A new proposal seeks to solve the paradox of quantum spin

BY ADAM BECKER – NOVEMBER 22, 2022 – Scientific American

The fact that electrons have the quantum property of spin is essential for our world as we know it. Yet physicists don’t think the particles are actually spinning. – oxygen/Getty Images

Electrons are proficient little magicians. They seem to flit about an atom without tracing a particular path, they frequently appear to be in two places at once, and their behavior in silicon microchips powers the computing infrastructure of the modern world. But one of their most impressive tricks is deceptively simple, like all the best magic. Electrons always seem to spin. Every electron ever observed, whether it’s just ambling around a carbon atom in your fingernail or speeding through a particle accelerator, looks like it’s constantly doing tiny pirouettes as it makes its way through the world. Its spinning never appears to slow or speed up. No matter how an electron is jostled or kicked, it always looks like it’s spinning at exactly the same speed. It even has a little magnetic field, just like a spinning object with electric charge should. Naturally, physicists call this behavior “spin.”

But despite appearances, electrons don’t spin. They can’t spin; proving that it’s impossible for electrons to be spinning is a standard homework problem in any introductory quantum physics course. If electrons actually spun fast enough to account for all of the spinlike behavior they display, their surfaces would be moving much faster than the speed of light (if they even have surfaces at all). Even more surprising is that for nearly a century, this seeming contradiction has been written off by most physicists as just one more strange feature of the quantum world—nothing to lose sleep over.

Yet spin is deeply important. If electrons didn’t seem to spin, your chair would collapse down to a minuscule fraction of its size. You’d collapse, too—and that would be the least of your problems. Without spin, the entire periodic table of elements would come crashing down, and all of chemistry would go with it. In fact, there wouldn’t be any molecules at all. So spin isn’t just one of the best tricks that electrons pull; it’s also one of their most crucial. And like any good magician, electrons haven’t told anyone how the trick is done. But now a new account of spin may be on the horizon—one that pulls back the curtain and shows how the magic works.

A DIZZYING DISCOVERY

Spin has always been confusing. Even the first people to develop the idea of spin thought it had to be wrong. In 1925 two young Dutch physicists, Samuel Goudsmit and George Uhlenbeck, were puzzling over the latest work from famous (and famously acerbic) physicist Wolfgang Pauli. Pauli, in an attempt to explain the structure of atomic spectra and the periodic table, had recently postulated that electrons had a “two-valuedness not describable classically.” But Pauli hadn’t said what physical property of the electron his new value corresponded to, and Goudsmit and Uhlenbeck wondered what it could be.

All they knew—all anyone knew at the time—was that Pauli’s new value was associated with discrete units of a well-known property from classical Newtonian physics called angular momentum. Angular momentum is just the tendency for a rotating thing to continue rotating. It’s what keeps tops spinning and bicycles upright. The faster an object is rotating, the more angular momentum it has, but the shape and mass of the object both matter, too. A heavier object has more angular momentum than a lighter object spinning just as fast, and a spinning object with more mass at its edges has more angular momentum than it would if its mass were clumped at its center.

Objects can have angular momentum without spinning. Any thing revolving around another thing—Earth going around the sun or a set of keys swinging around your finger on a lanyard—has some angular momentum. But Goudsmit and Uhlenbeck knew that this kind of angular momentum could not be the source of Pauli’s new number. Electrons do appear to move around the atomic nucleus, held close by the attraction between their negative electrical charge and the positive pull of the protons in the nucleus. But the angular momentum that they have from this movement was already well accounted for and could not be Pauli’s new number. The physicists also knew that there were already three numbers associated with the electron, which corresponded to the three dimensions of space it could move in. A fourth number meant a fourth way the electron could move. The only option, the two young physicists reasoned, was for the electron itself to be spinning, like Earth rotating on its axis as it orbits the sun. If electrons could spin in one of two directions—clockwise or counterclockwise—that would account for Pauli’s “two-valuedness.”

Excitedly, Goudsmit and Uhlenbeck wrote up their new idea and showed it to their mentor, Paul Ehrenfest. Ehrenfest, a close friend of Albert Einstein and a formidable physicist in his own right, thought the idea was intriguing. While he considered it, he told the two eager young men to go consult with someone older and wiser: Hendrik Antoon Lorentz, the grand old man of Dutch physics, who had anticipated much of the development of special relativity two decades earlier and whom Einstein himself held in the highest regard.

But Lorentz was less impressed with the idea of spin than Ehrenfest. As he pointed out to Uhlenbeck, the electron was known to be very small, at least 3,000 times smaller than an atom—and atoms were already known to be about a tenth of a nanometer across, a million times smaller than the thickness of a sheet of paper. With the electron so small, and with its even smaller mass—a billionth of a billionth of a billionth of a gram—there was no way it could possibly be spinning fast enough to account for the angular momentum Pauli and others were searching for. In fact, as Lorentz told Uhlenbeck, the surface of the electron would have to be moving 10 times faster than the speed of light, a flat impossibility.

Defeated, Uhlenbeck went back to Ehrenfest and told him the news. He asked Ehrenfest to scrap the paper, only to be told that it was too late—his mentor had already sent the paper off to be published. “You are both young enough to be able to afford a stupidity,” Ehrenfest said. And he was right. Despite the fact that the electron couldn’t be spinning, the idea of spin was widely accepted as correct—just not in the usual way. Rather than an electron actually spinning, which was impossible, physicists interpreted the finding as meaning that the electron carried with it some intrinsic angular momentum, as if it were spinning, even though it couldn’t be. Nevertheless, the idea was still called “spin,” and Goudsmit and Uhlenbeck were widely hailed as the progenitors of the idea.

Spin proved to be crucial in explaining fundamental properties of matter. In the same paper where he had suggested his new two-valued number, Pauli had also suggested an “exclusion principle,” the notion that no two electrons could occupy the exact same state. If they could, then every electron in an atom would just fall to the lowest energy state, and virtually all elements would behave in almost exactly the same way as one another, destroying chemistry as we know it. Life wouldn’t exist. Water wouldn’t exist. The universe would simply be full of stars and gas drifting through a boring and indifferent cosmos without encountering so much as a rock. In fact, as was later realized, solid matter of any kind would be unstable. Although Pauli’s idea was clearly correct, it was unclear why electrons couldn’t share states. Understanding the origin of Pauli’s exclusion principle would unlock explanations for all of these deep facts of quotidian life.

The answer to the puzzle was in spin. Spin was soon discovered to be a basic property of all fundamental particles, not just electrons—and one with a deep connection to the behavior of those particles in groups. In 1940 Pauli and Swiss physicist Markus Fierz proved that when quantum mechanics and Einstein’s special relativity were combined, it led inevitably to a connection between spin and group statistical behavior. Pauli’s exclusion principle was merely a special case of this spin-statistics theorem, as it came to be known.

The theorem is a “mighty fact about the world,” says emeritus physics professor Michael Berry of the University of Bristol in England. “It underlies chemistry. It underlies superconductivity. It’s a very fundamental fact.” And like so many fundamental facts in physics, spin was found to be technologically useful as well. In the second half of the 20th century, spin was harnessed to develop lasers, explain the behavior of superconductors and point the way to building quantum computers.

SEEING PAST THE SPIN

But all of these fabulous discoveries, applications and explanations still leave Goudsmit and Uhlenbeck’s question on the table: What is spin? If electrons must have spin but can’t be spinning, then where does that angular momentum come from? The standard answer is that this momentum is simply inherent to subatomic particles and doesn’t correspond to any macroscopic notion of spinning.

Yet this answer is not satisfying to everyone. “I never loved the account of spin that you got in a quantum mechanics class,” says Charles Sebens, a philosopher of physics at the California Institute of Technology. “You’re introduced to it, and you think, ‘Well, that’s strange. They act like they spin, but they don’t really spin? Okay. I guess I can learn to work with that.’ But it’s odd.”

Recently, however, Sebens has had an idea. “Within quantum mechanics, it seems like the electron is not rotating,” he proposes. But, he adds, “quantum mechanics is not our best theory of nature. Quantum field theory is a deeper and more accurate theory.”

