 I would like to welcome our viewing audience to the second 2021-2022 Hitchcock lecture entitled A New Measure, The Revolutionary Quantum Reform of the Modern Metric System by William D. Phillips. We are pleased to present this lecture to the public and hope you will enjoy it. My name is Marvin Cohen and I am a University Professor of Physics and Professor of the Graduate School in the Department of Physics here at the University of California at Berkeley. First off, let me tell you a little housekeeping for the lecture. As you watch the lecture online, you are welcome to submit questions for Professor Phillips on our website where you are viewing the lecture. There is a button that leads to a form. The question and answer period will be moderated by Hoger Muir who is Associate Professor of Physics. He will pose your questions to Bill Phillips and organize them during the lectures. Please feel free to use the form to ask any question that you may have. The Hitchcock lectures were endowed by Dr. Charles M. Hitchcock in 1885 to Institute of Professorship at UC Berkeley. The Hitchcock Foundation lectures began in 1909 and were later expanded and retitled the Charles M. and Martha Hitchcock lectures in 1932 thanks to a generous request from Dr. Hitchcock's daughter Lily Hitchcock Coy. Chemists Linus Pauling, astrophysicist Stephen Hawking, and oceanographer Sylvie Earl are among the many distinguished scholars who have served as Hitchcock professors in the more than a century since the lectures began. I'm very pleased now to be able to present to you William Bill Phillips, our Hitchcock lecturer. Bill Phillips received the B.S. in Physics from Juniata College in 1970 and his Ph.D. from the Massachusetts Institute of Technology in 1976. After two years as a Thiam Weitzman postdoctoral fellow at MIT, he joined NIST which was then NBS the National Bureau of Standards to work on precision electrical measurements and fundamental constants. There he initiated a new research program to cool atomic gases with laser light. He founded NIST's Laser Cooling and Trapping Group and later was a founding member of the Joint Quantum Institute which is a cooperative research organization of NIST and the University of Maryland. It is devoted to the study of quantum coherent phenomena. This research group has been responsible for developing some of the main techniques now in use for laser cooling and cold atom experiments in laboratories around the world. Dr. Phillips is a fellow of the American Physical Society, the American Association for the Advancement of Science, and the American Academy of Arts and Sciences. He is a fellow and the honorary member of the Opical Society, a member of the National Academy of Sciences and the Pontifical Academy of Sciences and a corresponding member of the Mexican Academy of Sciences. In 1997, Dr. Phillips shared the Nobel Prize in Physics for the development of methods to cool and trap atoms with laser light. And so without further delay, I present to you William Phillips and his presentation a new measure, the revolutionary quantum reform of the modern metric system. Thank you Marvin. Thank you for that kind introduction. It's a pleasure to be here again with you virtually. I'm going to try to share my screen now and we will hope that this all works. Okay now, almost there. Okay, I hope you're seeing my title slide. Okay, so I'm going to talk to you about a reform that has happened to the international metric system. As you've heard, I'm from a place called the Joint Quantum Institute, which is joint between the National Institute of Standards and Technology and the University of Maryland. And I want to acknowledge the people that I work with on a daily basis, Gretchen Campbell, who's my group leader, Paul Let, Trey Porto, Ian Spillman, Ida Titzinger, Charles Clark, and Nicole Younger-Halperin are all the permanent members of the laser cooling and trapping group. And it's my pleasure to work with them on a daily basis. Now, the topic that I'm going to talk to you about today is something that NIST, formerly the National Bureau of Standards, has had a lot to do with. The reforms of the metric system are very much something that we've been concerned about and something that we have been pushing. And that's part of the reason why I'm here to talk to you about it. Another reason is the International Union of Peer and Applied Physics, IUPAP. I am a member of Commission C2 of IUPAP, which is the commission that has, as its responsibilities, things like units and symbols and and constants of nature. And so the metric system is something that falls under our purview. In fact, the modern metric system is very much the result of the activity of IUPAP. And so as a member of that organization, I'm spreading the word about the new metric system. And I want to repeat the invitation. Please ask questions. Please write your questions in the appropriate form. And we're going to try to stop a couple of times during the talk to address your questions. So what is this revolutionary quantum reform of the metric system? Well, I claim that the reform that was made on the 20th of May 2019, which I'm sure you all know is World Metrology Day, was the greatest revolution in measurement since the French Revolution. And the nature of that revolution is that it's a change to the international system of units. The system at the Nassau-Dunitay, or the SI, is what officially we call the modern metric system. And that system has as base units, the units on which all the other units are based, seven base units, the kilogram, the meter, the second, the ampere, the kelvin, the mole, and the candela are the base units of the SI. And the revolutionary change that has happened is that today, every one of those base units is defined by fixing the value of a constant of nature. Now, you may wonder, how is it possible to define a unit by fixing the value of a constant of nature? In fact, how is it even possible to fix the value of a constant of nature? Isn't that what nature has done itself? Well, with apologies to Stephen Hawking, the late great Stephen Hawking, I'm going to explain how this had been done already earlier with another unit of measure, namely the unit of time. And I'm calling that a brief history of time, my version. Since a long time ago, we have defined the second to be a certain fraction of a day. So a second is equal to one day divided by 24 hours in a day, divided by 60 minutes in an hour, divided by 60 seconds in a minute. So a day has always been, that is, a second has always been one day divided by 86,400. But since about the turn of the century, around 1900, we've known that that day length is not something that is constant. It changes due to all sorts of things, tides and changing ocean currents, earthquakes, change how fast the earth rotates. And the way we know that is that it was possible to make clocks, other clocks that were better than the earth itself. It began with mechanical clocks around the turn of the century, but by the middle of the century, we had atomic clocks. Now, yesterday, I talked about atomic clocks a lot, so I'm not going to go into them in detail. Here's a picture of the first atomic clock, which I had to admit was actually a molecular clock. This was a clock made at the National Bureau of Standards in 1949. And it's generally recognized to be the first atomic clock, even though it had a molecule, ammonia, as the ticker of this clock. It wasn't too long after that, that in England at the National Physical Laboratory, the UK equivalent of the National Bureau of Standards, that they made the first cesium clock. And cesium is still the clock that determines what we mean by a second. So here's a picture of Perry and Essen, who made the cesium clock, and inside this long apparatus is the guts of the cesium clock. Now, yesterday I explained a little bit, very simply, about how an atomic clock works. So I'll just repeat that here very briefly. The idea is, you've got an atom, something like a cesium atom. It's got a nucleus, maybe some core electrons, and around the outside, there's a valence electron. Cesium is an alkali, and that means it's got one valence electron. Now, that electron is spinning, and it can spin in two different directions. It could be spinning like that in one direction, and it could be spinning in the opposite direction. And there's a difference in the energy between those two spin states because of the magnetism of the electron and the magnetism of the nucleus. If you've got a magnet here and you turn it over, that takes some energy to do that. And that energy can come from microwaves. So you shine microwaves onto the atom, and if the frequency of those microwaves corresponds to the frequency, or the energy difference between these two states, then you'll make the electron flip its spin. And when it does, you can tell that the frequency is right. And then you know the frequency is this number because we've defined the hyperfine frequency of cesium to be this frequency, which is another way of saying we've defined the second to be some 9 billion, 192 million, and so on cycles of the radiation that corresponds to the difference in energy between these two states. And so we have atomic time now. The definition