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Oral History Transcript — Dr. Robert Wagoner

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Interview with Dr. Robert Wagoner
By Alan Lightman
In Stanford, California
October 14, 1988

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Robert Wagoner; October 14, 1988

ABSTRACT: Family background; early interest in mathematics; early hobbies; early reading; influence of grandmother; education at Cornell; influence of Paul Olum; interest in philosophy at Cornell; influence of Fred Hoyle's Messenger lectures at Cornell; education at Stanford; engineering versus physics; influence of fellow graduate students at Stanford; thesis work with Leonard Schiff. on the gravitational collapse of rotating massive objects; first Texas Symposium in Dallas in 1963 and announcement of Kerr solution; interest in cosmology in graduate school; interest in Mach's principle; discouraging encounter with John Bachcall at Caltech; switch to nuclear astrophysics at Caltech; motivating influence of William Fowler; history of big bang nucleosynthesis calculations and the work of Alpher, Herman, Gamow, Fermi, Turkevich, Follin; reasons why big bang nucleosynthesis work wasn't done earlier and the initial motivation to make all the elements in the big bang; role of Fred Hoyle in big bang nucleosynthesis calculations; scientific philosophy of George Gamow; motivation of Fowler by Hoyle; interest of Hoyle in making all the elements in massive stars within the context of the steady state theory; Hoyle's suggestion of population III stars; Hoyle's explanation for the origin of the cosmic background radiation; early work of Tayler and Hoyle in 1964 on big bang nucleosynthesis and the cosmological restriction of the number of neutrino types;. work of James Peebles on big bang nucleosynthesis; first announcement of results of Wagoner, Fowler, and Hoyle calculations· and reception by the community; supporting evidence for the big bang model from the interstellar deuterium abundance and the calculations of Reeves, Audoze and others on production of lithium, beryllium, and boron; Wagoner's continuing worry about whether the big bang model is correct; introduction to and attitude toward the horizon problem; initial reception of the inflationary universe model; attitude toward the inflationary universe model; desire of Wagoner to probe the universe with physics that we know, and his concern over the uncertainties with the inflationary universe model; attitude toward the flatness problem; Wagoner's interest in letting observation, not theory, tell us the value of omega; prevalence of personal prejudice as a motivator among scientists and the danger of this prejudice; reaction to de Lapparent, Geller, and Huchra's work on large-scale inhomogeneities; worry over reconciliation of observed inhomogeneities of galaxies with the homogeneity of the cosmic background radiation; worry over validity of the cosmological principle; more discussion of Wagoner's preference for doing cosmology with well understood physical probes; outstanding problems in cosmology: dark matter, value of omega, nature of central engine of quasars, evolution of structure; ideal design of the universe and importance of extraterrestrial life; question of whether the universe has a point.

Transcript

Lightman:

Let me start with your childhood. Can you tell me a little bit about your parents?

Wagoner:

Sure. My mother's mother came from County Cork, Ireland. So I'm one-quarter Irish. The rest I'm not sure about. My father's parents grew up in Ohio. They had been there for many generations. I was lucky to grow up in Teaneck, New Jersey. I spent my first 18 years there. We had a very good school system. I had a great math teacher, and I was on the math team. I had very good science teachers, except for physics. I had a terrible physics teacher in high school. And that's why I went into mechanical engineering at Cornell — because I didn't know any better.

Lightman:

What occupations did your parents have?

Wagoner:

My father was a real estate manager for Western Union. My mother was a homemaker.

Lightman:

Did they encourage you in science?

Wagoner:

No, not in particular. I just discovered it myself. I remember in ninth grade we took a test of interest or aptitude. I forget what it was called. I decided at that time, based on that test, that I wanted to be a forest ranger. I really wasn't exposed too much to science, although I did read a lot of books on rockets during one year. The next year I read a lot of books on golf, because I was really into golf at that time. I tended to investigate different areas intensely for a certain period of time. I was on the math team in high school. I believe we won a math contest for the New York area.

Lightman:

So you had an interest in math. And you had an interest in rockets.

Wagoner:

I did win the science prize in my high school. I was interested in science, but I didn't know in what area.

Lightman:

Do you remember any books on science you read, besides the books on rockets?

Wagoner:

Willy Ley's books[1] on rockets were the ones that influenced me the most. He was one of the early German pioneers, along with Werner von Braun. He was a good writer.

Lightman:

And that got you interested in science?

Wagoner:

I'd say so. That's what sticks in my memory.

Lightman:

At this age, did you ever think of any questions that we might call cosmological — like where did the universe come from? Do you remember that kind of thinking?

Wagoner:

No. The furthest out I thought about was the solar system — rockets to the planets and maybe nearby stars. I didn't think about the universe at all [except for frightened wonder at the concept of eternity].

Lightman:

Did you want to travel in space, yourself?

Wagoner:

I was interested in that possibility. My interests shifted a lot. I was not focused on science continuously in high school. I did like math. That was really what drove me towards science.

Lightman:

So you went into engineering because you were turned off of physics in high school?

Wagoner:

And the climate at that time was such that there seemed to be a need for engineers, and there were good job opportunities. That was the reason.

Lightman:

You were already thinking about a job at that age?

Wagoner:

My father encouraged me to think about what I wanted to do in a practical way. He didn't know anything about science, although my grandmother was a math teacher. She started teaching me calculus at the end of high school. She lived in Florida, so I didn't see her that often. She did motivate me towards math.

Lightman:

Was that your mother's mother or your father's mother?

Wagoner:

My father's mother. My mother's parents were dead. She was my only grandparent.

Lightman:

Did you build rockets yourself, or did you just read about rockets?

Wagoner:

[Wagoner laughs.] I tried, but that was my first indication that I was not an experimentalist. I had a chemistry set, which was another disaster. But I did build and fly model airplanes. I didn't do too badly at that.

Lightman:

When you went to Cornell, did you ever make a conscious decision between engineering and math? Or between engineering and some other field of basic science? Did you know in the beginning that you wanted to go into engineering?

Wagoner:

When I got to Cornell, I was very happy in engineering, although, at that time, it was a five year experimental program, which was soon abandoned. I recall we had to take 18 units a semester for five years with very few electives. So I was inundated in engineering, although I remember I had an excellent calculus teacher, Paul Olum. You might have heard his name. Until recently he was the President of the University of Oregon. He was also politically very active at Cornell. When I returned there on the faculty later, I got to know him again. He was one of my heroes, really an excellent teacher. That was freshman calculus. I remember taking freshman physics and it was somewhat daunting. I stuck it out. It didn't make a great impression on me at that time.

Lightman:

Do you remember any other things that did make an impression on you at Cornell?

Wagoner:

Yes, I had another good teacher in applied math. I forget his name. He was a crazy guy, but he was an excellent teacher. He taught in the Engineering Mechanics department. Another person who made an impression was Max Black, the philosopher. I took a philosophy course under him.

