The Quantum Mathematician - Professor Chris Budd OBE

right well good afternoon everybody for those of you don't know me I'm Chris Birds I'm the aggression professor of geometry and I'm doing a series of talks this year on maths and the making of the modern world and next year this will evolve into a series of talks on maths and the making of the future world okay so today we have the somewhat scary topic of quantum theory and I've called this talk the quantum mathematician to show you a little bit how some of them some of the mathematical ideas which have emerged over the last few years have helped us understand quantum theory a bit but I agree with most people I've been chatting to as been waiting for the lecture to start that quantum theory is a somewhat mysterious and scary subject so I'll try and make it a little bit less mysterious and hopefully a little bit less scary in this talk and the approach I'm going to use as I'm going to kind of give you a history of the way that quantum theory was developed over the course of the 20th century and then we'll have a look at the impact that it is having on 21st century technology okay so that that's the plan for this talk so if I was given this talk at the end of the 19th century if I was giving a talk on physics I'll be in a very buoyant mood because at the end of the 19th century physicists and here we have some splendid 19th century physicists I think one of them is Michael Faraday we're pretty confident that they understand stood what was going on they had rules of physics sort of for example rules for thermodynamics or electromagnetism or mechanics which explains the way the world worked they were pretty sure they got it all right and all that was needed to be done was to work out a few of the constants in the formula that they were using and then the world would be predictable and physics would basically have finished well it wouldn't finish in terms of explaining but they wouldn't need to find anything more so that's where we were at the end of the 19th century okay there were a few little wobbles around which hadn't been quite resolved things like radioactivity which had been discovered by Becker Al towards the end of the 19th century and things like x-rays which weren't Anna discovered I talked about in one of my lectures earlier on this yeah but they felt that these were just sort of tidying up exercises and wouldn't require too much effort to sort out so that's where we were at the end of the 19th century and why they got to this position well is largely due to this guy Newton and Newton in 1692 essentially started modern science as we know it when he wrote the book the Principia and in the Principia he formulated the laws of mechanics and the law of gravity and he also gave a mathematical framework for being able to take those laws and use them to explain the universe in a deterministic way so that you could predict what was going on using my subject the subject of mathematics and this was incredibly successful as a theory Newton's laws work brilliantly for a long time they still do work brilliantly for things on arsal to scale on a human scale if you want to design a bridge you use Newton's laws if you want to drive a car use Newton's laws so they had done very well and in the nineteenth century there was this kind of triumph and it was a triumph in part due to this guy this is Maxwell James Clark Matt well who working in Cambridge formulated the laws of electromagnetism where he took the laws of electricity the laws of magnetism combined them together and found that that combination allowed him to understand light and radio and it was a great unification of the three subjects of electricity magnetism and optics into one set of equations and those equations show clearly at the time that light was a wave a wave made of electricity and magnetism so this was fantastic and you know the physicists were very very confidence that they had the world nailed okay and that was the end of the 19th century as we all know the 20th century brought in many changes in this museum you can see the exhibition about votes women this was a big change at the beginning of 20th century you had the invention of the car the radio and the airplane huge technological breakthroughs but perhaps one of the biggest things that happened at the beginning of the 20th century was the realization that this comfortable world of physics that had you know everyone was so happy with was completely and absolutely wrong okay it wasn't that the laws were wrong it's just that there was so much more out there and the little crack that these wobbles of radioactivity and x-rays Sean was the crack into a whole new way of looking at things so all this was to change as I say and it changed pretty early on with two huge theories in 1905 Einstein very much very influenced by Maxwell very much influenced by Maxwell brought in the special theory of relativity and the special theory of relativity gave a completely new way of looking at things which are very low and went very very fast okay and Einstein see relativity say built on Maxwell's theory but went way way way beyond that and pretty well at the same time Along Came quantum theory which is the subject of today which gave a theory of what was happening at the very small scale at the scale of the atom or smaller than the atom so these two theories have gone on to dominate 28th and now 21st century science they've completely transformed our way of looking at the world and as well as transforming the way of looking at world they have led to much of the technology that we now take for granted that we now take for granted in particular quantum theory this mysterious theory is at the heart of devices such as the modern computer and for good or bad the modern computer is changing our lives okay if it wasn't for understanding a quantum theory we wouldn't have built the modern computer so this really has dominated our lives so those of you who have been following my lectures will realize that I've been basing quite a lot of them on what are called the eight great technologies so the eight great technologies are eight technologies which the government feels we should invest in in terms of money but also in terms of research because they will lead us into the future