## Physics for the 21st Century

# Gravity Interview with Featured Scientist Nergis Mavalvala

**Interview: How did Einstein change the way we understand gravity?**

**NERGIS: **Einstein showed us a new way to think about gravity, which is to think about it in terms of space-time and to think of space-time as a fabric or a material that fills all of space. That material can be deformed. Einstein called it the “warpage of space-time.”

What can warp this space-time fabric? Mass. Heavy things can warp space-time fabric. One nice way to think about this is if you think about space-time as the surface of a cushion and so it’s nice and flat and stretched out, and now imagine you put a big, heavy bowling ball in the middle of it. What happens is your cushion deforms with a lnearittle dip in the center. Now, if you take a little plain marble and put it at the edge of the cushion, it’s going to fall in towards the bowling ball; it’s going to get attracted to the bowling ball.

Really the way that attraction happened was that the bowling ball caused the cushion to deform in such a way that the little plain marble had to fall in towards it, and that’s Einstein’s picture of how space-time works and that sort of, in some ways, got rid of this question of how does the plain marble know that the bowling ball is there? It knows that because the bowling ball deformed the space-time around itself. So that’s how our modern picture of gravity works.

**Interview: Is the “warpage” of space-time observable?**

**NERGIS: **Let’s take that analogy of the bowling ball. So you think of this bowling ball and imagine you now start bouncing it up and down. What would happen is the surface of the cushion not only deforms in towards the bowling ball but you also get little ripples on the surface of the cushion moving out away from the bowling ball. So not only does mass deform space-time or warp space-time but you also get waves on this space-time fabric due to the motion, the accelerations of massive objects. If you are now this little plain marble at the edge of the cushion, those ripples will come by and jostle you. That’s also the way in which we can detect a passing gravitational wave.

**Interview: What are gravitational waves?**

**NERGIS: **Gravitational waves are associated with the dynamical part of this space-time warpage that we’ve been talking about. The idea there is that if you put a massive object in space, it will deform the space around it in terms of making a curvature down into the space-time fabric. Now, if you take that same massive object and you vibrate it such that it’s deforming the space-time but in a time dependent way, so as it vibrates it’s making those vibrations get imprinted on the space-time fabric, that would then make a gravitational wave. As that wave radiates out from the massive object that’s accelerating it really arrives to us, as an observer, as a wave that’s propagated out from a source. It’s very similar to visualizing when you drop a rock in a pond and a ripple radiates out from where the rock was dropped. If you were a little boat or a little bug on the surface of the pond a little ways away, you will get jostled by the wave that comes by.

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

**NERGIS: **An area of great interest is gravitational waves themselves. Einstein predicted them. He also worried that they were so tiny that they would never be observable. Direct observation has eluded us for the last century since Einstein. So since the last 90 plus years, since Einstein first formulated these, there is indirect evidence of these gravitational waves. But, certainly we can’t say we’ve directly gone out there and measured a gravitational wave interacting with a detector that was designed to measure them.

**Interview: What are the implications if you are able to detect gravitational waves?**

**NERGIS: **There are two things that we dream of when we think about directly detecting gravitational waves. The first is that the systems that radiate gravitational waves—that are strong enough for us to detect in our detectors—should involve strong field gravity. This area of Einstein’s general relativity that’s been hard to measure any other way. The other part, which I think is just as exciting if not more, is to be able to do astronomy with gravitational radiation. Once you start detecting the radiation from these sources you learn a lot about what the emitters are and what kinds of sources emit these gravitational waves. There are certain things that one really can’t get at in any other way, which makes direct observation of the gravitational wave very attractive.

**Interview: What is LIGO (Laser Interferometer Gravitational-Wave Observatory)?**

**NERGIS: **LIGO itself, as a project, formed in the 1980s as a partnership between Caltech and MIT. And then in the early ’90s people started lobbying for these four kilometer-long detectors to be built. In the mid to late 1990s, the construction on those detectors began and was completed in ’98/’99, from which time onwards we’ve been putting in the detectors, making them work. Of course, there hasn’t been any detection as yet with that data but we’re still working on that and the detector is getting more sensitive.

