My amiable friend Professor Mozart dropped by the other day. Now that his NSF grant has been cut way back, he has more time to think about things, and it's a pleasure to chat with him. Some of his views, though, are more than a little peculiar, as the following conversation clearly reveals.

“I have to admit,” Mozart began sadly, “that particle physics over the last 40 or 50 years has been a disappointment. Who would have expected that in half a century we wouldn't learn anything really profound?”

“Nothing profound?!” I exploded. “What about parity nonconservation? What about the breakdown of time-reversal symmetry?”

“To be sure,” sighed Mozart, “we've learned that left can be distinguished from right and that time past is different from time future. But most ordinary people knew the difference between left and right all along, and who except the most highly trained physicists—temporarily, it now turns out—ever doubted for a moment that they could tell the future from the past? So establishing that the asymmetry is really there after all is certainly commendable. But about really serious problems we've discovered nothing—nothing whatsoever about the central puzzle.”

“And just what might that puzzle be?” I urged, for he seemed in danger of succumbing to an attack of melancholia.

He revived. “All particle physics has taught us about the central mystery is that quantum mechanics still works. Perfectly, as far as anybody can tell. What a letdown!”

“Letdown? It's a triumph!”

“Letdown!” he insisted. “Think of the previous half-century, when we went down from the macroscopic by seven or eight orders of magnitude. What delicious confusion! All the verities of the preceding two centuries, held by physicists and ordinary people alike, simply fell apart—collapsed. We had to start all over again, and we came up with something that worked just beautifully but was so strange that nobody had any idea what it meant except Bohr, and practically nobody could understand him. So naturally we kept probing further, getting to smaller and smaller length scales, waiting for the next revolution to shed some light on the meaning of the old one. But what happened? For 65 years, since 1925, we've been probing, at finer and finer levels.

In a Commentary in the July 2012 issue of Physics Today, I maintain that stubborn problems in the interpretation of quantum mechanics melt away if one takes literally Niels Bohr's dictum that the purpose of science is not to reveal “the real essence of the phenomena” but to find “relations between the manifold aspects of our experience” [1].

This same view of science, that it is a tool each of us uses to organize our own experience, also disposes of the vexing but entirely classical problem of “the Now.” Rudolf Carnap states the problem succinctly in his report of a conversation with Albert Einstein:

The issue here is not, as you might think, that the simultaneity of events in different places depends on frame of reference. Events whose temporal ordering is ambiguous relative to an event that I experience Now are irrelevant, because they are outside the backward and forward light cones of my Now and cannot affect or be affected by what I experience Now. Whether or not I choose to regard them as contemporary with my Now is entirely a matter of personal convention. The actual issue is that physics seems to have nothing whatever to say about the Now even at a single place, but deals only with relations between one time and another, in spite of the fact that the present moment is immediately evident as such to each and every one of us.

Any person's Now is a special event for that person as it is happening. By an “event” I mean an experience whose duration and location are restricted enough that it can usefully be represented as a point in space and time. My Now is distinguished from other events I have experienced by being the actual current state of affairs. I can distinguish it from earlier events (former Nows) that I merely remember and from later events that I can only imagine. My remembered past terminates in my Now.

Many scientists pride themselves on their ability to read difficult texts in areas of their discipline conceptually or historically remote from their own. It has become evident in the recent “science wars” between scientists and science critics that this ability can diminish rapidly with interdisciplinary distance. (I use the word “critics” in the neutral sense—cf. “theater critics.” I can think of no other term encompassing the full array of practitioners from sociology, anthropology, history, literature, and cultural studies who have turned their attention to the activity of scientists.) Fronts are opening in the science wars on which some scientists are misrepresenting and oversimplifying as egregiously as those at whom they direct their fire.

I shall illustrate this with one of the strangest and most notorious texts on the battlefield, Bruno Latour's “A Relativistic Account of Einstein's Relativity” [1]. This essay has been criticized by physicists for misconstruing the content of relativity and being filled with elementary technical mistakes. It is on display in Alan Sokal's famous spoof [2], one of its “mistakes” showed up in Steven Weinberg's much-cited article in the New York Review [3], and I know of two articles on the “Relativistic Account” scheduled to appear in anthologies devoted to the new and gloomy art of extracting technical errors from the writings of science critics.

