 Yes, the Okinawa five minutes are over. So yeah, welcome everybody to the next edition of the theoretical sciences visiting program seminar series. And we're very pleased to have Arthur Chobanyan with us from King's College in Pennsylvania, where he's an associate professor. So Arthur has also done his PhD in Pennsylvania, more precisely at the Pennsylvania State University, broadly in the field of quantum cosmology and quantum gravity. Then he moved on to become a lecturer at American University in Washington, DC. And then later on, he moved to King's College, where he's a faculty now. So yeah, his research has actually to a large part focused on conceptual and technical aspects that arise or that surround the so-called problem of time. That's a conundrum that arises when you put quantum theory and general activity together where time is treated very differently into the two series. And the question is, how do you treat actually time in a theory of quantum gravity? One of the messages to take away is that one should consider time as some internal degrees of freedom, so actually physical degrees of freedom. So it should be really, at the end of the day, measured by something like quantum clocks. And the challenges that arise is how do you actually treat such quantum clocks when they can fluctuate and be in superposition and so on and so on. And yeah, that's a challenging field in which Ato has been working. And I think that's also what he will tell us about. And so the stage is yours. Thank you very much for a brief trailer for my talk. I want to thank everyone who's involved with the TSVP. That's a great program. As far as I'm concerned, thank you for giving me the opportunity to come here to wonderful Island of Okinawa. And thank you for coming to my talk to all of you. So a little bit about me. So my background is probably a little bit different from most people on campus. My home institution is a lesser known namesake of King's College in London is located in Pennsylvania. And its primary mission is actually undergraduate education. So there's about 100 faculty. So far it's comparable to OIST, right? Somewhere there. But we have about 2,000 students, vast majority of whom are undergraduate. There's a couple of our graduate programs in specialized fields, but everything else is undergraduate. Our mascot is a meanish looking lion called Leo. So I'm here at OIST until middle of August, located in the wonderful, brand new building of Lab 5 that I think you can see from here. And you can find me on campus, you know, gazing at the ocean views, which you can actually do from this audio turn here. It's impressive. If you share some interests with me, come stop by, find me, talk. If you wanna chat about anything else, I'll be happy to as well. So if you read the title of my talk a couple of slides ago, I was saying something about quantum clocks and rulers that may have come here under the impression that I'm about to propose a new radical way for measuring time or distances using quantum systems. Let me, that's not actually what I'm here to talk about. It's closer to what Philip was saying. My current focus is trying to understand how to do quantum mechanics without reference to external time or space. And the idea is, I go about this by using simple made up systems or toy models. This is schematic. I'm not actually working with this particular system of geometrical figures. The idea is simple, you have a total, some kind of a total system that has some smaller subcomponents. And the hoop is that, you know, all of these components can be treated using quantum mechanics. And then some components can provide references for time or space relations for others, right? So maybe subsystem A can serve as a clock and maybe subsystem B can serve as a special reference. And then it makes sense to talk about motion of subsystem C without referencing external time or space. Now, if you read the title of my talk more carefully, I also mentioned gravity there. And so what does any of that have to do with gravity? And a chunk of my talk will be trying to convince you that doing this is actually useful to a longstanding problem in gravity. Here's the very, very short version of what I'm going to talk about. And actually this fairly famous picture is useful at explaining what it's all about, right? So you may have seen this. If you are a physicist, you definitely have seen it. If you're not and you watched some popular science TV or went to a popular science talk, you may have seen this picture. What is on this image? This is our representation of the cosmos, basically. Everything that's existed. So this sideways cup is a chunk of the universe and it showcases changes over time. Each cross-section of this cup is a slice of an instant. Time goes from left to right. It increases. It starts at the big bang, the beginning point of our universe, or at least hypothetically. And then it ends somewhere around our time. So this slice represents a chunk of universe as it looks. Today, as we go back, here we have these large bright spots or galaxies. As we go back, stars are more evenly dispersed. They haven't clustered yet. We go further back. We get to a point where the interstellar gas hadn't collapsed yet to form stars. There's so-called dark ages. We go further back. And at this point over here, universe was actually too hot to transmit light. It was a kind of plasma. And then fun things happen here and you get to big bang and then we don't really know how to go back beyond that or whether it makes sense to do so. Why do I bring up this picture? Is that it actually consists