Silke Weinfurter, "Analogue Gravity: Theory and experiment", Part 1&2

Transcript

also why i'm interested in animal gravity studies because they're based around two principles which when i was studying were the things that fascinated me the most in physics and the first thing is when you do physics you have always a rather complex system and what we do is we make as it seems sometimes a million approximations we throw things away we make the system so simple that we can actually solve it and when you do this still it seems that it describes some in some parameter space perhaps it will describe very well what's going on so the second one is and i think this is related to the first one is i can have two seemingly very different systems and yet in some circumstances these two systems can look alike in the sense that they exhibit the same properties on the same behavior so that's really the base of the core of analog gravity studies so and now coming back to these three seemingly very different images here on my first slide um i will explain or try hope to convey the idea why a faster vortex flow can look very very similar to uh fluctuations in the vast vortex flow can have the same properties than fluctuations around a black hole so what you see here is a picture by roger penrose uh over the kitchen of the black hole you have the singularity in the center here you see the sound uh sound columns future sound called the past sorry light continue here's lightning fluid within the sound form and what you can see is that when looking at these two systems and you look at the fluctuations and you can then show that in both systems fluctuations underlying the same amplification process which we are which is known as spoken radiation so that was just a very late description but of course i have to give you some more details and let me give you um an overview also of how analog gravity systems have been discovered and what these analog gravity systems are really they are a possibility of analog simulations of classical and quantum field series incur space times so choosing thought because george hasn't encouraged me not to use many equations and i thought maybe rather than me explaining what an analog gravity system is let me show you a popular science explanation for house which is taken from a video clip from a tv series which is called the big bang series probably all of you know it the ones who don't know this theory it's a very un usual theory in a sense usually all of these tv series are based around the life of lawyers and doctors here it's different it focuses around the life of four physicists or 361 engineer and one of them is leonard here on the right and leyland has some very exciting news for his girlfriend penny so listen do you remember when i said the similarities of the equations of general relativity and hydrodynamics suggest you could find the equivalent of unruh radiation in a large body of water i thought i said that to you anyway stephen hawking's team is looking into that and i've been invited to join them wow hockey and good for you oh it is just you know i'd be gone for a while how long three four months whoa when would you leave a couple weeks oh okay okay well just come visit you that's the thing you can't i'll be on a ship in the north sea on a ship aren't they afraid hockey will just roll overboard he's not gonna be there he's just sending a team to research his theory oh sure like when you send me to kill spiders in your bathtub so also of course that was a very nice explanation so i'll go through this um this idea step by step and then also let's at the end resume back to this kit and find all the arrows so let's first start very basic i apologize if all of you know this but sometimes it's good to build up gradually so what is a black hole a black hole is a region of space time from which gravity of the gravitational pullback is so strong that nothing not eaten like you can escape so as i pointed out before here this is this picture by roger penrose of a black hole you have this this video line here in the center is a singularity you have two different objects here these are the slide cones the future here future like on the past like so if you're an instant time in this point here all your future has to be within this future like home and so there is um around the singularity here in the center of this black hole here there is what's called this event horizon and if you are outside this event horizon you can still escape if you're beyond this horizon all your future your future icon is still towards the singularity and it will fall into the black hole and you can never return these other things here are vacuum fluctuations and it's kind of like a picture of the hawking process but i will come back to that now how can you find an object like that in a hydrodynamic system as leonard explained initially so about 30 years ago uh bill gillard gave a lecture on fluid dynamics and he thought about this analogy he thought about what if i have a flow that goes supersonic what happens to the sound words in this system and then he went back to his office and he worked it out and this was the beginning of another gravity so now let's go through this so here again we have these two seemingly very different systems our black hole and on the left and on the right we have our fluid dynamic system now let's look at sound waves and let's assume let's look at sound waves where we have in a river flow but the river flow initially here on the left is almost zero so if i look at sound waves how the propaganda system if i initiate a sound wave at that point here i see it propagates equally fast in all directions so let's now assume that the river is speeding up and it's going in this direction and if you see now my sound waves are propagating faster with the flow than against it now imagine you have a flow that becomes so the velocity of the flow becomes equally large than the propagation speed of the sound waves in the system so at that point here velocity exceeds the speed of sound so suddenly and perturbation the sound wave initiated at that point it cannot propagate to the left it can only be dragged along with fluid flow so basically everything is propagating to the right and so here we have a supersonic flange here we have a subsonic flow now let's assume um saginaw is sitting here and church is sitting here and i want to discuss some issues about the workshop and salvinia which the only way of communication would be through the sound waves in his water so church picked out have been a lot he's sitting here all these sound waves which make it into into this critical super supersonic region while zadina here would have no way of communicating back to george so this is how these analogies work if you think of in a webcam experiment but the analogy is much much deeper so at the first level so realize that perhaps fluids can exhibit these effective horizons as seen by the small fluctuations in this case are the sound waves however then when he worked out the equations of motions for these little sound waves in the systems he could find a more precise restriction and indeed he says that this small perturbation experience an analog effective emerging gravity system and a magic cancer or an effective gravitational field so this sounds very difficult to understand but in fact it's really trivial and it works this way so we have to do a little bit of quantum filtering her space-time but promise is very trivial so every one of you probably knows the weight equation now the wave equation here as we all know it can be rewritten in let's say a more fancy way and that means i can rewrite it in a relativistic way by simply saying oh i have a flat space-time geometry and i can hear combine space and time in this metric tensor here and there are only constant here's the speed of light so under here on the diagonal here this is a spatial part here there are only the ones on the dial so in some sense these two things are simply the same equation it's just a different way of writing it now this seems perhaps not so useful but if you wonder what happens to my wave if it doesn't propagate in flight space time in this room here for example uh what if uh it propagates nearby a black hole or a general curved spacetime geometry what if the gravitational field is not simply flat so then what you can do it's called the minimal substitution all you have to do at this point you say oh let me replace my minkowski spacetime my eta a b with a more complicated space than geometry with gravitational field g a b here and now all of these entries can be functions of space and time so in some sense whenever you see this kind of this guy here over here then you know already that oh that's just a way of propagating on a curved space type geometry so this was precisely what bill found he said he started with the fluid equations which are probably all of you remember from studying or continuity equation euler equations so these are simply the equations that describe a hydrogen having system you also have the equation of state but nevertheless so he starts from this is from these equations and if you then perturb this equations you get how and you're assuming that the fluctuations are small you get the equations of motion for these fluctuations in this system and you can actually rewrite those in this way and if you remember the previous slide that just tells you oh that's just a weight equation on a curved space type geometry and the trick build it then it's just a rewriting again of these fluctuations he introduced what's called this effective acoustic or geometric tensor and what's inside here now these are all properties from the background flow so in particular it's v is the velocity of the flow and c is the propagation speed of the sound wave now if you also remember the duncan experiment from the beginning i remember i said well if the speed of sound is equal to the background velocity this is where i get my effective horizon and that's precisely for the ones who have maybe more gravitational background this is when this g 0 0 this first entry here in a magic tensor is becoming zero so it goes from minus here through zero to plus and this is where we have our effective horizon so again the assumption that has been made were like the fluid flow is inviscid irrotationally compressible and