Michael Horne

Horne:

And then he kept coming back. You know, he’d come back for six months, stay, and he has made many, many visits to MIT over the late seventies and all through the eighties.

Bromberg:

Oh. So he was —

Horne:

But he was here.

Bromberg:

I had better tell the tape, because I just turned it on. We are talking about Anton Zeilinger, whom Professor Horne met Erice in 1976.

Horne:

That’s right. And by that time I had just started working with Cliff [Clifford] Shull at the MIT reactor where he was doing the new work then on neutron interference. There were several groups that had started that before he had. Sam Werner [spelling?] had a group in Missouri and they had built an interferometry. You know, everybody was using the same techniques in these first interferometers — silicon crystals and thermal neutrons. And they were just essentially doing the double-split experiment of the neutrons. And Abner [Shimony] and I saw that, saw those first papers, the one from Missouri. The one from Missouri by Werner, their experiment was very nice. They turned the interferometer so that the effect of gravity could be seen, so they could actually see the phase shift of the radiation due to turning the interferometer in the gravity field. The other group that had started this business was Rauch and his student Zeilinger and others, and they were in Vienna at a reactor. And one of the first experiments they did was a demonstration of the effect if you turn a neutron around once using magnetic fields, if you rotate it once. Then it’s not really like it was before you turned it. It actually introduces a negative sign in its quantum state, which with an interferometer is visible, so they could see this negative. If you turn it another time — so if you turn it twice — then it’s back to its original condition. So those are the two experiments that caught our attention.

Bromberg:

What made you —? I mean you were working up until this point on Bell’s theorem.

Horne:

Well, I thought Bell’s theorem was finished. Right? That is the original work with Abner for my thesis, in collaboration with Clauser, and then, tidying up some questions we had with Clauser in that ‘74 paper, was trying to improve the argument a bit. And then by then the experiments were done. You know, Clauser had done the experiment in California, and the quantum mechanics was beautifully confirmed. The Harvard experiment that gave a disconfirmation of quantum mechanics. Everyone knew there was something wrong with it, they just didn’t know what. So I figured we were through. In 1975 I was looking for some more fun things to do with quantum mechanics, and I saw these neutron interferometer papers coming out from the States and from Austria. Abner and I talked about them together and we even wrote a paper.^[1] We wrote a paper proposing that this turn a neutron around once and get a negative and then turn it twice and then it would be back to positive, we wrote a paper proposing that this experiment be done, not knowing that they were just finishing doing it in Vienna. It was a wonderful toy to see something as basic as interference which is the heart of quantum mechanics be doable now with something as massive as a neutron. We just thought, “This is something that is going to be fun to play with for a number of years.” So that’s why I made the transition. I thought the Bell physics was essentially done, the experiment had been done, the elements of reality don’t seem to be possible because 0 the quantum mechanics was confirmed. So I thought the Bell physics was essentially a finished package. So I saw these one-particle interferometers and thought I would like to play with them. And so I heard from someone — I don’t know who told me that there might be soon one of these same instruments running at MIT because one of the founding fathers of neutron diffraction was a professor at MIT, Cliff Shull. So I don’t remember who told me about him. He hadn’t done any interference yet, but as it turned out he was working on it trying to get one running. So I went over there sometime in ‘75, I’m not sure when. I went over and walked into the reactor where his office was and he was there with a couple of his grad students, and I introduced myself and told him about my background in Bell physics and my work with Abner and my excitement about these new one-particle neutron interferometers, and I essentially asked him, “Can I play?” And he says, “Sure. Just take that desk.” So I just started going over there every Tuesday, which was my day off at Stonehill, and weekends and summers and Christmas. That’s how I started.

Bromberg:

So you were really set up to meet Zeilinger, to meet someone from the Rauch group, I mean that was —

Horne:

Well, then what happened was, completely separate from Shull — And by the way when I went over there he had a student who was Joe Callerame who was currently trying — they had already cut the crystal and they had a new neutron beam and they were trying to make it show interference, and during the first few months I was hanging around there it started working. I was there the night that — what Joe did was put pieces of aluminum foil in one of the beams. He put pieces of aluminum foil and that would phase shift the radiation in that beam relative to the other. So the aluminum foil was playing the role of glass plates, you know in optical interference. And he put in one sheet of Reynolds Wrap and then he put in another sheet of Reynolds Wrap and watched the counts go down, indicating the phase shift was happening. And then he kept putting in more sheets and then it came back up, right? So there was interference. So we called Shull at his home in Lexington and he drove in. It was late one night. We went out and had a drink because the interferometer was working. So this was the third one. You know, there was the one in Missouri and then there was the one in — [Vienna].

Bromberg:

I see.

Horne:

But at this time there was no connection with the Vienna group or with Zeilinger. That connection happened because of a little carryover of the two-particle stuff. There was a meeting and there was going to be a conference in Sicily in ‘76. I was already hanging out with Shull and the neutron interferometer people. There was going to be a conference on Bell physics. I didn’t have anything new to present on the Bell physics, but you know it was something I had worked on and so I decided to go with Abner to the Sicily meeting. We also went with Frank Pipkin, who was the professor at MIT who had done the [Bell Theorem] experiment. So the three of us went together to Sicily to that meeting, and it was at that meeting that I ran into this person about my age — thirty-ish. Zeilinger had come to that meeting and his plan was to talk about their neutron experiments even though it wasn’t directly connected to two-particle quantum mechanics or to Bell stuff. It was so basic and fundamental he thought that would be a good place to go talk about it.

Bromberg:

So he was essentially also motivated to do physics that had to do with fundamentals of —

Horne:

That’s right. He was interested in the fundamentals of quantum mechanics. They were playing with one-particle interference with the neutron. And we started talking to each other over every dinner at that meeting, and we found out we very much liked each other’s ideas about what’s interesting. And I would talk a lot about two-particle stuff which he hadn’t really thought about, and then from my previous half decade in two-particle physics, and he would tell me what they were doing with their one-particle interferometer which I was just starting to get into with the MIT group. So we just bumped into each other at this meeting in Sicily. And then when I came back home sometime in the next few months or before the year was out Cliff Shull at MIT said, holding up a letter, “Do you know someone named Anton Zeilinger?” And I said, “Oh yes, I met him at a meeting in Sicily.” He says, “Well, he wants to come over for a postdoc. What do you think?” and I say, “Great. It’ll be fun. You’ll like him. And it would be fun to have him here. He is a very good person.” And so that’s how Shull and Zeilinger and I got started together.

