But I prefer to put it the other way around: the successof QBism in clarifying the murk at the foundations of quantum mechanics is a compellingreason for physicists too to embrace the widespread view of probabilities as subjectivepersonal judgments

Freud was writing about religion. But for a QBist his remark applies equally well tophysical science, contrary to the current views of most physical scientists

One would have thought that the Born interpretation calledfor a searching reexamination of the nature of probabilistic judgments

one’sunderstanding of quantum mechanics should differ dramatically depending on whetherone subscribes to the objective (“frequentist”) view of most physicists, or the subjective(“personalist”) view of most statisticians

Quantum mechanics is, after all, the first physicaltheory in which probability is explicitly not a way of dealing with ignorance of the precisevalues of existing quantities

Physicists generally believe that probability isan objective property of events, baked into their very nature by objective features of theworld. But many statisticians, mathematicians, and philosophers take probability to be anumerical measure of the subjective judgment of the person who assigns it, indicating, forexample, the odds at which that person is willing to make or accept bets.

De Finetti, in the 1930s, was one of the earliest and most eloquent advocates ofthe subjective view of probability, common today among statisticians and inherent inQBism, but anathema to most physicists

4.5.1 The abandonment of superstitious beliefs about the existence of Phlogiston, theCosmic Ether, Absolute Space and Time. . . , or Fairies and Witches, was an essential stepalong the road to scientific thinking. Probability too, if regarded as something endowedwith some kind of objective existence, is no less a misleading misconception, an illusoryattempt to exteriorize or materialize our actual36 probabilistic beliefs.

The sentiment is pure CBism, which makes me even more suspicious of its authenticity

4.4.3 Space and time are modes in which we think and not conditions in which welive.33

Remark 4.4.3, now a firmly established part of the Einstein canon, is definitely apoc-ryphal. It seems to come from a popular biography, written shortly after Einstein’s death,which cites it as a private remark to Ehrenfest, without offering any supporting evidence.

But Einsteinmay have been putting the blame on time itself, rather than on the use of time by thescientist

The little known remark 4.4.2, made in a 1950 interview, is my favorite of all Einsteinaphorisms

I include Einstein’s remark 4.4.1 to Schr ̈odinger, because they were the two founderswho most strongly rejected the Copenhagen interpretation.

4.4.2 At last it came to me that time was suspect! 32

4.4.1 The Heisenberg-Bohr tranquilizing philosophy — or religion? — is so delicatelycontrived that, for the time being, it provides a gentle pillow for the true believer fromwhich he cannot very easily be aroused. So let him lie there.31

Only by reporting it in words — there is no other way to represent personalexperience — can I attempt to communicate it to others. I also need language to comparemy own experience with the verbal representations to me by others of their own privateexperience

Ordinary language was enormously important to Bohr. An essential part of an ex-periment was reporting it to others. I always found this puzzling. If the outcome of anexperiment is an objective classical fact, why is it so important to be able to communicateit to other people in ordinary language?

4.2.5 Rather than a separate branch of knowledge, pure mathematics may be con-sidered as a refinement of general language, supplementing it with appropriate tools torepresent relations for which ordinary verbal expression is unprecise or cumbersome.28

4.2.4 However far the phenomena transcend the scope of classical physical explanation,the account of all evidence must be expressed in classical terms. The argument is simplythat by the word “experiment” we refer to a situation where we can tell others what wehave done and what we have learned and that, therefore, the account of the experimentalarrangement and of the results of observation must be expressed in unambiguous languagewith suitable application of the terminology of classical physics.27

4.2.3 How do we communicate physical experience at all?. . . By an experiment, wemust understand a situation in which we can tell others what we have done and what wehave learned.26

The private individuality of human experience, central to QBism, is not, as far as Ican tell, a part of Bohr’s thinking. Nor can it be found in any other version of quantumorthodoxy that I am aware of.

The phrases “our experience” in 4.2.1 and “humanexperience” in 4.2.2 fail to distinguish between the unique and immediate personal expe-rience of any single individual, and the collective experience of everybody, negotiated andexpressed through the medium of human language

Both quotations state that physics is not so much aboutphenomena, as it is about our experience of those phenomena

4.2.2 Physics is to be regarded not so much as the study of something a priori given,but as the development of methods for ordering and surveying human experience.24

4.2.1 In our description of nature the purpose is not to disclose the real essence of thephenomena but only to track down, so far as it is possible, relations between the manifoldaspects of our experience.2323 Niels Bohr, 1929. In Atomic Theory and the Description of Nature, Cambridge (1934)

Nevertheless, Bell’s remarks to Peierls, and the way in which he criticized Copenhagen,lead me to doubt that he would have rejected QBism quite as superficially as some of hiscurrent admirers have done. In these letters he seems open to a human role in the story,even if not at the most fundamental level.

All of these are fundamental QBist views. But John Bell was not a protoQBist. NoQBist would share his longing for objectively existing beables to replace the measuredobserv ables of quantum orthodoxy. Perceiveables might do the job, provided one acknowl-edged that they were joint manifestations of the world and the perceiver. But I very muchdoubt Bell would have accepted this

In Quotation 4.1.3 Bell gives a very concise statement of a view that measurementsare not limited to laboratory procedures and that the outcomes of measurements are notlimited to readings of devices in the laboratory.

s human inventions designedto help him make sense of the data that constitute his experience.

Answer: Because, while it is possible to learn how to use either without knowing whatyou are doing, it is impossible to make sense of either without taking account of whatpeople actually do with them. Given a bicycle, an intelligent extraterrestrial who hadnever encountered a human being would be incapable of grasping the nature of such anartifact. Without an awareness of its user, a bicycle makes little sense. One begins tounderstand a bicycle only when one learns that it is a tool for a creature with two lowerlimbs with feet at the ends to fit on the pedals and two upper limbs ending in handscapable of grasping the handle bars. The very names of these parts of the bicycle makeexplicit reference to the nature of the user. The nature of quantum mechanics, like thatof a bicycle, cannot fully be understood without explicit reference to its user. But thenomenclature of quantum mechanics is not as helpful as bicycle nomenclature in makingthis explicit. On the contrary, it hides the user from sight

In 2014, at a conference celebrating the 50th anniversary of Bell’s theorem, I learnedthat these three quotations, which I had come upon among nearly 2,000 pages of RudolfPeierls’ selected correspondence, were unfamiliar even to those who, like me, had readand admired almost everything the highly quotable John Bell had written about quantumfoundations

Theideal instantaneous measurements of the textbooks

4.1.2 I think we invent concepts, like “particle” or “Professor Peierls”, to make theimmediate sense of data more intelligible.— J. S. Bell, letter to R. E. Peierls, 24/2/1983

4.1.1 Our students learn quantum mechanics the way they learn to ride bicycles (bothvery valuable accomplishments) without really knowing what they are doing.— J. S. Bell, letter to R. E. Peierls, 20/8/1980

The quotations are arranged al-phabetically by writer

3.5.4. David Hume understood this almost two century before quantum mechan-ics. The certainties of classical physics are themselves matters of judgment.