of the second is that it's the duration of the some 9 billion periods for this particular cesium atom. And ever since the definition of the second was changed to be based on atomic time that happened in the 1960s, ever since then, these clocks have been getting better. So here's a plot of how good these clocks were at various epochs. So when Esen first started, these clocks were good to about a part in 10 of the 11 by the mid 1990s, these clocks were better than a part in 10 of the 14. Just amazingly good. But that performance at a part in 10 of the 14 was essentially stalled out because of the fact that the cesium atoms are moving so fast. And this topic was discussed in more detail in my talk yesterday. And yesterday I talked a lot about laser cooling and laser cooling allow these clocks to get better still. And that's what the progression of the improvement of these clocks was like after the advent of laser cooling. And here's a picture of one of those clocks at NIST. This is Don Mekoff and Steve Jeffords and they cool atoms down below a micro Kelvin and launch them up here. They fall back down. It's sort of like what happens in one of these water jet fountains, where you have a jet of water going up, and it falls back down. So this is called an atomic fountain. And these clocks are good to about a part in 10 of the 16. They are allowing us to make the most accurate measurements of any physical quantity that's ever been measured. These clocks are the best at doing that, parts in 10 of the 16. So here I want to emphasize what has happened over history. We started off with the rotating Earth as being the timekeeper. And for many, many years it was the greatest thing there was to determine time. Observatories like the famous Observatory in Greenwich, England looked at the skies and used the rotation of the Earth to keep time. But eventually it was found by having better technology, first mechanical clocks and then atomic clocks, that this clock, the rotating Earth, was not as good as these new technologies were. That meant you could measure time better than what you could define time to be. And the only thing to do was to change the definition of time. And the definition of time was changed from this admittedly an artifact, an artifact that everyone has access to. But nevertheless the Earth, there's nothing special about the Earth. And obviously the Earth's rotation changes. To change the definition of time from that to something that is universal, the property of a particular atom. And as far as we know, it's completely universal, throughout the entire universe really, literally universal, that all seasoned atoms are the same and take the same rate. So this was a very important thing that was done about time. And it's the beginning of changing the definitions of units from something based on an artifact, something artificial to something based on a constant of nature. So before we go on, I want to just pause and see whether anybody has any questions. I've even suggested a few questions in case you want to ask me about these things. But if anybody has put anything into the questions, Holger, what do we have? We actually have a question that fits right to one of the slides you showed. And it was actually even asked before you started talking, but it fits so well. Wonderful. It is by Ashwin in Berkeley. And he's asking the definition of the second is in terms of cesium. Why cesium as opposed to any other alkali atom? Okay, very good question. And it's actually a question that I know the answer to. So it turns out that's a lot of things that cesium is good for. Cesium is the heaviest non radioactive alcohol I have. Well, rubidium turns out to be a little radioactive, but it's got a lifetime of billions of years. Let's forget about that. If you go beyond cesium to Francium, things are really radioactive. Okay. So cesium is stable. And it's the heaviest alkali. What that means is because it's the heaviest alkali, this hyperfine frequency, the frequency difference between having the nuclear spin and the electron spin in one direction and having in the other direction. And I told a little bit of a lie there, but it's not a really bad lie. The two that the two energy levels are essentially like that. That energy difference is the biggest of all of the alkalis. You want it to be big because if something messes up the frequency, let's say a magnetic field, then it's a smaller fractional change in the frequency. So we want to have the big frequency. That's good. The other thing is that cesium the heaviest of the stable alkali. That means that for a given temperature, it's moving slower. And the slower it moves, the easier it is to take care of all kinds of things that mess up the ability to measure its frequency. For one thing, because it's slower, it stays in the apparatus longer. So we've got longer to look at it. And because it's slower, we don't get as big a Doppler shift and we don't get as big a relativistic time dilation. So all these things are good that that cesium is heavy. The other thing is it's got a really high vapor pressure. That is, you don't have to heat it up very much in order to get a lot of cesium gas. And that's good because of course, you don't want it to move fast. And if it was hotter, it would be moving faster. And here's another thing that I think might have been one of the most important things. When cesium atoms hit a metal surface, if that metal has what we call a work function, the amount of energy is required to pull an electron out of that metal. If that is high, then the electron on the cesium atom will get sucked into the metal. And cesium has the lowest ionization potential of most atoms. So it's really easy for the metal to suck the electron off of the cesium. And now you've got a cesium ion and that's really easy to detect. And you've got to detect these atoms somehow to make an atomic clock. So all these things were part of the reason why cesium was chosen. Now here's one of the great pieces of luck. It turns out that cesium is really easy to laser cool. So when laser cooling came along, this was great also. There's only one bad thing about cesium. When two cesium atoms collide at really low energy, it shifts the clock frequency a lot and that's a bad thing. So almost everything else about cesium is great. Excellent. And for those of you in the audience, the way Bill and I are going to do it is if you have a question that fits right to the slides that Bill has been showing, then we're going to address it right now. And other questions we're going to address at the end. So even if I don't ask your question right now, don't worry Bill, get to them in the end. But there is actually one question that fits extremely well right now and it came in a few minutes ago. If time was defined by the rotation of the Earth, how do we actually know that mechanical clocks are better than Earth's rotation and not vice versa? Yes, exactly. Well, when somebody makes a mechanical clock and understands how that mechanical clock works, then they've got a pretty good idea. What kinds of things could be changing the ticking rate of that clock? So let's say you make a pendulum clock. This was the first kind of mechanical clock that was good enough to see that the Earth's rotation rate was changing. So you make that pendulum clock and you know because you've studied physics that the rate at which the pendulum swings back and forth is determined by only a few things. The moment of inertia of the pendulum, the acceleration of gravity and you know that these things don't change very much. And so when you see that the Earth's rotation rate is changing and there's no good reason for it, then you think, no good reason for your pendulum clock to change. Then you think, ah, maybe that's what's going on. And then you make another kind of clock. You make a clock made from a quartz crystal that vibrates at a certain frequency and you find out that that clock is also showing that the Earth isn't constant in its rotation. So you make a number of different clocks that you believe are constant in the way they behave and that gives you the confidence to know that it's really the Earth that's changing when you make these observations. It's a really good question. And maybe related to it and then we'll let you proceed with your slides. Anne in Berkeley is asking, don't you need to have a good definition of time and frequency in order to measure the hyperfine energy levels accurately? Yeah. So what happened was people used the old definition of time to make a measurement of the hyperfine frequency. And then at some point they said, let's take the best measurement of that hyperfine frequency using the old definition of time and let's define the hyperfine frequency to be that measured value. The beauty of doing it this way is that you, there's no discontinuity in your understanding of what is meant by a second. If you take the best measurement of the hyperfine frequency measured with the old definition of the second and then you use that measurement to redefine the second, that means your new definition of the second is the same as the old definition of the second to as well as you could measure the hyperfine frequency. And that's the best thing you can measure. So