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**Interviewer: What motivated the beginning of the Eot-Wash group?**

**ERIC:** The question of what’s called the “Principle of Equivalence.” Do all materials fall with exactly the same acceleration in a gravitational field? And, we sat down and designed an apparatus. None of us really had ever done a gravitational experiment before. And, that was a very good thing it turns out. It was very fortunate, because we didn’t know the standard way of doing things. And so, we came up with our own ideas. And, that turned out to be very fruitful. We still profit today from these insights we had in the very beginning. We found within eleven months, we had cobbled together an apparatus. Then we applied for money from the National Science Foundation and at first they said, “Well who are these guys?” They don’t know anything. They’re not gravitational physicists.” But the fact that we had published a paper helped. At any rate, they said, “We will support you.” And, “How long do you think it’s going to take?” We thought, well, maybe three years at most and this field will be exhausted. But, we kept on finding new questions. Theorists came up with new scenarios for something new. And we could test it, it was fun, and we could get good students. Since this process just continued this way for twenty years, we’ve been able to do new kinds of experiments in gravity and develop the technology of torsion balances to a whole new level. So, it’s been a great experience and fun for us, fun for the students, and interesting to the general theoretical community as well.

**Interviewer: What is the motivation for your research? **

**ERIC:** One reason that these experiments have turned out to be so interesting over a number of years is that there’s a big problem in physics that’s not solved yet: connecting gravity to all the other known forces in nature. All the other forces in nature, we explain in terms of quantum field theories where the uncertainty principle allows a particle over here to exchange a particle over there and influence its behavior over there. And then, we have a theory of how gravity works. It’s Einstein’s general relativity, which has to do with energy and mass curving space-time and objects freely falling following the shortest path in this curved space-time. These are two completely incommensurate ways of looking at the world. They are inconsistent with each other. They each have their problems. Unifying gravity with everything else is a kind of a Holy Grail for fundamental physics. And so the ultimate goal of course is to have one theory that explains everything, including gravity, including strong interactions, including electromagnetic interactions, including weak interactions. So, this goal is a very compelling one, and certainly to me, because it’s hard for me to believe that quantum mechanics doesn’t operate in the gravitational realm as well as in everything else. The interesting thing is: because we have reasons to think maybe general relativity isn’t the final story on gravity, people have speculated about possible experimental ways to see that something is wrong—or not completely accurate—with the conventional picture of gravity. We will take the things we believe in our hearts ever since we learned physics, the inverse square law, the Principle of Equivalence—that are very, very important, very consequential ideas— and we will just test them to the best of our ability in the hope that maybe there will be something new there, which many people have suggested. Or, perhaps, we will just put physics on a firmer foundation. In either case, we’re doing a useful and important science. Of course, it would be extraordinarily exciting if we could find violations of these principles that we’ve all accepted for many, many years.

**Interviewer: What motivated your first inverse square law experiment?**

**ERIC:** We heard a physics colloquium from another theorist, Nima Arkani-Hamed. And he was trying to come up with an explanation to: Why is gravity so weak compared to everything else? If you want everything to be unified, you have a great problem explaining why one thing is depending how you measure it—thirty-nine powers of ten weaker than another. How could they come from the same thing if they’re so different? And, he had a very clever explanation of how this gravity could be so weak. And it used the ideas of string or M theory, which have extra dimensions. He came up with a plausible scenario that would explain the observed weakness of gravity. By saying, it’s actually not weaker than anything else. It just looks weaker than everything else because the lines of gravitational force, so to speak, can escape into these extra dimensions. His explanation was that gravity appears so weak, because most of its strength resides in places we can’t go. And the test of this is, very simply, to study the interaction between two point masses, as you bring them closer and closer and closer together. You get them sufficiently close so that their separation is comparable to the size of these extra dimensions.

