Okay, so welcome back to the second part of this afternoon session, the third talk will be given by Roderick Mössner from Breslin on the fine structure constant in QSI. Okay, so hello everyone, I'd like to thank the organizers very much for putting together this meeting, inviting me here and going through all the trouble of making sure things actually work, which in hybrid meetings isn't so easy. So today I'm going to explain to you what the title means and the conclusion of the talk literally is the fine structure constant. First author of this paper happens to be at the school that I'm organizing at the moment, which is why I'm also delocalized that cell who's sitting here with wearing a mask. So Chris Laumann is lecturing up there as well. So several of us are here. Okay, outline is very simple. I'm going to say a few words about quantum spin ice, then how QED emerges there, calculating the fine structure constant. And if I've got time in the end, I'm going to say something about not just the photons in the system, but also the gauge charge excitations. And I'm going to try to unpack this as things go along. Okay, so the title is the fine structure constant. Of course, all you know, the fine structure constant is one of 137 in QED famously, and there are many ways of defining it. And famously, Pauli is said to have said that when I die, my first question to the devil will be what is the meaning of the fine structure constant. So even at the end of this talk, you will not know what the meaning of the fine structure constant is, but I'm going to try to tell you what the value is of the fine structure constant in an emergent system. Sorry. He may not have said this at all. The thing that he may or may not have said I read is the devil. Okay. Okay, so then several definitions of this are one perhaps, which is very physical is the ratio of the Compton wavelengths to the bore radius. So, you know, energy terms, you know, the Compton wavelength being the wavelength of a photon, which corresponds to the rest mass and electron. And similarly, the bore radius tells you something about the binding energy of a nucleus. And it turns out then that the maximal stable nucleus you can expect to have is roughly one over alpha. So atomic number of 137. And the subject of this talk is that we don't just have QED that lives around this, but we also have systems where we have QED as an emergent low energy theory. And so that will also have an alpha and the question then is, well, what is its alpha? And is it different? And if it is different, what are the consequences?  And this, if you're not interested in materials, you can simply switch off for the next few slides. So rare earth pyroclore magnet. So a lot of frustrated magnetism takes place on the pyroclore lattice, which is shown here instead of corner shearing tetrahedra. And the typically for the strongly frustrated systems we're looking at on the so-called A site, which is one of the pyroclore lattices here, there is a magnetic rare earth ion. And because of the coupling in tetrahedra, this is highly frustrated, as I'll show in a second. And there are many, many samples now, and many compounds, which people are looking at. So all of this started in the well late 90s, when it was recognized by Harrison Bramwell, that homium dysphysium titanate were really very special. They found a residual entropy at low temperatures, about which I'll also say a couple of words in a few slides. But things have moved on since then. So these task of spin ices are strongly anisotropic easing systems. But now people are looking at less strongly easing systems, so systems where transverse degrees of free and transverse terms in Hamiltonian play an important role. So here's an incomplete list of systems which have been proposed here. And I'm going to give you a few, I'll tell you a few words about one of them that we've been studying just as a motivation for why quantum spin ice may be moving from the realm of a purely theoretical idea to a more material idea. So if you actually look for a candidate quantum spin ice material, so there are several challenges and several levels. So first is you actually need some material, which is somewhat promising. You then need to identify a likely Hamiltonian for this. You then need to establish the phase diagram of that, which is a completely separate problem. And then you would ideally like to know where the Hamiltonian parameters of that material that you're guessing based on whichever consideration actually plays your system. And then you hope that your system is actually going to be placed in an interesting spin-liquid phase. So in Zerium-Circunate, the example that we've looked at, there's some, so we know what the local degrees of freedom look like. You can then write down the simplest nearest neighbor Hamiltonian. And there's a priori, no particular reason for assuming that the further neighbor terms are completely negligible, but at least you can symmetry classify the nearest neighbor terms. And then you can try to fix the pre-factors by essentially fitting simultaneously to as many different experiments as possible. And one of the very nice developments in the field separately from the availability of these nice samples, which have been coming online for a while, is that there are lots of experiments available. In particular, there are these four d-neutron scattering experiments now, where you can have four spatial resolution and inelastic scattering as well. And then you can fit those. You can then combine this with fits to magnetization curves and so on, so susceptibility and finite fields. And then you can try to extract some model parameters. But you're always limited by the fact that we don't actually know in a controlled way to analyze three-dimensional, strongly correlated magnetic Hamiltonians. And so you still end up doing some mean field theory or some approximate treatments, which may or may not be reliable. Okay, but if you do this for zirium circumnates, what I just said, then you end up with a mean field phase diagram and the best guesses based on essentially best fits to these experiments all have this thing living in a quantum spin ice phase. So the statement would be that if the terms in the Hamiltonian that you have left off do not lead to instabilities, and if you can cool the system to low enough temperature that the dynamics becomes quantum coherent, then you should have a quantum spin ice. This is work in progress. And I think it's imaginable that in the next four or five years, there will actually be a system where with some confidence we can say that it's a quantum spin ice. Okay, so this is the material side of things about which I won't say anything more for the rest of the talk. And now I'm going to come to the core of the talk, which is given that we believe we know the UV degrees of freedom. And we believe that we know what the Hamiltonians doing looks like. But nonetheless, we've got this hard many body problem. What we try to do instead is we try to write down the effective low energy degree of freedom. So there we've got a different set of pre factors, like point structure constant speed of light and so on. And we try to fix those from studying the short distance degrees of freedom. And then we say, okay, for low energy, long wavelength analysis, then the effective low energy degree of low energy system is going to be what we are studying. Okay, so let me walk you through this. So we're starting say with classical spin ice, we're getting about the quantum dynamics, just to explain this degeneracy. So classical spin ice has easing spins living on the sides of the pyrochlor lattice. There's an effectively anti ferromagnetic exchange between them. And if you ask what are the ground states, you find that the ground states are those states when each state for even two spins point in and two spins point out. And then there's an excitation gap. So you can flip a spin, but that costs you finite energy, the size of the easing exchange. And if you do this, you have these excitations. So okay, so if you do this, you have excitations which have the following property. So if you have two spins pointing in two spins pointing out, you can think of the spins essentially as a flux field. And you see that on each tetrahedron, the total amount of flux coming in equals the total amount of flux going out. And this is like say Kirchhoff's current law, if there's something conserved, it's divergence vanishes. And so that's what you have here. So the divergence of the spin field on the lattice vanishes. And if you've got an excitation, it no longer vanishes. And so just like say Gauss's law where you have divergence of E is row, can basically say the divergence of the spin field defines a charge for you, right. And so the excitations are charged in this sense. So in the same way that in that electric charges are charged according to Gauss's law, here similarly, if you have tetrahedron violating the ice rule, you end up with something which is charged according to this emergent Gauss's law. Okay, so that's the important starting point. And then the emergent electrodynamics. So there's several ways of seeing this. I think the cleanest way of seeing this is okay, we believe these are the degrees of freedom, we write down the simplest theory, which incorporates all the symmetries and which incorporates this physics of the divergence free field. And then we say this is the low energy theory. But here I'm trying to give you some pictures to motivate why this is a sensible thing to do. And this is starting with the ice rule states. So you can see here on this cartoon of spin ice and each tetrahedron, which I've just plotted as a cross here, there are two spins pointing in and two spins pointing out. But if you flip a spin, then this is the same as creating a charge anti charge pair. And the important thing is that these charges are de confined. But it's to say you can flip further spins and then rather than creating more charges, you actually move the charges if you do it in the right way. So this is shown here. Okay, and since there's a degeneracy, there's actually no unique path, no unique assignment of arrows, which you have to flip to have these two charges here. So I first showed you this zigzag path. So what's shown here is a path which is much more straight, but there are other paths which wiggle to different degrees, which are all consistent with the two charges of these locations. And so then we do statistical mechanics. We average over all of these. And if we average over all of these, we get a density of flipped spins. And that density of flipped spins actually looks just like an electric field in three dimensions. So you start off with Gauss's law. You know, div s is the charge. And then if you do all of this averaging, you have