Rest of world: (sobbing) You can’t just call everything a pudding!

J. J. Thomson: (points at atom) pudding

This post carries further on in the vein of my earlier writings on how the way most physicists talk about “the Copenhagen interpretation of quantum mechanics” is largely ahistorical.

• In re “Copenhagen” and “COLLAPSE”
• From Gender to Gleason
• Underappreciated

It’s common to present “the Copenhagen interpretation” as a kind of dynamical collapse model, in which wavefunctions are ontic entities (like a sophomore’s picture of the electromagnetic field) that evolve according to the Schrödinger equation, except in moments of “measurement” that take place in unspecified conditions. This portrayal is typically intended to make “the Copenhagen interpretation” sound like a mutant form of Newtonian mechanics where $F = ma$ almost always, except at peculiar instants when $F$ suddenly becomes $ma/2$ and then switches back again. Of course, this is abhorrent and pathological.

When I was a child, my parents bought me a magnet from a museum gift shop. It had a long handle, likely made deliberately to resemble a magic wand, and as educational toys go, it served its function, since I went around poking all sorts of things to see if the magnet would grab them. I suspect this is a common enough type of learning experience. One discovers, for example, that it will pick up paperclips but not pennies. Having calibrated one’s understanding of the magnet, one can then use it as a tool — say, by telling which of two matchboxes is filled with paperclips, or that something is different about a wire coil connected to a battery versus one that is not.

What concerned Bohr himself was that this transition — between the calibration phase, when an object is under scrutiny, and its later use as a laboratory instrument — is conceptually nontrivial. First a lens is a strangely curved block of glass we must work to comprehend, and then it is a means to overthrow Aristotle. There are not two different dynamical laws, but two different languages.

Here’s how John Wheeler put it:

“Bohr stresses […] that the stick we hold can itself be an object of investigation, as when we run our fingers over its surface. The same stick, when grasped firmly and used to explore something else, becomes an extension of the observer or—when we depersonalize—a part of the measuring equipment. As we withdraw the stick from the one role, and recast it in the other role, we transpose the line of demarcation from one end of it to the other. The distinction between the probed and the probe, so evident at this scale of the everyday, is the without-which-nothing of every elementary phenomenon, of every closed quantum process.”

[From “Law Without Law”, in the Wheeler–Zurek collection, p. 206]

The commonalities and contrasts with QBism should be evident enough. Extension of the observer, yes; depersonalize to mere dead “equipment”, no, for it is the latter move that gets one into trouble with Wigner’s Friend. And, on a perhaps more practical level where the choice of research problems is concerned, Bohr takes the quantum formalism pretty much as given and leaves “the quantum principle” not explicitly defined.

It may also be illustrative to consider how Rovelli’s “Relational Quantum Mechanics” treats this point. I tentatively infer that Rovelli thinks giving a special role to an agent means imposing two different dynamical laws, one for systems of agent-type and another for all nonagent physical entities. Even if he doesn’t spell it out, that seems to be the mindset he operates with, and the background he relies upon. Of course, he balks at that dichotomy. I would, too!

First, of course, there was the doubt and the pain.

But we’ve already covered that.

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.

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.

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.

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