of two parts. Well, so the cup itself shows the geometry of this chunk of the universe over time and how it evolves. It starts very compact. Then it rapidly expands. Then the expansion sort of slows down as the cup tapers off. Slows down, slows down, slows down. Then somewhere here begins to accelerate. So it gets larger at a faster rate. So over here, you may have thought, well, if it goes like this, maybe it'll turn into sort of a closed sphere. But here it definitely starts to expand some more. This is known as accelerated expansion. So the cup itself is geometry, which is synonymous with our current description of gravity. And it is fundamentally described by general relativity, fundamentally in the sense that this is the most basic description of space-time geometry and of gravity that we have and that works. The stuff inside the cup is matter, right? There's light, there is, oops, there's stars. And the most fundamental description for the stuff inside the cup is given by sort of broadly quantum physics. So standard model of particle physics, quantum mechanics. I will kind of use quantum physics to broadly encapsule all of those things. So matter is quantum and gravity is geometrical. And the two descriptions, the two fundamental descriptions of different parts of this picture don't actually work very well together. And that is the longstanding problem to which I'm referring the problem of quantum gravity. The union of the two, I would argue, and I think most people would agree, requires some adjustment from both, requires a different way of doing quantum mechanics and definitely a different way of doing gravity. And so the stuff that I mentioned on the previous slide, the stuff that I do is I am actually trying to make quantum framework a bit more compatible with the way gravity works. That's kind of my best pitch, right? For the rest of the talk, I will elaborate on these points a little bit. So the first thing, if you're not a physicist, this part might not make sense to you. Gravity equals geometry. How come our theory of gravity is a description of space and time geometry? Surely gravity should describe this, okay? How things fall, why they fall, and so on. How did it come to be? How did this come to be? And so I'm gonna rewind a couple of thousand years back. So gravity did start off as a theory describing how things fall. There was a theory of gravity due to Aristotle that got somewhat preserved. And he did try and answer questions for why do some things fall down while others rise up? He had an interesting answer for that. Well, I don't know if he had the answer or somebody else came up with, but his work includes an interesting answer. So I'm not gonna necessarily attribute authorship here. I'm not a historian. The answer was that the cosmos, his cosmos, was spherical and a spherical cosmos has a well-defined center, okay? So there's a preferred location in a spherical cosmos, the middle of it. And all terrestrial objects are made up of some combination of fire, air, water, earth, and they all have a proper place. And if you let them be, they will each sort of stratify, kind of like if you have a mixture of olive oil and water and you let it sit, that it will separate. I like to think that that's what Aristotle was heading in his mind when he was thinking about that. And so this does explain phenomena that you can see every day fairly well. Rain drops fall, rain drops are finding themselves in air. They need to be closer to the center of the cosmos and so they fall down. And air bubbles, for example, rise in water while rocks, which are presumably made primarily of earth, sink. One thing that is missing from this description of gravity that you probably also associate with gravity is motion of celestial objects, planets, satellite stars, and indeed, that was not part of Aristotle's description of gravity. Ancient Greeks did track planets that you could see with the naked eye. There's four of them plus earth. They knew that they moved them in interesting ways, but they did not connect them to these gravitational phenomena. That happened much later, about 2,000 years later. Isaac Newton was living in a slightly different informational background than Aristotle. By his time, the heliocentric model of the cosmos was accepted where the sun was at the center, not earth. And so the exploitation of gravity of Aristotle didn't make sense anymore. There was no, the center of earth was not no longer the center of the cosmos. There was no reason for heavy things to go there, or at least that wasn't the reason for heavy things to go there. There was also early use of telescopes, decent measurements of planetary motion, and not just of planets, but also of some of the larger satellites of Jupiter and Saturn. So there's a lot more data. And the theory that Newton constructed together with his laws of mechanics was a theory of objects pulling on each other, all massive objects pull on each other. Therefore, they basically disconnected this, apple falling and orbital motion of the moon around earth are sourced by the same force. So gravity has to do with both of those now, right? Really quickly, the actual force of gravity in his model of it, in order to compute it, you'd need to know masses of two objects, let's say earth and moon, you'd need to know the distance between them. And then you can compute the force mass one times mass two, it gets weaker over the distance divided by distance squared, multiplied by a proportionality constant, which is really, really, really small. And so gravity is mostly noticeable when objects are really, really, really