Quantum field theory is where the quantum world of subatomic particles meets the most famous equation in the world: E = mc², which encapsulates Einstein’s discovery that matter can turn into energy and vice versa. (Quantum field theory is also what gives rise to the spin-statistics theorem.) Because of this ability, when subatomic particles interact, new particles are often created out of their energy, and existing particles can decay into something else. Quantum field theory handles this phenomenon by describing particles as arising out of fields that pervade all of spacetime, even empty space. These fields allow particles to appear and disappear, all in accordance with both the strict dictates of Einstein’s special relativity and the probabilistic laws of the quantum world.

And it’s these fields, according to Sebens, that may contain the solution to the puzzle of spin. “The electron is ordinarily thought of as a particle,” he says. “But in quantum field theory, for every particle, there’s a way of thinking about it as a field.” In particular, the electron can be thought of as an excitation in a quantum field known as the Dirac field, and this field may be what carries the spin of the electron. “There’s a real rotation of energy and charge in the Dirac field,” Sebens says. If this is where the angular momentum resides, the problem of an electron spinning faster than the speed of light vanishes; the region of the field carrying an electron’s spin is far larger than the purportedly pointlike electron itself. Therefore, Sebens asserts, in a way, Pauli and Lorentz were half-right: there isn’t a spinning particle. There’s a spinning field, and that field is what gives rise to particles.

AN UNANSWERABLE QUESTION?

So far Sebens’s idea has made ripples, not waves. When it comes to whether electrons are spinning, “I don’t think it’s an answerable question,” says Mark Srednicki, a physicist at the University of California, Santa Barbara. “We’re taking a concept that originated in the ordinary world and trying to apply it to a place where it doesn’t really apply anymore. So I think it’s really just a matter of choice or definition or taste whether you want to say the electron is really spinning.” Hans Ohanian, a physicist at the University of Vermont who has done other work on electron spin, points out that Sebens’s original version of his idea doesn’t work for antimatter.

But not all physicists are so dismissive. “The conventional formulation of how we think about spin is leaving something out potentially important,” says Sean Carroll, a physicist at Johns Hopkins University and the Santa Fe Institute. “Sebens is very much on the right track, or at least he is doing something very, very useful in the sense that he’s taking the ‘fieldness’ of quantum field theory very seriously.” Still, Carroll points out, “physicists are, at heart, pragmatists…. If Sebens is 100 percent right, the physicists are going to say, ‘Okay, what does that get me?’”

Doreen Fraser, a philosopher of quantum field theory at the University of Waterloo in Canada, echoes this point. “I’m open to this project that Sebens has of wanting to drill deeper into having some sort of physical intuition to go with spin,” she says. “You have this nice mathematical representation; you want to have some intuitive physical picture to go along with it.” Plus, a physical picture might also lead to new theories or experiments that hadn’t occurred before. “To me, that would be the test of whether this is a good idea.”

It’s too early to say whether Sebens’s work will bear this kind of fruit. And although he has written a paper about how to resolve Ohanian’s concern regarding antimatter, there are other, related questions still remaining. “There’s a lot of reasons to like” the field idea, Sebens says. “I take this more as a challenge than a knockdown argument against it.”

ADAM BECKER is a science writer at Lawrence Berkeley National Laboratory and author of “What Is Real?”, about the sordid untold history of quantum physics. His writing has appeared in the New York Times, the BBC, and elsewhere. He earned a Ph.D. in cosmology from the University of Michigan.

A response to Adam Becker’s “What is Real?”

QBism Group, Physics Department, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston MA 02125, USA – February 17, 2019

From Gender to Gleason: The Case of Adam Becker’s What Is Real?
Blake C. Stacey

Abstract
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.

Overview
Imagine a biography of Isaac Newton that treated as a shocking revelation the fact that Newton was arrogant and abrasive; that accused Newton of being unscientific when, regarding a mechanism behind gravitation, he replied “I feign no hypothesis”; that yearned for an Aristotelian understanding of the Earth-Moon interplay; that mourned the absence of women in the story of classical mechanics, while briefly dismissing Émilie du Châtelet as “Voltaire’s mistress”. Now, take that equation, replace Newton’s arrogance with Niels Bohr’s verbal obscurity, and solve to find Adam Becker’s What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics (2018). I had to take What Is Real? in small doses. It is not literally true that every time I dipped into it, I found an error of physics or a misrepresentation of history. That is, however, a good first approximation of what the reading experience was like. Becker professes great concern about biases in physics, while perpetuating them. To summarize the remainder of this review in a sentence: Becker needed a villain, and he chose Niels Bohr. I was counseled to keep this short, but I did not do a very good job of that, because I fully expect that people will be quoting this book at me for years to come, and I would like to have to write a response only once.

My colleague Chris Fuchs noticed many problems, and reported a selection of them in his review for the American Journal of Physics [1]. Tom Siegfried found other issues that both Chris and I had missed [2]. I think his review expresses the big picture rather well: Becker’s main argument insists that the [Bohrian] interpretation embraces the philosophy known as positivism (roughly, nothing unobservable is real, and sensory perceptions are the realities on which science should be based), and then demonstrates positivism’s fallacies. He does a fine job of demolishing positivism. Unfortunately, the [Bohrian] interpretation is not positivistic, as its advocates have often pointed out.

Becker throws about the word positivism the way a TV pundit invokes socialism, and with comparably solid justification. He calls the philosophers Charles Morris and Hans Reichenbach positivists; neither of them were. Physicists get tagged with the p-word as well, generally without more reason than extremely selective quotation.

The ideological target of What Is Real? is the “Copenhagen interpretation of quantum mechanics”. In my opinion, this is a term we should expunge 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 [3–5].

Strangely, Becker acknowledges these divisions at times, yet agglomerates them back together when he needs a place to land a rhetorical blow (e.g., “It took someone who had always known Copenhagen was rotten, who had seen David Bohm do the impossible”). I worry that those who read Becker’s book without having learned the subject first will come away with a sense of getting a complete picture. For example, Becker quotes the philosopher Jeffrey Bub lamenting about the “Copenhagen interpretation” in a 1997 monograph. But he doesn’t mention Bub’s later turn to the Dark Side, that is, to an informational
interpretation of quantum mechanics haunted with the specter of Copenhagen [6]. He certainly doesn’t mention that in 2017, Bub wrote a paper titled “Why Bohr was (Mostly) Right” [7]!

For another example, in chapter 2, he claims that Dirac disparaged Bohr’s idea of “complementarity”, saying that it was too vague to “provide you with any equations which you didn’t have before”. This is true, but in the same interview — an interview in 1963, not contemporaneous with Bohr’s presentation in 1927, as the book insinuates — Dirac is equally harsh on the good old uncertainty principle. Dirac called the uncertainty principle “qualitative” and “of secondary importance”. He also reveals how much he trusted Bohr’s scientific
judgment: When confronted with the idea that the fundamental law of conservation of mass/energy might be violated, Dirac said, “I was rather prepared to accept it if Bohr proposed it” [8]. The same interview archive reveals that Hendrik Casimir saw the lack of mathematical detail as an advantage. He regarded Bohr’s dwelling on complementarity as a way of training intuition, honing his ability to tell what quantum mechanics would predict without having to do all the intricate calculations [9]. Seen in this light, what Becker disparages in Bohr is simply the skill that we try to develop in all physics students: the facility to, as John Archibald Wheeler advised, “never calculate without first knowing the answer”.

The first three printings of Becker’s book mangle the explanation of the Einstein–Podolsky–Rosen thought-experiment, the foundational example upon which the study of quantum entanglement is built. Moreover, the error is one that should never happen, given a serious effort to engage with what Einstein and company were trying to prove and how Bohr was trying to respond. I emphasize that this was not an error of interpretation, but one of description; Becker issued an erratum after being corrected by N. David Mermin and David Albert, two Davids with very different interpretations of quantum mechanics [10]. (A side note: In his main text, Becker says that Bohm gave his version of the EPR experiment in terms of polarized photons. He then “corrects” this statement in his endnotes, saying that Bohm’s example really used electrons. In fact, neither is true: Bohm’s textbook sets up his version of EPR using atoms and Stern–Gerlach magnets.)