I believe such attacks miss the point of Latour's essay. While I have not myself succeeded in making complete sense of it, there are texts by Nietzsche, Hegel, and Kant in which there is virtually nothing I can make sense of. Nevertheless, I have not concluded that they are charlatans. Critics of the science critics ought to exercise similar caution. The straightforward explicit style toward which scientists strive (and pick up any issue of Science to remind yourself how successful we are in achieving it) is inappropriate in disciplines where the objects and aims of inquiry have themselves an ambiguous and uncertain character.

Latour takes an anthropological slant on things. Physicists recently discovering his “relativistic account” are not the only ones he puzzles. Many distinguished British critics of science find him a far-from-easy read, and they have fired more accurate salvos in his direction than some of the interdisciplinary ballistic missiles I have seen launched from the science side.

A quantum computer is a digital computer capable of exploiting quantum coherence among the physical two-state systems that store the binary arithmetic information.

To factor an integer is to find its (unique) expression as a product of prime numbers.

The most impressive, most important, and best-known thing a quantum computer can do is to factor with spectacular efficiency the product of two enormous prime numbers. But what on earth can quantum mechanics have to do with factoring?

This question bothered me for four years, from the time I heard about the discovery that a quantum computer was spectacularly good at factoring until I finally took the trouble to find out how it was done. The answer, you will be relieved—but, if you're like me, also a little disappointed—to learn, is that quantum mechanics has nothing at all directly to do with factoring. But it does have a lot to do with waves. Many important waves are periodic, so it is not very surprising that quantum mechanics might be useful in efficiently revealing features associated with periodicity.

Quantum mechanics is connected to factoring through periodicity. It turns out, for purely arithmetic reasons having nothing to do with quantum mechanics, that if we have an efficient way to find the period of a periodic function, then, as we shall see below, we can easily factor the product of two enormous prime numbers. And a quantum computer provides an extremely efficient way to find periods.

All of the above is of considerable practical importance, because the great difficulty in factoring such a product—where the two enormous prime numbers are typically each several hundred digits long—is the basis for the security of the most widely used encryption scheme (called RSA [1] encryption) for protecting private information sent over the internet. In 1994 Peter Shor discovered [2] that a quantum computer would be super-efficient at period finding and thereby pose a potential threat to innumerable secrets. Whence the explosion of interest in developing quantum computation. The threat is only potential because no quantum computer capable of anything like serious period finding currently exists.

I suspect the emphasis has been put on factoring rather than period finding because factoring is more famously associated with RSA code breaking, although, as it happens, period finding can be used directly to crack the RSA code, without any need for a detour into factoring.

In 1963 I applied for academic positions in the United States from Birmingham, England, where I was finishing two postdoctoral years in Rudolf Peierls’ wonderful department. In those early post-Sputnik halcyon days you then applied for assistant professorships and collected the offers that came in reply. Peierls had suggested that I send such a letter to Walter Kohn. Disappointingly, he offered only a two-year postdoc. But I had never been to California and Peierls clearly had a high regard for the man, so this otherwise noncompetitive proposal was tempting. I asked the people at Cornell, who did come through with a faculty position, whether I could defer it for two years to do a postdoc in La Jolla. They said two would be too many but one would be OK. Walter said one was fine with him, so in August 1963 I showed up in La Jolla.

Walter was not there. He was finishing a sabbatical in Paris. But there were several wonderful postdocs, the Physics Department was still located right on the beach, Dorothy and I found a house in Del Mar on a cliff overlooking the Pacific for $128 a month, and life was good. (I had written a letter from Birmingham to an acquaintance from college who was then a postdoc in La Jolla, asking what it was like there. All I remember from his reply was “Volleyball is standard on the beach at noon.”)

Eventually the moment of truth arrived. The boss returned. The holiday threatened to end. Walter invited me to his office to say hello. It was immediately clear that this was a kind, charming, witty man. After we had exchanged pleasantries, he told me about a little theorem he and Pierre Hohenberg had proved back in Paris. The proof was one of those clever three-line arguments that wouldn't have occurred to me if I had thought about it for a hundred years, but was utterly simple and transparent when Walter laid it out in front of me.