Lightman:

I've read something by him, on metaphors. He wrote a paper about the use of metaphors in science.

Wagoner:

I took a logic course from him, which I really enjoyed.[2] I started reading, on my own, a series of books[3] by this crazy guy Korzybski. I really got into that. He had some wild ideas in philosophy. Alfred Korzybski, I remember. So, I really got interested in philosophy. But the big event that turned me on was Fred Hoyle's Messenger Lectures in 1960 at Cornell. I think these series are still going on. [Richard] Feynman gave a series somewhat later. Fred talked about cosmology.

Lightman:

Didn't a book come from that?

Wagoner:

I've never seen a book on those lectures.

Lightman:

But he talked about cosmology in 1960. So you were a junior then or something like that?

Wagoner:

That was my fourth year of the five year program. I entered Cornell in 1956. Dennis Sciama was visiting Tommy Gold, who had just taken over the astronomy department, but I didn't know what was going on.

Lightman:

But you did hear these lectures by Hoyle.

Wagoner:

Right. I think I met Sciama. But I just saw the light then and was really turned on by it, and I started reading Fred's books[4] on cosmology that summer. I had a summer job at Cornell. I read Sciama's book The Unity of the Universe[5] and Fred's book called Frontiers of Astronomy, I think it was. Quasi-popular paperbacks. That was just great. The next year I took an E & M [electricity and magnetism] course in physics by a terrible lecturer. But I was turned on by physics. Because I was motivated through cosmology, I got turned on to physics.

Lightman:

When Hoyle gave his lectures on cosmology, did he talk about the steady state model?

Wagoner:

Oh yes.

Lightman:

Did he talk about the big bang model also?

Wagoner:

I don't recall too many details. As I recall, he did. Of course, the steady state was the big thing he and Tommy were involved with.

Lightman:

Do you remember any personal viewpoint on the steady state model?

Wagoner:

No. I didn't know enough to really get much out of the lectures except a feeling of excitement. And, of course, Hoyle is a fantastic lecturer, so that helped motivate me too. It was for a general audience, so it was a broad view of astronomy and cosmology. He didn't focus on the steady state. That was really a turning point for me.

Lightman:

So you decided you would go into physics at that point?

Wagoner:

When I got my degree, I had an NSF fellowship, but in engineering. And I thought that I wanted to go into physics, although I was still interested in aeronautical engineering — going back to the rocket thing. I had taken some courses in aeronautical engineering and plasma physics at Cornell my last year there. So I looked around for a place where I could make my decision. And Stanford had this great program, Masters in Engineering Science, something like that. There was no thesis [required]. You could take essentially whatever courses you wanted for a year and get a Masters. So I had my engineering fellowship, I signed up for that program, and I essentially took all physics, making up my physics background. That was 1961. One of my first courses in physics was with [Robert] Hofstadter that fall. He was teaching the mechanics course. That was the quarter he won the Nobel Prize. I've been lucky for lots of people when I go to a new place. He wasn't a great teacher, but that was inspiring. And so I took a chance and took all those physics courses and applied to the physics department here [at Stanford] during that year and managed to get in and switch my fellowship to physics. Of course at that time, I was very lucky because my timing couldn't have been better. That was the optimal time to be a graduate student as far as support goes. I think at least half of the graduate students here in physics had NSF fellowships. There was plenty of money for everybody.

Lightman:

It was the reaction to Sputnik.

Wagoner:

Exactly. Perfect timing after Sputnik. Money had become available because of Sputnik.

Lightman:

You said you got fired up on physics because of Hoyle's lectures on cosmology. When you came here and started doing physics, did you intend to make cosmology the area you were going to go into? Or were you just interested in physics as a whole?

Wagoner:

Talking to my fellow graduate students, I remember, was one of the best aspects of education here and still is. My roommates — right down this hall — were Heinz Pagels and Ron Adler, who's now working at Lockheed. They were both interested in general relativity. Heinz was more interested in particle physics. But we used to have great discussions on philosophy, religion, and physics. I got turned on to gravitation at that time, talking to them. But I still wasn't sure. I recall I started my thesis work with Peter Sturrock, who was still in the physics department at that time, before he and some other faculty formed Applied Physics. I had taken a plasma physics course from him. I wasn't especially turned on, but I thought I wanted to work in astronomy. We couldn't find a good problem. So I started working with Leonard Schiff, who was getting interested in gravitation, as you know, at about that time. 1961 was the year he proposed the gyro experiment. That's when it started here. This building was built in 1961. I started working with Leonard. In some ways it was good and in some ways it was bad because he was department chairman and had been for a long time. He had to spend a lot of time on departmental matters. In those days, a chairman decided everything. It was a great system. Few committees. They just found someone and they hired them. So I saw Schiff maybe once a week or once every few weeks. And I had to find a problem on my own.

Lightman:

He didn't give you a thesis problem?

Wagoner:

We decided on the general area. And that was another piece of luck. Quasars were identified in 1963, a year after I entered the department. And strong radio sources were known, so the motivation was to try to understand these strong radio sources and maybe quasars — the mechanism of producing them. So my thesis[6] was on the gravitational collapse of rotating massive objects asking what would happen to a rotating collapsing body in general relativity, as a possible model of these objects. It even involved some computer calculations. It was a reversed initial value problem, where you solve all the equations on the plane of symmetry of these collapsing objects. It's an initial value problem in space and not time. You work off this plane of symmetry at all times. You try to solve the field equations in the neighborhood of this plane to see how the matter evolves in time in the neighborhood of the plane. You [try to] draw inferences about what's happening off the plane.

Lightman:

Did you expect to see jets? Jets weren't known then?

Wagoner:

They were in the radio. That was a major motivation. Would there be any gravitational effects that could produce jets? Of course, this was a very limited investigation because it wasn't global. I was also influenced by Max Schiffer, who was teaching in the math department at that time. His first name was actually Menaham. He retired a few years ago. He and Felix Bloch were the most fantastic lecturers — at least classroom lecturers — I've ever heard. He would give lectures on general relativity with no notes, just beautiful. They just flowed. [It was the] same with Felix for statistical mechanics and some other courses. Most people share my views about Schiffer, but some don't about Felix. Especially Schiffer influenced me a lot. He was on my thesis committee, and so I discussed the math with him quite a bit. At that time, there was one computer at Stanford, a Burroughs computer in the basement of Encina Hall. I did have to do some numerical work in this thesis. But it was really exciting in 1963, going to the first Texas Symposium in Dallas in December. Especially because of the Kennedy assassination, it was very emotional. At the meeting [there were the] Burbidges, [William] Fowler, Hoyle again, Maarten Schmidt, speaking about quasars. One thing I remember, which you'll appreciate. Roy Kerr stood up at that meeting — I was sitting near Chandrasekhar — and announced his solution[7] [to Einstein's equations for a spinning mass]. There were some questions asked, and it was obvious that the general feeling was [that this solution was] very special. Only Chandrasekhar stood up and said that this could well be a very important result.