nobody's going to notice that you changed the definition. And that's the way we always want to do it whenever we change the definition of any unit is to do it so that no one won't notice. And from then on, things are going to be better. Thank you. Let's go on. Okay. Right. So let me see if I can find my way to my next slide. Okay. Wrong slide. I'm sorry. That's for stopping the next time. Okay. Now, this is, we'll get it. Don't worry. We're almost there. Okay. Good. This is where we were before. Right. And now what I'm going to do is talk about length. So this is an even better story, the short history of length. Okay. Time was something that people are really interested in, even in ancient history. But length was really important because length involved commerce and it involved construction and people have been building things and selling things for a long time. And so the earliest approach to length was to use the human body as the standard. A foot is a foot, right? A yard is the distance between the center of your body and the tip of your fingers. A fathom is your wingspan. This was really great because it meant you always had your standard of length with you. The trouble is it wasn't very consistent. If you were buying fabric from a short fabric merchant, you might not get as much cloth as you were expecting because this guy measures it out by stretching the fabric out from his nose to his fingers. So people wanted a better way of doing things. Something that would be more consistent. Well, so one way of doing it was historically to use not whatever human body you happen to have, but the body of the monarch, the king or the pharaoh. And that's how they did it in ancient Egypt. The royal cubit of ancient Egypt was the length of the pharaoh's forearm. Now, these guys were really clever. They realized that it wasn't very convenient to always go to the pharaoh to determine length. So they made an artifact. This is a picture right here of the stone artifact that was made in ancient Egypt to represent the length of the pharaoh's forearm. And then people made wooden secondary standards that were the same length and took them out in the field and did things like build the pyramids. And they were required by law to recalibrate their field standards, these wooden standards to recalibrate them every month against the stone standard. And the penalty for not calibrating was the death sentence. So these guys were really serious about metrology, so serious that the pyramids are incredibly well made. The baselines of the pyramid are consistent to a small fraction of a percent. They're square to 12 arc seconds. They were really well done because these people were serious about metrology. And the way they did length was with a single artifact standard. The idea of artifacts spread out through the whole world, but it was often something that was an artifact that applied to a particular town. So you would go into a medieval town. This is the town of Regensburg in Bavaria. And there would be in the wall of the square of the town. This is on the city hall would be the standards of length. And here a tourist who happens to be the spouse of a metrologist is comparing her fathom against the Regensburg fathom. And you can see this is probably a good place to be buying fabric because they had a pretty big fathom. But if you were to go into the towns in surrounding Bavaria, you would have a different length standard. Now this was a really vexing problem, but it was extremely common. Come the French Revolution. The revolutionaries have all these wonderful revolutionary principles. And one of them they decided was, we're going to fix this problem. And the way they fixed it was by defining a new standard of length, which they called the meter. And because they wanted something that would be available to everybody, it would be super democratic. They said, let's use something that everyone has access to, to define the meter. Let's use the earth. And they defined the meter to be one 10 millionth of the distance between the pole and the equator along a meridian that goes through Paris. Okay, so maybe it wasn't all that universal because it had to go through Paris, but you get the idea. So what did they do? They sent out surveyors, people who were really skilled in the art of knowing where they were and measuring the distance between points. So they sent a team of surveyors to the north toward Dunkirk and to the south toward Barcelona. And they measured the length of the meridian between Dunkirk and Barcelona. And then knowing something about what the shape of the earth was like, they extrapolated to the distance between the pole and the equator. And they brought that measurement back. It took them years to do it. They brought them back to Paris and compared it to the old standards of units. And they did just what the revolutionaries in Paris did. Now, first, let me say this is the revolutionary dream. They wanted something that was good for all time and for all people. And they cast this metal to sort of emphasize this idea. You see this mythological angel actually measuring the earth. But that's what they really did. They did measure the earth. But they realized that measuring the earth was great to do once, but you didn't want to do it every time you wanted to measure something. So they did what the ancient Egyptians did. They made an artifact. And this is a picture of a platinum rod that was deposited in the archives of Paris in the year 1799. And it is one meter long based on this years of surveying of the size of the earth. So that was 1799. Some decades later, following the famous Coventine de Metres of 1875, the countries of the world agreed to adopt the metric system as their own standard of measurement. The United States, by the way, was one of the original signers of this treaty in 1875. And one of the things they agreed upon was to make a new meter. And this new meter was not the distance between the ends of a rod, because the trouble with the ends is you have to touch it to know where the end is. They put two scratches on a rod, and the meter was the length between those two scratches, which were very carefully made to be the same as the length of the meter of the archives. So this was deposited in a vault in Seve just outside of Paris, and it became the standard of length for the entire world. The distance between those two scratches, sometime a little bit after 1875. But by the late 19th century, people had learned that light was a wave, and that by making devices called interferometers, you could measure lengths using the wavelength of light as the thing that determines your length. So in this cartoon version of what's called a Michelson interferometer, you send light into the interferometer, and it comes off what we call a beam splitter, a half-silvered mirror, so that some of the light goes straight through, and some of the light is reflected. And each of these, the reflected light and the straight-through light, get bounced off another mirror that sends them back to this beam splitter, and some of the light from that light coming back goes this way to a detector, and some of the light from this fixed mirror goes, gets reflected off this beam splitter and goes to the detector, and the two beams of light interfere with each other and produce an interference pattern like you see here. Now the beauty of this is that if you move this mirror just one-quarter of a wavelength of light, now the wavelength of light is about a millionth of a meter, and so a quarter of the wavelength of light is, it turns out to be less than two-tenths of one-millionth of a meter, you move the mirror by that much and it changes this spot from being dark to being bright. So this interferometer can measure changes of distance that are much smaller than you can see on the scratch that's on the, on the bar that defines what we mean by a meter. So people started using interferometry as a de facto standard of length. People just said, we're going to say that the wavelength of this light is a certain, a certain length, and we're going to make measurements of length using it. And then you had the actual definition of the meter, which was the distance between these two, two scratches. And so we had the same situation as we had with time. The standard of length was not as good as the technology that allowed people to measure length. Well, it took them a long time to fix that, but they had to fix it, and they fixed it in the year 1960, which is by the way the year the laser was invented. And here's a picture of a Krypton lamp. It puts out a very pure orange light, and they defined the wavelength of that orange light to be a certain number. And so this became the new definition of the meter. But almost as soon as they redefined the meter to be based on the wavelength of this lamp, people started making lasers that had light that was more pure, that was more easy to use as a standard of length than was that Krypton lamp. And so this is a picture of what's called an iodine-stabilized helium neon laser. It produced an extremely pure and extremely stable beam of light that was always the same, the same wavelength. And people started using it as a defect to a standard of length. So people would