He asked me to think about how to generalize the theorem from the ground state to thermal equilibrium. I returned to my office to consider it, and quickly realized that a new variational principle for the free energy that I had formulated in Birmingham for an utterly unrelated purpose, seemed to be tailor-made for generalizing the Hohenberg–Kohn theorem to nonzero temperature.

I have a colleague who goes around declaring that the laws of physics require consciousness to cease with the death of the body. What he really means is that although he has no idea what underlies the phenomenon of consciousness, he can't imagine it's more than an extremely subtle manifestation of physiological processes that come to a halt when the body does. I'd be inclined to agree if he'd put it that way, but he doesn't. He insists on saying “Science has shown it,” which I take to be shorthand for “Stop thinking and believe me.” He invokes “science” as a blessing to sanctify what he says, or as a club to beat into submission those he disagrees with.

The public should be warned about such abuses of the name of science, and two sociologists, Harry Collins and Trevor Pinch, have set out to do that. “What everyone should know about science” is the subtitle of The Golem, their award-winning book of essays. Written “for the general reader who wants to know how science really works and to know how much authority to grant to experts,” it is a central text in a growing controversy between scientists and those who study science. Collins and Pinch take as their image for science the mythical golem, a “lumbering fool who knows neither his own strength nor the extent of his clumsiness and ignorance … not an evil creature, but a little daft.” Their aim is to explain “what actually happens” in science. Prepare, they enjoin the reader, “to learn to love the bumbling giant for what it is.”

This is a fine goal. Scientists who set themselves up as sorcerers are a menace to the public and to science itself. People ought to have a better idea of what science can and cannot do. Unfortunately, however, though there are many fascinating tales about science in The Golem, Collins and Pinch infer from these studies a seriously deficient picture of the scientific enterprise. Here are some typical conclusions:

1. “Scientists at the research front cannot settle their disagreements through better experimentation, more knowledge, more advanced theories, or clearer thinking.”

2. “The truth about the natural world [is] what the powerful believe to be the truth about the natural world.” […]

“Enter!” ordered Professor Mozart, as I knocked briskly on his door. Bracing myself against the ambience of stale Havana smoke, I walked in and got right to the point. “W. A., I've got a favor to ask you.” He looked up inquisitively. “As you know,” I continued, “I have now achieved a modicum of fame as a columnist with Physics Today.”

Mozart snorted derisively. He is not altogether pleased with my publishing our private conversations. “Because I am a columnist Physics Today has decided not to review my recent book of essays. I have thus been unable to bring it to the attention of my literary fans, except by the crude and low-density expedient of inserting advertising transparencies into all my public lectures.” His look of derision modulated to outright scorn, but I persisted. “W. A.—Bill—could you write a review of it?”

“Ha!” he offered.

“What does that mean?” I inquired, having learned not to be put off by Mozart's moments of withering contempt. “The book appeared before I invented you, so there's no conflict of interest.”

“The problem, my friend, is that I thought your book was dreadful.”

“That's not a problem,” I explained. “A hostile review will do just as well as a friendly one. The only point is to make my readers aware of the book; they'll judge for themselves. But only one book review has appeared in the entire United States, in an obscure journal of physics pedagogy. Most people don't even know the book exists. Even an unsympathetic review will bring it to their attention and an attack so vicious that it sets them talking would be just what's needed.”

“It won't work,” he protested. “Physics Today doesn't even print Letters to the Editor from nonexistent people, so there's no way they'd do an entire book review.”

“Ah, but they might in a Reference Frame column,” I pointed out, “particularly if the review is negative. So you can pillory me to your heart's content, and still do me a favor. How can you resist!”

A wicked gleam came into his eye. “I'll do it!” he declared, and a week later a manuscript slid under my door which I reproduce verbatim below.

“Two Experiments that ‘Proved’ Relativity” is Chapter 2 of The Golem: What Everyone should Know about Science. This prize-winning book of essays by the sociologists Harry Collins and Trevor Pinch is at the center of an ongoing debate between scientists and those who study science. In Chapter 2, Collins and Pinch use examples from the history of relativity to show the lay reader how they believe science reaches its conclusions. Here I use their essay to show readers of Physics Today how I believe Collins and Pinch reach theirs.

The two experiments are the Michelson–Morley experiment and the Eddington solar eclipse expedition of 1919. I learned a lot about both from Collins and Pinch, but I found unconvincing the lessons about the nature of science they draw from these studies of relativity. I focus on their treatment of the Michelson–Morley experiment, and how it bears on the acceptance of special relativity by the scientific community.