Bromberg:

So what year did he actually come for the postdoc?

Horne:

So he came and spent — he brought his family, brought his wife Elizabeth, and he had two children at the time. I think possibly one; his oldest daughter was around. And they moved in and spent a year here in the Boston area. And so we started talking, you know, almost daily about what to do with this new toy. You know, what would be fun to do with this new neutron interferometer. We were not particularly talking about two-particle quantum mechanics at that time. Years later we started talking about it, but I can tell you the reasons. But that was years later. So I actually — I should summarize what we did during that decade. The idea was to find interesting things to do with this new interferometer, and that is basically following nature. Disturb it in some way, you know, rotate it, turn it on its side, subject it to various fields — things that would definitely cause a phase shift. Then we would do calculations to see what the phase shifts would be, and then we would do an experiment to see what they were. We didn’t anticipate any surprises, but this was a whole new thing to do, subject neutrons to various perturbing influences and see if the quantum mechanics did what it was supposed to do.

Bromberg:

In that whole group is there a lot of connection with what the quantum optics people are doing with their interference or are they just two separate worlds.

Horne:

They were sort of separate. We didn’t — by then quantum optics had gotten fairly sophisticated. I wasn’t particularly knowledgeable about quantum optics. In fact I really knew very little about say what was going on in Rochester. Very interesting experiments were taking place with optics, and quantum optics was becoming a very rich field with a rich theoretical structure to it, and it was second quantized, it was quantum mechanics applied in a new area and I wasn’t in that area. I wasn’t working over there. What we were doing was sending these neutrons one at a time to this two-path gizmo and we — it was so basic we felt all we had to do was just take the de Broglie waves and do the calculation. The master equation for our work was the Schrödinger equation, but it was actually even more basic than that. We just needed to know the de Broglie wavelength and then work out it would change due to the perturbation we were playing with that year. So we rotated them and we tilted them and we perturbed them and there was always lots of interesting questions about the detail of, at this point, the de Broglie optics. Inside these crystals there were lots of interesting questions about how to work that out in detail. Because it wasn’t just here’s a place where the beam gets split; it was a thick region where it gets split, you know, inside this crystal. So there were lots of interesting things about the interferometer itself that needed to be worked out. And Danny [Daniel] Greenberger had been working on some of those questions once he started working with the Missouri group. Greenberger got involved with Overhauser, who was one of the people who first played with Sam Werner with the neutron interferometer in Missouri, and Danny saw some things from past experiments that puzzled him. Way back in the early sixties people had done electron interference. And one of the interesting things they had done with it was Aharonov-Bohm experiments. And Danny was, unbeknownst to me at the time, was looking back at those experiments and was puzzled about how they were able to see the effects they saw even though there were magnetic fields in the rooms. And he got really interested in these questions about electron interference. And that’s how he got started thinking about one-particle interference, whatever the particle. Incidentally I had started reviewing some of those old electron experiments motivated by now doing the neutrons, and I came up on the same puzzle that Danny did, right? I thought, “Gee, I wonder how that experiment worked back in the sixties even though there were magnetic fields.” And it turns out there was a compensating effect. And we both had independently worked on that, but we didn’t know about each other. What happened was Danny was very much interested in what might be done with these neutron interferometers. He was specifically interested in the gravity experiments that had been done at Missouri. Somebody told him that a new person would be starting to do experiments with neutrons up at MIT, and so he came up to talk to these people, Cliff Shull. And that’s where he ran into us. He came up and he was interested in basic quantum mechanics. Some of his interests were some experiments having to do with the nature of time and how it could be studied using a neutron interferometer. He had a background in relativity and basic — I don’t know all these details. He still works on these sometimes even today.

Bromberg:

Yeah, well of course he’s on our list.

Horne:

Yeah. So you should talk to him about the particular things that he was thinking about in going up to MIT to meet Shull. He wanted to know — It turned out Danny had written a paper back in the sixties that suggested that this gravity experiment be done, but he didn’t know that it could be done. Right? He didn’t know anybody to do it. He might have even come up to visit Cliff Shull early in the seventies, you know before these interferometers got created, with the idea that maybe he could make one. So this predates the Rauch group in Vienna and the Missouri group. He was interested in trying to make a neutron interferometer before anybody else starting making them. And then of course it turns out they showed up on the scene years later without his being involved, and so he started getting involved — first with the Missouri people and then with the MIT people. So that’s the background that got me bumping into Danny. By ‘78 the three of us knew each other, Danny and Anton and me, and we were bumping into each other at MIT. Danny would come up from New York say for a weekend or for a week. Sometime in the summer he’d come for a couple of weeks and we’d talk about neutron interference and various questions that were coming up at that time about the instrument and about how to use it. So there are sort of two types of problems like getting a deeper understanding of what’s going on in the crystals and thinking of new fun things to use it for. And so that’s sort of the gist of the late seventies and all of the eighties.

Bromberg:

And so you were not like Abner Shimony trying to work out any of the ontological or epistemological conclusions of Bell’s theorem. That was not —?

Horne:

That was over. That was over. But Abner would occasionally show up at MIT with his idea about what we might do.

Bromberg:

I see.

Horne:

That is, there were proposals for slightly modifying the Schrödinger equation. One of them came from Poland, introducing a nonlinear term, and Abner realized that this sort of proposal could be tested with a neutron interferometer. And so he came over and said, you know, we had various things we were doing and he said, “Here’s one you might want to do,” You can check this non-linear, non-orthodox term that people were thinking about sticking in the Schrödinger equation. And we did the experiment. Shull and his group did the experiment. That was one proposed by Abner. So you know I had ideas for things to do and worked with Shull’s students while they went and did them, like a proposal on rotation. I spent a lot of time talking about rotating the thing, because the effect of rotation had been studied back in the 19th century with optical interferometers, and we thought, “Gee, we should do the neutron version.”

Bromberg:

I see. I didn’t realize that.