in this particular parameter regime you can map the hydrodynamic systems the behavioral defluctuations you can map that one to one upon at that point classical field series in terms based on so with this um i understand you get the supersonic flow and you can't move sound in the other direction right in my head i think about planes that are going supersonic right um and then but this last one the fluid velocity i don't how do you get the sound seems to be going in advance of the object or no no not in advance so the flow here so what's happening here here the flow is even faster so here it is really it's exceeding the background flow it's exceeding the sound speed so it has actually get the same thing in this airplane so i'm coming back to that so maybe we can wait a few things so basically this is just at that point they're equal here um the flow is even faster okay okay um now that sounds crazy and of course as just pointed out there is an issue here supersonic flows that seems a little bit uh you should get the attention that was very high because when i whenever you go supersonic you encounter easily shock waves and shockwaves what that means is that all the parameters in the fluid flow instantaneously change and this linearization process of course is no longer valid so this idea that fluctuations are small basically that i can assume that it's irrotational invisible and incompressible it's not incompressible anymore if you get shocked with however when i said small fluctuations the analogy does not only restrict itself to sound waves you can also look at fluctuations on the free surface so for example surface waves and the analogy just carries through if you have to modify you have to apply certain boundary conditions on your fluid dynamic system but still you can clean your eyes and look how small perturbations behave and you get the same behavior again you can describe the propagations through this simple wave equation concur in a general purpose based on geometry now given that that it works for this as well um in fact all of you have really looked at analog and i don't know space time and the system i'm talking about is actually the kitchen sink when you do your dishes and when if you're lucky the water top is not precisely above the sinkhole so it hits the flat surface and then what you get perhaps not in such a nice way but because here um they use silicon oil but the same goes for water as i will show you in a while you see this kind of behavior this kind of pattern so the water would hit the metal plate of the sink the bottom of the thing and then you would get this ring around inside this ring everything is very smooth and outside here you would have what's called usually hydraulic jump so here you have a lot of wrinkles so that actually it's an analogy of an uh effective whitehall horizon so what is a right or horizon so a whiteboard horizon is a time reversal for black holes so if i have a black hole nothing can end everything can enter but nothing can escape once you're beyond the black hole horizon in a vital horizons it's the other way around nothing can enter but everything can leak so in the river flow imaginary and the opposite situation here in the situation that here the system is subsonic here at supersonic if i want to send in a perturbation from this direction it can also only propagate up to this effective vital horizon and then the weight is arrested now and this is what's happening in here because the flow is very very fast here at the same the floor exceeds the propagation speed of the little surf ripples on the water surface here so that's very smooth nothing can propagate here and at that point here because the radius gets larger and larger so here the flow has to speed down and slow down sorry so here the floor is low enough again so on this side it's subsonic and here it's supersonic so and if you like you can simply repeat this experiment in your kitchen sink i have done that one thing what you can actually you can visualize the this behavior you can actually look at the circular the equivalent of this muff cones which are called here the frog cones and which simply see if you would take a little stick here and you place it in different distances from the center you can see there's this opening behind and the angle here is related to the ratio between the background velocity and the velocity of the surface weight and if you take a disk and you put like things here from different distances you can see that this cone here towards gets deeper here and it opens when you go to the edge so in this way you can map out some of the behavior and in fact really every one of you has looked at an effective white on horizon so why so now you could say well this is very neat maybe to explain your channel how black hole or light on horizon works but can we do can we use that for something can we do some make some news out of it can we use that to um to advance our understanding of classical and quantum fields basically so and coming back to the original paper in 81 so the title build shoes at that time was experimental black hole evaporation questionnaire and what he realized back then well if the two systems my fluid flow on the one hand and my fluctuations around black hole geometry if the equation of motions are the same approximations in both systems are valid these two fluctuations have the same behavior we should also see the same effects to arise in this system and in particular he was thinking of talking radiation he was posing a question can we use that system to uh experimentally mimic black hole on evaporation so in more general life this is also these are the three different effects um i will discuss which we can see or which we hope to see in another gravity system so the first one is experimental black color evaporation the other thing we can also mimic retaining black holes we can look at super radiant scattering from rotating black holes and we can also look at cosmological particle production and the real value of these systems is really that you can say well it is a good approximation it's a good analogy in some parameter space but of course if i look at my fluid flow there are a lot of deviations and the key question is is these are the effects which we're looking at are they robust against these deviations so you can actually test experimentally tested universality and the robustness of vocal radiation super radiant scattering and cosmological particle reduction and that is very important because we are still lacking a definite quantum gravity theory and quantum fields to incur space-time there are sometimes means to believe for example if you look at black hole evaporation process if you look at the radiation coming from the black hole and you would for example trace it back to the black horizon you would get a tremendous blue shield blue shifts to energies where you say when you come closer and closer to this horizon they get blue shifted to energy scales where we simply don't trust um quantum fields to increase space time anymore and one would feel perhaps a little bit uncomfortable with the lack of a quantum gravity theory to describe what's going on so the question is really that for example booking radiation really probe the uv physics or can i still describe it with quantum fields in curved space line and the same question arises in this analog gravity system if you think about it if i have a fluid flow and if i go to shorter and shorter distances eventually you have to think of the molecular structure of water or one level before that it is a dispersive media so will this kind of deviations will they out of the hawking process or can or is it such a universal robust effect that it doesn't matter what the uv physics is so this was one of the motivations i think bill had in mind to see how independent of the system these effects really are so coming back to the big bang theory and now let's do some corrections so first probably quite funny because phil told me that actually they they called him to get the pronunciation of his name right that's very good but they finally they didn't care so much about some other details so one was they said like hawking wants to detect non-radiation in fact it's unknown who wants to detect the hawking radiation it is in the hydrodynamic system you don't quite have to go to the north spoon you can actually do that in an undergraduate laboratory in canada in vancouver it's a very beautiful place and much much warmer so let's start with this experiment which was described in the big bang theory and this is i found another web there actually fantastic images out there this is how journalists imagine us working on black holes um it's actually not so far off we have a lot of cameras not so many my microphones so anyway so let's start with perhaps the most prominent case that is on black hole evaporation in the laboratory so in order to do that let's start at first one has to get a general understanding of what really is hawking variation we have to get a certain understanding of this effect the second is how can we set up the tabletop experiment to conclusively test hawking's unrest prediction and so what does it really mean i have detected one of these effects in particular here hoping radiation and uh why is it of interest i've already said that why is it interesting to you to run these analog simulations so let's go back again so classically nasa can escape a black hole but if you include quantum effects it can evaporate away so falcon radiation is a very very important process because it tells us what the final fate of a star so starting collapsing from the black hole and the question then is what's happening to it and the hawking process is important because it is a process that allows the black hole to radiate away the mass so now how invalidation seems like a very exotic effect it isn't really so let me first start with this very popular popular explanation of hoping radiation which is also taken um from i don't know i think i also took this from roger penrose books but anyway so the first paper on it was in uh 1974 by stephen hawking and perhaps a naive way of understanding what horton radiation is about is the idea is that you have vacuum fluctuations so the vacuum is not reality you have these fluctuations here these are these wiggles here and all the time you perhaps if