Big, big thanks to David Mermin, Herschel Snodgrass, and Jacob Barandes, who were each a wonderful help in tracking down mistakes and gently explaining where I got things wrong (though I suspect that in attempting to fix these, I have introduced new ones–I can be reached through Facebook or Linkedin if anyone finds further errors).

Thanks also to Abner Shimony and to Alexander Stibor!

And thanks to two people I have never met: Jeremy Bernstein, who wrote a letter containing four of his concerns about the book, and Arnold Sikkima, who posted a list of both errata and recommendations on his website.

↑↓

Note: Where relevant, new text for the paperback will be in blue.

Second note: no notes about decoherence yet; I’m still working.

To get to an erratum on a specific page of the hardcover, use your internet browser’s “find” function (e.g., for an erratum for page 3, search for “p. 3″).

List of pages for errata or comments:

List of Illustrations: xi

Note to Reader: see postscript under “Methodology.”

Introduction: Entanglement: 3, 4, 6, 7

The Socks: 15, 17-18, 18, 20

The Arguments: 26, 31, 34, 44, 46n, 47, 49, 56n, 58, 66, 70, 77, 78, 83, 98, 117, 125, 128, 132, 136, 138

The Search & The Indictment: 189, 220

The Discovery: 240, 252, 257, 255-6, 259, 264, 276, 280, 284, 289

Entanglement Comes of Age: 298, 299, 301, 308-9, 311, 312, 325-6, 326, 331, 332

Glossary: 337, 338, 340, 343, 344, 345

Longer Summaries: 347, 348, 349, 350

then follow errata for:

Notes, Index (most important here is that some of the references to Bell’s specific papers got mis-indexed), Permissions page, Acknowledgments, and the note about the author. .

.

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ERRATA

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p. xi, p. 128, p. 138

The performance was actually called The Blegdamsvej Faust, after the street Bohr’s institute is on.

↔

{Introduction: Entanglement}

p. 3

Einstein wrote that in explaining things, one should be as simple as possible, but not more so. In my introduction of what Bell did, I oversimplified and overstated–and the effect of this for the reader, of course, is to make things confusing and complicated.

What Bell’s second 1964 paper did briefly and beautifully demonstrate was the utter lack of any common-sense mechanism correlating entangled particles.

p. 4

Here is another case where I oversimplified and thus complicated things. Throughout the book I tended to use “entanglement” as shorthand for “long-distance entanglement.” So when I mention “hints of entanglement’s spooky presence” on p. 4, what I am referring to is the fact that this strange correlation was known to exist over short distances–e.g., between the two electrons within a hydrogen molecule. Further (though no one seems to have commented on this till Einstein around 1930) the equations of quantum mechanics gave no upper bound on the distance such particles could be separated and still correlated.

p. 6

Here I am not taking into account the number of different hidden variables theories that exist. Really I am describing a de Broglie-Bohm type only.

p. 7

Another case of over-vagueness and grandiosity about Bell’s justly famous discovery.

Here is how this description will read in the paperback:

But no one following Bohr, Heisenberg, Pauli, Dirac, or Born dared grasp, measure, or even name the deepest of all the puzzles, entanglement. Then along came John Bell. An admirer of Einstein, Schrödinger, and de Broglie, he followed their minority views to their natural conclusions and brought unexpected clarity where before there had been fog. And what the fog had been hiding was vividly and wonderfully strange.

↔

{The Socks 1978 & 1981}

p. 15 & p. 301

Much as I love the antipodal contrast of “high energy” with “low temperature” physics, it is more accurate to refer to Mermin’s profession as “solid state” or “condensed matter” physics.

pp. 17-18

Talking about Bell’s theorem in accessible English is full of pitfalls, and one of those into which I fell is on p. 17, when I spoke of entangled particles not being “coordinated at the source.” What I was trying (and failing) to get at clearly was the point that entangled particles remain entangled even when apparently separate.

This is a case where the word “particle” is particularly misleading. Unlike twins who once were a single egg and ever after reveal the results of that long-ago fact, two entangled “particles” are one up to the moment we measure it/them and break the entanglement.

Here is how I re-wrote this sentence for the paperback:

More than forty years after Bell’s discovery, the completely mystifying unanswered question remains: if there are no connections between the detectors, and if what is arriving at them is not a pair of particles bearing identical ‘genes,’ what in the world causes identical lights to flash when the detectors are on identical settings?

Another pitfall I fell into is on the next page (18), where I quote d’Espagnat’s humorous version of Bell’s inequality:

“The number of young non-smokers

plus

the number of women smokers of all ages

is greater than or equal to

the total number of young women, smokers and otherwise.”

The quantum theory does not really “violate” this logic, as I claimed, but it does flout it. As David Mermin reminded me: “Quantum mechanics does not violate a tautology. It violates the premises behind the tautology: that it makes sense simultaneously to assign gender, age, and tobacco use to a person.”

p. 18

I didn’t like my use of the term “shared history” at the end of this page, and rephrased that sentence as follows:

With the possibility ruled out that Bell’s strangely connected particles start out complete with their synchronized instructions, we might wonder if instead there is some kind of signaling going on.