**Interview: What are the results for Initial LIGO?**

**NERGIS: **Initial LIGO, so far in the data that we have analyzed for various kinds of sources, there have been no positive detections yet. In other words, there hasn’t been some signal that survived all of our tests to say okay, this was really from a gravitational wave source in the sky. If you build a detector that has better sensitivity and the difference in sensitivity between Initial LIGO and Advanced LIGO is about a factor of 10—so you have 10 times better sensitivity—in principle, you can see a source that’s 10 times weaker if it were at the same distance.

**Interview: How do you measure a gravitational wave?**

**NERGIS: **One of the ways, a fairly sensitive way, in which one can measure a gravitational wave is using a laser interferometer. To see how laser interferometers can be used to measure gravitational waves, the first question we have to ask ourselves is what does a gravitational wave look like to us as an observer? The gravitational wave, once it’s emitted by the source, as it travels through space, is really warping the space-time. It’s shrinking and stretching the space-time perpendicular to its direction of motion. So, if there is a gravitational wave going in this direction here, as it moves through space-time, it actually shrinks and stretches the space-time. It’s literally doing that.

**Interview: How does the interferometer work?**

**NERGIS: **The way that the laser interferometer works is that you start with a laser beam and use a partially reflecting mirror—it’s called a beam splitter, which can take half the light and reflect it, and half the light and transmit it. So, now you have these two light beams that are going at right angles to each other. Now, imagine that some distance away you put two mirrors that reflect those two light beams. Then the light beams reflect off those mirrors and they come back to the beam splitter. Now comes the crux of an interferometer, which is interference. That’s where the word interferometer comes from. So, those two light beams interfere on the beam splitter. The way that you can think of that is that the light took a certain amount of time to travel along one arm of the interferometer, reflect from the mirror and come back, and the light on the other arm took some different amount of time. Now, when they return to the beam splitter, you can see that there’s a phase shift between the two lights beams because they took different amounts of time to return to the beam splitter. We can measure that via the interference pattern that appears on the beam splitter.

**Interview: What is wave interference?**

**NERGIS: **Interference is a phenomenon that’s associated with all waves whether it’s a light wave or a gravitational wave or a water wave, one can have interference. When you have two waves—let’s think of them very simply as little sinusoids. Imagine you have this sine wave in space and imagine now that you had some way of adding a second sine wave to it. In the case of our laser interferometer, it’s quite easy to see. You have the wave coming from one side of the beam splitter and you have another wave coming from the other side of the beam splitter. The beam splitter has this very nice property that it can add them or subtract them. So, now if you take these two sine waves, you can add them in a number of ways. The simplest way you could add them is… They are completely in phase so all the peaks line up on top of each other. Now, if they’re completely in phase and all the peaks line up on top of each other, you get a bigger wave than each of the waves alone, and that’s called constructive interference. You are interfering the waves so that they add up constructively. Now, you can also make a wave where all the peaks don’t exactly line up and if you now add them up, the peaks subtract with the valleys and you get nothing; you get destructive interference. So, that’s how one understands interference. It’s basically an addition of two waves and you can arrange the phase with which they add so that they can either add up completely, subtract completely, or everything in between.

**Interview: Describe the LIGO interferometer?**

**NERGIS: **Let’s imagine for a moment that we were actually looking at it from an aerial view. What you see when you look at it from outside is a big central building and then at right angles to each other coming out of that big building are two arms. We call them arms; they’re basically concrete enclosures that run for four kilometers. It’s like a tunnel. It’s a concrete tunnel that runs for four kilometers in one direction and then, at 90 degrees to it, it runs for four kilometers in the other direction. It’s big. It’s about a little bit over a meter in diameter and inside this stainless steel pipe is a vacuum, so outside is air and inside is vacuum. The light itself travels in those beam tubes that are a vacuum on the inside for four kilometers. Four kilometers away are two other buildings in which are vacuum chambers, which house the two end mirrors of the interferometer. The light travels out, reflects from those, and comes back to the central building. We detect the interference pattern that happens on the beam splitter. That interference pattern is just another light beam. It comes out of the vacuum through a glass window and then we detect it on a photodetector, and that’s a very simplified version of what really happens in there.