3.5.3. I once remarked to R ̈udiger Schack that I would never bet my life on anything.He pointed out that I do it every time I cross a street. We build our lives around beliefs

3.2.4 Without intelligent beings there cannot be language

3.2.2. For a QBist, language — ordinary or technical — is even more essential thanit was for Bohr. Language is the only way one can try to represent to others one’s privatepersonal experience, or get from others a sense of their own private experience. Scienceconcerns that which is common to the worlds each of us infers from our own uniqueexperience. Language is essential to an understanding of our common science because it isthe only way we have to get a sense of what is common to our different private experiences.

Einstein’s many wonderful skeptical questions is “No, a mouse cannot collapse a wave-packet”, because no mouse is able to learn and use the quantum formalism to update itsexpectations.

discussion section taught by the remarkable Stanley Cavell, then a beginning graduatestudent. He taught me how to think/write.

3.1.1. Although I am trying to write philosophically about the nature of science, I mustacknowledge that my formal education in philosophy is limited to my first undergraduateyear at Harvard, 1952-53, when the famous Humanities 5 was offered for the first time byProfessors Henry Aiken and Morton White.

This paper owes its existence to GordonBaym, who has repeatedly urged me, at least since 2009, to write something — anything— about my own view of quantum foundational issues. This final form of my manuscripthas benefited from the close critical reading of an earlier version by a perceptive referee.

where I finally came to understand what theyhad been trying for so long to explain to me.

It occurred to me that nobody had a personalstake in their favorite interpretation of classical physics. Therefore if I published a furtheressay applying QBist thinking to a problem in strictly classical physics, certified as aprofound puzzle by Einstein himself, then it might elicit some genuine criticism, ratherthan just expositions of the letter-writer’s preferred way of solving the problem. I did so inPhysics Today, March 2014,65 To my further disappointment, the article elicited no letterswhatever, critical or favorable. Nor did a companion article in Nature.66 Physicists haveno interest in the interpretation of classical mechanics. That’s part of the problem

I first write about my understanding of QBism in Physics Today.63 That brief essayelicited several critical letters to the editor. They all had one thing in common. Each writerhad no problem understanding what quantum mechanics was all about. Each describedtheir own understanding — they were all different — and, to my disappointment, hadnothing whatever to say either for or against the point of view that I was advocating

n Section II I set forth the interlocking contents of QBism as concisely as I can, toencourage you to consider them as a whole, before you reject any of them as unacceptableand cease to read others that help to support it.

1 I gave a unified review of the Bell and BKS theorems in N. D. Mermin, Revs.Mod. Phys. 65 803-816 (1993), now available, with minor errata incorporated, as arxiv-1805.10311

It is myhope to interest those who, like me, are impractical enough always to have been bothered,at least a bit, by not knowing what they are talking about

My purpose is to answer the question of what one is actually doing when oneuses it. Since many physicists never find it necessary to ask that question, they may well beunpersuaded, perplexed, or even appalled by my answer. Those who are appalled shouldbear in mind that I am offering here a philosophical answer — viewing science as an aspectof the nature of human understanding — to a philosophical question: What the hell are wetalking about when we use quantum mechanics?

nd I have suggested calling it “CBism” when the same way of thinking aboutscience is applied to puzzling, if less notoriously vexing, classical issues

The way of thinking about science I shall describe was developed in the early yearsof the 21st century by Christopher Fuchs and R ̈udiger Schack, collaborating with CarltonCaves until 2006. Some people maintain that these developments add little if anythingto what Bohr, Heisenberg, and Pauli had been saying from the beginning. One of mysecondary purposes is to make it clear why this is wrong. Fuchs and Shack are advocatinga view of science that is anathema to most physicists. While they were driven to it in partby the quantum “no-hidden-variables” theorems of Bell and of Bell, Kochen, and Specker,1the perspective of Fuchs and Schack also casts an illuminating light on strictly classicalphysics.They have called their understanding of science “QBism”2 (pronounced the same as“cubism”),

if and when quantum mechanics is successfully modified, the motivationwill come from unambiguous deviations of actual data from its predictions

ndicating the false preconceptions at the root of such vexing interpretations couldundermine the motivation for such modifications, which have so far been entirely fruitless.

For decades, some physicists have been searching for modifications inquantum mechanics that lead to changes in its physical predictions too small to have yetbeen observed. Such modifications are motivated not by failures of the existing theory, butby philosophical discomfort with one or another of the prevailing interpretations of thattheory.

his suggeststhat the problem might lie in some implicit misconceptions about the nature of scientificexplanation deeply held by virtually all physicists, but rarely explicitly acknowledged. Idescribe below such unvoiced assumptions that most physicists share. Acknowledging theirexistence, and rejecting them as wrong, clarifies and unifies a range of obscure remarksabout quantum mechanics by many of the giants of physics, among them people who havetraditionally been held to be in deep disagreement. Abandoning these misconceptionshelps make better sense of quantum mechanics. But it requires physicists to think aboutscience in a radically unfamiliar way.

We do not understandthe meaning of this strange conceptual apparatus

y secondary aims areto explain why this perspective differs significantly from what Bohr, Heisenberg,and Pauli had been saying from the very beginning, and why it is not solipsism,as some have maintained

This new view of physics requires physiciststo think about science in an unfamiliar way

a range of obscure remarks about quantum mechanics madealmost from the beginning by some of the giants of physics, many of whom areheld to be in deep disagreement

describe here such unvoiced but widely shared assumptions.

suggests that the problem mightlie in some implicit misconceptions

Because it has no practical consequences for how we eachuse quantum mechanics to deal with physical problems, this cognitive dissonance

There is a gap between the abstract terms inwhich the theory is couched and the phenomena

We still lack any consensu

Bell’s theorem, from my point of view, was the biggest breakthrough during my career. But very few people [laughs] would agree with me. For me, it was the most eye-opening thing ever.

when you read about this breakthrough, how much of the breakthrough is about — Mermin: I didn’t read about it. I was told in confidence

There’s too little communication. Most of the communications I’ve had with other people are like my communications with Asher Peres. They’re personal communications by emails. And that’s my main source of scientific stimulation these days: emails with other people

I wrote what I thought was a ringingly clear explanation of our way of thinking about quantum mechanics. I posted it on arXiv and published it in Reports on Progress in Physics, which is a leading English scientific journal, and I got basically no reactions, no responses, positive or negative, from anyone.

