On 25 March 1935, the Physical Review received a paper from Albert Einstein, Boris Podolsky, and Nathan Rosen, with the title “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” A few days later, on 30 March 1935, I was born. My life with Einstein was off to a promising start.

Some would call it an inauspicious start. Abraham Pais, for example, says in his otherwise admirable biography of Einstein [1] that “the only part of this article that will ultimately survive, I believe, is this last phrase [No reasonable definition of reality could be expected to permit this], which so poignantly summarizes Einstein's views on quantum mechanics in his later years.” But today, in this centenary of the Einstein annus mirabilis, as the EPR paper and I both turn 70, it is, in fact, the most cited of all Einstein's papers [2]. The debate over its conceptual implications rages hotter than ever, and for the first time, practical (well, for the moment still gedanken practical) applications of the EPR effect have emerged in cryptography and in other areas of quantum information processing.

Being only five weeks old, I was unprepared to pay attention to the article that appeared in the New York Times on 4 May 1935 under an elaborate set of headlines and subheads:

And I was completely oblivious to the stern rebuke from Einstein himself, published three days later in the Times, which declared that “any information upon which the article … is based was given to you without my authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press.”

Apparently Podolsky had tipped off the Times to the article, which did not appear in the sacred press until the 15 May issue of Physical Review. It is not clear that Einstein ever forgave him, and I wish I had been old enough to send Podolsky a cross letter myself.

Anyone growing up in America in the 1940s knew that the preeminent genius of our age, and perhaps of any other, lived in Princeton, New Jersey, had a predilection for baggy sweaters, and was always badly in need of a haircut—as far ahead of his time in dress and grooming as he was ahead in science during his 1905 annus mirabilis.

Attitudes toward quantum mechanics differ interestingly from one generation of physicists to the next. The first generation are the founding fathers, who struggled through the welter of confusing and self-contradictory constructions to emerge with the modern theory of the atomic world and supply it with the “Copenhagen interpretation.” On the whole they seem to have taken the view that while the theory is extraordinarily strange (Bohr is said to have remarked that if it didn't make you dizzy then you didn't really understand it), the strangeness arises out of some deeply ingrained but invalid modes of thought. Once these are recognized and abandoned the theory makes sense in a perfectly straightforward way. The word “irrational,” which appears frequently in Bohr's early writings about the quantum theory, is almost entirely absent from his later essays.

The second generation, those who were students of the founding fathers in the early postrevolutionary period, seem firmly—at times even ferociously—committed to the position that there is really nothing peculiar about the quantum world at all. Far from making bons mots about dizziness, or the opposite of deep truths being deep truths, they appear to go out of their way to make quantum mechanics sound as boringly ordinary as possible.

The third generation—mine—were born a decade or so after the revolution and learned about the quantum as kids from popular books like George Gamow's. We seem to be much more relaxed about it than the other two. Few of us brood about what it all means, any more than we worry about how to define mass or time when we use classical mechanics. In contemplative moments some of us think the theory is wonderfully strange and others think it isn't; but we don't hold these views with great passion. Most of us, in fact, feel irritated, bored, or downright uncomfortable when asked to articulate what we really think about quantum mechanics.

I'm one of the uncomfortable ones. If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be “Shut up and calculate!” But I won't shut up. I would rather celebrate the strangeness of quantum theory than deny it, because I believe it still has interesting things to teach us about how certain powerful but flawed verbal and mental tools we once took for granted continue to infect our thinking in subtly hidden ways.

Many years ago I was writing a talk, “My Life with Landau,” for a conference commemorating the 80th anniversary of the birth of the great L. D. Landau [1]. I knew I was going to have to deliver it before an audience that included Michael Fisher, and I found, to my distress, that as I sat there at the keyboard the image of Michael kept intruding on my thoughts, questioning my assumptions, denouncing mean field theories, and otherwise disrupting my concentration, in the way that we have all come to know and love. Finally, to chase him away, I wrote “Some day I would like to give a talk on ‘My Life with Fisher’” and strangely enough, that got rid of him. But I've known ever since that the time would come when I would have to pay for that liberating moment.

I first heard of Michael Fisher in 1963, at the beginning of my postdoctoral year at La Jolla. I met another young postdoc, Bob Griffiths, and in response to the intellectual sniffing out that goes on on such occasions, Griffiths let it be known that what he was up to was proving that the free energy of a spin system exists. “That it what?” I said. “That it exists,” said Griffiths firmly. “I'm using some ideas I got from Michael Fisher.” Well, I thought, this Griffiths seems like a nice guy anyway. And I decided that this mentor of his, this Fisher, must be a man with deep philosophical interests—a sort of Plato of thermodynamics.

I didn't hear of Fisher again until I got to Cornell in 1964 and Ben Widom told me one day that Michael Fisher was coming for a visit. “That's nice,” I said, and remembering him as Griffiths’ mentor, looked forward to meeting such a quiet and contemplative man. The visit lasted over 20 years, and turned into the most wonderful thing that has happened to me in my professional life.

