Some time ago, I had one of those odd little thoughts that could be the spark of an essay. But in this particular case, the point I wanted to make felt like it could be made most clearly by demonstration, rather than explication. So, I wrote a concise report on “An Underappreciated Exchange in the Bohr–Einstein Debate.” Judging by the modest splash of positive e-mail that I received after posting it, I think I layered the whimsy and the serious point adequately well.
First, of course, there was the doubt and the pain.
Let’s talk about the papers I managed to get out the door and into public view. In retrospect, the list is pleasingly not insubstantial:
- Christopher A. Fuchs and BCS, Are Non-Boolean Event Structures the Precedence or Consequence of Quantum Probability? (arXiv:1912.10880) — a tribute to a colleague, written for a memorial volume but finished too late
- John B. DeBrota and BCS, Discrete Wigner Functions from Informationally Complete Quantum Measurements (arXiv:1912.07554) — technical, a sequel to arXiv:1812.08762, to which we also made extensive revisions this year
- BCS, Ideas Abandoned en Route to QBism (arXiv:1911.07386) — historical and conceptual, with some technical bits; written to show that not everything from the ’90s has held up as well as Daria and OK Computer
- BCS, Sporadic SICs and Exceptional Lie Algebras (arXiv:1911.05809) — technical, based on guest posts at the n-Category Café
- BCS, Quantum Theory as Symmetry Broken by Vitality (arXiv:1907.02432) — my weird manifesto, written after what is colloquially known as a “long dark night of the soul” made me appreciate honesty with renewed force
- John B. DeBrota and BCS, Lüders Channels and SIC Existence (arXiv:1907.10999) — technical, published in Physical Review A
- BCS, On QBism and Assumption (Q) (arXiv:1907.03805) — conceptual
- BCS, Invariant Off-Diagonality: SICs as Equicoherent Quantum States (arXiv:1906.05637) — technical
There was also From Gender to Gleason, my review of Adam Becker’s book What is Real? (2018). By the time I was done, it was as lengthy as a paper, but the arXiv isn’t really a host for book reviews, so I just posted it here at Sunclipse and moved on.
Looking at academic publishing from the perspective of Fully Automated Luxury Gay Space Communism is an interesting experience.
Consider, for example, the term predatory publisher for shady outfits that will accept anything for the right fee and put it on a website that calls itself a “journal”. Scummy behavior, right? But is it really “predatory”? What fraction, exactly, of their customers are being conned, and how many are walking into the deal with their eyes wide open? A used-car salesman might be a sleaze, but if you’re going to his dealership to pay cash for a getaway car, the relationship is more of a symbiosis.
I’m sure it’s convenient for the legacy institutions to present the situation as saintly scholars being exploited by deceptive newcomers. [cough]
Suppose the Web came to be, but there never were any respectable Open Access journals. No “Open Letter to Scientific Publishers” in 2001, so no Public Library of Science; no Budapest Initiative in 2002 or Berlin Declaration in 2003. Would the morass of “predatory” OA really look all that different? Perhaps not. Websites are cheap, calling yourself a journal is easy, and as we just noted, there’s a ready market.
But without the cover of PLOS and the like, would “predatory” OA have a veneer of respectability to offer its customers? Well, consider that paying to attend conferences is a thing that academia finds universally respectable. So, a “predator” could do what outfits like WASET do now: offer “conferences” with no standards, no dedicated space, perhaps not even a physical event. And if you’ve got a paper, great! For only a modest additional fee, it can go in the conference proceedings, which will conveniently be available online.
Quality is always the hard course of action. Legitimate OA journals were optional; only the pay-to-play racket was inevitable.
There’s an aspect of Vannevar Bush’s “memex” that, I think, would still be difficult to achieve with current software, and that is its intensely personal character. The memex that his 1945 essay “As We May Think” imagined was to be “an enlarged intimate supplement to [the user’s] memory.”
A modern analogue would have to be something like a personal wiki, hybridized with a social-media platform. Every post you make is intended to be retrievable: cross-indexed, hyperlinked. Like, if every time you posted to your Mastodon instance, it was also added as a page to your own MediaWiki setup. And you could share pages from your MediaWiki with just a few clicks, sending any set of them you wish to another Mastodon user. Instead of just sharing a news story, you could pull up every news story you ever shared, along with whatever comments you made about them, and all the ways that you had decided to tag them.
It’s not beyond what software can do, but we don’t generally seem to have worked toward what Vannevar Bush had in mind. There wasn’t supposed to be just one Memex for everybody.
