Myriad year clock

Transcription

>> Great to see so many people have turned out for this. I was to understand that this lecture is being streamed live to the internet so I'm even more anxious than just talk in front of you and it appears on YouTube later on so all my gaps and technical mistakes will be preserved for posterity so if you're spoofing mistakes now then you can pick me up from them later. So welcome to UCL and like I said we're very glad to see you all here. I'm gonna talk about space and would like to take you on a bit of a journey out to the final frontier of space because part of the reason I want to do this is because there's a lot of gloom and doom in the world in the news these days, but my perspective is actually that human beings have just done extraordinary things and carry on to do extraordinary things, developed radical new technologies that's actually a benefit to all mankind and that work is going on right now, it goes on in places like UCL, in Cambridge, in Oxford, in the American Space-- NASA, there are astonishing things going on now and I think we should be, we should be really upbeat about this kind of things. So, on to the topic. Einstein was, he developed a number of radical ideas at the start of the 20th century, which at that time couldn't be tested and now with the kind of engineering technologies we have, the space-borne platforms, we can test Einstein's ideas very, very vigorously. But more importantly than that, we utilize his ideas, we use his ideas to make these technologies work so what I'm gonna try to show you in the course of the lecture is the relationship between Einstein's ideas and things that are around us everyday, your cell phones, the GPS device in your car, the kind of space-borne technologies that we use to measure the way in which the planet is changing. I'm gonna show you how all those technologies hinge upon Einstein's ideas. So he's a great man himself. Einstein was born in 1879, he's got a bigger nose than me so I think I'm heading the right direction at least, and he was born of a relatively humble family, his dad was an engineer, and he grew up not as a remarkable sort of child actually. People quite often realize Einstein was not good at math at school. In fact, he actively disliked math in school and his teachers actively disliked him. So, if you find yourself in that category then you know you too could be the next Einstein, could be sitting here, so what caused Einstein to change? Well, it was this, a discussion he had with his uncle, his uncle was so involved in engineering and his uncle told him that mathematics was a bit like a detective story where X, the unknown quantity, is the villain of the piece and that caused Einstein to actually become interested in mathematics and after a while he realized it was fascinating and of course, he had a great aptitude for it but from that small moment of inspiration, we went on to produce one of the greatest mathematical geniuses the world has seen, and Einstein went on to develop the two radical theories, special and general relativity. And those theories predicted things that were very strange, they predicted things that no other kind of physics at that time would suggest it's going to happen. Einstein predicted things about the way in which clocks would behave in space. He predicted things about the way in which photons, which I'm gonna talk about a bit later on, which with photons interact with matter. Now he predicted those things without an experimental platform to test these ideas so those were theories, they weren't laws. So Einstein's path through science is very different from Newton's. When Newton predicts his ideas then actually there was an immediate testbed to his ideas so in his lifetime Newton thought that he was right, no doubt about it. He could prove that what he did was right. Now, one defection I had in preparing this lecture about Einstein is some of Einstein's ideas were tested in his lifetime. But what did they gave rise to? They gave rise to one of the most destructive weapon systems the world has ever seen which is the atomic bomb. So Einstein thought his ideas being taken and used. Of course, you can't say that nuclear power is an [inaudible] thing but developing atomic weapons is of course in some respects a terrible thing, and so Einstein had to live with that. So I'm gonna close off with that, things I think Einstein would like to reflect upon today in terms of what he did. The next of it is around this guy here which is a Richard Feynman, he's my hero, and he's also a physicist. Now Feynman said that if knowledge is gonna be of some use it's no good if all it does is tell you what happened yesterday. He said that if knowledge is gonna be worthwhile in society it's gonna tell us what's gonna happen tomorrow, it's gonna enable us to predict what's gonna happen, it's gonna enable us to build things that we don't yet think are possible. So I'm gonna talk about space technology so in the next few slides is a brief introduction to some of those space-borne technologies that I want to talk about. So up here, up in orbit on right hand side you got GPS spacecraft. Now GPS spacecraft they orbit quite far out, so the Earth is about 6-1/2 kilometers from the middle to the edge, okay, radius