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Interview of Robert Dicke by Alan Lightman on 1988 January 19,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
This interview discusses Robert Dicke's childhood experiments; early reading; education at University of Rochester; attitudes of older scientists about research in relativity; work on the Eotvos experiment; early reading in cosmology; early work in the 1950s setting a limit to the cosmic background radiation; motivation for predicting the cosmic background radiation; preference for an oscillating universe; Dicke's evening seminars at Princeton; the origin of the flatness problem, which Dicke first proposed in 1969; Dicke's lecture at Cornell on the flatness problem, attended by Alan Guth; the anthropic argument in connection with the flatness problem; attitude toward the inflationary universe model; attitude toward Center for Astrophysics (CfA) red shift surveys by de Lapparent, Margaret Geller, and John Huchra; Dicke's amazement at the existence of so much matter in the universe; discussion of the anthropic principle; images and metaphors in scientific work; the relationship between theory and observations in cosmology; attitude toward extrapolating the big bang model back to very early time; why Dicke prefers an oscillating universe; the origin of the universe; the question of whether the universe has a point; the question of why cosmology was not taken seriously as a science for a long time.
Could you tell me briefly how you got interested in science as a child?
That was a long time ago. I don't rightly know. It's a little hard to say.
Did you build things when you were young?
Yes. I had chemistry sets, and I was interested in insects. I had insect collections. I got interested in astronomy from reading.
Do you remember any particular ideas or books that impressed you?
Millikan's book on the electron plus and minus.
You read that as a youngster?
As a young teenager. And I badgered my father into buying The Source Book in Physics.
Yes, Magie, that's the one. I just did a lot of reading at the library I guess.
You read the Magie book in high school?
That's fairly sophisticated.
I'm not sure that I got 100% of it either, but I think I read it.
Were you studying physics at that age?
I had a high school physics course, but it didn't amount to much. My high school physics teacher wasn't really trained for the job.
Were you studying physics on your own, outside of school?
I was doing quite a bit of reading on my own, yes. I was reading calculus too, in high school. In those days, there was virtually no high school calculus course. If you wanted to learn calculus, you did it on your own.
Were you parents interested in science?
My father was a patent attorney, trained originally as an electrical engineer.
Do you remember in Millikan's book, or in any other books that you read at this age, any particular scientific ideas that appealed to you?
I remember being interested in the cosmological question in high school [laughs]. I actually did an experiment. It was absolutely crazy.
Can you tell me about that?
Yes. From the standpoint of action-at-a-distance, if a light bulb emits light, the light has to be absorbed somewhere. So I put a flashlight in a Wheatstone bridge and then pointed it up at the sky and pointed it at the floor. The idea was that if space was empty, the light wouldn't have anywhere to go.
And if not, it might be like the closed loop of a conductor?
Yes. If space was empty, then pointing the light up at space would unbalance the bridge. And if space were full, the light would be absorbed.
And there would be no difference [in the resistance measured by the Wheatstone bridge].
No difference. So I guess from the experiment, you'd have to conclude that space was full [laughs].
That's a very clever experiment for a high school student. And you took that seriously?
Yes. It didn't have a very sound basis. I thought it was a serious question. I don't know what significance I put in the result.
So you were already thinking about large distances in space?
Yes, I guess, in that connection.
As a high school student, were you aware of any cosmological theories?
Not really, no. I had no background in relativity, or anything like that. I remember I did some other scientific things in high school. In chemistry class I made a Wilson cloud chamber, to see alpha particle tracks. I was interested in physics generally. But I must say our high school course was pretty poor.
Mine was too. In this experiment you did with a flashlight and the Wheatstone bridge — I know it's hard to remember — when you thought about the possibility of the universe being filled with matter or being empty, do you remember trying to visualize a universe that kept going or a universe that had a finite size?
I'm sure I thought of it in terms of a finite size. I certainly had no idea of an expanding space.
Tell me a little bit about your undergraduate education. Did you immediately know that you wanted to go into physics?
I got into physics really quite by accident. I was admitted to the University of Rochester in electrical engineering. I was going to study that because my father had a background in that. And then, when I looked at the catalogue more carefully, it looked like, gee, that physics department first-year course looks just great compared with the nuts and bolts of the engineering curriculum, so I decided I would major in physics for one year and then transfer to engineering after that. I never transferred. One of the reasons was that I had such excellent teachers. Lee DuBridge put on demonstration lectures every week, and I learned a lot from him. By the end of the first year, I think I was pretty much seduced to taking physics.