massive. And then you get the force with which earth pulls on the moon, moon pulls on earth. The model together with Newton's laws of mechanics worked wonders, they explained all of this stuff very well, predicted a bunch of new stuff. And the one thing that really did bother Newton and contemporaries about this law was that this force acted over distance, right? Earth and moon are separated by what's mostly empty space, what is causing this pool of one object on the other. Most other forces that Newton and contemporaries dealt with and modeled were contact forces like friction and that sort of direct push of one object on the other. This was a non-contact force, there was no good explanation for it, it did bother them, but they kind of ignored, well, didn't completely ignore the fact that this was troublesome, but lived with it because it was so successful. So during the next couple of centuries, so I'm getting to more recent stuff gradually, other long distance forces have been studied and modeled using what's called the field model of interaction. So by other long distance forces, I mean electricity and magnetism. And the idea of a field model of interactions is that the objects don't directly push on each other or pull on each other, but that their interaction is modulated by field. There is something, for each interaction, there is a field that permeates all space, it has some neutral state. And when there is an object that has the appropriate charge that interacts with that field, it bends the field around itself in some way and the bumps in that field pull on other bits of the field, they can propagate, right? This bit of the field pulls on that one, that one, the bumps and folds and wrinkles can propagate out, and then they can affect the motion of other objects that are interacting with that same field. So in the sort of most modern iteration of it, the objects themselves have actually been replaced by other kinds of fields. And so it's really one kind of field, bumps in one kind of field interact, creating bumps in another kind of field and that field back-reactive. And so on, this is how we get around action at a distance today, basically. So the field model was super successful in capturing features of electromagnetism and people were hoping that you could do the same thing for gravity. So what's the field? What are the properties of the field that carries the pull of Earth on the moon, the sun on Earth, et cetera? And due to efforts of this gentleman and some of his contemporaries, we have more or less sort of the modern, most fundamental description of gravity that works that we know of called general theory of relativity. This is a statue of Einstein in Washington DC near the National Academy of Sciences. He's holding a piece of paper. There's a bunch of equations written. One of them is E equals MC squared. The other one, I can quite make the symbols. I think it's photoelectric effect. That's what he actually got the Nobel Prize for, I think. And then it's this one, Einstein field equation for gravity. Now, the equation is technical. It relates objects called tensors to each other, but qualitatively, it's saying something simple. The objects in red over here have to do with local space type curvature, how space and time geometry curve. The highlighted, the blue object over here has to do with how matter and energy are distributed around. So I believe this quote is sort of attributed to John Wheeler. And one way to interpret this equation is that matter tells space time how to curve, right? The matter distribution determines what the curvature looks like on the other side. And then through additional equations of motion for matter motion, space time geometry also dictates how matter moves, right? So there's the picture. I want to kind of demystify this a little bit over the next couple of slides, right? When I say space time geometry, I do mean some things that you normally associate with geometry, right? Length, angles, areas, volumes are associated with geometry of space. And then if you've ever drawn a position versus time graph, you've done a little bit of space time geometry, right? So in addition, you add time intervals, angles on a position versus time graph correspond with speeds, and then there's of course some slightly more generalized objects. You can have areas that involve time and so on. And so you do get some funky things there, too, a little bit. And right, so also those things can curve, right? What does curved regular geometry mean? Well, some of the postulates of Euclidean geometry that you've used will no longer hold if your geometry is curved. So for example, you could have two short lines you could have two or more shortest paths between a pair of points in curved space. The angles of a triangle might not add up to 180 degrees. The ratio of the circumference to the radius of a circle might not be two pi and so on, right? Pi is a two pi. Somewhere there, somewhere there, something like three. All right. So in practice, right, on the scale of solar system, these effects are small. Even though they're small, they are measurable and they're kind of intuitively dramatic, right? So bending space, one way it manifests itself is that a light ray passing by a massive object. So for example, the sun will bend its path. So the yellow here represents the actual path the bent light takes. And then the gray line here is extrapolated to where it appears that the light came from, right? If we assume it came from a straight line, we look at it and we say, ah, light came from somewhere over here, whereas the light ray actually