and will lead the UK forward in technological advance and recently they've decided to add a ninth technology on to the eighth grade technologies and the ninth technology is quantum technology the technology that I will be getting onto towards the end of this talk so that's how important it is it's up there with machine learning which I did last year week with energy with robots and even even the production of food that's one of the other technologies as something that government feels will be dominant force in the next few years so that's how important it is without quantum theory we would not be able to have the technology that we enjoy today however and this is the essence of these conversations I was having earlier quantum theory is deeply deeply mysterious it runs completely contrary to quotes common sense now as a mathematician I'm familiar with much of what I do running contrary to common sense I'm often told off for doing things which are not particularly common sensical but you wonder where the common sense is just a product of our own minds no our own way of looking at things and really there's more to the universe than common sense and this is what quantum theory does it kind of opens our mind to a completely new way of looking at things and questions the nature of reality and the nature that a mathematical description of reality helps us put things together so here's a couple of quotes which I really like the first one is by Roger Penrose great hero of mine one of the most important mathematicians of the 20th century very famous for his work on gravity and also on tessellations I will quote this in full quantum theory has two bodies of facts in its favor one is that it agrees totally with experiment incredibly well the experiment and the second which for me is geometry professor is very appealing it's based on beautiful beautiful mathematics mathematics which makes your eye water it's so nice the only problem is that it makes no sense okay sonic problem and there we are order a merits ee she knows we talked about and here's Richard Fineman who won the Nobel Prize for his work on quantum theory and has written some of the best books on Constance theory and was one of the pioneers and leaders of constancy in the 20th century and he said I can safely say nobody understands quantum mechanics and if nobody includes Richard Feynman then I feel I'm in good company ok so there we are that's what I've got to try and get round a subject which nobody understands it makes absolutely no sense but somehow works somehow it works ok that's the plan right so I thought when thinking about this talk that the best way to describe quantum theory was to take you through a journey for how we came to understand the way that quantum theory works in the universe and the story all starts with with this guy which is Max Planck so he is generally regarded as one of the two fathers of quantum theory quantum theory essentially had two births and he was the father for the first birth so quote Max Planck was studying a fairly in a sense mundane topic he was looking at how a body which when it's heated gives off radiation okay so this is called blackbody radiation and basically the higher the temperature of a body the more radiation it gives off and this is incredibly important concept in climate change and next year when I look about how math predicts the future I'll be talking about climate change and we're talking about black body radiation quite a lot but one thing that was bothering the 19th century physicists they hadn't kind of worked out was that if a body emits radiation than it a committe radiation at all the wavelengths that Maxwell predicted radiation could occur at so those from the low frequencies radio waves infrared and so on through the optical frequencies and then up to the higher frequencies like ultraviolet and Beyond and the problem was the basic prediction from Maxwell's classical theory was it would emit radiation at all these frequencies and therefore words emit essentially an infinite amount of radiation and that's not what was observed and this was a paradox at the time and Planck had a thought about it and he proposed that energy words came in sort of discrete amounts he called these quanta after the Latin for things and that the energy of the quanta was proportional to the frequency so in other words the higher the frequency the more energy would be produced and that kind of limited the amount of energy that could come out of the higher frequencies and the proportional constant was this number H and that is being called Planck's constant ever since so this was the first break with traditional physics and using this very simple formula that energy was proportional to frequency he came up this somewhat scary equation here which explained this scary equation tells you how much energy is emitted at a frequency F and a temperature T I won't bother you with saying how that's derived or even scaring you with asking you to understand it except to say that's what the shape of the curve looks like for the different wavelength so the amount of energy peaks in this sort of area and then drops down for small wavelengths of high frequency and the point about this was that it agreed completely with experiment okay so using this kind of basic quantum idea Planck came up with this formula they tested those experie and it worked and that's how science works okay you proposed an idea you see what the implications of those ideas are you test them against theory so people started to think there was something in this idea that energy came in discrete amounts and was proportional to frequency but they shouldn't really believe it and then look a bit later about 1903 or 1904 some more experiments were conducted where light was shown on to metal so you'd have a piece of metal here and you'd shun light onto it and they found to their surprise that the amount of the energy of the electrons that came off the metal when the light was shine onto it didn't depend upon the amplitude of the light but depended on the frequency of the light now why was that important it was important because Maxwell predicted that the energy of light from his equations was proportional to the amplitude that was the size of the waves but this seemed to run contrary