The presentation of relativity in The Golem starts with a peculiar statement of the principle of the constancy of the velocity of light: “Einstein's insight [was] that light must travel at the same speed in all directions.”

This is the kind of simplification anyone might make in presenting a technical matter to the lay reader. But this particular reformulation of the postulate that the speed of light is independent of the speed of the source also happens to reinforce the view that Collins and Pinch develop—that doubts about the Michelson–Morley result put at risk the logical foundations of relativity.

The lay reader is told little about the actual content of special relativity. Time dilation and length contraction are briefly mentioned. The inclination everybody has on a first hearing—to regard these phenomena as outlandish—is heightened by qualifications such as “if Einstein's ideas are correct” and “if the theory is correct.” To this touch of skepticism Collins and Pinch add a dash of moral indignation by also mentioning the “sinister” mass–energy relation and the explosion of the atomic bomb. The bomb is cited as an incontrovertible piece of evidence for the validity of relativity. No other compelling evidence is offered.

The subject of Einstein–Podolsky–Rosen correlations—those strong quantum correlations that seem to imply “spooky actions at a distance”—has just been given a new and beautiful twist. Daniel Greenberger, Michael Horne, and Anton Zeilinger have found a clever and powerful extension of the two-particle EPR experiment to gedanken decays that produce more than two particles [1]. In the GHZ experiment the spookiness assumes an even more vivid form than it acquired in John Bell's celebrated analysis of the EPR experiment, given over 25 years ago [2]. The argument that follows is my attempt to simplify a refinement of the GHZ argument given by the philosophers Robert Clifton, Michael Redhead, and Jeremy Butterfield [3].

Consider three spin-½ particles, named 1, 2, and 3. They have originated in a spin-conserving gedanken decay and are now gedanken flying apart along three different straight lines in the horizontal plane. (It's not essential for the gedanken trajectories to be coplanar, but it makes it easier to describe the rest of the geometry.) I specify the spin state |Ψ〉 of the three particles in a time-honored manner, giving you a complete set of commuting Hermitian spin-space operators of which |Ψ〉 is an eigenstate.

Those operators are assembled out of the following pieces (measuring all spins in units of ½ ħ): σzi the operator for the spin of particle i along its direction of motion; σxi the spin along the vertical direction; and σyi, the spin along the horizontal direction orthogonal to the trajectory. (Any three orthogonal directions independently chosen for each particle would do. But we're going to be gedanken-measuring x and y components of each particle's spin, so it's nice to think of the x and y directions as orthogonal to the direction of motion, since the components can then be straightforwardly measured by passage through a conventional Stern–Gerlach magnet.) The complete set of commuting Hermitian operators consists of

σx1σy2σy3, σy1σx2σy3, σy1σy2σx3.

Even though the x and y components of a given particle's spin anticommute—a fact of paramount importance in what follows—all three of the operators in (1) do indeed commute with one another, because the product of any two of them differs from the product in the reverse order by an even number of such anticommutations. Because they all commute, the three operators can be provided with simultaneous eigenstates.

I've been asked to talk about questions I would ask physicists 200 years after Einstein's annus mirabilis, if I could be magically transported to the year 2105. Why me? Because five years ago the New York Times had an article about ten questions physicists would like to ask their colleagues in the year 2100. Most of those questions made me uncomfortable. They seemed temporally provincial—too absorbed with issues of the current decade or two. Consider, for example, question 4:

4. Is nature supersymmetric and, if so, how is supersymmetry broken? and question 7:

7. What are the fundamental degrees of freedom of M-theory and does the theory describe nature? It would surprise and disappoint me if the context and terms of such questions made sense to anybody but historians of science, after the passage of 100 years of research. The only question of the ten that struck me as reasonable was

Dimensionless parameters are likely to survive all but the most radical upheavals in our conception of the world. Indeed, the concept has been with us at least since the hydrodynamicists of the 19th century, and though fundamental constants are a 20th-century invention, they have been with us now for the better part of a century. This question, alone among the ten, satisfies all the criteria I'll describe later.

I felt uncomfortable not only with most of the questions, but with the whole exercise. Too many unimaginable things can happen in a century to render our current concerns irrelevant or obsolete. Just think about how physics changed in the century behind us.