two charges like this, the spin density distribution is precisely that that you get for two charges separated by this distance. So this effectively at long distances, dipolar field, and at short distances, the Coulomb field one over r squared, I'm coming out of the side of these charges. So this is how classical spin ice is related to this Coulomb physics. And then the basic idea. Okay, sorry. There's no fast forwarding that I'm aware of, which can save you the pain. So this is the basic idea behind this. So the central ingredient is this high degenerate of the classical grand state manifold, which is reflected in the residual entropy that was mentioned earlier on. And then you can ask, okay, I've got this huge degeneracy. I'm basically doing, I'm basically doing statistical mechanics and this. And then you can ask if I just decide that I only allow these low energy states, and I add quantum dynamics, I've got a problem which is a lot like the problem of the Landau level, where you have a completely general Landau level, and then you add interactions say between electrons living in them, it's very similar. You've got a completely general set of classical spin ice states. And then you add quantum dynamics to them. And you can see the quantum dynamics can't be a single spin flip. There's a single spin flip creates a pair of charges and takes you out of the spin ice manifold. But rather you have to flip a loop of spins arranged head to tail, because that doesn't create any defects in this divergence free background. Okay, so this is what's known as the ring exchange operator. You simply take these spins, you reverse them. And so this is the simplest model, simplest microscopic model for quantum spin ice is the easing exchange, which gives you the spin ice manifold, and the ring exchange terms which give you quantum dynamics. And this kind of treatment is controlled when the easing exchange is much stronger than the ring exchange. But the problem is if it's much stronger than the energy scales don't work out very well. So what we're looking for in practice is that the easing exchange dominates and the ring exchange isn't all that much lower so that you can see it's affected at relatively reasonable temperatures. Okay, and then the classical spin ice is these energy scales just work out in a way that you basically don't get to see the ring exchange physics at all. Okay, so that's that. So we start with a microscopic Hamiltonian. And then we assert, if you don't believe me, read any of these papers, we assert that the low energy action actually is a quantum Maxwell action with an electric field and a magnetic field, which is just exactly the same form as Maxwell, Maxwellian physics. And so then we expect the low energy degrees of freedom to be effectively phonon photons, just like normal photons, emergent photons. And then there are charges of the magnetic field and charges of the emergent electric field. So that's the basic, these are the basic degrees of freedom of the long wavelength theory of quantum spin ice. And what we're trying to do now is make a connection between this Hamiltonian and the pre factors of that Hamiltonian. Okay, so we're going to use exact diagonalization techniques. And as you know, three dimensional quantum spin models are not very friendly towards exact diagonalization. But I'll tell you how we tackle this. But basically the idea is, we've got these different pre factors that we need to fix. And we actually only need to fix two different quantities. So essentially, the strength of the color energy and the speed of light. And if you combine those two, you get the fine structure constant of quantum spin ice. The special thing about the fine structure constant of quantum spin ice, it's the one dimensionless quantity which characterizes the theory, the other two, the other things like the speed of light actually dimension for quantities. And they change, for instance, if you just double the lattice constant, but if you double the lattice constant, say the, or do something like this apply pressure to your system, the fine structure constant remains unchanged, more or less. Okay, numerical plan of attack. I mean, you know the world record for exact diagonalization on spin systems is 50. But we don't need to do a complete exact diagonalization because we are restricting ourselves to the spin ice manifold. Even though that's got an extensive entropy, it's considerably less than that of free spins. And we were able to do or we rather self was able to do a complete exact diagonalization using up to 96 spins. So that that turns out is already is still small. I mean, the cube root of 96 is not a spectacularly large number. But nonetheless, I'll show you in the next few slides how the analysis proceeded to extract the various, the various quantities that we're looking for. Okay. So what we basically did is to get independent estimates for these quantities is to vary between different topological sectors and also vary the shape of the unit cell. So we basically got lots of data points. And then the hope is that the, you get in some effective averaging, which averages out the noise, which may be due to some fortuitous resonances of at finite sizes. And so that you can then fit to a large data set and obtain reliable estimates. So I think the central insight in all of this was that if you want to know what the strength of the Coulomb interaction is, so sort of the properties of the electric field, you do not in fact need charges, right? Because if you need charges, then you need to go outside the quantum spin ice manifold and your Hilbert space explodes. But you use the fact that they're different topological sectors, which in simple parlance means you can take a system with periodic boundary conditions and a non-zero electric flux. So this is shown here. You've got this pair of charges. You just take them around the cylinder, unilate them, and then you've put in a flux line. So if you now do the same course grading I showed you earlier, then what you'll find is that everything averages to zero, but there's, except for there's a non-zero flux in one direction. Okay. And then you can vary this flux. You can put a flux, you can have a counter flux going the other direction, which cancels it, but you can also have a flux in one of the other dimensions and so on. So you basically get a three-dimensional flux vector, which tells you in which direction the average electric field points. Okay. And so this triplet of fluxes is then one of the things that we, so okay. So then given this triplet of fluxes, you can then ask what is the ground state energy, right? And so since the electric field, the electric field lines have an energy, which is proportional to e squared over epsilon. Looking at those vector, which are permeated with a non-zero electric field allows you to get the essentially the, this e squared over epsilon without putting in effect, without putting in actual charges into the system. Okay. So here's the equation, which was used to extract the answer. And so this is what we got. So there's all these different values of the fluxes and so on plotted on the x-axis and effectively an energy on the y-axis and we use, and the color code tells you the density of the points is otherwise you, so most of the points actually do lie on this line and the width of this is given by rare outliers. And if we do this, we get the following results. So as I said, we get a dimension for quantity for this. The dimensions that are involved here is a lattice constant and the strength of the ring exchange. Questions? Okay. So that's that. Then for the photon, yeah. The thing is you actually need a number, right? So this is not universal. The number could have been anything. So if you had a reliable way of extracting the difference in energy between the ground state and the state with a non-zero flux, then you would have the answer, right? It's just I'm not aware of how you could do this. The only things that I'm aware of are always things which work up to the, up to the pre-factor. And since you have to solve a full quantum problem, I don't know any shortcuts either, but yeah, that doesn't mean they don't exist. It just means I don't know them. Okay. Other questions? Yeah. So in this case, it's negative. So in this case, it's such that the ground state wave function is no less, but I don't think that matters all that much. Right. I think it doesn't matter all that much. Okay. Was there another question on this? Yeah. As I, can you read it because I don't want to touch this and then not be able to go back to the current settings? Oh, can you show it there? Brian Skinner, go ahead. Yeah. Please give more details. Yeah. Okay. So the other thing we wanted is the speed of light. And so there, quite obviously, if you want to measure the speed of light, you take omega goes to c times q and then you fit the straight line. But the problem is, even if you've got a linear size of eight or something, you really don't have enough points to be deep in this, in this linear regime, as I'll show next. So what we basically did is take the full dispersion, say that we know which lattice this takes place on. We take the lattice, the plus sign of that, to get the dispersion as a function, not just in the linearized version, but in the, for the full Bria zone, since this is rotationally averaged, we get a curve which broadens. And then we plot all the data points we get from these different samples and then fit this line. And what I was saying is basically, we don't have any data points in the strictly linear regime, we just have it where it sort of starts deviating. But again, we have the points lying pretty narrowly on this line, expected from the lattice, the plus sign, then here's the speed of light. Okay. So these were the two ingredients. So now, if you're not interested in the technical stuff, just forget the last few slides, these are the answers. So this is what I showed you and the combination between the two of them is that the fine structure constant of quantum spin is 0.08. So you may say in contradiction to the title I gave you, 0.08 is not a large number.  