back. Pay it forward instead.”

This is something I hope to do, having recognised what I have gained from my own intellectual forefathers, who I never had the chance to meet, but nonetheless guided me every step of the way.

Wherever you are right now, Jon (hopefully surrounded by a multitude of full, wooden casks), I hope from the bottom of my heart that, as you requested, there’s an Irish cheesecake awaiting you (I think Zixin, Maria & Yuval are sorting that one out) — which I’m assuming is just an ordinary cheesecake with the bottle of expensive whiskey you just cynically conned out of me, poured over the top of it (in which case you're still not getting it for ten years, so there).

Dowling stories are de facto mandatory at this point. Here are a couple of lesser known ones.

Story: Free Speech Alley

The first time I visited Jon at LSU, we ate at the group's regular lunch hangout. The walk back to the department goes via Free Speech Alley, which Jon told me was a designated area on campus where everyone had the right to stand on their soapbox and engage in free speech. I was shocked. How can they have a 'designated area' for free speech? This is the land of free speech! My shock was further exacerbated when Jon explained that firearms were allowed (everywhere) on campus. "Typical", I thought, "the bloody Republicans putting the 2nd Amendment ahead of the 1st, as usual" (Jon was anti-gun, so, recognising the constitutional right of those on campus to possess them, his out-of-the-box approach to solving the conundrum was to tell his students that although he would not violate their constitutional rights to bear arms, he would wield his and refuse to teach them if they did). The area was a bit like the Speaker's Corner in London's Hyde Park, except in Free Speech Alley it's full of fundamentalist Southern Baptists wearing poster boards with extreme religious hate content. As we walked past one young lady wearing a poster board with "Your [sic] going to hell!" written on it, she pointed at me, and yelled "I hope you're not one of those practising homosexuals!!", to which Dowling candidly yelled back "Practise makes perfect!". She had nothing to say to that (in retrospect I wish I'd shown her my Grindr profile and had a chat).

Story: Deepak Chopra's private email group

You've probably caught onto the fact that Dowling and I are magnets for crazy people by now. But even by my standards, when we both got unexpectedly added to a private email group run by Jack Sarfatti and Deepak Chopra, the level of craziness was slightly over the top (whatever you do, Deepak, please don't ever start taking drugs). Jon and I wanted out, but because it was a CC-all list, not a properly set up listserv, there was no way to unsubscribe. Dowling's strategy was to respond to every message with a limerick, with escalating absurdity, until they capitulated and removed us out of frustration. In the end it worked (but only after a formal complaint being sent to the Chancellor and Provost of LSU). Reading Deepak's cringeworthy words of wisdom was so amusing, and his momentous insights so incomprehensibly stupid and juvenile, that we simply had to look him up and learn more about him (oh, instafamous via the Oprah Winfrey Show — now I get it). We discovered there's an online Deepak Chopra Bullshit Generator, that generates random Deepak Chopra bullshit (the Generator passes the Chopra-Turing test btw). We clicked the 'bullshit' button and hit jackpot with the first randomly generated quote:

"Quantum mechanics is the modality of reckless thought",

a quote we have used regularly ever since.

Here's a highly condensed version of the (actual — yes this is real now, not bullshit) conversation with some of the key highlights (pull your bongs and mushroom pipes out):

Jon: I don't know why I'm getting all these emails but I sure wish I wasn't. On travel with only access on my smart phone and they are eating up my data plan.

Deepak Chopra: it may may be important to remember that no one knows how or if photons hitting the retina and sending an electrical current to the brain create the experience of a 3 D world appearing to evolve in time. False. The only light there is is the light of awareness that makes the formless appear as form with color shape dimensionality .

[Editor's note: Deepak what the fuck is 'color shape dimensionality'? Seriously dude, do you need an MRI?]

Jon: There once was a man from Nantucket. Who kept all his cash in a bucket. His daughter (named Nan), Ran away with a man, And as for the bucket –– Nantucket!

[Editor's note: nice.]

Deepak: Time is a concept No matter how hard you try you cannot experience a past or future. Experience is always now

[Editor's note: thanks for that, Deepak. Please use punctuation in future attempts to use a three line paragraph to explain the otherwise simple notion of "now is now".]

Jon: There once was a lady named Alice, Who used a dynamite stick as a phallus. They found her vagina, in North Carolina, And bits of her tits were in Dallas.

[Editor's note: in the field of quantum information theory, a two-party interactive protocol typically denotes the parties as 'Alice' and 'Bob', following the first two letters of the alphabet (yes, you're correct in thinking that as we extend to multi-party scenarios that we introduce C=Charlie, D=Dickhead, E=Eve, etc etc.). Evidently, Alice's decision to deploy dynamite may suggest Bob was facing some serious personal issues at the time, which undermined ordinary implementation of the two-party interactive protocol.]