is about 6-1/2 thousand kilometers and GPS satellites orbit about 20,000 kilometers. They're up here. They're moving around about 4 kilometers per second so it takes you and me, well, I'm not feeling up to it, about 12 minutes to walk a kilometer. The GPS satellite goes a kilometer in a quarter of a second. Could we use GPS satellites to work out where we are on the surface of the Earth? I'll explain a bit more about that later. Then we got what we call Law of Orbiters like this one up here. Now these are used to measure the gravity field and they're used to measure how sea level is changing globally, and they're used to measure how the ice caps are changing so all critical environmental measurements. Now, the Law of Orbiters they tend to be a bit close to the Earth, maybe about a thousand kilometers up the surface, about here, they're a lot more smaller than this, bear in mid, and they move really, really fast. They might move 8 or 9 kilometers per second. Now, in all these technology to talk about measuring environmental measurement or navigation technologies like GPS, we need to know where these spacecrafts are out in space. And we also need to know what the distances are sometimes between spacecraft and sometimes between the spacecraft and the surface of the Earth, what we call tracking stations that try to determine where the satellites are. So I'm gonna talk about those ideas, how we measure ranges between spacecraft and how we work out where satellites are out in space, because if we're gonna get knowledge on science out of these technologies, we need to know those things, we need to know distances between spacecraft and between the Earth and the spacecraft, and we need to know where the satellites are out in space. What I'm gonna show you is how none of that would work if it hadn't been for Einstein. So a bit more detail on these technologies. GPS, well, I'm sure you're all familiar with GPS these days, it's in tom-toms, it's in mobile phones. And of course that in itself is a miraculous technology. I always try to tell our students that you can just flip one of these things on and then in a few seconds you know where you are to within a few meters with respect to the central mass of the Earth and that in itself is sort of miraculous. It would've taken us, 20 years ago it would take several weeks of setting up optical instruments to measure where the stars are, and hours and hours of calculation. Now, all of us can just flip on a device and work out where we are within a few seconds. But actually, if you got the right techniques and you know how to utilize the data from the satellites you can work out where you are to within a few millimeters and you can use that information to determine how the planet is changing shape over course of years which then forms the earthquake cycle, understand how tsunamis happen. So this is a map of velocity vectors of the continental plates entirely derived from GPS data and that's how we work out where the big earthquakes are going to occur. That's how we work out how strain builds up along subduction zones. All that comes from GPS, so GPS isn't a technology that tells where we are at a few meters, it can tell us where we are at the level of a few millimeters. The Law of Orbiters enables to measure the changing surface of the sea, and they enable us to measure how far sea level is rising, how far it's falling. Now, this is an example of an El Nino determined from a Law of Orbiter and that's how we discovered El Ninos by using Law of Orbiters but in order to measure that El Nino which is a sort of a wave of warm water moving across the Pacific, takes quite sometime to do that, it's about 20 centimeter high, and about a thousand kilometers across. We have to know where the spacecraft is up in orbit at the level of the centimeter to get that kind of resolution. >> That kind of data understanding things like El Ninos has led on, led to a lot of understanding of how the world works from a climate perspective. In this example, one of them says this, when an El Nino occurs, warm water moves across like so and that displaces the jet stream. It moves northwards and it changes the entire shape of the weather system so that next year or 2 years afterwards and we now know that in the late 1920s there was an El Nino, and that caused this catastrophe known as the Dust Bowl. The Dust Bowl was-- how did dust bowl happen? So because the rain didn't fall in the Midwest, it fell in the Canadian Rockies that meant that the grain basket of the US didn't receive the rain it needed and so you couldn't grow crops. The top soil was blown away and there was an environmental disaster. So the company actually of the Wall Street crashed which was an economic disaster, an environmental disaster caused by the El Nino led to the great depression. So, but now we know what an El Nino is, and we would not have been able to do that, we would not have been able to understand or measure an El Nino without the space-borne technologies that I'm gonna talk about. So like I said, the problem is working out where is the spacecraft? That's kind of the question, where is the spacecraft? How far away is it? What are its coordinates? So we're gonna look at two problems. One is, how to measure the distance