bent. So visually it would seem that when you're looking at something next to the sun, the object shifts in the sky a little bit. Now the effect is really, really, really tiny. For the sun, you get the deflection of this angle is super exaggerated. This is the actual angle if I drew it, you wouldn't see it. It's about 3,600th of one degree, somewhere on the order of an arc second of the angle. It is, you wouldn't notice it with the naked eye, but it can be measured precisely that it is there. Another sort of well-known time bending effect is that if you are closer to a massive object, the time runs a little bit more slowly. If you're farther away, it runs a little bit faster. And on Earth, we have a lot of very precise clocks, some of them we've sent into space. And this effect, even though a small, is measurable and actually important in some applications. So for example, the clocks on the GPS positioning satellites run around 40 microseconds slower than the, sorry, the other way around. The clock on Earth's surface runs around 40 microseconds slower than the GPS clock per day. So that's on your accumulate. So the GPS clock accumulates extra 40 microseconds to us over one day. That's not a huge amount of time, but it's a very visible amount of time for an atomic clock. And it's actually a very disruptive amount of desynchronization. If you want to pinpoint your position on Earth very precisely, I think it leads to a discrepancy on the order of kilometers, which if you're in a city, it's a big deal. You end up on a completely different part of it. So gravity today is a theory of space and time geometry. Now, the tension comes because the gravitating stuff is made up of atoms and smaller things. So general relativity equations deal with bulk matter. So what you write there, the various tensorial objects, you write assuming that matter behaves as it does sort of on every day scale like solids and liquids and so on. But of course solids and liquids consist of smaller bits, smaller bits consist of even smaller bits. And then at some point you get to atomic scale and subatomic particles. And the gravitational effect of the bulk should of course come from the cumulative effect, each little bit gravitates and that should all add up to the gravitational deflection that's created by the sun or the time dilation that's created by Earth. Earth is made of protons, electrons, neutrons. So presumably each one of them contributes to this thing a little bit. Now, once you get to that scale, however, you have to treat matter using some type of quantum theory, right? Quantum mechanics, quantum field theory, whatever you have. And quantum theory has some pretty striking features that are not good friends with gravity. Let's put it that way. So let me try to describe a couple of those. One thing that happens in every quantum theory is a distinction between state and measurement, right? So if you wanna learn something about any system, you measure things, right? You wanna learn something about a friend, you ask what their name is. Well, they're not a friend yet, I guess. If you don't know their name, a person, you ask their name, where they're from, how old they are, these are measurements. You're asking, you're getting an answer and then you're keeping a ledger, right? You're writing all those things down for some reason. Well, maybe in your mind you just have a good memory. So roughly speaking, the ledger that you have as a state is your description of the state of that person and the questions that you're asking are measurements, right? And so typically we think of, you perform an exhaustive set of measurements and you know all the risks to know about a system. And that's your complete description of the state. In quantum mechanics, so the backtrack. In ordinary life, you think that if you know everything, the risks to know about a system, you can predict the outcome of any future measurement that you make on it. However, in quantum mechanics that is manifestly not true, if you have the most complete information in quantum theory, there is always measurements to which you only know the probabilities of their outcomes. You don't know for sure what's going to happen and it's not the question of performing more measurements. Performing more measurements doesn't actually help you, okay? So the second thing that's pretty odd and there's more things that odd, I'm not just being very, very selective, is that if your quantum system can be in one state or and then you know a second state that it could be in, actually you can superimpose those states, you can combine them in a variety of ways to get a whole bunch of other things that are also valid states. So let me try and illustrate this with a completely made up system. I'm going to call quantum lunch, right? So if you're not a physicist, this is all jargon mambo jumbo. Let's hope that this won't be, right? So imagine that the cafeteria in the center building began offering something called quantum lunch. So it's a quantum system. I get to make the rules for how it works. There are, it consists of, there's three measurements that you can perform on it. It consists of a drink, a main dish and a side, right? You can measure what's for drink and it's either tea or juice. I have very appetizing options here. You can measure the main dish. It's either tofu or chicken cooked somehow, presumably. And then the side dish is super salad. And now the rule of the rules of this particular made up quantum system is that the status of it is completely specified by specifying either the drink or the main dish or the side. If you've measured