Lightman:

When you say the general feeling was that Kerr's solution was very "special," do you mean "peculiar?"

Wagoner:

Nongeneric — a very particular solution, mathematically elegant, but not very astrophysically relevant. That was the feeling.

Lightman:

And Chandra thought it might be?

Wagoner:

Yes, at least that's the way I recall it.

Lightman:

It certainly didn't have any singularities, which is the problem with most of the solutions.

Wagoner:

For a certain range of the rotational parameter, it was okay. That meeting was so motivating for me as a graduate student, as you can imagine.

Lightman:

Did you present any of your own work?

Wagoner:

No, I was in the very beginning phases of my thesis. [But I remember being impressed by Kip Thorne's talks.] I finished my thesis in 1965, another important year. When I went to Caltech, the microwave background had just been discovered. Maybe I'm getting ahead of the story.

Lightman:

Before we go to Caltech, you must have had a course in general relativity or studied it here at Stanford.

Wagoner:

With Schiffer. He wrote a book[8] based on that course, with Adler and Bazin.

Lightman:

Yes, I know that book. As I remember, that book doesn't have any cosmology in it. It's just on general relativity.

Wagoner:

Very little. It does have some. But Schiffer didn't stress cosmology in his course.

Lightman:

Did you study cosmology while you were here?

Wagoner:

Yes. I read every book I could get my hands on in cosmology.

Lightman:

The steady state theory was still in good shape then?

Wagoner:

Well, there was a big debate about the radio source counts.

Lightman:

Oh yes, the radio source counts.

Wagoner:

And the quasars were starting to become a problem.

Lightman:

Do you remember having any personal viewpoint as to steady state versus hot big bang?

Wagoner:

No. I was interested in cosmology, but at that time more in a philosophical way. I was more interested in doing calculations in general relativity with respect to the strong radio sources and quasars — understanding that. I wasn't interested in doing calculations in cosmology at that time.

Lightman:

Did you have views even though you weren't interested in doing calculations?

Wagoner:

I had no strong views at that time, as far as I can remember, for preferring one model over another. I was very interested in things like Mach's principle. Those aspects of cosmology I was interested in — trying to formulate some realization of Mach's principle, understanding inertia and things like that.

Lightman:

There was one of Hoyle's theories. Was it the Hoyle-Narlikar theory?[9]

Wagoner:

They worked on Mach's principle with their scalar field. But Sciama's stuff[10] on Mach's principle influenced me the most.

Lightman:

Tell me a little bit about Caltech. Your post-doctoral period there was fruitful.

Wagoner:

The first thing I remember about Caltech was meeting John Bahcall, who was then an assistant professor there with Willie [Fowler]. The first time I met him, I introduced myself, and he said "What area do you work in?" I said "I work in relativity." He immediately got very upset and said "You don't want to work in relativity. Switch to some field related to the real world." John was very frightening to me at that time. But the real reason I switched was the microwave background. I thought it was interesting, seeing what the implications of that were, although I did work on other things at Caltech.

Lightman:

When you say switched, you mean from something in relativity to something else.

Wagoner:

To nuclear astrophysics.

Lightman:

Yes. To nuclear astrophysics. You really hadn't had much background in nuclear astrophysics had you?

Wagoner:

None. I had taken the standard courses in nuclear physics. But, no, I hadn't.

Lightman:

What was your personal motivation in working on this problem[11] of cosmological nucleosynthesis — as opposed to just doing what Hoyle said you should do or Fowler said you should do? What was your personal motivation?

Wagoner:

Willie [Fowler], as you know, is a great motivator. Willie made me realize that using the data that existed on nuclear reactions; you could really say something definite in cosmology — which was exciting. I had a well-defined model and could produce a specific answer.

Lightman:

By "well defined model" do you mean the big bang?

Wagoner:

The hot big bang. I began to feel that it was established at that time.

Lightman:

After the microwave.

Wagoner:

Right. I wanted to explore the consequences of that. This was a physics problem that you could do in cosmology. Previously, there weren't many solid physics problems in cosmology where you could get definite answers.

Lightman:

Couldn't you have done this calculation[12] some years earlier?

Wagoner:

In fact, there are some interesting historical precedents. This calculation could have been done and should have been done in 1953. The history is that soon after Alpher, Gamow and Herman began their investigations,[13] [Enrico] Fermi and [A.] Turkevich developed a nuclear reaction code. They had about thirty nuclear reactions. And within the Gamow model, they calculated[14] the abundance of the elements. Of course, the model was wrong.

Lightman:

It started off with only neutrons.

Wagoner:

That's one of these two basic questions that I'm trying to understand. Why did Gamow miss the obvious point? If he had just gone back a factor of ten, in time, he would have realized that neutrons and protons had to be in equilibrium. Why didn't Fermi realize that? It wasn't realized until Hayashi in 1950.[15] I do not understand why these fellows didn't realize that their model was inconsistent, or at best unrealistic, if it just started at that time. They were so close. Hayashi was the big breakthrough. But Alpher, Follin, and Herman in 1953 then did the entire calculation[16] systematically and formulated the hot big bang model in its full mathematical structure. It was physically correct. They incorporated all the correct physical processes. They produced the correct thermal history of the universe in their paper. In fact, they even commented on the helium abundance. Why didn't anybody then apply the Fermi and Turkevich reaction network within that model? It just lay dormant.

Lightman:

What's your opinion about that?

Wagoner:

My opinion is that the initial motivation was to make all the elements in the big bang. It was beginning to be realized that stars were going to do most of it. Burbidge, Burbidge, Fowler, and Hoyle[17] was on the horizon — the 1957 classic paper which showed how the stars produced the heavy elements. That was in the wind, I believe. Fred [Hoyle] was pushing these views before 1957. He was the initiator. I think that's why it wasn't pushed. Because people said "if the [early] universe can't produce everything, let's forget about it." That's my guess, although I'd like to go more deeply into that question. It's a very interesting question. You're absolutely right. In 1953, everything was there, although the cross sections weren't known as well.

Lightman:

But you still could have used the best of whatever was available.

Wagoner:

You would've gotten a pretty good answer, I think. It's interesting to look at the Fermi and Turkevich paper, which was not actually published by Fermi and Turkevich. It was published in the 1950 review article by Alpher and Herman in Reviews of Modern Physics.[18] The result of the calculation is published. That's the only place it is published. That's two big questions. How did Gamow and Fermi miss on the neutron-proton ratio, and why, when the mistake was realized, didn't they redo the calculations? I think it's because they wanted to make the heavy elements. They realized the mass gap could not allow them to do that, at mass 5 and 8. So they said, "[if] we can't make everything, we're not interested." That's my guess.

Lightman:

It had to be all or nothing.

Wagoner:

Well, Gamow was that way. He wanted to make everything, in a simple way. He felt it had to be beautiful and simple. I don't know what Fermi wanted.