to a spacecraft? I'm gonna show you how we do that achieving a ranging accuracy of between a centimeter and a millimeter. And the second part is to predict the orbit of the satellite to say where it's going with time and we're gonna try to explain how we can do that at a level of a few meters to a few centimeters. So those are the two problems we're gonna deal with. I'm gonna show you that we couldn't do any of that, at least to the kind of levels we need to do it without Einstein's ideas. So, first of all, the range between a spacecraft and a tracking station, so how do we do that? We'll here's the trick. Most of these spacecraft carry clocks on board so they know what the time is, but these aren't any other clocks, these are atomic clocks. Now the first atomic clock was invented in the National Physical Laboratories in Teddington, not far away, not far away from here. Now, what's special about atomic clock is how accurately it can slice time up in to little bits. So the conventional clock is actually the ones on your watches and so on. They might slice time into a second, that's the division of time, and it adds that lots of seconds and it tells you what the time is. Now atomic clock can take a second and it can slice it up into atleast a million, million pieces. Actually, the latest atomic clocks can do that to a thousand million, million pieces, so it can break at a second and it can tell you accurately what's the time now within that division of a second. Now those clocks on board the spacecraft are used to generate signals that the satellite sends out and those signals have got a very, very precise frequency. So if you could hear the signal coming down from the satellite you'd do a sort of [noise making] type of effect and that's-- the higher the pitch of that then the higher the frequency of the signal, and that's what the atomic clock enables us to do, it generates a very, very stable frequency and that frequency is used to broadcast the signal from a spacecraft down. Now [inaudible] signal, you can think of it as being a time mark. As the signal comes out from the spacecraft it says "I sent this signal and looks at its watch and it says the time now is 12 o'clock." So you can imagine a satellite, what it broadcasts is a signal and on that signal the little marks saying the time on my clock is now say 12 o'clock. That signal travels through space and it arrives in the tracking station. Now the tracking station has also got a clock on board so when the signal arise, tracking station looks up the time on its clock and it says "Okay, that signal's now arrived let's say at a minute past 12." So when it picks up the signal it can see that that signal was transmitted at 12 o'clock. So the difference between what the tracking station clock says and what the time mark on the signal tells you the propagation time of the signal through space, it tells you how long the signal was going through space from where it left the satellite and was picked up by the tracking station, so with clock, if you like, the time of flight of the signal, this is where the first of Einstein's ideas comes in, because if we knew how fast that signal was traveling then time multiplied by speed gives you distance. I think most of you can probably get that one, right? There's more math later, brace yourselves but, so time times speed equals distance. So how soft is the signal traveling? Well, the signal is traveling at the speed of light in vacuum for more most of its path, and the speed of light in vacuum, 3 times 10 to the power of 8 or 299,792,458 meters per second. That constant speed was predicted by Einstein. That idea was not understood before because we had to figure out what the speed was and that's an engineering problem but the science was that a radio signal in space will travel at a very particular and constant speed and so we know that. So if we know the speed and we know the time of travel we can work out with distance. So the whole trick about ranging between the spacecraft and the surface of the Earth involve two clocks, one up in space, in the spacecraft, and another clock down on the Earth. Now, that all sounds very simple but of course it wouldn't work under normal circumstances. Now why wouldn't it work? Well, we come back to Einstein's ideas again. This time we're gonna have two clocks down on the Earth. Now if I got two clocks on the surface of the Earth, they're both running at the same speed, let's say that fantastic clock is the atomic clock, we can compare one to the other, and they're reading the same time the whole time, good, we're working. Now what if we put one of the clocks on a spacecraft and send it up into orbit? Now the first thing that Einstein predicted was that if one clock is moving relative to another then the clock that's whizzing away out in the space will start to run more slowly than the one on the Earth. So the clock can no longer synchronize. The clock in space is running at a different rate to the clock on the Earth. Now, that was predicted from special relativity. General relativity also said that the clock up in space compared to the clock down on the Earth is gonna be affected by the mass of the objects nearby. So if you have a big massive object like a planet close to the clock