Do you remember when you first got introduced to cosmology as a discipline of physics? Was that as an undergraduate?
No. Except for a few places — and Princeton was one of the exceptions, with Bob Robertson there, and Einstein — relativity and cosmology were not regarded as decent parts of physics at all.
Why was that?
I don't know. I asked Weisskopf one time — he was at Rochester when I was a graduate student — shouldn't a graduate student pay some attention to relativity? And he explained to me that it really had nothing to do with physics. Relativity was kind of a mathematical discipline [laughs].
Was it in graduate school that you began studying relativity theory and cosmology?
I can't recall as a graduate student getting involved at all with those things. I got interested in cosmology as a tool for getting at the fundamental gravitational questions, which I had become interested in. It looked like cosmology was a handle at getting at these things.
Was your experiment with the weak equivalence principle along the lines of the kinds of fundamental questions that you were asking?
This is the way I got into it. I was on a sabbatical leave at Harvard that year, and I wanted to do something quite different from what I had been doing, so I did some reading and got interested in the question of how Mach's principle was related to relativity. As an experimentalist, it became clear to me that the Eotvos experiment was really a very fundamental experiment, and it hadn't been done with modern techniques at all. I wanted to take a crack at that. So when I got back, I started to work on the [Eotvos experiment.] I'm not sure I would have ever done it if I had known how long it was going to take and how much trouble it was going to be. From the Eotvos experiment, and my interest in the scalar-tensor theory, it became clear that there were some implications for geology and astrophysics. So I sort of got interested in astrophysics through the back door. First I was interested in gravitation and then this provided a tool for real observations.
Were Mach's ideas one of your motivations for the scalar-tensor theory?
You said that you got interested in cosmology as a handle on your general interest in gravitation. Do you remember when you first began getting interested in cosmology and what were the problems that most interested you?
When I got interested in relativity theory, at that time, the only things available were just model calculations — De Sitter theory, Einstein-De Sitter solutions and so on. Tolman's book was my main source of information. I'm trying to think what the first step was. I think on cosmology, the necessity for having a hot beginning in the connection with trying to understand the composition of stars was one of the leading things [motivations]. In retrospect, I think our reasons for considering to look for the background radiation were a bit misguided.
I have some questions about that I'd like to return to later. When you first started getting interested in cosmology, do you remember having a preference for any particular cosmological models? I guess the Steady State model was around, and the standard open and closed Friedmann cosmologies. Did you have a preference?
No. And as I said, in those days, one didn't know how much physical significance to put in these things. In the mid-1950s, there was a lot of interest in the Steady State model and in evolving cosmologies. I can't really recall just what my interests were at that time. I remember one thing though. I remember our own water vapor measurements at one centimeter [wavelength] that set an upper limit to radiation coming from space, [corresponding to a maximum temperature of] some twenty degrees or so. And I also remember reading about some experiments at Bell Labs in which they tried to set noise levels. I don't think they interpreted this in terms of radiation coming in, but they had gotten some residual temperatures of 3-5 degrees.
Was that in the late 1950s?
That was about in the mid-1950s.
Let me ask you a little about your motivations for considering and predicting a microwave background. I know what you say in your paper of 1965, but do you remember what your motivation was at the time? Do you remember your chain of reasoning?
Yes, I think I can construct that pretty well. First of all, I wasn't impressed with the thought that you could suddenly make all that matter that we see around us in 10-20 seconds or so. It seemed to me that a more reasonable thing was that the universe would be oscillating, collapsing and expanding again. At that time, I had heard some lectures from one of the astronomers at Caltech, in which he was talking about the Population I and Population II stars. From these lectures it was quite clear that the old stars in the galaxy were relatively free of metals [heavy elements] and later on they were getting dirtied up. In an oscillating universe, it was clear that you would have to clean up these dirty stars [that is, transform their heavy elements back into hydrogen in each cycle]. The only way to do that would be to get the universe hot enough to decompose the heavy elements. It would have to be pretty darn hot. So this led me to the view that the universe would have to be expanding out of a high-temperature state. I remember making a crude estimate that it [the temperature of the blackbody radiation today] would be about 45 degrees or something like that. If it was much more than that, we'd get too much energy. The energy density would be too high. I remember talking to the boys in the group about this.