**Interviewer: Why can’t we see these extra dimensions?**

**ERIC:** These dimensions are curled up. They’re not like x, y, and z. You can go forever along the x-axis and never come back to where you start—with these curled up dimensions, you can go forever. You keep on coming back to where you start. That’s a property of the extra dimensions that people suppose in order to hide them. If they were like our ordinary dimensions, we could say they’re nonsense. Your ten space dimensions, it’s nonsense. But, if seven of them are all curled up, then that’s not necessarily nonsense. It could be real. And this intrigued us that here was such a direct way of testing the real geometry of the world in a plausible scenario for how gravity could be so weak. And, in fact, he proposed a particular case where you would find that the inverse square law would break down for distances less than about a quarter of a millimeter. And, you would find gravity suddenly got much stronger than you would have expected if Newton were right. So, that was an interesting scenario. And, we thought this is something we really want to test.

**Interviewer: What is a torsion balance?**

**ERIC:** It’s useful to get some idea of what the scale of the experiment is. So, the detector pendulum has a diameter, which is about the width across my fingers here. The thing weighs about thirty-five grams. It hangs from a fiber, which is twenty micrometers in diameter. That’s maybe a quarter of the diameter of a hair on your head. It’s about a meter long. And, underneath this detector pendulum, there is—very tightly stretched—a beryllium copper foil that is ten microns thick. That’s about an eighth of the diameter of a hair on your head more or less. And immediately underneath that about a few microns away is this rotating attractor underneath.

**Interviewer: Describe your first inverse square law experiment.**

**ERIC:** So, for our first experiment on the inverse square law, we sat down once we decided to do it, which didn’t take very long since we heard that colloquium and we said, “this is what we want to do.” We tried to think how you could do it. We wanted the frequency to be different than the frequency of the disturbance in the experiment, because that helps separate what you’re looking for from systematic problems. And, we knew that we had to have a conducting box around our torsion pendulum detector that prevented it from seeing the attractor. We knew that other people hadn’t done that in their tests. But, we knew that if you wanted to get the shorter and shorter distance, this idea of having a conducting box, a conducting shield around your detector is very important, and becomes more and more important as you want to study smaller and smaller length scales. Electrical problems get worse and worse as you look at smaller and smaller scales. So, we said, “we need to have a conducting membrane in there.” The easiest way we could think to do that was to have it horizontal.

**Interviewer: How did the membrane affect your design for testing the strength of gravity?**

**ERIC:** How can you get something to twist the torsion pendulum? We came up with the idea of the holes—something that is cylindrically symmetrical, sitting above a cylindrically symmetrical attractor that rotates steadily. And then, in that case, if it’s cylindrically symmetrical, the only thing gravity can do is tug straight down. It can’t twist this object. But then, if you put holes in this cylindrically symmetrical thing and in this cylindrically symmetrical attractor underneath, gravity now can twist the pendulum. And, that was an attractive idea because we could make our test bodies essentially the holes in these things. They were like thin cylindrical pucks, flat pucks. And with flat objects, you can get the most amount of matter in close proximity to another flat object. If you have spheres, they only touch in one place. But, if you have flat things, they can touch all along their surface. So, that seemed like a good idea to us.

**Interviewer: What else did you test for? How do you test for new physics?**

**ERIC:** Another idea was to cancel Newtonian gravity to a pretty high degree without losing our sensitivity to new physics that happens at short distances—new forces that only work over short distances. The way we did that was we made our attractor have two parts, one with a set of holes and one below that was thicker. The holes were just halfway in between the other holes. The idea was that there would be a Newtonian twist on the detector. Suppose we had ten holes, which is what we had in our original pendulum, ten holes equally spaced around the circumference and the attractor had ten holes. If you measure the torque on this—the detector with ten holes—as the attractor rotates around underneath, it’s going to wiggle back and forth ten times per revolution of the attractor. So, we have a signal that wiggles back and forth exactly ten times for every revolution of the attractor. Now, what we did was we made a second attractor—part of the attractor underneath, as holes lay exactly halfway in between. And, it was thicker. And, the holes were bigger. And, it was designed so that if Newton were right, the torque on this detector that had ten times the frequency of the rotation would just be canceled by a equal magnitude, but out of phase torque from the bottom holes. So, that was our trick so to speak. And then, we would just measure the torque as you changed the vertical separation between the detector and the attractor. And, see if it behaved the way it should if Newton were right.