So, when I wrote a paper pointing out what was wrong with the paper that used Bell’s theorem, I sent a copy of it to Charlie Bennett, who I had known for years, asking whether he could take a quick look at it and tell me whether I’d said anything foolish or stupid. And the next thing I knew, the phone rang early in the morning, waking me up. And it was Charlie Bennett, who was very excited by what he viewed as the way in which I had modified his work with Brassard. And he was calling to say that we had to write a joint paper on this. And since all joint papers he wrote on the subject were also joint with Gilles, it should be a paper by the three of us. So, we then got to work on a joint paper, and they wrote a very long paper, and I cut it down to a very short paper, and they expanded it back to a moderately long paper, and I cut that down to a somewhat less short paper. At one point in the process, I said, “The hell with it. We’re never going to agree on anything. Why don’t we just write papers of our own?” And they said, “No, no. We will write a paper together.” [laughs] And so, what emerged was a rather uneasy compromise. And then I started running into Brassard at conferences all over the place, and we also became good friends. And that’s the history of our joint work.

So am I, although I’ve pretty much stopped writing for the past couple of years.

so much nonsense

I have a few sympathizers of my own — or I had; some of them have died — but we haven’t persuaded many people

Hans Christian von Baeyer

possibly Ulrich Mohrhoff, who writes about physics from the Pondicherry Ashram in India

Chris Fuchs

Mermin: I would say that at the moment, I and a few close friends understand quantum mechanics, [laughs] and we’re trying to explain it to the rest of the world

I’m under the illusion that I understand quantum mechanics,

people have been asking me questions about old papers that are decades old, that I find in some cases — to my dismay — I have trouble [laughs] understanding what I was saying. Not often. Usually, I’ve written them clearly enough that I can still understand them if I have some reason to look back at them.

Dabbler suggests a certain superficiality, and I don’t regard my work as superficial at all.

The other things I’m well-known for and that are most highly cited are almost all things I spent maybe a day or two days thinking about, then maybe another day writing about

Well, the quantum mechanics, I’ve been writing about that for such a long time that that’s becoming more of a part of my scientific identity

It’s kind of funny, because neither of the subjects is anything I’m officially known for. They’re both kind of hobbies.

possibly a couple of people who wrote blurbs for the dust jacket [laughs] feel that way about it. And those two are, by far, the most important to me

My own view is that my 2005 book on relativity, It’s About Time, has ways of looking at special relativity that I’m not aware of anybody else ever having suggested. But I think I’m probably the only person in the world [laughs] who thinks that way about the book

Mermin: The work that gives me the greatest pleasure is my semi-popular expositions of quantum mechanics and relativity

Zierler:

from Bell’s theorem, the fact that you can distill the strangeness from some very simple experiments that can be black-boxed. And the data in those experiments are basically just yes/no answers to certain questions, and you don’t really have to know how the yes/no answers are arrived at

I finally stopped paying attention to, is high-temperature superconductivity

But I like the idea of pointing out to people that they’re wrong about things

Mermin: Well, with relativity, it’s that the subject is basically something simple that everybody feels they understand — space and time — and what makes it really fascinating is the fact that their understanding about it is wrong. And that’s always wonderful, when you discover that something you thought about all your life is wrong.

Mermin: My practical motivation was that for years, I’ve taught courses for non-scientists, and the reason I like doing that is I like trying to extract what’s really interesting about a subject from the formalism – the network of abstractions that physicists generally erect around it. And it’s a serious intellectual challenge to do so, and there are not many things that you can actually do it with — and I think quantum mechanics and relativity are rare in that sense, in that you can extract things that ought to be of much more general interest.

Mermin: My books on relativity

It’s a problem with academics more generally, that they tend — with many exceptions — to take themselves much too seriously, and therefore they have less fun. [laughs] Fun is important. It has to do, I guess in part, with my distaste for scientific administration and all the kinds of secondary non-intellectual aspects to the field

why do you think there is an abundance of self-seriousness in physics

People in physics were very surprised to hear that he wasn’t Neil. And I refused to say who he was.

You’re Professor Mozart. Mermin: No! Most people thought he was Neil Ashcroft. [laughs]

you have seen all the columns in one place in my newer book of essays, Why Quark Rhymes with Pork

Well, I always had an interest in writing,

That got a lot of attention

Zierler: You mentioned the Physics Today columns as being possibly a reason behind your election to the National Academy of Sciences. And I want to talk about — how did the “Reference Frame” column begin?

And members are required to vote on proposed members in all fields, whether you know anything about the field or not. You have a minimum number of people you have to vote on in other fields. And it therefore is helpful to have a name that is familiar to people from a large range of scientific fields. I find myself, when I vote in these elections — as I feel duty-bound to do — that if I’ve actually heard of somebody in another field, then I vote for them, because I figure that if I’ve heard of them, they must really have accomplished something

I always had the feeling that it had a lot to do with my name being well known. And the reason my name was well known was: one, I was co-author of a famous, widely-used textbook, and two, I had a lot of columns in Physics Today that were funny, [laughs] as you remarked, and got a lot of attention

Zierler: What was your reaction when you learned that you had been elected a member of the National Academy of Sciences? What was your reaction to that news? Mermin: Great pleasure and surprise, both. I was at a conference in Spain

My wife was a Professor of English at Cornell. And it would have been hard for two people to go somewhere together. And we liked it here

I really retired, and moved into the internet world of physics

I retired in 2006

Zierler:

that’s an obscure backwater in the currently raging field of quantum information theory.

Mermin: My current view of the problems in quantum foundations is that the problems arise from a failure to understand the nature of scientific knowledge. Now, no practicing physicist worries about the nature of scientific knowledge. It’s the kind of thing that philosophers should worry about, but even they don’t worry enough about it.

I became interested in foundations of quantum mechanics in the early ’80s, and that was an extremely obscure field at that point. Very few people were working in it, and it was regarded as somewhat disreputable. And what brought that into prominence was the arrival of quantum computation and quantum information theory. And that was a rare case where I didn’t leave the field, in fact. Zierler: Why not? Mermin: Because I was still interested in what are now viewed as philosophical aspects of it.

Mermin: Yes. There’s some wonderful quote, I think from Newton, about wandering along a beach and picking up beautiful pebbles. And I’ve always liked that.

