In today’s blog we talk to Dr. Silke Weinfurtner of the School of Mathematical Science of the University of Nottingham, PhD at Victoria University of Wellington, on exploring quantum fields in curved spacetime via analog black holes.

**David**: Is there room for creativity in your experimental setup or is it fairly standard and constrained?

**Silke**: There is a tremendous amount of creativity. If you’re trying to mimic a black hole process in the lab, you do have a lot of choices to make. You have to make the choice of which medium to use. You need to find a system that you can manipulate in a certain way. I can choose classical fluids depending on what I want to see. I can take superfluids, optical systems, and so on. So usually people will be drawn into the field from a particular area, like superfluidity, or optics, and they would of course use that system. Also, how you set up this experiment and how you make it work, and how you extract the information, all of this is something you choose. There are many choices to make. We are trying to make a range of abstract idea turn into reality. It’s the same as if you take an artist who has to take a medium like paint or shaping something out of stone, or whatever, you need to find a medium in which you get the message across. And I would almost see it in a similar way. And that’s how I see the creativity in that.

**David**: How are the waves that reach the boundary of your system connected to what falls into the sink to mimic something like the conservation laws in Hawking radiation?

**Silke**: What black holes really are is amplifiers. They take the quantum noise, the quantum vacuum, and they turn that into this Hawking radiation. They are amplifiers for quantum fields. They can also amplify classical fields around black holes. It’s just that for a gravitational black hole we don’t believe that there are suitable signals, classical signals that would be amplified. In this analog situation it is different. You have to see what is really going on around the analog black hole. And let’s assume, for example, that I can change the temperature just as I like. Say, magically, if I change the temperature of my fluid so that it would turn into a superfluid that wouldn’t freeze. And if you have it at room temperature you could, as we did, create signals. You could send monochromatic waves into the black hole. You could stimulate the system. If you don’t do this you would have classical noise. That’s noise from vibrations from the pump or vibrations from the room, from the bathtub. You would have fluctuations in your system which makes things messy. The surface is not completely still. If you reduce those. let’s say you do a very good job in noise isolation, you would have thermal noise. A thermal spectrum in your system and your analog black hole would perhaps take those. And if you further eliminate the thermal noise in the system, you cool it down more and more, then at some point the thermal noise is much suppressed and only quantum noise in the system is left over. The surprising thing is that Hawking radiation does not care what signal it amplifies. What you don’t get is entanglement or intrinsically quantum features. So there is a difference in the radiation created. So what is this negative energy? The background has an energy which is not its zero energy and then there are some signals that can increase or decrease this background energy. And negative energy simply decreases the overall energy to the background flow.

**David**: You mimic horizons but you can also mimic the ergosphere. Would it be possible and useful to mimic spacetime more rigorously such as the instability of orbits?

**Silke**: The ergosphere is easier to reach than the horizon. What you need for the ergoregion is that the total flow velocity, the radial and the angular one, exceeds the propagation speed of the surface waves in our system. And so it’s easier because you use the total flow velocity and the black hole horizon is where only the radial velocity component of the fluid flow exceeds the ripple speed. So in this sense, ergospheres are very easy and straightforward to set up and you can set it up in your kitchen sink or bathtub flow. The whole point is not to mimic exactly a particular spacetime geometry. In fact, we cannot. We could mimic part of the Kerr solution but the problem is the angular momentum has a different fall off when you go away from the analog black hole. It is intrinsically different and you would have to use a very complicated system to exactly mimic the gravitational field. So it’s not about setting up a specific gravitational spacetime geometry. What you want is something that has the necessary horizon structure. For Hawking radiation, it’s just the gravitational field at the black hole horizon so it’s a local thing. So it’s not a quantity that depends on the exact shape of spacetime. It’s a local quantity that is defined by the surface gravity at the event horizon. So you have a scattering process but it all depends on the properties at a single sphere.

**David**: And the nearby spacetime doesn’t influence that.

**Silke**: Exactly. That is the real thing. Actually, that is not quite true because there are these graybody corrections. Some things scatter back out. But analog gravity can determine how important these deviations are. But the theory is that quantum fields couple minimally to gravity. At high energies people in quantum gravity will say that there is an overarching quantum gravity theory that takes over and quantum field theory in curved spacetime should not be valid. So you should doubt derivations based on the assumption that what you get is valid at all energy scales. In the analogs, things are exactly like that. If you go to smaller and smaller energy scales, the things looks completely different. You have water molecules, your theory has higher order corrections. And what is nice is that they don’t matter. The Hawking process does not depend on those so there’s a certain robustness. Analog gravity gives an experimental component to a theoretical field and abstract ideas become reality. That’s what physics is really about.

**David**: In thinking about making abstract ideas become reality, in astrophysics there is a very contentious topic which is measuring black hole spin. Could superradiance from accretion disk radiation become a tool to measure spin?

**Silke**: With quasi-normal modes, black hole ringdown, if you get a signal, then you can infer the black hole geometry. If you have a theoretical model that predicts a certain superradiance spectrum, and I measure a spectrum, can I invert that and infer the angular momentum? It doesn’t necessarily always work but you get some information. It depends on how many free parameters there are and your theory but it’s possible. We did something like that for black hole ringdown which was really beautiful because there you can say that you can really test your theory. We calculate the ringdown spectrum and then we make the measurements and see which is the right theory to use. And for this there are free parameters like the angular momentum. When I look at superradiance it means I send something in and get more back. The particle current has increased. But I need to know what I sent in. And that’s a hard thing. When it comes to black hole ringdown, it doesn’t matter what the initial signal was. The same frequencies will be excited. The decay does not depend on what perturbed it. So these are characteristic modes of that system. Of course, if you have very high control of what you sent in then yes.