it seemed to be that the energy seemed to be related to the frequency this OK was again a bit of an anomaly and it was sorted out by no less a man than Albert Einstein snares Albert Einstein we all associate Einstein with the theory of relativity a rightly so rightly so but in 1905 however I don't know how he did it I think he was at this time still a patent clerk he published three papers 1905 three papers each of those papers on its own would have got him a Nobel Prize okay the most famous paper was the one on the special theory of relativity that did not get him a Nobel Prize he also wrote another paper on Brownian motion which is sort of understanding how molecules move around randomly which has led to the kinetic of gases and a huge understanding of the way that gases behave that didn't get in the Nobel Prize but he wrote another paper on the photoelectric effect third time lucky that did get in the Nobel Prize okay I don't know what we was you know must only sunning in the air that that was an incredible year 1905 ten years later he published his general theory of T which was an equally extraordinary achievement okay so he was Einstein and he came up with this incredible concept that lights as well as being a wave also was like a stream of particles and he called these particles photons and the photons had discrete energy and the amount of energy was as Planck had predicted this number H times the frequency and he explained the photoelectric effect very simply a photon one of these sort of particles of lights would hit the metal and every time it hits if it had a enough energy it would knock out an electron and that an electron would have this energy the same energy as the photon and the more photons you had the more electrons will come off and that was his explanation and again it completely described the photoelectric effect and it gave everybody confidence that perhaps light had this particle-like nature but already that was beginning to look a bit mysterious and strange because Maxwell's equations predicted that light was a wave there was tons and tons of evidence that light was a wave and here was Einstein coming along saying maybe like is also a stream of particles Newton thought it was a stream of particles but that idea had been rejected so light seemed to be sort of having a schizophrenic attitude to light it was particles and it was waves what was going on okay so um carry on with the story around about 1912 Rutherford up in Manchester at the time Rutherford came from Nelson in New Zealand I've been to see his memorial there so he was working in Manchester and he was investigating the atom and by shining alpha particles at the atom and seeing how they were bounced off he came to the conclusion that the atom was mostly empty space at the center of the atom was a nucleus which was positively charged and that was bouncing alpha particles off and orbiting the atoms other like a sort of solar system were electrons okay so the the electrons would go around the atom and the theory for that was that the positive charge would attract the electrons towards it and that would cause them basically to accelerate towards the nucleus and and if you spin around the nucleus then then that's balances out that you have centripetal acceleration which which allows that to happen so that's rather FIDs model the electron of the atom which again agreed with the experiments that he was doing but had a slight problem and the slight problem was that it wouldn't work according to Maxwell's theory so Maxwell's theory says that if you accelerate electrons then you emit radiation now I do this all the time we do it all the time if you take out your mobile phone and talk to somebody then the electrons in the antenna accelerate and that causes them to give out radiation and that radiation goes off to another phone and it allows you to speak to them that's how a phone works if the electrons go around the atom gave off energy by accelerating then they would lose energy and will collapse into the atom and the atom would just go poof and stop existing so it's a nice theory but it just didn't work and it was fixed by the second person who we can argue is the the second father of quantum theory which was the Danish mathematician stroke physicist Niels Bohr Niels Bohr had a marvelous predict a quote which I use a lot when I think about climate change he said it is very hard to predict anything especially about the future the other story about him is that he had a horseshoe hanging above his laboratory and someone said why have you got a horseshoe and Niels Bohr said well to bring me luck and someone said surely you don't believe in that do you he says I understand it works even if you don't believe in it and he not by luck but my brilliance came up with the idea that the way the Aten might work was the electrons would orbit not in any old orbits but with orbits of energy which was multiples of these sort of quantum levels that Planck had predicted these discrete amounts and that providing it stuck to that quantum level it would be stable that was Bohr's model of the of the Otto will show you presently that that has to be extended but with that model he had these kind of energy levels corresponds to number quanta he then said if an electron does lose energy it would do it by jumping from one orbit to the other it would then emit energy this would be these famous photons we can work them out and he came up with his formula and that the energy between different orbits was University proportional to the square of this number and this was a formula which again checked out exactly with experiment so that gave people confidence so that was quantum theory up to about the beginning of the first world war in the First World War people had other things on their minds but at the end of the First World War Bohr again played a huge role in the next phase of concept theory and what he did was he moved back to Copenhagen and founded the Copenhagen Institute for quantum theory which is now called the Niels Bohr Institute various and he started thinking very differently from this kind of mechanistic view of quantum theory that they'd had up to then which think that maybe what's happening at an atomic level isn't something we can know exactly it's more we just