Horne:

And then there was also the question of putting matter inside the interferometer to make phase shifts, but not just the matter itself, put the matter in motion. And there were famous experiments back in the 1850s — Fizeau in France, you know, had done the so-called Fizeau Effect where he studied the effect of moving matter in an optical interferometer in various experiments. Famous experiments from 1850. And so we said, one of the things I started thinking about doing was, “Let’s do that with neutrons. Let’s put the aluminum” — or whatever we were using as phase shifters — “and let’s put it in motion and see the neutron Fizeau Effect.” So that was one of the things I had worked on in the beginning. And you know Abner had his and various ones came up with various suggestions. So by ‘78 there were starting to be meetings about neutron interferometry and lots of experiments had been finished with Abner’s suggestion and the Fizeau Effect and the gravity effect that Danny had been interested in and had actually got done in Missouri. So all these things were doable and were starting to be done, and we started meeting not only at Cliff’s labs but at conferences that were taking place. And one of them that happened early, in the late seventies was at Grenoble.^[2] And Danny went and Abner went and Shull went and I went. We all went there to talk about the things we were doing, each of us and together, and that’s the first time I met Rauch, right? I knew about Rauch because he was Anton’s mentor, he was his advisor, but I first went to Grenoble and ran into some of the other people besides Anton.

Bromberg:

And that’s in Vienna?

Horne:

And they were in from Vienna, but it was in Grenoble that they were going to have this meeting, because Grenoble has a great source of neutrons, and years later that reactor would be used to do other experiments, many with Rauch involved in it, and Anton, where the neutrons were very slow and you had a much longer de Broglie wavelength. So it was at that meeting I presented my work on the Fizeau Effect and met some of the people from Europe who had a background in playing with neutrons. Some of them, their ideas on the thing with neutrons had come from Europeans who first built these instruments to do X-ray interference of the same wavelength. They were the ones who started the crystal interference business. But they were doing it with X-rays.

Bromberg:

Was that an interesting cross-fertilization?

Horne:

Well that’s how the instruments came to be.

Bromberg:

I mean from your point of view, did it enlarge the way you were thinking about things, or just didn’t have all that much effect?

Horne:

Well, that’s how these instruments got started, from people who came from another direction. My basic interest from the beginning — I’m going to have to get me some sugar by the way because I have taken my insulin for the day and have to start eating at regular times. Let me run and get some juice.

Bromberg:

Okay, and maybe I’ll get some water. [recorder turned off, then back on...] Let’s see now.

Horne:

So I think I’ve described — You’ve already talked to Abner, and so you know how we got together [on Bell experiments] and what we worked on and about Clauser being independently doing the same thing and then we got together. So since we started today I think I’ve described how the second part of my career, which was the one-particle neutron interference, got started and how the various players got together. Anton was already doing neutron interference as a student with Rauch, and I had joined the MIT group just looking for something fun to do, and then we both ended up working here off and on for fifteen years, Anton and I. He would come for visits and Danny would come up and join us.

Bromberg:

And that got us up to about Grenoble.

Horne:

Grenoble was just one of many meetings. This business went on for fifteen years. Nothing particular to report except you know they were just very fundamental experiments. That is, you know, we would do one and then move on and do another one.

Bromberg:

Well of course the transition — I don’t know if this is the next transition, but you get this transition to using entangled particles.

Horne:

Okay, well that’s the next chapter. I can tell you that story. So basically the first period is the Abner-Clauser two-particle entanglement specifically addressing Bell experiments and showed it up. Einstein’s elements of reality don’t exist. In the second period, the one which we were just describing —

Bromberg:

Right.

Horne:

— was one-particle interference and with various little neat, never-done-before experiments, but none of them worth singling out particularly. We could just do things that had never been doable before. But then there was a time when I went back to more than one particle and that started in ‘85. And it started because Anton was here on one of his many visits and we were sitting in Shull’s lab, and one of the drawings that we always had in Shull’s lab — it was almost like we had a tablet of them printed. It was a diamond. Right? And when we wanted to start talking about what we were doing with the current experiment that’s been going on for years, we’d always point to the diamond because there is the two paths and we’d talk about what we were doing on each path. It was just the talking stage. So those sorts of figures were all around us, these single diamonds for a two-path interferometer. We got an announcement for a meeting to take place in Finland to celebrate the 50th anniversary of the Einstein-Podolsky-Rosen paper.^[3] And Anton knew I had been involved in the Bell EPR business but hadn’t for about ten years been actively doing anything. By the way, during that ten years — just as an aside — during that ten years it had all of a sudden become widely known, that more people were interested in this Bell stuff then back when we started. I think there’s a graph in this AJP collection of papers that shows how many people referred to the Bell paper, and there’s like nobody all through most of the seventies and then by the mid-eighties it goes wow and it goes flying up, you know, like this.

Bromberg:

Which of these AJP papers?

Horne:

Yeah. There’s a volume. I think Ballantine is the Editor. It’s at least fifteen years old now. It’s a green paperback, 8 1/2 by 11 size. It’s a collection of the key papers in this foundation business. It might be called — You haven’t seen this?

Bromberg:

I didn’t know about this.

Horne:

The whole foundations of quantum mechanics. Let me get you this. You should take a look at this book.

Bromberg:

Absolutely.

Horne:

Turn it off for a second.

Bromberg:

Yeah. [recorder turned off, then back on...]

Horne:

So there’s ‘85, and we saw that this meeting was going to take place in Finland on the 50th anniversary of EPR, so Anton and I said, “Gee, it would be fun to go to that.” But what can we present, right? Because we haven’t been doing any two-particle stuff, what could we do that would be — And so we said, “I wonder if there is something about” — you know, I had been telling him about two-particle quantum mechanics, you know, of the simplest variety, where each of your two systems only possesses a two-dimensional state space, right? Two states, and what’s an entangled state is this one goes with that one and then this one goes with that one that’s entanglement. All the examples that we did with Clauser and everybody were so-called polarization where it’s up-down, right? So Anton and I said, “I wonder if there is something we could do that would be a fusion of what we currently do.” And we were looking at this diamond, and that old stuff, right? And we said, “Well, up-down in the old days, left to right, up goes with up, down goes with down, and we need two diamonds!” And this path is connected to that one and this one is connected to that one. So hey, so we started thinking about what came to be known to us as a two-particle interferometer. This source in the middle emits a pair of particles — and you’re told that the two members of the pair go opposite. Right? That’s the nature of this emitter.

Bromberg:

Right.

Horne:

It emits pairs that go opposite. But classically you say, “Oh that means either they go along those two legs of the diamonds or they go along those two legs of the diamonds as they retreat from each other.”

Bromberg:

Right.

Horne:

But quantum mechanics says that’s not what really happens. They go both this way and that way. So that’s our entanglement. But it’s entanglement of particles as they just travel through space, not something subtle, like the up-down or anything of polarization. So that’s where the double diamond came to be, and we called it the two-particle interferometer. So we played with it for about an afternoon just on paper, and we saw that it was completely analogous — not surprisingly — to a Bell or Bohm or you know a standard polarization entanglement.

