Raman Sundrum

Pavlish:

It is June 29th, 2007. I am here to interview Professor Raman Sundrum at Johns Hopkins University. Professor Sundrum has worked much on nonconventional solutions to figuring out what the cosmological constant is. He will tell us more about that today. Also, I would like to ask you, Professor Sundrum, how did you become interested in cosmology and in the cosmological constant in particular?

Sundrum:

From a technical angle, is I think how it started. That is, as a particle physicist by training, we have had a certain problem of the Standard Model, a theoretical problem of the Standard Model, I should say, not an experimental conflict of the Standard Model of Particle Physics, that has been with us for about 30 years or so, which is to try and understand how the weak interactions become, by what mechanism they become a short-range force as opposed to a long-range force. The problem there, which is broadly called the Hierarchy Problem, has a technical Quantum Field Theory aspect to it. There are some features that seem robustly to follow from fairly general principles of Quantum Mechanics and Relativity. I think about 1993 or so, I became aware of what many people had known before, which was that there is a very similar appearing technical problem to do with the cosmological constant. That is, given that General Relativity says that in principle spacetime can curve and does curve, why there is not a huge effect that gives rise to a very very large curvature that would be much more noticeable than any of the gravitational effects that we take for granted. And that the rationale for why such a large curvature should be there had exactly this kind of quantum and relativistic robustness, a very similar feel to it, again, from a technical point of view, to the Hierarchy Problem which in some sense many of us are trained to think in terms of in Particle Physics.

Pavlish:

How did you come across this analogy, this similarity?

Sundrum:

This was, again, broadly known, broadly appreciated. These problems had been massaged and thought about in the more abstracted language of Quantum Field Theory. Off the top, it looks like talking about the weak nuclear interactions is quite a completely different physical regime, a different physical force than General Relativity and the cosmological constant. Evidence has been given from a vastly different scale of distance than where we observe the weak nuclear force. It takes some theoretical massaging to see the analogy between the two. But this had really been worked out by the time I was interested in the problem. The nature of that similarity was old hat. It could be found in review papers and indeed I was greatly influenced by a classic review paper by Nobel Prize-winner Steve Weinberg, on the cosmological constant problem, which many people start thinking about that problem theoretically at least as a result of that review.

Pavlish:

You are speaking about General Relativity now, so you are looking at the cosmological constant from that perspective. But as I understand it, you have been, actually, not using General Relativity in your own work.

Sundrum:

Right. I think that for me, the particular challenge was the following: that, again, when you think in terms of the technical similarities with the Hierarchy Problem, you find that you can in some sense state the nature of the problem in terms of what for us is a kind of ‘lingua franca’ of Quantum Mechanics and Relativity, namely Feynman Diagrams. In Feynman Diagrammatic terms, if that is the right way to think about it, then you see this common strand, the same twist which makes the problem seem fairly tough and robust. So, I sat down, to really just say, look that is how you understand that there is a problem. Even Feynman Diagrams, which again, many of us absorb as textbook material is a fairly sophisticated tool built upon what we would call more fundamental principles like Relativity and Quantum Mechanics. So, I thought, in this particular instance, that if these diagrams were causing the trouble, then I would like to look under the hood of that machinery, the Feynman Diagrams, and see what assumption may have crept in, or what new physics may be going on which would violate the usual assumptions that validate using the Feynman Diagrams.

Pavlish:

If you would backtrack a bit for me here, you are talking about how these diagrams are causing trouble. Are you talking about the problem of reconciling Quantum Field Theory and General Relativity?

Sundrum:

Now, here there is a funny thing. That normally, we say that Quantum Mechanics and General Relativity have a difficult association with each other. We know they somehow coexist in the real world so it is a beautiful puzzle to say: Well, it seems like it is difficult to write down a theory which allows them to coexist. And in fact you do see this directly in the diagrams. Again, the Feynman Diagrams are sufficiently broad and flexible that you can phrase the question: What is so hard about putting Quantum Mechanics and General Relativity together? And rather quickly, with these sophisticated tools you can see what you are up against, you can see what kinds of problems you are up against. And indeed, String Theory is an attempt, a fairly successful attempt in many ways, to try and make that reconciliation work. And you can think of String Theory as in some sense a deformation of those diagrams. That is, there are subtly different rules and you get a Quantum Theory with General Relativity in it. However, the interesting thing about the Cosmological Constant Problem in diagrams is that it appears that the Cosmological Constant Problem is in some sense in a different regime and seemingly disconnected from the problem of putting Quantum Mechanics and General Relativity together. And it can best be phrased in the following terms: that the problem that string theory attempts to answer and that is usually called the problem of putting together Relativity and Quantum Mechanics is one which occurs when the waves, say gravitational waves or electromagnetic waves in the presence of gravity; when the wavelength of the waves is very very small, say ten to the minus thirty-three centimeters or creeping up to that level. However, the problem of the cosmological constant appears when the gravitational wavelengths, that is the gravitational field has wavelengths even when the wavelengths are incredibly large, wavelengths, if you like, approaching the size of the universe. But certainly — already the size of this room. So, it seems like a vastly different regime. Rather, it seems to be sensitive to what matter fields are doing at short wavelengths, at wavelengths that we have already tested. The robustness of the Cosmological Constant Problem in Feynman Diagrams is that these diagrams which are made out of lines and vertices where the lines intersect; it appears that every vertex and every line, that is every ingredient to the relevant diagrams for the cosmological constant has been tested experimentally in some other Feynman Diagram. Okay? Every piece of the diagrams that are relevant has already been tested and tested extremely well. But, when you put them together, according to the rules of Quantum Mechanics and Relativity as summarized by these Feynman Diagrams, you find that in this new combination they seem to spell that the cosmological constant is very likely to be very very large and spacetime is likely to be so curved that neither of us could be sitting here. That was the puzzle for me, which is, how is it that the whole is different from the sum of the parts, each of these parts having been tested so beautifully in some experiment or another. I should say, that is not true of the usual problem of Quantum Mechanics and General Relativity which String Theory attempts to address, is a problem where the relevant Feynman Diagrams that are misbehaving in some way — well, we have never actually gone to those regimes. Even the parts of the diagrams that are relevant have not been experimentally tested. So it is an in principle problem. Just because humans have not tested it does not mean that it has not happened, for example in the Big Bang. So, we really would like to understand it, hopefully to find something that we could predict based on it. But, the cosmological constant problem is even more robust, in my view, because it looks so much like every piece of the diagrams, of the puzzling diagrams, has been tested. What could be missing in how they are assembled? We usually assume that Feynman Diagrams are the answer to the question: how do you put Quantum Mechanics and Relativity together when particles are not interacting with each other too strongly? We think that is what it is doing. So the puzzle for me is what might be missing. And that is the scenario that I was working on. And, in some sense, still am. It was a program.

Pavlish:

Is this a whole research program involving other collaborators as well, looking at the component parts of Feynman Diagrams and trying to reconcile that with the whole understanding?

Sundrum:

By and large it is work that I have done alone in a series of papers. There is one paper which I think really makes it simpler to understand, but sacrificing the exactness of Relativity, which after all is an experimental question. That paper I wrote with my next-door neighbor here, David Kaplan. In fact, that was the one where in some sense we got the closest to saying, well, here is an alternate set of Feynman Diagrams. And you see the little twist that is occurring here. We are sacrificing this sacred principle.

Pavlish:

What is that?

Sundrum:

The principle is, well, in some form or another we call it the principle of relativity, but in a more technical sense it is Lorenz [sp?] invariance. It is the statement that many of us have some familiarity for when we are riding in a train, say. We do not know whether we are moving or the train beside us is moving. So, we usually say, that there is a kind of frame invariance that we have in physics, where a moving observer will in the coordinates that he has, have the same laws of nature written in his coordinates as of the stationary observer. Of course, stationary actually has no absolute meaning given that that is the rule. There is probably slightly more to the principle than just that, but let me stop at that. That is enough to say what I mean. We posited something that again other people had posited for other reasons, but with respect to the cosmological constant we posited that there is an absolute frame that is there. And, again, to a good approximation there is an absolute frame with respect to which motion is measurable in absolute terms. So, only one train is standing still because it is in that frame. This is something that came up early in the history of Relativity and maybe you know it better than I, but when you posit such a thing, you say well, oh, what is the physical property of that special frame? Sometimes the quickest way to discuss it is to say, oh, there is some sort of ether or substance that defines that frame. And of course, there are some experiments that really try to test that hypothesis. But these experiments are performed in a certain regime. By and large, almost all our experiments are frame dependent, so the existence of certain frames involve non-gravitational particles, objects, and so on. And it may be that this ether is something which gravity sees, which gravitational waves see, but to a good approximation is not seen by non-gravitational waves, matter, and particles.