know probabilities it's like if you toss a coin I don't know that coin will come down heads or tails but I could say it will with probability about 1/2 come down ahead per out 1/2 come down the tail and so rather than know exactly where an electron was you might have some probabilistic way of describing where it probably would be okay so this was his view it's very different from the view up to then but it's a view which has turned out to be correct correct this was called the Copenhagen interpretation now as I said one thing that Einstein had come up with was this idea that light could be both like a wave unlike a particle and de Broglie who came who was in the early 1920s came up with the revolution idea well if light can be light a wave and a particle maybe other things can be like that maybe electrons can be like that maybe an electron can behave sometimes like a wave and something like a particle maybe all of us are a bit like a wave and a bit like a particle again this is weird how can something be a wave and a particle together but this was verified by an experiment which was conducted in the 20s called the double slit experiment were an electron beam gun something was just shot out electrons they put a couple of slits in front of it and if you do this with light then you can see what's called an interference pattern on a screen behind you get black and white areas where the waves and the light interfere constructively or destructively with each other you see this very often if you wear glasses you often see interference patterns particularly if it's raining what was weird if you do this for electrons it did exactly the same thing come on this can't happen if you got a hole there the electrons that go through it and a hit there or hit they should get two white beams forming instead you got an interference pattern exactly consistent with what you would expect if the electron was behaving like a wave its electrons seem to be behaving like a wave and a particle what's going on this this was weird so the first person to kind of really get his hand around what was really going on was Schrodinger no I liked Schrodinger Schrodinger you only think of a mathematician or a scientist you think of someone that sits in their office all the time and does nothing other than science okay Schrodinger was not like that so Schrodinger was an Austrian physicist who to all intents and purposes had three wives simultaneously possibly I think in three different countries or maybe two in the same country once I got a bit confused he had so many whilst he was married to one of them he went on a holiday with one of his mistresses and was so I don't know creative during that time that he came up with the idea of the Schrodinger equation which helps us understand the nature of the subatomic universe when he done all this when he done on his work he he actually went over to Dublin in the 1940s the invitation of de Valera and spent most of the remainder of his professional life and in Dublin okay so he was rather important person in the Irish Free State so his idea was that you a function sigh which is a function of space X and T time which describes the probability of a particle like an electron being at this point X in the time T so it just describes the probability you have to integrate this over a region of space to know the probability of it bit of the particle being in that region it doesn't exactly tell you where it will be at any one time see this is his wavefunction and he wrote down the equation for that so we're going to have our first scary equation of the day so brace yourselves guys here we are wow this is possibly well it's hard to say what's the most important equation in physics a equals MC squared is pretty important F equals MA law gravity but it's up there with them this is Schrodinger's equation this is the fundamental equation for quantum theory now I don't expect most of you in the audience to understand this I'll just describe a few things this tells you how the wave function changes with time this weird operator here tells you how it changes with space this thing here tells you the energy of the system so if you have a Tommy nucleus this is something you can write down h-bar is the Planck constant divided by 2 pi it's called the Dirac constant here is the number I the square root of -1 the imaginary number shouldn't really exist but there it is playing this huge role in this amazing equation and that equation describes everything as firemen said that equation is the equation for a frog okay final was right of course he was right so um this is surging this equation which is a say sure thing who came up with on this holiday with his mistress oh I may or may not recommend that as a good way of coming up with the equations but anyway and this is what a typical solution of this equation looks like it looks like a wave and this helps us understand why particles behave like ways why an electron behaves like a wave in the particle because an electron to a certain extent obeys this equation and because it's base this equation for its probability it has that sort of solution and that allows you to work out the probability of it being in one place or not now the probably this equation is it's damn hard to solve we do solve it nowadays with big computers and because we can solve it would be computers we can do chemistry because this equation describes chemistry very well very well at the time they could really only solve it for one problem and that was the the hydrogen atom where you had a single nucleus and a single electron okay but it was solved in that case and you can find the wave functions for that and you can find the allowable wave functions and the allowable wave functions precisely corresponding to the orbits that borer come up with by difference we're thinking about things this is a much better way of thinking about things and it reproduces Bohr's results this wonderful picture here shows you the various different types of orbit which are predicted by the wave function solutions of Schrodinger's equations there are many different types of orbit all of which you can verify experimentally so Schrodinger's equation really works what was interesting though was dirt in the Bohr Institute there are many other people and