Lightman:

So getting back to 1966 and Fowler's suggestion to you [that you work on element production in the big bang], was it his suggestion more than Hoyle's suggestion that was influential to you?

Wagoner:

Hoyle motivated Fowler. I don't know the exact sequence, but Willie motivated me directly. Fred came into the calculation, but they were discussing it before they brought me in. Another interesting question is Fred's motivation. Why does a steady-state man want to get involved in a big bang calculation? In fact, I talked to Fred a little bit about this in Bologna last May. And I think he agrees with the statement, but I couldn't really get him pinned down. His real motivation ... if you look at our 1967 paper,[19] you'll see that more than half that paper is not on the early universe, but on what he calls bouncing massive stars. He wanted those guys, within the steady state theory, to make the helium, [as well as the microwave background radiation].

Lightman:

I was wondering why there was so much attention given to the massive stars.

Wagoner:

That was Fred. But he sort of dragged me into that to some extent because I wrote quite a few papers[20] in the next few years on massive stars — other aspects as well. And massive discs also.[21] So I was interested in this. The reason I was interested is this statement that we made in our paper — I don't know if we were the first to make it. We referenced Jim Felton in 1966,[22] but I haven't gotten back to that paper again. This was Fred's idea: to point out — what people must have realized, but again I don't have any reference — that if you just thermalize the nuclear energy in the universe (at a moderate redshift), it gives you three degrees. He wanted to make the helium as well as the microwave background in an early generation of stars. So he initiated the idea of population III stars as doing everything — within steady state, you see. I was struck by that coincidence. I still am. That's the only natural way to get the microwave background without essentially any adjustable constant — such as a CP violation parameter within ordinary baryosynthesis theories. With no adjustable parameters, except possibly the red shift at which these stars turn on, you make the amount of radiation in the microwave background. So it's a striking coincidence but, of course, the big sticking point is thermalizing the radiation. But I was struck by that. That partially motivated me towards massive objects as well as the big bang. I try to maintain a balanced view.

Lightman:

When you started that calculation of nuclear networks in the big bang context, were you expecting to find the result that you did, the agreement with helium?

Wagoner:

Oh yes, because Roger Tayler and Fred Hoyle in 1964 had gotten roughly the right number based on the correct physics.[23] Interestingly enough, I discovered, going back to that paper, Hoyle and Tayler say explicitly in that paper that if there are more types of neutrinos, we should be able to know because you'll make more helium because of the increased expansion rate. Their [priority of discovery of this result] is [contrary to] what's claimed by everyone else, including the recent article[24] in Scientific American by [David] Schramm and [Gary] Steigman. I wrote [Schramm and Steigman] and they were shocked, because they mentioned Hoyle and Tayler's paper in connection with the helium [but not in connection with the neutrino prediction]. So [Hoyle and Tayler] were the first, not Shvartsman in 1969[25] or myself in 1967 in my Science paper.[26] [Hoyle and Tayler] in 1964 explicitly noted it. Even Fred had forgotten. He told me that Roger had forgotten that too. It seems everybody had forgotten. But they did explicitly predict that.

Lightman:

But they didn't do a detailed calculation?

Wagoner:

No. They just did the neutron-proton ratio freeze out calculations giving you the helium. And Zeldovich, the same year, did a similar calculation.[27]

Lightman:

So you really weren't surprised then by your results?

Wagoner:

Not for the helium. Now, of course at the same time, Jim Peebles[28] was doing the calculation with a limited network of a few reactions up to helium 4. He had about six or seven reactions, including all the relevant nuclei. And, over a range of parameters, he calculated the helium 4 and the deuterium. He couldn't get the helium 3 accurately because he didn't have enough reactions. He didn't have lithium 7 in there. And his deuterium was not an extensive calculation. But he got, of course, the same answer as Hoyle [for the helium] for the correct reason. So that's why we focused on an extensive reaction network, so, first of all, we could be sure that leakage past mass 4 wouldn't affect the abundances below and also to see what else was made past the mass gap of 5 and 8.

Lightman:

Do you remember how people reacted to your results? Were most people accepting of your results?

Wagoner:

The first reaction I remember... Willie is a very fatherly guy, and he took me to the National Academy of Sciences meeting in April 1966. The abstracts are published in Science, and I presented our results for the first time in April of 1966 in front of the National Academy. I would say it got a good reception.

Lightman:

Did people consider it as supporting the big bang model?

Wagoner:

Yes, they did, based on the helium. There are two phases to the story. There are really three phases to the story. Helium, deuterium, and lithium. But because of Peebles' calculation as well...

Lightman:

Which agreed with you on the helium.

Wagoner:

Right. We stressed the helium.

Lightman:

And you mentioned that Hoyle and Tayler had gotten the right answer for the helium also.

Wagoner:

Right.

Lightman:

You think that was the strongest argument in favor of the big bang model — the helium?

Wagoner:

First of all, we weren't sure stars couldn't make deuterium as well as helium 3 and lithium 7. And the abundance of deuterium at that time was not well known. It was only known in ocean water and meteorites. So we didn't know what even the interstellar value was.

Lightman:

That's still a sticky point, isn't it?

Wagoner:

Well, not the average interstellar value in our vicinity of the Galaxy, but its meaning. We had done the first careful calculation. In fact, it was great working with Willie. Almost every day, I would get a note from Willie to look at a given reaction. We would look at it either theoretically or experimentally and try to track it down, or both. We tried to understand every reaction — 80 or 100 reactions. So it was a day to day interaction with Willie on the nuclear reactions, while I developed a computer program. Actually, the computer program is another interesting part of the story. As you know, at that time, there was quite a group at C-tech, quite a group of young researchers. Dave Arnett, Giora Shaviv, Vahe Petrosian, Don Clayton, besides Bahcall, John Faulkner, Jim Gunn, Kip Thorne, and Peter Strittmatter. I remember Dave Arnett was working on a nucleosynthesis code in stars, explosive nucleosynthesis. And mine was essentially the same code — explosive nucleosynthesis. The trouble is you start out in equilibrium, and it's a very stiff equation. You've got to allow for the fact that you have these rates running back and forth very rapidly, giving you a very slow net rate. How do you handle that? The answer is very simple in retrospect. You use backward differencing. You can see algebraically that it comes out beautifully. But it wasn't immediately obvious. So it took me about a year to get that code to run stably. I remember I spent the summer of 1967 in Cambridge, England. The only building at Fred Hoyle's new institute that existed at that time was the computer building. I had essentially an IBM 360-44 to myself. I could turn it on and turn it off during my program run and watch the instabilities develop and try to understand them. So I had a giant computer to myself at that time. It was fantastic. To be frank, the final answer didn't come from that numerical experimentation. But it was an interesting experience.

Lightman:

You recall that the results of the work were accepted pretty widely and interpreted at the time to be in strong support of the big bang model?

Wagoner:

The support did grow with time. I sensed that. I gave a talk at a later Texas Symposium on Relativistic Astrophysics in New York a few years later. People had already accepted it. It wasn't anything new.