And in that way, I changed fields frequently. The other reason I’ve changed fields is usually when that happens, it’s in a fairly obscure, tangential field of physics, which is terrific, because it means there are not many people working in the area. There aren’t many other papers you have to read before you can become an authority. And that’s the situation I flourish in, that I like best. But often, the field I tiptoed into then becomes a big field, and all of a sudden, there are conferences and huge numbers of papers, far more than I could read. And at that point, the field becomes, for me, much less interesting, much less pleasant, and so I look around to see if there’s some other [laughs] obscure field where I can make a small contribution.

Mermin: A paper appeared arguing that Bell’s theorem provided a good basis for quantum cryptography. I read this paper and realized that Bell’s theorem had nothing to do with it, that it was just completely irrelevant.

Zierler: Were you surprised at how rapidly the term was adopted? Mermin: No, because it wasn’t that rapid. It took a couple of decades.

Science needs new terms all the time! I mean, anytime you come upon a phenomenon, a structure, you need something to call it. So, that’s commonplace.

It refers to The Hunting of the Snark, by Lewis Carroll

Asher had come up with what he claimed was a very simple version of Bell’s theorem that he sent me, and I wrote back and explained to him that it didn’t work as a version of Bell’s theorem, but it did work very nicely as a version of something else that was known as the Kochen-Specker theorem. So, I published the Kochen-Specker version of Asher’s argument, and Asher insisted on publishing — even though I still claim it doesn’t work — his own version of the argument. And those two papers together have since been called the Peres-Mermin magic square

Mermin: When I became interested in quantum foundations. Zierler: Which was when? Mermin: In the early ’80s.

A few years ago a self-styled new edition called “Ashcroft, Mermin, and Wei” appeared in Asia, but we had nothing to do with it

It no longer sells anything in the United States, because a long chain of publishers took over the book from earlier publishers, and the most recent one raised the domestic list price to over $400. So, sales in the United States dropped to zero, probably 20 years ago. And they’ve now cut it once from $400 to $200, and then again from $200 to $100, but sales are still not picking up in the United States. Meanwhile, it’s been translated into French, German, Portuguese, Japanese, Russian, and Polish, and foreign prices were never very high, so it still sells 2,000 or 3,000 copies a year in Europe, mainly

Zierler: Why is that? Was there not a good solid-state physics textbook at that point? Mermin: There was Kittel, which we all thought was awful. Zierler: [laughs] Why? What was the problem with it? Mermin: It explained nothing. It had a lot of pictures and a lot of graphs and a lot of talk and didn’t teach you what the theory was underlying all this stuff. So, our idea was to write a book that had all the phenomenology that Kittel had, but that described things in a rigorous way, the way Peierls did. So, it was sort of combining the two books. We thought about it for a couple of years, and then we started trying to work on it. And it turned out that Wilkins had no patience for writing. He was too busy with his armies of graduate students. So, we suggested to John that this was not a suitable project for him, which he basically agreed to, although friendly relations basically ceased at that point between Wilkins and Ashcroft. For some reason, John did not blame it on me. He blamed it on Neil, which is peculiar, because it was a joint decision that John really did not belong in the project, which even John agreed with. Anyway, then Neil and I worked together for eight years, putting the book together.

“What’s the question to which the answer is ‘9-W’?” And the question is, “Do you spell your name with a V, Mr. Wagner?” “Nein, W.”

By the way, you mispronounce “Wagner”. The W is pronounced V

Zierler: No, I’m a historian of science.

But I ended up with a fairly small total number of graduate students over my career: fewer than 20, which is unusual for a theorist. Well, that’s not true. There are two types of theorists: those that have a small number of students, and those that have armies of students, with whom they have group meetings, which I have never done in my life.

there was a lot of government funding, and a lot of it through the Defense Department as well as the National Science Foundation. Where they got the money to pay all those faculty salaries, I have no idea. I just wasn’t interested [laughs] in such questions at the time.

Mermin: Peierls said I should write to a guy named Walter Kohn. And Walter wrote back and said, “We have no faculty positions, but why don’t you come here as a postdoc?” When I got the offer from Cornell, I wrote back and said, “I got offered a postdoc at La Jolla. Is it okay if I went to La Jolla for two years before coming to Cornell?” And they wrote back and said, “One year would be very nice. Two years is too much,” which is obviously the right answer, since if I went for two years as a postdoc, the chance of my going back to Cornell would be greatly reduced. So I wrote back to Walter and asked if one year would be OK, he said fine, and that’s what I did.

Solid-state physics was not considered physics. In fact, it was taught only in the applied physics part of engineering. Yes. Harvard was awful in those days

So, I applied to Cornell. And Peierls must have said something good about me to Bethe and Geoffrey also spoke well of me. And almost by return mail, I got a job offer.

And most people who were graduate students had come from other places and knew that there was an outside world, but I didn’t, and I knew no physics, so I was terribly educated there. Birmingham was just an eye-opener

Mermin: Harvard was a weird place in those days. They considered themselves not only the most important department of physics, but in some ways, the only department of physics. Nobody read anybody else’s papers, as far as I could tell. I learned about being a scientist from a fellow student of mine, Pierre Hohenberg, whom you probably knew. We were undergraduates together at Harvard. We both loved the mathematics lectures given by George Mackey. And Pierre was also a graduate student at Harvard. It was he who told me that there were things called “journals” in physics, and that there was a place in the building called the “library” that had not only books, which I knew about, but also journals, and that people wrote articles in journals that were often relevant to the problem you were thinking about. It took a fellow student to tell me that was what I ought to be doing. Nobody in the faculty ever said, read this and that paper. It was a strange, inward-looking place

Zierler: Why was it so good? Mermin: It presented the subject in a coherent, unified way. He wrote absolutely beautifully. His technical arguments were extremely well constructed, brief, coherent. It was a lovely book. So I had a very favorable impression of him. And he offered me a position, so off I went. And I basically learned physics by attending Peierls’ lectures. He was giving a course based on his book, and he just opened his beautiful world to me.

smaller book by Peierls that I somehow came upon, which I realized was one of the best physics books I had ever read on any subject.

I knew Kittel’s book was awful.

I realized he was a lovely man.

I said, “What do I do?” And Paul said, “Go to Birmingham. Work with Peierls.” So I went from this vision of Copenhagen, a magical paradise, a charming city — I had never been abroad — to Birmingham, the home of the dark satanic mills, a horrible industrial city.