.

historical note on Feynman and Bell’s Theorem (re: pp. 20 & 312)

It was not Mermin’s paper which alerted Feynman to Bell’s theorem. Mermin suspected that Feynman had just come up with Bell’s theorem on his own. However, Clauser (reluctantly) had told Feynman about the Freedman-Clauser experiment sometime between 1969 and 1972. At the time, Feynman was dismissive. When Shimony, trying to track down how Feynman came up with Bell’s inequality, asked Clauser about this visit almost forty years later, Clauser couldn’t remember whether he had specifically cited Bell to Feynman or not.

As Shimony points out, things can feel as if they come from the subconscious which were actually once heard and then forgotten (he remembers a melody he wrote as a teenager which he later heard on the radio “attributed–correctly!–to Prokofiev’s Peter and the Wolf”). Clauser’s visit may well have subconsciously planted the seed which a decade later produced Feynman’s version of Bell’s inequality.

↔

{The Arguments 1909-1935}

p. 26

Perhaps I was too hurried in my treatment of Planck’s quantum breakthrough, with which almost every popularization of the quantum theory begins. Planck’s box–usually called a “blackbody”–must have reflective inner walls and absorb all light that falls on it.

p. 31

This is a comment about methodology in response to Jeremy Bernstein’s concern that the book was deceptive to a reader less erudite than himself–a concern that mostly stemmed from a misconstruction of the “Note to Reader” section.

As the notes make clear, the person to whom we know Einstein told the “madmen of Prague” story was Philipp Frank (and the date was probably 1911). Ehrenfest visited Einstein in Prague in February 1912. Though we have no report of Einstein’s also telling this story to Ehrenfest, it is unlikely that the story-telling Einstein–still in the same office with the same view of the insane asylum–would not have told the story to the story-enjoying Ehrenfest.

Einstein had redirected his efforts in physics, however, between the time of Frank’s visit and that of Ehrenfest. In May 1911, Einstein wrote to his best friend Besso, “I do not ask anymore whether these quanta really exist. Nor do I attempt any longer to construct them, since I now know my brain is incapable of advancing in that direction.” He began to work in the direction of the general theory of relativity in June of 1911, leaving behind his intense focus on the quantum theory for four and a half years.

Still, at the Solvay Conference in October 1911, Einstein was talking about the quantum theory, and Ehrenfest in the same month published his “Ultraviolet Catastrophe” paper–so in February 1912 it is still quite likely Einstein and Ehrenfest would be talking about the quantum theory in Einstein’s office.

Ehrenfest, von Laue, and Einstein definitely were talking about X-ray diffraction in a coffeeshop in Zurich after Lawrence Bragg’s speech in June of 1913 (see Martin Klein, Paul Ehrenfest, p. 294-5, who also reports that the discussion became an argument and that Boltzmann’s old antagonist, Zermelo, was also present and argued with Ehrenfest and Einstein about Brownian motion). Whether they would have gone on to discuss “the madness of the quantum theory”–as Einstein did in (early?) 1911 and in May of 1912, as well as other times throughout his life–is likely but of course not certain; again a look at the notes makes clear what is known and what is conjecture.

p. 34

The pure frequency emitted by an electron “jumping” from one Bohr orbit to another is the difference between the energies of the starting and ending orbits, divided by Planck’s constant, h.

p. 44

Trying to talk about “spin” in English is another famously dangerous activity. To speak broadly, Sommerfeld showed that atoms would respond in a quantized way to an external magnetic field. (In any given direction, the component of an atom’s magnetic field can only take a quantized set of values.)

footnote on p. 46

I garbled this discussion. Here’s my rewrite for the paperback:

Sommerfeld was wrong only because neither he nor anyone else yet knew about spin. This, along with electron angular momentum, affects an atom’s behavior in a magnetic field. Not knowing about spin, Sommerfeld based his calculation only on the angular momentum. Like spin, it is quantized. But unlike spin (which has exactly two allowed values, up or down), angular momentum has an odd number of allowed values, one of which is always zero. Silver has a binary response to the magnetic field due to the spin (up or down) of a single unpaired electron in its outermost energy level. But if Stern and Gerlach had used a different atom–one in which the spin had added to zero (ups canceling downs), but the angular momentum did not–Sommerfeld might have been correct to predict a beam splitting into an odd number of piles.

p. 47

Apologies to Pauli. In my over-eagerness to slip in the definition of momentum for readers that may not have yet encountered it, I misled. At the bottom of the switchbacks, Pauli will indeed travel further than Heisenberg or Laporte before he needs to start pedaling again, and his greater mass will play a part in this (in overcoming air resistance). The three young men’s velocities, on the other hand, will likely be close to equal, so the concept of momentum–mass multiplied by velocity–does not help us further in analyzing this situation. (A study of momentum becomes useful in cases of collisions or separations. The total momentum before and after the collision or separation will be conserved, as is demonstrated every day on pool tables and in car crashes.)

p. 49

It turns out that neither Sommerfeld nor Einstein was riding the streetcar with Bohr in 1923. The paperback will contain a postscript to the Note to the Reader explaining the situation (to be found on under “methodology” on this website), but I’ll add a few more notes here:

First, I am really grateful to Jeremy Bernstein, who pointed out that I had mis-read Bohr’s mention of Sommerfeld in describing this streetcar ride. Then, when I contacted the Niels Bohr Library to check this, Felicity Pors there told me that “newer research in connection with the Einstein Papers publication suggests that Einstein only visited Copenhagen in 1920.” (Sommerfeld had come in the fall of the previous year.)