say we're going to say that the wavelength of this laser is such and such, and we're going to report all our wavelengths in that, even though, again, it was not the official definition of length. So again, people had to change the definition because you had a technology that allowed you to measure lengths better than the very definition of length itself. So the obvious thing would have been to redefine the meter in terms of the wavelength of this wonderful laser that had been made. That would have been the obvious choice. Fortunately, they didn't make the obvious choice. Instead, they made a brilliant and beautiful choice. They defined the speed of light. Why does that work? Here's a universal expression. The speed of light is equal to the wavelength of light times the frequency of the light. People had learned by this time how to measure the frequency of light. So what that means is that if you were to define the speed of light and measure its frequency, you immediately know what its wavelength is. And that's what they did. The definition reads this way. The meter is the length of path traveled by light in one over 299,792,058th of a second. What that does is, of course, it defines the speed of light to be this number of meters per second. Now, the beauty of this is that if you make a better laser that's more stable, more pure in its light, this definition is still good. If you figure out a better way of measuring the frequency of light, and people did, then this definition is still good. In fact, these are the people who did. Jan Hall and Ted Hench learned how to make better lasers. They learned how to measure the frequency of those lasers. And they got the Nobel Prize in 2005 for doing that. People had already been using those new techniques that they had developed to make better measurements of length. So this is a really beautiful way of doing things. So you see what the concept here is? You started with an artifact. You changed it to a constant of nature based on a particular atom, krypton. And then you change it to a universal constant of nature, the speed of light. The beauty of this is that we should never have to change the definition again. As technology gets better, this is still going to be good. And now, on the 20th of May 2019, the international metrology community took this beauty, this brilliance that was applied to the definition of the second, I'm sorry, to the definition of the meter, and applied that beauty to the definition of the kilogram. And for that matter, to the ampere, the Kelvin, and the mole. So why did we have to do that? And how was it done? That's the next part of the story. But before we do that, let's see if there's any questions. And here is a couple if you're interested in knowing about those. So what do we have, Holger? Very at a point where I actually, anyway, the first question that you have on this slide, I like a lot, and I like to dress it up a little bit. I think every high school teacher in physics dreads the question, dear teacher, how can I measure the speed of light? And then somebody points out, you can measure it, it's defined. Exactly. So what? And I tell me, if you were in a physics class where your teacher asked you to measure the speed of light, that's not what you were doing. In fact, I joke that it's illegal to measure the speed of light because the speed of light is legally defined. So what are you doing when you measure the speed of light? You're really realizing the definition of the meter. So if, as a student, if any of you out there measured the speed of light after 1983, you were not measuring the speed of light. What you were doing was calibrating your meter stick or whatever you used to measure distance in measuring the speed of light, that's what you were doing. You were calibrating that meter stick, you were not really measuring the speed of light. And so that's what's happened. Whenever we've made these changes in the definition, and you'll see how that works out for some of these other things, when the definition was changed, this same experiment that used to be called measuring the speed of light is now called realizing the meter. And of course, we needed both ways. Before we redefined the meter, we needed to measure the speed of light. After we redefined the meter, we need to know what a meter is, and you do that by doing exactly the same experiment. So we have a number of more questions, but they are not specifically to what you just said. They are about clocks. They are about the humanitarian aspects of science and technology education. So Bill, save them for later. Do you want to comment on the second question or do you want to go on? Well, okay. So clocks are really good, and I haven't really said how good they are. I said that those fountain clocks were good to a part in 10 to the 16. The optical clocks that have come after and will soon replace them are good to a part in 10 to the 18. So you might ask, since C is exact, and we can measure frequencies to a part in 10 to the 18, do we measure lengths to part in 10 to the 18? And the answer is no. And the reason is that when we build an interferometer to measure lengths, those laser beams that are in the interferometer are not what we call plane waves. A plane wave is a wave that is infinitely broad. And so the wave fronts, the surface that corresponds to instantaneously, say the crest of a wave or the trough of a wave, that should be a plane in a plane wave. And it never is because our laser beams always have a finite size because we can never make anything infinite. That means that there's a curvature. And that curvature isn't the same everywhere in the apparatus. And that means that the distance between peaks of the wave might change because of that curvature. And so people do all kinds of wonderful things to make sure they understand the curvature very well, but there's a limit to how well you can do. And you can't do this well. I think people do, maybe you know, because you've made interferometers yourself, I think the limits are in the order of a part in 10 to 11, a part in 10 to the 12. Does that sound right to you? Okay. Okay, so shall we go on? Please. Okay, so this is what I just showed you before, that we're going to change the definition of the kilogram. Why and how? So for that, I'm going to give you a life history of mass. So in ancient times, it was the same old story. There were artifacts. Here are a set of stones that were the mass standards for ancient Babylon. This was great. It had all the advantages that these artifacts have and all the disadvantages that if you go to another place, then they're going to have another set of artifacts, and you're going to have a hard time comparing things. So the French revolutionaries figured that with their spirit of democracy and universality, they were going to solve this problem too. And they solved it in a way that made a lot of sense. They had the meter, and their idea of the meter was it should be the measure of all things. And they applied it to the definition of the kilogram. So new mass standard that they call a kilogram, it's equal to the mass of one liter of water. A liter is a cubic decimeter. That is a cube with a tenth of a meter on a side. And that is supposed to be that volume. The mass of that volume of water is the new thing, the new standard of mass, a kilogram. So that's great. Everybody has water. You got your meters. You got your standard deposited in the archives of Paris. The trouble is it wasn't that easy to get exactly a liter of water. Water wet surfaces. It produces a meniscus. The meniscus, the surface of the water is curved. The density of water changes with temperature. There's all kinds of things that make it hard to have a liter of water. They used all kinds of tricks. They made a liter or something else, dunked it in the water, measured the amount by which the mass changed like Archimedes did. But it still wasn't a very good way of doing things. So they made the best measurements they could and they made an artifact. This is such a universal way of doing things. They made an artifact and here it is. This thing that I'm holding in my hands is the kilogram of the archives. It was deposited in the archives in 1799, a cylinder of platinum whose mass is as close as they could make it to the mass of a liter of water. And now it becomes the new standard of mass for France, 1799. 