I write an occasional column in Physics Today, commenting on various peculiarities of our profession, and the pitfalls of devising questions for colleagues 100 years from now struck me as a good topic. So in February 2001 I published an essay inspired by the article in the New York Times, giving my own list of ten questions, designed to highlight the futility of the whole exercise.

To set the stage for making inquiries a century into the future, one cannot do better than to recall the tale of Enoch Soames, as told by Max Beerbohm, in 1897.

Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem. I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’”

In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago.

Given my capacity for intellectual development (“inconsistency,” in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue.

This amnesia, combined with the evolution in my thinking that had distanced me from my long-forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as “the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics.”

I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics.

I first heard this joke from Rudolf Peierls in 1961. Since then the size of Physical Review has doubled, doubled again, and is on the verge of completing its third doubling. Physical Review Letters is nearly as big as Physical Review was in 1961. The journals of other physical societies have undergone comparable expansions, as have the numbers and sizes of the commercially published physics journals.

I was recently asked to address a group of Cornell alumni and librarians on how the library is used by a typical physical scientist. I did point out that they had selected a distinctly oddball specimen, but they persisted. So to give them a sense of the calamitous conditions we have created, I went systematically through the current periodicals section of the Cornell Physical Sciences Library to count how many journals I felt I ought to look at but didn't. My criterion was stringent: a journal made my list only if it would be downright embarrassing to admit that I never looked. I had to be able to imagine a colleague responding to my confession with amazement: “You never look at X?!” Counting only once those with multiple versions (A, B, C,…) I still found 32. In one case, uncertain whether an admission that I never looked would occasion a blush or merely a nervous giggle, I randomly opened a random issue and found an article I had not seen before, expanding interestingly upon earlier work of my own. That information had not been conveyed.

It is in this context that we must view the resistance of many scientists to current efforts by library administrators to make draconian cuts in their subscription lists. Keeping up with everything is driving the libraries into bankruptcy. Early signs of this problem and how physicists might respond surfaced over ten years ago. My colleague Ken Wilson and I, physics department representatives on the library committee and therefore conscious of the looming catastrophe, responded to announcements of two new physics journals by writing a letter to Physics Today announcing that our library could not afford any more subscriptions.

At the heart of the puzzlement induced in many by the quantum theory lies a tension between reality and knowledge, between facts and information. Do the basic entities of the theory, quantum states or their wavefunctions, directly correspond to something in the real world so that something—wavefunction stuff—actually does pass through both slits in a two-slit interference experiment? If so, then either we are faced with the puzzle of how something real can suffer abrupt changes in response to faraway events or, if we banish wavefunction collapse from the theory, we are faced with a reality that absurdly evolves to encompass myriads of alternative histories growing ever more unalike. These puzzles melt away if the basic entities of the theory are merely representations of knowledge, only to be replaced by others. Whose knowledge? Knowledge of what?

The new gedanken technology of quantum computation provides an unfamiliar perspective on such vexing questions, by using the quantum theory, not to expand our understanding and control of the physical world, but to exploit the quantum behavior of the physical world as a novel way to encode and process information. The information is primary; the underlying physical system only matters as a vehicle for that information. Quantum computer scientists view a set of n interacting spins-½ not for the insight it offers into the nature of magnetic materials, but as a way to represent and manipulate integers, through their n-bit binary representations as orthogonal states in a “computational basis” that specifies whether each individual spin is up (1) or down (0).

Quantum computation differs in several crucial ways from ordinary classical computation:

1. • The states of a quantum bit (which I here call a Qbit, in quixotic defiance of the fashionable but orthographically preposterous “qubit”) are not restricted to 0 or 1, as in a classical computer, but can be in arbitrary superpositions of 0 and 1.

2. • Even more foreign to classical intuition, the state of the entire computer can be what Schrödinger called verschränkt (entangled), with individual Qbits having no (pure) states of their own at all. While a classical computation flips classical Cbits between 0 and 1, a quantum computation subjects the Qbits to the much more general unitary transformations that specify the time evolution of quantum states.