So okay, so just before we get there, so the speed of light in quantum spin ice for reasonable parameters, whatever that means, is about 10 meters a second. So Usain Bolt is faster than this. But it's really a human speed from that perspective. And it's very, very different from the speed of light in free space. And this has a lot of implications say, in principle, you could shine light onto spin ice and turn it into emergent light inside. But it really doesn't work very well, because the phase space factors don't agree. Okay, but one of the things that I really like you to take away from this is that the fine structure constant quantum spin ice is an order of magnitude bigger than the fine structure constant of the photons that are hitting us all the time. And an order of magnitude actually is a lot. So relatively speaking, it has a high fine structure constant. Okay, let me just say you can also perturb the model. They're too natural, too simple perturbations, we could think of one as something that's known as a rock cyclism potential. Again, you don't need to digest particularly what that means, but basically counts the number of resonances which are possible and assigns an energy to them. And another one is just a further neighbor exchange. That's the first thing that we tried and it worked, which is why we use that one. So if you do this, so you get a perturbation parameter, which is the size of these perturbations called u and zeta here. And if you vary mu from minus a half to one, so at the so-called rock cyclism point is it's known that the quantum electrodynamics breaks down and the fine structure constant vanishes in the square root behavior. And then you see that you can increase the value of the fine structure constant by putting in a negative rock cyclism potential. If you put in the nearest neighbor exchange, the further neighbor exchange, it turns out that you can again change the fine structure constant, you can make it quite considerably bigger by more than a factor of two. And then when you hit point two, the system actually becomes unstable and goes into a different phase. And there's some arguments and it's not clear to what extent they apply outside for quantum spin ice. But in QED, there's some arguments which make you believe that actually QED itself becomes unstable at a fine structure constant of point two around there. So in that sense, point one is a fine structure constant is very large because it's only a factor of two within what you can actually do. But no one really knows what happens in detail at this very strong coupling. So but what I'm trying to say, not only relative to alpha QED is our quantum spin ice strongly coupled, but it's also a PSP strongly coupled compared to the maximum possible value. So was it a first order transition or? Yeah, okay. That I don't know. So whether you can think of it as an instability brought about by some collectivists, I don't know. How much time do I have left? That much? Okay. Wonderful. Questions? Okay. So then I'd just like to take one brief detour on a separate piece of work which relates to this, however, which is the question. So this is the basics of quantum spin ice, the photons, the speed of light, and so on. So this thing is strongly coupled. So I'm going to say a few more words about this. But I'm going to return to the question of what actually happens to the charges because I'd like to advertise. There's also a question, is there some, yeah, some other estimates we can do. So here's an example of something where you can do a very simple calculation and get what apparently looks like compared to exact diagonalization, a reliable result. And so I'd like to motivate this the following way. So I said, you can do some finite size ED as long as you restrict yourself to the ground state, spin ice ground states. If you put in charges, the scaling gets worse. It doesn't get catastrophically worse. If you only put in two charges, it's just like L, because the charges can only have L cube locations and so on. So it doesn't just blow up completely immediately, but you certainly can't do 96 sites.  And so the question, the reason that it's worth looking at the quantity I'm showing here is that two monopole density of states is because if you flip a single spin, which is what say a neutron may do, you actually create a pair of monopoles, a pair of charges. And these charges then, you know, they're various form factors, but the density of states is what you would see in principle in in elastic neutron scattering. So the two, the two particle density of states is a very natural quantity to look at if you're interested in looking at a fractionalized model. Okay, so just to clear up this detour, neutrons coupled to spins, but the spins fractionalized into these charges. So you can never create a single charge by itself the way you can create a single magnum by itself. So you always get two. So the natural thing to look at is actually a two particle quantity in here, the density of states is just the simplest thing to start with. And so there's a very cute way of looking at this, which is, those of you who've worked on MBL are probably familiar with thinking of a spin system of actually defining a hypercube, where basically each dimension of the cube corresponds to one spin. And if the spin points down, you're sitting on the left hyperface, if it points up, you're sitting on the right hyperface, so that flipping a spin always corresponds to going from one hyperface to the other. Okay, and so here we have this hybrid view of things. So we have these charges, which the location of which determines where the defect tetrahedra are, but we still have the spins, the dynamics of which this is the fundamental quantum dynamics. And the spins are more naturally thought of as living on this hypercube and the charges are more naturally thought of as living on the real cube.  And then the next shortest closed loop that you can have on the hypercube is actually length eight, you have to go around the parallelogram two times. So then we do what theoretical physicists are good at. We say we ignore everything above length six, so we just pretend that we have got a lattice, which has got closed loops of length three, but no longer closed loops. And so this turns this hypercube into a cactus known as a Housimi cactus. And the Housimi cactus is soluble. So you then can basically, I've got a hopping problem Housimi cactus, I can get a spectrum, I can then translate the spectrum and effectively, so okay, I get a spectrum and the spectrum is the solid line here. So this asymmetric line shape, a steep singularity here, and then this slower come down here. And then we compare this to a 32 site two to charge simulation, where we also got the two particle density of states out and they're basically overlap. There's a lot of uncertainty in this, say there may be processes which are present neither on the Housimi cactus, nor on the 32 site ED, which would make this just wrong. So we don't know, but the agreement here is actually quite good. So in other words, if you do low energy, low temperature, neutron scattering, the in zero's order, the thing that you should be looking for is a line shape like this. That's all I'm saying. If you find it, it doesn't mean you've got quantum spin ice. If you don't find it, it doesn't mean you don't have quantum spin ice, but this is definitely kind of thing to look for. Okay, sorry. Yeah, so it's basically convolutions of things which have, what are they called? What are the singularities of the band bottom called funho singularities? Yeah, so it's basically about just that physics. And it's depending on, yeah, and then it depends the dimensionality you're sitting in, but this is what you get. And if you change the sign of the hopping, it just gets flipped. No. Okay, so I don't know. I sort of suspect that they're not perfectly protected because, you know, the Housimi cactus is, lives in a different dimension than the actual physical system. But I also suspect that it's the, you know, the weakness of these other, the other perturbations, which preserves the sharpness of the onset would be my guess. Okay. All right. Okay, so let me, so this is the end of the results section. I'm going to say a few more things about the interpretation. But before I do this, I'd like to thank Sal, the Chris Lowman, who's the Leonardo building and Sid Moran Pudi, who's at MIT. And the last bit I did with Masa Ute Gawa, who's Tokyo. But I'd like to finish with a following observations. So famously, right, the integer quantum all effect paper was submitted. I think I can't remember what the submitted title was, but the ref repointed out that it's actually what's actually being measured is not E squared over H, but it's actually the fine structure constant. And one of the miracles of their topological physics is that you can take a dirty, relatively dirty semiconductor sandwich and extract the fine structure constant of the vacuum of QED to an accuracy of like 10 digits. So I haven't much they've got these days. Okay. And one of the, you know, ironies of life is this was so good that the standard standard of units was changed. And I think now with a change of the standards of units, the original title of Clitzing's paper was correct. And this one's incorrect, but I don't remember the details of that. Okay.  So exactly the opposite happens here, right. In quantum spin ice, we have a tunable fine structure constant. So we still have topological physics, because this is a spin liquid, that's an emergent gauge field. So that's what you can use to define a topological phase. The point now is we have quantum, you know, alpha quantum spin ice, which is large and tunable. So it's exactly the opposite of the quantum Hall effect version. So we go to a different vacuum and the different vacuum has completely different properties from our vacuum. And the miracle still remains that our vacuum, you know, there's that, you know, the permittivity and whatever of gallium arsenide don't matter. And you can still extract alpha from the quantum Hall effect. Okay. So just to summarize, so in quantum spin ice, we've got emergent QED with photons, electric and magnetic charges. There's promising experimental progress. We are moving towards qualitative and quantitative descriptions, I think more so than I would have hoped a few years ago. So we've got effective theories, finite size numerics and relatively simple analytical models. And between those, we're basically getting a grip on sort of the universal long wavelength physics. But in experiment, you actually most of the time do not measure the universal long wavelength physics. And for that motivates the study of sort of less, less universal, but arguably more characteristic and more, yeah, more characteristic features, which are seen at intermediate time and length scales. Thanks very much for your attention. I guess you probably remember that the limeshift causes a fifth power of a fine structure constant. So the question is, is there a solid state analog of the lamb experiment? So you could propose, which would measure this right. So in principles, it looks like just about every phenomenon QED in principle exists here as well. So spin ice is special in that there's a perfect symmetry between the charges. So rather than having a hydrogen atom, you're going to have positronium. And experimentally, the issue is that having the two charges orbit each other this way involves the collective