Pavlish:

What are the responses of other physicists in the community to a conjecture like this, to a new ether? Are they pretty receptive?

Sundrum:

I think it is fair to say, I think the quickest way to summarize it is there is a small cult of interest in a sea of skepticism. But, in a way, to be honest, this is probably the right response, because I think there would be great receptivity if one gives a completely worked out model, which means a completely worked out set of Feynman Rules which describe Quantum Mechanics and Relativity in whatever new incarnation you want. The community is very open to crazy ideas in that sense, or at least in unorthodox ideas. But you must show that you agree with the data that has already been taken, that you also agree with some general principles. For example, even though we have not always tested that probabilities always add up to one, I think we take it on faith that that is the meaning of probability. They always add up to one. And in Quantum Mechanics you need to check that the probabilities predicted by these Feynman Diagrams, the quantum probabilities, always add up to one. That is a principle. It has nothing to do with the data directly. So, if you show people that you have got a complete Lego block-like mechanistic mechanism for Quantum Theory that obeys a certain set of rules and agrees with the data, I think people will be less skeptical. For me this is a struggle to try to understand what might be under those Feynman Diagrams, not necessarily to claim that I have a complete theory. I do not. The closest we came is this paper with David Kaplan. There, we pointed out that here are a set of Feynman Diagrams. But there was one part where we could not tell you exactly what the rules were. In a sub-sector, in the gravitational sub-sector. We could tell you why we had something rather than nothing. But, there was some part where we said, you have to give us this black box. You have to give us this black box, which is that General Relativity is an approximation to a theory with a preferred frame. And that is something that other people have studied independently for other reasons and is an ongoing debate. Here is a paper [shows paper] which has nothing to do with us, because we did not do it, but this Higgs Phase of Gravity referred to in the title is an attempt to see whether you can write effective theories, or long wavelength theories of gravity where there is a preferred frame. And this is right up to the minute research. It is ongoing.

Pavlish:

Is that a theoretical paper?

Sundrum:

Yes. These are theoretical papers, because really we do not have any experimental evidence that goes against the presumption that General Relativity is exactly right. So these are theoretical papers. I think this is where, in some sense, the interest and the edge of research is, the edge of theoretical research is. The main ingredient in the paper I wrote with Kaplan, in my view, the main remarkable thing is that you posit that this does make sense: gravity, General Relativity, in the presence of a preferred frame. But then, given that, we show that with that kind of a black box, with a particular incarnation of that kind of General Relativity, that we could make the Feynman Diagrams work in this way. That is, here is a little twist: we are playing by otherwise standard rules, but here is a little trick and it can greatly suppress the previously too large size of the cosmological constant.

Pavlish:

And also make the parts add up to the whole or is that a separate problem?

Sundrum:

In a sense, the way it works there is that the diagrams that you normally draw are a subset. The trick in this particular paper is that there is a hidden sector and there are hidden particles and they give rise to hidden lines and vertices in the Feynman Diagrams and that these hidden contributions are canceling, for a symmetry reason, for some natural reason we can point to, they are canceling the bulk of the contribution that we normally worry about. At least that was the plot of that particular paper.

Pavlish:

And you explain these hidden particles?

Sundrum:

And we explain them. Normally they would be a disaster in that they would allow empty space to suddenly, incredibly rapidly fill up with stuff, and as we know from ordinary experience, this does not happen. The trick was, it is kind of a very very simple plot, yet why doesn’t empty space decay into stuff? That was where the preferred frame of General Relativity plays the key role. It is the only thing that can suppress that from happening. And that was the idea that we really pursued. There was this trick to it, this twist to the story. I think the people who have looked at it would say, look that is reasonable, however, only given this rather big black box of a certain type of General Relativity in a certain type of preferred frame theory. The thing that I think has also attracted some interest in this set of papers that I have been involved with is that they point to an experimental consequence. Physicists, theorists especially, are willing to give some allowance to theoretical ideas that are not fully formed because they are hard problems, if there is also a way of testing them experimentally. An experiment with half an idea is better than having half an idea with no possible prediction. These ideas came with a natural place to look. Not a money back guarantee but at least a very strong implication that Newton’s Law should break down at short enough distances. [is that correctly transcribed?] It is called the one over r-squared law, but it should not be the one over r-squared law for sufficiently small r. [is this correctly transcribed?] That was the prediction. There are experiments that have been going on trying to study Newton’s Law at ever smaller distances. The fact that there is this kind of prediction to it, that even a high school student can understand, this has been something that has also spurred some interest in this. Even people who said, “I am not sure I understand that guy’s whole story,” say “but yeah we can test this. Let’s do it.” I think there have been those two types of interest and that is how things stand.