In chapter 7, while trying to explain “contextuality”, Becker invents an analogy about neutrons that is more esoteric than the thing he is trying to define, which seems poor pedagogy. And in the process, he pretends that energy and momentum can be measured simultaneously, then doubles down on the error and says that energy and position are simultaneously measurable as well. There’s writing for the masses, and then there’s just being wrong.

What follows is a bit better, phrasing the issue of “contexuality” in terms of a roulette wheel, which makes me wonder why neutrons were brought in to begin with. And then it all goes awry again when it confuses the result that a hidden-variable model for quantum mechanics has to be “contextual” for a proof that quantum mechanics itself is “contextual”. Just because all excuses share a property does not mean that an honest explanation has that property too. When the condition is defined in a mathematically precise way that does
not lean on hidden-variable models, one finds that quantum mechanics is not contextual at all [11].

On a related note, Becker poses the testing of Bell’s inequality as a trilemma. Doing the experiment, one might find that the results deviate from the predictions of quantum theory (and thus, “instant Nobel Prize” — the Nobel figures largely in his rhetoric). Or, if the results accord with the quantum predictions, one could embrace a many-worlds picture.

Thirdly, if the results agree with quantum theory, the other option is that nature allows for nonlocal influences. In re the first choice, enough Bell tests have closed enough loopholes that I feel comfortable saying that the quantum predictions are trustworthy. I am still skeptical that a fully consistent and genuinely predictive version of the many-worlds creed has ever been posed [12–15]. And if the theory is not logically consistent, I doubt that it can be the logical conclusion of any argument. Setting that path aside for the moment, then, we are left with the third horn of the trilemma: In brief, we are told, quantum physics must be nonlocal. I have seen this argument presented before at much greater length and in greater detail, and I remain unconvinced [16, 17], as are physicists who probably see themselves as a good deal more mainstream than I.1 1A sampling from proponents of various “interpretations”: [18–23].

Details
Becker accuses John von Neumann of “sounding a positivist note” in his textbook, Mathematical Foundations of Quantum Mechanics (1932). I must admit that I take this a bit
personally, because several years ago, I discussed that very passage at length in my own
deep dive on von Neumann — spoiler, it’s not positivist. In fact, Schrödinger (who is one of
Becker’s good guys) articulated the same sentiment, and he attributed it all the way back
to Democritus of Abdera [24]. There is a wide gulf between saying that we ultimately use
our sense impressions to judge between one scientific theory and another, and saying that
unobservables are unmentionables. The latter is a positivistic attitude; the former is just,
well, life, man.
In that 1932 text, von Neumann presented what he claimed was a proof that quantum uncertainties could not be explained away as merely our being ignorant of a deeper,
classical-type layer of reality. His mathematics was correct, but one of his assumptions
was unwarranted, a fact first pointed out by Grete Hermann [25, 26], a philosopher, mathematician and member of the anti-Nazi group known as the Internationaler Sozialistischer
Kampfbund. Hermann’s observation was, however, ignored for many years, and it’s tough to
say why [27]. She was a woman, a philosopher trying to talk to physicists (though she earned
praise from von Weizsäcker and Heisenberg), and a socialist. Take your pick, I suppose. It
is also worth noting that the set of people who cared about the philosophical foundations
of quantum theory was, at the time, pretty darn small. In 1928, Hermann Weyl predicted
that “the fate of the general scheme of quantum mechanics” was to be “submerged” in an
improved future theory. A decade later, Hans Kramers declared that “everyone knew that
the quantum theory was provisional”; to him, it was not at all definitive that “after some
years, Schrödinger’s equation would still be considered the root of everything”. Heisenberg
shared this attitude, speculating that quantum mechanics might break down at sufficiently
high energies.2 When the pioneers of the subject did not yet trust it in their bones, why
would anyone waste time philosophizing about it?
To his credit, Becker raises the possibility that Hermann’s work languished in obscurity
because of sexism. But his assertion is so brief that I almost wish it weren’t made at all.
Two points:

1. While she had correctly taken down von Neumann’s “proof” that no “hidden variables”
   can underlie quantum physics, Grete Hermann herself did not believe in hidden variables!
   She had her own reasons, due to her own philosophical concerns about causality. Becker says
   nothing about this! It’s hard to take a man seriously when he says he wants to promote the
   cause of women in science, and he doesn’t even describe what the most important woman in
   his story actually did. Hermann’s “interpretation” of quantum mechanics seems to have been
   2See the proceedings for the 1938 Warsaw conference, New Theories in Physics (International Institute of
   Intellectual Co-operation, 1939). I found Bohr’s contribution to these proceedings much more clear than his
   reputation led me to expect, and both more approachable and more thought-provoking [10] than his reply to
   EPR. Catherine Chevalley notes that Bohr’s Warsaw paper and the following discussion with von Neumann
   are among the important documents which “have been entirely omitted in the discussion of the so-called
   Copenhagen Interpretation” [28].
   4
   akin to Bohr’s, and perhaps even more radical — but Bohr is the great villain of Becker’s
   book, and nothing that lends him respectability can be allowed.
3. Sexism in science is a tangle of thorns now, and I’d say it was the same then. Scientific
   men are great believers in meritocracy — “We judge the work, and the work alone” — so
   much so that they cannot conceive the possibility that, even if the playing field were level, not
   everybody gets to join the game. A two-sentence toss-off does no justice to this problem. If
   you’re not willing to see beyond mustache-twirling, why are you even talking? We will return
   to this point momentarily, but first, the question of von Neumann and “hidden variables”
   requires further exploration.
   Becker goes into roof-raising passion about how von Neumann’s proof was uncritically
   accepted for years, and how those no-good Copenhageners used it to shut down all discussion
   of possible alternative positions. His evidence? Well, it’s pretty thin on the ground. He
   offers a passage in a book by Mara Beller, who selectively quotes the autobiography of
   the philosopher Paul Feyerabend, who (decades after the fact) recalled the aftermath of
   a lecture by Bohr. Feyerabend, not primarily a physicist or a mathematician, read the
   room and thought Bohr’s supporters were invoking von Neumann to win the post-lecture
   discussion, while neither they nor their opponents understood the details of the proof itself.
   Beller leaves out the end of the story: “I found this very strange,” Feyerabend wrote, “but
   was relieved to remember that Bohr himself had never used such tricks” [29].
   According to Eugene Wigner, the mathematical proof that von Neumann included in his
   textbook was not the fundamental reason why he himself rejected the possibility of “hidden
   variables”. Instead, von Neumann’s conviction was primarily motivated by a more heuristic argument [30]. Heisenberg, too, had a qualitative argument for dismissing any putative
   hidden-variable completion of quantum theory, one that differed from von Neumann’s concerns as well as Hermann’s [4]. If he had found von Neumann’s theorem conclusive, would
   he have bothered? I don’t know, but Procrusteanizing the interplay of formal and heuristic
   arguments can’t be a good way to do physics history.
4. 
   In those years when, according to Becker, von Neumann’s flawed proof was uncritically
   accepted, it was (you can tell where this is going) found unsatisfactory by multiple authors,
   among them Reichenbach. This is all described in Max Jammer’s The Philosophy of Quantum Mechanics (1974), which Becker has presumably read, since it’s listed in his bibliography.
   So, in fact, is Reichenbach’s Philosophic Foundations of Quantum Mechanics (1944), which
   makes the omission of Reichenbach’s criticism rather puzzling. Reichenbach’s critique is less
   specific than Hermann’s, but both of them hit the note that von Neumann had just assumed
   too much. Various folks also found von Neumann’s axiomatization of quantum mechanics
   unsatisfying; it’s not like the man was deified. When I read Nikolai Sergeevich Krylov’s 1950
   textbook, he sounded almost angry at von Neumann’s treatment of “statistical operators”,
   but perhaps translation from the Russian will do that [24]. Of the others who found fault
   or limitation in von Neumann’s work, the writing of Lüders [31] appears to have been more
   productive than that of Temple [32]. However, the latter case illustrates that the editors of
   Nature were willing to publish a letter attacking one of von Neumann’s fundamental axioms.
   (The root of Temple’s concern appears to be that the “canonical quantization” procedure
   5
   for making a classical theory into a quantum one does not yield a unique answer. This point
   was hashed out in a rather mundane cycle of publications [33, 34], the sort of day-to-day
   scientific exchange that makes for much less dramatic copy than cries of censorship! and
   suppression!) Von Neumann’s flawed theorem was at the frontier of mathematical sophistication for a theory that was not yet fully trusted on physical grounds. While many may
   have accepted his conclusions too superficially, we should not forget the contributions of
   those who took greater pains.
   Becker accepts hearsay about Bohr and passes it off as Bohr’s own position about the
   philosophy of physics [1], while at the same time, he ignores indirect evidence that Einstein
   knew about, and was unimpressed by, von Neumann’s attempt to rule out explanations of
   quantum randomness in terms of “hidden variables” [35, p. 286]. I can find no justification
   for this: It is not an extraordinary claim, requiring an extraordinary standard of support.
   On the contrary, what would be exceptional is Einstein not knowing about work done, on a
   problem that deeply concerned him, by a man in the same building.
   In his concluding remarks, Becker laments, “hardly any women or people who aren’t
   white appear anywhere in this story at all.”
   As one of the whitest guys I’ve ever met, I am the wrong fellow to provide a definitive take
   upon this point, so I will content myself with a list of people that he could have mentioned,
   but didn’t:
   In the early days of quantum mechanics, there were Satyendra Nath Bose, Ishiwara Jun,
   Nagaoka Hantaro and Hendrika Johanna van Leeuwen. On the philosophical side, Karen
   Barad offers a refreshingly clear reading of Bohr (sometimes, it takes a stiff dose of feminist
   theory to clear out the cobwebs that a physics education will leave). Susan Haack, a pragmatist I have gradually grown more radical than, could have illuminated the distinctions
   among philosophies that Becker lumps together. Mary Hesse is likewise noteworthy in this
   regard, and Bertha Swirles Jeffreys and Dorothy Maud Wrinch should not be forgotten. Of
   those who furthered von Neumann’s work on quantum logic and quantum probability, more
   names spring to mind: Araki Huzihiro, Paulette Destouches-Février, Husimi Kôdi, Nakamura Masahiro, Mary Beth Ruskai, Maria Pia Solèr, Umegaki Hisaharu, Yanase Mutsuo,
   Watanabe Satosi. . . 3
   And that’s just me checking the references I had close at hand — including the sources
   that Becker himself invokes, like Max Jammer. Rather incredibly, while mourning the lack
   of diversity in physics, he manages to portray it as an even whiter shade of male than it
   really was.
   To paraphrase the teenagers I meet on the subway: I doubt your commitment to the
   Revolution, tovarisch.
   Lee Tsung-Dao came close to deriving Bell’s inequality, four years before Bell, but apparently he got tied up in extra complications due to kaon physics and never took his ideas
   to their full conclusion.4
   3
   I myself am convinced that the work of Maryna Viazovska [36] is relevant to quantum foundations, but
   that is a point I am still working to make [37, 38].
   4As recounted by Jammer [39, p. 308]. Oddly enough, kaon physics was the setting where I had my first
   real encounter with Bell’s inequality, as an undergraduate. I think my physics education was fairly ordinary,
   6
   Together with Yang Zhenning, Lee had won the 1957 Nobel Prize in Physics for predicting
   that the weak nuclear force does not conserve parity. The experimental confirmation of parity
   violation was by Wu Chien-Shiung, but she didn’t get a share of the Nobel. Wu also did
   work relevant to quantum foundations, essentially implementing the setup for the thoughtexperiment of Einstein, Podolsky and Rosen. Becker mentions this — believe me, by this
   point, I was almost expecting him not to. He says, rightly, that she was “renowned for her
   work in nuclear physics”. Fine. But not indicating just how important her work was, and
   not mentioning her being slighted for a Nobel when he makes pious complaints about the
   hazards of bias in physics? Throughout What Is Real?, the Nobel Prize is a signifier of
   greatness. Never does Becker challenge the glamor — and the problems of the Nobel are
   low-hanging fruit in the study of science’s cultural biases [40].