motion of a large number of spins, because that's what's involved in moving the electric field lines along and doing this coherently is currently not experimentally realized. So that's right. So is there any corrections to crystal field levels? I mean, so crystal field levels for what I'm saying here are infinite temperature. Okay. Yeah, yeah. So there will be ground state correction of the energy. But if you talk about defects, there's an even stronger effect, which is if you take one spin out of spin ice. Okay. So if you take this spin away, you also have charges except for the only half the size. And so then you have basically a dipole, a charge, anti charge pair of half the size present, and you can ionize this to get the stationary charge, immobile charge, a defect charge there. And then everything that you said about something orbiting it, all of that's possible. And yeah, I mean, yeah, I think, I think as far as actually doing experiments, I concern that that isn't possible at the moment, but there is, in principle, something you could measure having this defect charge surrounded by an opposite charge which is bound to it and asking, what is its spectrum? I mean, so the likelihood that you will see corrections to this, of course, grows with alpha considerably, right? But I suspect that, you know, so if I were to ask what are the most striking features that you expect to see at look for things like triangle radiation, rather than, you know, the lamp shift, because, you know, there's nothing sacred about the speed of light here. And in principle, you can kick one of these things to move faster than the speed of light. So, you know, I think that's a lower order effect. And it's perhaps a more spectacular effect. And that's, that's why I start looking for, for strong coupling QED. What about magnetic flux sectors? Are they very magnetic flux sectors? Are they very high up in the... Okay, so just to use language. So in, in gauge theoretic length, so what we called magnetic monopoles in, in like 10 years ago, in this language are electric charges. That's what you talked about, right? You talked about electric flux sectors. What about... That's right. So these were the electric flux sectors. The magnetic flux is actually a lot lower. So this is, again, different from QED. I mean, I'm not going to get into, like, what magnetic monopoles do in normal QED, but yeah, the magnetic, so the magnetic flux sector has a characteristic energy scale, which is that of the ring exchange, and not that of the easing exchange. So it's actually down there. And so... Are you talking about the defect or you're talking about the state on the torus? On the torus. So it's basically the energy scale in center 2D, easing gauge 3D would be the energy scale of the vison. Yes. And that's typically, you know, in these kind of systems where you have a very high energy constraint giving you the constrained Hilbert space, the vison energy is typically a lot lower. That's the same here. So can you find it in your exact diagonalization? Check, check that your alpha is... I mean, one goes as alpha, right? The other goes as one alpha, something like that. Yeah, so the problem is that the, is separating out the photons from the purely magnetic degrees of freedom because they live at the same energy scale. So basically, it's much more likely that the photons enter a continuum determined by these magnetic excitations. And this is another reason why things become very difficult to analyze at these low temperatures, but these degrees of freedom are there. Photon continuum. The photons enter a continuum. So this is, you know, the separation I've shown you isn't strictly right in the sense that the param, so there's no reason why this thing at the zone corner should be below that. That's it. So the speed of light is so small, you should see it as a dominating effect at some temperature in the heat capacity. Is this feasible? And if I integrate the total entropy that is in this photon system, has it anything to do with the residual entropy of the classical system? Okay, so the answer to the first question is, as a matter of principle, there really is nothing stopping you from seeing that contribution to the specific heat. And if your measurement is accurate enough, you should see that there are two or not three photon polarizations. I think all of this should go through and there have been things approaching claims that you can do something like that. I think not everyone's convinced, but I think that it's not unlikely that this is going to work. Then the total entropy of the total polling entropy is going to be everything below the electric charges. To the extent that the photon branch is not separated from the magnetic excitations, I do not see how you can do a quantitative, you know, a half log three halves for the photons either. I think it must be split between the two. Perhaps there's a clever way of arguing how things should come down at low frequencies. We haven't thought about that. I think that might be possible. But I think just a straight integral would be the spectral weight here and not just the spectral weight there. Thanks a lot. So if I understand correctly, in real materials, in the material part, the models which describe them, they differ from the generic model for which you did your calculation. So that means that for each of these materials you have your own fine structure. That's correct. Is there any kind of upper limit for this alpha? Yes, so we expect that the fact that it became unstable at point two may not be a complete coincidence, but we don't have a particularly strong argument for this. I mean, you saw that even with relatively strong perturbations, it only changed effectively with a factor of two both ways. But this is the first determination and no one's looked at it systematically. Well, with these two perturbations and in principle, you could look at other perturbations and see what happens. It's just that's a lot of CPU time and it would be nice to do this systematically, but there's no way of doing ED systematically on families of models. There are a few questions online. So the first question is by Brian Skinner, who says, at a conceptual level, I don't understand how you are able to extract e squared over epsilon from your numerics instead of just epsilon. Since we are looking at states with electric field, but no charges, I would think that the proportionality between the squared electric field and the energy density is just excellent. So the size of the flux that you can put in is given by the size of the charge. So basically, it's true the energy is electric field squared over epsilon times electric field squared like in the capacitor, but the size of e is fixed by the size of the flux going through is fixed by the size of the charge. So it's like having a capacitor with epsilon times electric field squared and putting one charge in one capacitor plate and the other charge in a capacitor plate. It's that quantization which allows you to extract e squared over epsilon rather than just epsilon. Another question is what modifications do we need to make to realize the vacuum value of alpha? Okay, so the vacuum value being that of ideal quantum spin ice, anything. It's a non-universal quantity and unless you do something special, fine-tuned or clever, anything will change alpha. And last question is how you choose your model or system that it is icing or not other orientation direction that xy or hyzenberg. Okay, so the, okay, it's the short answer is point group symmetries of the pyrrole lattice. Slightly longer answer is you have each side has a local three-fold rotational axis. So you can either have an easing axis, easy axis or easy plane. That's the difference between easing and xy. And then it's an issue of, okay, so that's the next level. And then the next layer down, it's an issue of, you've got a certain amount of angular momentum. And if you think of an Anderson super exchange type calculation, whether or not you've got a matrix element between safety up in the down state depends on how much angular momentum you can actually move in one of these virtual hops. And then the classical spin Isis, which are the most strongly easing, there isn't a lowest order matrix element flipping things. So this is why it's very strongly easing. If you go to these others, you actually also have xy magnets, right? So it's not like you either get this or that, it just depends on details. Some of them are easing, some of them are xy. So both are possible. But there are reasons which are understood why the classical spin Isis are so strongly easing. Okay, I don't see other questions right now. So let's thank the speaker. And in principle, we still have a question session for all the afternoon speakers. So if there are questions, no, I guess we went already over time. So thank you.


The Tarzan and the Diamonds of Arshere. Tom joins the Tarzan Gregory Safari and agrees to proceed with them to their common goal to in Baca and the forbidden city of Arshere under the leadership of the Eight-Man. Tarzan and his friends are searching for Helen Gregory's brother, Brian, while Tom is after the legendary gem of the Hesseharians, the father of diamonds. Helen vanishes mysteriously, and Tarzan, leading the expedition to proceed under Tom and Darno, goes in search of her. On the trail, Larsen stumbles into what appears to be a man-built causeway, and Darno finds, scratched on the wall, words printed in English. Luke, a word in English. Nella, but this cannot be English. I have never heard that word before. A moment, Darno. Let me look at it. Ah, look at this. Examine it closely. What? I can make no thing of it. It looks like... Tonya depressed, like a word written upside down. Exactly. You see how the letter E is reversed and the L inverted? It is the word Helen. No, then no, you are right. Then she must have been here in this causeway. Obviously, my friend. See here, following the word Helen another word. Captive, also inverted, and a mark which may assume to be an arrow pointing in that direction. But why are the two words written upside down? Yes, I cannot understand. Place your back to the wall and scratch the word Helen with your fingernail. You will write upside down. Oh, of course. Then, my little Helen is a prisoner, but of whom we knew that. Yes, Wolf, if we knew that. Well, what we've been going to do now, follow this tunnel in here, or go to the jungle? I would say follow the causeway. It is wide enough to take the entire safari. It will save us cutting our way through the jungle. Yo, and with the torches, we can see first. Oh, that's a good idea. Bien. Then we shall go up and start the natives into the causeway. Come, Wolf. We will all go up, Darno. I anticipate trouble with the Mburi and the Minas. Trumbo? É pour quoi? Yeah, é pour, é du tout. Those fellows have been all right out in the open. But down here, they don't know. We will soon find that out. Come down, Wolf. Be careful of these steps, my guy. Hey, Wolf, here. Hey, Mburi, come. Wanda, Larsen, come back.  