The bits and pieces are present, but there hasn’t been the drive to put them together in a way that makes the package readily usable. We have software for sharing personal records and observations (social media), and we have platforms for making association trails (e.g., Wikipedia, TV Tropes, etc.). But the Memex that VB envisioned was an individual possession that facilitated social exchanges. In slogan form: The memex was like building your own Wikipedia, with adjustable privacy settings, one blog or microblog post at a time.
… or, The Case of Adam Becker’s What Is Real? (2018).
It is easy to argue that the founders of quantum mechanics made statements which are opaque and confusing. It is fair to say that their philosophical takes on the subject are not infrequently unsatisfying. We can all use reminders that human flaws and passions are a part of physics. So, it would be nice to have a popular book on these themes, one that makes no vital omissions, represents its sources accurately and lives up to its own ideals.
Sadly, we’re still waiting.
I was having an e-mail conversation the other day with a friend from olden days — another MIT student who made it out with a physics degree the same year I did — and that led me to set down some thoughts about history and terminology that may be useful to share here.
My primary claim is the following:
We should really expunge the term “the Copenhagen interpretation” from our vocabularies.
What Bohr thought was not what Heisenberg thought, nor was it what Pauli thought; there was no single unified “Copenhagen interpretation” worthy of the name. Indeed, the term does not enter the written literature until the 1950s, and that was mostly due to Heisenberg acting like he and Bohr were more in agreement back in the 1920s than they actually had been.
For Bohr, the “collapse of the wavefunction” (or the “reduction of the wave packet”, or whatever you wish to call it) was not a singular concept tacked on to the dynamics, but an essential part of what the quantum theory meant. He considered any description of an experiment as necessarily beginning and ending in “classical language”. So, for him, there was no problem with ending up with a measurement outcome that is just a classical fact: You introduce “classical information” when you specify the problem, so you end up with “classical information” as a result. “Collapse” is not a matter of the Hamiltonian changing stochastically or anything like that, as caricatures of Bohr would have it, but instead, it’s a question of what writing a Hamiltonian means. For example, suppose you are writing the Schrödinger equation for an electron in a potential well. The potential function $V(x)$ that you choose depends upon your experimental arrangement — the voltages you put on your capacitor plates, etc. In the Bohrian view, the description of how you arrange your laboratory apparatus is in “classical language”, or perhaps he’d say “ordinary language, suitably amended by the concepts of classical physics”. Getting a classical fact at your detector is just the necessary flipside of starting with a classical account of your source.
(Yes, Bohr was the kind of guy who would choose the yin-yang symbol as his coat of arms.)
To me, the clearest expression of all this from the man himself is a lecture titled “The causality problem in atomic physics”, given in Warsaw in 1938 and published in the proceedings, New Theories in Physics, the following year. This conference is notable for several reasons, among them the fact that Hans Kramers, speaking both for himself and on behalf of Heisenberg, suggested that quantum mechanics could break down at high energies. More than a decade after what we today consider the establishment of the quantum theory, the pioneers of it did not all trust it in their bones; we tend to forget that nowadays.
As to how Heisenberg disagreed with Bohr, and what all this has to do with decoherence, I refer to Camilleri and Schlosshauer.
Do I find the Bohrian position that I outlined above satisfactory? No, I do not. Perhaps the most important reason why, the reason that emotionally cuts the most deeply, is rather like the concern which Rudolf Haag raised while debating Bohr in the early 1950s:
I tried to argue that we did not understand the status of the superposition principle. Why are pure states described as [rays] in a complex linear space? Approximation or deep principle? Niels Bohr did not understand why I should worry about this. Aage Bohr tried to explain to his father that I hoped to get inspiration about the direction for the development of the theory by analyzing the existing formal structure. Niels Bohr retorted: “But this is very foolish. There is no inspiration besides the results of the experiments.” I guess he did not mean that so absolutely but he was just annoyed. […] Five years later I met Niels Bohr in Princeton at a dinner in the house of Eugene Wigner. When I drove him afterwards to his hotel I apologized for my precocious behaviour in Copenhagen. He just waved it away saying: “We all have our opinions.”
Why rays? Why complex linear space? I want to know too.
Time again for the New Paper Dance!
B. C. Stacey, “QBism and the Ithaca Desiderata” [arXiv:1812.05549].
In 1996, N. David Mermin proposed a set of desiderata for an understanding of quantum mechanics, the “Ithaca Interpretation”. In 2012, Mermin became a public advocate of QBism, an interpretation due to Christopher Fuchs and Ruediger Schack. Here, we evaluate QBism with respect to the Ithaca Interpretation’s six desiderata, in the process also evaluating those desiderata themselves. This analysis reveals a genuine distinction between QBism and the IIQM, but also a natural progression from one to the other.