I write bleary-eyed and disheartened, after a long proofreading session mainly devoted to inserting into the galleys calls for the restoration of what was capriciously and destructively altered in the editorial offices of Physical Review. I proofread simply by reading the galleys, without reference to the original manuscript. My writing is a process that does not converge: I cannot read a page of my own prose without wanting to improve it. Therefore when I read proofs I entirely ignore the manuscript except to check purely technical points. Proofreading offers one more shot at elusive perfection. Proceeding in this way. I come to the end of a paragraph with a lurching sensation. The last sentence seems to be a non sequitur. Can I be failing to get my own point? Turning to the copy-edited manuscript, I find a marginal message: “Author: Please note that we discourage single-sentence paragraphs.” As an application of this principle, one short emphatic paragraph has been attached to the end of another, to which it is entirely unrelated. If you set asunder what Physical Review has joined, it makes sense again.

What is the justification for such a rule? Excessive use of single-sentence paragraphs blurs the distinction between the sentence and the paragraph, makes for a visually unattractive page and becomes boring. But the occasional single-sentence paragraph is a powerful device. It gives a pause in the rush of thought, it focuses attention, and it can contribute powerfully to the rhythm of the prose. The Constitution of the United States of America, whose prose Warren Burger enjoined us to admire in its 200th-anniversary year, is chock-full of beautiful single-sentence paragraphs. A blanket prohibition is absurd, and enforcing it by paragraph grafting is almost certain to do violence to the clarity and even the meaning of a well-written essay. So I go through the galleys restoring the three or four indigestibly merged paragraphs, adding my own marginal messages (“Editor: We discourage gratuitous confusion”) in the hope that my counterinstructions will not be ignored.

A bit later I come to a reference to nature, “Nature herself,” I remember writing, “has proved to be quite unambiguous…” The galley reads, “Nature has proven quite unambiguous….” Not bad, I think, getting rid of that unnecessary “to be”—should have spotted it myself. But then I notice that nature has been depersonified.

What's wrong with this story? What strange, irrational, one might even say unprofessional act have I just described?

Was it wasteful of me to inflict this burden on so many in-baskets, knowing that considerably fewer than half the recipients will look at my paper? Not at all! I will be content if a dozen people take a serious look—that will be enough for my message to propagate—and I have followed the best strategy to bring that about.

Was I, then, foolish to waste paper, postage, and secretarial time in this old-fashioned effort at communication, when email would have done the trick effortlessly? Not yet! Not all my correspondents communicate in that way, I lack the electronic addresses of many of those who do, and surely somebody (though I have no idea who) is paying for all those email transmissions, so the monetary savings to society as a whole may be at least in part illusory.

Was it, perhaps, absurd of me to lavish extreme care on these preprints, rearranging the footnotes for easier reading, and even worrying about the proper choice of fonts to convey to my readers as clearly as possible the relations between the tiny sections and subsections?

Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation, disagreement about the meaning of the theory is stronger than ever. New interpretations appear every year. None ever disappear.

Probability theory is considerably older than quantum mechanics and has also been plagued from the beginning by questions about its meaning. And quantum mechanics is inherently and famously probabilistic.

For the past decade, Carl Caves, Chris Fuchs, and Rüdiger Schack have been arguing that the confusion at the foundations of quantum mechanics arises out of a confusion, prevalent among physicists, about the nature of probability [1]. They maintain that if probability is properly understood, the notorious quantum paradoxes either vanish or assume less vexing forms.

Most physicists have a frequentist view of probability: Probabilities describe objective properties of ensembles of “identically prepared” systems. Caves, Fuchs, and Schack take a personalist Bayesian view: An agent assigns a probability p to a single event as a measure of her belief that the event will take place [2].

Such an agent is willing to pay less than $p for a coupon that will pay her $1 if the event happens, and she is willing to underwrite and sell such a coupon for more than $p. Surprisingly, the standard rules for probability follow from the requirement that an agent should never face certain loss in a single event. (For example, if p exceeded 1, she would pay more than $1 for a coupon that returned at most $1; if p were negative, she would pay somebody to take a coupon from her that might cost her another $1.) Avoiding certain loss is the only constraint on an agent's probability assignments. The probability of an event is not inherent in that event. Different agents, with different beliefs, will in general assign different probabilities to the same event.

The personalist Bayesian view of probability is widely held [3], though not by many physicists. It has profound implications for the meaning of quantum mechanics, which Fuchs and Schack call quantum Bayesianism—QBism for short. Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.