you like you can think of creating particle anti-particle pairs and when this is happening nearby this event horizon this black hole horizon here the gravitational force is so strong to separate these particle pairs and the particle is getting emitted away and the anti-particle is falling into the black hole when an anti-particle has a negative energy and therefore it reduces the energy it is the mass of the black hole however i personally don't like this explanation at all there's a very simple way of understanding it's a very simple scattering process and it's actually so simple um which also takes a little bit of the misawa or forking radiation but this is how one can understand how communications in a more feasible or more down-to-earth way so what is really a black hole so a black hole has a gravitational potential right if i'm zooming in in this area is this gray area and it has a boundary and the boundary is this event horizon so the boundary condition i'm putting on here is that nothing can escape now i can now say let me look at my fluctuations here let me not specify if i'm talking about classical or quantum fluctuation let me just look at small field fluctuations outside my black hole now if i'm focusing on the radial direction i can say well in general always i have a second order wave equation so i have two solutions ever in particular here if i want to write or left moving mode so inward or outward or black hole horizon in general i should have that on both sides i have not yet imposed my boundary condition now let's think about it a little bit a different way so presume i have a conserved quantity right so then i could write that as an elastic scheduling process now there is such a thing which i can get from the wave equation remember the wave equation occurs based on geometry i can actually derive such a conserved quantity sometimes it is referred to as the energy i personally it's not always correct also the norm the most correct and general way to describe it is called the particle curve never mind what it is you can calculate that from um in the analog systems very easily it's related to the amplitude to the frequency to the velocity of the wave now if you look at this um scattering process now well if it's an elastic scattering everything that goes into the potential now we look we basically look inside and outside but everything that goes into it also has to come out again so now i'm causing the boundary condition that tells me that nothing is coming out okay so this solution here is gone but at the same time i can calculate this conserved quantity let me say i'm sending in one i can readjust my units any time so i say whatever sending it has amplitude one or one particle current it's just a redefinition and then what i can see is here i can calculate these quantities and if i replace that here what i realize that this guy here on the right which is going into the black hole has a minus sign so it seems almost as if it would source the whole process so this is what is referred to as this um negative energy partner that falls into the black hole remember here we're inside the black hole and what we're seeing here is that so this this is the guys are coming out it's alpha squared this is the guy that falls in is this minor big minus peter's word and what we see because it's one here so for this equation to hold what's coming out has to be bigger than one what that means is you have extracted energy or practical current out of this process so and that's that's basically how what's happening to the few fluctuations around the black hole horizon is just a simple scattering process once you've got the right answer quantity you can work it out it's really trivial and how can you associate a temperature to this effect it's also very trivial because you can compare you can actually say okay let me say what if i look at the ratio of how much is falling into the black hole with respect to how much is coming out if i write that down you can see that that actually has the form of a boltzmann distribution so you can calculate this quantity from the fields here on the side and what's the only thing it depends on really is the the surface gravity at the horizon so the whole process is determined by the gravitational field the strength of the gravitational field and if i now compare that with a stand-up also distribution where there's a temperature i can actually associate a hawking temperature to this process and this is why black holes have a black hole temperature now i've been very careful here because it's very important i have not specified what kind of fluctuations i have in mind i just said that this is an amplification process it works in a certain way you also have to stimulate it in the right way but this is this amplification process and black holes are linear classical quantum field amplifier so now this one of this this amplitude amplifier works in a particular way right it doesn't source to some somehow hasn't the power plucker so it takes its energy from inside it basically evaporates away is mass by absorbing negative particle current fluctuations now it has in order to detect this effect you have to look at percolation frozen process right it's always these two guys one is falling in the other one going out remember this scattering process has uh one is going in and then these are the two one you send it in or it takes a fluctuation and it converts it into this true fluctuations the one that goes into the black hole and the moment it should follow this kind of behavior which is that it can associate a boltzmann distribution to it and it is the distribution only depends on the surface gravity of this effective horizon so that's basically what this process is about and when you want to set up an analog gravity experiment my opinion you should try to see how much can you recover from these properties of that effect so now let's come back to because we're doing a perfectly classical experiment and usually people would say oh you want to see open radiation it's quantum now the thing is the following if you look at any analog system any system in the lab even if you work with of course ultra cold atoms whatever superfluous it's not always you're not at zero temperature which means of course if i have zero tempo all that's left with is my quantum noise well if i have a non-zero temperature then i have thermal population thermal noise in my system and if of course you've got a little bit there's a huge magnitude separation of amplitudes here of course but then beyond that i have classical noise vibrations and all these kind of things and even beyond that you can for example stimulate the system and excite a certain fluctuation in in your analog gravity system now what we are doing we are running this amplifier at this level huge order of difference but we say well the classical amplification should follow if it is linear to the scale it should follow the same physics in order to go we could in this particular experiment we can never go down here but people now try to repeat these things or there actually is a chance to go down to this level so i don't even try so and so the question is now so is there no difference between this classical equivalent of talking radiation or what we call a stimulated hulking process and this here this quantum quantum talking radiation the difference is this pair of modes created if you go down somewhere between here you can calculate this threshold where you are then you will see that the correlations between the guy that falls into the black hole and the guy that's been emitted away that these are stronger than classical correlations where they become they can be a tunnel and that depends very much how close you come down here now i've already talked about that the issue is about testing how dependent this process is on the uv behavior system of how the system really looks like at small scales now this is the experiment we did together with greg lawrence he's a civil engineer as a professor in civil engineering he's a postdoc ted tedford and on the other hand i was phil andrew met henries was an honest student at the time he's now my phd student and myself and we did a very simple experiment this is our setup it's a one dimension it's an open channel flow which is in the civil engineering building where undergraduate students test some aspects of bernoulli equations uh and do some of their um their so how it works is um we have this water flow we have the obstacle in the floor which changes the depths of the water um this is a water reservoir water gets pumped back in it's a stationary flow and the back end here we have a wave generator sitting that stimulates the system now the basic idea is that as i mentioned already this analogy also does not only hold for surface waves for sound waves it also falls by surface waves and the reason why it's much easier to work with these surface waves is because actually their propagation speed is proportional to the height of the flow so the shallower they use the slower they propagate at the same time if you have a constant fluoride in the system the shallower the flow because of conservation of mass the faster the flow the fluid has to the fluid has to speed up the faster the fluid flow is so if you decrease the height of the flow you speed up the background flow and you slow down the fluctuations on the top if you remember the acoustic line element here's another acoustic you should really say affect it because it's not for surface waves not sideways and what you see here is that this is exactly what you want you want to find the region where those two are the same the propagation speed of the fluctuations and the background flow now what you get is actually a set of effective black and white on horizon and it's again here the flow is speeding up the perturbations are slowing down so here you get the black one horizon then at this point here the flow is slowing down again and the perturbation of kicking up now this is how the experiments look like this is of course very much at the beginning of initially at the end we generated waves which were about millimeter high maximum this is just for demonstration so we're sending waves dancing the downstream end of the floor the west's propagating up to a point here as you can see they cannot propagate beyond a certain point and