Yeah, some bully. There ain't no shatani down there. No tambi, doctor. Look, we go this way, Mburi. No more cut trail. Go plenty fast. Where won't Darno go? We go to Big Hole along Big Road down there. No. No can do. Watamishi gong a tapika in Devil Hole. Get sick. That place better Watamishi. Plenty taboo. There is no shatani. Not catch'um, we devil. Not there, Mburi. We go to come along us. No can do. Plenty taboo along that place. Watamishi no go. Mburi no go. But we pay dog, we pay some bully.  No go. This place taboo. That place taboo. Mburi, now Watamishi no go, no more. All come to here plenty taboo. But if we stay topside and cut trail, you go there. No more go. No can do. All this place taboo for Black Boy.  No argument will persuade them. Whether we follow the causeway or continue to cut trail, we must go on without our bearers. Well, those Black Rascals would rather tie on the spot and break one of their hidden taboos. If I had been allowed to use the fifth committee... There will be no whipping wolf. If they will not go, they will not go, and flogging them will not help matters. On the contrary, they would very likely turn on us. Yeah, sure, that's right. Well, then we camp right here, eh? And wait for Tarzan to come back if he does. No, no, we will go on. Ma Petitelein has been taken through that causeway. We must follow. We may even find her in there. We must be somewhere near to Invaka, perhaps even to Acheer. We know Ellen is alive. We can go on much more quickly with the native. Alors, what do you say, Larsson? Well, he was hired for the trip. In and out, we ain't injured. Boom, boom. At you, we're... Uh, Mokra said it. He can make better time without the native. Very well, and you and Larsson have the supplies brought here. We will go over them and make up individual packs of absolute necessities. Throughout the remainder of the day, little tome, Wolf and Larsson sort over bales, bundles and boxes, sitting here, rejecting there. Only such bare necessities, as are absolutely essential to their journey, are selected and stacked near the opening to the causeway. Well, now we bear lieutenant our supplies for the rest of the trip. Ah, they won't take us far. They will take us as far as necessary. I don't like the tone of voice you say that even. Just what do you mean? When these things have given up, we will no longer need supplies of any kind. Exactly, Mokra. Either we shall be in Acheer or dead. But according to the map, we are very near to Mbakka. Yes, darn-o, to Mbakka is a mountain. It is not Acheer. Well, Larsson, you and Wolf make individual packs of this. Let Mbakra's pack be light, Larsson. You may add the extra weight to mine. Yeah, sure. Well, we better get busy, Wolf. Mbully, Hala, 26. Here, up on that. You are positive. You no more go along this safari, Mbully. Mbully, now what the mission? No can do. This place plenty taboo. Bien, bien. You see all this cekula? You take.  You give this chit paper to big Franz Waibwana. He give Mbully Pesa. Can do, Buanna. You no come along, what the mission? No, we go on. This chit paper tell French Commissioner where we go. We are ready, Lieutenant. Come, darn-o. Nandezako, Mbully. Mbully, Nandezako, Buanna. That place had big taboo. Much taboo. Here, Mbakka, here. Give me your hand on these steps. Oh, well, we are all ready to go on. We will each carry a torch and proceed as far as possible before making camp. Let's carry out this vain and spooky place.  You know Africa better than that, Larson. If we listen to every native superstition, we would never leave the coast. By the way, have you noticed the rock tone? A mass of tangled roots, vines and creepers? Those things must have been growing there for centuries. Yeah, yeah. Well, this ditch is pretty deep. All of the 20 feet, I would say. I wonder where the other end comes out to. Back there. This was undoubtedly a canal at one time. Where the water it carried came from, I have no idea. It probably emptied into that river we crossed eight or ten days ago. Just look at those huge granite blocks in these walls. Where could they have come from? Nom-tam-nom-tam-nom. A magura that is not a wall. There is none on the other side. This must have been a waft where some large ships were docked. Look up there, that heavy iron ring. Donovetta, you're right. But that ring is stone. Not iron. Look how those blocks fit together. No cement. No nothing to hold them together. And see up there? That's a water mark. Here is the end of the wall. We step carved into the stone like those we saw coming back there. Hey, the canal makes it turn half. Maybe we get the camp half. No, we go on, unless magura is there. No, no, let us on team. Look out half. Some rocks and dirt have caved in. Baby, look at that on that big rock. Some kind of a hidden shrine. Bring those things closer. Look here, Donov. These carvings and hieroglyphs. Nom-tam-nom-tam-nom.   Skulls. Carved into stone. I do not like them. They are gruesome. Come away. I don't like them either. Look how those empty eyes are getting stared at us. They make me feel like someone was watching us. Perhaps someone is watching us, Wolf. I have had the feeling for some time. That's a grand eye, too. But I did not wish to mention it because of... Because of me, Lieutenant. Ho-ho.  Frightened by what their imagination places in dark corners. Brave little magra. Nevertheless, remain close to the lieutenant. I know her myself. I do not wish to see you vanishing thin air. The tunnel straightens out again. I can't find any dust. Just light way up there in front. Hurry up, eh. I think we've been come to the end of this thing practice soon. You see light? We thought we'd have his own. But it cannot be daylight. It was just beginning to get dust when we entered the causeway. It is probably moonlight. I think Larsen is right. We have reached the end of the causeway or some sort of opening. I won't be sorry to get out of this hole. There's curls. Watch every move you make. Hold yourself together, Wolf. Those things are merely age-old carvings placed there by a long forgotten ray. Aye, aye, aye. I know. But whatever they are, I don't like them. They look to me like a morning. I feel like they were swallowing us. All hieroglyphs look practically the same to me, Tom, but those with the carvings of those horrible faces, do you suppose they bear any relation whatsoever to the ones we first found? Aye, aye. I cannot say, Donald. I made a copy of the first ones we found. But you did not copy these others. No. No, to tell you the truth, these faces were not agreeable to me either. I was as anxious to leave them behind as our friend Wolf was. Well, yeah. At the Naval Academy, I made a study of some of the more ancient languages, Egyptian and some others, a set idea they spoke and talked. I did not get so far with the arrow glyphs. Wish now that I had devoted more time to that study. It is an interesting subject.  He has perhaps found the opening. Larson! Yes, sir, Lieutenant! Have you reached the end of the causeway?


This tasty beverage is the product of an infinity cocktail. Now for the uninitiated, an infinity cocktail is a batched cocktail that you're constantly subtracting from and adding to. It's an extension of the infinity bottle, the concept of taking the last smidge of a bottle that's almost empty and adding it to another bottle with the last bits of other spirits in the same category. The point is it's constantly changing by virtue of what you add to it. Some people are super into this. I'm not one of them.  No way. I'm saving this for when nukes are headed towards LA. But I'll happily pour off a little from bottles as I acquire them and make a big franken cocktail out of it. I know, I know, six of one, half a dozen of the other. I got the idea to do this from Aaron Goldfarb, a Brooklyn-based drinks writer. I'll link to the article below, and Aaron, if you're out there, thank you. Before I show you how to start one of these bad boys, know that this doesn't work with all cocktails. It works best with what we in the Barbas call aromatics, which are drinks that contain only booze. Old fashion, Manhattan, the Sazarak, you get the idea. Because if you want to make an infinity cocktail with a whiskey sour or a daiquiri, too bad. I mean, you're welcome to try, but I don't recommend it. But if you do, let me know how it goes. Now if you've been watching my videos for a while, you'll know I'm an absolute rum fanatic, so deciding what cocktail to start was pretty easy. I had to do a rum negroni. So I made five different negronis from these bottles, but instead of making them in the glasses, I poured them directly into the bottle in the center and threw it in the freezer. Whenever I want some, I just pour over ice. Oh, that's another benefit. It's super low effort. After I've poured off a few drinks worth, I make a couple more rum negronis using different ingredients. The more you add over time, the more complex the drink gets. Just don't pour off too much without refilling. And the end result is this fabulous drink that you really can't get any other way. I mean it when I say it's one of the best drinks I've ever had. If you have a large-ish bottle selection, you absolutely should start one of these. They're a lot of fun and they taste incredible. And if you do decide to start one, leave a comment and let me know what cocktail you choose. If you liked it, hit like. Consider subscribing if you haven't already and if there's something you think I should try, let me know in the comments. To infinity and beyond.


I'm Meg Gillis. I'm at Griffith University studying Criminology and IT. I'm majoring in Network Security. I started studying Psychology and it wasn't really for me. I wasn't ready to start studying. I'd always been interested in crime. So I did a Diploma of Justice at TAFE and then that led me into a direct pathway to Criminology and IT. I work full-time as a dental nurse. I have two days in the middle of my week where I'm at uni. It's Thursdays and Thursdays and Sundays are my study days. Everyone asks how I do it. I don't really know. I like to keep busy here. I chose Griffith for two reasons. One of them was that it had trimesters. Also because when I did apply for this double degree, it was only one of its kind in Queensland. Now I've found something that I'm really passionate about. My dream job would be an intelligence analyst. I just think it would be great. It's a fast-paced environment which I really enjoy. The flexibility of the trimesters allowed me to spread out my study load. It allowed me to continue working full-time.