the drink of it as being tea, that's it. You don't need to measure anything else. In principle, that's your complete information about the system. The problem is that a state of tea gives you 50, 50% chance of measurement of main dish yielding tofu or chicken. And this is a fundamental, this is how quantum systems work, right? It doesn't make a huge amount of sense for lunch, obviously. But really, so this quantum lunch is described by single piece of it, by only any one of those three measurements, right? So supposing you want to eat tofu, right? So you go to the machine and you just wanna make sure that you set it in this, you know, that your lunch, that quantum lunch is prepared in a definite state of main dish and that that state is tofu. You go there and you get confused because you notice that the machine only allows you to pick tea or juice as states, okay? So bear with me. So this is terribly confusing, but fortunately there is a physicist behind you in line and he says, well, you can combine tea and juice states to get other states, okay? And so if you want tofu, you just order T plus juice. If you want chicken, you order T minus juice, all right? This is stretching the example a little bit, but bear with me. So he say, how do I get salad? And the friend says, aha, this is where imaginary numbers come in. See that I button on the screen? That's the imaginary unit, the square root of negative one. If you want salad, you have to order T minus I times juice, then you'll definitely get salad. The point I'm trying to make is that quantum systems have sort of mutually exclusive measurements that on the face of it, you wouldn't think of as mutually exclusive if the system were big and large, right? There's no reason for you to not be able to tell whether there is tea and tofu in your lunch. And the other thing is that the states can be superimposed and these superpositions can actually be measured, right? So if your quantum lunch is in the superposition of T plus I times juice, actually you can check that that's the case by measuring the side dish and you'll get soup. And that corresponds to the superimposed state, okay? So I'm sure this makes only a very limited amount of sense to anyone who's not a physicist. The physicist may have noticed that I've used the components of a spin-half system to make up my quantum lunch. There are other systems that are sort of more well known and that are real, that behave in a very quantum mechanical way. So let me talk about one of those. Electron and a hydrogen atom. And a hydrogen atom consists of a single proton. And a single proton nucleus and a single bound electron. And when I first learned about that, I had a picture that was kind of like this, that there is a heavy nucleus and a lonely electron orbiting it a little bit like a planet going around a star. But that picture is wrong because an electron orbiting a proton would do two things. First, it would have a continuous set of values for energy because there's no reason this orbit cannot be a little bit smaller or a little bit larger. There's no limitation on what kind of orbit it can have. And each one would have a slightly different value of energy, so it would have all sorts of possible energies that it would have. And second, it would actually be completely unstable because going around an electron being a charged particle would actually emit radiation, electromagnetic radiation, lose energy and spiral into the nucleus. So the best you can do, if you wanted to spatially represent what an electron is doing in a hydrogen atom is to plot the energy orbitals. So if you have done chemistry or physics, you will perhaps see in a picture a little bit like this. These display, these are spatial plots of different energy states of the electron, different orbitals, right? The word was changed from the word orbit just to make them slightly different, not to imply this picture. Each state corresponds to a specific definite energy and actually also angular momentum, but I won't focus on that. And what you're looking at is a heat map. The brighter spots are the places where the electron is more likely to be found, the dark spots are where it's almost impossible to find it. Each row corresponds to a single value of energy, right? So this is how the electron is distributed in its lowest energy state, the nucleus in the middle, it's pretty close to it. First excited state, second excited state, third excited state. One thing to note is that generally, when, so these states are states of definite energy, when you know energy off an electron that's bound to a hydrogen atom, you don't actually know exactly where it is around it, right? So if you look at this orbital, is it over here? Is it over here, over here, over here? It's probably not over there cause it's pretty dark, but you could find it anywhere where there is some probability of finding it somewhere, anywhere there is some red or orange. Location of the electron and energy that it has are kind of like the, let's say the side dish and the drink in the quantum lunch. You cannot specify both of those things simultaneously. So this is relevant, right? In that state of definite energy off a bound hydrogen atom is a state of superposition of various positions that could be here, here, here, here if we look at the state, for example. And so the question for trying to say, write Einstein's equation for an electron to see how it curves space-time is, where exactly is it going to be curving space-time? If it's distributed like this, is it curving space-time over here? Is it doing it over here, over here, over here? Is