**Interview: When the laser light comes back to the beam splitter what do you measure?**

**NERGIS: **What are we really measuring? The interference pattern that we really measure is actually the intensity of light. If you have completely constructive interference you have a very bright beam at the output of your beam splitter. If you have completely destructive interference you have a very dim beam at the output of your beam splitter. That depends on the position of the mirrors off the interferometer. When we measure the brightness or dimness of the interference pattern that’s a direct measure of the position of the mirrors, of the path that the two light beams have to travel and return on. It’s essentially just a light beam whose brightness or dimness is proportional to the position of the mirrors.

**Interview: How do you measure the interference pattern?**

**NERGIS: **We take that light beam that’s coming off the beam splitter and we let it shine onto a photodetector. Now a photodetector is a device that takes light or photons and converts them into electrons, which is current. What we are really doing in the end is we are actually measuring a current that’s proportional to the light beam that hit the photodetector. We turn that current into a voltage and we could just simply put that out onto an oscilloscope and measure a voltage that’s proportional to the position of the mirrors because the interference pattern arranges that for us. So really in the end, we’re measuring a light beam that translates into a current, which we turn into a voltage. Then we could put it on an oscilloscope, but what we really do is take that voltage, turn it into a digital signal, store it on our computers, and then analyze that signal for gravitational wave sources.

**Interview: On what scale are you measuring these displacements?**

That is actually perhaps the most mind-boggling number of all the numbers that I have every encountered. What we are really doing is—the laser beams travel for four kilometers down to the mirrors and come back and the measurement that we’re ultimately making—measuring displacements of about 10^{-18} meters. The relative displacement of the two mirrors even though they’re separated by kilometers is 10^{-18} meters.

**Interview: What is your current research focused on?**

**NERGIS: **My most recent research has been in an area that sort of spans quantum optics and quantum measurement. It’s completely driven by the desire to make more sensitive detectors for gravitational waves. So, if you look at LIGO, where it’s operated in the last few years and where it’s going to be in the next few years, very quickly you realize the limits to detecting gravitational waves using these laser interferometers is the quantum nature of the laser light itself. The quantum mechanics of light is the fact that light is composed of photons. The accuracy with which we can measure the phase of light is limited by quantum mechanics. That has led me to start looking at ways to do better and that’s really what my research is about—how to do better than the simple quantum limits set by light.

**Interview: What specific experiment are you working on right now for LIGO?**

**NERGIS: **One of the experiments that my fabulous graduate students and I have been working on for the last few years, is we have built an experiment that mimics some of the conditions in Advanced LIGO, so the next generation of LIGO detectors that we expect to be starting in 2011.

**Interview: Describe your experiment.**

**NERGIS: **The experiment that we’ve built here essentially has a very powerful laser that hits a very small, light mirror. The LIGO mirrors are large; they’re about the size of a dime and they weigh 10 kilograms—in Advanced LIGO they weigh 40 kilograms. Here we have a one gram mirror and that one gram mirror is hung from a pendulum like the LIGO mirrors are so it’s free to move when it’s being bombarded by photons. We have a very intense laser beam that is reflected off of this light, one gram mirror and then by measuring the motion of this mirror we can reconstruct the quantum properties of the photons that are hitting the mirror. That’s one aspect of the experiment that we’re doing here and it’s important to do because we expect that same effect to be a limit to how well advanced LIGO can do. If we could measure it and then think of clever ways to improve it… We hope to be able to make improvements to the advanced LIGO detector or beyond, the next generation after those.