Whenever we do an experiment, there is a beautiful additional feature which we have. We can measure at every point around our analog black hole. This is almost as if you had gravitational wave detectors fully around the black hole. And this allows us to distinguish between different azimuthal numbers. One of the big advantages in the analogs is the access you have to the system. You can stimulate it. You can interact with it. You can also look in so many places. We use optical techniques to have thousands of points around the analog black hole. So we can extract so much information. We can do wonderful signal processing. And something that looks like noise can become a clear signal. And this is something that is very hard with a quantum system because you cannot interact with it in the time domain. When you interact with a quantum system, you change it. The information you get back is very sparse, which is why the classical experiments give you a different insight. Although in a quantum system there is additional physics, there is less interaction with it.

**David**: Could counterrotating disks generate less amplification compared to prograde disks and could this be used to infer bulk differences in black hole accretion?

**Silke**: Superradiance amplifies only the corotating waves. The net gain in the corotating is bigger than the net loss in the counterrotating but as far as I know that is only for gravitational waves. Only for spin 2 excitations. For others, that is not the case. The symmetries of the system mean that what is corotating with a certain azimuthal number will not change. Everything in that channel will stay in that channel and I can say how much goes into this channel and how much go out of the same channel. And then we compare in versus out. If you don’t know what you send in, you cannot evaluate what you get out unless it’s just much more. It’s only for gravitational waves that you get a net gain. But then again you would really need to know what you are sending in. It’s really this in versus out. There’s no other way. Instabilities is a different thing because they would grow and you could catch them.

**David**: Hawking radiation is an observer-dependent quantity. Could there be regions in our galaxy with lots of stars where the cluster is accelerating at large values with respect to us such that this temperature would be larger in a measurable way? Or would it still be way too small?

**Silke**: The Unruh effect is tremendously hard to measure. If you look at the accelerations you need to have to get a decent temperature, it’s just crazy. And nobody has built such an Unruh detector. What would be something you could accelerate where you wouldn’t have any other noise? With Bill Unruh and two other colleagues - one is a leading expert in ultracold atom experiments, and a colleague of mine at Nottingham who has worked on the Unruh effect for thirty years - we worked out a proposal to build an analog detector for a Bose-Einstein condensate. That work has just been published in Physical Review Letters. This is harder than the Hawking effect. In order to make this effect bigger, you need to accelerate more. But the accelerations are crazy. But you need to accelerate to the speed of light and the energy you need is infinite.

**David**: Maybe modifying the LHC in some way?

**Silke**: Ha ha ha. What analog spacetime is, is a superfluid at rest. It has to be a very well controlled superfluid. Then you need to build a particle detector. And what we found is that you can use a laser beam. And you can rotate this laser beam around a circle and that’s acceleration. Then use an interferometer to see how this laser beam interacts with the Bose Einstein condensate and we find that it depends on the acceleration. And that’s what we’re working on. Of course you can’t generate an acceleration that is stronger than near a black hole.

**David**: Is it fair to say that theory is ahead of experiment?

**Silke**: Oh yes. Ultimately we want to test quantum gravity but we don’t have predictions from quantum gravity and quantum field theory in curved spacetime has many predictions, like Hawking radiation, Penrose process, superradiance, particle creation, black hole ringdown, Casimir effect. People felt the same way about gravitational wave detection but it would be absolutely fantastic to measure the Unruh effect or to measure Hawking radiation. It is not going to solve quantum gravity but it would definitely drive our understanding of how to approach quantum field theory in curved spacetime. It has not been checked. Theory is miles ahead. At Bill Unruh’s birthday celebration conference, I asked Bob Wald what we know with certainty about quantum field theory in curved spacetime and he said that we now know how to calculate things. And that really summarizes it. And I would add to that, that we have derived methods and techniques to extract information. But we have never verified it. I’m a believer of quantum field theory in curved spacetime. I think it is a robust effect. I think that is what the analogs tell us. But there is a difference between believing and knowing.

**David**: Do you work mostly by yourself or in groups?

**Silke**: We have all team work. We all do theory and experiments alike. So students would develop some theoretical models. Sometimes it’s finding a new analog system where one could see an interesting effect and then one is supposed to set up this experiment to see if it’s there. So it is very interactive. We have office spaces that are all connected. There’s too much to do that you can’t really do an experiment on your own. And we form teams that are very interdisciplinary, get external collaborators which offer something which we don’t have.

**David**: Is there a good textbook on quantum field theory?

**Silke**: The standard one is *Quantum fields in curved space* by Birrell & Davies. It’s a bit old.

**David**: From the 1980’s?

**Silke**: I know. I know. But the only other ones there are… there is a more theoretical one by Parker which is more mathematical. And then there is a new one by Mukhanov. I have the lecture notes but if the book is like the notes it might be a good place to begin.

**David**: Thank you very much for taking the time. I’ll send you the transcript and you can change it as you want.

**Silke**: Ok. Thank you very much. Have a nice evening.

**David**: Thank you professor!

## 留言