**Interviewer: Can you describe how you measure the gravitational attraction between the two discs of the torsion balance?**

**ERIC:** I will try to show you with my hands how these holes can apply a twisting action to the pendulum. A twisting action we call the torque. Suppose my fingers represent where holes are on the detector. The fingers of this hand represent where the holes are on the attractor. Whenever the two holes line up, so the one set is exactly below the other, then gravity again can only pull it straight down. Why would it twist it this way rather than that way? There’s no way to distinguish. Similarly, when the holes are exactly in the spaces, again the—why can it twist it one way rather than the other? It can’t. It’s problems start to be symmetrical. There’s no reason for it to twist counterclockwise or clockwise. But, at any other point, gravity is going to try to line things up. Gravity, as the attractive interaction, is going to try to line up the holes in one with the holes in the other. And, since it tries to line them up, the only way it does that is by twisting the torsion pendulum. That twisting action winds up the torsion screen a little bit. It deflects the torsion pendulum slightly, and we measure that angular deflection by shining a laser beam off mirrors mounted on the pendulum. See how the beam come off at a slightly different angle? We measure that angle. We measure it, with the precision of about ten to the minus nine radians. That’s quite a small angle. I like to tell people how small it is. If you have a friend, and she holds up a millimeter vertically in San Francisco and you’re here in Seattle. And somehow, you can see through the curve of the Earth so you can see her holding this little millimeter up. The angle that millimeter would make in your eyes is about a nanoradian. So, we’re measuring torques with a precision of a fraction of a nanoradian. When I say measuring torques with a precision, we’re really measuring angular deflections. And, that angular deflection times the torsion spring constant is a torque.

**Interviewer: What are the results your inverse square law experiments?**

**ERIC:** Our latest published result says that the inverse square law holds down to a separation of fifty-six microns. That’s smaller in diameter than the hair on your head. With ninety-five percent confidence and the largest that an extra dimension could be is forty-four microns. That’s the important bottom line. We know the inverse square law now works down to that distance, and that any extra dimension has to be smaller than forty-four microns. That’s an interesting number, because this whole notion of extra dimensions not accessible to the ordinary world has been used to explain all kinds of things. But the smaller you make them, the less dramatic effect they have. It’s also useful to know that people are trying other ways to test these ideas— other than the direct mechanical experiments we’re talking about such as proton-proton collisions in Geneva.

**Interviewer: What is your motivation for measuring the inverse square law at even shorter distances? **

**ERIC:** We have a new carrot in front of us to aim for. Another theorist came up with an idea to explain the dark energy. The dark energy is a kind of repulsive gravitational effect. The Universe’s expansion is accelerating rather than being slowed down by gravity as we’d all assumed it would be. And, it turns out that actually in Einstein’s general relativity, there is a way to get a repulsive effect on gravity. And it’s if you have a system with an efficiently negative pressure. That’s one statement. And, the second statement is the quantum mechanics predicts there should be something with a very negative pressure. That is the vacuum energy associated with all the fields of quantum mechanics. You may know that the uncertainty principle in quantum mechanics says if I have a mass on a spring oscillating, and I cool that thing down to absolute zero, it doesn’t ever go to rest, because the uncertainty principle forbids something from having a definite location and a definite momentum. So, that even at absolute zero, the oscillators are all jiggling around. Now, this is an analogy, which the uncertainty principle applies to all kinds of things, including the electromagnetic field, that even at absolute zero, or in other words, even in a perfect vacuum, there is still energy. Quantum mechanics says there’s still energy there. And, that energy turns out acts like a negative pressure also. And so you say, great. We’ve observed a negative pressure. And, quantum mechanics tell us there ought to be such things there. The only problem is the magnitude. The one we observe is depending how you figure it. You know a hundred powers of ten weaker than what the quantum mechanics would say. And, people have tried to solve this problem. It’s a very important problem. It’s called a cosmological constant problem. You might be able to solve it, if gravity became very weak at short distances.