1875, they agree there should be a new standard of mass called the international prototype of the kilogram. They make it to be as close as they can to the 1799 kilogram of the archives and they deposited in a vault in Sev near the meter, the international prototype of the meter. And here's a picture of it under three glass bell jars. And they made copies and gave them to all the people who were the original signatories of the treaty of the meter. And every once in a while people would bring their copies to Sev to compare them. And this was the standard of mass for the entire world. But now I want you to think about this. This is the definition of the kilogram. The kilogram is equal to the mass of the international prototype of the kilogram. Simple definition. Where in the 21st century, the unit of mass is an artifact, a piece of actual metal that was made in the 19th century based on an object made in the 18th century. That is scandalous. It's such a scandal that newspaper comic strip made fun of it. Here's the comic strip. So in this comic strip, a student in her elementary school says to her science teacher, am I right that we have redefined the meter as the distance traveled by light in a fraction of a second? We've seen this already. And the science teacher says yes, it's because the previous definition based on global distances was inaccurate at best. Okay, isn't this fantastic? This isn't a comic strip. They've really got it right. And then she says, and similarly, haven't we redefined the second which used to be a certain fraction of a day? And he says, yes, very good. And then she says, so why haven't we redefined the kilogram? And he says, we haven't. And she says, no, the official definition of the kilogram is still the mass of the international prototype kilogram and actual lump of stuff that's stored someplace. He agrees that this is incredibly unscientific. And she says, exactly what if somebody sneaked in and shaved off a piece of the kilogram? And this upsets him so much that he has to lie down. And now we find out that this was her whole plan to begin with to upset the teacher so much that he couldn't continue with his class. Well, nobody has sneaked in and shaved off a piece of the international prototype of the kilogram, but its mass is changing nevertheless. This is a plot of the comparison of a lot of copies of the kilogram made in exactly the same way as the international prototype of the kilogram. And it shows a comparison of them over almost a century. And you'll see that the mass of all these kilograms is going in the same way. It doesn't take too much imagination to think maybe the mass of the international prototype of the kilogram is changing, obviously in the other direction. The international prototype of the kilogram is getting a little bit lighter. So it looks like everything else in the universe is getting heavier, but it can't because by definition, the international prototype of the kilogram is a kilogram. We've got to fix this. This is just intolerable. And so we're going to use the same approach as we used for the meter. We're going to define a constant nature. So what are we going to define in order to fix the kilogram problem? Well, in order to explain that, let me remind you of what must be the most famous equation in all of physics. E equals mc squared. What does this mean? It means that the energy of an object at rest is equal to the rest mass of that object times the square of the speed of light. Great. Here's another equation. Not quite as famous. It says that the energy of a photon, a particle of light, is equal to Planck's constant times the frequency of the light. Now we've learned that we can measure the frequency of light. So that means if we can identify a single particle of light, then we can do something interesting. Let me equate those two equations and solve for the mass. What it says is that the mass, what do I mean by that? If I've got some object like an atomic nucleus, and it emits a photon like a gamma ray, and I measure the frequency of that photon, which we know how to do in principle, and I take that frequency, multiply it by Planck's constant and divide it by the square of the speed of light, I've got the mass change of that nucleus. Now we could in principle measure the frequency of the gamma ray. We've defined the speed of light already, and you see if we define Planck's constant, we've got a new way of measuring mass. Now we don't actually do that, and the reason is that while it is possible to make these measurements with an atomic nucleus, we haven't done it well enough yet. And so it's not a good replacement for the current definition or the previous definition of the of the kilogram. But this guy, Brian Kibble, taught us how to do it by using an electromechanical device that we now call a Kibble balance or a Watt balance. And this movie is going to show us how that is done. Okay, so first I want you to remember how we traditionally weigh things. If we want to weigh an unknown mass, we put it on a balance, and we put known masses on the other side of the balance until the balance balances. So once we've put enough known masses on this side of the balance, we add them all up, and that's going to be equal to the mass on the other side of the balance. Okay, we've done that. You've done that. That's how we measure masses. Now I want to invite you to think about a different way of doing it. Instead of putting masses on the other side, let's put a coil of wire and some permanent magnets that will create a force on this coil of wire. So we've got wire, we've got current, electrical current going in this coil of wire, and we've got a magnet. And you know that if I put a coil of current into a magnetic field, that there's going to be a force on it. And I can calculate what that force is. So if I know how much current is going in this coil, and I know exactly where in the wire is it's going, and I know how strong this magnetic field is, and I know the exact direction of the magnetic field relative to where the current is going in the wire, I could use all of that to calculate what the force is, and then compare that to the gravitational force on the other side of the balance. And that would be another way of measuring mass. But we don't do that because you can't do all those things that I just said you would need to do. We can't know the magnetic field well enough. We can't measure its direction well enough. We can't know where the current goes in the wires well enough to make this work. But here's where the genius of Kibble comes in. He says, okay, let's imagine something different. Let's take that coil of wire, the wire in which we put current before, and put into this magnetic field, and let's take the leads and run them to a voltmeter. Now what's going to happen is we're going to move this coil. Now, just like an electric generator, if you move a coil of wire in a magnetic field, you're going to generate a voltage. Now we've hooked that up to a voltmeter, and the voltmeter doesn't draw any current. So what we're going to do is we're going to move the coil, whoops, oh no, just start all over again. Okay, here we go. So we move the coil and it generates a voltage, and we move it in the other direction. It generates a voltage in the other direction, okay, and we measure the voltage and we measure the velocity. This we call the velocity mode. I'm sorry, it was there a moment ago. Then we do the other experiment, the one we already did that I already described. We put current in here. The current feels a force because of the magnetic field. We compare that force to the gravitational force of the mass on the other side of the balance, and now we've got two different experiments. Here's the mass on the other side of the balance. The acceleration of gravity tells us what the gravitational force is. That comes from the weighing mode, okay? We multiply it by the velocity from the velocity mode. So notice what's going on. We've got a measurement from one part of the experiment, the weighing mode. We multiply it by a measurement from the other part of the experiment, the velocity mode, and that's got to be equal to the current which we measure in the weighing mode times the velocity that we measure in the velocity mode. Why are those two things equal? Because this is mechanical power, and this, you know, it's force times velocity, that's mechanical power, and this is current times voltage, that's electrical power, and those two things have to be equal in a proper system of units. So we set them equal to each other and we solve for the mass. This is a new way of measuring mass. We measure the current in the voltage. We divide it by the acceleration of gravity and the velocity, and we got the mass, a new way of doing mass. But now you say, wait a minute, you promised me that this was going to have to do with Planck's constant. What does this have to do with Planck's constant? And the answer is the way we're going to measure the current and the way we're going to measure the voltage are going to involve Planck's constant. Because we are now going to use a quantum way, the quantum Hall effect to measure the resistance, which is going to allow us to measure the current. We're going to use the Josephson effect, which is going to allow us to measure the voltage, and it's going to all work out. Here's how it goes. These guys, Brian Josephson, taught us that if we have two superconductors and we put a tunnel junction between them, a little bit of insulator, and the current goes through that thin part of the insulator, that if there's a voltage across that junction, then there will be an AC current and the frequency is going to be given by this constant of nature, 2e over h where e is the charge of the electron in Hertz per volt. That's what Brian Josephson taught us. Klaus von Cleansing taught us that if you have a certain two-dimensional semiconductor and you put it in a magnetic field and you put current through it and measure the voltage in the perpendicular direction, the ratio of that voltage to the current has the units of resistance and it's given in these