Bromberg:

Now you had been deeply involved in that stuff at one point. Had he also?

Horne:

No, he had not been involved in it, but we both sat there together and we just said, “Look. The two-particle quantum mechanics? We’ve been doing one particle for fifteen, for ten years. What’s the connection? Can we make our connection between this one-particle quantum game we keep playing, and this?” or “Can we make a connection between that and this old stuff that I used to do.” And it just, boom, it became that, right?

Bromberg:

Yeah. And I should tell the tape that “this and that” means one diamond versus two diamonds.

Horne:

Yeah. Two diamonds. So we worked it through and we found out that such an arrangement — we didn’t know how to actually produce one at the lab, because we didn’t know where to get a source that would emit pairs of particles in opposite directions.

Bromberg:

Yeah, I noticed you were talking about positronium annihilation and —

Horne:

Right.

Bromberg:

You didn’t think of cascades, atomic cascades?

Horne:

We thought about cascades, but cascades don’t have the desired oppositeness direction to them.

Bromberg:

Oh. Okay.

Horne:

The cascades are very fuzzy. That is, the particle goes this way and the other one can go anywhere over here with some distribution, right?

Bromberg:

I see.

Horne:

We wanted something that really was — But what we didn’t know about was down conversion. We didn’t know about that.

Bromberg:

Yes. Which the optical community was at that point really beginning to.

Horne:

And they were — completely unknown to us and vice versa. We didn’t know about them; they didn’t know about us. They were moving towards producing pairs of just the sort we were thinking about there on our piece of paper. So anyway, we gave the talk in Finland and people liked it. They thought it was interesting to see this —

Horne:

That was ‘85. That year Danny had a meeting in the World Trade Center. Danny had a nice meeting. There must have been a couple hundred of us there, you know foundations of quantum mechanics. There’s a nice publication for that, and it’s also green.^[4]

Bromberg:

Yeah, and I’ve seen that.

Horne:

Right. By the way that’s the same green paperback, same color as the other book I told you to look for. It’s that same — this Ballantine is also that same dark green. We were all sitting there listening to the talks, and two people there talked about down conversion — [Yanhua] Shih and —

Bromberg:

Not the Mandel group?

Horne:

I think the Mandel group might have been there too, but I think there were at least two groups there that talked about down conversion, but we were just, you know, we didn’t pay any attention. They actually were talking about sources that were just the kind we wanted, but we just glazed over and weren’t paying enough attention. Anyway, so it wasn’t until ‘87 that I happened to drop back by Shull’s lab one day, some Tuesday, and there was a stack of Phys. Rev. Letters lying there that I hadn’t looked at, months old most of them, and I was thumbing through one of them, and on one page I saw this picture that was a diamond inside a bigger diamond.

Bromberg:

Right.

Horne:

Right. And it was the picture from Ghosh and Mandel’s paper. And I said, “Gee, that’s our figure where you just unfold it,” you know, have them opposite each other instead on top of each other, and make them the same size instead of one littler than the other? I said, “See, they’re doing our experiment. There it is, right there. They’re doing two-particle interference.” So we had an idea independently of the whole world, but the whole world got without ever needing us, right? You know the [unintelligible word] two-particle interferometer. I wrote Mandel after seeing that paper and sent him my little paper from Finland, and he wrote back and says, “Your approach is very simple, very clear.” I’d looked at — they had a paper where they talked about their theoretical underpinnings and what led them to do this experiment, and it was typically a 10- or 20-page Phys. Rev. Paper, heavy machinery —

Bromberg:

Lot of annihilation operators.

Horne:

Lots of annihilation. It was just like I couldn’t even read it. I didn’t even know what it was about, most of it? But our discussion was half a page. Well, we had exactly the same final result, we said it behaves just like they said it behaves, but our way of discussing it was just extraordinarily simple. And so he urged us to publish it. He said, “This is so much simpler than the way we describe it, you should publish it,” and then he turned out to be the referee, you know.

Bromberg:

By the way, do you keep letters like that, like the one he —?

Horne:

It might have been on the phone. It might have been on the phone. Anyway, so that’s the ‘89 paper with Abner [Shimony] and Anton [Zeilinger] called “Two-Particle Interferometry,” Phys. Rev. Letters.^[5] You know, it’s sort of like the horse is already out of the barn. There’s the Ghosh-Mandel, which is actually a real experiment. All we’re doing is just talking about it. And we pointed out that it’s a complete analog to the old polarization versions and that therefore Bell’s theorem applies. And subsequently Mandel and various other groups that had down conversion sources actually did some Bell experiments, you know.

Bromberg:

Did James Franson enter into this whole thing?

Horne:

Yes, and about that time — sometime in there — we saw Franson’s proposal, which was really quite remarkable because his was an ingenious new type of entanglement. Right? Whereas ours was just “this direction is entangled with that one and this one with that one,” right? His was, if you have a pair — [phone interruption; recorder turned off, then back on...] Franson imagined a situation where the two particles of the down conversion source don’t ever come together. There’s just one branch going out one way and the other going out the other way, but each of those branches has two routes to get to the end of it — a long route and a direct route. So classically you could say, “Let’s catch the particle simultaneously at the end of these branches. Let’s catch them classically.” They were produced at the same time. These down conversion particles are produced at the same time, so if you catch them at the same time you know it’s a pair and it was produced at the same time. Classically you could say, “Well, if I catch them at the same time, that means both of them must have gone the long route through their respective branches — or the quick route through their branches.”

Bromberg:

Right.

Horne:

But quantum mechanically it’s not either this or that; it’s the old both and again, right? So there was a new type of interferometer, two-particle interferometer, but is completely different than the one we have described. Which were alternative routes. These are alternative routes where they never came back together, right? Now I liked that paper. That’s a great paper, the Franson paper.

Bromberg:

Did that interact at all with what you were doing or it was just a nice paper that was —?

Horne:

No, it opened my eyes to that there must be lots of variations, that is there must be many ways to have these simple entanglements. Once we had broken out of the idea that a simple entanglement doesn’t have to be a polarization entanglement. You know, that you can have simple entanglements that are spatial, and then Franson shows there’s another way to have a simple spatial entanglement. It was a very exciting time, the late eighties, when I saw these various ways of making new kinds of entanglements. So anyway, you see our role of getting back into more than one particle, you know after, ten years of neutrons, was a conference paper in Finland that had no real effect. It had no real effect on anybody. Then the quantum optics people a few years later actually were doing the experiment, and then variations of it started popping up. And then so by 1990 there must be five or six groups around the world easily doing down conversion interference experiments.