In the 1961 interview which describes this streetcar jaunt, Bohr had said that “Einstein came to Copenhagen, maybe in connection with his receiving the Nobel prize in 1921. During that summer Einstein was traveling and gave lectures, I think in Göteborg….” This puts the conversation on the streetcar squarely in 1923, which is of course where Pais and others have it. Already, as I have noted in my book, this hypothesis makes Bohr’s statement (as translated by Pais) that “I naturally fetched him from the railway station” a bit strange. Looking at a map of Copenhagen shows that the ferry port–where Einstein would have arrived had he been coming from Sweden–is less than two miles from Bohr’s institute. Bohr would have picked Einstein up at the ferry port, not the railway station. (The translation that Felicity Pors has given me says “apparently” rather than “naturally,” which perhaps suggests more ambiguity in Bohr’s memory.)

The railway station makes perfect sense, if Einstein was coming from Berlin.

The second thing of note, in terms of dating Bohr and Einstein’s streetcar journey, is that the Bohrs were staying with Niels’ mother, “because we had expected that we could move in at the institute,” which opened officially in 1921. At the time I wrote the scene, I trusted Pais’s assessment of the timing and assumed that the institute’s upper residential floors had just taken longer to get ready. But it’s certainly more likely that the Bohrs were hoping to move into the institute before it opened, sometime in 1920.

footnote on p. 56:

Nobel is spelled wrong.

p. 58:

Here I again sloppily talked about “entanglement” when I meant specifically “long-distance entanglement.”

My reference to the study of “quantum effects writ large” was similarly sloppy–I was actually trying to evoke with one brushstroke several quite varied disciplines, including that of the quantum cryptographers who deal with quantum effects at great distance, and that of the low-temperature specialists who create Bose-Einstein condensates and other large-scale quantum objects.

p. 66:

Here I misleadingly presented several ideas (including the critical one of “quantum state”); also I had been longing to get in the story from Dirac’s travels which so well compares Bose-Einstein statistics to Fermi-Dirac statistics. What follows is my rewrite of the second half of this page for the paperback:

Bose’s key idea was the complete indistinguishability of light quanta, making meaningless any system that treated them as individuals. This indistinguishability meant strange things for quantum states. The likelihood of one of these fundamentally indistinguishable particles entering a given state is affected by the states of the particles that surround it.*

Bose’s biographers tell a story about the statistics that result (known as Bose or Bose-Einstein statistics). Paul and Margit Dirac, visiting Calcutta in the mid-fifties, were in the back seat of Bose’s car. Bose invited several students to sit in the front seat, which already held him and the driver. Alone in the back seat, the Diracs–whose thinness made a striking contrast with Bose’s jovial rotundity–asked if they weren’t too crowded. “Bose looked back and said in his disarming fashion, ‘We believe in Bose statistics.’”

The differences between Bose statistics and any other “express indirectly a certain hypothesis about a mutual influence of the particles,” wrote Einstein in 1925, “for the time being of a quite mysterious kind.” In their 2001 Nobel Prize lecture, the University of Colorado experimentalists Eric Cornell and Carl Wieman share Einstein’s wonder: “This mutual influence is no less mysterious today, even though we can readily observe the variety of exotic behavior it causes.”

* A notoriously elusive concept, quantum state is perhaps best defined as what can be known about a quantum object. Bose-Einstein statistics allow amazing feats to be performed by unentangled particles in a definite quantum state. By contrast, entangled particles are in an indefinite state–neither here nor there, neither yea nor nay–until one is measured.

p. 70:

Again, a bad translation of spin into English. Here is the version for the paperback:

Almost simultaneous with Einstein’s papers on Bose-Einstein condensation, Pauli had finished two papers. In the first, he made “a funny [komische] reflection” on the Stern-Gerlach experiment of 1922. He realized that its characteristic two discrete piles of silver atoms were due to a single electron in each atom–the outermost one–which, he wrote, “in a mysterious unmechanical manner . . . succeeds in running in two states with different momentum.” These two exclusive options would soon be called spin up and spin down (though not by Pauli, who found talk of electrons as spinning balls “inadvisable.”)

p. 77:

This is the mistake that everyone caught! Momentum is a vector, just like position, and three numbers describe it: so many feet per second in each direction times so many pounds.

lower on the page:

A better translation of the math into English would be to say that QP means “a position measurement following a measurement of momentum.”

p. 78:

I had heard a recording of Dirac speaking and thought it sounded like the Queen’s English, but having read Graham Farmelo’s beautiful biography of Dirac, The Strangest Man, I now know that what I heard was a distinctive Bristol accent.

p. 83:

Jeremy Bernstein correctly points out that I gilded the lily in my attempt to evoke what Schrödinger’s Christmas 1925 might have been like, with this still-unidentified woman who was presumably present at the birth of wave mechanics.