it some combination of those? And general relativity really isn't equipped to handle this fuzziness. This is not just a problem for gravity. This is a problem for any field theory, right? Except all of the other field theories have quantum versions of it. So in order to deal with this fuzziness of particles that interact with fields, all of the fields have been quantized, except gravity. And so seems like this is also what you might need to do with gravity in order to make sense of how bulk matter gravitates if it consists of these small bits. And so sort of a quick shout out to the quantum machines unit. They're working on ways to superimpose much larger things than an electron to put them into a spatial superposition where the combination of them being here and here. So if you want to know more about the work on that, talk to them. So the problems in getting gravity and quantum theory to play nice with each other, they kind of cut both ways. Quantum theory is actually also not very accommodating of some of the features of gravity. And one of the big reasons is that all successful quantum theories that we have, quantum field theory, quantum mechanics, they use space and time in some form as background structures. So here's all of quantum physics. And it sits on those pillars of space and time. There's three spatial dimensions. That's probably the time. And then you find out that those are not solid. You have to incorporate them into your theory. Not only can these elephants move, but they also move in response to what's happening on the thing that they're carrying. So just a quick example of Schrodinger equation. It gives you the rate of change of wave function in response to how it's distributed in space. And of course, to talk about rate of change of something or how something is distributed in space, you need a notion of space and time geometries. And all of the other quantum theories have objects like that in their formulation. Incidentally, this picture also is a good place to point out why there are so many approaches to quantum gravity. So once you let the elephants move, what are you going to hold fixed? Are they standing on something? Is there a tortoise? Does the tortoise move? Is it sitting on something or the tortoise is all the way down? So what are you going to allow to not be fixed in your theory? This becomes a basic question. So I kind of see the work of trying to bring the two fundamental descriptions of stuff in our cosmos together, sort of a giant puzzle. For the moment, it contains mostly theoretical pieces. So what I described to you is a theoretical tension. It's not really very practical in that you don't really usually need to compute something like time dilation created by a hydrogen atom or anything like that wouldn't really be measurable. So the trouble with that is that you don't really know where to start. Do you work with the gravity? Make it more quantum? Work with quantum physics? Make it more gravitational? Do you try and create sort of a giant framework where all of them will fit and then some? And so my particular side of this puzzle is I research ways of trying to do quantum physics without referencing external time and space with the view of also making those things dynamical like they are in general relativity. I'm going to take a sip and then say a few more words about that. So I will try to be compact and it will take too much of your time beyond this point. So how do I do stuff? So here's an example of a textbook physics problem. And the idea here is to force a student to figure out where this car is going to land given how it went off a cliff. There's lots of problems like that, nothing very special about this one. I do want to point out that this problem includes things which are external to the problem it involves. It includes reference to space, time, velocities, things like that that require experimental apparatus to measure that are not part of the problem itself. The problem doesn't involve rulers or clocks. And if you take an undergraduate degree in physics, all the courses do that at all levels. But you probably won't spend a lot of time talking about what clocks and rulers are, what they do. And the reason is because there are very many different good clocks that all agree with each other. So you probably know what this clock and that clock are. One wind-up clock, pendulum clock. This is an atomic clock, I think an atomic cesium clock, the one that's used for definition of SI unit of second. This is a biological clock of my three-year-old son at the day after we arrived to Okinawa. There are processes in his body that tell him that despite the light of day that it is time to sleep and he falls asleep. So clocks are not necessarily things dedicated to timekeeping, but any processes that take a predictable amount of time so that all synchronize with each other. So earth rotating a certain amount of times around its axis as the earth goes around the sun, human body going through certain biological processes, and so on. So when you ask what exactly the clock measures, there are two extreme views. One is that it's measuring, there is such a thing as a flow of time, and then the clock is a flow meter, you immerse it in the flow of time, and the time flows and then makes changes to the clock in a way, and then you read off the flow of time. So this is a flow meter and a river. On the other side, there is the view that clocks track relations between events, right? And actually most of our timekeeping, at least in the long run, involves things like that. So for example, when I arrived to Okinawa, the sign