Bromberg:

And Shih was certainly doing a lot of interesting stuff.

Horne:

And Shih was in there too, but he was in there from the beginning, right?

Bromberg:

Well, from about the late eighties, because he just got his degree in the late eighties.

Horne:

I think he was a —

Bromberg:

He was a Carroll Alley student and I think he just —

Horne:

I think it might have been Alley that was talking at Danny’s meeting in ‘85. Remember I said there were several people who —?

Bromberg:

Yeah.

Horne:

In retrospect we now know we were talking about experiments that use down conversion, but we didn’t notice. Yeah, I think that Alley — and Shih might have been involved with it — I think they did a Wheeler delayed choice experiment that they described at Danny’s meeting, and I think the source was down conversion.

Bromberg:

They certainly were working with down conversion from the start, those guys.

Horne:

Yeah.

Bromberg:

So somehow these two independent lines, neutron interferometry and optical, are really coming together in a way in which you’re reading each other’s stuff and getting ideas from each other it sounds like.

Horne:

That’s right, yes. That’s right. In other words we were totally unaware of the trajectory that the quantum optics people were following in the middle of the eighties. We just weren’t paying attention and weren’t reading journals.

Bromberg:

Even Abner Shimony wasn’t paying attention?

Horne:

Mm-mm [negative]. It was completely separate. So that brought us back. So now we have double interests. We are still pursuing our one-particle neutron interference experiments, although by this time they are starting to run their course. There are not many new ideas for “hey, let’s do this with them.” Anton continued after he — he continued and did some experiments with neutrons, single-particle neutron interference at Grenoble, and then since then in the last ten years, five years back in Vienna he’s continued to pursue single-particle interference with atoms.

Bromberg:

Mm-hm [affirmative]. Right, right.

Horne:

He wasn’t the first. I think Dave Pritchard at MIT and some of his —

Bromberg:

Clauser did some atom interferometry.

Horne:

Yeah. Later he did an atom too. There are several groups that have done atoms, but I remember it was in the late eighties that we first, when Anton and I were still hanging around MIT, we visited Pritchard and his student then was named Martin and they had a beautifully functioning atom interferometer. So it was just the two-route game again just like with the neutrons but these were atoms. Anton has pursued that nonstop ever since. He went on to do a — he built his own atom interferometer and did a lot of experiments over the past five years. And then recently he did a bucky ball interferometer.

Bromberg:

Oh.

Horne:

Right. The particle that takes two routes is actually sixty or seventy carbon atoms, he did both types. It was together in a hollow sphere. It was a giant molecule.

Bromberg:

I have a vague knowledge of it. I don’t have a clear —

Horne:

It’s seventy carbon atoms all lumped together to make a hollow ball.

Bromberg:

Okay.

Horne:

That’s the particle that now is going through the interferometer.

Bromberg:

It’s really extraordinary. You know I noticed that he’s part of some European group in this — there’s a recent volume that they put out on quantum information that I think Zeilinger is one of the editors of, and there is this European commission group to look at stuff like this. It sounds as if the European governments are interested in looking at this so that if it becomes a technology they’ll have some leg up on it.

Horne:

Yeah.

Bromberg:

Does his belonging to a group like that have any influence on your collaboration or ?

Horne:

No. We still talk regularly. We haven’t jointly published any papers for about three or four years.

Bromberg:

What I’m really wondering is whether belonging to a group like that might push him towards applications and because you two are then linked it might be pushing you in any direction or another.

Horne:

Well, since about 1990 when the more than two-particle entanglements came on the scene — which we didn’t quite get to —

Bromberg:

That’s right. We’re not up to that yet.

Horne:

So maybe I should try to get to that. So we got back to two particles starting in ‘85, Anton and I did, and then we saw that the quantum optics people were already there, you know, at least two years later and actually doing the experiments. Sometime in about those years, like ‘88 or something, Danny asked one day — I think it was sitting right here [in Horne’s kitchen] with Anton — he says, “Do you think there would be something interesting with three particles that are entangled? Would there be any difference, something new to learn with a three-particle entanglement?” You know, and so he was thinking of a polarization version, and of course immediately I started saying three diamonds, you know like from Mitsubishi. Because I always like to keep going back to space and stay away from polarization, right? So that’s the first time — sometime around there is the first time I did the three diamonds.

Bromberg:

Why do you like to keep away from polarization?

Horne:

Well just because I, you know, as Feynman said, the ultimate mystery, the only mystery of quantum mechanics is the two-slit interference experiment.

Bromberg:

Which is space?

Horne:

And that’s, you know, its equivalent. But if you talk to people, you know if you talk to general students or something like that where I teach, and you want to tell them any of these stories, polarization is sort of like “huh?’ you know, “Spin? What?” They don’t know what that is. But you know, did the particle go through this hole or did it go through that hole? So anyway, Danny said, “What if I considered more than two? What about three or four. Would there be something new there, something interesting?” And I think Anton and I encouraged him to pursue it, and he started working on it and he worked on it for like a year, part of the time here, part of the time on a sabbatical in Europe close to Anton. I wasn’t intimately involved. Anton was probably closer involved but not actually working on it. He would talk to him occasionally. Danny would report back sometime over that year things like, “I have a Bell’s theorem without inequalities” is the way he put it. “I can prove Bell’s theorem without inequalities.” Prior to that he was reporting things like, “Inequalities are popping out all over,” right? And in between those two moments, between “inequalities are popping out all over” and “I have a Bell’s theorem without inequalities at all”, he began to suspect that the incompatibility that was working here between the Einstein point of view, tried out in a three-particle or four-particle context, the incompatibility is closer to the surface. You know, that it’s not as hard to exhibit as it, say, was at Bell’s original theorem.

Bromberg:

So when you guys were talking around this table here were you already thinking that with three particles you could cast some light on Bell’s theorem?

Horne:

Oh, no, no.

Bromberg:

That was just Greenberger.