It is not even clear that Schrödinger and this lady were at the rest-hotel where they claimed to be. Schrödinger’s biographer Walter Moore reports that the Schrödingers had stayed in the same room in the three previous years (twice at Christmas) “as is attested by the hotel registry. There is, however, no record of his stay there in 1925, although we know from his letters he was there, or at least gave that address to his correspondents.” (Schrödinger: Life and Thought, Cambridge University Press, 1989, p. 195)

My reasons for describing her as I did were as follows: all of Schrödinger’s other girlfriends were attractive and, as far as looks were concerned, had more in common than not (all six pictured in Moore’s biography have rounded features and vivacious, girlish looks, very different from Schrödinger’s wife Anny). It was winter, so she would have to be muffed in some way. Of course it is possible she was ugly and poorly dressed, and I have cut back on the purple prose in the paperback.

p. 98:

David Mermin: “Here you go again, jumping on poor Bohr. I fail to see why Bohr’s insistence that ordinary language only made sense at the classical level ‘might blind him’ to some of the more extravagant quantum effects. After all, Bell’s theorem extracts its spectacular conclusion entirely from data that is describable in ordinary (classical) language.”

I had lost my way en route to the point that Bohr’s approach to the quantum theory manifestly hid the possibility of long-distance entanglement from him and those who followed him. My complaint should not have been with Bohr’s insistence on classical language but with the language he actually used–full of multivalent words employed in obscure ways (as Bell points out, even the famous “complementarity” in the hands of Bohr takes on almost the reverse of its naïve meaning).

Perhaps this complaint would disappear if I could read Bohr in the Danish?

As an example of this aspect of Bohr’s writing which I find frustrating, I present the word “individuality,” which appears in the 1929 introduction to Atomic Theory and the Description of Nature, in Bohr’s 1935 reply to EPR, and in 1932 through 1955 in Atomic Physics and Human Knowledge (John Wiley & Sons, 1958, pp. 6, 17-18, 24, 58, 90. These books don’t have indices, so these lists may well be incomplete.).

Here is the word at a crucial juncture on the second page of the reply to EPR (Physical Review 48, p. 697):

The impossibility of a closer analysis of the reactions between the particle and the measuring instrument is indeed no peculiarity of the experimental procedure described, but is rather an essential property of any arrangement suited to the study of the phenomena of the type concerned, where we have to do with a feature of individuality completely foreign to classical physics.

What does Bohr mean by the word “individuality” which he italicizes? It comes in the midst of a description of entanglement, and for a while I wondered if “individuality” was Bohr’s word for entanglement.

Here is one of Bohr’s earliest uses of the word, in 1929 (in the “Introductory Survey” of Atomic Theory & the Description of Nature, Cambridge University Press, 1934, pp. 7-8):

Above all, the previous development [the pre-1925 quantum theory] had led to the recognition of the impossibility of carrying out a coherent causal description of atomic phenomena. A conscious resignation in this respect is already implied in the form–irrational from the point of view of the classical theories–of those postulates … upon which the author [i.e. Bohr himself] based his application of the quantum theory to the problem of atomic structure. The fact that all changes in the state of an atom are described, in agreement with the requirement of the indivisibility of the quantum of action, as individual processes by which the atom goes over from one so-called stationary state into another stationary state and for the occurrence of which only probability considerations can be made, must, on one hand, greatly limit the field of application of the classical theories. On the other hand, the necessity of making an extensive use, nevertheless, of the classical concepts–upon which depends ultimately the interpretation of all experience–gave rise to the formulation of the so-called correspondence principle, which expresses our endeavors to utilize all the classical concepts by giving them a suitable quantum-theoretical re-interpretation.

A few pages later (pp. 10-11), he emphasizes the importance of the word: “there can be no question of giving up the idea of the individuality of the elementary particles; for this individuality forms the secure foundation on which the whole of the recent development of the atomic theory depends.”

The Oxford English Dictionary lists “indivisibility” as the first of five meaning of this word. (The Oxford American Dictionary on my computer lists only two meanings for “individuality” –the common one, dealing with an individual’s distinguishing characteristics, and a second meaning of “separate existence.”) Could “indivisibility” –i.e. quantization– be all Bohr was getting at?

It doesn’t seem so–as above, he sometimes uses “indivisible” and “individual” together. Here is another example, this from late in life (1955):

This mutual exclusiveness of the experimental conditions implies that the whole experimental arrangement must be taken into account in a well-defined description of the phenomena. The indivisibility of quantum phenomena finds its consequent expression in the circumstance that every definable subdivision would require a change of the experimental arrangement, with the appearance of new individual phenomena….[I]n one and the same experimental arrangement there will in general appear observations corresponding to different individual processes.