units, h over e squared, Planck's constant divided by the square, the speed of light. So you see both of these expressions involve Planck's constant and the charge of the electron. So when you measure the voltage, you're going to get an units of h over 2e. When you measure the current, you're going to use a resistor, which is h over e squared, and you're going to measure the voltage across that resistor, which is h over 2e. So the current is proportional to e, not surprising, right? Because the current is just electrons that are flowing, so it's proportional to the charge on the electron. So you multiply that by the voltage, which is h over 2e, and you get that the mass is proportional to e, which is what I promised you. And using that idea, people made balances like this. This is the one at NIST. This thing can measure kilograms to about a part in 10 to the eighth, which is better than the amount by which those kilograms are changing due to whatever it is that's making them change. We don't know because we don't know what a kilogram is. We don't have anything that's stable so we can figure out what else is changing. And now we do. So this has become the new definition of the kilogram. This is part of a team that did it. These guys are serious about metrology. They're so serious about metrology that they tattooed the values of Planck's constant and the other constants onto their forearms. This is really serious. These guys are like those metrologists in ancient Egypt. They take metrology seriously. So I don't know how much time we have. I guess we've still got a little bit of time. Let's see if there's any questions about this. Now I have to admit the answer to this question is going to be a little bit involved. So we might want to let it go until the end if you're really interested in that because it involves a whole bunch of equations and stuff like that. And we're physicists and we love equations, but one of the things that I believe is a principle you should always abide by and that is never do algebra in public. So do we have any other questions? Questions that I see on the spreadsheet are mostly about time measurement and I think they'll save them for later because they wouldn't interrupt the flow of your lecture right now. Okay. So why are you burying that winter code? So that was that picture was actually taken inside the Archives of Paris. I visited the Archives of Paris with a guy named Terry Quinn who used to be the head of the International Bureau of Weights and Measures, famous guy. In fact, I've got his book on measurement right here in my bookcase. I'm looking at it right now. And he arranged for us to get a tour and especially to see the measurement standards in the Archives of Paris. So this thing in the Archives of Paris was that very object that was deposited there in 1799. And their idea when they built the Archives of Paris, which contains lots of other stuff, it contains documents, it contains the Constitution of each of the Republics of Paris. They thought the best way to preserve things in the Archives was to keep the temperature and the humidity very constant. Rather than to control it, they made a building with really thick walls so that the temperature would change extremely slowly. And it happened to be December when we were there. And there have been plenty of time for the temperature to get cold since it had been several months that the outside temperature was cold. But it took a long time to do that. And they thought that rate of change of temperature was the thing that would hurt things. And so they made the Archives building without any way of controlling the temperature. And so it was really cold in there. And that's why I'm wearing a coat. Actually, one thing that I was always curious about, I once read that this is not pure platinum, but a platinum iridium alloy. Do you know why they chose that particular material? Yes. My understanding is that platinum iridium is tougher than pure platinum. That pure platinum, like pure gold, is rather soft. And so they alloy it with something in order to make it harder. Why alloying it with iridium makes it harder? I have no idea. Maybe Marvin knows. It's a materials question. But the other thing is iridium is also one of the densest materials that there is. We didn't really talk about why platinum. The reason why platinum is because as one of the densest materials there is, there's a smaller correction due to the buoyancy of the air. It's not negligible at all. The buoyancy of the air is very important, but it's not nearly as bad as water, for example. So I forget what the density of platinum is, but it's close to 20 times the density of water. So platinum and iridium are both extremely dense materials, and they are the ones that were chosen both for the toughness and for the high density. How these things were made is really quite incredible. They cast the metal in a vacuum so that when they made these things, if it included a bubble, the bubble would enclose vacuum rather than air. And then they could beat on it until the bubbles collapsed, and they kept beating on it until the density stopped changing. And then they figured the thing really had the density of the actual metal. So it was really quite a, this was done in the 19th century. This was amazing. Wow. And here are actually questions straight on weight measurement that just came in. So I'll ask it and then we'll let you go ahead. And it's by Bill in TLH. I'm not sure what that stands for. Are weight measurements sensitive enough to measure the mass loss due to radioactive decay? That's a great question. I have no idea. So I'm guessing that the answer would be yes for certain kinds of radioactive decay. So for example, let's say I had something with a short lifetime that emitted alpha particles. Now, you know, not being a nuclear physicist, I don't know what that would be. But if I had something that that that emitted alpha particles, an alpha particle has a lot of mass, right? Now, if the question means, is it sensitive enough to measure the weight change due to say a gamma ray? Well, that's a different story. But I can tell you this, you can put a nucleus into an ion trap, measure its mass by measuring the frequency of oscillation in of the nucleus in that ion trap, have it emit a gamma ray and remeasure the mass and you can tell that difference, not to a part in 10 to the eighth, but maybe to better than a part in 10 to the sixth. So the answer is there are ways of weighing things that can see the weight change of a radioactive decay that is electromagnetic and not just a particle emission. So I think that that sort of answers the question. Excellent. I think we'll let you go ahead. Okay. So before I go on to tell you about the rest of this, I want to talk about one other way of measuring mass when you've defined Planck's constant and it's a completely different way. And that makes it beautiful. Imagine you've got a single app and it happens to be at rest and it's in the ground state and you shine in some light so that it makes a transition to an excited state. When the atom absorbs that light, some of the energy of that light goes into making the internal energy of the atom change. But the light is also carrying momentum. That is, it exerts a push on the atom and that makes the atom start to move with a velocity that we call the recoil velocity. And that recoil velocity is Planck's constant divided by the mass and the wavelength. Now, if we define Planck's constant and we can measure the wavelengths exceptionally well, that means if you measure the recoil velocity, you can get the mass of the atom. Now it turns out that using something called atom interferometry, which our friend, Hugo Meurler, is an expert in, you can measure that mass really well and then you can measure the velocity really well, okay, which gives you the mass. Now this is the thing I want to emphasize. This gives you the mass of the atom in kilograms. People are used to measuring the mass of the atoms in things like atomic mass units. That's not what this is. This is measuring the mass of the atom in kilograms. Then you do the following. You make a sphere of silicon. And this sphere is the most spherical thing that's ever been made. It is spherical to something like a part in 10 to the 7th. It's just ridiculously spherical, okay? And you measure the lattice spacing of the silicon atoms. It's a perfect crystal. It's a near perfect sphere. And you measure the lattice spacing of that crystal. And that means, and then you measure how big it is, okay? When you've done all those things, you've essentially counted how many silicon atoms are in this thing. And since you know the mass of a single atom, well, it wasn't silicon, but you can compare the masses of silicon to that other atom very accurately. So it's a long chain of things, but it means you then know what the mass of this object is. And you make it to be a kilogram. And it now becomes your new kilogram, not a new artifact, because you've used the definition of Planck's constant to create this thing. And anybody can recreate it. So it's not like the international prototype of the kilogram, where there's only one. Anybody can make one of these things, and they did. And all over the world, people