here is roughly where the affected vital horizon lies and the question really is what is happening exactly to this wave when it penetrates the effective light on horizon what we're doing actually is in order to get all the information we looked at the free surface of the system and what you can actually see you send in a particular wave here and this is the ingroin wife and you can see it actually gets converted to a pair of waves you can filter everything out else out here is a superposition of these positive and negative particle current waves you can look at it also separately you can do an inverse fourier transform to simply just leave these positive and negative patterns there and then you can also test all the other aspects as i said before you can actually see how much is actually converted to this positive norm or negative norm waves and you can actually find appropriate quantities to show that indeed they're following this all small distribution and as a last step you can simply show that the slope of this which should only be determined by the effective surface gravity is indeed uh you can also get the surface gravity simply from the background flow you can compare that with the excitations and you can see that the both are the same so hope that wasn't too detailed but this was just an example to convince you you can actually use these analog gravity experiments and the same principles for the later experiments will be repeated in other systems so it's a care it fulfills these three quantities here and now we can go back and ask ourselves so what if i could cool down this system to temperatures to very very small temperatures close to zero temperature what would be the temperature i have to go to what is the temperature of the fat and the temperature of the effect is 10 to the minus 12 kelvin so there is simply no way of ever seeing any quantum effect in such a system so now people use other systems such as optical analogs of the event horizon and let me quickly explain you the idea is the same this is why i also took my time in the first experiment because the principles are saying we just have to replace some things for example the sound where the surface waves are of course are now replaced by light it's an optical system so the equivalent of the river flow and meets whatever that role applies needs to exceed the speed of light in this medium and that's of course it seems rather impossible however you know that in mediums with a refractive index you can use medium such as water or glass to reduce the refractive individual life however you would need something that drastically reduces the refractive index and such system exists for example in fiber optics which is you also use the telecommunication and how it works is that information caralytic is confined to the core of the optical fibers so you have these light pulses which propagate through the optical fiber and what's happening is that every pulse of this is actually modifying um the refractive index in the system and depending on the intensity of this light pulse you can higher the intensity the more you can modify the refractive index so when this life once is propagating through this media it changes the refractive index and this is also called from the rest from the viewpoint of the moving past this looks like the media is really moving also the optical fiber is is not it would be the same if i were to repeat the water experiment rather than having a water flow the water flowing i could have the flow imagine i have an infinitely long flume and i have the obstacle and i can move the obstacle through the flow so um right so the policies is establishing a moving meteor it's also called the curve effect in nonlinear it should be non-linear optical fiber optics and the medium naturally moves with the speed of light because it's a pulse itself so how does it work if i have this light pulse here and let me assume i'm probing this lighthouse now as a profile i can see this should be proposed that when the profiles is slowed down by the powers until they have the same group velocity and then what then is happening is of course this is basically it can propagate up to this point when it's being slowed down because this pulse is modifying the refractive index it falls down this profile and then you have of course again it's also a dispersive media that disperses me dispersive effect can actually um release this blue shifted probing pawns now what you get here is also a set of white a black hole horizon side the back part of his body of his vital horizon the problem is black polarizing this is how you can understand this analogy here but without the probing parts you can the idea is that already here you get this white whole horizon coming here and it's also emitting this pair of photons this positive and negative known photon hairs and one of the things of course in this non-lineability to have non-linear effects so it's it's a much more difficult system actually and it's not so well understood exactly precisely what is happening um and one of the things for example you have this modification of this pulse here and that's because of um the steepening of the files is equivalent to this optical shock so everywhere you encounter this short way now there have been some very nice results already oh i want to actually so i have to do this now oh it's gone there was there was something beneath us sorry there was a paper there was meant to be some some texan showing the paper by danielle fantio and his group was published in prm and what they've done they set up such an optical system and they looked at this propagation sodium propagation in the electric medium and i've seen they observe the evidence as i said let me just read that for you report the experimental evidence of photon emission that on the one hand bears all the characteristics of hoping radiation and the other is distinguishable and several separate from other known photo emission mechanics so what they've done they couldn't quite show the same three features as we showed which is simply because they can for example not really calculate or know the shape of the pulse it's very hard to reconstruct the shape of the pulse which is also related to the gravitational surface gravity in this particular system they also had some other things that the radiation was sent perpendicular to this effective horizon so there's still some open questions to be resolved however it's a very interesting system and um yeah so it's it's very promising so daniel still also looks at other media to see some media which might be more appropriate to repeat this experiment to get some more information of what is going on now at the same time more recently than that another paper came out and they looked particular they said if i send in a solid on pulse can i see this conversion because it's also this dispersive medium can at least see this this is a conversion to positive and negative normal psychological negative frequency it really should be called negative norm radiation and what they've seen is that depending on the the input of the piles you can see there is a regime where you get clearly two of these so they have a sending some solid only fiber optics for example they use this two different systems sorry about that so they use this um there they repeated these are two groups the one group is danielle again the other one is really chronic and they look at in daniel's case again in vital medium and in phoenix case in photonics or fibers now and what they've seen here already is that they get this nice result that you really get this this decay of this pulse into this positive and negative frequency mode so the question is now for example to look at correlations of these two partners and to see this but it's a nice example of how these analog gravity studies motivated to look for such an effect in optical systems so what else are the black holes so where are we at that point um as i mentioned before it would be great to repeat all these experiments at lower temperatures so that you can access the quantum hawking radiation and one of the people who has made some considerable process is jeff steinhauer he's working in super fluids both engineering condensates and what he found is that he was able to set up a background flow that exhibits a black hole horizon he has not quite seen the effect but if he would take this background flow and use some numerical simulations he thinks that the parameters are very very promising that you can actually see the the effect should be there but it's a matter of detecting a treaty an alternative proposal is to use a different boundaries so instead of having an open system one that flows so if you're looking at terroidal bose einstein collins sites where the condensate is splitting around the velocity is going in this direction and again you hear a black polarizer and a vital horizon similar to the setup i was showing in the open channel flow the way to get that here for example was suggested by fush jane to for example use a quantum de laval nozzles here to simply tighten um have a strong confinement here so to speed up the flow and you just have another nozzle to slow it down again however because of the different boundary conditions you also get instabilities here so this kind of the opposition collins that superfluids are being used in other for other purposes uh for a metrology measurements but perhaps one can also use them to look at traces of talking variations but here also because of the fact that it's a closed system you can also encounter these instabilities so it's not so clear but this is also very interesting feel interesting um setup to explore so i think here is a natural break because now i'm starting with the differences great thanks so much so now coming back initially i said i would like to talk about in principle so i talked about black hole evaporation and then now i want to talk about cosmological particle reduction and then super radiant there would also be uh radiation but i won't cover that so and we were talking about um the perfect analog gravity system i was asked this question and i'm saying for me where the other locks work the best because there are the best amplifiers is actually we can we come to the possibility of mimicking cosmological particles so um let me get right into this let me first explain