I have to apologize for this one. We've done something to you that may be a little bit confusing. Today is over here on your left and this is 400,000 years ago over here on your right. So old is over here on the right and young is over here on the left and time goes this way. What's shown here first of all is the temperature in Antarctica. That's this blue curve down below here and what you'll notice is it sort of goes down and up and down and up. This is not temperature in the globe, this is temperature in a place in Antarctica which is called Vostok, but if you blur your eyes it is sort of temperature on the globe. And what you'll notice is that this really really really does not look like a random curve. It's sort of warm, cold, warm, cold, warm, cold, warm, cold, warm, cold. And you can see this just going tick, tick, tick, tick, tick. And if you look carefully you'll see some other faster sort of tick, tick, tick, tick, tick running down below here. There are techniques that people have worked out for you analysis to tell you what are the wiggles that went into making this curve. If you was on there this is what you get. There's a big tick, tick, tick, tick, tick at about 100,000 years spacing. There's one at 41,000 years and there's a couple at 23 and 19,000 years. And this is a remarkable thing because these are features of Earth's orbit and they were predicted decades before they were discovered. Molankovic and other workers before him said we know that sunshine on the planet is being varied by these things. And when you climate scientists finally get a good enough record you will find a peak under each of these arrows. And this one actually is an interaction of these two so they really predicted that one too. And so when it happened people actually found that. There's really no question that we could need to worry about that the ice ages are driven by features of Earth's orbit. They are not driven by CO2 or the brightness of the sun or continental drift. They're driven by wiggles in Earth's orbit. But these Earth's orbit wiggles have very little effect on the total sun that reaches the planet. All they do primarily is move the sun around. So some places we'll be getting more sun, other places we'll be getting less sun. And what's really strange I show you here is sort of mid-summer sun at the South Pole and when you see here when it was very cold mid-summer sun was actually high at the South Pole. It turns out that temperatures at the South really do depend on sunshine at the South. But they also follow sunshine in the far North. In fact the whole world follows sunshine in the far North. When ice was growing in Canada the whole world got colder in concluding places that were getting more sun. When ice was melting in Canada the whole world warmed up including places that got less sun. Now that's weird. Some places listened to their sun, some places ignored their sun. How did that happen? Well you'll notice the second curve up here. This is CO2 in the atmosphere. When the ice grew in Canada a huge number of things changed on the planet.  And it shifted some CO2 from the air into the ocean. When the ice melted on Canada these things changed back and it shifted CO2 out of the ocean and into the air. If you try to explain why the temperature in Antarctica really wasn't following the sun in Antarctica the temperature at the equator wasn't following the sun at the equator. If you ignore the CO2 no one has ever explained it successfully. If you include the effects of the CO2 it all makes sense. And so the ice ages are caused by features of Earth's orbit but they're globalized by CO2. And that helps us to understand that CO2 really does have an effect. Now, how's we then look at the future? This is the same plot as you saw before except I've squeezed it down to show you the level that we will go to. People taking this course are likely to see us go off of this page if we don't change our behavior. Some of you are likely to live that long. And so it is, you know, this was important to this but we may be going here. Now it is indeed true that as the CO2 gets higher it takes more to make a big difference but we are making a very big change to the atmosphere in something that we have very, very high confidence will affect the climate.


Ladies and gentlemen, please take your seats. Our ceremony will begin shortly. Please take this time to silence and set all mobile devices to airplane mode. You will be asked to stand, if able, at the appropriate time throughout the ceremony. Please render appropriate customs and courtesies during the singing of the national anthems of the Federal Republic of Germany and the United States of America. Military members in uniform should render a salute during both national anthems. It is customary for American civilians to place their hand over their heart during the singing of the United States national anthem. As a reminder, this ceremony is considered an outdoor event. Military members, please wear your cover. Ladies and gentlemen, please take your seats. Our ceremony will begin shortly. Kuchintag and good morning, ladies and gentlemen. On behalf of the Commander, United States European Command, General Christopher Cavoli, represented by the Deputy Commander, Lieutenant General Stephen Basham, and the Commander, United States Africa Command, General Michael Langley, welcome to the activation and assumption of command of United States Space Forces Europe and Africa, where Colonel Max Lance will assume command. I am Major Vernon Greer, and I will guide you through today's events. We want to thank you for joining us in person on this historic occasion, and we bid welcome to those attending virtually from locations around the world. We're fortunate to have a number of distinguished and special guests here with us today. Please hold your applause until all have been recognized. Mrs. Jennifer Saltzman, spouse of General Chance Saltzman. Mrs. Angie Basham, spouse of General Stephen Basham. Mrs. Leslie Lance, spouse of Colonel Max Lance. Senior Master Sergeant Sarah Demerist, spouse of Senior Master Sergeant Travis Demerist. Mayor of Ramstein-Miesenbach, Mayor Rolf Hechler, representing the host community of Ramstein Air Base. Deputy Mayor Anya Pfeiffer and Deputy County Commissioner Walter Alter representing the Kaiser-Slautern military community. State Secretary Nicole Steingoss and Mr. Daniel Schefner representing the institutions of the state of Rhineland-Falz. Parliamentary State Secretary Thomas Hitchler and Dr. Joe Weingotten representing the German federal level. Deputy Commander Allied Air Command. Deputy Commander Combined Space Forces Component Command. Air Marshal Johnny Stringer. Commander Deutschland Space Command. Major General Michael Trout. Deputy Chief of Staff, Plans, Allied Command Operations. Major General David Ray. Commander United Kingdom Space Command. Air Vice Marshal Paul Godfrey. United States General Consul Norman Thatcher Sharpe. Commander United States Air Forces in Europe Air Forces Africa and Allied Air Command General James Hecker and his wife Mrs. Terry Hecker. Command Chief United States Air Forces in Europe Air Forces Africa. Chief Master Sergeant Randy Kwiatkowski and his wife Mrs. Stacy Kwiatkowski. Command Senior Enlisted Leader United States Africa Command. Sergeant Major Michael Woods and his wife Mrs. Jennifer Woods. Deputy Chief of Space Operations United States Space Force Lieutenant General Deanna Burt. Senior Enlisted Advisor to the Deputy Chief of Space Operations United States Space Force Chief Master Sergeant Tina Timmerman. Finally, we would also like to welcome all other host nation and NATO partners, flag and general officers, commanders, senior enlisted leaders, family and friends here with us today. Ladies and gentlemen, please stand for the arrival of the official party. Ladies and gentlemen, today's honors will be given to General Salzman. Please remain standing for the presentation of the colors and the playing of the national anthems of the Federal Republic of Germany and the United States of America. And right and right, Father, then let us all strive. Bread and right and freedom are the happiness and the joy. Oh, say can you see what so proudly last gleaming, whose broad stripes and bright stars. Thank you, technical sergeant Doolittle, for the wonderful renditions of the national anthems and to the United States Naval Forces Europe and Africa Band, led by musician third class Durbin. Thank you also to the United States Space Force Honor Guard for presenting the colors. Chaplain Grosskopf will now give the invocation. Today marks a significant and special occasion. And so as you are willing, please join me in a moment of prayer and meditation. In this moment, we pause to ask blessing from the one who is truly and totally above all things. From the almighty above, we ask for the strength, protection, and wisdom for all guardians who serve our nation through the Space Force, that in their service, they may have the character to act with integrity, live the connections of their brothers and sisters in arms, have the commitment to overcome all the challenges with which will come their way and the courage to act when it is needed. As Space Forces Europe and Africa activates today and their history has begun to be written, we ask for the almighty's hand to guide this organization that the guardians leading and serving in it may direct all those under their care to endure Semper Supra. Amen. Thank you, Chaplain Grosskopf. Ladies and gentlemen, please be seated. Welcome to Ramstein Air Base, Headquarters NATO Air Command and United States Air Forces in Europe and Air Forces Africa, here in Rhineland-Faltz, the land of innovation. It is my distinct honor to introduce our guest speaker, the Chief of Space Operations, United States Space Force, General Chance Saltzman. Commander troops, please put the formation at ease. Well, good morning, everyone. What a historic day. And I should also add, what a great German winter day. I mean, who needs the sun? Who needs to be dry? This is the kind. This is what you expect when you come to Germany in December and it's a fabulous day. Today marks a significant milestone for both United States European Command and United States Africa Command. The last component in Europe activated 78 years ago and it's been 15 years since the last component was stood up for US-African. Today, we reset those counters as we stand up United States Space Forces Europe and Africa to support both of these important combatant commands. Thank you, General Langley and Lieutenant General Basham for hosting us today for the stand-up of this new component. And to you as well, General Hecker, your support, especially in this time of conflict and the AOR, has been instrumental to getting us to this day. The relationship with the Air Force is special with the Space Force and I look forward to our continued partnership and I know how it will enhance the lethality of AFRICOM and UCOM forces as the nation navigates the challenges of global security and competition. I would be remissed if I also didn't think the space Illuminati that has graced us here. I'll just call out a couple of those, AVM Godfrey, Godders from Great Britain and Major General Michael Trout, I saw him earlier. So thank you, Michael. We just spent three great days in Berlin talking about the critical nature of space to this theater and others and it's so refreshing to work with like-minded nations, allies, partners with this important endeavor. So thank you all for being here. In fact, no matter the service, the combatant command, or the domain, I think we all understand that we are stronger with our allies and your presence gives us a lot of honor. Thank you. Finally, to Colonel Lance, Leslie, as well as the rest of Lance's family in attendance here or around the world. Thank you for answering my call. Thank you for your continued service to the Space Force and thank you for your service to these two combatant commands and our nation. As I mentioned earlier, this is an important date in the history of the