So, I emerged with a Ph.D., knowing virtually nothing about physics, and having written a thesis that was of no interest to anybody but Paul. And then, a wonderful piece of good luck happened to me. Everybody who got a Ph.D. in theoretical physics at Harvard applied to the National Science Foundation for a postdoctoral fellowship, and most of us got them. And then you wrote a letter to the Bohr Institute at Copenhagen, which was then called the Institute for Theoretical Physics. It was basically run by Aage Bohr, Niels’ son. And you said, “I have a physics Ph.D. from Harvard. I have a postdoctoral fellowship from the National Science Foundation, and I would like to spend a year or two in Copenhagen at your institute.” And for the first time ever, Aage Bohr replied in the negative. He said, “Terribly sorry. We have no office space left. You can’t come.” So, I went to Paul and said, “What do I do now?”

Mermin: Yes. My dissertation consisted of convincing Paul that what he suspected was a key to superconductivity actually had nothing to do with superconductivity. So, my thesis basically consisted in putting together an argument that Paul’s suggested thesis topic would not work. Probably one of the few Ph.D. theses in the history of theoretical physics that was entirely negative. [laughs] And it was bizarre. At some event many years later, probably Paul’s 60th birthday party, everybody did little talks about how wonderful it was working with him, which indeed it was. And then he got up and said he didn’t understand why people thought he was so wonderful a thesis supervisor, and then he went through each of us, one by one, explaining why he basically made no contribution to our education. And when he came to me, he said, “And David Mermin’s thesis topic exploded.” [laughs] That was his characterization of it.

I knew I didn’t want to be a student of Schwinger’s,

Everybody called him “Dick,” and he paid frequent visits to see Hans Bethe and to give talks. He gave his famous lectures on the character of physical law the year after I got to Cornell. And he was clearly charming. Fascinating. Fun to read, fun to listen to, fun to talk with.

Mermin: But each, as far as I can tell, behaved as if the other did not exist

Mermin: There was a tension between Schwinger and Feynman, right from the beginning. I have no idea what it looked like from Feynman’s point of view. Zierler: You mean a personal tension, or a theoretical tension? Mermin: There was certainly a theoretical tension. I mean, their styles were totally different. And I had the feeling it was a personal tension, but I have no direct evidence of that at all. It’s one of the curious things about 20th century physics. I’ve never seen anybody write about the relations, if any, [laughs] between Schwinger and Feynman

But it was common knowledge that Schwinger had done extraordinary things in physics at that point. And there was also rumored to be somebody named Richard Feynman, who Schwinger didn’t like and never talked about, who was also said to be pretty good.

But I did take practically no physics courses as an undergraduate. Zierler: I want to ask: with such a strong background in math, entering the physics graduate program, what were some of the benefits and pitfalls of not having the physics background, entering into the physics graduate program, coming from a math background? How did that help you, and how was that a disadvantage? Mermin: It helped me in the sense that math was no problem. But I knew very little about applied math, which was more pertinent. The chief problem was, for example, that I had never had any course in quantum mechanics. The only physics course I had beyond introductory physics was a course in electromagnetic theory, which by sheer accident, was given by Edward Purcell, who was one of the best teachers in the physics department, and an utterly delightful man. He was basically the only physicist that I had any sense of. I doubt that he had any sense of me, since I just sat quietly, absorbing all the wonderful things he was telling me. So I got to Harvard in physics and discovered that the only thing to do there in theoretical physics was to take courses from Julian Schwinger. My first exposure to quantum mechanics was an utterly wacky course taught by Schwinger, in which he developed his own very strange approach to quantum mechanics, under the assumption that you knew all about it. I knew nothing about it, so I was probably the only person ever to learn quantum mechanics in the way Schwinger was then trying to formulate.

feeling these frustrations about the absurdity of pursuing these mathematical theories,

Zierler: What was your thesis on? Mermin: It was weird. It was producing an elementary proof of a famous result called, I believe, the Jordan curve theorem, that a circle divides the plane into an inside and an outside. And in fact, it was that thesis that made me realize that mathematics could be extremely boring, because everybody knows that a circle divides the plane into an inside and an outside. To have to write 50 pages to prove that rigorously seemed quite absurd. It was at that point, and only at that point, that I realized that I really did not want to pursue mathematics, in addition to the fact that I wasn’t as good at it as I felt I should be. The people who were smarter than me went on to win Fields medals and stuff like that, but I had no way of knowing that these were [laughs] among the best young mathematicians in the entire world. Anyway, I decided not to go to graduate school in math.

And he in turn interested Gleason in quantum mechanics, and Gleason proved the very famous result in foundations of quantum mechanics, known to this day as Gleason’s theorem. And he was my undergraduate thesis advisor. The thesis had nothing to do with physics or quantum mechanics.

George Mackey. Interestingly enough, Mackey had developed, just at that time, an interest in foundations of quantum mechanics, by which he meant giving a mathematically rigorous foundation to the subject. He did not consider Von Neumann to have done that

Not only faster and smarter, but much, much better educated.

And what I discovered in college for the very first time was that the world had people who were much better at mathematics than I was.

I read a lot, mainly fiction. But I also read many science popularizations like Eddington, Jeans, and Gamow.

I can ignore levels from bands en-tirely below the Fermi energy.

The view that it should not betouched seems to have been shared bythose who translated our 1976 text intoFrench, German, and Portuguese justwithin the past decade

Mermin replies: I am a realist.

How arewe supposed to understand state-ments such as “Filled Bands Are Inert,

or many years I have been eagerlyawaiting the second edition ofNeil Ashcroft and David Mermin’sSolid State Physics

bozon

even in particle physics the rate of new information has slowed down

So how does the black hole information problem get resolved? I know it is something involving the theory on the boundary. Polchinski: There are two questions. The first question that we always ask ourselves at conferences is what happens to the information? It’s lost; it comes out, it remains in a remnant. Basically those are the three choices. In any AdS/CFT duality, a black hole is just the dual description of a gas of hot gluons, and this is very satisfying because the black hole thermodynamics is telling us that a black hole behaves like a thermodynamic object. In this duality, it is literally dually described as a gas of hot particles. And the Hawking evaporation is just ordinary evaporation in this case, and so the information just comes out with the evaporating gluons on it. Now, there is still a puzzle, which is the following

So they started studying what happens if you throw stuff at a D-brane, and this led to Maldacena’s recognizing this duality between gauge fields and strings. This entropy counting is neat, but the gauge/gravity duality is amazing, because it really says that gravity and string theory are not anything new; they’ve always been present in the framework of quantum field theory or gauge theory, if we simply knew how to read the code, and Maldacena told us how to read the code. This has many implications. One is it does resolve the information problem at least implicitly, because it shows that you can formulate the quantum mechanics of the black hole in terms of the gauge theory which is purely quantum mechanical — it satisfies the ordinary laws of quantum mechanics. It shows that Hawking was wrong about the breakdown of the laws of quantum mechanics. What does break down in some sense is locality. The fundamental degrees of freedom in the gauge theory are not local in space time.