Yes. Jim Peebles mentioned that he heard about this from you at one of your evening seminars.
The way I recall, it wasn't even at one of the evening seminars at first. Maybe it was for him, but I remember gathering together a group down in the lab.
This would have been in the early 1960s?
It was probably a year and a half to a year before that  paper. And we certainly talked about it at the evening seminars too.
So, by having an oscillating universe, you wouldn't have to explain the creation of matter.
Well, you wouldn't have to explain the creation of all of it, because in every oscillation you'd create a little more [matter] and have it exponentially growing. This also gets around the entropy problem. You could add entropy every time [oscillation] but you add more matter to go with it so that the specific entropy [entropy per particle of mass] stays more or less constant.
Well, this may be a naive question, but, for the given amount of matter that we have now, wouldn't you have to explain the initial amount of matter whenever the oscillations started?
Hopefully, you could explain this as a single quantum fluctuation, with just a few particles created initially in a tiny universe that expands this far and then collapses again.
I see. So the first oscillation would have been...
Just a quantum fluctuation.
And then so few particles, on subsequent oscillations, would increase [in number] to what we have now.
Yes. At the time, it wasn't so crazy to think about. We didn't know about the singularity theorems. Let's see, what was Landau's colleague's name?
Lifshitz. Lifshitz was calculating models that would bounce — highly disordered [models]. There was something wrong with them, but at the time a lot of people thought that these universes bounced. Now you can still make them bounce, but it's not so easy.
So, around 1963, you imagined that these oscillations would have begun with some quantum fluctuation? Was that part of your thinking?
Yes, in a vague way. Still vague.
Could you calculate how many new particles would be produced in each oscillation?
I had no theory.
You had no theory for that. But if you could have calculated that, I guess you could have said how many oscillations there would have been from then until now.
Well, after all, when you put numbers in an exponent, a pretty small exponent with enough oscillations can get pretty big.
It seemed to me in reading your 1965 paper, which of course only had a piece of your full thinking that somehow you were trying to postpone consideration of the initial conditions.
Well, we knew nothing about it [laughs]. The main idea at that time was just that we see the dirty stars; we see that the stars start off clean. Then, even a single bounce demanded that it [the early universe] be hot.
At the time that you were thinking about this, did you have a preference for the oscillating model as opposed to...
Very definitely. It was the only way you could generate all that matter, from my viewpoint.
Let me ask you a little about the so-called flatness problem that I think may have first appeared in print in your article with Peebles in 1979.
It actually appeared in print before then.
Did it appear before that?
Yes. There's a little book I wrote for the American Philosophical Society." Lecture notes or something.
What year was that?
The Jayne Lectures of 1969. There are a few sentences in there.
Was it around 1969 that you first began thinking of this puzzle [the flatness problem] or was it even earlier than that?
I can't remember whether it was any earlier than that. I think probably it was in connection with preparing these lectures.
It seems that in the astronomical community — maybe" the time was right, but for some reason or another — that this puzzle that seemed to demand a physical explanation first caught on after your article with Peebles in 1979.
Actually, there was a period of time when I was quite interested in these paradoxes, and I was going around giving a set of colloquium talks on them. One I gave at Cornell, and I hadn't known this, but Alan Guth actually put in print that he was there. He was stimulated by this, which makes me very happy.
That was in 1979, wasn't it?
I have no idea now. Much after this other thing [the Jayne Lectures in 1969].
When you were going around giving colloquia and discussing this puzzle, do you remember what kind of reaction you got? Did people take it seriously?
I can't say really. At least one did [laughs]. I can't even remember all the puzzles. I think I had some four puzzles. One was flatness, one was the causality one, and one was the Dirac coincidences.
Yes, you talked about that in your paper in Nature in 1961.
Maybe there wasn't a fourth.
Was the matter to antimatter ratio one of the puzzles?
Possibly. Yes, I think so.
One of the things that interests me about the flatness problem — besides the fact that it turned out to have been extremely influential in Alan Guth's motivation — is that there seem to be sharp differences in. reactions to this problem even now, and even more in 1979, when I first heard it myself. Some astronomers think that the universe is as it is. [In this view], we have only one universe, so any arguments that are based on the possibility of their having been an ensemble of universes with all different values of omega today and all different kinds of initial conditions don't make any sense. This is one type of reaction. Other people take it [the flatness problem] as something that demands a physical explanation.