Let me trace for you Michael's trajectory through the acknowledgments sections of my publications. He first shows up at the end of the 1966 paper in which Herbert Wagner and I give our version of Hohenberg's theorem.

A bad habit is something you do, without being fully aware of it, that makes life harder than it needs to be. It is a bad habit of physicists to take their most successful abstractions to be real properties of our world. Since the distinction between real and abstract is notoriously problematic, you might wonder what it means to wrongly confer reality on something abstract. I shall illustrate our habit of inappropriately reifying our successful abstractions with several examples.

Perhaps the least controversial examples are provided by quantum mechanics. The quantum state may well be the most powerful abstraction we have ever found. Are quantum states real?

In considering what that question might mean, recall that in the early days Erwin Schrödinger thought that the quantum state of a particle—in the form of its wavefunction—was as real a field as a classical electromagnetic field is real. He abandoned that view when he recognized that nonspreading wavepackets were a peculiarity of the harmonic oscillator, and that the wavefunction of N particles is a field only in a 3N-dimensional space.

But that does not prevent advocates of the de Broglie–Bohm “pilot wave” interpretation of quantum mechanics from taking the wavefunction of N particles to be a real field in 3N-dimensional configuration space. They give that high-dimensional configuration space just as much physical reality as the rest of us ascribe to ordinary three-dimensional space. The reality of the wavefunction is manifest in its ability to control the motion of (real) particles, just as a classical electromagnetic field is able to control the motion of classical charged particles.

For the past decade and a half Christopher Fuchs and Rüdiger Schack (originally in collaboration with Carlton Caves) have been developing a new way to think about quantum mechanics. Fuchs and Schack have called it Qbism [2]. Their term originally stood for “quantum Bayesianism.” But QBism is a way of thinking about science quite generally, not just quantum physics [3], and it is pertinent even when probabilistic judgments, and therefore “Bayesianism,” play no role at all. I nevertheless retain the term QBism, both to acknowledge the history behind it, and because a secondary meaning remains apt in the broader context: QBism is as big a break with 20th-century ways of thinking about science as cubism was with 19th-century ways of thinking about art.

QBism maintains that my understanding of the world rests entirely on the experiences that the world has induced in me throughout the course of my life. Nothing beyond my personal experience underlies the picture that I have formed of my own external world. This is a statement of empiricism. But it is empiricism taken more seriously than most scientists are willing to do.

To state that my understanding of the world rests on my experience is not to say that my world exists only within my head, as recent popularizations of QBism have wrongly asserted [4]. Among the ingredients from which I construct my picture of my external world is the impact of that world on my experience, when it responds to the actions that I take on it.

If you ask Google to search for “no quantum world,” you will get nearly 300 hits. They all give the following quotation (or recognizable corruptions of it):

Over 90% of them attribute the statement to Niels Bohr, with phrases like “Bohr's dictum …,” “Bohr insisted that …,” “Bohr proclaimed …,” “Niels Bohr said, in a frequently quoted passage …,” “Niels Bohr wrote [my emphasis] …,” and even “Explain and evaluate Bohr's philosophy of quantum theory with reference to his assertion ….”

Here is yet another example of the power of the internet to enrich our knowledge. There is only one problem. Bohr, who took writing very seriously indeed, never published such an assertion in any of his writings, although he repeatedly refined, reformulated, and often simply repeated his position on the philosophical foundations of the quantum theory.

The statement actually comes from an essay by Aage Petersen, “The Philosophy of Niels Bohr” [1], which he published in the Bulletin of the Atomic Scientists shortly after Bohr's death. Petersen introduced the words with

So what may now be the most celebrated of all Bohr quotations on the nature of the quantum theory is at best an attempt by a close associate to characterize Bohr's general response to the highly problematic notion of a “quantum world,” written too late for Bohr to respond.

When you ask Google to list only those pages that also mention the actual author of the words, Petersen, the number of hits drops from 286 to 18. The status of this “quotation” as hearsay is in danger of being lost.

I'm particularly sensitive to this risk because in the 1980s I used to enjoy giving physics colloquia on Bell's theorem and its implications for our understanding of quantum mechanics. I was always fond of Petersen's recollection of what Bohr used to say, and I felt that his formulation captured something important about the situation revealed by Bell's theorem.

The story you are about to read is true. The names, to be sure, have been changed, but not to protect the innocent. Professor Mozart would have been only too pleased for me to use his real name, but we agreed that you, dear reader, might think you were reading a piece of special pleading on behalf of a particular person. Far from it. The point of my tale is not that one physicist has been badly dealt with by the National Science Foundation; indeed Mozart has been very well treated over the years and considers himself lucky to have escaped this time with the wherewithal to keep supporting a solitary graduate student. No, the point of this tale is to illustrate more vividly than reams of surveys or statistics could possibly convey what has happened to NSF support for research in condensed-matter theory.