and take another clock out here that's much further away from this then the clock that's further away is gonna run faster. So special relativity says the clock runs lower, general relativity says the clock runs faster. Okay, if we apply those two ideas together they don't cancel out, that would be good, wouldn't it? [ Laughter ] >> But they don't. So, Einstein's series predicted how clocks would actually behave in the space environment. He predicted how much slower they would run, and how much faster they would run. So how much of this is a big deal? Well, let's take GPS as an example. If we didn't take general and special relativity into account then per day we would start to get our understanding of time wrong by about 38 microseconds. Okay, that sounds like a tiny amount, but remember that the distance we're measuring in spacecraft is the speed of light times time, so if we've got time wrong by 38 microseconds, that means when they get the distance of the spacecraft wrong by a whopping big 11 kilometers, so that would mean that all this attempt to position things at the millimeter level, well, that's the law, that just wouldn't happen. Actually, you couldn't even use GPS to position your car or even to go rambling, it just wouldn't work. Now, interestingly, when the US Air Force, US Air Force paid for GPS, now they didn't invented it, a bunch of scientists and engineers invented GPS but, so initially these scientists said "well, you're gonna put atomic clocks on the spacecraft and fly them at 4 kilometers per second 20,000 kilometers away. So if you do that then those atomic clocks are gonna go wrong by something like this everyday. You think the Air Force believe them? No, they didn't. The Air Force wanted an Einstein switch on the spacecraft so that if Einstein was wrong they could just switch the spacecraft back to operating like a normal clock, so you can just think you like some big, you know, ring spanner on the side of the spacecraft. Einstein was wrong, right, okay. Back to normal physics. But actually as it happens Einstein was quite right, and that's what you observed so you make the corrections to the clock based on relativity and then you measure the range of the spacecraft and everything works out. >> Now, you might say at this point, well, how do you know it works? Because if you can measure the range of the spacecraft using clocks, but somehow the clocks are wrong in some kind of way, how do you know it's right? One way we've got of validating that is actually is to fire lasers at the spacecraft, and we bounce laser lights off the spacecraft, time how long it takes for the laser to come back again and then we time that round trip and you could do that with quite a cheap clock, little quartz oscillator will do for that and we find agreement between our ranges based on the clocks compared to the lasers and how well does that agree, well that agrees at centimeter level. So we think it all stacks up. Okay, so that explains a little bit about the relationship between GPS and spacecraft ranging and clocks so look at the general and special relativity where clocks are concerned and we looked at the speed of light in vacuum as being constant. In the next step, I'm gonna talk about photons. Now before we can get there we have to understand a little bit about how technologies like GPS work. Now, how it works is that the satellites are flying around up in there in orbit, and the US Air Force has got tracking stations on the surface of the Earth and they're measuring range with satellite all the time. Now, from those ranges they work out where satellite is going to go in the next few hours, and they turn that into little mathematical formula and they upload that to the spacecraft, so once the spacecraft got that formula, it can predict where it's going to be with time. So as the satellite is flying around, it's using that formula to work out where it is going to be in the future, and then it broadcasts signal down to you saying here's where I am in space 'cause it's predicted orbit. I know the time, it sends that down as well. So it sends down some information saying where the spacecraft is and what the time on its clock is, and if your little device can measure ranges to four or more spacecraft then it can work out its position. I'm not gonna talk about that. The key thing is for GPS to work we've got to be able to predict where the spacecraft are going to be in the future, 'cause in realtime the spacecraft have to say here's where I am right now, that's what it's gonna do. So, what's the relationship between photons and working out where the spacecraft is going to be in the future? And that's to do with using physics to write down equations that tells us what the forces are acting on the spacecraft 'cause if I want to know where a spacecraft is gonna be in the future, if I know all the forces that are acting on it I can write down equations that describe those, I can say where it's gonna go. It's a bit like me saying if I poked the Earth with my finger in a certain direction with a certain speed, then I can say it will go off in that direction, and that's the trick. It's writing down equations that describes forces on spacecraft. So, what are the forces acting on a GPS spacecraft? Well, there are quite