Space Force as we mature our organization and our partnerships to take on the challenges and responsibilities of the space domain. The activation of Space Force's URAF is a critical step in this process. It is the fourth space component to activate as the Space Force establishes a series of components to directly support combatant commands with capabilities and effects. Today, we will integrate our Space Forces at the operational, the component level, something that will provide a cadre of space experts who can work with the Joint Force, our allies, our partners to integrate space activities into our shared operations, activities, and investments. From this day forward, Space Force URAF will enhance the security of our nation, our allies from Iceland to South Africa. Its area of focus covers 51 European countries and territories and 54 African nations. And we are not just giving UCOM and AFRICOM a space component, but literally one of the best guardian teams in the service. A truth demonstrated by the fact that this team was awarded the very first Space Force Polaris Team Award, the award for the top team in the service that embodies our guardian values of character, commitment, connection, and courage. That level of expertise will be invaluable to the combatant commands because space has become more and more central to joint operations. We are better connected, more informed, more precise, and more lethal thanks to space. The Joint Forces missions increasingly rely on space, and the Space Force is committed to ensuring that the force has the space resources it needs to succeed. That is particularly important here in the European and African theaters of operation. The Space Force is already very actively involved in supporting efforts in the region with our support to Ukraine being most visible in this effort. But our support to the region goes far beyond that. For example, the team here in theater debuted the first-ever execution of Orbital Warfare in UCOM's premier Tier 1 exercise, Neptune Eagle. The lessons learned are serving as a blueprint for all future Neptune events across three combatant commands. And this guardian team has also trained over a thousand personnel from the Joint Force and 25 European and African nations covering topics from foundational space concepts to advanced asset integration. This targeted development, education, and outreach generates substantial learning that is both informing future space component organizational constructs and educating our allies and partners on what space brings to the fight. So as you can see, space has long been part of UCOM and AFRICOM, and I'm thrilled that as of today, our guardians are officially joining the team as a distinct service component. We may be a small group compared to the numbers of soldiers, sailors, airmen, and Marines at UCOM and AFRICOM, but we are lean by design and I can assure you that this team punches well above its weight class. We have proven time and again that the effects of space and of our individual guardians go far beyond our numbers. And no one exemplifies this better than Colonel Max Lance, Gonzo. We wouldn't be here today without your hard work. About a year and a half ago, I called Max and I told him I needed him for a key job and he said yes, and then he asked me what the job was. I'll be forever grateful for his commitment, his dedication to the space force. And up to today, Colonel Lance has served as the director of space forces for headquarters U.S. Air Forces in Europe and AFRICOM, where he has led our space integration efforts in support of these two critical combatant commands. But I gave him one small additional duty. Along the way, he had to lead the planning effort to establish this service component, and here we are. There is no better officer to serve as the first component commander. He has seemingly done it all. He has commanded at squadron, group, and he even served as the commandant of one of our academic institutions in the space force, leading a multi-service military and contract faculty teaching space professional continuing education to 5,000 joint and international students per year. When it comes to war fighting and supporting to the joint force, he deployed in support of Operation Southern Watch in 1993 in support of Operation Iraqi Freedom in 2003, where he served as the space and information warfare planner in the Combined Air and Operations Center Strategy Division. My history with Max goes back two decades in you safety exercises, austere challenge, where he literally taught me about AOC operations and space integration. So as we formally established U.S. Space Forces Europe and Africa, my charge to the guardians is this be bold, be collaborative, be creative, solve problems, find answers. The missions of both U.S. European Command and U.S. Africa Command are critical and they need your best. And to the new commander, Max, on behalf of Jennifer and I, thank you and to the Lance family for your continued service. We wouldn't be here today without your commitment to success of the space force, and finally, thank you to all the guardians, airmen, soldiers, sailors and Marines throughout European Command and Africa Command, who have been working so hard to meet the challenges in both AORs and who will be continuing to work hard to ensure the success of U.S. Space Forces URAF. I look forward to working with you all and as we like to say in the space force, Semper Supra. Thank you. Thank you, General Salzman. It is now my privilege to introduce the commander, United States Africa Command, General Michael Langley. Good morning, everyone. I'm proud to be here today because this is salty. This is the time of year, the holidays that signifies the spirit of giving. You're giving in AFRICOM and UCOM. We are receiving. We're receiving the guardians. The guardians. So, I just say thank you. So good morning, Ambassador Gutman, General Salzman, General Basham, distinguished guests, colleagues and friends. What an absolutely historic day. The guardians are joining the force across Europe and AFRICOM. It's great to be here with all of you at this event as we activate Space Force, component of UCOM and AFRICOM under the command of Colonel Max Lance. I know this unit will be the best. It's already in the best of his hands. So, Max, as a fellow Texan, congratulations to you and your wife, Leslie, and welcome aboard. And to all your fellow guardians today, welcome aboard. Welcome to the AFRICOM family. Now, on the continent of Africa, it spans 11.2 million square miles. Now, I know that the U.S. Space Force, you're at. You'll be on the watch. The importance of space operations, commerce with our daily lives can't be overstated. I'll just say that again. Space operations are in our daily lives, our operations, our activities, and our investments. Communications, navigations, weather forecasting, it all depends on what you do. All the space-based assets, ensuring the Joint Force has the right information at the right time will work with all of other components to ensure that space planning and support is embedding all of our operations. Similarly, new guardians will aid our allies and partners to integrate ongoing future efforts of shared operations, activities, and investments across the whole continent of Africa. Space for your significantly increases the capability and capacity of the Joint Force are promoting stability and security to all our partners. We know that no nation can confront today's challenges alone as we develop our own space capabilities. African nations continue to ask for this exquisite capability. Today, 22 African nations have space programs and that 50 African satellites are already in orbit. That's because of your help.  Tunisia and Djibouti are the latest additions. These capabilities allow our African partners to monitor and address strategic implications of climate change, navigation, confront the scourge of illegal fishing and combat the activities of our violent extremist organizations on the continent. They provide a critical data that improves governance, increases stability, and reduces suffering across the continent. So in closing, I'll just say this. Space collaboration is well nested within Africa. Africa in our 3D construct was development, defense, and diplomacy. It facilitates the approach of the African-led US-enabled operations and they are the solution to the shared challenges of our African partners. So General Salsman, I want to say thank you for your commitment to supporting Africa and bringing forward Space Force resources to aid in a more stable and secure Africa. I know that the high ground is in the best hands of the guardians that work alongside our allies and partners to guarantee the celestial commons remain free and accessible to all. Let me tell you one thing. I know this weekend signifies across DOD Army Navy. Air Force will be watching too. But let me tell you guardian something the Marine Corps doesn't have a football team and you don't have a football team because America wants you on the watch. So you win every weekend. So we'll still be cheering for Army or Navy over the weekends but we know that we are on the watch. So guardians, you're along with the Marines on the watch watching over America in all our national assets. Thank you General Legley. United States Space Forces Europe and Africa is privileged to serve two combatant commands. It is my honor to introduce the deputy commander United States European Command Lieutenant General Stephen Basham. Thank you. Ladies and gentlemen, fellow general officers, senior enlisted leaders, distinguished guests from Rhineland Falls Mayor, very good to see you again my friend. Allies, partners on behalf of General Chris Cavoli UCOM Commander and Supreme Allied Commander Europe allow me to add my appreciation to all for joining us here on this historic day. General Saltzman Jennifer thank you for your tireless devotion to United States Space Forces. General Legley thank you for your leadership at Africa come as we continue to work together in this vital space domain and finally congratulations to Colonel Max Gonzo Lantz and to you Leslie on this momentous occasion. As we reflect on our rich history of space endeavors we see a long evolution bringing us to this significant milestone from the early days of space exploration to today's cutting edge capabilities. We stand at the forefront of a new era in space security Space knows no boundaries and our cooperation with our European allies and partners is essential. Our enduring transletic network is the cornerstone of our collective security and today's activation reinforces our commitment to that network it is a testament to the strength of our alliance that we stand together united in our dedication to safeguarding and benefiting from the space domain space has rapidly become a pivotal domain for our national security interest it underpins not only our military operations but also our daily lives our commitment to this domain is a reflection of the growing significance of space in a rapidly changing world as we look to the stars we recognize the need and importance for collaboration and cooperation in space as articulated in our national defense strategy cooperation with like minded nations provides us enduring strength and asymmetric advantage only by working together will we be able to bolster space situational awareness protect critical space assets and ensure peaceful and secure use of space both regionally and globally the establishment of the US space forces Europe and Africa will serve to expedite the progress we are making in this direction for example funding was approved this year to support establishment of the space operation center in Poland marking a significant step toward increasing space interoperability with the Polish armed forces other milestones include enhancing our various partnerships and satellite communication to demonstrate the power of collaboration and strengthening our space capabilities the deployment of defensive space systems throughout the theater showcases our commitment to