Such considerations…have completely solved the corresponding paradoxes confronting pictorial representation of the behavior of material particles. Here, of course, we cannot seek a physical explanation in the customary sense, but all we can demand in a new field of experience is the removal of any apparent contradiction…. (Atomic Physics & Human Knowledge, p. 90)

Here “individual” seems to be different from “indivisible”–does it mean “unique”? What does “individual” add to the words “phenomena” or “processes”? We know that Bohr agonized over every single word and phrasing in his writing, so it must be important. Why use a word freighted with many other meanings and levels of meaning when trying to explain an already complex situation?

As a writer and physics student, I have continually–and respectfully–struggled with these kinds of questions when reading the ostensibly classical, modest language of Bohr over the nine years of working on this book. But perhaps, as I wrote above, many of my problems stem from not being able to read Bohr in Danish. And of course they probably also stem from my lack of knowledge.

p. 117:

the energy (E) of this light-quantum is proportional to the frequency (nu) of a corresponding light wave.

lower on the page:

In January of 1928, four months before, quantum theory had made its uneasy truce with special relativity (the part of relativity that deals with frames of reference moving at constant speeds.)

p. 125, 4th full paragraph:

Bohr was acutely aware of entanglement. What he does not seem to have recognized (or thought important) was the fact that it could operate over infinite distance.

p. 128:

The Blegdamsvej Faust

p. 132:

Again, I should have written “all the experimental magic of long-distance entanglement.”

p. 136:

Of course Rutherford did not see pieces of atoms. He saw scintillations which were the result of those pieces hitting a screen.

p. 138:

The Blegdamsvej Faust

↔

{The Search & The Indictment 1940-1952}

p. 189:

On the subject of the controversy about what Oppenheimer did or did not say to any member of the Communist party, I should perhaps have made clearer the (obvious?) point that there is no particular reason to trust the accuracy of the report to the head of the KGB which I quoted on this page.

p. 220:

Miriam Yevick has found a fascinating letter Bohm wrote her from Brazil around this time. In the paperback, I have managed to insert a few quotes from this letter:

Mathematical abstraction, he explained, can deceive. “It grants an illusory sense that, as you say, nothing has been put over on you….In his proof that there can be no causal interpretation of quantum theory, von Neumann implicitly assumed that there can be no ‘hidden variables’ in the measuring apparatus. Nobody could have seen from von Neumann’s math that this was assumed. I was able to see it because I had a counter-example”–Bohm’s own theory–“so that I knew, by God, that von Neumann had ‘put something over’ on everybody, including himself.”

↔

{The Discovery 1952-1979}

p. 240:

Jeremy Bernstein was upset that I described Bell as “looking a little angry” in response to Jauch’s dismissal of the merits of the de Broglie-Bohm approach.

As is clear from the notes and introductory “Note to Reader,” this conversation is a collage of relevant statements from Jauch’s Are Quanta Real? and Bell’s papers and interviews, including the wonderful essay Bernstein wrote of Bell in Quantum Profiles. In this collage, Bell then goes on to talk about the books he would like to write, including one on “the psychology behind people’s peculiar reactions to” the hidden-variable question. This statement, as I make clear, is a direct quote from an interview Bernstein conducted with Bell, and of course Bell was not angry when he said it to Bernstein. Perhaps Bell never said anything of the sort to Jauch. Perhaps he did (when people find a felicitous way to talk about something, they rarely use it only once).

What is certainly true was that Bell did get angry in his discussions with Jauch on this general subject.

p. 252:

Positronium–the strange pair made up of an electron and its antiparticle–cannot really be described as an atom.

p. 255-6:

Two more cases of misleading in the effort to over-simplify things:

p. 255, note: The electric part of any electromagnetic wave can be thought of as a superposition of a vertically-oriented wave with a horizontal one (the same goes for the magnetic part, but it’s the electric part that, by convention, determines the polarization). The relative amplitudes of these components will determine the “tilt” of the electric component of the wave–its polarization. (In the simple case of a vertically-polarized wave, the amplitude of the vertical component would be 1, the horizontal component, zero.)

Circular polarization can be thought of in the same way, but in that case, one component lags a quarter of a cycle behind the other, of equal amplitude. The two superposed waves are syncopated. (In the case of elliptical polarization, there is not only a lag but also a difference in amplitude.)

p. 256, parenthetical at top of page: The relationship of polarization to its horizontal and vertical components is the same as that of the slope of a graph to its rise (y component) and run (x component).

p. 256, first full paragraph:

I was exactly backwards with the polarization of light reflected from water: glare is horizontally polarized, so the molecules in Polaroid sunglasses are arranged in horizontal rows to catch it. (The verbal trap for the unwary is that this kind of horizontal polarization can also be described as “perpendicularly polarized”–perpendicular, not to the ground, but to the plane of reflection. This is the plane containing the “V” created by the light ray hitting the water and reflecting off it.)