   Similarly, Becker drops in the name of Melba Phillips, who did important work in nuclear
   physics and helped to introduce group theory into the practical application of quantum
   mechanics [41], only mentioning her as a friend of Bohm.5 Phillips lost her professorship
   after invoking the Fifth Amendment before a McCarthy-era committee, a point that is surely
   relevant to Becker’s observation that “political considerations” play into science. For all the
   time that Becker spends on Bohm’s Marxism and his troubles with the red scare, does the
   five-year blacklisting of Phillips not merit a line? I know that it is an easy trap for a reviewer
   to complain that an author did not produce the book that the reviewer would have written,
   but here it seems that Becker did not write the book that he himself wanted to.
   Another name belongs here: Subrahmanyan Chandrasekhar. At one point, Becker goes
   off on a tangent about gravitational physics, where he mentions some work that Oppenheimer
   and colleagues did on the gravitational collapse of dead stars (the “Tolman–Oppenheimer–
   Volkoff limit”). This struck me as a weird thing to mention. It wasn’t even the only work
   that Oppenheimer did on the problem in that year! Why select it for special attention?
   By 1939, the year of the Tolman–Oppenheimer–Volkoff limit, gravitational collapse was
   already a well-established controversy. Arthur Eddington was troubled by the possibility of
   endless collapse as early as 1924. In 1935, he said, “The star has to go on radiating and
   radiating and contracting and contracting until . . . gravity becomes strong enough to hold
   in the radiation, and the star can at last find peace.” He loathed this possibility so much
   that he wanted “a law of Nature to prevent a star from behaving in this absurd way!”
   Eddington rejected Chandrasekhar’s conclusion that too-massive white dwarfs would
   collapse under their own gravity, and his influence delayed the acceptance of Chandrasekhar’s
   work by some years. This is, I’d say, a far better example of a cult of personality holding
   back scientific progress than any of the events that Becker makes much hay of. Why not
   include it in your book about the flaws of physics?
   Well (you can tell where this is going), Bohr was on Chandrasekhar’s side [42].
   in that the appearance of philosophy was avoided; the closest approach we had was screening Feynman’s
   Messenger Lectures over the January break. Thus, at first I found Bohr’s philosophical opinions irrelevant.
   At a second encounter, they were obscure; at a third, subtle yet unsatisfying.
   5Bohm’s letters to Phillips are reproduced in C. Talbot’s David Bohm: Causality and Chance, Letters
   to Three Women (Springer, 2017). I do not know of letters from Phillips to Bohm being published; it is
   possible that they have not been preserved.
   7
   Becker writes that Oppenheimer and colleagues “used a very early forerunner of a computer” to do their calculations. I guess it’s not wrong to call a Marchant mechanical desk
   calculator an “early forerunner of a computer”, but it’s not exactly the image that sprang
   to my mind when I read that passage. More importantly, he says that it was “difficult for
   other physicists to take the idea of collapsed stars seriously”. The portrayal in Becker’s
   source, Thorne’s Black Holes & Time Warps (1994), hits a rather different tone. Physicists
   and astronomers took the possibility seriously in that they accepted Oppenhemer et al.’s
   calculations as correct, but they generally figured that some as-yet-unknown physical effect
   would prevent collapsing stars from going all the way to the black-hole stage.
   So, the excursion into gravitation manages to blend “huh? why did you choose to write
   about that?” with “are you trying to do anything except carry out character assassination
   on Niels Bohr?”. It is also an example of the genre convention where an author adds to the
   Feynman legend. (In this book, Feynman is literally “a legend”, complete with the requisite Nobel Prize.) Becker credits the “ironclad arguments that finally convinced the physics
   community that gravitational waves must be real” to Feynman and Bondi, neglecting the
   contribution of Felix Pirani [43]. Elsewhere, his portrayal of Feynman’s role in the field
   of quantum computation neglects to mention that Paul Benioff had discussed implementing Turing machines with quantum time evolution two years before Feynman’s lecture on
   “Simulating Physics with Computers” [44]. But nobody ever went broke over-estimating the
   appetite of science-loving boys for Richard Feynman.
   One famous Feynmanism that Becker carries over uncritically is that the double-slit
   experiment “contains the only mystery” of quantum mechanics. This was fine in 1964, but it
   is simply no longer a viable claim. We now know that it is quite simple to construct a theory
   based on local hidden variables which displays interference in a double-slit-type scenario.
   (The explanation turns out to be rather pretty: In order to be consistent, the “vacuum
   state” has to be a statistical distribution over the hidden variables, meaning that it carries
   an unobservable phase factor which can convey a signal, like hearing the pitch at which an
   instrument plays a rest.) Simply put, to find the real mystery, we have to dig deeper [45,46].
   Becker notes that Feynman’s reception of Hugh Everett III’s interpretation of quantum
   mechanics was rather frosty: “The concept of a ‘universal wave function’ has serious difficulties,” he said at the Chapel Hill conference in 1957. Thus it is interesting that when Becker
   describes the “deep obscurity” in which Everett’s imagery languished through the 1960s, he
   neglects the portrayal that Feynman gave in his 1962 course on gravitation [47]:
   The traditional description of the total quantum mechanics of the world by a complete Monster Wavefunction (which includes all observers) obeying a Schrödinger
   equation
   i
   ∂Ψ
   ∂t = HΨ
   implies an incredibly complex infinity of amplitudes. If I am gambling in Las
   Vegas, and am about to put some money into number twenty-two at roulette,
   and the girl next to me spills her drink because she sees someone she knows, so
   that I stop before betting, and twenty-two comes up, I can see that the whole
   8
   course of the universe for me has hung on the fact that some little photon hit the
   nerve ends of her retina. Thus the whole universe bifurcates at each atomic event.
   Now some people who insist on taking all quantum mechanics to the letter are
   satisfied with such a picture; since there is no outside observer for a wavefunction
   describing the whole universe, they maintain that the proper description of the
   world includes all the amplitudes that thus bifurcate from each atomic event.6
   One can hardly find a more straightforward presentation of an Everettian view, a view that
   Feynman apparently takes seriously but does not find compelling. (Feynman’s commentary
   in this lecture about the vagueness of some traditional language about “observers” borders
   on the caustic; one feels that Becker would approve.) Later in life, Feynman said,
   In fact the physicists have no good point of view. Somebody mumbled something
   about a many-world picture, and that many-world picture says that the wave
   function ψ is what’s real, and damn the torpedoes if there are so many variables,
   N R. All these different worlds and every arrangement of configurations are all
   there just like our arrangement of configurations, we just happen to be sitting in
   this one. It’s possible, but I’m not very happy with it.
   This we read in the very “Simulating Physics with Computers” lecture that Becker describes.7
   I find Feynman’s statements over his career difficult to square with Becker’s description of a
   man who “had few qualms about the Copenhagen interpretation” (even leaving aside the illdefinedness of “the Copenhagen interpretation”). If Feynman had “few qualms”, they were
   very precisely calibrated ones that leave no popular interpretive tradition entirely unscathed.
   Turning to the topic of Feynman’s doctoral advisor, John Archibald Wheeler, we find
   that according to Becker, Wheeler eventually disdained the ideas of Everett for political
   reasons:
   Ever the scientific diplomat, Wheeler had tried to maintain his commitment to
   the ideas of Bohr, his late mentor, without explicitly denouncing the ideas of
   Everett, his former student. This wasn’t a difficult position for him to hold while
   Everett’s work languished in obscurity and remained cloaked in the language of
   the “relative-state formulation.” But now DeWitt was calling Everett’s view the
   “many-worlds” interpretation and saying that Wheeler was partly responsible for
   it—and the fact that it was showing up in science-fiction magazines didn’t help
   either. So Wheeler publicly distanced himself from Everett’s work and DeWitt’s
   spin on it. “[Everett’s] infinitely many unobservable worlds make a heavy load
   of metaphysical baggage,” Wheeler wrote in 1979.
   According to Peter Byrne’s biography of Everett [48], the events happened the other way