Occasionally, I think of burning my opportunities of advancing in the physics profession — or, more likely, just burning my bridges with Geek Culture(TM) — by writing a paper entitled, “Richard Feynman’s Greatest Mistake”.
I did start drafting an essay I call “To Thems That Have, Shall Be Given More”. There are a sizable number of examples where Feynman gets credit for an idea that somebody else discovered first. It’s the rich-get-richer of science.
Continue reading To Thems That Have
C. A. Fuchs, M. C. Hoang and B. C. Stacey, “The SIC Question: History and State of Play,” arXiv:1703.07901 [quant-ph] (2017).
Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 323. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott’s code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.
Also available via SciRate.
It feels like a good time to enumerate the science things I’ve written or co-written over this past year. In reverse chronological order:
Continue reading My 2016 in Official Physics Writing
An image burbled up in my social-media feed the other day, purporting to be a list of “17 Equations that Changed the World.” It’s actually been circulating for a while (since early 2014), and purports to summarize the book by that name written by Ian Stewart. This list is typo-ridden, historically inaccurate and generally indicative of a lousy knowledge-distribution process that lets us down at every stage, from background research to fact-checking to copy-editing.
Continue reading 17 Equations that Clogged My Social-Media Timeline
I’ve had a few scholarly items come out in the past several weeks—new stuff, and updated versions of old stuff. Here are their coordinates:
Continue reading New(-ish) Publications
There’s nothing deader than an equation. You write that down in a square on a tile floor. And on another tile on the floor you write down another equation, which you think might be a better description of the Universe. And you keep on writing down equations hoping to get a better and better equation for what the Universe is and does.
And then, when you’ve worked your way out to the end of the room and have to step out, you wave your wand and tell the equations to fly.
And not one of them will put on wings and fly.
Yet the Universe flies!
It has a life to it that no equation has, and that life to it is a life with which we are also tied up.
I saw that documentary as a kid, and that little speech was one part that stuck with me ever after. For the story of how Wheeler made this point to his physics classes, see arXiv:1405.2390, page 292.
I finally have my thesis in a shape that I feel like sharing. Yes, this took over three months after my committee gave their approval. Blame my desire to explain the background material, and the background to the background….
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, “more is different,” and I address this from several perspectives. Spatial host–consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory.
The idea of natural selection “acting at multiple levels” has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.
A certain mindset sees the movie Aliens and thinks it would be awesome to be a Space Marine. Because it’s like being a Marine, but in space.
A certain mindset skims a bit of cyberpunk fiction and thinks the future will be amazing, because Ruby-coding skills will clearly translate to proficiency with katanas. You know, katanas.
A certain mindset learns a little about the Victorian era and is instantly off in a fantasy of brass-goggled Gentlemen Aviators, at once dapper and wind-swept, tending the Tesla apparatus on their rigid airship. All art in the genre carries the tacit disclaimer in its caption, “(Not pictured: cholera.)” In the designation steampunk, the -punk has nothing to do with anarchy (in the UK or elsewhere), the suffix having been conventionalized into a mere signifier of anachronism. A steampunk condo development promises units for the reasonable price of 2 to 7.5 million dollars apiece.
[To be fair, Gibson and Sterling’s The Difference Engine (1990), which is in some part responsible for the whole wibbly-wobbly steamery-punkery, did spend some of its time with the run-down and the passed-over. It also, I’m guessing unintentionally, underscored the incoherence of the premise, when in its final pages, Ada Lovelace describes a fanciful notion of the late Charles Babbage, whose fictional version dreamed of doing computation with electricity. The fictional Babbage’s never-implemented plan relied on such hypothetical devices as resistors and capacitors. The book’s plot begins in 1855; the Leyden jar was invented 110 years earlier. Carl Friedrich Gauss built a working telegraph years before the historical Babbage even designed his Analytical Engine. But our aesthetic can’t allow that, of course.]
It is against this background that we should read “Silicon Valley is a Science Fictional Utopia,” a recent piece in Model View Culture. I have enjoyed and appreciated MVC quite a bit in the past few months, which is why I was rather flummoxed to find a statement in that essay that just refused to parse. The overall thesis sounds roughly right to me, but not all the examples seem to fit as written. Here’s the part that jumped out at me:
Continue reading Those Who Aspire to Solaria