Horne:

No, he didn’t have particularly in mind an improved or a different version of the Bell theorem. He just said, “I wonder if anything interesting happens with three-particle” — it could have been just purely a quantum mechanical question. You know, “What are the details of quantum mechanical entanglement for three particles?” with no particular regard to adding a new chapter to the Bell story. But what he actually found out was that he could prove the incompatibility of the Einstein point of view in the context of a three-particle entanglement. He could prove it quicker and shorter and sweeter than say the original Bell proof. And he said we should write it up. And I said well you know — He started writing and he’d get up to thirty pages and he’d say, “I have thirty pages and I still don’t have it all in there.” Because Anton and I kept saying, “Well we have lots of other little pieces that we should put together if we are going to write a paper.” We just kept sitting on it. Nothing ever came out. We never wrote anything. And then one day Abner — Abner probably told you this story —

Bromberg:

No, he didn’t.

Horne:

One day Abner went out, one day in ‘89 or sometime, I was with Abner at BU talking about something — down conversion probably, because by then we were very excited about down conversion — and he said, “Oh by the way, what’s this thing you and Danny and Anton have proven?” And I said, “Well, what thing?” And he says, “Well,” and he showed me this [N. David] Mermin article that was in Physics Today or something. And I said, “Oh. How did he know about that?” And it turned out that Danny had talked about the new three-particle, simpler way of proving Bell’s theorem at George Mason University, and then he talked about it again at some talk in Europe, and people heard it. Right? Some people in England, I think that his name was Redhead.

Bromberg:

Yeah. Michael Redhead.

Horne:

Yeah, Michael Redhead heard it, and Mermin heard about it either directly or indirectly from somebody, and they looked at it and said, “Wow, this is a revolutionary breakthrough.” So it’s clear we needed to write something, right? Because everybody was commenting on it. People were commenting on something that had never been published, including in Physics Today. So you know like Mermin had a column or he has a column in the magazine. So we decided to get Abner’s help, because I said well, if we’re going to write this up, I decided, I convinced them that I had some pieces in mind, pieces back from 1969 that were never published. Specifically a step-by-step self-contained discussion of how EPR — you know, sentences that you can quote from Einstein, Podolsky and Rosen — lead you, you know, you can’t avoid, getting to the form of theory that Bell was contemplating, you know hidden variable theory, and then shoving in the contradiction in the original Bell fashion. That had never been written or published anyplace, the detailed look at the EPR paper and you’re led to Bell, right? You know, it’s spelled out in detail, good for a sophomore. So we decided to put that in, and because it was going to involve so much Bell physics we decided — and since Abner was the world’s resident authority on Bell physics — we decided to get Abner to join in our write-up. So instead of just Danny and Anton and I writing up this unpublished stuff the four of us wrote it up. And that’s the 1990 American Journal of Physics paper.^[6]

Bromberg:

Right.

Horne:

Called “Bell’s Theorem Without Inequalities.” And that has several parts to it. One is a review of how EPR leads to these hidden variable theories, a review of Bell’s way of showing that it can’t be done, then Danny’s new proof in the context of four [particles]. He originally did it with four. Then we pointed out that it could equally well be done with three, and then when we switched to three we switched from polarization to space so we could exhibit the Mitsubishi triple diamond, right? Gives us a chance to put that out there. And then Abner put in a section about, is a new experiment called for. What we really felt was no, you know. I mean, the experiment had already been done that shows that you can’t have these elements of reality and you don’t need an extra particle to show you can’t have them. That was a point of some controversy. A lot of people outside of our group kept thinking, “Gee, this really means we can do a better experiment,” but I’ve never been convinced of that. Because the proof of incompatibility is so brief you’d think that would mean you can do a better experiment, but I don’t think that follows. Right?

Bromberg:

I see.

Horne:

Oh, I should mention there’s a whole world out there of what we call loophole busting. That is, there are all these people who just say, “You know, I can still keep the Einstein point of view in the face of quantum mechanics because your detectors don’t count all the particles, and I can come up with this pathological scheme.”

Bromberg:

Yeah.

Horne:

So one of the things that people had in mind was maybe the three particles would be a better way of blocking some of the loopholes. And people are still contemplating that. In fact Danny and I currently are working on something along those lines.

Bromberg:

Are those people who don’t feel that there’s been closure yet on the Bell theorem, is that kind of a lunatic fringe or is that quite a serious group of physicists or how do you —?

Horne:

My personal feeling is it’s closer to the first. In the quantum mechanics, the quantum mechanical predictions for these multi-particle entanglements are confirmed to like ten standard deviations beyond where the cutoff point is. But you know, you can come up with these pathological things where all kinds of screwball things happens because you don’t count all the particles, and if you strain hard enough you can say, “Look. You haven’t shot down the Einstein point of view yet.”

Bromberg:

Yeah, okay.

Horne:

It’s not a field I’m particularly interested in.

Bromberg:

Now I’m a little confused because — By the way, have you eaten what you need?

Horne:

No, I think the juice ought to help me, and I can give us a sandwich in a second. So what was your —? Something confusing?

Bromberg:

When is the GHZ paper, the one that everyone refers to? That’s not the one you were just talking about?

Horne:

That’s the first published version, and it’s actually GHZ and Shimony.

Bromberg:

Oh. Okay.

Horne:

Danny wrote and put Anton and my name on a paper for that George Mason proceedings. There’s a meeting at George Mason and he put out a little paper. That one had circulated a little bit, but it’s not very clear.

Bromberg:

No, it’s not. That’s the one in the volume edited by Kafatos I think.^[7]

Horne:

Yes. Right.

Bromberg:

Yes. And it wasn’t very clear and — I mean at least when I read it.

Horne:

Right, yeah, that paper doesn’t do a lot for me.

Bromberg:

And I wondered whether you got much reaction to that paper because I had trouble with it.

Horne:

Well it didn’t have any circulation, you know, because it was just a conference. I don’t know whether it was one that Mermin saw or Redhead saw it. I think Mermin said he had just heard Danny talk once. So, as far as “the GHZ paper,” there is none, except that George Mason conference paper.

Bromberg:

Okay.

Horne:

We did later, say in ‘93, we wrote, we tried to describe, several of these developments, you know, the three-particle GHZ way of proving Bell’s point, and also talking about some of these really remarkable two-particle experiments that were made possible by down conversion. So we wrote a Physics Today article, a news article. That’s in ‘93. It was called “Multi-Particle Interference,” right, and it had a few — it mentioned some Bell stuff in passing, but it wasn’t just Bell physics. See, you’ve got to remember, I thought Bell physics was done in 1974 or ‘73. I wasn’t ever particularly interested in pursuing Bell physics anymore. When Danny kept saying after that year, playing with three, “Hey, Bell’s inequalities are popping out all over,” or “Hey, I can prove the incompatibility without inequality at all,” to tell the truth I sort of glazed over. You know, it’s a lot of, “Oh, that’s good. You can work that out.”