p. 257:

Shimony notes that it was Costas Papaliolios, a Harvard experimental physicist interested in these matters, who showed him and Horne the apparatus that Holt eventually used for his test of Bell’s inequality.

p. 259:

Here, I am (sloppily) using “entanglement” to mean “long-distance entanglement,” and Commins is talking about short-distance entanglement.

p. 264:

It would be more accurate to say that

Freedman shone light through a filter so that it carried photons of exactly the right amount of energy to excite the atoms to the planned two-photon cascade.

p. 276:

Clauser is spelled wrong. Physical Review Letters is spelled wrong.

p. 280:

A point I made clear in the notes but perhaps should have made clearer in the text: IBM spelled out its name it atoms in 1990. This feat, obviously, did not come up in Clauser’s discussions with Horne in 1974, but only in Clauser’s subsequent explanation of the point of these discussions.

p. 284:

I mangled my discussion of Aspect’s clever idea. Here is how I describe it in the paperback:

Sound waves, unlike light waves, need a medium–hence the silence of outer space. They move by repeatedly compressing and then relieving pressure in their medium. Aspect’s ultrasonic wave cycled between a swiftly oscillating high, striping the water in an alternating pattern of dense and thin; and a flat low, leaving the water unaffected. The striped pattern acted as a diffraction grating, bending the light to send it to the side polarizer; without it, the light traveled straight through to the main polarizer. The wave cycled between striped and flat quickly–“the switching between the two channels would occur about every ten nanoseconds,” Aspect explained, four times faster than the photons would travel the twenty-one feet separating the oven from the water.

p. 289:

Here I accidentally conflated experiments. The experiment in which the effect of gravity may be seen in the interference of a neutron with itself was performed in 1975 in Ann Arbor, Michigan by Roberto Collela, Al Overhauser, and Sam Werner (and thus known as the COW experiment). Werner subsequently made the University of Missouri a center for beautiful neutron experiments.

↔

{Entanglement Comes of Age 1981–2005}

p. 298:

The conference at which Greenberger described doing an entanglement experiment with back-to-back interferometers was only a few floors up from street level, not at the top of the World Trade Center.

p. 299:

Physical Review Letters is spelled wrong.

p. 308-9:

Ghirardi is spelled wrong, twice.

p. 311:

Another case of overstating. Here is how I re-wrote the second-to-last paragraph for the paperback:

Over the years between 1964 and 1990, Bell’s theorem had gone from an unknown result to a respected one–albeit one with roots in an unloved quantum subculture. Unlike Clauser and Freedman’s 1972 experiment or Fry’s 1976 one, Aspect’s in the early eighties had achieved some fame. About entanglement over long distances, it was felt that all had been said and done that needed to be said and done. But a decade later, at the turn of the millennium, quantum optics labs in Innsbruck, Geneva, and Los Alamos (to name a few) would be full of new excitement about the possibilities of using entanglement in increasingly dramatic, long-distance, and potentially useful ways. For those who now work in these newly wide-open fields, it is a frustrating and poignant irony that, if only Bell could have lived out his biblically allotted three-score years and ten, he would have seen such wonderful things begun by his half-secret hobby.

p. 312:

(See note to p. 20, above.) It was not Mermin’s paper which alerted Feynman to Bell’s theorem; possibly–as Shimony notes–it was Feynman’s grumpy conversation with Clauser, sometime between 1969 and 1972.

p. 325-6:

I wanted to get another Feynman quote into this discussion. Here’s how it will go in the paperback, in context:

“You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. It has not yet become obvious to me that there’s no real problem. I cannot define the real problem, therefore I suspect that there’s no real problem, but I’m not sure there’s no real problem. So that’s why I like to investigate things. Can I learn anything, from asking this question about computers, about this may- or may-not-be mystery as to what the world view of quantum mechanics is?”

Well, could a classical computer simulate a quantum system? “If… there’s no hocus-pocus, the answer is certainly ‘No!’ This is called the hidden-variable problem.” He proceeded to walk the audience through his version of Bell’s theorem. “I’ve entertained myself always by squeezing the difficulty of quantum mechanics into a smaller and smaller place, so as to get more and more worried about this particular item. It seems to be almost ridiculous that you can squeeze it to a numerical question that one thing is bigger than another”–a Bell inequality.

“What I’m trying to do,” he told the computer scientists, “is get you people…to digest as well as possible the real answers of quantum mechanics, and see if you can’t invent a different point of view than the physicists have had to invent to describe this.

“In fact”–Feynman looked up at his audience, his brow wrinkling–“in fact, the physicists have no good point of view.” He grinned at the surprised faces in the crowd. “…So, I would like to see if there’s some other way out. . . . I don’t know”–he shrugged–“maybe physics is absolutely okay the way it is.”

p. 326:

After the hardcover was published, I discovered Peter and Jennifer Shor’s wonderful limerick on the subject of quantum computation and cryptography (for more fun reading, also see Shor’s review of Lee Smolin’s The Trouble With Physics on Amazon).