was aligned with Aries constellation. I'm not promoting horoscopes and astrology, just using it as an example. Now the sun is aligned with the Taurus constellation. So there is this change of relations between the sun and earth that's happening at the same time as something's happening in my life. And then similar argument can go for space and rulers. Do they measure something that's actually there, or do they measure relations between objects? These two views are not exactly mutually exclusive unless you take very extreme versions of them. You can sort of work with combinations of the two. Normally, we unconsciously adopt this view because it's much less clunky, right? So if we are trying to solve this problem, we're just saying that laws of physics tell us how car moves over time. If we're taking sort of a relational view, we need to include the time and space references in our description of physical laws. We'd say something that sounds a little awkward, something like car's location reference is correlated with some reference timekeeping device here. Now, this is clunky, but actually it is productive. It is a productive view if you want to internalize time and sort of suck it into your quantum theory and make it an inside internal object. So let me use a very briefly used the simplest example of a relational model that I know of. So imagine a one-dimensional universe that's one-dimensional, one-space dimension. There's also time. So this is an example of spatial relationality. So I'm not actually going to worry about time. There is the river of time, and that's that over here. Now, there are these three-point-like objects, which I will call particles, not because they're protons or neutrons or something like that, but because they have no shape, they all just take exactly a point in space. And the only thing they can do is move around back and forth along this one line. And so the state of them, the configuration of them is completely described if I say where they are and what their state of motion is. So I'll use XA to label where A is from the origin, how far it is XB to label where B is from the origin, XC how far C is from the origin. Since the origin is completely arbitrary, this universe has no special features aside from those three objects. There is an arbitrariness in the description of where those things are. And the sort of undergraduate textbook approach for analyzing a problem like that would probably be to fix the origin somewhere and then worry about it later. You would fix it somewhere, you solve for what the position of A is relative to the origin B and C as functions of time. And the way in which the arbitrariness of the origin comes in is that there are going to be equivalent solutions that only differ by where you place the origin. If you want to make this system explicitly relational, there's a thing you can do if you formulate this in the language of Hamiltonian mechanics, I'm not going to go into details. The way to do it is to impose a constraint on the total momentum of these particles and fun things happen when you do that. When you analyze the system this way and you try to solve this, you do not get a definite solution for where this is as a function of time, where that is as a function of time, or that is as a function of time relative to the origin, instead you get definite solutions for the relations only for where this object is in relation to that one, where that object is in relation to this one. And there is a quantum analog of that analyzed extensively by the chair here. So you can do the same thing in the quantum version of the system, you can impose the constraint and again, fun things happen. Basically when you solve this constrained quantum system, you can no longer assign probabilities for where A, B or C are individually, but only for relational data, only for where C or B are say from the perspective of A or where B is from the perspective of C, and so on and so forth. Time relations can conceptually and technically be treated in the same way. So if you want to know how some, instead of looking at some system and how it changes over time, you combine it with some reference system and see how different states of this system relate to different state of the other system. And so you have some kind of a history of a co-evolution of one system and the other. Now, this is just a pretty picture. I'm not trying to imply that my models involve complex biological systems. My models still are a lot more like the particles that you saw on the other slide. This is just a little bit more pleasant to look at. You can see why temporal relations might be more complicated because to run along the time is a little bit more involved than to just shift the origin back and forth. That's a very simple operation to see what happens at a later time. You actually have to evolve both things and that is equivalent to solving dynamics. Nevertheless, these systems can be set up the same way. Constraints give you some of the same magical results, but there are definitely technical issues. And we just wanna say, right, there's lots of interesting problems to solve and wanna give kudos to the Cubits and Time Unit for sort of combining the work in relational observables in quantum gravity with the work that's done in quantum information. Because I think that has definitely led to some new and interesting ideas. And then I want to end on a lighter note to see if anyone is still awake. So I took the liberty of adjusting the comic to local geography. And yeah, there you go. So in the US where this comic originates, it's common to think of