a lot of them. First big one is Earth gravity so, and that's quite a complex thing itself but we think we know about that, we know about mathematics. We can describe the Earth's gravity field very well. Then you've got the gravity field of the moon and the sun. They simply pull on the satellite and change its trajectory in space. But now in terms of a hierarchy of magnitude, in other words, going now with the small and smaller forces the next one is bit of a surprise. It's the radiation from the sun and I'm going to explain that in much more detail in a few seconds. But you also got because the spacecraft heats up from this radiation hitting it then it emits heat and that causes the force. We've got radiation, electromagnetic radiation, light and heat, hits the Earth, is emitted by the Earth, bounces off, hits the spacecraft, that pushes the spacecraft in its orbit. The spacecraft itself is transmitting signals, those are photons. As the photons are pushed away from the spacecraft, there's a recoil force which is what Newton-- that's Newton's third law says the photons are pushed away from the spacecraft, spacecraft pushes back into the other direction. And then we have tidal effects and there a few things, general relativity and some other planets. Okay, so let me explain about photons. So, I'm sure you've all seen Star Trek and you all know what a photon torpedo is, right? So, how many of you think a photon torpedo might actually work? Hands up if you think a photon torpedo might work. It's me and [inaudible]. Nobody in my group put their hand up, that's terrible, right. So, could a photon torpedo work? Well, you're gonna know the answer. If you get one thing out of this lecture, it's how a photon torpedo would work. Alright, it's worth staying awake for it I can show you. So what are photons? Well, actually this room is full of photons. Photons are little blobs of electromagnetic energy, blobs of energy. So, the light coming from my tie that you can see, the only reason you can see it is because photons are being-- are coming off my tie continually and they're hitting your eye and exciting the rods and cones and sending a signal to your brain. Photons also come from heat. As my body is a certain temperature, the whole room is at a certain temperature then there are photons coming out of everything continually. The microphone system, the microwave systems here, that transmission is all based on photons, so why aren't we falling over because of all these photons hitting, well because these forces are so tiny but you'll see in the space environment it becomes a bit of a problem. Now, here's the issue. How can photons actually cause a force? How does that work? How does light actually hit something because that's non-intuitive, right? Well, here's the math slide, because that's from Einstein's special theory of relativity. Now, I'm sure you've all seen that equation for E equals MC squared. Now what is that? Well, the M is the mass of a particle and C is the speed of light in vacuum, so the energy that that particle has is E equals MC squared and that was used to developed atomic power and atomic bomb. That was the idea that it was based upon. However, that's not the whole story. That's a slightly more complete equation. Now, I'm not gonna through all the terms but the key thing is that rho term there is the momentum of the particle. Now, for a photon, the M zero term is zero. So, photon has no mass. Right, no mass at all but it does have momentum. Now, what is momentum? Now you might know [inaudible] what momentum is but in physics, momentum is the product of the mass of an object times its speed and so something that's big and is moving fast, it got lots of momentum. Something that's light and moving slowly doesn't have much momentum. So, when a truck hits you, you know. Now, so that's what momentum is. So, momentum is related to force. So, if momentum is transferred to a body, it fills the force and what Einstein's theory predicted is that although a photon has no mass, it does have momentum. Because it has momentum, when a photon hits something then it will transfer that momentum to the object, it will be absorbed and then you will feel a push. Now, we never bother by that, we don't think about that mechanics on the surface Earth but in space it's different. So, radiation from the sun flies through space, hits spacecraft, some of it bounces off, some of it is absorbed. Now, those photons of course transfer momentum to the spacecraft and they cause a bit of a push. So, if we could work out where all the photons are coming from and which part of the spacecraft they hit, we could add up all that information and work out the resulting force on the spacecraft. Now, some of those photons cause spacecraft to heat up and those photons are emitted back out into space and as they are emitted from the spacecraft they create a recoil force so that as the spacecraft heats up and emits its radiation, there's a push on the spacecraft as well. This question, how big are those forces? What differences do they make? Well, on the table in front of you, you got one of these. Okay, so could you pick one up, pass them around and just feel how heavy they are, feel them pushing down in your hands. Okay. So, that's the force