Bromberg:

I see. [laughs]

Horne:

“In other words, the first person who really said, “Wow, this really is” — You know, Danny couldn’t clearly present it as something revolutionary. Danny wrote that George Mason thing. The first person who actually trumpeted it was Mermin. Mermin said, “Wow, look at this!” He paid more attention to it than I did. So that takes us from…

Bromberg:

We’re sort of up to the Physics Today paper of ‘93 right now.^[8]

Horne:

Now so the next thing that came up that I was involved in with Anton was, “Can we actually make in the lab a three-particle entanglement?” Right? That’s what we talked about a lot all through the early and mid-nineties, “Can we actually make one? Is it possible to produce one on a tabletop?” And so I think that’s the last paper that I wrote that I co-authored with Anton. I think it’s ‘98. It’s called “Three-Particle Entanglement”? The content — I don’t know the title — is how to produce a three-particle entanglement in the laboratory. A proposal for making three-particle entanglements. I don’t know exactly the title. And then a year or two later they actually carried it out.

Bromberg:

In his lab.

Horne:

In his lab. Right. But I wasn’t part of that, because I wasn’t over there involved in the experiment or anything, but I was involved in the proposal as to how to do it. And then that’s basically it.

Bromberg:

And you’re also interested in the physical origins of entanglement. Isn’t that something that you worked on?

Horne:

Yeah. Well, yeah.

Bromberg:

At what point is the entanglement occurring?

Horne:

Yeah, well, that’s one way to put it. The question that we’ve often asked is, “Who ordered this?” — as Rabi used to say about some experiments fifty years ago with molecular beams and they’d get a surprising result and he would say to his collaborators, “Who ordered this?” when they saw this surprising result. I’ve always liked that expression. “Why did things behave this way?”

Bromberg:

Right.

Horne:

And that’s not a very — Not many people think that that’s a worthwhile question.

Bromberg:

Really?

Horne:

In other words, I think most people say, “Well, we know the quantum mechanical rules. The rules contain this aspect. Namely that entanglements can exist”, right? “And we know the quantum mechanical rule. It’s called superposition principle.” Right? And that’s what leads to these entanglements. You realize that entanglement is nothing but the superposition principle applied to a more-than-one-particle system.

Bromberg:

Right, right.

Horne:

That’s all it is.

Bromberg:

This combination of states or that combination of states.

Horne:

So somebody says, “Well so why do we have this?” and they’d say well, “Superposition principle. You add these things together.” And you know, Feynman says in his lectures that that’s the only mystery.

Bromberg:

Yeah, but Feynman was content to live with that mystery.

Horne:

That’s right. He goes on to say, “You can’t answer it.” He says the only mystery is the two-slit experiment, and that just means the only mystery is the superposition principle. That’s the only thing about — that’s the heart of quantum mechanics is that “Thou shalt add these amplitudes and you don’t add probabilities,” right? You add these amplitudes.

Bromberg:

But it seems to me that —

Horne:

And he said, “Don’t ask what’s behind it. You won’t find an answer as to why it’s like that. It’s just that’s the way it is.” So when someone asks the question, when someone considers the question I just described, most people would say they’re not sympathetic to that question. And by the way I have no answers. But it just sort of struck me as something — and it strikes Anton the same way — that there must be a reason. There must be some deep reason why these sort of strange linkages are a necessary part of the world. I mean, why do they link up like this? That glosses over the, that theory glosses over that. The answer is superposition principle. So what we’re asking is, “Well then why the superposition principle?” And most physicists don’t quantum mechanics would say, “Well, you’re not going to answer that question.” It’s just that’s the rules. You see what you’re dreaming of is deriving quantum mechanics. Right?

Bromberg:

Yeah. Is it deriving from quantum mechanics or understanding at what point —? I don’t know. Does it —?

Horne:

At what point does it have to show itself. Yeah.

Bromberg:

At what point does the entanglement —

Horne:

Have to show itself, right? Yes.

Bromberg:

And what’s the physical thing that’s correlating the two? That seems to be a question physicists would be willing to entertain.

Horne:

Yeah.

Bromberg:

That’s what I thought you were doing in that experimental metaphysics volume that was I guess one of the volumes dedicated to Shimony.

Horne:

Right. What was my paper in there?

Bromberg:

I thought you were trying to understand what was the origins of entanglement inside a crystal. I don’t have any notes on it here, but as I remember it you had various sources within this crystal because it had finite dimensions that were–

Horne:

Oh yes. Oh, oh, I know that paper.^[9] Oh, yes. Oh, I think that’s a very nice paper. Nobody knows much about it. Frankly nobody knows that paper. Yeah. I imagine that every spot in the source, every spot is a source of radiation, sort of like Huygens, right, you know? Every spot on the previous wave front is the source of another little wavelet. Except in that paper I was imagining that every spot in the source material, in the source medium, is a source of pairs of spherical waves. Right? Two-concentric wavelets coming out.

Bromberg:

Right.

Horne:

If you then sum over the whole source, you know to see what the total output will be from all of those little sources, you derive momentum conservation. In other words, if the incident radiation that’s stimulating the medium comes in this way, then when the two particles are produced out of all of these wavelets adding together, if this one goes off at 15 degrees that way, this one will be going off at 15 degrees this way. Right? If this one goes off at 20 degrees, this one will come off at 20 degrees. So I was struck that by using a sort of a two-particle Huygens construction. I could derive conservation of the momentum, right? I was deriving it, right? And that’s classical physics, but I was deriving it from a bunch of little wavelets.

Bromberg:

In fact the whole thing that really was striking me about that paper and one other is that there is no wave particle duality somehow in what you’re doing. The waves and the particles are so meshed in conception that you are sort of moving back and forth from wave to particle without —

Horne:

Exactly. I never appreciated this duality. It’s just like quantum mechanics says there is nothing but these waves as far as your basic machinery and what you’ve got to calculate, and then you just use those amplitudes at the end to say, “Well, will I catch a particle here?” or “Will I catch one there?” or “What’s the probability of catching one here or there?” So I get your point. There’s nothing there except these little amplitude wavelets, right, and then just add them up together. I sort of liked that paper, but I’ve never done anything with it. I doubt if anybody has ever seen it or it did anything for anybody.