**Interview: What is the goal of the mini-mirrors experiment?**

**NERGIS: **The goal of the mini mirror experiment is to be able to measure directly through the motion of the mirror this quantum radiation pressure noise.

**Interview: Why is there a need for the mini-mirrors experiment?**

**NERGIS: **In Advanced LIGO we expect, at most frequencies where we’re trying to measure gravitational waves, that the measurement of gravitational waves will be limited by the quantum mechanics of the light, the fact that we have these fluctuating photon numbers. So really part of the motivation of the mini-mirror experiment is to explore ways to do better than that. How do you take this photon number fluctuation and manipulate it so that you can improve the sensitivity of advanced LIGO? That’s really part of what we’re trying to study in the mini mirror experiment.

**Interview: What is the Heisenberg Uncertainty Principle?**

**NERGIS: **So, here is a nice way to think about what quantum mechanics says versus classical mechanics. In classical mechanics you would be able to know perfectly well that the particle is located at this position and has this momentum. Quantum mechanics says nuh-uh; you can’t do that. You have uncertainty in your measurement of what the particle’s momentum and position are. This is actually one of the building blocks of quantum mechanics. It’s also the thing that many students and scholars and physicists in general struggle with. It’s one of the things that distinguishes the quantum world from our everyday classical world. The statement of the Heisenberg Uncertainty Principle is straightforward and the ideas that led to it are much harder to wrap our heads around. If you have a particle and you know the position of the particle very, very well, so you know exactly where it’s located in space, then you can’t know very well it’s momentum or its velocity.

**Interview: What is radiation pressure?**

**NERGIS: **Radiation pressure noise is another manifestation of this fluctuating number of photons and it comes about because the photons carry momentum and that momentum is imparted to the mirror when the light reflects off of it. Now, if the number of photons is fluctuating, then you will also get a fluctuation in that momentum, because the number of photons hitting the mirror is fluctuating and the intensity of the light fluctuates. That is what we call radiation pressure noise.

**Interview: What is squeezing light?**

At the heart of thinking about squeezed light, we have to understand first the Heisenberg Uncertainty Principle for light. The Heisenberg Uncertainty Principle applies to a number of different quantities that are used in the real world, in the measurement world. We already talked about the position and momentum of a particle. Now, there’s an equivalent Heisenberg Uncertainty Principle that arises from energy and time, which are also two quantities that you can’t measure perfectly well simultaneously. If you think about this in terms of light, what it basically says is that the energy that a laser beam carries is proportional to the number of photons and if you know exactly how many photons you have in a light beam, you can’t know perfectly well when they arrive.

**Interview: How do you reduce the uncertainty of the position and momentum of light?**

**NERGIS: **In the case of our interferometers in LIGO or even in our radiation pressure experiment, you can ask how the quantum uncertainty of the light enters the measurement. When we measure our interference pattern, we’re measuring the number of photons, and so the quantum uncertainty in the number of photons inherently puts a fuzziness on the position of the mirrors, which the phase of the light measures.

**Interview: How do you apply your data from the mini-mirrors experiment to Advanced LIGO?**

**NERGIS: **Well, ultimately what we’re trying to do is to understand how much noise there is and to test certain techniques for removing it from the detector whether it is using squeezed light or other ideas that I haven’t talked about. That’s what we want to do in the mini mirror experiment. We want to first show that the mirror is being driven by these quantum fluctuations of the light and then to test ideas for how to reduce those fluctuations.

**Interview: Would you spend your entire career looking for gravitational waves?**

**NERGIS: **I really do feel like I could spend my entire career working on this. It would be absolutely fantastic if we detected a gravitational wave this year or next year, but I think in the next decade we certainly will. If we don’t, we have learned something very, very important about nature. The payoff will be enormous regardless. If we really start detecting gravitational waves routinely, then we’ve opened a new window into the universe, and if we don’t, we have set off a new direction of head scratching as to what is it about nature we don’t understand.