of about 1 newton at sea level. So imagine how much small that force would be if you cut it in half, okay, it'd be a lot less, right, cut in half. So, the first order force on a spacecraft due to the sun, you'd have to cut back into 10,000 little bits. So imagine how that's pushing down in your hand, the tiny, tiny force. Now, if we want to actually try and describe those forces mathematically, they're gonna help us position the spacecraft at a level of few centimeters then we actually have to divide that into a million bits and then mathematically describe the push from those photons. So, it's 1 percent of the first order force. So this is the problem of mathematical modeling. So, we do that. That is one of things we specialize in my group. We sort of create mathematical models of the spacecraft and we simulate photon fluxes using pixel arrays and we work out which parts of the spacecraft the solar radiation hits and then we work out how much momentum was transferred, how much radiation bounces off, how much heat is transferred, and then we add up all those and it give us a resulting force on the spacecraft. >> Now, we use computer technology to model real estate geometric spacecraft. Every single component on the spacecraft, we create mathematical models of those and we use quite sophisticated models of the interaction of the radiation with the matter to work out resulting forces so we can work out which bits are shadowed, where the radiation goes off. We then mathematically flip these pixel arrays all the way around the spacecraft and we build up a kind of mathematical function, that means a mathematical formula that describes all the forces acting on spacecraft. That includes radiation coming from the sun as well as radiation coming from the Earth, then it becomes quite a complicated problem because the Earth is emitting lots of different kinds of radiation, different frequencies, different intensities, and different directions, so computationally quite a difficult problem. Now how well does it work? Well, what I'm gonna show you now is our orbit error based on how sophisticated these models are that we're using to describe these forces. So, in the first one, if we just use all the gravity forces we talked about and we model solar radiation pressure then after about 12 hours of the satellite being in orbit, our orbit error, that means our inability to predict the orbit, might be around about 8 meters so this is modeling all the gravity forces and solar radiation pressure. If we include thermal radiation then that orbit error after 12 hours drops quite dramatically. [Inaudible] add this antenna thrust, this is the radiation emitted by the spacecraft, it goes down again, particularly the Earth radiation, it almost flat lines. Now, so we do all these mathematical modeling of forces on the spacecraft, we can predict where the satellite is gonna be 12 hours from now within 10 centimeters. That means a satellite is flown 173,000 kilometers from the space and yet we can say where it is using that. And none of that would work if it hadn't been for Einstein's laws. None of these was predicted by anybody else, it was Einstein's idea. So, for us at UCL, in my group, we've worked on these ideas quite sometime, we worked with US Air Force and we worked with NASA and the European Space Agency on this kind of problems. I just wanted to give a little bit of the credit to my group, they are most of them over here and those, the people, they work on relativistic model of the clocks, they work on photon pressure on spacecraft, they work on all kind of positioning applications with this kind of devices. So, this subject area where we work in, I thought to say a few things about that, it's called space geodesy. Now in space geodesy, it's about measuring planets from space but it was relatively unknown science until it appeared in the [inaudible] annual about 4 years ago. Question number 20, what is the science of measuring the gravity field of the planets and space, space geodesy. So, a field formula [phonetic] has some credibility to come and give a long lecture. Okay, so briefly, my conclusions. These space-borne technologies enable us to do things today that are-- would have seem miraculous 20 years ago. We can work out where we are on the surface of the planet to even a few meters, even to within a few millimeters, we can do that in realtime. We can work out where a spacecraft is up in orbit. Maybe the spacecraft is a thousand kilometers away moving 8-9 kilometers per second or we can work out where it is to within 10 millimeters. Now, that's not just mainly be a sort of ooh, wow, cool, blimey mate type thing, actually we can use those technologies to the benefit of all mankind for environmental measurement, for logistics, for security, and none of those ideas would work if it hadn't been for Einstein. Einstein's theories, special and general relativity underpin all of the science that makes that engineering possible. So, I think that if Einstein had been alive today, I think he would have been pretty chaffed actually, I think he would look at that and he'd go, great stuff. So, next time you are using a smartphone or a tom-tom within yourself or you're looking at some report on sea level change or how the ice caps are