increasing collective awareness and protecting our combined assets while maintaining the principles of freedom democracy and the rule of law finally right here at Ramstein air base we find a symbol of the enduring and robust US-German partnership this partnership plays a key role in fortifying our strong and strategic relationships through the activation of this new command we are proud of the partnerships we hold in this domain and the new ones that will blossom from this activation clearly no nation can confront today's challenges alone over the last two years the German, French, and British armed forces have taken steps in this arena by establishing separate commands dedicated to space in doing so they join a growing group of nations around the world that value the importance of prioritizing resources and operations across the universe together alongside our allies and partners our mission is clear we will protect our interests, safeguard our assets and promote stability in space across the region today's activation is a significant step forward in our commitment to space security and a shared vision that enables uninterrupted services from space on behalf of the populations we all serve I'd like to express my deepest appreciation to all those who made today's activation possible our achievements with allies and partners demonstrate our power of collaboration and together we will meet the challenges ahead to ensure a safe and prosperous future for all thank you and welcome again to our newest component US Space Forces Europe and Africa thank you General Basham the organizational change you are about to witness is the activation of United States Space Forces Europe and Africa as Senior Master Sergeant Demerist removes the flag from its casing may I draw your attention to the image in your program and the shield on stage while I describe the flags features the silver-gray outer border is in the shape of a delta a shape also formed by today's human formation the delta signifies defense and protection from all adversaries and threats emanating from the space domain the background is Victory Blue honoring the heritage of the US Army Air Corps on the background is the outline of the European and African continents showcasing the Space Forces Europe and Africa areas of responsibility the Polaris Star is positioned at the delta's apex reflecting the Space Force mantra Semper Supra which means always above the star's four points mark the United States Space Force core values of character connection, commitment and courage the cluster of small stars below represent the 12 organizational members of the North Atlantic Treaty Organization while the larger stars in the cluster symbolize each of the three organizations that will be supported by United States Space Forces Europe and Africa United States European Command United States Africa Command and the North Atlantic Treaty Organization below is a five point star that is drawn from the hap Arnold Heritage of the United States Air Force each point is defined by a delta that represents each of the other United States military services Ladies and gentlemen I present to you the flag of United States Space Forces Europe and Africa Ladies and gentlemen please stand at the center of the Secretary of Defense United States Space Forces Europe and Africa is hereby activated effective 8 December 2023 Ladies and gentlemen please be seated we will now commence with the United States Space Forces Europe and Africa Assumption of Command General Basham, General Langley and Colonel Lance please come forward the Assumption of Command Ceremony has been a part of military history dating back to the 18th century during that time organizational flags were created with color arrangements and symbols unique to a particular unit to this flag the soldiers would dedicate their loyalty and trust when an Assumption of Command was to take place the flag was passed to the incoming commander to indicate a change in leadership this gesture was accomplished in front of the unit so all could witness their new commander assuming this position this symbolic tradition has survived throughout generations of military history and today it will serve as the key element of this military ceremony at this time General Basham and General Langley will officiate the Assumption of Command General Basham will pass the Space Forces Europe and Africa flag to Colonel Lance symbolizing the transfer of responsibility for United States European Command followed by General Langley passing the flag symbolizing the transfer of responsibility for United States Africa command today Colonel Lance has been entrusted to Assume Command of the United States Space Forces Europe and Africa ladies and gentlemen please stand thank you General Basham and General Langley ladies and gentlemen please be seated in keeping with tradition the flag remains entrusted to the command's senior enlisted leader symbolically expressing the special trust and responsibility afforded to the command's enlisted members at this time Colonel Lance will receive his first salute from the guardians of Space Forces Europe and Africa it is now my privilege to present the first commander United States Space Forces Europe and Africa Colonel Max Lance Commander troops please put the formation at ease Guten Morgen, Serviette Gäste und Herzlich Willkommen it is great to be back in Germany this is my third time living in Germany once when my father was stationed at Spangdallem in the early 80's and again as a captain in the early 2000's here at Rammstein Deutschland des Wunderbar let me start with recognizing the leadership and vision displayed by General Salzman General Langley General Cavoli and General Basham it is not insignificant to add a service component to two combatant commands these generals understand the role space plays in modern warfare but more importantly have a vision of the critical role it can and will play in the future thank you for trusting us with such a special mission to the many senior leaders General Hecker, local dignitaries team Rammstein partners friends and family members thank you for being here thank you for the support you've given to you ahead of time for the support we'll be seeking from you in the future we're honored that you have taken the time to be a part of today's activation ceremony I especially would like to thank the many representatives of our allies and partners that are present thank you for being such good teammates let me also thank the team that put this ceremony together in addition to every member of the component staff I want to highlight that guardians from local units have attended today's event and are part of the formation I especially want to recognize the guardian that led the entire effort Senior Mass Sergeant Rob Lefty Yarns great job to everyone thank you Chaplain Grosskopf, thank you for the prayer and especially for incorporating the space forces core values into your sentiments senior I'd also like to thank our vocalist US Naval Forces Europe in Africa Quintet Band thank you for sharing your talents with us today and making this ceremony special finally thank you to the very recently created United States Space Force Honor Guard each member of today's honor guard was originally a member of the Air Force Guard before recently transferring their enlistment to the space force welcome guardians looking sharp great having you on the team absolutely it would be logical to think the beginnings of this component activation started four years ago when the space force was created personally I draw an arc that starts almost 20 years ago when then Captain Lance Captain Shuler and Captain Salzman who was an instructor at the Weapons School at the time and other guardians participated in an austere challenge exercise here at Ramstein thanks for the taxi sir our task for that exercise was to integrate space effects into the air campaign we concluded that exercise having failed miserably being extremely frustrated we did not have the structure the systems the policy the authorities the doctor and the personnel the education you name it we didn't have it to ensure that space was a worthwhile contributing member of the joint fight essentially the only thing we left that exercise was with desire a desire burned in from our time at weapons school that space needed to be properly integrated into theater operations for us to be successful in deterring a future war while we had no idea where our efforts that began in that exercise would lead over the years we realized the best solution would be presenting space forces to theater commanders as close as possible to how the other services present forces what we have termed normalizing the presentation of space forces this also required us to broaden the understanding that not all space forces should be considered global that there was in fact a case to develop regional space capabilities that would support theater forces fast forward too many years the establishment of the united states space force a few promotions more for some than others and we finally find ourselves in the most amazing situation the opportunity to finally normalize how space forces are presented to the theaters sound structural changes that turn the pickup game we've been trying to attempt to play over the last couple of decades into a professional team organized trained and presented for success no doubt the component we're standing up today will never be a small under ranked or less resource than at this very moment starting tomorrow we will gain in strength understanding and resources in order to add value to u-comm and to african every day we will get better and the theater voice for space will only grow we are activating the component because presence matters for the first time in this theater space will have a seat at the table presence will allow guardians to hear commander assessments first hand to hear what is not spoken to feel the priority of what needs to be done and to sense where risk is being taken presence is also critical in building relationships with allies and partners more than any other domain security in the space domain requires like minded nations working together side by side I have no doubt that this will be the most rewarding aspect of this position working with the best of the best from other nations so many whom made the extraordinary effort to be here in the audience with us today finally if I can ask for your indulgence I would like to end my comments today on a personal note I'm guessing some of you experienced some anxiety this morning as I jumped right into my comments eager to talk about space thinking that I somehow forgot to mention my wife on this moment this occasion not so fast I prefer to end on a high note and for me there's no higher note than my relationship with Leslie the beautiful amazing woman sitting in the front row rock star seating today Leslie is the source of my strength my joy a gifted teacher and the loving mother of our son what has become painfully obvious to me is that I'm completely unworthy of the support she unselfishly provides she has served our nation alongside me always willing to sign up for whatever was next not knowing what was around the corner I could not have been more blessed to find such a partner in life Leslie let me tell you that I love you okay to the guardians airmen civilians contractors that comprise united states space forces europe and space forces africa space for your af happy birthday now let's get to work thank you thank you colonel lance and congratulations ladies and gentlemen this concludes today's historic activation and assumption of command ceremony please stand for the departure of the official party and remain standing for the playing of the united states space force song on behalf of general basham and general Langley thank you to those attending both in person and joining us online we invite you to join us for a small reception in the back of the hanger to congratulate colonel lance and his family on his new command have a great day and I'll be back soon