Well, not necessarily physical. An anthropic explanation is possible, too, I think. With an ensemble of universes, this is the only kind we could live in.
Yes. When you thought about this puzzle, did the anthropic explanation occur to you?
No. At the time I wrote these notes [the Jayne Lectures of 1969], I doubt it; that [the anthropic explanation] had been used earlier, in connection with the Dirac argument [Dirac's large number hypothesis] about the gravitational constant. But I don't think I was thinking of it in this relation. I had the feeling that this [the nearness of omega to one] implied the universe was very nearly flat for a good physical reason.
And they were just reasons that we didn't...
That we didn't understand.
But we needed to find some reasons? We couldn't just blame it on initial conditions?
No. That really requires a terribly delicate balance to get that set up right.
In stating the implausibility of that balance, did you conceive of lots of different possible ways that the universe could have been set up?
I guess I was thinking — again this might be an argument for a bouncing universe — that the universe bounces and it is still closed so that it collapses again but it has to bounce to a quite reasonable size and it can only do this in a very nearly flat universe.
Let me ask you a little about your reactions to some of the discoveries that have been made in the last ten or fifteen years. Do you remember your initial reaction to the inflationary universe model?
Not very well, I'm afraid. Also, I must confess that in the last ten years or so I haven't really been keeping up too well with these things, so my present-day impressions aren't all that good. But it [the inflationary universe model] certainly is a very clever way of getting around some of the paradoxes that have been bothering me. Exponential growth is a great idea. The thing that I found a little hard to swallow was the delicate balance that's required to have the phase change held off long enough so that you can expand enough first.
Some of the modifications of the inflationary model have tried to deal with that, but I guess it's still something that's not clear cut theoretically.
Have you been interested in the work on the large-scale structure of the universe? I'm thinking of the De Lapparent-Geller-Huchra bubble-like structures.
Yes, I'm following that.
How do you react to that kind of picture? Does that alter your personal views of the large-scale structure?
Well, it's surprising to see a structure organized on such a large scale, as well organized as it is, with bubbles and sheets and so on. It does suggest that structure in a highly condensed, early phase played an important role.
Did it surprise you?
Yes, I would say it did. Although ever since Jim [Peebles] put together that galaxy map based on Shane's catalogue, I was impressed by the appearance of those filaments in there. They seemed real. I kept arguing with Jim that they were real, and he kept saying that they were a figment of the imagination.
So you always suspected...
So I always suspected that there was some structure there.
At this time, did you have any particular preference for a homogeneous universe versus an inhomogeneous one?
No. That the universe is organized as much as it is, and is as uniform and isotropic as it is, might also be an effect of the anthropic principle. If you get the thing [the universe] too badly organized, why I doubt the thing would be very hospitable — [for example], some parts collapsing before other parts get started expanding.
I guess that would be all right as long as we weren't in one of the collapsing parts ourselves.
Well, you can't run things too fast or too slow.
Wouldn't it be all right for just our local part of the universe to be in a piece that was running about the right rate? Would it make a difference to us what was happening in the other parts?
Well, if other big pieces that were close to us had collapsed completely, I think there could be some rather disastrous radiation conditions for us. I think you have to have a reasonably well organized universe.
Is this question of the organization — which I guess is related to the flatness problem — something that still bothers you, or do you think that the inflationary universe model has [answered it]?
It still bothers me. I still am amazed at there being so much matter on such a grand scale and have this all come out of one explosion. I think there may still be a bouncing universe [Laughs].
How does a bouncing universe solve this problem of the large-scale organization [of the universe]?
I'm not sure it does [laughs]. Jim [Peebles] has argued, I think quite correctly, that in the collapse phase in homogeneities grow so rapidly and so strongly that you can't come out with an organized state.
Do you think that we might still be missing a big piece of physics in understanding these things?
Some new physics? I doubt it.
Do you think we just have to understand it in terms of what we know?
More observations would probably help.
I guess the inflationary universe scenario, if correct...
It certainly is impressive the way it takes care of the flatness and causality problems with one mechanism. The string business I don't understand enough to comment at all.
You mentioned the anthropic idea a couple of times. What do you think about some of the recent work that's been done on the anthropic principle? I know that your statement of [the principle] in your 1961 paper in Nature was rather mild.
Yes, I would call it a very conservative statement. The really exciting one is Brandon Carter's, which would have all of the physical constants adjusting themselves...
In order to allow life to form.