you a little bit about tell you the story about cosmological production why it's also and all of these effects are amplified complete amplification they can all be understood just have different if you think about the stimulated versions what are you feeding into the system what is the how do you stimulate the system but anyway all of those are amplifiers and uh one thing which is very promising and has some very nice results by chris westbrook already is cosmological party reduction so first i will talk about how it works then again the question how can we set up a tabletop experiment to mimic that mechanism that is responsible for the creation of particles in our universe and then um again why is it interesting to do such simulations now again sorry if i'm a bit too detailed um but let's start again from the basics so you can also you know write down a gravitational field that is matching our observations of the universe as a whole and what we can see that is expanding which we know from the redshift of the spectra of distance galaxies so one very popular way of explaining it imagine you take a balloon you don't quite fully fill it up with air and you put little dots on the balloon and then they keep on blowing air into the balloon and then you see that all of the dots on the balloon moving away from each other further and further away so this is what we're seeing if you look in all directions it seems that our universe is expanding it seems like on a large scale it seems isotropic uniform in all directions homogeneity no electrical formation so and there is one unique space time that describes all of that can be describes also these expanding universes which is this friedman robertson walker type universe that's how they're called and you can actually you don't even need the einstein equations to show that that is the unique solution um stephen weinberg did that i think in his phd it's his work he looked at maximally symmetric three-dimensional subspaces with positive eigenvalues you can see that this is the unique solution so there is some sort of gravitational field this really uniquely describes our universe as a whole so now again remember that what we how can we get that now what i'm focusing on i say one can i will show you how you can recover such an effective space time geometry from a superfluid and when i say that it's again have in mind that in all of these analogs i had this when you look at the small fluctuations you had this wave equation on this effective curve and geometry and it's all a matter now of because this geometry depends on the parameters of the system so the speed of sound and the background flow and so forth so if i want to set up a different geometry different for example than hawking a black hole geometry then i would have to tweak my system externally such as smaller small uh fluctuation in the system it's see this uh for example expanding universe or they propagate to the codex experiences this position condensate as an expanding effectively expanding minimum so how can we understand that how is that working so first of all what is a causation condensate it's ultra cold guys of atoms there are of atom right it is here in the cold collision regime as you call so you only look at you look at the bosons only two particle interactions are only collided onto molecules and what you can do if you cool the system down to temperatures low enough you have this condensation you have a face transition and you can replace your bosons your field operators shouldn't say that but you can basically describe it as a macroscopic fluid and this microscopic fluid is irrotational in visiting compressible so it's precisely where the analogues work very well you can describe it it has a density and it has a phase it's random but it hasn't been it takes a place now what is very interesting is if i look at small fluctuations in such a system right i can ask i can look at sound waves again in such a super fluid and the speed of sound depends on the density of my condensate and it also so basically density is given the number of atoms which turn upon and say divided by the volume and then i can also look at there's another thing that ends here which is u of t which is basically the interaction strengths of their atoms so how strongly these these atoms these bosons collide with each other and interestingly what one can do for example one can change the speed of sound as a function of time so if you do that so one way which is very simple it's very easily can be done and has been done many many times in many experiments is to change the interaction strengths so imagine you have your bose action cone inside sitting in your trap more like this not like this but let's blow it up and then what i can do is i can use external magnetic fields and you can change these interaction strengths we have what's called the fetch quad resonance if you use the right kind of atoms you can do that so now let's assume um we are all sitting in this conference that we're part of his conan then we exchange information all of us send every second we send sound waves to everyone in this room we send it to various people now let's say i'm not part of this i'm outside and i'm changing um the sound speed in the system and the way i'm doing it making it slower and slower and slower and slower so you're sending every you know i have an internal clock you're sending off your signals with a certain rate and you realize all the signals from the other people take longer the distances between the signals to arrive get longer and longer because the speed of sound is slowing down slowing down and slowing down so the distance where i'm receiving information from other people it's long and normal so now there are two explanations one is of course if you know well somebody's playing with the speed of sound the other thing could be what if we it's a situation like on this balloon where let's assume that there we have uh in the real universe we have the speed of light which is constant but you know the universe is expanding so you have this redshift redshifts now here in this situation it also looks for small fluctuations in the system if the speed of sound goes slower and slower and slower it seems the time for example it takes to propagate from one end to the condensate to the other takes longer and longer and longer it seems that the condensate is effectively expanding and that's precisely how you mimic this expanding universe versus now again one particular interesting case is for example if i want to what's called uh which is related to inflation it's a deceiter universe and that has a very particular form let's come back here so in some sense these are these kind of friedman robots in boca universe and then depending on how i basically change this particular parameter which tells me if i'm on the distances on a spatial slice how they basically change as a function of time and so this is the parameter in which you to to mimic various scenarios for example if you have a side hit universe or one which is ever expanding or it's contracting all these things you can do is simply by choosing a particular scale part and you can also then ask yourself well if i'm setting up an analog gravity system what i can do is i can change the scale factor for the boson interactions so how the interaction strength changes as a function of time and when you work through a way through the analogy you can see well if you were for example want to mimic a particular decision universal inflation you have to depending if it's a two-dimensional three-dimensional condensate you have to choose a particular way function for the how you change the interaction strains and the change in the interaction strength then is related to what's called this hubble constant and so you can basically mimic inflation in these systems so for these small fluctuations in these condensates little sound waves they see they're going through an inflation if you do it right so now not so quick okay so how can we understand that if you change the speed of sound uh or if the universe is expanding why do you create fluctuations why something happening if i'm there someone is tuning the speed of sound very quickly why do we actually do something to this system and the most the simplest examples of understanding that is actually parameter resonance so it's a sinusoidal change or a rapid repetition can also be a succession of sudden changes in the systems of interaction strains are simply the size of the universe if you would go like this the size would get larger and smaller nothing smaller so and then you can i like this very much because we encounter parametric resonance many many cases for example when you're sitting on the swing you actually use parametric resonance to get up crazy now let me say so the situation if i want to would be if i want to think about this analogy the universe would be like a cyclic cyclic scale factor and in our cases we would change the speed of sound sinus in a sinusoidal form in a manner and this can be this is basically already well known it's parametric resonance so this whole thing of the connection to the scientific universe is just another way of looking at it but parametric resonance is well known so one particular nice thing which i found on the web and there's also beautiful paper about that you find many videos so this is a tibetan singing bowl and there's a nice explanation about it so if you um grab it with some rubber it will show if you stimulate it in the right way what's happening here the boundary gets deformed in in a particular way this paper it's nicely explained and that drive is was half of the driving frequency this is the characteristics roughly half of the driving frequency is stimulated in ripples on the free surface so now let's look at that so so i think this is a very for me it's not quite right but for me this is how i imagine the universe when it goes through a rapid phase of inflation and you create all the particles so this is i think it almost looks like you would boil the water here right so it can even create has such a strong effect that you actually fondly drop that bouncing before the analogy is completely gone and it's a little bit of a wavy analogy but i think you demonstrate how you can actually excite fluctuations by using uh parametric resonance and now let me show you