Now, I have to say that the information problem always bothered me a lot more than entropy problem. The information problem is a sharp paradox. Hawking points out via this thought experiment that some law of physics must break down. He says it’s quantum mechanics, and you can argue with that. But the fact that some law of physics must break down, nobody has ever gotten around that.

My feeling is that the most important thing about the information paradox is that it led us to discover AdS/CFT duality. A paradox is like a thought experiment and the lesson of the experiment was AdS/CFT duality

We now have this duality. We know then that there is one quantum theory which has two descriptions, one in terms of gauge fields and one in terms of gravity, and we do the calculations in terms of gauge fields, which we understand very well, and the information comes out. We do the calculations in terms of gravity, the way Hawking first did it 25 years ago, and we still get Hawking’s answer. We still haven’t found Hawking’s mistake. It wasn’t a trivial mistake;

The most recent electromagnetic observations seen in association with GW170817, show that gravitational waves also experience the same Shapiro delay as photons to about O(10−8)O(10−8)\mathcal {O} (10^{-8}) [13,14,15,16,17].

Following the detection of neutrinos from SN 1987A [6, 7], it was pointed out that the neutrinos also encountered a Shapiro delay of about 1–6 months due to the gravitational potential of the intervening matter along the line of sight [8, 9].

which is straightforward to verify, albeit not so straightforward to derive from scratch

use of the identity (1 − ξ)−1 ≈ 1 + ξ

where we have used the approximation √1 + ξ ≈ 1 + ξ/2

have approximated the trajectory of the light as a straight line from P to E

The straight path approximation is incorrect in the first order[edit] The time delay can be split into two different parts: 1) The Shapiro time delay, caused by a variation in the speed of a photon if it is submerged in a gravitational potential. 2) The geometric delay, caused by the increased length of the total light path from the source to the target, which is due to gravitational deflection. This article focuses primarily on Shapiro time delay and tries to downplay the relevance of geometric delay. It states that: "the contribution from the change in path, being of second order in M, is negligible". The straight path approximation is actually incorrect in the first order. — Preceding unsigned comment added by 2001:1C00:F20:8100:45EF:C2D7:33F9:FF75 (talk) 13:07, 19 November 2019 (UTC)

Is the Shapiro delay due to time dilation or path length increase?[edit] The beginning of the article states, "The time delay is caused by spacetime dilation, which increases the path length." The term spacetime dilation, although accurate, may be unclear (I've never seen it before). Also, the increase in path length is only a partial cause of the delay. The statement would more accurately read: "The Shapiro time delay is caused both by gravitational time dilation and by a relativistic increase in path length." The contributions are roughly equal. This can be seen from the coordinate speed of light in the Schwarzschild metric, which is dx/dt = √(-g00/grr). To obtain travel time t, one solves this for dt and integrates over the path x, where the path is approximated as straight. The fact that g00, which represents the time dilation factor, and grr, which represents the path length factor, are both present means they both contribute. This is clearly laid out in the textbook Gravitation and Inertia by Ignazio Ciufolini and John Archibald Wheeler (Princeton Series in Physics, 1995), pp122-125 71.32.47.71 (talk) 20:35, 26 December 2018 (UTC) Kathleen Rosser

Linde: At first, not read Guth's paper. I first heard about Guth's paper. I didn't have it before me, but since I had discussed this point with Rubakov and his collaborators, who had suggested a similar idea, then everything was quite clear for me. Lev Okun' from ITEP called me and asked have I heard anything about Guth's paper for explaining the flatness of the universe. I told him that "No, I haven't heard about it, but I know what it's about." [Linde laughs.] And I told him how it works without seeing it. So, it doesn't matter. It's just how the things work.

Linde: Probably it was about the 20th of October, 1981. So after that I told Steve, "Would you like to hear what I can answer you?" "Yes." And he with his [wheelchair] came to some room of the Sternberg Institute. We closed the door, and I told him something in a more detailed way about this scenario. He is sitting here about one hour and a half and saying [to] me the same words: "But you did not tell this before. But you did not tell this before." [Linde laughs.] Lightman: That's what he was saying to you. Linde: Yes, I was explaining to him the details. Lightman: You were beginning to convince him that you were right? Linde: Yes. And he was saying, "But you did not tell this before." Lightman: He was probably embarrassed that he had objected so strongly to your theory. Linde: No, I don't think so, but I gave him some new information.

Now Steve came to this Institute and gave his talk. I came to this talk occasionally. I didn't know what it would be. Typically, one of [Hawking's] students [at that time] translates his English into ordinary English and then somebody translated it to Russian. Steve is absolutely impossible to understand. Now he speaks into a computer and it's much easier for him. But they were not quite prepared to give this lecture. Steve [would] say a few words, and the student [would] say one word, and he did not understand what Steve wanted him to say. People asked me to translate it. And the talk looks like that. Steve [would] say "ah, ah," then his student [would] say one word, and then I was speaking for five minutes, since I understood what he wanted to say. So I was making my talk. [Both laugh.] [Then] Steve said that there was a very good suggestion by Linde at the quantum gravity conference, and I translated it and the whole institute was there to hear. "But I believe that this suggestion is wrong," said Stephen, and I translated it. And during half of an hour, he explained to everyone, and I had to explain [in translation] to everyone why my idea is wrong. So after that, I stopped my translation and said that I have translated but I disagree [more laughter].

The story goes [that] Steve came and gave a talk. He had a paper[13] with him in which he had proven with two co-authors that it is impossible to improve Guth's scenario. Simultaneously, we received a large paper[14] by Guth and Erick Weinberg in which they also proved [the same thing] — not simultaneously, [but] somewhat later. Lightman: When you say impossible to improve, what do you mean? Linde: They had studied the "old inflationary universe model," and they had tried to see any way to make the universe smooth. Lightman: Less inhomogeneous? Linde: Yes. And the statement was that it was impossible. Lightman: So they just weren't considering potentials of this type [used by you]. Linde: Yes, they were not considering the possibility that exponential expansion can occur inside the bubbles. Everyone believed that inside the bubble should be empty space. And in many realistic theorists, this is true. There were very nice papers[15] by Sidney Coleman from here [Harvard] discussing it, and in all known cases, inside the bubble there was empty space. So everyone was quite confident that this was the only solution

Lightman: At this time, what did you think stopped the expansion? Linde: Because of the curvature of the potential, the ball [representing the value of the Higgs field] rolls rapidly, then it oscillates and heats universe, and then inflation stops. Lightman: So you knew that the exponential expansion would stop inside the bubble? Linde: Yes, I knew it, and the whole picture had appeared at once. It was not necessary for me further to change essentially some of these features. Though, about half a year or maybe a year later, I somewhat improved something connected with the initial stages of the evolution of the bubble. There were some problems connected with the curvature of the universe, and this is temperature. So the first picture was rather naive. I understood that it is naive, and I was worrying whether the main results are correct.