Condensed-matter theorists have been maintaining for some time, in these pages and even on the op-ed page of The New York Times, that their discipline is being starved by NSF. In reply, NSF has insisted that things are hard all over, and scientists from all over have tended to agree. So I offer the tale of Professor Mozart as a benchmark against which to test the plight of your own field. Have things like this been happening to people in your corner of science?

My tale begins several months ago, when NSF phoned Professor Mozart to tell him that a small condensed-matter theory grant he shared with Professor Beethoven would be renewed, but with a 20% cut—Mozart was to lose 30% and Beethoven 10%.

Mozart was told that four of the five reviewers had given the proposal E's (the highest possible rating) and one a G (two notches down from the top or two notches up from the bottom, depending on the case you're trying to make). Mozart was informed that he, not Beethoven, was responsible for this blemish, and was urged to get his act together if he expected to get any support at all in the next round.

Mozart, who knows perfectly well how things stand in condensed-matter theory and had been expecting far worse, was actually relieved by this turn of events.

A major impediment to writing physics gracefully comes from the need to embed in the prose many large pieces of raw mathematics. Nothing in freshman composition courses prepares us for the literary problems raised by the use of displayed equations. Our knowledge is acquired implicitly by reading textbooks and articles, most of whose authors have also given the problem no thought. When I was a graduate teaching assistant in a physics course for nonscientists, I was struck by the exceptional clumsiness with which extremely literate students who lacked the exposure even to such dubious examples treated mathematics in their term papers. The equations stood out like droppings on a well-manicured lawn. They were invariably introduced by the word “equation,” as in “Pondering the problem of motion, Newton came to the realization that the key lay in the equation

F = ma”.

To these innocents equations were objects, gingerly to be pointed at or poked, not inseparably integrated into the surrounding prose.

Clearly people are not born knowing how to write mathematics. The implicit tradition that has taught us what we do know contains both good strands and bad. One of my defects of character being a preference for form over substance, I have worried about this over the years, collecting principles that ought to govern the marriage of equations to readable prose. I present a few of them here, emphasizing that the list makes no claim to be complete. We are constantly assaulted by so many egregious violations of even these simple precepts that I offer them in the hope that a few sinners—not only writers, but copy editors, publishers of journals, and even the authors of the mathematics subsections of literary style manuals—may read them and repent the error of their ways, or even be inspired to further beneficial studies of the sadly neglected field of mathematico-grammatics.

Rule 1 (Fisher's rule). This rule, named after the savant who reprimanded me for abusing it when I was young and foolish, simply enjoins one to number all displayed equations. The most common violation of Fisher's rule is the misguided practice of numbering only those displayed equations to which the text subsequently refers back. I call this heresy Occam's rule.

Longtime readers of Reference Frame may remember my opinionated, cigar-smoking friend Professor Mozart, who last appeared in Physics Today in August 1999, having dropped in on me after seven years of retirement on a small tobacco plantation in Connecticut. Another eight years having passed, there he was again, at my office door. “W. A.!” I shouted with surprise and delight. “How's the tobacco business?”

“Left it,” he growled. “Taken the pledge.” And indeed, he gave off no smoky aroma. “Bought a vineyard. Napa Valley. Took up poetry. Thirty-third anniversary of the November revolution of 1974. Third of a century. Time to celebrate with commemorative verses.” He sighed. “Brought the project to the attention of the Poet Laureate. Doesn't know enough physics. So,” he added in a business-like tone of voice, “I did it myself.” And before I could say another word of welcome, he declaimed:

At this he took a deep bow. “Very nice, Bill,” I said politely, “but don't you think 18 unrelieved couplets get a bit bumpy?”

“The uniformity is relieved by the random variation of 8 feminine (twaddle-model, glory-story, …) and 10 masculine (name-game, charge-large, …) rhymes.

In 1988, on the 80th anniversary of his birth, there was a conference in Tel Aviv in memory of Lev Davidovich Landau. I announced at the beginning of my own talk—“My Life with Landau”—that I was going to break new ground as a scientific expositor, by following the practice of humanists and reading from a manuscript that I had prepared in advance.

To my surprise Rudolf Peierls, who was sitting in the front row, shook his head emphatically. Professor Peierls disapproves, I told the audience. “Yes,” he said, “this is not a good way for a physicist to give a talk.” “Well,” I said, “it's better than what most physicists do now, reading their talk from plastic sheets while projecting it on a screen.” He looked at me with that sweet half-smile of his and said “That is also a bad way to give a talk.”

In preparing this lecture I reread Bird of Passage, Peierls’ 1985 memoirs [1]. There I discovered that these views, like everything else I ever heard from him, were not casually put forth. They were based on experience and reflection. He says (p. 256):

Nevertheless, as in Tel Aviv in 1988, so in Santa Barbara in 1997, fully mindful of the fitting-in problem, I will try to follow a written draft without trying to reproduce the text verbatim. Today it will be easier because, most regrettably, Peierls is not here with us to explain exactly what is wrong with this approach.

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.