Yes. There are some very intriguing coincidences there, too; the one about getting by the beryllium 8 point.
Do you think that this could possibly give us some new insights? Do you think these are useful arguments?
Well, first of all, I think that in the form in which I stated [the anthropic principle], there isn't a lot of controversy, because it's a rather straight forward question. The other [form of the anthropic principle], I don't know. It would require quite a revolution in the way of doing physics. You have to understand these physical constants as functions of something if you're going to do it in a field theory way; functions of what then? Well, a universal scalar [field] is one possibility. If you have that, you could conceive of constants that would vary with the structure of the universe, and pick out of all these possible structures the one that you feel most comfortable to live in.
One of the things that I'm interested in is how scientists use metaphors and visual images in their work. There seems to be a variation from one scientist to the next. Do you use visual images much in your own work?
I think in my research I use analogues a lot — not necessarily visual images, but analogues. Something that you learned in high school electrical engineering might be useful in cosmology — Analogous structures.
Have you found either analogues or images useful in cosmology in particular? I'm thinking of the expanding balloon analogy for the expanding universe.
I must say that I think always in terms of comoving coordinates. It's a great big, big girded structure with flexible girders that stretch.
Do you ever try to imagine the very early universe, other than with what equations one might be able to write down? Do you ever try to picture it?
No. I don't know enough.
Let me ask you a little bit about the way that theory and observations have worked together in cosmology, say in the last twenty years. As a theorist and an observer both, you are in a particularly good position for thinking about how this interplay has worked. Do you think that the theory and observations in cosmology have gone in separate directions or have helped each other?
I'd say that without the observations the theory would have gone completely haywire. [laughs] completely. That interplay has been very important. It's also been important to the observations. When you're doing experiments, you don't do any old experiment. You always have some kind of a theoretical model in the back of your mind. It might be crazy, but you have some kind of a theoretical structure that you want to test — and so it is with cosmology.
When you were thinking about the cosmic microwave [background radiation] experiment, I guess the oscillating universe model was an idea that...
It certainly was one that I found interesting.
That certainly was a theoretical idea.
How comfortable do you feel with taking our Big Bang model and extrapolating it backwards in time to the first few minutes or the first second?
A little uncomfortable, I must confess. It's a tremendous extrapolation but not as uncomfortable as I feel about extrapolating [the theoretical Big Bang model] beyond that. There's still one point in cosmology that I find very disagreeable, and that's the idea of time and space having no meaning up to a certain point and then suddenly appearing. A universe which is suddenly switched on I find highly disagreeable.
I know Stephen Hawking has been working in the last five or seven years in trying to understand the initial conditions. I guess he's thinking about the universe as having been made out of a quantum fluctuation, as you were thinking earlier.
Yes. Except when he thinks about it, it makes sense. [Laughs]
So you're a little uncomfortable with time and space suddenly arising from nothing before.
Yes. I guess what bothers me is a sudden barrier, a discontinuity, whether it's in time or space — because I'm used to continuity. To have space exist on one side of a sheet and not exist on the other I would find most disagreeable [laughs].
A worrisome thing about the inflationary universe model, to me, is that we do have to take seriously some kind of physics back at an extremely early time.
Well, that's an extrapolation which is hardly warranted by the observations. I think it's a sheer fantasy.
And yet you're still attracted to the theory because of its explanatory power?
Yes. That may not be a sufficient reason.
Let me ask you a couple of final questions even more speculative than the ones I've asked you already. Let me ask you to take a big step back from your normal scientific caution. If you could design the universe any way that you wanted to, how would you do it?
Well, I think what I'd like to do — bearing in mind Carter's ideas about variable constants — is built in a scalar field that things could be functions of, so that you could have evolving constants, depending on the structure of the universe. I'd like to have the universe bounce and gradually grow in size, with each bounce contributing more particles and more entropy. I'd like to have the whole thing go in accordance with what the elementary particle people would believe, if they ever had a way of testing it [laughs].
Why does the oscillating universe model appeal to you?
You don't have to start.
Except from some initial quantum fluctuation?
Well, you have a space with some gravity waves running around in it. So you have a purely empty space to start with, nothing but gravity. And then, in a quantum fluctuation, a few particles appear and start a little thing [universe] oscillating. And not just one, but many, many probably — which leads to many universes, each one doing its own thing.
So there would be some larger space that would have different universes inside of it?