changing, I think, tip your hat to Einstein. Thank you. [ Applause ] >> Thank you very much, Marek. We have time for just a couple of questions. Does anyone have a question, right, yeah? >> I guess what I wanted to ask was this. When-- Yes, I just wanted to ask this. When a signal leaves a satellite it initially is traveling in a vacuum. Before it reaches the tracking station, it has to come through an atmosphere with ever increasing density. Do, we have to take that into account or is that, is the effect negligible even on the very small scale we're working at? >> No, it makes a big difference. So, the question was, how does the atmosphere affect the speed of the transmission of the signal and we have to model all of that. Now, there are various tricks we can play by observing on multiple frequencies to get rid of some of the affects but essentially, we have to model it as well and the delays can be as much as 80 meters in terms of distance. [ Pause ] >> Is it easy to explain why Einstein's two theories say that the atomic clock in space should be going both quicker and slower than a clock on the ground? >> Actually, I think special relativity, when you look at it, you have to write down a thing called the Lorentz term. Square root of 1 minus V squared over C squared. And that's not too difficult actually, not too difficult. I think general relativity is much harder. I wouldn't be able to give you, I mean, [inaudible] might-- I could refer you to my student with help in that. I think generally relatively harder but I think what we get in my group, for example, because we rely upon this stuff everyday, we get a kind of-- like a faith in it, because it works so well. So I think a quicker route to understanding or at least confidence in theory is to look at experimental data and go, right, I'm plugging the models and my, my, it works. >> Any more? >> Do you have any qualms about the measurement concern that at the moment is suggesting that neutrinos can travel faster than light? In fact, I mean qualms about the geodesic technology. >> Yeah. Well, it's funny 'cause I-- Tricia and I were talking about that just actually at the start. I don't believe it in the slightest. Not to say that an object couldn't travel faster from the speed of light. The key thing is if it goes through the barrier, if you try to take-- because what the equations tell us, if you start with an object and you make it faster and faster and faster, as you approach the speed of light, then you end up dividing your formula by zero, and we know everything from engineering, from science tells us that's a no, no. Now, what if you could jump flow over that? What if there was some kind of quantum effect that make-- you can jump over the speed of light? Okay, it's not impossible. However, with that [inaudible] experiment, I think there's-- that's one experiment and if we look at the data coming from supernovas, looking at the arrival time of neutrinos, the photons, there's a lot of evidence that says the speed of light is not exceeded. But and also, I think that that story was jumped upon by the media to be honest actually. I'd be quite skeptical. [ Inaudible Remark ] >> I'm just thinking about the radiation of the sun and it not being as constant as, you know-- you know, it fluctuates hugely. How does this-- how do you take this into account with your work? >> So, you're quite right, the reason the sun changes, let's think of the solar cycle and it varies between 9 and 14 years and the radiation of the sun goes up and down by about 4.4 percent in the solar cycle. But because you got satellites sitting at a place called L2, Lagrange 2, there are observatories, that one called SOHO and now there's SDO, the solar dynamics observatory. They are measuring that radiation flux continually. So we have a great source of data that tells us how those things vary. But you're quite right, we didn't take that into count because it does change overtime. >> I think we have time for a very, very quick one. >> I don't want a hard one. [ Laughter ] >> Thank you. Are you saying that today's space age would be unimaginable without Einstein having lived when he lived because-- >> Yeah. >> If he was alive today, he wouldn't have lived when he lived and we will be in the space age. >> That's exactly what I'm saying. What I'm saying is that actually, none of this if-- if we haven't had an Einstein who predicted all these things and gave us the mathematics to describe how things behave, we couldn't use these things the way we can today. We could have something but it really wouldn't work anywhere near as well and that's-- that I think is the really inspiring thing about Einstein. He started from humble beginnings, he wasn't even that keen on mathematics and he have us this framework which enables all this technology. I would also like to encourage people to come and work in science and engineering. Is there any of you-- you know actually it's pretty cool, you know. We wave our geek flag high and we get to do some pretty neat things these days. So any of you, if you're thinking about a career in science and technology, okay, it's not big money, you know my wife will tell you, right, but it's a great life and you'll be contributing in the field. Okay. Thank you. [ Applause ]