Here is my rewrite to fit the limerick into the paperback:

Two men from Bell Labs with large mustaches and unusually fine writing styles, Peter Shor and Lov Grover, found algorithms for a quantum computer to run that are far, far faster than any classical computer could ever be–Shor’s, in 1994, for factoring large numbers, and Grover’s, in 1996, for searching a database. “If computers that you build are quantum,” Shor explained (in a Science News poetry contest), “Then spies of all factions will want ’em./Our codes will all fail, and they’ll read our email,/Till we’ve crypto that’s quantum, and daunt ’em.”

There wasn’t room in the paperback to include Prof. Volker Strassen’s reply, which he wrote for his introduction of Shor at the 1998 International Congress of Mathematicians:

To read our E-mail, how mean

of the spies and their quantum machine;

Be comforted though,

they do not yet know

how to factorize twelve or fifteen.

p. 331:

Confusion here. A fullerene molecule (or “buckyball”) is a hollow sphere of sixty carbon atoms, famously arranged like the seams of a soccerball. (Bigger fullerene molecules are composed of seventy carbon atoms, in which case they are a bit more ellipsoid, like a rugby or Australian football). Zeilinger’s group was using a carbon-sixty molecule that had been fluorinated, which is what made it knobbly (but not long). (The long and knobbly molecule which was illustrated by a poster hanging on the wall at the same lab was insulin, with which they were hoping to demonstrate interference someday.)

Some loose talk at the end of this page, which I have rewritten as follows:

Zeilinger is fast chasing down Clauser’s dream of interfering “small rocks and live viruses,” believing that a careful enough experiment can show anything existing in a placeless quantum-mechanical limbo.

p. 332, last full paragraph:

Chris Fuchs does not apparently profess.

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{following are rewrites of my more problematic glossary entries}

p. 337:

accelerator–A machine that accelerates charged particles to near the speed of light, letting them collide with a fixed target or with each other, to study what is created out of the energy of their collisions.

angular momentum–The momentum of an object constrained to move in a circle. For intrinsic angular momentum, see spin.

p. 338:

Fermions have half-integer spin, carrying intrinsic angular momentum in odd multiples of [h-bar over 2]…

p. 340:

hidden variables (also known as hidden parameters): “To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined.” So begins John Bell’s famous paper “On the problem of hidden variables in quantum mechanics.” The hypothetical “better defined states” would then be described by unknown quantities in addition to the wavefunction. These are the “hidden variables”–“‘hidden’,” explains Bell, “because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.” While the final sentence of the EPR paper (“We believe, however, that such a theory is possible”) is often interpreted as a call for hidden variables, Bell showed that only if they were non-local could they reproduce the results of the quantum theory.

under interference, I cut the second paragraph for being not well worded.

p. 340, lower down:

local: Not distant. Examples of local connections are a sound wave hitting your eardrum, a light wave hitting your retina, or someone pushing you. Instantly arriving home after clicking your ruby slippers, mind reading, influencing faraway events by the power of positive thinking, etc., would be nonlocal events.

p. 343:

quantum state–What can be known about a quantum object.

An ordinary classical state can be, in theory, completely known. All a dog’s attributes, for example, can be listed: his location in three dimensions of space and one of time, his momentum, his energy, et cetera. But a quantum state, described by the Schrödinger wave (or psi) function, is maximally known when about half of these attributes (or “observables”) are known (if position, then not momentum; if time, then not energy).

p. 344:

state–The condition and attributes of a given object. In classical physics, this can be specified by giving the values of a list of “observables”–the object’s position and momentum, for a start.

statistical mechanics–The study of how free-moving atoms create the observable properties of (in particular) gases. (For example, the temperature of a gas is merely the average of the kinetic energies of all its atoms or molecules.) Ludwig Boltzmann, fighting atomic doubters on all sides in Vienna, and J. Willard Gibbs, serenely isolated at Yale, developed this subject in the late nineteenth century and the first few years of the twentieth. Equally isolated at his patent office (and in ignorance of the work of his predecessors), Einstein re-developed the whole discipline from scratch in 1900-1904. This work laid the foundations not only of his famous 1905 paper on atomic size, but also of his principal contributions to the quantum theory, all of which, notes Pais, “are statistical in origin.” (see Subtle is the Lord, 56)

p. 345:

superposition–Two simple waves, added together, produce another wave. This leads to interference.

Superposition is one of the main features of quantum mechanics. “Schrödinger’s cat” is the classic reductio ad absurdum. It describes a situation where “an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved”–Schrödinger emphasized–“by direct observation.

“That,” he explained, is what “prevents us from so naively accepting as valid a ‘blurred model’ for representing reality,” a “blurred model,” in which the whole world is fundamentally wave-like.