Lightman:

What do you think about the situation today? Do you still think that the nucleosynthesis calculations and the agreement between those predictions and the observations are one of the strongest supports of the big bang model?

Wagoner:

A few years ago I wouldn't have answered this way, but a couple of things have happened. In 1973, the interstellar deuterium was observed. The year before, I wrote a paper[29] pointing out how important this would be. When it was discovered, I felt much more confident, for the additional reason that people had been looking at other ways to make deuterium, such as in supernovae explosions and things like that. And the inevitable consequence of almost any scenario, for very good nuclear physics reasons, is that you usually produce too much boron and beryllium if you try to make the deuterium.

Lightman:

In a star?

Wagoner:

Boron and beryllium are so rare — deuterium is much more abundant — and you tend to make all three of them by spallation. You need fast expansion and low density to make deuterium, so you don't eat it up. In most scenarios where you try to make deuterium, other than in the big bang, you made too much boron and beryllium. So none of the galactic scenarios were working at that time, [while] our calculations were very definite for deuterium. We had good cross sections. So when the interstellar value was announced, it was very exciting that it agreed for one value of the present density with the abundances of the other elements. That's when I first started to feel more confident. Because we didn't only have helium 4, we had deuterium, which is the only nucleus that couldn't be made in stars. So I felt, at that time, that deuterium is the key nucleus. You can make the helium, in principle, in an early generation of stars. But I feel you can't make the deuterium any other way. That's a strong point. The other thing that happened around that time was that Reeves, Audouze, and company did a careful calculation[30] of the galactic cosmic rays interacting with the interstellar gas. They had enough spallation cross-sections to do a reasonably accurate calculation.

Lightman:

And this would alter the deuterium abundance?

Wagoner:

No. What they found is that you can get a beautiful match with essentially no adjustable parameters." You know the galactic cosmic ray flux, you know the interstellar abundances, you know the relevant spallation cross sections, and you have carbon, etc. impinging on hydrogen and helium. They calculated the lithium 6, the beryllium 9, the boron 10, and probably the boron 11, although it wasn't so sure at that time, [and everything] agreed beautifully with the observed abundances. So there was a beautiful, natural way to produce six, nine, ten and eleven. Precisely those guys [elements and isotopes] that you cannot produce in the big bang. Everything else could be produced by stars, everything heavy. So it was a beautiful match. The big bang, the galactic cosmic rays, then stars. That was the next thing that gave you confidence. The last thing happened a few years ago with the lithium 7. In our best fitting model, the lithium 7 was always a little out of whack. That was the one that tended to agree worst with the observed abundances. Two things happened at about the same time. And this was done[31] by Schramm, Steigman, and their group, because I quit computer calculations in 1973 when I moved to Cornell from Caltech. Essentially I have been out of the big bang game — in detail— since 1973. With the new cross sections, the lithium 7 abundance that we calculated came up a little bit, and Spite and Spite discovered[32] these halo stars, which seemed to be better C.R. Seancea Academy samples of primordial material. They are old halo stars, in which the abundance of lithium did not depend upon surface temperature, indicating it was not depleted by convection. And this abundance was lower by a significant factor, of order 5 to 10, than the standard lithium abundance. Both those came in the right way to get better agreement. Calculated abundance rose, and observed abundance went down.

Lightman:

Did this increase your faith?

Wagoner:

Well, it was a confirmation of a prediction, in a sense, based on the other agreements. So that gave me more faith. But frankly, I'm still bothered by the Hoyle argument that I mentioned before - [that if you release all the nuclear energy in the universe and thermalize it, you get the microwave background]. It's so beautiful and natural. I was interested in the calculations[33] of Bond, Arnett, and Carr on these population objects — to try and see if you could produce the helium, etc. But there's still no natural way to thermalize the radiation.

Lightman:

Did Hoyle put that argument in print or was it something he just talked about?

Wagoner:

It's in our 1967 paper. Two lines. But someone may have noted it earlier.

Lightman:

Let me ask you about your reactions to some of the recent developments in theory and observation. To get a little bit of background on that, do you remember when you first heard about the horizon problem?

Wagoner:

Well, that's interesting. Alan Guth was at SLAC [Stanford Linear Accelerator], and he came to my office one day with this inflation idea, to try it out. That's the first time I thought about [the horizon problem]. I never worried about it much before.

Lightman:

Do you think you might have heard of it before?

Wagoner:

Yes, but I can't document it.

Lightman:

But you knew you weren't worried about it before?

Wagoner:

Right, I wasn't worried about an initial condition which seemed special. My feeling then, and to some extent still [is], that since we don't have a theory of quantum gravity, we don't know that there's a horizon problem. Because you cannot extrapolate back past the Planck time, you don't know whether you might solve it [the horizon problem] before that time.

Lightman:

You mean the horizon may have behaved [in the era of quantum gravity] with a completely different time dependence.

Wagoner:

Exactly. It could have broadened out then. It's unlikely, but without a theory I think its [unknown].

Lightman:

Did your view of the horizon problem change any as a result of Guth's work?

Wagoner:

Frankly, not to a great extent. We were at a conference together the next year or so, and it was very interesting. It was in San Francisco. A lot of famous particle physicists were there, like [Murray] Gell-Mann, etc. [Guth] presented his views on inflation — this was a year later — and he was virtually ignored by the particle physicists. They did not think it was important at that time. His views were not accepted until a few years later. It was very interesting. I'm still not a believer in inflation.

Lightman:

Why?

Wagoner:

I don't think it's necessary. As I said, one reason is that until we have a theory of quantum gravity, we don't know that there's a horizon problem. I'm perfectly willing to live with inflation. I'm just not an apostle of inflation.

Lightman:

Why do you think that inflation has caught on so widely?

Wagoner:

Because it's the most natural solution to the horizon problem. It's certainly a possible solution. It's well founded physically.

Lightman:

But you, yourself, are not a believer of that?

Wagoner:

I'm not motivated to adopt it. My position, which I've stated in some recent papers, is that one of my goals in my research has been trying to probe back into the universe. What I'm doing now with supernovae[34] is a probe of the recent past. Then there is my work on] gravitational lensing,[35] etc. and the nuclear stuff. I'd rather probe with a probe whose physics we know, like supernovae or nuclear reactions, rather than with a probe whose physics we don't know, like galaxies or some speculation about particle physics. I think it's very dangerous to try to learn about physics from cosmology. I'd personally rather go the other way: learn about cosmology from physics. I know in practice, it's hard at high energy. It's extremely exciting and interesting but dangerous to probe cosmology using probes whose physics you haven't verified. How do we test inflation other than looking to see if omega is one? It should be a test, but not a very selective test, let's say, 18 t r among other possibilities. In principle, there is large-scale structure. In principle, that might be an imprint of this early epoch, although to completely unravel that story could be difficult. In principle, it may be possible. I just am not motivated myself to worry about those problems right now. I'd rather understand problems that we can really get a handle on.