this is some simulations my student did a phd student andrea's finger so what we do is we change the let me should say first we take the position and condensate we use this wigner simulations so we do the whole engine condensate and twice of this frequency here we have the sinusoidal changes and what you can see is what you can see is that half of the driving frequency you create here what i'm plotting here is the amplitude and here is the wavelength so at a certain wavelength i'm producing a lot of fluctuations in the system so by changing the induction strength you get all these little fluctuations in the information and what we can see is here also that first i get excited and also this is a super fluid and you don't uh you also have if you like later on we'll come back to the quantum aspects you also have the coherence we have damping of this mode so first you stimulate the system you create a fluctuation then you stop and they're dumping out just as in ordinary water because of non-linear effects now okay so this is parametric resonance um what about uh inflation where you just have an ongoing expansion there's also a very easy way to understand that again sorry for using all these equations but it's very simple so you have a second order wave equation here and what you can see is simply you have a frequency of a mole imagine you have a universe and i look at the certain fluctuation it's propagating in my system it has a certain frequency now i have the hubble parameters the rate of change how quickly is this universe changing now if you can see if the frequency of the mode is much much faster it doesn't care about the change in size of the universe because by the time the universe has changed it has propagated many uh cycles so it doesn't really care if you can almost if this is much much larger you couldn't neglect it it's simply a plain way now if the frequency gets comparable to the hubble frequency already then i cannot describe it with a nice plain wave might be some vessel function whatever however when this thing becomes equal when this then basically have this sign change and you basically then have it's not propagating at all anymore it's just being dragged along with the space-time geometry and this is when you excite this field mode and this is how it works and people call wrongly so somehow the super hubble horizon mode it's really just a statement of frequency this of your mode and the time the time scale the the rate of change in the system so in this mode here the frequency because of the particular setup is time dependent what you can see actually is that this when this gets smaller at some point it's what people call across the hubble horizon it's a super horizon mode which just gets wrapped along is based on fabric but what's really so basically it's getting really amplified which means that this ratio this by that is going below one and then of course at some later point you can free this mode again with smelting of moles when this thing here comes larger than h of an h for example when the expansion changes however so so this is the same same mechanism parametric resonance perhaps is a little bit easier to understand and this the difference also here is that you're not only inside a single mode like half of the driving frequency as in the parametric resonance you excite a spectrum of modes so you have fluctuations of course you have a certain spectrum which means the number of fluctuations with a different frequency or different wavelengths is different depending on the spectra but they still have all sorts of fluctuations and rupees now this has been done uh and they call it the acoustic analog of the dynamic or cousin effect in a bose-engine reconnaissance um the person that's done that is chris westbrook yeah on the right um and that's done a beautiful experiment um let me explain that so they took a condensate opposition conan said in a secret form and what they did is they changed here they modulated it seems because they you can also use external trapping frequency to change the density of the condensate for example and change the speed of sound you also when you do these things you quite lightly also change perhaps the effective interaction strengths and so on but important is by doing this by changing the trapping uh the trap in a sinusoidal wave you basically excite in a similar way as in particular so you excite these fluctuations here of course again with half of the driving frequency you get you expect a characteristic the most you expect the most fluctuations now let's look what's happening here um and that's very interesting so this is just this is time of flight measurements um you take the condensate you switch off the trust uh and what chris has he has a detector uh which is like a mash so he lets upon it say when you switch off the trap it really expands like crazy falls down and it on this mash then basically you can from the position in the mesh you can reconstruct its velocity because if i have a condensate so the condensate um fluctuations have a certain velocity which are propagating strokes so the condensate has a zero velocity so everything which was in the ground state the common side of the system that will stay in the center the fluctuations to have a certain momentum they will propagate out so basically i get the momentum distribution gets knocked onto space it's like a period transform and so what he sees is again what you expect so imagine this is not quite the case but imagine it's a roughly homework in the center of the track the condensate is hot roughly homogeneous which means it doesn't depend explicitly on the position when that is the case what that means is that momentum is conserved now if i say a small fluctuation system it has a little momentum in order to have it conserve the momentum i have to create a pair of it one going to the right or one going in this direction now what that means again it's a per-particle process process so whenever i see one with a plasca i expect one with a minus k so here you see what you're seeing here these are these pair created modes which are sitting roughly at the half of the driving frequency which which i modified throughout so and now it comes to my favorite bit and perhaps the outcome of this will also be a little bit frustrating because this is about quantum and it will make a very strong argument that perhaps so we only have seen classical effects and it's anyway it's very hard in column fields in her space time to really get quantum effects so there's a question now so when i look at these fluctuations there comes this question this is now classical are these you know these fluctuations do they follow a classical or a quantum statistic for example are these fluctuations classical or quantum so now i'm in a superfluid before when we were involved everybody would say well this has to be classical excitations now here um here we're in a superfluous that does not necessarily mean that these fluctuations are quantum fluctuations depends on the occupation number so if the occupation number is very large these fluctuations just start to behave classical so one of the things you can look at it's not i don't i'm not an expert on this entanglement issues and so on but there is an easy way to understand a little bit when in these systems how you can actually distinguish between when is a fluctuation classical and when it is quantum and one of the ways to do statistics or another way is to look at correlations and so whenever you create these fluctuations as i said you create a pair of fluctuations one going to the right one going to the left they are correlated so at first at that point already means whenever i see the one to see the other they are perfectly correlated they're classically correlated at that point now one first way of going a little bit beyond and ask are they quantum chord stronger than classical so a nice way to look at um going towards entanglement have to make it's not not very precise it will make some more precise statements one way of looking at it is the strengths of the correlation so what do i mean by that so imagine i'm producing these fluctuations in my system the right and the left movement and then i can ask myself of course um i'm producing one i can't say i'm producing this with a certain rate but what are the fluctuations around this rate and quantum correlations is when i say well if the autocorrelations the fluctuations within um this guy here how much this fluctuates and this fluctuates if the autocorrelations are bigger than the cross correlations or the fluctuations with respect to each other the cross correlations are bigger than the autocorrelations then you have the stronger the classical correlations now in some cases that can also then be mapped onto entanglement but for this you need to look at a different measure it's not quite so clear if this simple statement which also people you know refer to as a violation of koshi swags you can also look at the covariance matrix and so on and you can actually show that for within some restrictions these things are the same so you can actually ask when are these when are these pair created particles which have the same mechanism following the same procedures in our universe when are they quantum correlated when are they coming so what chris did he has published that but when he gives his presentation he always talks about it he did check he has some mechanism to check if he he can look at the statistics of the fluctuations he can deduce it from the density of limited correlations he can basically calculate these guys here and he can see if indeed are the classical quant and he has published it which basically means they're all classical so how comes now we're here in the superfluid 10 to the minus 6 kelvin and again he has done a perfectly classical experiment so what is the reason for that the reason is simply that when you have an animal gravity system you start with some temperature and the temperature is not zero and as i pointed out remember you have quantum noise but then you have thermal noise and so forth so depending on the initial temperature and the temperature of the effect if it's difficult sometimes to associate one temperature to one effect because it doesn't have to have a thermal spectrum but you could always associate the temperature to a mold and so there