Bromberg:

[Asks about Yenhua Shih’s bi-photon concept] — I never understood where that fits in the way in which people think about these things, whether this is just a little bee in his bonnet that is not generally thought about or whether it’s a really important idea that everybody picks up on.

Horne:

Well, it struck me as a valid way of describing entanglements. It’s just a verbal way of capturing what we were already reviewing a while ago, that an entanglement is — system A has this state times system B has this other state, plus another product like that, right? Or it’s, like I said, it’s just superposition. Now when a pair of particles have that kind of a state, neither one separately has a state. Right?

Bromberg:

Yeah, right. Absolutely.

Horne:

In other words it’s just there and you say, “What’s the state of those two things over there?” and you’d say, “It’s this superposition,” right, “It’s this superposition.” Well what’s the state of just the object that’s the one over on the left? It doesn’t have a state. Right? So I think when Shih says you can’t speak of these as two objects, it’s just one object, it’s just another way of saying that, right? In other words you know the — I was always very sympathetic to his wanting to emphasize that repeatedly. It seemed to be a valid way to present it verbally. It’s sort of like his version of — you’ve already run into my favorite, is “both and” as opposed to “either or.” Right? You know, that is, whether you are doing one particle or two particles in quantum mechanics what the superposition principle says — and the superposition principle is all the entanglement is, right? — what it says is, unlike classical where you have either this happen or that happen, what quantum mechanics says is that they actually both happen. Right? Simultaneously. That seems to be what she is saying. In other words I didn’t see it as a variable menace and groundbreaking insight into learning new things about entanglement; it’s just his verbal way of stressing how strange they are.

Bromberg:

Okay.

Horne:

It’s his way of describing them, right? It’s a single thing, you would say.

Bromberg:

I’m going to ask you one final question. The quantum optics people were using this whole mechanism. We already talked about it; that derives from Roy Glauber, with annihilation operators and such. As your two fields began to interact, did the neutron people also begin to use all these?

Horne:

No. No, because —

Bromberg:

Because neutrons don’t get annihilated and —?

Horne:

The quantum mechanics we did with neutrons was the most elementary variety of wave mechanics. You know, that is, the propagation of the single neutron through the contraption you had set up for it in the lab was just described by a single scalar wave, you know, an amplitude really — a quantum mechanical amplitude — and it’s physical interpretation is the square of it in any spot is proportional to the probability of finding the particle there. Just a standard Born interpretation of a quantum wave. So that was the extent of our quantum mechanics, right? It was just, that’s all we needed were these waves. There was no sophisticated annihilation machinery, right? There were no operators like in quantum optics. None of this heavy machinery was needed for all the things we did. We could get a complete account of the experiments with just this simple, elementary way of working. So then when we started talking about pairs, both originally on our own but then later saw the quantum optics people were doing pairs, we personally from our background didn’t see any need for the heavy-duty calculus. I have a notebook from the late eighties where I went through like a half a dozen of the [Yanhua] Shih and Mandel experiments, and I would use my simple little way of calculating the final formulas. And I’d get all the same formulas, right? So I could show just by example after example. I didn’t need this machinery to get to the same answers. So I not only don’t use it, I don’t need it for the things I try to do. Now I don’t know how far that might go. I might hit a wall sometime, right? I might hit a wall and say, “Gee, I can’t go any farther unless I adopt the heavier machinery.” But I never ran into it as far as I got that I needed it. And also I’m not an expert on it. You know, so it’s fortunate that I didn’t need it because I didn’t know much about it.

Bromberg:

Well, if you needed it you would become expert on it so you don’t have to worry about that. Well good, that’s the end of my questions for today.

Horne:

So you had asked earlier how was it doing physics at Stonehill, and I think it’s been perfect for me, given my temperament. After I finished grad school and had the opportunity to have that really great thesis topic, because, of Abner, then I needed a job. And Bob Cohen, as chairman of the physics department at the time, got lots of letters from people in the neighborhood in Eastern Massachusetts. You know, in small colleges when they had an opening they would often just send a letter to department chairmen in the area, you know, at big universities like BU or Northeastern or Brandeis. So Bob Cohen got such a letter from the then only physicist at Stonehill, which was Chet Raymo, and said, “Gee, this looks like it might be a good place for you to look for a job.” So I went down and interviewed and got that job. Do you know Chet Raymo?

Bromberg:

No. I know the name Raymo, but not Chet.

Horne:

He was the physics teacher there in the sixties, and he wanted to do other things and so he talked the administration into hiring me and I would do the physics and he could continue to do things that he wanted to do more, which was write, write popular books on nature and teach students about writing and he ended up writing a column in the science section of the Boston Globe. It’s been going out for twenty-five years.

Bromberg:

Oh.

Horne:

So Chet Raymo was the physicist at Stonehill and hired me so he could do the things he was more interested in.

Bromberg:

But I mean you don’t have to teach like four courses a term?

Horne:

I do.

Bromberg:

And it’s not exhausting?

Horne:

I did it ever since 1970, so I’ve now been doing it thirty-two years. I was teaching general physics, one for math and chemistry and one for biology, and I was free in my third course to do whatever I wanted. Often I’ve taught courses for general interest, you know general students, about quantum mechanics or about relativity or about both. Or occasionally I would do an intermediate course for somebody who wanted to do some physics beyond general physics and do something at the intermediate level. Okay, there was no major. And I very diligently never started one, right? So I thought it was good for me to not have the politics of a high-pressure university physics department working over me, you know, where you know you have to produce or you don’t get tenure. And for me it was best to — I had my friends, Anton and Danny and Cliff Shull and Abner, and they were all connected to major, you know, bigger places, but they were my contacts to the real world of physics and it’s been perfect for me. I’ve been involved in some, what I thought were exciting developments in foundations of quantum mechanics. But I was never under any pressure, you know. I taught at this school where I didn’t have any majors. I was just a service department teaching general physics for the chemistry students and the biology students, but I didn’t have any students.

Bromberg:

How big is that school? How come they have no majors?

Horne:

Well, it was a couple of thousand students, and to have a real physics department I think you need at least four or five professors to start an undergraduate physics major program, and I just didn’t think — you know, there were enough physics major programs in the country. If occasionally a student came and said, “Gee, I just really like physics after taking your course,” I would say, “Well, you should go somewhere else.” I’d just tell them, “You should transfer, switch to another school.” So it’s been perfect for me — a low-pressure place where I was the physics department. Right? So it couldn’t have been better.

Bromberg:

That’s interesting.