   round:
   6Because of course Feynman’s roulette wheel would be in Las Vegas with “a girl”.
   7Erroneously locating it at Caltech, rather than MIT’s Endicott House conference center.
   9
   Everett ordered multiple copies of the [December 1976] magazine, sending them to
   friends, including Wheeler, who had already begun to publicly dissociate himself
   from the many worlds interpretation. Being praised in Analog probably added
   salt to Wheeler’s festering wound.
   This may simply be a careless exchange, but I can’t help but think that it introduces a minus
   sign, making Everett look better and Wheeler worse. Whatever his personal motivations,
   Wheeler made a lengthier case than that to “leave the observer out of the wave function”,
   and he did so in a paper published in 1977, for the proceedings of a conference that took
   place in 1974 [49]. Already in 1974, Wheeler had published an article in American Scientist
   which lists Everett’s relative-state interpretation as only one “discovery about the quantum
   principle”, in a lineage with Planck’s quantization of energy and a notch less sophisticated
   than Birkhoff and von Neumann’s quantum logic [50].
   Becker writes, “After his failure to reconcile his student Everett’s work with the ideas of
   his mentor Bohr, Wheeler had set aside his interest in the foundations of quantum theory.
   But the Bell experiments, as well as long talks with Eugene Wigner, his colleague at Princeton, had brought Wheeler back to his former interest in the subject.” I find the causation
   here implausible. Everything I have read of Wheeler’s papers suggests that it was not the
   Bell experiments that brought his attention back to quantum theory, but the prevalence
   of singularities in his gravitation research, undoing the calm image of a world built from
   clean spacetime geometry, and leading him to the notion of “law without law”. Becker cites
   Freire’s The Quantum Dissidents (2015) for this historical claim, but Freire gives only an
   association, not a claim of causality:
   In the early 1970s the quantum foundations illness that had once inflicted Wheeler
   came back. The buzz around Bell’s theorem experiments was brought to him
   by his colleague at Princeton, Wigner, and he got involved with Edward Fry’s
   experiment (Misner et al. 2009, p. 45).
   Chasing down Misner, Thorne and Zurek’s 2009 feature in Physics Today [51], we find that
   “got involved with” does not quite summarize what they write:
   There was great excitement in Wheeler’s group when the violation [of Bell’s inequality] was indeed reported in an experiment by Edward Fry of Texas A&M
   University, and even more so when Alain Aspect confirmed its violation in measurements that are spacelike separated and hence causally independent.
   Fry’s result was published in 1976 [52], too late to be considered a causal contributor to the
   relapse of “quantum foundations illness” in the “early 1970s”. Moreover, Misner, Thorne
   and Zurek only mention Wigner as a participant in Wheeler’s graduate course on quantum
   measurement, which he first announced in the fall of 1977.
   What we have here is rather remarkable: a myth generated by citation telephone, with
   the chain beginning in a widely-read professional magazine only a decade ago. (Myths are
   empirically part of the weaving of history, insofar as we cannot understand its course without
   accounting for their consequences.)
   10
   Becker portrays Dirac rather favorably. As mentioned above, Dirac criticized the vagueness of “complementarity”; his prediction of antimatter is credited as a “great success” of
   quantum field theory, and his Nobel Prize is duly mentioned.8 Nowhere does Becker hint
   that historians and philosophers of physics have seen in Dirac a positivist or instrumentalist
   inclination [53]. If the assertion of scattered philosophers is enough warrant to tag Bohr
   with the p-word, why is the same not true for Dirac? True, the charges against Dirac have
   been disputed [54], but so too are those for Bohr. Likewise, Becker gives Schrödinger a bit
   of a hero treatment: He was the one who could have opposed Bohr’s vagueness at the Como
   conference, had he only been there, etc. But read Schrödinger’s Mind and Matter and My
   View of the World — Erwin was weird. People call Bohr opaque and confused, but never
   admit that Schrödinger is out there finding inspiration in the Upanishads.9
   And speaking of the 1927 Como conference: despite Becker’s portrayal, Bohr probably
   did not discuss the thought-experiment known as the “gamma-ray microscope”. He added
   that to the written version of his talk, months later [56]. Becker claims that Bohr using the
   gamma-ray microscope to support his view is strange, because the thought-experiment, due
   to Heisenberg, presumes that position and momentum exist before they are measured, and
   are just disrupted by the measurement process. But if you actually read Bohr’s lecture, it’s
   clear that he is using the gamma-ray microscope as a warm-up example at the beginning of a
   section. After explaining it, Bohr goes on to say that a “closer investigation of the possibilities
   of definition would still seem necessary in order to bring out” the real conceptual issues [57].
   He’s perfectly aware of the shortcomings; he’s the one who told Heisenberg about them.
   This bit of science history is so well known, it’s in a play.
   In Michael Frayn’s Copenhagen, the ghost of Heisenberg and those of Niels and Margrethe
   Bohr look back over their lives and try to make sense of them. This thought-experiment
   comes up, and Bohr explains how Heisenberg’s analysis fell short. Heisenberg whines, “I
   know — I put it in a postscript to my paper.”
   Niels Bohr deadpans, “Everyone remembers the paper — no one remembers the postscript.”
   When I saw Copenhagen, Margrethe Bohr was played by Mariette Hartley, whose character Zarabeth taught Spock to eat meat in “All Our Yesterdays”. She was also in Columbo
   twice. So, [very Peter Falk voice] just one more thing:
   Have you ever known something obscure that you wanted the world to share — like a
   book of poetry that moved you, one you found in the dustiest corner of a secondhand store
   — and then seen someone promote it widely while getting it horribly wrong? That, I am
   afraid, was my reaction to Becker’s treatment of the remarkable mathematical achievement
   known as Gleason’s theorem.
   Becker’s description of Andrew Gleason’s work is an example of “bait in the text and
   switch in the notes” [1]. In the main text, he portrays Gleason’s theorem as a no-go proof
   8Should a prediction based on the “Dirac sea” of negative-energy electrons be considered a triumph of
   QFT per se? Should Dirac be called the one who “originally pioneered” QFT when the quantization of free
   electromagnetic fields predates the Dirac equation? You see the paranoia into which one descends while
   reading What Is Real?, where the smallest detail soon provokes distrust.
   9According to Helge Kragh, Bohr nominated Schrödinger for the Nobel Prize, and it was the weight of
   his recommendation that secured the award [55].
   11
   for hidden variables, part of the “ilk” of von Neumann’s flawed result. In the endnotes, he
   clarifies,
   Gleason’s proof actually didn’t mention hidden variables. Gleason was a mathematician, not a physicist, and his proof had to do with certain features of Hilbert
   space, the mathematical structure underlying quantum physics. But Jauch and
   his colleague Piron pointed out to Bell that Gleason’s proof had an obvious corollary that ruled out hidden variables — and that this corollary seemed far stronger
   than von Neumann’s proof, or their own.
   Presenting the corollary as the result is, in this case, a serious error.
   Gleason’s theorem begins with a brief list of postulates, which are conditions for expressing what “measurements” are, in terms of Hilbert spaces. To each physical system
   we associate a Hilbert space, and each possible measurement we can perform on that system corresponds to a particular mathematical gadget — in Gleason’s original version, to an
   orthonormal basis [58]. The conclusion of Gleason’s argument is that any mapping from
   measurements to probabilities that satisfies his assumptions must take the form of the Born
   rule applied to some density operator. In other words, the theorem gives the set of valid
   quantum states and the rule for calculating probabilities given a state.
   Now, one corollary of this result is a statement that intrinsic hidden variables don’t work
   as an explanation for quantum probabilities. But that’s not how Gleason set up the problem,
   and it’s not the primary reason that the theorem has been invoked since then. Instead, the
   motivation is to re-derive the mathematical apparatus of quantum theory given only a portion
   of it. Specifically, we start in the setting of Hilbert space, and we make a presumption about
   what means “measurement”. From this starting point, Gleason tells us how to rebuild the
   rest of the quantum-mechanical formalism. Crucially, measurement is primary, and the
   set of legitimate quantum states is secondary. Notice how this runs spiritually counter to