is a threshold of how hot is your system allowed to be initially so 10 to the minus 6 was not enough so that was the outcome and perhaps maybe also the measurement wasn't maybe he wants to redo it and everything you know it's not so it could also be another but it seems that he started with a psa that was too boring coming back to this quantum you can start with the superfluid you may for example also as in our system we had a perfectly nice correlated beams whenever we saw the positive known partner we saw the negative one they were beautifully classically correlated and of course nobody would have a doubt that there is any quantum ask for the question are they in tunnel because it seems nonsensical i think in the other way perhaps one should also not so naively assume just because you are working in this regime that you will actually get quantum correlations so the system the question of really getting quantum effects in these analogs is still is an open has not been i think nobody has ever shown this uh has ever reproduced foreign so right and however these are beautiful systems precisely to study you know how uh be get aware of what's going on in the system study questions on the fundamental statistics of the field asking all these questions i think the idea for that and i think i have no doubt that eventually someone perhaps chris or somebody else will actually come up with an experiment to to actually produce a pair of internal phones arising from from such an analog gravity system so there are people actually i've also started to collaborate with professor peter grigo in nottingham we're also trying to to repeat chris's experiment to some extent when we're trying to go down to the level where we can see quantum effects and at the same time i think yeah schmidt maya also has a very promising ideas and promising setups that he could also look for this kind of behavior one of the things which i believe is very favorable for these experiments is to work with so-called atom chips that's just fancy words for um you can have a very controlled uh atom trap so you can actually manipulate the condensate in a very fancy ways in very controlled ways which are suitable for this kind of experiments so now we're coming to the last one um i said so the first one was how black holes lose a mass then we moved on how our particles created in our universe and the last one is uh how does uh if you have a star and it's collapsing and it's not symmetric collapse it may acquire something in the momentum or it has already some angular momentum so when it collapses it forms a rotating black hole and there is a process again similar to the hooking process how black hole can lose its angular momentum and this process is referred to super radiant scattering or also that some people refer to it as a penis process so how is this working um so what is a retaining black hole so a retaining black hole in principle does not only have a mass it also has an angular momentum it can also have a charge here if it's a square newman black hole so a curved black pole is basically after a white curve uh whole geometry and what you can show in these systems is that there are certain systems a certain situation when again we have a scheduling process i will explain this if i would send in something with uh norm one it would come out with something that's larger than one so it's again an amplification process this time it's known as the black hole in the black hole the black hole is a very particular amplifier it takes things from the uv and basically sends away um this great shifted radiation so it not only amplifies it it also drastically changes wavelength of what it is amplifying here you can send in long wavelengths into a black hole it's coming back out again so and what it is actually you have an inner horizon which is the event horizon and you also have an outer horizon which is defining the the herbosphere and if something is coming in between these things it can still escape right not of course once across the event horizon but what you have to imagine is when you enter this region here you have what's called frame dragging which means nothing can counter propagate so at the moment a wave would come in it would get threatened along with the rotation of a black hole but instead of getting falling back in it basically requires particle current or normal energy holiday light and this stage and then it basically gets sent off again and it has extracted it has stolen some of the angular momentum um so again it's a process similar this is amplification process again here crucial is also again this inner horizon which puts this boundary but now you can see the spectra is very different because look at this in here i know i shouldn't use equations too much but what you can see is this is the frequency of the wave i'm sending in and this here is that you can set one is simply the unsignal number this is the angular velocity of the black hole at the horizon so if the frequency becomes uh two actually the minus should multiply to be plus i'm sorry about it if omega so imagine this is a plus if omega is more smaller than this has a minus sign if it's larger than that as a plus sign only when this becomes gets a minus sign here then you can actually have again this amplification force is just similar to the whole radiation so here it means that the long wavelengths of the systems where omega is very small that those are being amplified while the small ones are not so now coming back is there a system where we can see that such effect in fact this drawing was actually someone who was by science news and someone was making this picture about the vancouver experiments uh he chosen the wrong geometry because that was a non-rotating black horse this is a rotating black hole as i will argue in a second so it's very unfortunate but it's very nice for me now to just hear from the rotating elements so how can we get this system and again um it's very simple in fact this is how we started to do some of our first experiments we went to the i didn't have a lab at the time but i wanted to test something so we went to the local tool store in italy and we bought this bucket for people used for decon costing their uh leaves and the garden and what we did we cut the bucket we put a hole in the center we took these holes in there and what we did is basically we used some food dye to map out some of the fluid characteristics and what we set up here is a stationary draining flow it's very bad because we don't recycle the water at that point but what you can see is this kind of geometry so if i look at that you um you can then think about what other velocity is doing and you can basically look at the effective geometry arising in such a system and what you can see is so the back so how do i get these two horizons so the black polarizing lies again when the speed of the surface waves is equal to the radial component of the flow so now i have a two component velocity field one is a radial one right because the fluid is training and one is the angular velocity because the way i feed in the water i give it an angular momentum so i have this two component velocity field and the black polarizer is again when the radial component when the radial velocity is equal to the speed of the surface wave the aerosphere is given when the total velocity radial plus angular velocity is equal to steam sound so uh here you have this frame dragging region and here this is horizon now if if it would only have this horizon ascending a long wavelengths and it would just drown because for the hawking partner you need things that want to escape here they get dragged in and send back out so the aerospar is really crucial but you also need this boundary conditions for this scattering process to to basically um produces negative normals so right so again i explained that already you have these ingoing ones and the transmitted ones and you can again in a similar process you can steal some angular momentum from the flow to uh have the superintendent scattering of my surface waves in this faster vortex flow so this is the experiment which we've set up over the last couple of years um some technical drawings here at the moment still in italy we're discussing of moving into the uk now and this is the flume here this is what we get from it the vortex these are the people involved here and what we see here we are now developing some very special what we have to do we have to map out the whole free surface of the flume and that's a real challenge because we want to have very tiny amplitudes so we use some very fancy mechanism which we're developing with a startup company in germany in vienna and rather than me explaining you this setup i made this video and my student matt who was also part of the vancouver experiment it has such a nice explanation essentially the nice way to think about our experiment is that it acts like very large bathtub so the vertex that forms in the center here is very very similar to the vertex that forms above the drain in your bathtub hence the name for this through the navigable phenomenon backup vortex flows our experimental setup is three meters long one and a half meters wide and half a meter deep what we do is we pump water out of our reservoir located beneath the tank the water is pumped into two inlet arms located on the opposite ends of the tank the rate of water that we pump into the tank is at about 6000 liters an hour um i didn't explain as much so we want to get the free surface so the way uh he works it's a bit complex you can explain this already we put rhodamine dye in there rhodamine or fluorescent we put fluorescent dye you know and then what we can do there two ways if you have on the side if you have open channel flow you have this block of water right and you put this loader window in there and then you have like a tower length a two-dimensional light sheet and then uh what you can actually get because of the luminescent effect you can basically map the free surface and the free surface if you want to do the fuel theory experimental things has all the information frequency wavelengths and amplitudes and from this i can calculate the norm and everything so once you have the free surface you can reconstruct the spectrum and what we do here with the two-dimensional one which is a real challenge actually is what