Lightman:

So you think there's too much uncertain physics in the inflationary scenario?

Wagoner:

Right. That's my own point of view.

Lightman:

Let me ask you about a closely related question, and that is the flatness problem. Did you also first hear about the flatness problem in your discussion with Guth, or did you know of the flatness problem earlier than that?

Wagoner:

Yes, I knew of it. I had worried about it and thought about it.

Lightman:

Do you remember when you first started thinking about the flatness problem?

Wagoner:

Yes, when I worked on nucleosynthesis, we worried about whether we could close the universe, and the implications from our results that the universe was open. We wondered how natural that was.

Lightman:

Natural meaning in the sense of...

Wagoner:

In the sense of the flatness problem. Omega being one was so natural.

Lightman:

So you were thinking about that in the late 1960s then. Is that right?

Wagoner:

But not to the extent that people did later — not deeply. I didn't think deeply about the problem.

Lightman:

Did you ever think deeply about the problem?

Wagoner:

I used to have this counter-argument. You just take the time reversed argument with a star. I drop a star from any possible initial condition, with different energies, bound or unbound. Start it in with positive or negative energy. Start a star collapsing and it's going to look like omega equals one when it reaches high density. So in the time-reversed problem, it's not unnatural [that omega approaches one]. Initial conditions decide what energy that star has, whether it be positive, negative or whatever. But if you're inside that star, when it reaches high density, you don't know how it started. It looks like omega equals one to you.

Lightman:

As long as the initial energy of the star was small compared to the binding energy of maximum collapse.

Wagoner:

Right. So I didn't really worry about [the flatness problem] too much, and that was one reason.

Lightman:

So you were never convinced by, for example, the argument that Dicke and Peebles made in stating the flatness problem?

Wagoner:

No. You mean in their Conundrum paper?[36]

Lightman:

Yes, in their Conundrum paper.

Wagoner:

I read it. To put it another way, I don't feel that our nucleosynthesis calculation necessarily requires that the universe be closed with some non-baryonic manner.

Lightman:

No, I don't think it does either. I'm really asking you a different question.

Wagoner:

But I'm saying I wasn't trying to close the universe in our nucleosynthesis calculation by throwing in some other stuff, for our paper.

Lightman:

Yes. So when you say that the expansion of the universe today is like the time reversed problem of the star, do you mean by that that the initial conditions...

Wagoner:

Well, think of an oscillating universe even though we can't calculate at the "bounce." At maximum, it can have arbitrary energy. So it looks flat at high density. So what. It's very flat at high density. That's not a mystery. It's not a mystery that's its very flat at high density. It's a consequence of dynamics, from an arbitrary initial condition.

Lightman:

But we're not at high density now.

Wagoner:

I'm saying in the early universe. The problem is why was the early universe tuned so well.

Lightman:

Yes.

Wagoner:

It wasn't tuned. It could reach that way from many initial conditions. It's a time reversed way of looking at their argument.

Lightman:

I'm playing devil's advocate now because I want you to state your argument as strongly as possible so I can understand. Let me look at a particular time, the Planck time, which probably has particular significance in the evolution of the universe. And at that particular time, let me see how finely tuned omega has to be in order to have an omega of a tenth, 1060 Planck times later. You would not consider that to be a peculiar situation, to be that close to one at the Planck time?

Wagoner:

Again, drop a star until it reaches the Planck density inside its horizon and you get the same result for the star. Exactly the same result.

Lightman:

Can you really argue by looking at the time reversed problem? I don't understand whether that’s really applicable.

Wagoner:

I don't think any of these arguments are relevant because I think they are philosophical. Let observation decide what omega is. It's a philosophical argument. I'm not interested in it for that sense. It's fine if it motivates models like inflation that can be tested. Great. I'm interested in finding out what the universe really is, by observation. That's what I'm interested in. That's my own motivation. For that reason, I try not to prejudice myself because I'm trying to measure qo with supernovae. So I don't want to get hung up with any prejudices. [That's] very dangerous in science, in my opinion. Although [prejudice] is a motivator, it can also be a dangerous motivator, if you're doing the observations or interpreting the observations.

Lightman:

In this case, you're doing theory. You're proposing observations based on your theory.

Wagoner:

Right. Although I will be involved with the Space Telescope, so I may turn into a quasi-observer.

Lightman:

Do you think it would be dangerous for you to have a prejudice, for example, about the value of qo in the work that you're doing right now?

Wagoner:

It could be subconsciously dangerous even though I could convince myself I'm treating the data fairly. I think there have been cases where people have been misled subconsciously, interpreting their data by prejudices which motivated them initially to do the problem. Most people are motivated by prejudices, or a lot of people are. It's natural.

Lightman:

Would you say the same of theorists?

Wagoner:

Yes. There have been a lot of ideas created to get omega equal to one — such as this quark-hadron phase transition stuff,[37] which is fine, but again you don't know the physics there, although you're closer to possibly getting the physics than for inflation. Fine. People are motivated to have omega be one. That's fine. I'm motivated to measure omega — by looking at distant supernovae, or whatever. [I think we need] some probes that we understand, that we can use to measure omega. That's my approach, so I've become a less pure theorist.

Lightman:

I respect that argument.

Wagoner:

I've evolved in that direction. I used to be more doctrinaire, a long time ago.

Lightman:

What changed your thinking on that?

Wagoner:

Experience. I worked on some theoretical problems based on observations that later turned out to be wrong. I've become wary.

Lightman:

The observations turned out to be wrong?

Wagoner:

Yes.

Lightman:

Why would that make you more cautious of prejudice? It seems like that would make you more cautious of the observations.

Wagoner:

I'm saying that these observations were wrong in part because of prejudice, subconscious prejudices. I've been burned three times.

Lightman:

Let me shift to another topic. When you first heard the results[38] of De Lapparent, Geller, and Huchra on the large-scale structure — the bubble work — and perhaps similar work by Haynes and Giovanelli[39] — did those results surprise you?

Wagoner:

A better word would be worry. I was worried. They worried me for the following reason. As we have been looking further out in space, we're discovering inhomogeneities on larger and larger scales. At the same time, the microwave background, as we look with better sensitivity, remains smooth. That's my gut reaction to that situation. Something smells very interesting. So it's mostly the scale that worried me, not the topology. It's mostly the scale. [It's the] same thing with the "great attractor." We're seeing larger and larger scale structures... What's happening to the cosmological principle? It's working great in the microwave background; it's not working so well for ordinary matter. As you know, another factor of ten in the isotropy measurements of the microwave background could cause us to reach a real theoretical impasse. That would be exciting. In a way, I hope that happens. I'm not involved directly in that area, but that's my feeling.

Lightman:

When you say that you were worried by these observations, do you think that your faith in the big bang has been slightly shaken?