Australians as walking upside down. Whereas really, if you're over here, Australians are no longer upside down and the Brazilians are. All right, thank you very much for listening. Yeah, thanks very much for the nice talk. Are there any questions? Oh, you have a question? Thank you for your talk. That was very interesting. I come from neuroscience, I'm very little about physics, but I have delved into it a bit about the concepts of string theory. The things you're studying, what are your opinions and relativity to string theory and the fields that you can measure these parameters in? So I am not in string theory. So string theory, I guess is, like I would term it more. So if we do the puzzle analogy here, right? The string theory, so if you have like gravity over here and matter over here, string theory really is trying to find a unified theory of all of them at once, as opposed to say attempts to quantize gravity on its own and not necessarily have like a unified theory of gravity and matter, but at least one where the two can use the same language. So that's kind of my perspective on it. There's lots of other efforts to bring the two theories together and they all suffer from a different set of technical issues, but I do believe that this problem, kind of the problem of incorporating life geometry is a problem in all of them in some way, shape or form. Yeah. So thanks for the talk. It's a bit of an open-ended question. Are there any toy models or laboratory experiments you could use to explore these ideas? So there's, yeah, the toy models that I work with tend to be picked not for necessarily their realizability as table top experiments, but for kind of the theoretical features that they have. They resemble gravity in some way and you can solve them on a piece of paper without use of heavy computing. So off top of my head, not at the moment. But I think on the quantum information side, people are interested in quantum reference frames in terms of things that you can experimentally explore with them and Phillip might actually know more about that. So actually this relational notion of time, there has been one experiment that people have carried out when you simply make quantum clocks and you define a relational notion of time through correlations or entanglement of the clock in a system. So that is that mic on because for zoom it will matter. It is on, yeah. Yeah, so there's been an experiment about 10 years ago on realizing theoretical framework or description of time evolution through entanglement of a quantum clock with something else. That's in terms of this relational notion of time passing the only experiment that I'm explicitly aware of. Now this idea of quantum reference frames, that's something that has been realized to some degree in experiments, but not so much to stand in as relations for space and time. The quantum reference frames are something much more general. And for instance, there are instances in quantum optics where that turns out to be relevant or basically, but the quantum reference frame stands in for something else that has a somewhat more abstract meaning in that case. It's something that is associated with a gauge group such as in Maxwell's theory. So and basically you then define what you mean by lights and matter relative to a choice of quantum reference frame. And so they do appear in certain quantum optics experiment. But in terms of references for time and space, it's still something that is much more difficult to realize in an experiment. But mathematically, the framework is the same for portraying these quantum reference frames that act as references for space and time as those, for instance, for quantum electrodynamics. So first, thank you very much for the talk. I have a question about, I would like to have your opinion about, Einstein equations makes the links between matter and space time, right? But if matter is quantum, see the right hand side has to be quantum or classical according to you of the equations. So yeah, you have T menu that describe matter. Right, right. Matter is quantum. What about the left hand side? So, I mean, you can't really write it with like, you know, quantum side on one side and the classical side on the other side and make complete sense of that. So they probably both need to be quantum. Yeah, that's... So some people are trying to, for example, to make semi-classical approximation like the Georgie Penrose model. I don't know if you heard about it. You have matter is quantum, but you assume that space time is classical. So you can derive the kind of Schrodinger equations with gravity. And I don't know if you heard about it. So some people try to contest gravity, but up to now we didn't succeed. So there's definitely some like intermediate stages where you treat matter as, you know, semi-classical, right, the first one thing you, you know, yeah. There's lots of things you can do. One thing you can do is you make a geometry dynamical, but not coupled to matter. And so that's really cheating, right? You have quantum field theory on curve space time. You could derive semi-classical corrections to classical variables and then you can jam them in those equations. But then when, you know, right, like, and so, yeah, so these could be useful, absolutely. But they're not sort of a full, you know, right, not the complete deal, let's say. Does that make sense? Yeah, thank you very much. Any further question? If that's not the case, then let's thank Artur again. That's a nice talk. Thank you. If you do come up with another question, so he's here until August, so you can bug him. So thanks for...