used kibble balances. They're the, I guess, the red dots. And then people made silicon spheres, those are the blue dots. And when everybody all over the world agreed, then the international metrology community gets together and says, yes, we're going to make this change. We're going to change the definition of the kilogram. And in 2018, in Versailles, the countries of the world got together, 60 countries who are the signers today of the Treaty of the Meter got together and agreed unanimously that they were going to change the definition of the kilogram. And after they did that, they played this movie. It took more than 140 years. Groundbreaking science. And the agreement from the World Scientific Community. At times, it seemed impossible. Actually, for so many measurements. Any time. Anywhere. But we did it. We have my special holograms. They see a bullet. One bullet. This one on a motor. Bro, come die. This one was a sonnet. And this one's full of it. He's delirious. And the sonnet. The youth, the wreck. But I'm sick. I'm naked. Yeah. I'm a sonnet. I'm a sonnet. I'm a sonnet. This one told to me. Do casa rismeto. And guess now. So I don't know. Congratulations. Congratulations. Congratulations. Masalto. Congratulations. Shut the relevant location. Lana. Suites. Parabens. Oguela. Momento. Oguelita. Onexobo. Magrush. Capai. Aiku. Congratulations. Congratulations. I've probably seen that movie a hundred times. And every time I see it, I still get emotional. The idea that 60 countries of the world could get together and unanimously agree on anything gives me a little smidgen of hope that maybe we can do better as we go along. Well, there's a little bit more to the story. The ampere definition was changed as well. It used to be that the ampere was that current, which when put through two infinitely long straight wires, one meter apart in vacuum would produce a force of two times ten to the minus seven newtons per meter. Today, the ampere is defined by defining the charge on the electron. And an ampere is just a certain number of electrons per second. What a beautiful definition. And now that both E and H are defined, it means that two E over H and H over E square are now exact. And we can do all these electrical measurements using the quantum Hall effect and the and the Josephson effect. But that's not all. There's more. The mole, a mole used to be the amount of substance that had a number of microscopic entities that were equal to the number of carbon 12 atoms in 12 grams of carbon 12. Now, Avogadro's number is simply a number. This is Avogadro's number. 6.02214076 times 10 to the 23rd per mole. That's it. That's Avogadro's number. The Kelvin, it used to be that the Kelvin was one over 273.16 of the triple point of water, basically defining the triple point of water to be 273.16 Kelvin. Okay, just a little bit above the freezing point of water at standard temperature and pressure. And I love this definition. Now, the definition of the Kelvin is done by fixing the value of the Boltzmann constant. What that means is that by temperature, we mean what is the amount of energy that the atomic constituents of a substance have? Because that's what Boltzmann constant is telling us. Boltzmann's constant times temperature tells us what the energy, the thermal energy of the microscopic constituents is. And I really love this because this microscopic approach to what temperature is is really the modern way of thinking about temperature. People thought about temperature long before they understood that materials were made up of atoms and molecules. But now that we understand that and we understand the basis of thermodynamics in statistical mechanics, this is definitely the way to define what we mean by temperature. And so I just love it. And also, it means that maybe us atomic physicists will be the ones who do the best temperature measurements because we can measure the velocity distributions of atoms in a gas, not quite well enough yet. But maybe this is where the future lies. So the French Revolution brought us the metric system. Meters were the measure of length, kilograms were the new unit of mass. The convention de Metres gave us an international agreement. So the entire world is adopting the metric system. And then finally, on the 20th of May, which is World Metrology Day because it is the anniversary of the day on which the Treaty of the Meter was signed, we had the biggest revolution in measurement since the French Revolution. And so this image of liberally leading the people means that we are finally free of artifact standards of measurement. The new international system of units has all the base units defined by defining constants of nature. And now you can keep the international system of units in your wallet. Just seven numbers define sufficiently everything we need to know about the system of units. So it seems that we finally realized the dream that the French Revolutionaries had, a system of units that is good for all time and for all people as this medal cast in the 19th century illustrates. All time, all people. But maybe not. Maybe the problem is time itself. Because today we have still tied the definition of time to a specific atom, the cesium atom. So on this table, all these other constants are universal. Maybe we should talk about luminous efficacy, except for this one. This is specific to cesium. And today we have other atoms which are giving us transitions, transitions in the optical part of the spectrum. Atoms that are ticking at something like 10 to the 15 cycles per second instead of something like 10 to the 10 cycles per second. And these are better than cesium. So again, we face the situation where the definition of the unit, the definition of the second, is not as good as the instruments we have. The technology that we have today for measuring time. And so for the future of time, only time will tell. Thank you very much. That's a wonderful talk, Bill. For all of you in the audience, the paradox is that Bill and I actually cannot see you. So please, if there are questions for discussion, put them in the spreadsheet. Those we can see. Actually, since you could go ahead. Well, let's see. I see now that I'm not sure whether, can you see the questions? I can see questions. Okay, then that probably means that people in the audience can see the questions as well. And so let's leave it on for just a moment and I won't stop sharing. Maybe somebody, maybe we did start sharing. Anyway, if we can see the questions, that's the key thing. And if I need to go back to sharing to answer questions, we'll do that too. So let's have some questions. And if people like these, they can ask these as well. There are questions about very technical things, but I want to save them for a little bit later because you closed on this wonderful humanitarian, humanistic aspect. Fixed countries can agree unanimously on some things. That means something good. And there's Tina from Croatia who asked, science, technology, engineering, and mathematics deserve presence in public conversation because it underlies progress, individual and national, and it underlies global security. Do you have any understanding on why human development missed such important phase today? I believe it means the missed opportunity to have STEM discussions more. Yeah, I don't know. We live in very strange times. In some aspects of the world, very dangerous things are happening. In other aspects, people cooperate by, for example, immediately publishing the genetic sequence of a new strain of the coronavirus. I mean, this is something that the ability to sequence DNA has been one of the great achievements of our time. And it's something that's internationally known and internationally shared. This is great, and it allows us to produce vaccines quicker and to save people's lives. And yet at the same time, we have threats of war in places where, for sure, lots of people are going to die if war comes to pass. The disconnect between the level of cooperation that is very often connected to science and the level of conflict that seems to be quite a part from the kind of cooperation that we can have in the scientific sphere. I'm at a loss to understand why human beings behave this way. Let's go to more technical things, because those maybe we understand better. But this is a great perspective. Thank you for sharing it. People are excited about time measurements. So I'm going to ask a question from AC and San Diego. Why is the NASA Deep Space Atomic Clock recently launched to be used in space navigation? Why does it use mercury atoms rather than cesium? Yeah, well, the reason why it uses mercury atoms is because they can produce a better result than the and more compactly. That's probably the key thing is that they can produce a better result more compactly than cesium. The best cesium clocks are these atomic fountains. Let's see if I can return to a picture of an atomic fountain so that you can get another picture of how big this thing is. Can you see that fountain now? I cannot. Oh, okay. I'm wondering whether I have to reshare. Okay. So I'm going to try to do that. And maybe it will work. Still have to reshare. Right. Okay. So I'm trying to do that now. Okay. Here we go. Okay. Now I need