Wagoner:

Yes. When I see the cosmological principle breaking down as it is continually tested at increasing scales, I get a little worried. The breakdown's not drastic, but I do get worried. More and more models are not consistent with those two facts, the microwave background and large-scale structures. So maybe we're in for a surprise. I hope so. It's unlikely.

Lightman:

Why do you say you hope so?

Wagoner:

Because I think it would be great. We'd have to go back to the drawing board.

Lightman:

You would like that?

Wagoner:

Well, we'd learn something new about the universe, [something] fundamental.

Lightman:

Even though you took great pleasure in finding agreement between your nucleosynthesis calculations and the observations, you would still look forward to the possibility of having to go back to the drawing board?

Wagoner:

I've always been schizophrenic this way. I've always been wary about being misled, so I've always tried to think of alternatives. I've thought about cold universes and things like that. Again, I was initially motivated by this Hoyle thing and the fact that the theories of baryosynthesis are untestable, I believe. Not in principle, [but] in practice, you're not going to be able to measure that particular CP violating parameter. It's somewhat of a miracle, maybe, that it will just turn out to be right. I'm a little uneasy. Uneasy, that's the best way to put it.

Lightman:

But you like the idea of being shaken up?

Wagoner:

Yes. If it turned out the early universe was not the model we used in our calculation, I would not be unhappy. It would not be a disaster for me. That's just the way I feel.

Lightman:

Do you think that theory and observation have worked well together in cosmology in the last ten or fifteen years? You can go back twenty years if you want.

Wagoner:

Let me start off with one area that's of particular concern to me, the distance scale, and the Hubble program. I think that was an unfortunate program, basically because it was not based on a physical understanding of your probes of the universe. It was based on an empirical understanding of galaxies or stars or H II regions, [believing] they could be standard candles without a physically well-defined model you could independently test. You have to have an independent test that your object is standard or whatever. I think that was a sad part of the history of science, that Hubble program. There were other approaches. Walter Baade developed a method I'm working with in 1926.[40] That method, the expansion method, was used for Cepheids, but in principle it could have been used on supernovae earlier than it was. But there was all this folklore about all these standard candles, which just kept disappearing with time. Because there weren't independent checks of a well-defined physical model. You're going to get in trouble in cosmology if you don't have well understood probes. That's been one aspect I've been unhappy about. The other aspect is the early universe. I think it's too speculative. It's exciting. It's fine for people to work on it, but I think it's a little over emphasized as compared to other areas in cosmology where we need more work, such as good distance measures, understanding quasars, etc. There's lots of fundamental problems to be worked on in astrophysics compared to the number of people. [For example,] jets. Why do we have jets on galactic as well as extra galactic scales? Is there something fundamental going on there? There's been a lot of good work on jets, but it's still a great problem.

Lightman:

What do you think the outstanding problems are in cosmology right now?

Wagoner:

Outstanding problems? The nature of the dark matter, the nature and distribution of the dark matter, I think, is the most immediate outstanding problem.

Lightman:

When you say dark matter, do you mean dark matter that we have evidence for that doesn't emit physical light? You're not talking about the inflation dark matter?

Wagoner:

Right. The dark matter we know is there, the clumped dark matter. There may be additional dark matter, but let's start with the clumped dark matter. I think it's great. All the direct detection schemes are great ways to try to find out if it's non baryonic. The other way, to try and find out if it's baryonic, is very important. So I think that's the most outstanding immediate problem, in addition to the usual problem of H0 and q0. Of course, q0 is another aspect of the dark matter problem. That's the only way to measure the total density of the universe. [Another outstanding problem is] the nature of the central engine in quasars and strong radio sources. You might not consider that cosmology.

Lightman:

When you say the nature...

Wagoner:

How do you make these jets, etc.? How does it work?

Lightman:

You want to know in detail how it works?

Wagoner:

No, I want someone to show me a mechanism that works naturally — a self-consistent, completely defined model that produces jets in a natural way.

Lightman:

What about theoretical problems in cosmology? What do you think is the most outstanding theoretical problem in cosmology?

Wagoner:

The most outstanding theoretical problem is the evolution of structure — coming back to this problem of the connection of the microwave background and the present observations, and hopefully eventually relating back to the early universe. The evolution of structure, I think, is another very important problem. But let's go at it from all points of view.

Lightman:

Do you think the N-body simulations contribute to the understanding of that?

Wagoner:

To some extent, but I'm sure they're misleading as far as their lack of hydrodynamics. But that's being fixed up. I think we'll gain much more understanding given the correct hydro, thermodynamics, radiative transfer, and so on. So that's an important problem. I think we should understand [how to] relate the present structure to the microwave background structure before we start making speculations about the early universe. Let's first pin down the nature of recent universe. That's my [view].

Lightman:

Let me ask you to take a big step backwards — I should say to look at things from the point of view of an ordinary person. If you could have designed the universe any way that you wanted to, how would you have done it?

Wagoner:

I've never thought about that question. If you want an off-the-cuff answer. I really haven't thought about it — I hope it would have been designed so that there are other civilizations that we can communicate with. It's getting a little worrisome because we haven't heard anything yet. It would mean an awful lot. That might be the most important observation made, communicating with other civilizations. So I hope intelligent life is not unique. That's the first thought that pops to my mind. It would be an interesting universe, since, being populated, civilizations can learn something [from each other]. I'd hate to think that we're alone. It would seem very strange. I wouldn't understand it.

Lightman:

There's a place in Steven Weinberg's book, The First Three Minutes, where he says that the more the universe is comprehensible, the more the universe also seems pointless.[41] Have you ever thought about whether the universe has a point or not?

Wagoner:

I used to think that it was very presumptuous of us to think that we were anything very special in the universe. I really got worried about people being too concerned with their everyday life and not looking out to be aware of their cosmic environment, to put things in perspective. I tended toward that view, at least in my public lectures, to try to make people aware of their cosmic environment, so they wouldn't get so completely wrapped up in parochial concerns. I think it's good for people to look out and realize the context of their life. So, in that sense, I think it's good for people to be aware that we really are, in a sense, insignificant, as far as our position in and influence on the universe. I think it's good for people to be humbled a little bit in that way. They get the full perspective. So that's my main view on that issue. Maybe we are insignificant. In certain senses we are, and in certain senses we're not. It's fantastic that we can contemplate the universe, that bits of matter can try to understand their complete surroundings. It's fantastic. It's lucky. And maybe there are even luckier civilizations, that we could communicate with, who have learned so much more. It would be fantastically exciting to learn what they might have learned. I'm not a great science fiction reader, but I was influenced a lot by The Black Cloud[42] by Fred Hoyle, which I read an awful long time ago.

Lightman:

That's about some intelligent life that floats down?

Wagoner:

Yes. It's in a diffuse form in interstellar space. So, when people talk about other civilizations, I'm sure they're going to be much different than we could possible conceive. We wouldn't recognize them at first. That's my own bet.

Lightman:

That might be a good place to end the interview.