   the Everettian approaches, in which the Monster Wavefunction is all, and measurements
   are convenient illusions (the details of the justification varying with the particular brand
   of Everettism). Becker seems almost allergic to the idea of taking “measurement” as a
   conceptual primitive, an attitude that, to be fair, I expect that many physicists share. But a
   clear-cut presentation of Gleason’s theorem shows that it is, at the very least, mathematically
   fruitful to embrace this heterodoxy.
   In setting up the premises of Gleason’s theorem, we invoked the notion of Hilbert space.
   It is quite natural to ask whether the need for Hilbert space can be deduced from a still earlier
   starting point. This has been a major concern for the “quantum logic” community, and one
   of the most significant discoveries in the project of getting to the place where Gleason can
   take over is a 1995 theorem by Maria Pia Solèr [59].
   I could go on. For example, in multiple places, Becker mixes up who was a student
   and who was a postdoctoral researcher or other type of colleague. If you can’t explain the
   academic career ladder, how can you hope to explain the mysteries of quantum mechanics?
   In summary: Errors pervade this book like the smell of turpentine. It is possible that
   the vaguenesses, the omissions and the misleading portrayals are no worse than many other
   books. Perhaps, when stacked up against the sins physicists normally commit when brushing
   12
   past the history to get to the harmonic oscillator, this book is only typical [10]. But usually
   physicists serve up the folk tales as an incidental part of something else, and this isn’t section
   1.1 of a textbook. It is packaged and sold as a serious investigation into the history and
   philosophy of quantum physics.
   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.”
   — Rudolf Haag [60]
   3 The literature of prior reviews
   All that said, I wouldn’t say that I agree with every position taken by those who have
   critiqued Becker. For example, while I think Peter Woit makes several good points in his
   review [61], the roughly Zurekian position where he ends up is not one I find satisfying. Or,
   rather, it is one I grew increasingly discontented with as my interest in quantum foundations
   intensified. While we could get into technical considerations here [62], there is a simpler
   emotional core. Ultimately, like Bohr’s pronouncements, the Zurekian zeitgeist assumes
   what I would like to see explained [63].
   For a second example, I’m not satisfied with the “shut up and calculate” attitude that
   Sheldon Glashow endorses in his review [64]. As I wrote in a commentary upon another
   book [65]:
   “Shut up and calculate!” is not a stable position. Even the most ascetic claim —
   the assertion to shut up and calculate with one mathematical formalism rather
   than another — is in some way a claim about the character of the world. Perhaps
   bound up with historical happenstance and social convention, but a claim about
   Nature nonetheless: Were the world a different way, would we not, after we shut
   up, calculate in a different fashion?
   The teachers I recall fondly were not the ones who declared, “You’ll learn it because it will
   be on the test, that’s why!” Why do physicists calculate in the particular manner that our
   profession learns to do, instead of any other? Why, out of all the mental contrivances that the
   mathematicians have thought up or stumbled across, do we use this specific set of arcana?
   13
   Some statements in the opening chapters of Quantum 101 go unchallenged as we progress
   onward, through quantum field theory into Higgs-boson territory, right up to the frontier,
   where people are trying to devise quantum gravity. Think on it: Physicists are trying to
   make a quantum mechanics of space and time themselves, using rules invented for hot gases
   in glass tubes! Is this merely a failure of imagination, or are there good reasons — physics
   reasons — why the mathematical alternatives should be kept on the sidelines? This is not
   an idle question, but a matter of increasingly active research.10 I regret to say that Becker
   elides this. For example, he dings Anton Zeilinger for offering “positivist” vagueness about
   quantum measurement. Yet he ignores the actual mathematics that Zeilinger and Brukner
   did to try and start making those intuitions precise [68]. Overall, this elision provides a
   skewed picture of how the physics community actually regards the founders of quantum
   mechanics.
   Glashow is right to raise the question, “What’s so remarkable about radioactive halflives?” We should in fact be willing to carry this line of questioning further. For example, is
   Pauli exclusion really so mysterious as all that? Chemistry students take on board the filling
   of electron shells as one more rule, with no more mystique than a table of electronegativities.
   To identify what is truly enigmatic about quantum mechanics, to pinpoint those “quantum
   mysteries” that genuinely deserve the name, we have to define in a robust way what we
   mean by “classical”, and then we have to prove a theorem that no model which satisfies that
   criterion can reproduce the predictions of quantum theory.
   Glashow points out the prominence of Schrödinger’s cat in Becker’s book. Like Glashow,
   I’m not incredibly impressed by this thought-experiment, but my sense that it says nothing
   terribly deep about quantum physics may stem from a different source. Schrödinger’s cat
   is full of red herring. It is a deceptive little fiction that does great violence to the words
   from which it is built. A living cat breathes. Indeed, this is a vital part of what it means to
   be a living cat. By definition, a living cat is a system that can exchange 100 billion billion
   molecules with its environment and still be considered “the same cat”. This is simply not
   a system for which any physicist can have expectations so precise that they call for the full
   apparatus of quantum theory to manage.
   Another problem with Schrödinger’s cat, on top of its flagrant disregard for the meaning
   of “cat”, is that it relies upon a single question that admits of only a yes-or-no answer.
   You could pose the same “paradox” for any theory expressed in probabilistic terms. It
   says nothing substantial about the particular features of quantum theory that make it truly
   special. In order to get at those aspects of the physics, we must have more flexibility in
   the ways that we can interrogate a physical system. We need to be able to ask a variety
   of questions that have at least three possible answers apiece. If we are restricted to binary
   experiments, we have to be able to combine them, choosing one binary interrogation for one
   system and another for a second. (These are statements of the Kochen–Specker and Bell
   theorems, respectively, with the equations stripped out to protect the innocent [69].) And
   when we do get at those deeper mysteries, what do they tell us about nature? Well, put
   four rabbis in a room and you might get five opinions, but this is where my colleagues and
   10For one perspective, see [66]; for another, try [67].
   14
   I have arrived, after many physicist-years on the question [70–72]:
   It is not always the case that facts are there on the ground, waiting for us to come along
   and read them off. In order to be satisfactory, science also has to encompass the situations
   when the “outcome of a measurement” is a thing a scientist elicits, an event that is a
   consequence of an active intervention upon the world. This goes deeper than the possibility
   of disturbing what was already there: At root, the choice of performing one experiment over
   another is the choice of instantiating one or another arena for fact creation. What a world
   to have evolved in! But we have a handbook for managing our expectations as we interact
   with it, a handbook that any individual among us can pick up and use: It is called quantum
   theory.
   One of the great problems of philosophy is how we, any of us, can obtain something that
   can play the role of solid truth, starting from anything so personal as experience. Quantum
   physics suggests something remarkable: that there is a gradation to the answer, and that it is
   quantifiable. In plenty of situations, it would be folly to act in any way other than as though
   a measurement simply tallied what was already present — the number of people standing
   on the National Mall, for example. Yet the poets have something legitimate, too, when they
   ask whether the tree that one of us sees is the same tree seen by any other. What happens
   to Alice, is an event for Alice. Should Bob try to share in Alice’s personal experience, what
   he gets is an experience of his own, standing in the same relation to the original, we might
   say, as a sonnet does to love. Science does not have to collapse in the face of this. On the
   contrary, it might even prosper. While hardly knowing it, we have been developing the tools
   to handle exactly this eventuality — and it started with hot gases in glass tubes.