Linde: Oh, no. Zero point oscillations do not reheat anything. One cannot produce energy by zero point oscillations. So it was necessary for the classical field to oscillate near a minimum of the Higgs potential and here, you see, there were two ideas: First that you have exponential expansion inside the bubble, and second that you have another mechanism for reheating the universe.

inde: That's right. What had been assumed by Guth is that this wall [expands] with the speed of light, while here [inside the bubble], space is Minkowski space. But what occurs is that if the bubble is very, very smooth, then inside [the bubble] it is also De Sitter space. This was the first revelation. And another revelation was that it was quite possible to create particles, since this field rolled down [the potential hill], oscillated there, and produced particles. Lightman: But couldn't you produce particles in Guth's [model] too. [The quantum field] could oscillate back and forth [at the bottom of the potential well]. Linde: Oh, you see, in Guth's picture, it was assumed that the field inside [the bubble] is already at the minimum [of the potential energy], so it's not oscillating. All the energy [release] comes from collisions with the walls. It is actually so. In those types of theories which he has considered, this is a true result. He has not made any mistake.

Lightman: Yes. Guth says himself that if he hadn't done what he did, other people would have done it. It [the inflationary universe model] was just in the air, like special relativity. Guth has a very modest view about what he did.

In 1981, when Guth had written his paper, some people in Moscow also had written a similar paper. They [had] submitted their paper for publication in Physics Letters. But they were a bit too late, and [the editors] told them that already a paper by Guth is published. Among these people was [V.A.] Rubakov, who is now a well-known person.

About three years before this paper by [Alan] Guth,[8] I had studied similar problems with one of my colleagues at the Lebedev Institute, and we understood that the vacuum can decay and reheat the universe. We understood that the universe could be exponentially expanding and bubbles would be colliding, and we were seeing that it would lead to great in homogeneities in the universe. As a result, this [possible process] is bad [doesn't agree with observations] so what is the reason to publish such garbage? But at that moment, we did not realize the main advantages of this [exponential expansion], that it could possibly solve the flatness and horizon problem.

I was thinking about everything, and that includes general relativity theory, since actually this theory is rather complicated. It has many branches and there was a lot of material which had been worked out for many years. People have studied it, and quantum gravity is extremely complicated. I was just lucky that such beautiful things were at the surface so I could see them. You see, my mind is not very technical. I work best of all in those places where I can use my intuition. Lightman: That's very interesting. I'd like to start asking you questions about that. I've noticed from your technical papers and in your paper in Physics Today[6] and your lectures that you describe things intuitively, with pictures and so forth. I know there have been certain physicists in the past who have used images and visualization and pictures more than other physicists. I think Einstein used a lot of visual images. All of his Gedanken experiments were based on mental images rather than on writing out equations. Even here [at Harvard] we make a joke in the physics department that Weinberg is very technical and [Sheldon] Glashow is very intuitive. So there do seem to be different styles of doing physics. One question that I've been very interested in, and some psychologists are interested in too, is how physicists use mental pictures. Maybe not exactly pictures but, for example, the way we say in quantum mechanics that sometimes things act as particles and sometimes as waves. I guess we're attempting to make a connection to our daily experience with the world. How do you use images in your work? Do you find images useful or harmful? Linde: Typically, I just use them. Of course, I use mathematics, certainly. Lightman: Of course. Linde: But first we usually have a rough idea of how it could work and why, and what is the purpose. Without understanding the purpose of what we are doing, you may try many different ways and you just solve equations without understanding why it is necessary.

Linde: I was thinking about everything, and that includes general relativity theory, since actually this theory is rather complicated. It has many branches and there was a lot of material which had been worked out for many years. People have studied it, and quantum gravity is extremely complicated. I was just lucky that such beautiful things were at the surface so I could see them. You see, my mind is not very technical. I work best of all in those places where I can use my intuition.

Shapiro: Well, [laugh] I enjoy thinking about my life [laugh] sometimes. I’ve forgotten an awful lot, unfortunately.

Shapiro: I suppose the one that’s most famous is the Fourth Test of General Relativity. There aren’t many fourth tests. [laugh] Well, the story of that is also interesting, which I didn’t go into in all of its details, for example, but got me into a lot of controversies with some well-known physicists. [laugh] Zierler: Such as? Shapiro: Leonard Schiff, you remember Leonard Schiff?

Shapiro: Yeah, my daughter, for example, was then taking chemistry in high school. She had this chemistry book several inches thick. She didn’t really even know what a wave was, and the book had material on molecular orbitals. There was no way she or her fellow students could learn that material. Their teacher probably didn’t know much of it either. All they could do was memorize, and then forget. They had no understanding of that material. I thought this was crazy. It seemed to me that this situation arose largely because textbook companies can make more money if they can sell more expensive books, and revise them every year. You know how it goes.

Shapiro: Oh, yeah, I was a PI on this experiment for both a Mariner flight and a Viking flight. I think the Viking flight was sort of my last gasp of involvement with NASA. I had one more – the Voyager mission - but I resigned from it. Too many meetings. [laugh]

The first one who had a really sensible idea was John Michell, whom you may or may not have heard of— Zierler: No. Shapiro: —from the18th century—who actually was the first one we knew of to think of black holes, although he didn’t call it that of course.

Shapiro: Chuck Counselman Zierler: And what was his project? Shapiro: I gave him the project of investigating the secular variations of the eccentricity of Mercury’s orbit, and how that would affect the 3:2 resonance between Mercury’s spin and its orbit, which had just been discovered, and I was a part of that discovery. But that’s another long story. And that was his thesis, and he did very well with it. He calculated what I suspected, namely that mercury’s spin-orbit resonance would go in and out of resonance as its eccentricity increased and decreased, respectively, in response to the corresponding changes in its eccentricity due to planetary perturbations.