[1] e.g. W. Ley, Rockets, Missiles, and Space Travel (New York: Viking, 1951); The Conquest of Space (New York: Viking, 1949)

[2] Editor's note: Wagoner indicates that the textbook used was Critical Thinking: An Introduction to Logic and the Scientific Method, 2nd edition (Prentice-Hall, 1952)

[3] e.g. A. Korzybski, Science and Sanity

[4] F. Hoyle, The Nature of the Universe (New York; Harper, 1950); Frontiers in Astronomy (London: Heinemann, 1955)

[5] D.W. Sciama, The Unity of the Universe (Garden City: Doubleday, 1959)

[6] R.V. Wagoner, "Rotation and Gravitational Collapse," Physical Review D, vol. 138, pg. B1583 (1965); "Possible Mechanism for Producing Strong Radio Sources." Physical Review Letters, vol. 16, pg. 249 (1966)

[7] R.P. Kerr, "Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics," Physical Review Letters, vol. 11, pg. 237 (1963)

[8] R. Adler, M. Bazin, and M. Schiffer, Introduction to General Relativity (New York: McGraw Hill, 1965)

[9] F. Hoyle and J. V. Narlikar, "Cosmological Models in a Conformally Invariant Gravitational Theory. I. The Friedmann Models," Monthly Notices of the Royal Astronomical Society, vol. 155, pg. 395 (1977)

[10] D.W. Sciama, "On the Origin of Inertia," Monthly Notices of the Royal Astronomical Society, vol. 113, pg. 34 (1953); "Inertia," Scientific American, vol. 196, no. 2, pg. 99 (1957)

[11]R.V. Wagoner, W.A. Fowler, and F. Hoyle, "On the Synthesis of Elements at Very High Temperatures," The Astrophysical Journal, vol. 148, pg. 3 (1967)

[12] See Ref. 11

[13] R.A. Alpher and R.C. Herman, "Evolution of the Universe," Nature, vol. 162, pg. 774 (1948); "On the Relative Abundance of the Elements," Physical Review D, vol. 74, pg. 1737 (1948); G. Gamow, "The Evolution of the Universe," Nature, vol. 162, pg. 680 (1948); R. Alpher, R. Herman, and G. Gamow, Physical Review D, vol. 74, pg. 1198 (1948)

[14] E. Fermi and A. Turkevich, unpublished calculations referred to in R.A. Alpher and R.C. Herman, "Theory of the Origin and Relative Abundance Distribution of the Elements," Reviews of Modern Physics, vol. 22, pg. 153 (1950)

[15] C. Hayashi, Progress in Theoretical Physics, vol. 5, pg. 224 (1950)

[16] R.A. Alpher, J.W. Follin, Jr., and R.C. Herman, Physical Review D, vol. 92, pg. 1347 (1953)

[17] E.M. Burbidge, G.R. Burbidge, W.A. Fowler, and F. Hoyle, Reviews of Modern Physics, vol. 29, pg. 547 (1957)

[18] See Ref. 14.

[19] See Ref. 10.

[20] e.g. R.V. Wagoner, "Synthesis of the Elements Within Objects Exploding from Very High Temperatures," Astrophysical Journal Supplement, vol. 18, pg. 247 (1969); "Physics of Massive Objects," Annual Reviews of Astronomy and Astrophysics, vol. 7, pg. 553 (1969); "Production of Helium in Massive Objects," in Highlights of Astronomy, ed. De Jager, (Dordrecht: Reidel, 1971)

[21] e.g. J.N. Bardeen and R.V. Wagoner, "Uniformly Rotating Disks in General Relativity," The Astrophysical Journal Letters, vol. 158, pg. L65 (1969); E.E. Salpeter and R.V. Wagoner, "Supermassive Disks," in Eternal Galaxies and Quasi-Stellar Objects, ed. D.S. Evans (1972)

[22] J .E. Felton, "Energy Density of Starlight in the Metagalaxy," The Astrophysical Journal, vol. 144, pg. 241 (1966)

[23] F. Hoyle and R. Tayler, "The Mystery of the Cosmic Helium Abundance," Nature, vol. 203, pg. 1108 (1964)

[24] D.N. Schramm and G. Steigman, "Particle Accelerators Test Cosmological Theory," Scientific American, vol. 258, pg. 66 (1988)

[25] V.F. Shvartsman, JETP Letters, vol. 9, pg. 184 (1969)

[26] R.V. Wagoner, "Cosmological Element Production," Science, vol. 155, pg. 1369 (1967)

[27] Ya B. Zeldovich, Usp… Fig. Nauk, vol. 80, pg. 357 (1963); English translation in Soviet Physics — Uspekhi, vol. 6, pg. 475 (1964)

[28] P.J.E. Peebles, "Primordial He Abundance and Fireball II," The Astrophysical Journal, vol. 146, pg. 542 (1966); Also Physical Review Letters vol. 16, pg. 410 (1966)

[29]R.V. Wagoner, "Big Bang Nucleosynthesis Revisited," The Astrophysical Journal, vol. 179, pg. 343 (1973)

[30] H. Reeves, W.A. Fowler, and F. Hoyle Nature, vol. 226, p. 727 (1970)

[31] J. Yang, M.S. Turner, G. Steigman, D.N" Schramm, and K. Olive, Astrophysical Journal, vol. 281, p. 493 (1984)

[32] M. Spite and F. Spite, "Lithium Abundance in Two Halo Stars," C. R. Seances Academy of Science, Serial II (France), vol. 293, pg. 299 (1981); Lithium Abundance at the Formation of the Galaxy," Nature, vol. 297, pg. 483 (1982)

[33] B.J. Carr, J.R. Bond, and W.D. Arnett, Astrophysical Journal, vol. 277, p. 445 (1984)

[34] e.g. R. V. Wagoner, "Determining qo from Supernovae," The Astrophysical Journal Letters, vol. 214, pg. L5 (1977); R. V. Wagoner, in Physical Cosmology, ed. R. Balian, J. Audouze, and D.N. Schramm (North-Holland, 1980)

[35] Peter Schneider and R. V. Wagoner, "Amplification and Polarization of Supernovae by Gravitational Lensing," The Astrophysical Journal, vol. 314, pg. 154 (1987)

[36] R.H. Dicke and P.J .E. Peebles, "The Big Bang Cosmology - Enigmas and Nostrums," in General Relativity: An Einstein Centenary Survey, ed. S.W. Hawking and W. Israel (Cambridge: Cambridge University Press, 1979)

[37] Alcock, Fuller, and Mathews, The Astrophysical Journal, vol.320, pg. 439 (1987); Applegate, Hogan, and Scherrer, Physical Review D, vol. 35, pg. 1151 (1987).

[38] V. de Lapparent, M.J. Geller, and J.P. Huchra, "A Slice of the Universe," Astrophysical Journal Letters, vol. 302, pg. L1 (1986)

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[41] S. Weinberg, The First Three Minutes (New York: Basic Books, 1977), pg. 154

[42] F. Hoyle, The Black Cloud (??)