to. Okay. It just takes a little while. Okay. Now are you seeing the fountain clock? Yes. Okay. Great. So there's human beings next to it. Dawn and Steve give a nice scale so you can see how big this thing is. So in order to make a clock as good as a part in 10 to 16, this is a few parts in 10 to 16, it has to be this big. Now the mercury ion clock is got an ion trap. And it's got another nice feature that you put it out in space. Well, actually, even if even on the ground, it works really well because of the fact that the ions are held for a really long time. Here the cesium atoms are only held for a second. But it does really, really well on the earth. If you put it, it will work entirely differently. You would have to completely redesign it to have it work in space. And I'm not even sure that there's a trap that would work because it would mess up the clock frequency. Whereas the trap that they use for the mercury ions don't mess up the clock frequency. It doesn't mess up the clock frequency. Now the mercury ions, if I'm remembering correctly, are not quite as good as this clock. They're about a part in 10 to 15. Is that your recollection, Holger? Something like that. Yes. Yeah. So it's not quite as good as the cesium. But I think the key thing here is put the best clock you can right now into space. And that's what they did. And that was mercury. Not the best clock that's operating, but the best clock that they could package and put into space. One of the things that Holger and I are thinking about right now is what advice can we give to NASA for the next 10 years about what kind of clocks ought to go into space? Considering the fact that we might have years of development on the ground to make these things space qualified. So I hope that answers the question. Maybe part of the question was why not cesium? Because cesium defines what we mean by a second. In many cases, you don't care whether the clock is giving you an SI second. What you care about is it's stable. Often that's the only thing that matters. So having a clock that is stable is more important than having it be cesium. In fact, a lot of the GPS clocks, which give us navigation on earth, are rubidium rather than cesium. And it's just fine as long as they're stable. That's the key thing. Fantastic. There's actually something that I think was mentioned on one of your slides that I'm going to ask. And this may be more interesting to the physics people in the audience, but there is a way to take the elementary charge E, the Planck constant H, and the speed of light C, and combine them to a pure number, which is 1 over 137. And that's famous as the fine structure constant. So given that you've been defining H, C, and E, how is this allowed and not in conflict with nature? Exactly. So the fine structure constant is indeed a constant of nature that has no units. And it is what it is. It will be the same number in every system of units. And it's equal to E squared over H bar C. And I've now told you we've defined E, H, and C. And of course, 2 pi is perfectly defined as well. So that has to be wrong. And the answer is that in the system of units in which we have defined E, H, and C, the expression that I'm showing here, I hope you can see it, this expression is not the fine structure constant. In the system of units, the SI, the metric system, the sometimes called the MKSA system, meters, kilograms, seconds, and amperes, in that system of units, the fine structure constant is E squared over 4 pi epsilon naught H bar C, where epsilon naught is the electric permittivity of the vacuum. Now, in the old system of units before we made the change, epsilon naught was defined. The reason it's a little complicated, why epsilon naught was an exact number, but it's because of the fact that the old definition of the ampere defined the magnetic permeability of the vacuum, and the old system defined, through the meter, defined the speed of light. Now, there's a relationship between the permittivity of the vacuum and the permeability of the vacuum and the speed of light. So that means that if you define any two of them, the other one is defined. So since we had defined the permeability, the magnetic permeability of the vacuum, and the speed of light in a vacuum, it meant that implicitly we had already defined epsilon naught. So that was the case before the new definition. We didn't know what E and H were, that is, we measure them to a certain degree of accuracy, but they weren't perfect. So that means before the redefinition, the fine structure constant had experimentally measurable quantities, namely E and H, but not epsilon naught and C. So after the redefinition, epsilon naught turns out to be a measurable quantity. In fact, it's the only measurable quantity in the fine structure constant, because all the rest, as the questioner points out, have been defined. So you got exactly the same situation, epsilon, the fine structure constant is something you have to measure. And when you measure it in the today, what you're doing is measuring epsilon naught, where that's one way of thinking about it. When you did it before May of 2019, when you measured the fine structure constant, you were measuring the ratio of E over H. So it sounds funny, but that's the way it is. Just like before the meter was redefined, when you made that particular measurement, you were measuring the speed of light. And after 1983, you were calibrating your meter stick. Excellent. Bill, let us ask our directors here, how are we doing on time? Can we get one more question in or should we better wrap up? I'm seeing the time as being 8.37. And I think that we're supposed to quit at 8.40. So it sounds to me like we can have another question. All right. Let me actually ask one about personalities. I hope this is allowed, but since I was a grad student, I was always impressed by the fact that Klaus von Glitzing won the Nobel Prize for the Quantum Hall Effect on his own, whereas usually in experimental physics, those prizes are shared. Do you have any insight into how that happened? Well, I think the answer was that his contribution to the Quantum Hall Effect was just so overwhelming that there was no one else who had an equivalent contribution to the Quantum Hall Effect. You might say, well, there were some people at metrology laboratories who really did extremely good work on really pinning it down, but compared to the discovery that this was something very closely related to a fundamental constant, I think that, look, we don't know what the Nobel committee thinks. We won't know for 50 years what they think, because the deliberations are sealed. But that's my guess is that thinking was, gee, Klaus von Glitzing made such a huge contribution. And when you look at history, when those kinds of things happen, then it's more likely that a single person gets the Nobel Prize. I mean, Einstein got the Nobel Prize alone for the photoelectric effect. Sometimes you'll see that they give the prize for two different things. And then, because they thought, oh, these two things really both deserve to be recognized, so let's divide up the prize. You can only give the prize for two different things and to three different people. It's a funny rule. But take, for example, laser cooling. This is something very near and dear to my heart. So many people contributed to the development of laser cooling that I thought there would never be a Nobel Prize for it, because you wouldn't be able to identify three people who were the contributors. I thought the work was something that certainly deserved recognition. But identifying three people, well, I remember being in Stockholm at the time. And after an exposition in Swedish of what laser cooling was all about, but we were given an English translation that we could follow along, then the head of the Nobel committee turned to us, Steve Chu and Claude Comintonugy and myself, and said, as leaders and representatives of the most successful groups in laser cooling, we invite you to come forward and receive the prize from the hands of His Majesty the King. So obviously their thinking was that they wanted to recognize the field and they did that because they had no choice by picking out the people that they identified as being representing the key groups. Now, maybe not everybody agreed that those were the key groups, but I think that if you asked people what were the top six groups, those three groups would have been in everybody's top six. I love how modest you are when telling the story. This is truly noble. And with that, perhaps we give another round of applause to Bill. Thank you very much. The sharing has stopped, so now we should see Marvin. Okay, well, I'm sure that this issue, that all the issues that we discussed have far-reaching implications, not only for the sciences, but also for human endeavors. And they'll be discussed after your talk and for a long time. So I want to thank you, Bill, for this presentation today and for being our Hitchcock lecturer. We appreciate you, our viewing audience, taking the time out to view our presentation. Thank you for watching. And this concludes the presentation and I wish you all good health. And again, thank you very much. Thank you very much. It's been a pleasure to be with you.