References
[1] C. A. Fuchs, “Copenhagen Interpretation Delenda Est?,” American Journal of Physics
86 (2018), 957, arXiv:1809.05147.
[2] T. Siegfried, “‘Beyond Weird’ and ‘What Is Real?’ try to make sense of quantum
weirdness,” Science News (6 January 2019).
[3] D. Howard, “Who invented the ‘Copenhagen interpretation’? A study in mythology,”
Philosophy of Science 71, 5 (2004), 669–82.
[4] K. Camilleri and M. Schlosshauer, “Niels Bohr as philosopher of experiment: Does
decoherence theory challenge Bohr’s doctrine of classical concepts?,” Studies in History
and Philosophy of Modern Physics 49 (2015), 73–83, arXiv:1502.06547.
[5] C. A. Fuchs, “Notwithstanding Bohr, the Reasons for QBism,” Mind and Matter 15
(2017), 245–300, arXiv:1705.03483.
[6] J. Bub, “Whose Information? Information About What?,” in Quantum [Un]Speakables
II, ed. Reinhold Bertlmann and Anton Zeilinger, (Vienna: Springer, 2017), 143–54.
15
[7] J. Bub, “Why Bohr was (Mostly) Right,” arXiv:1711.01604 (2017).
[8] “Oral History Interviews: P. A. M. Dirac – Session V,” https://www.aip.org/
history-programs/niels-bohr-library/oral-histories/4575-5.
[9] “Oral History Interviews: Hendrik Casimir – Session II,” https://www.aip.org/
history-programs/niels-bohr-library/oral-histories/4550-2.
[10] B. C. Stacey, “Misreading EPR: Variations on an Incorrect Theme,” arXiv:
1809.01751 (2018).
[11] C. A. Fuchs, “Quantum Mechanics as Quantum Information (and only a little more),”
arXiv:quant-ph/0205039 (2002).
[12] H. Janssen, Reconstructing Reality: Environment-induced decoherence, the measurement problem, and the emergence of definiteness in quantum mechanics – A critical
assessment, Master’s thesis, Radboud University (2008).
[13] A. Kent, “Does it make sense to speak of self-locating uncertainty in the universal
wave function? Remarks on Sebens and Carroll,” Foundations of Physics 45, 2 (2015),
211–17, arXiv:1408.1944.
[14] L. Jansson, “Everettian quantum mechanics and physical probability: Against the principle of ‘State Supervenience’,” Studies in History and Philosophy of Modern Physics
53 (2016), 45–53.
[15] A. L. G. Mandolesi, “Analysis of Wallace’s proof of the Born Rule in Everettian quantum mechanics II: concepts and axioms,” Foundations of Physics 49, 1 (2019), 24–52,
arXiv:1803.08762.
[16] C. A. Fuchs and B. C. Stacey, “Some Negative Remarks on Operational Approaches to
Quantum Theory,” in Quantum Theory: Informational Foundations and Foils, edited
by G. Chiribella and R. W. Spekkens (Springer, 2016), arXiv:1401.7254 [quant-ph].
[17] C. A. Fuchs and B. C. Stacey, “QBism: Quantum Theory as a Hero’s Handbook,” in
Foundations of Quantum Theory, edited by E. M. Rasel, W. P. Schleich and S. Wölk
(IOS Press, 2019), arXiv:1612.07308 [quant-ph].
[18] W. Unruh, “Thoughts on non-locality and quantum mechanics,” International Journal
of Quantum Information 4, 1 (2006), 209–18.
[19] M. Smerlak and C. Rovelli, “Relational EPR,” Foundations of Physics 37 (2007),
427–45, arXiv:quant-ph/0604064.
[20] P. C. Hohenberg, “An introduction to consistent quantum theory,” Reviews of Modern
Physics 82 (2010), 2835–44, arXiv:0909.2359.
16
[21] B.-G. Englert, “On quantum theory,” The European Physical Journal D 67, 11 (2013),
238, arXiv:1308.5290.
[22] M. Żukowski and Č. Brukner, “Quantum non-locality — It ain’t necessarily so. . . ,”
Journal of Physics A 47 (2014), 424009, arXiv:1501.04618.
[23] R. F. Werner, “Comment on ‘What Bell did’,” Journal of Physics A 47 (2014), 424011.
[24] B. C. Stacey, “Von Neumann was not a Quantum Bayesian,” Philosophical Transactions of the Royal Society A 374, 2068 (2016), 20150235, arXiv:1412.2409.
[25] G. Hermann, “Die Naturphilosophischen Grundlagen der Quantenmechanik,” Die
Naturwissenschaften 42 (1935), 718–21.
[26] G. Hermann, “Die Naturphilosophischen Grundlagen der Quantenmechanik,” Abhandlungen der Fries’schen Schule 6 (1935), 69–152.
[27] N. D. Mermin and R. Schack, “Homer nodded: von Neumann’s surprising oversight,”
Foundations of Physics 48, 9 (2018), 1007–20, arXiv:1805.10311.
[28] C. Chevalley, “Why do we find Bohr obscure?,” in Epistemological and Experimental
Perspectives on Quantum Physics, edited by D. Greenberger, W. L. Reiter and A.
Zeilinger (Springer, 1999).
[29] P. Feyerabend, Killing Time: The Autobiography of Paul Feyerabend (University of
Chicago Press, 1995).
[30] E. P. Wigner, “On hidden variables and quantum mechanical probabilities,” American
Journal of Physics 38 (1970), 1005–09.
[31] G. Lüders, “Über die Zustandsänderung durch den Meßprozeß,” Annalen der Physik
8 (1951), 322–28. See http://www.physik.uni-augsburg.de/annalen/history/
historic-papers/1951_443_322-328.pdf. Translated by K. A. Kirkpatrick in “Concerning the state-change due to the measurement process,” Annalen der Physik 15
(2006), 663–70.
[32] G. Temple, “The fundamental paradox of the quantum theory,” Nature 135 (1935),
957.
[33] H. Fröhlich and E. Guth, “The fundamental paradox of the quantum theory,” Nature
136 (1935), 179.
[34] R. Peierls, “The fundamental paradox of the quantum theory,” Nature 136 (1935),
395.
[35] D. Wick, The Infamous Boundary: Seven Decades of Heresy in Quantum Physics (New
York: Copernicus, 1995).
17
[36] M. Viazovska, “The sphere packing problem in dimension 8,” Annals of Mathematics
185, 3 (2017), 991–1015, arXiv:1603.04246.
[37] B. C. Stacey, “Geometric and Information-Theoretic Properties of the Hoggar Lines,”
arXiv:1609.03075 quant-ph.
[38] B. C. Stacey, “Sporadic SICs and the Normed Division Algebras,” Foundations of
Physics (2017), arXiv:1605.01426 [quant-ph].
[39] M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of QM in
Historical Perspective (John Wiley and Sons, 1974).
[40] J. Emspak, “Are the Nobel Prizes Missing Female Scientists?,” Scientific American (7
October 2016).
[41] “Oral History Interviews: Melba Phillips,”
https://www.aip.org/history-programs/niels-bohr-library/
oral-histories/32719.
[42] K. S. Thorne, Black Holes & Time Warps: Einstein’s Outrageous Legacy (Norton,
1994).
[43] P. R. Saulson, “Josh Goldberg and the physical reality of gravitational waves,” General
Relativity and Gravitation 43, 12 (2011), 3289–99.
[44] P. Benioff, “The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines,” Journal of
Statistical Physics 22, 5 (1980), 563.
[45] R. W. Spekkens, “Evidence for the epistemic view of quantum states: A toy theory,”
Physical Review A 75, 3 (2007), 032110, arXiv:quant-ph/0401052.
[46] R. W. Spekkens, “Reassessing claims of nonclassicality for quantum interference phenomena,” PIRSA:16060102 (2016).
[47] R. P. Feynman, F. B. Morinigo and W. G. Wagner, Feynman Lectures on Gravitation
(Addison-Wesley, 1995).
[48] P. Byrne, The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured
Destruction, and the Meltdown of a Nuclear Family (Oxford University Press, 2010). I
recommend Adrian Kent’s review of this book, and not just for the phrase “discomfited
heteronormative eels” (arXiv:1103.4163).
[49] J. A. Wheeler, “Include the observer in the wave function?,” in Quantum Mechanics:
A Half Century Later, edited by J. Leite Lopes and M. Paty (D. Reidel Publishing,
1977).
18
[50] J. A. Wheeler, “The Universe as home for Man,” American Scientist 62, 6 (1974),
683–91.
[51] C. W. Misner, K. S. Thorne and W. H. Zurek, “John Wheeler, relativity, and quantum
information,” 62, 4 Physics Today (2009), 40–46.
[52] E. S. Fry and R. C. Thompson, “Experimental test of local hidden-variable theories,”
Physical Review Letters 37, 8 (1976), 465–68.
[53] H. Kragh, “Paul Dirac: Seeking Beauty,” Physics World 15, 8 (2002), 27–31.
[54] A. Bokulich, “Paul Dirac and the Bohr–Einstein debate,” Perspectives on Science 16,
1 (2008), 103–14.
[55] H. Kragh, “Quantenspringerei: Schrödinger vs. Bohr,” RePoSS: Research Publications
on Science Studies 14 (2011).
[56] A. De Gregorio, “Bohr’s way to defining complementarity,” Studies in History and
Philosophy of Modern Physics 45 (2014), 72–82.
[57] N. Bohr, “The quantum postulate and the recent development of atomic theory,”
Nature 121 (1928), 580–90.
[58] A. M. Gleason, “Measures on the closed subspaces of a Hilbert space,” Indiana University Mathematics Journal 6, 4 (1957), 885–93.
[59] M. P. Solèr, “Characterization of Hilbert spaces by orthomodular spaces,” Communications in Algebra 23, 1 (1995), 219–43.
[60] R. Haag, “Some people and some problems met in half a century of commitment to
mathematical physics,” European Physical Journal H 35 (2010), 263–307.
[61] https://www.math.columbia.edu/~woit/wordpress/?p=10147
[62] M. Schlosshauer and A. Fine, “On Zurek’s derivation of the Born rule,” Foundations
of Physics 35, 2 (2005), 197–213, arXiv:quant-ph/0312058.
[63] J. B. DeBrota and B. C. Stacey, “FAQBism,” arXiv:1810.13401 (2018).
[64] S. Glashow, “Not So Real,” Inference 4, 2 (2018).
[65] B. C. Stacey, “Book Review: What Is Quantum Information?,” Theoria 34, 1 (2019),
153–55.
[66] M. Appleby, C. A. Fuchs, B. C. Stacey and H. Zhu, “Introducing the Qplex: A novel
arena for quantum theory,” European Physical Journal D 71 (2017), 197, arXiv:
1612.03234.
19
[67] A. Wilce, “A royal road to quantum theory (or thereabouts),” Entropy 20, 4 (2018),
227, arXiv:1606.09306.
[68] Č. Brukner and A. Zeilinger, “Information invariance and quantum probabilities,”
Foundations of Physics 39 (2009), 677–89, arXiv:0905.0653.
[69] N. D. Mermin, “Hidden variables and the two theorems of John Bell,” Reviews of
Modern Physics 65 (1993), 803–15, arXiv:1802.10119.
[70] C. A. Fuchs, N. D. Mermin and R. Schack, “An Introduction to QBism with an Application to the Locality of Quantum Mechanics,” American Journal of Physics 82
(2014), 749–54, arXiv:1311.5253.
[71] H. C. von Baeyer, QBism: The Future of Quantum Physics (Cambridge, Massachusetts:
Harvard University Press, 2016).
[72] R. Healey, “Quantum-Bayesian and Pragmatist Views of Quantum Theory,” in
The Stanford Encyclopedia of Philosophy, ed. E. N. Zalta (Metaphysics Lab, Stanford University, 2016), https://plato.stanford.edu/archives/spr2017/entries/
quantum-bayesian/