people usually do is called prophenometry which is something a bit more fancy work you would produce uh project apparent stripes and then if the wave comes it deforms that pattern and from the deformations you can reconstruct the shape now with this company in germany and i have developed something using two cameras uh it's a bit it's a better master they have some random path on that project and from this they can actually reconstruct the surface and the challenge we have because we need it over a very large area in a very high accuracy so it hasn't nobody has ever done that so let's see if um so just currently like um we think we're all set in some sense we have just finished some theory discussions and studies um where we said okay um one thing which because you said well wait a second aren't you just doing what everybody else has done for years and years and you just could give it a fancy name call it analog gravity systems is it actually useful and so i wanted to give an example why i believe it's very useful so you can't read that very nicely but what should be seen here is this is a parameter space is a is related to the radar velocity the free parameter that b is related to the angular velocity and then we can also change the height at infinity right so these are the three if you want so parameters which it's a bit more complicated the whole system but within some approximation this is what we can change and what we then did we did include some more fluid dynamics details what we can actually calculate we can say okay can we understand these amplitude amplification forces so i have a parameter space which is very large this part here i cannot access because my approximation breaks down i don't have a good description for it this space here is hard to access because it's just hard to have such high flow rates in these kind of things so i here's my parameter space and i want to find my points here but what is the maximum amplification which i can get in this and is it in the linear part of the regime so it's a huge parameter space and the challenge is now to find one point where we can do this experiment and where the effect is large enough to be seen and for the large enough to be seen it means what is the amplification i send one in what is times what am i getting and what we can see is this is kind of like what we did we calculated actually fluid parameters these are things for example constant angular velocity at the rise these are of constant surface gravity of the horizon and then we calculate that and go from fluid parameters to analog space then geometry parameters and then here we have the angular velocity at the horizon here the surface gravity and what you can see beautifully is that it mainly depends on higher angular velocity but it also increases with increasing surface gravity so uh and one of the things also samina asked me in the break and pointed out so this analog usually in a real rotating black hole we can anyway only mimic part of it but if you would only have this part it would only depend on this quantity because i have another three parameter in here i only don't it doesn't only depend on this it also depends on the surface gravity so i can see this effect the space time geometry is a bit more complex so but you can still see this effect and perhaps somewhere here we can do this experiment somewhere 1.1 maybe we can see that so this just if you want to understand when this effect is the largest it really is mass seems necessary to to have the analogues based on geometry so i think this beautifully shows that it's it's not just adding a new way of fancy way of looking at it it really adds some value to this system now i'm almost done i have a few more things so a long long time ago 1980 i would say the first analog experiment it wasn't it's not really an analog gravity experiment but in this spirit it was fought by michael baird and he looked i think i'm running out of time i cannot really explain i can do this later if you ask me i don't have foam effect it's an effective quantum mechanics and he's which is unobservable in quantum mechanics he says in his favorite script and then says um he finds a water equivalent of that and what he does he looks um so there are no form effect um very quickly so if you have a cylinder there's a certain radius r and there is a magnetic flux the cylinder is penetrable and you have a beam of particles with the charge you see that this particle is experienced away from these locations and you can quantify from the charge and from the magnetic flux you can quantify a number and if this is to the next integer of this number you can calculate that you can see that that gives you how many wavefront dislocations you have so this number is one you have one this number is two and so forth and what he says actually you can see that for surface waves if you have only a rotation no draining or rotational and he repeats this experiments here and he says he can find the analog of this this quantity which he calls after here and he can calculate the analog and when i tune the things the right way then i can reproduce this effect here so these are surface waves that's the serum and what you can see if you take for example let's take the one which is very obvious let's take this one and you can see already here that this corresponds to this situation now why i'm interested in this because it's an old experiment i think it is really great this idea um but now you also have to include the analog spacetime geometry and it was sam dolan and oliveira they did some studies and they said wait a second if i not only have rotation if i only have drainage radial velocity what i'm seeing then i also have on top of that i have this effective space same geometry i have this frame dragging region and what they said okay here i'm sorry that the features are so bad but what he's basically pointing out to here's the effect with zero radial velocity if you take this into account what you're getting actually you get this additional pattern which is caused by the frame draining so this is not just an analog for it's an analog and analog basically here you can see some water equivalent of iron or form and you can also see some frame draining effects at the same time so i think this is a very exciting system and hopefully we will soon see some of that if it's not us also daniel departure is working on this he is using the fluid of light it's a very exciting medium it's graphene dissolved in methanol and he basically again of course he works in his optical system she uses food of life and he also wants to look for superintendent's country there's not more information so this is the only picture founders so now coming to the summary outlook perhaps and coming back to some of the questions what is it useful for and right so let's start with with the very top so what is the general idea to test some of these ideas in quantum gravity in table top experiments doing this analog simulation the idea is for example the reason why we need to do this why can we not study just the real world well it's very hard to do to have observation and access to existing like hoping radiation cosmological parties would actually do of course have some window of observation and but in all of these effects they're very hard they're very unaccessible so by having these experiments you really get some sort of feedback you can set them up you can study them you can test their robustness and so forth and i think i should have also there are some also i don't know if there has been an experiment on radiation but so far what people have done or working on are these kind of things here um you can ask another question could you perhaps at some point because this is here about quantum gravity could you perhaps at some point go a step beyond that and find analog systems for full quantum gravity proposals perhaps more in the sense of quantum gravity phenomenology or other things so but can you actually try to mimic and test some robustness perhaps the merchants of space styles or already horrible issues gravity in some sense has is a gravity theory a full gravity theory with including lawrence violations which should add to the renovatability to the theory so there's a lot of feedback by basically joining these seemingly distinct areas in physics and try to steal some concepts from one the other and try to to integrate all of that together because after all physics has its amazing ability that it repeats itself so and now let's just say what are what are the things particular these analog gravity experiments what do they try to address besides of being cool experiments so one of the things is how robust are these effects uh which you know were predicted within quantum field theory in classical and quantum classical quantum fields we encourage space and in particular i'm raising this question well you always just hear quantum fields through interrupts space-time and also this is a workshop called quantum quantum gravity quantum effects i'd say it's very important to add this classical because i think there is much more classical at least in this analog as it is quantum because the quantum things are very fragile entanglement in all these things stick coherence initial temperature effects all of that really makes it hard to access um but i believe soon there will be experiments that's not what i'm saying it's not impossible to say it has to be have to be very careful when you look at that um right how much and it's also a question of how much can we control these systems how much can we cool down about the engine and condensate right can we actually cool it down uh to a point much below that it has to be much below actually it has to be much below the chemical potential which is very hard to do experimentally and can we do that uh to a low enough temperature can we really see the analog cooking so as i said already um can we also we get some sort of feeling of how to to do these experiments how difficult they are we have this highly controlled environment perhaps inside this knowledge we get maybe it stimulates also to look for observational effects and last but not least as i mentioned anyway already can we get some of these motivations or some of the insights from the analog gravity system can we can we map them onto cool bone and gravity proposal thank you thanks you