Yes. If they were closed, they'd be closed universes. That is to say, they'd be cut off from each other, but very nearly flat.
Why do you like the idea of having lots of independent universes?
You don't have to explain why only one. It also takes care of the anthropic principle.
Yes. In this situation, with these independent universes being created from quantum fluctuations, do you imagine that would go on infinitively in time? Would new universes be [continually] created out of quantum fluctuations?
It's hard to know. I would guess they [new universes] could probably continue to do this. You can steal your energy from the gravitational field I guess — at energy content zero.
If each universe had energy content zero, why would you have to steal energy from anywhere to get the thing started?
Well you have these gravity waves running around representing some positive energy, and you get a little bit of a start from that.
You have to have this energy localized so it's a little excessive. That little excess is enough to account for the closure — a small, weak closure.
I've got a couple of more questions along those lines. Do you have any interest in philosophy?
Do you think that philosophical considerations have ever played a role in your scientific thinking?
I guess you have to say that some of these arguments are philosophical — [for example], why I prefer a closed universe to an open one. I'm not quite sure whether what the physicist would call philosophy the philosopher would call philosophy.
I guess I'm asking you about what a physicist would call philosophy.
I think it's probably played a role. I can't really say why.
Let me ask you a final question. There's some place in Steve Weinberg's book Gravitation and Cosmology where he has this curious statement that the more we learn about the universe, the less it seems that the universe has a purpose.
I don't understand that, but it's certainly a philosophical statement [laughs].
When you say that you don't understand it, do you mean that it doesn't make sense to you, or you don't know why he said it?
It doesn't make a lot of sense to me, because I'm not sure that it's the purpose of the universe to have a purpose [laughs].
So you have never personally worried much about this question of whether the universe has a purpose.
No. The closest thing to a purpose I can see is through the anthropic principle.
But the way that you have stated the anthropic principle, it doesn't require a purpose.
No. It doesn't require any great revelation or any great revolution.
If you've got lots of universes to choose from...
Then it [the universe] has to be a pretty old one but not too old.
And that doesn't require a purpose. And that's the way you tend to view it?
Sometimes I don't ask my [interview] questions in exactly the [best] way. Do you have any idea why people weren't asking these [cosmological] questions [like the flatness problem] earlier? You mentioned that people weren't taking cosmology as a whole as a serious subject. Do you think that might have been a reason?
It's a puzzle to me how cosmology got so separated off from the rest of physics. Here is all that matter in the universe, and it doesn't seem to bother anybody. It's there, [but] where did it come from? Questions of this kind just weren't asked. If you go back even earlier, these purely mathematical models — isotropic and homogeneous spaces — were purely mathematical exercises. Not completely so. There were certainly people like Robertson who were interested in the observational questions and observational support. One of the reasons that Bob Robertson left Princeton to go to Caltech was to be closer to the observations there.
Maybe to put some powder in his rifles.
I'm just totally baffled by stating a puzzle like this [the flatness puzzle] in 1969, which — even if you take it a little bit seriously — is so overwhelming and [yet] having very few people pay attention to it for so long. It's unbelievable to me.
Or just look out or look around you. All that matter. Where does it come from? Nobody asked the question [laughs].
Maybe people just didn't think they had any hope of explaining it in terms of first principles.
Yes. That's certainly true.
 R.A. Milikan, Electrons (+ and -), Protons, Photons, Neutrons, and Cosmic Rays (U. of Chicago Press: Chicago, 1935)
 W.F. Magie, A Source Book in Physics (McGraw Hill: New York, 1935)
 R.C. Tolman, Relativity, Thermodynamics, and Cosmology (Clarendon: Oxford, 1934)
 "Cosmic Blackbody Radiation,” The Astrophysical Journal, vol. 142, pg. 414 (1965)
 E.M. Lifshitz and I.M. Khalatnikov “Investigations of Relativistic Cosmology,” Advances in Physics, vol. 12, pg. 185 (1963)
 "The Big Bank Cosmology -– Enigmas and Nostrums” in General Relativity, An Einstein Centenary Survey, ed. S.W. Hawking and W. Israel (Cambridge University Press, 1979)
 Gravitation and the Universe, The Jayne Lectures for 1969 (American Philosophical Society, 1969), page 62
 "Dirac’s Cosmology and Mach’s Principle,” Nature, vol. 192, pg. 440 (1961)
 This statement actually occurred in Weinberg’s book, The First Three Minutes