Deepak Chopra: You know neural correlates of experience . No one knows how the brain or any physical matter causes experience ? The biological basis of experience or consciousness is unknown ( hard problem )

[Editor's note: no I don't. I have literally no idea what you're fucking talking about, Deepak.]

Some other physics wannabe: I would argue that the 3-D world discovered by the brain is not due to one retina hitting photons but two... If only with one, you would only perceive 2-D...

[Editor's note: ok so I'm feeling vindicated right now in my usage of the term 'wannabe'.]

Jack Sarfatti: You sound like a clueless New Age lite weight. I hope I am wrong. Have a nice day. These days it’s important to be able to filter out reliable information on the web. The wheat from the chaff.

[Editor's note: oooooh! Sarfatti comes in with burn of the century. Ouch, that's gotta hurt. <the wannabe crawls into a corner, devastated that they can't be as awesome a scientist as Jack – it's not that they didn't do the hard work, they just weren't born with the natural intellect that Jack has>]

Jon: There once was a moron named Jack, Who's pronouncements were totally whack. The lab of his mind, Produced nonsense in kind, Like smoking some unaltered crack.

[Editor's note: Jack, is there any crack leftover?]

Deepak Chopra: They are experiencing memories and emotions from the past not the past The past does not exist Reality is free of memory and imagination and is always now

[Editor's note: there will be no more editor's notes from now on, since I simply can't be fucked with this anymore.]

Some other highly ranked professor I don't know: UNSUBSCRIBE ME PLEASE NOW.

[Editor's note: backtrack one step. I agree. Carry on.]

Yet someone else: please unsubscribe me from this thread. I'll simply conclude by saying that a block world is a possible ontology for physics but not the only possible ontology. Those of you who like the block world can keep it, just don't tell me that no other ontology is possible

Deepak Chopra: Correlates of experience (NCC ) The biological basis if any of consciousness or experience is unknown It's the 2nd most open question in science The first open question in Science is "what's the universe made of ? " We neither know the nature of existence nor why or how we are aware of it

Some random dude: By the way, I think you're a pretty bright fellow. Too bright to be making sweeping pronouncements regarding everyone else's knowledge state. If you simply can't resist them, might I suggest that you at least hedge them a little? E.g., you might try prefacing them with "As far as I know," or "To the best of my knowledge," or "My personal buddies in the publishing industry are laboring under the unfounded assumption that...".

Another random dude: Without our minor misunderstanding based upon basic science and biology, how can we obtain consciousness to go to the far abroad in space?

Deepak Chopra: The brain does not observe That's an assumption That assumption is the basis of the "hard problem" The observer is dimensionless / nonlocal with a local point of view . The observed is also dimensionless but taking on the qualities of experience or qualia . The infinite observes itself as the finite . Past future and present are concepts as our space time and dimensionality What we perceive is not what is .

Someone else: UNSUBSCRIBE !!!!

Jon: There once was a douche bag named Chopra, Whose books read like fake Chinese opera. About quantum mechanics, He utterly panics, And pedals his bullshit on Oprah.

[Editor's note: here's a rendition of the Dowling interpretation of Chinese opera.]

Someone else completely random: Deepak's sentences are easy to comprehend IF you look your own mind. You can then verify his comments. But, I stress, you must look DIRECTLY at your own mind.

[Editor's note: make sure to do it DIRECTLY.]

Deepak: Time is never an experience T=0 always No one can ever experience the "past " or "future " no matter how hard they try . The only experience consciousness has is an an intermittent stream of sense perceptions, images feelings and thoughts. These are interpreted and conceptualized as space time and matter. Consciousness is that in which all experience occurs, in which all experience is known & interpreted & out of which all experience is made. The universe is consciousness U=C

[Editor's note: Deepak Chopra is cancelled.]

Jack Sarfatti:(sent to the Provost and Chancellor of LSU, and the Dean amongst others, to which there was no reply.) Who is Jonathan Dowling? Violation of Professional Ethics by Alleged Faculty Member of LSU If he really is a professor at LSU he is violating professional ethics. I suspect it is not really him?

[Editor's note: if you don't think it's really him, why would you write directly to the Provost and Chancellor of a major university to find out?]

Me: For the third time, please unsubscribe me from this list.

Jack Sarfatti: Peter I have removed u several times I never added u to begin with Write private emails to those sending mail Don't spam the whole list yourself

Me: Writing private emails to everyone on the list creates just as much spam for everyone on the list as writing to everyone on the list via writing to the list, Jack.

Jon “Dundee” Dowling, with his crocodile tooth Akubra hat.