Pavlish:

You began this research; you said, in 1993 — your interest in the cosmological constant?

Sundrum:

Yes.

Pavlish:

How did the year 1998 disrupt or affect your research in the cosmological constant?

Sundrum:

Actually I should say… you asked about collaborators… there was that year or maybe just the turn of that year, in 1999, a very big effort that I was involved with, with three other collaborators on the cosmological constant problem, in a little bit of an orthogonal direction to everything I have been talking about up until now, but roughly speaking trying to use extra dimensions of space, so again a modification of General Relativity to try and address the cosmological constant problem.

Pavlish:

In light of the new observational evidence?

Sundrum:

For me, none of the ideas I have worked on since 1993 would ever have given an exactly zero cosmological constant. And so there are even ideas I have worked on which never got written up because I was never satisfied, but none of them that I ever obtained would have suggested that the cosmological constant should be zero. In fact, this is a bit of a coincidence, but, how small the cosmological constant could be was always fixed, it was always bounded by how well Newton’s Law had been tested. And roughly at the time that I was interested in this, Newton’s Law had been tested down to distances to the order of about a centimeter. If you converted this to saying: well, what bound is that on the cosmological constant, you found that that was roughly speaking an order of magnitude or so above the scale which was discovered the cosmological constant is and at which Dark Energy was discovered. So, I was always roughly imagining that if my ideas were relevant, that the cosmological constant would be nonzero and roughly in the ballpark of where it happened to be discovered. Now, that may just be a coincidence because gravity tests had pushed Newton’s Law to a certain scale. The 1998 results were exciting in the sense that they were at least compatible with this strain of thought, but theoretically they did not completely blow me away in the sense of saying, “Wow, I was trying all this time to get zero and now I am supposed to get something nonzero.” That was actually quite the opposite. I was expecting to get nonzero and in some sense it is remarkable that you could see such a thing.

Pavlish:

Do you believe that other physicists became more receptive to your ideas as a result of the experimental confirmation or the observational discovery? It had been my impression that in general the physics field just believes that there was no cosmological constant.

Sundrum:

I think it was a bit divided. Let me try and get three strands of the conversation. One was that the extra-dimensional story was played out soon after that discovery. I do not know if you want the names of my collaborators. They are quite famous: Nima Arkani-Hamed, Savas Dimopoulos, and Nemanja Kaloper. Ultimately, we turned to a set of Feynman Diagrams, if you like, but there was some twist that we were trying to exploit. Something we thought was the thing that other people had missed in the general no-go theorems, this loophole. I think generally we feel like, at this point in time we feel like it was a good try but I think we do not buy it. That turned out to have attracted much much much more attention that ideas that I think are still possible, which however have attracted at best minor interest. That finishes that thread. That was certainly where I was, I was at Stanford University, at the time as a post-doc, soon after this came out. It did not greatly affect us because in an odd way, you will understand with some physics education, that when you are faced with a massive discrepancy then you just round off everything and just try to deal with a coarser problem. You are faced with a huge cosmological constant being predicted and you see a small one. Well, small is close enough to zero so that is the way we were dealing with it. Even the ideas we worked on there were suggestive of a small but nonzero cosmological constant. The fact that that is what people saw was good, certainly. The question you had brought up before I tried to finish that thread was… The elephant in the room is that the community prior to that discovery was greatly split by two possibilities. One was that the unreasonable smallness of the cosmological constant consistent with zero up until 1998 was due to a symmetry, which fundamental physics loves, a reason why zero was special. Why a zero cosmological constant was special rather than a positive or a negative one. That was the most symmetric possibility. The problem was nobody actually had a symmetry that could do it. The closest thing was supersymmetry and since we know enough that it is not an exact symmetry in the real world there was no reason why we should get exactly zero. The general belief that the two problems we have discussed — one, the cosmological constant problem and the other problem of putting together General Relativity and Quantum Mechanics at arbitrarily short wavelengths if you like, that they were somehow connected and further progress on the general problem of putting together Quantum Mechanics and General Relativity was key to solving the problem of the cosmological constant. There was among especially String Theorists, or some fraction of string theorists a hope or maybe a belief that that was going to be the case. Again, this is reflected in the Feynman Diagrams because a Feynman Diagram is again a web of lines. And some lines are on the ends of the diagram that is, trailing off of it, and some are internal, that is both ends of the line are attached to the diagram, to the web. At a technical level, the problem that String Theory tries to answer is how to make sense of the diagrams where the graviton line has both ends attached to the diagram. And yet the bulk of the cosmological constant problem comes from where the graviton lines just have one end attached to the diagram and the other trailing off. Apparently there is no very tricky problem understanding what is going on with the diagrams. You were just calculating and getting too big an answer. So it seemed like there were these two regimes of where the graviton lines were. This is more physically said as: is the gravitational field being treated Quantum Mechanically or is it being treated classically with only matter being treated Quantum Mechanically as a crude approximation? The cosmological constant problem already emerges even when gravity is treated classically. Yet all of the efforts of String Theory have been to deal with the case where gravity is treated Quantum Mechanically. So the question was whether the second of these would somehow have some new insight which would solve the first even though it does not seem necessary. That was one half of the thinking. But by that time already, the anthropic principle had emerged (far earlier) and significant people like Steven Weinberg had already taken it very seriously, tried to work out consequences, tried to work out at what scale the cosmological constant would have to be discovered for the anthropic principle to hold water. So there was a second strand of belief or at least tentative belief going on before the discovery. After it, after many years now have passed and developments in String Theory have taken place and we understand how many dimensions [correct transcription?] String Theory allows, and that it allows a large number of possible universes compatible to the anthropic principle, the only thing that has happened is that the belief that there is a symmetry principle has weight in some weird way. The symmetry principle that Kaplan and I wrote a paper about is a modern version of the belief, if you like, in the symmetry principle. But by and large the world does not seem to take the symmetry principle idea too seriously, especially since the symmetry is not exact, it does not give you exactly a zero cosmological constant, apparently. The alternative, which is the anthropic principle view, has taken hold. A lot of activity has been on this front. Its implications go beyond General Relativity, then, to other areas where it might also be at work, where this principle may have something to say. In some sense, that was one of the biggest impacts of the 1998 discovery, is that away with a symmetry that is exact and then maybe the anthropic principle has some merits.

Pavlish:

That is within the theoretical particle physics community?

Sundrum:

I would say that is certainly true within the theoretical particle physics community. Probably, more broadly than that, in my view, the theoretical particle physics community has some of the best expertise to judge that question. I think, certainly, the anthropic principle has caught on with some of the top thinkers in particle theory, and they are quite influential and they may be right. The jury is out. One of the big struggles right now is, “Great, this is happening. How are we supposed to test such a theory?”

Pavlish:

Such as the anthropic principle?

Sundrum:

Such as the anthropic principle. You see, again, whatever attraction there is to some of my more mechanistic modifications of General Relativity to answer the cosmological constant problem, maybe one of the main attractions is, “Yes, there is at least something you are supposed to go and test.” Whereas the anthropic principle, while many people find themselves attracted to it, because it again bypasses all the Feynman Diagrams, in some sense there are whole universes each with its own different set of Feynman Diagrams that are relevant. Most of them predict incredibly large cosmological constants but they also predict that nobody could live there. So, that bypasses the problem of Feynman Diagrams in a clever way. People find that attractive because they find that Feynman Diagrams are more robust, if you like. The tact that is taken has been from both to apply the anthropic principle to non-gravitational phenomena and there, hope to find more accessible experimental implications, say at particle colliders. It is rather difficult to find implications of the anthropic principle directly, as it applies to the cosmological constant. It does not seem to predict something you can go out and check directly.

Pavlish:

Thank you very much for your time, for sharing your expertise.