A few years later I wondered why light should slow up when approaching a massive body and yet masses should slow up on such approaches. So with a (later) postdoc, I carried out such a calculation—a little tricky!—and it showed that if the speed of a mass exceeded about c divided by the square root of two, then the speed of the mass slows as it approaches the massive object. The so-called “Shapiro delay” has had probably its biggest impact on astrophysics by allowing pulse-time-of-arrival measurements sensitive to the Shapiro delay to allow the determination o the highest so far available values for the masses of pulsars in binary systems and to place important constraints on the equation of state of pulsar material.

Shapiro: That his theory of general relativity predicted the result of the experiment. And we confirmed that the prediction was right on. I was hoping that it would not be correct. Zierler: Because you’d be instantly famous, I guess, right? Shapiro: Exactly.

Shapiro: I was in this period of time on a subway…the tube in London. And it was crowded, and so I was standing. And the guy sitting in front of me was reading a book on matrices. How often do you run into someone on the subway reading a book on matrices? So I started talking to him. And he started asking me what I did and what I was doing, and I was a little vague. And he kept pushing and pushing and pushing me, till finally I told him I was working on this project. And he was so incensed, he got off at my stop, not his, to argue with me how this was a terrible thing for me to be doing. [laugh] Zierler: [laugh] Shapiro: The dipole project excited a lot of passion [laugh] in those days.

Shapiro: This was an idea that came out of Lincoln Laboratory and the company, TRW to create an artificial ionosphere that was jam-proof and that allowed radio communications point-to-point anywhere around the world. The idea, which was from Walter Morrow of Lincoln Lab and Harold Meyer of TRW, was to put in orbit around 450 million copper dipoles, which were each about an inch long. And a colleague and I worked on the orbital dynamics of these dipoles, which had very high area-to-mass ratios, and we discovered sets of sunlight-pressure resonances that could bring the dipoles down from orbit monotonically from altitudes of several thousand kilometers in a few years. This “guaranteed” short lifetime in orbit was my main contribution to project West Ford, and got me involved in international politics. For example, my work (and my name) was mentioned at the UN by Adlai Stevenson, our UN Ambassador, quoting my work on this project. And I had to make a trans-Atlantic call to London, a rather unusual event for those days, To uncover what a scientist in London had done wrong in claiming that our resonances would break down before the dipoles came down from orbit. It took me only a couple of minutes of questions to figure out what he, Desmond King-Hele, had done wrong: he had assumed tha the orbital inclination stayed constant, which was a bad, and incorrect, assumption to make. When he corrected that error a few days later, he got the same results as my colleague, Harrison Jones, and I had obtained. Zierler: [laugh] Shapiro: —and it was an amazing experience for a relatively young kid. This was the beginning of the Space Age. We realized that because of the high-area-to-mass ratio of these dipoles, they were subject to large solar-radiation-pressure perturbations. And we – my colleague at Lincoln Lab and I - realized that radiation-pressure resonances, if you chose the orbit properly, could act monotonically to push these dipoles from altitudes of around 4,000 kilometers down to the ground in a couple of years. And our proposal to utilize sunlight pressure was from almost the beginning a major consideration because there was all sorts of opposition, especially from astronomers, as soon as the project was declassified. The dipoles, they said, were going to put them out of business. Did you ever hear of Allan Sandage?

Shapiro: And I was told that there was a bank account in Moscow that had my royalties there. Zierler: Really? Shapiro: That’s what I was told by someone who should know. And I was told that the royalties had to be picked up in person. But by then, I had actually gone to the Soviet Union, in 1959, and didn’t have any idea about this translation at that time. So I missed out on whatever [laugh] royalties—

Shapiro: Well, at the time in my part of the lab, it was mainly radar projects. And they were worried about clutter, how to distinguish objects of interest, in particular planes, from the background clutter. It was basically a separation of signal from noise issue. And I worked on that type of problem for a short time. And then along came the scare that the Russians were developing intercontinental ballistic missiles capable of hitting the United States. So I was chosen to be one of about 10 – 20 people working on a special project to figure out how we could defend the US against such ballistic missiles. And I wrote a book on the results of my mathematical studies with the very sexy title, The Prediction of Ballistic Missile Trajectories from Radar Observations. Zierler: And who was your audience for this book? Were you writing to policymakers, the broader public, fellow scientists? Shapiro: No, certainly not the broader public. [laugh] That wasn’t the kind of book it was. The real audience for it turned out to be the Russians. Zierler: [laugh] Shapiro: I found out years later they not only translated it—I mean, they translated it, made all new figures, and published it. And I have a copy right in my [laugh] bookcase here at home of their translation that I didn’t get till years later.

Zierler: Totally fine. So why in the end did you choose Harvard? Shapiro: That’s a good question. I didn’t know anybody there. I went around and visited. [ ] Again, I applied to Columbia, because my parents would have liked me back in New York. But every graduate student I spoke to there without exception warned me against coming to Columbia. Zierler: Really? Shapiro: Yes, and the reason basically was they felt they were kept as slaves for 9 or 10 years as graduate students. Zierler: You mean before they defended? Shapiro: Yep, before they were allowed to finish, they were kept as slaves for their thesis advisors. The time to graduate was usually five, six years, something like that. At Columbia, the graduate students were kept on average, I guess c. 10 years—I don’t know the average really. But they were all telling me that it’d be 9, 10, 11 years.

Shapiro: No, I was thinking about going to graduate school, only graduate school. I didn’t have any other plans. I applied to a lot. I applied to Yale, Harvard, Princeton, and Columbia. I remember my application to Harvard. They asked for a 250-word-minimum essay on why I wanted to go to graduate school. I gave them 37 words. Zierler: [laugh] Shapiro: And I said to myself, if they’re going to reject me on this basis, I don’t want to go there. [laugh] Zierler: [laugh] Shapiro: And they accepted me. [laugh] Zierler: Do you remember what you said? Shapiro: No. It was basically that I wanted to be a physicist and in order to be a physicist, you needed a PhD.

Zierler: Is it uncontroversial to say that he was the greatest physicist you ever knew? Shapiro: Hmm, Hans Bethe. I’ve known a lot of physicists, and Julian Schwinger of course I knew at Harvard. And he was quite different as well as bright, but not Feynman’s type at all. Very contrasting [laugh] personalities. I preferred Feynman’s [laugh] type myself, but I appreciated Julian. Zierler: Because you could talk to Feynman? He was easier to talk to? Shapiro: Yeah, not that I found Julian hard to talk to. I didn’t. He was easy for me to talk to too. He sort of liked me for some reason I never understood. [laugh] So I got along with him well. But Feynman was more my type of person [laugh] so to say.