**Interviewer: Why would gravity become weak at these short distances?**

**ERIC:** If gravity became weak at short distances, the properties of the graviton—the particle in the strength area that explains gravity, these big floppy gravitons—couldn’t see all of the short distance physics that was happening inside them. And, that’s where most of these hundred powers of ten comes from—things at very, very short distance fields. So, he predicted that we ought to see gravity getting weak at short distances. And, his argument was, for this to work, that it had to happen at least by twenty microns. And, it’s nice to have some kind of physically motivated goal to shoot for.

**Interviewer: How did you upgrade your torsion balance?**

**ERIC:** It was simply to arrange—instead of having holes—we would have wedges. The argument there is: What you want is the biggest change in the area of overlap for a given angle change between the detector and the attractor. Because, as the attractor rotates underneath, what you want to see is that the energy, the gravitational energy of this system. How rapidly does it change as you change the angle of the attractor underneath? We wanted to make that as big as possible. The way you make it as big as possible—keeping the same general strategy of the ten-hole experiment and the forty-two hole experiment—is by instead of having holes, having wedges. And now, we have a hundred and twenty wedges. Our objects are now like one millimeter thick, but one-twentieth of a millimeter thick. So all the scales are finer, which is suitable to looking for shorter length scales. We’re trying to push shorter length scales.

**Interviewer: What factors limit the distance you can measure the inverse square law?**

**ERIC:** One of the things that sets a limit on the minimum separation we can get between the detector and the attractor is the fact that there’s a foil in there. Another limitation is the fact that the ground in any laboratory is constantly shaking up and down. This torsion fiber is very stiff against stretching, but it’s still a spring there. So, the pendulum typically is bounding up and down by a few microns just from the ground shaking. And it’s interesting to notice that most of the vertical accelerations of the lab are due to human activity, cars and trucks. We’ve measured this vertical bouncing as the function time of day. Here in Seattle, it doesn’t stop until about midnight. And, it starts up at about five in the morning. So, you know it’s clearly human activity.

**Interviewer: Are there other factors beside human activity that limit the separation you can measure between the two discs?**

**ERIC:** Seismic activity is one limit. That prevents how close we can get the detector to the foil. Another limit of course is dust. If you get any dust in there, you will never get to the very close separations that you want. For two reasons; the dust physically can prevent you from getting there. And, the dust is also an insulator, dielectric. It’s charged up and makes the electrical fields that mess you up. So, cleanliness is indeed next to Godliness in this kind of an experiment.

**Interviewer: What is the size of a dust particle that can limit your experiment?**

**ERIC:** We’re talking about one little mote of dust. Not a collection of stuff, but just one little particle. It’s a few microns. We try to keep it as clean as we can.

**Interviewer: What type of environment are the experiments conducted in?**

**ERIC:** These are all done in a quite a good vacuum. In fact, you know we have surfaces very close together in there. We’re trying to get to minimum separation. And, the pressure is what you call viscous drag—the thing that makes a shock absorber resist, or the thing that an airplane has to fight passing through the atmosphere. The viscous drag is essentially negligible. So, there’s low enough pressure that the viscous effects are negligible. The dominant losses in the system are actually in the metal of the torsion fiber itself.

**Interviewer: Do you have any predictions for the results of the wedge pendulum?**

**ERIC:** And, what the answer is, I have no prediction. I would love that if we found something. Obviously, that would be profound. I can’t imagine the more exciting discovery than finding that the world really has more than three dimensions. I mean that’s a fantastic thing. It would be a fantastic boost for string theory too if we found it. If we don’t find them—that doesn’t mean the string theorists are going to fall on their swords.