A radioactive atom, for example, is usually in a superposition of both having emitted a neutron and not having emitted a neutron. The thought-experiment runs as follows: Schrödinger’s cat is trapped in a box with a vial of poison that is triggered by a quantum event, the emission of a neutron. After a certain amount of time, the atom will definitely be in a superposition of both having emitted the neutron and not having emitted the neutron. Does that mean that the poison is consequently in a superposition of being both inside and outside its bottle? Does that mean that the cat is, as a result, in a superposition of having been killed and also remaining alive?

But anyone who opens the cat box will see either a dead cat or a live one. Does the act of measurement then “collapse the wavefunction,” forcing the cat to either die or live?

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{Longer summaries}

EPR, p. 347:

It’s too strong to say that “the second atom…is prepared to tell us its position or its momentum.” Whether the second, untouched atom is prepared to tell us its position or its momentum depends on what we measure on the first atom. But without action at a distance, what we call an element of reality cannot be (instantly) affected by a measurement on another, faraway element of reality. So we come to the conclusion that, if there is no action at a distance and quantum mechanics is complete, position and momentum do have simultaneous (if inaccessible) reality, contrary to what the theory seemed to suggest.

GHZ, p. 348:

When detectors A and B are set to measure along the y axis, and C along the x axis, our results in always contain an even number of “spin down”s.

(–1, –1, and +1) or (+1,+1, and +1) do not exhaust the options–there are also (+1,-1,-1) and (-1,+1,-1).

p. 349:

In the paperback, I also emboldened the letters for the detector aligned vertically, to increase the contrast between A and A.

Ekert’s quantum key distribution, p. 350:

Three bases is ideal.

↔

Following are the necessary changes and additions to the Notes, Index, etc.:

{notes}

p. 351:

xiii “Science rests on experiments…conversations.”: WH, Physics and Beyond,  xvii.

xv “Sommerfeld…something else”: Bohr 1961 interview in Pais, Niels Bohr’s, 229.

xv “I know that you understand…quantum theory is”: Bohr-Richardson, 1918 in Pais, Niels Bohr’s, 229.

xvi “That is a wall…examination”: AE quoted by the astronomer C. Nordmann, 1922 in Clark, 353.

xvii “I have not found…”: Pais, Niels Bohr’s, 228.

pp. 362-3:

66 “Bose looked back…”: Chatterjee, Santimay and Enakshi, Satyendra Nath Bose (New Delhi, India: National Book Trust, 1976), 82.

66 “express indirectly. . . mysterious kind”: Einstein, Preussische Akademie der Wissen-schaften, 1925, in Cornell and Weiman, Nobel Lecture, 2001. Eh. and ES had complained about the nonseparability of the particles; this, his second paper on Bose, was AE’s reply. ES still wondered; AE (2/28/25) responded, “The quanta . . . are not treated as independent of one another…. There is certainly no error in my calculation” (Pais, “Subtle,” 430; Moore, 183; Howard, “Nicht,” 67).

70 “[komische] reflection…momentum”: Pauli-Landé, 11/10 & 11/24/24 in Enz, 106-7.

p. 380:

138 The Blegdamsvej Faust

p. 394:

219 “resultlets”…“that place”: Bohm-Yevick, 1/1951, 1/1952 & undated; Peat, 131.

220 “very foolish”: Bohm-Yevick and Bohm-Phillips in Peat, 132.

220 his initial surprise: Peat, 129.

220 When recounting to Miriam…bum!)”: “von Neumann thinks the idea consistent, and even ‘very elegant’ (the unprincipled bum)”: Bohm-Yevick, undated; Peat, 132.

220 “It grants…including himself”: Bohm-Yevick, 1/28/52 (unpublished letter, collection of Miriam Lipschutz-Yevick).

220 “comparable to…the translation”: Bohm-Yevick, undated in Peat 131-32.

220 “I am convinced…right track”: Bohm-Yevick, undated in ibid., 134.

p. 407:

325 “Might I say immediately . . . it doesn’t look so easy”: Feynman, “Simulating Physics with Computers” in Hey, 136-51; 147-50 cover Bell’s Theorem (unnamed).

p. 408:

326 Two men from Bell Labs:

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{index}

many changes here, but the only ones I will note have to do with Bell’s two papers of 1964:

p. 420:

Bell, “On the Problem of Hidden Variables in Quantum Mechanics,” 246-8, 340

p. 434:

“On the Einstein-Podolsky-Rosen Paradox” (Bell), 246-8, 251, 252, 253-4, 257, 282, 284

p. 434, next column:

“On the Problem of Hidden Variables in Quantum Mechanics,” 246-8, 340

↔

{permissions page}

p. 444:

Philosophical Library: Excerpts from Letters on Wave Mechanics, edited by K. Przibram. Reprinted by permission of the Philosophical Library, New York.

↔

{Cody’s erratum}

Dakota Reis is spelled with only one “s.”

↔

{about the author}

p. 445:

Louisa Gilder was born in Tyringham, Western Massachusetts. She graduated from Dartmouth College in 2000, and wrote this, her first book, over the course of nine years, mostly in California (first in Oakland, then Bodega Bay) but also during most of a year in Wyoming and several years in Massachusetts. She now lives in Tyringham again.

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