one of these is glycol oh sorry get on sir sir in a sec polishes say on one thing very important this equation here is what we call a linear equation it's a linear equation because this number sign here and here appears like this and here like this there are no squares or anything and that means that this is a very important property of mathematics many of the equations I work with Linnea that if if you have sigh one as a solution and situ is a solution so you have two possible wave functions which describe something then so is and what you get when you add them together and this tells us something completely weird it means that a particle can actually simul taneous lis exist in two states at the same time this is called the superposition principle this is where quantum theory seriously starts to deviate from common sense that something can be two things at once fortunately common sense doesn't apply to the universe so it actually can be in two states at the same time and we're going to see presently how this is very important in technology okay so at the same time as Schrodinger there was another guy called Heisenberg hoon he had of a different perspective there's Heisenberg here Schrodinger more or less came to blows about this and again this is where the maths gets a bit scary he wanted to formulate all of quantum theory in terms not in terms of waves like Schrodinger did but in terms of matrices and matrix functions if you don't want a matrixes I don't really worry I'm not going to go into any detail but they're basically the mathematical operators mathematical operators which are important in things like Google and here his view was that lots of things were happening in the quantum theoretic well like this sort of superstition of states and you never know exactly what's happening until you look at it by looking at something you force it to make a kind of decision about what it's doing and what it's doing turns out to be related to the water called the eigenvectors of these matrices and this seems a very different perspective from shirting as Schrodinger's was more well there's a wave function I can compute it I know what's going on but again when you do computations you find it worked and Polly who was another one at Bohr's group was able to derive properties the hydrogen atom which were basically the same so that was Heisenberg view of a Heisenberg also came up with a very important formula which is this which is called the uncertainty principle which says that if you make an error in if you have an uncertainty in measuring the position of something which is XL to X and you have an uncertainty in measuring its momentum Delta P then these two the product was bounded by this number and that basically means that if if you make a very small error in position then you have a large uncertainty momentum or if you have a large uncertainty in a small uncertainty momentum you have on a large uncertainty in position and and this is again one of the fundamental laws of the universe you can't know exactly the position and the momentum of something at the same time you similarly can't know the frequency and the duration of a signal at the same time I'll illustrate this with a joke okay and the joke goes as follows I have a glass of water in front of me there's my glass of water that'll do and you ask a quantum theorists is that glass of water half-full or half-empty and the only thing the quantum theorists can say is I don't know and the reason is the half if it's awning is full the implication is that it's filling up in other words its momentum is positive if something is half empty the implication is that it's losing water and so its momentum is negative if you say it's half something you are making a very precise description of its position so you know its position exactly it's 1/2 and if you know Delta X exactly you don't know the momentum and so you can't tell whether it's full or empty so there we are predicted by that formula okay if you say oh it's vaguely 1/2 then you might be able to do it but that's not okay so that that's that was a big debate was going Heisenberg and Schrodinger mollusk came to blows about this but it was resolved by this guy it's his Paul Dirac one of my big heroes he was born in Bristol until recently I lived in Bristol he was born quite close to where I lived he went to Bishop Rhodes primary school which is very close to where I live he went to British Bristol University and then went on to Cambridge he's considered along with Maxwell Einstein and Newton and Galileo as one of the greatest physicists of all time okay he's an amazing guy it's a shame we don't make more of him in the UK here are some of his achievements he unified Heisenberg's and Schrodinger's Hughes he showed that they were equivalent and he wrote a book about it called the principles of quantum mechanics which for many years was the fundamental textbook in upcountry mechanics he discovered antimatter if you watch Star Trek you'll know that the Starship Enterprise is powered by antimatter or matter antimatter reactions if it hadn't been for Dirac that would not be possible so you discovered antimatter he's discovered it for the electron there was an antiparticle called the positron you know so every particle has its antiparticle he invented a thing called the Dirac Delta function which is one of the key techniques in mathematical engineering okay I use it all the time really brilliant but what his proximally his biggest achievement was that he found the equation for the electron which was a sort of an extension of Schrodinger's equation which allowed quantum theory to be combined with Einstein's special theory of relativity see he combines quantum theory with the special theory of T again this is Dirac's equation it's very very similar to Schrodinger's equation the difference being that these things here are are not numbers they are matrices and this is one of the other great equations of all time the equation for the electron in farm you know wrote a book about the 18 greatest formula at all time and that's one of them so that's Dirac again I won't go into detail but this equation for the electron explained other things about the electron these have been experimental verified to huge precision huge precision I am pleased to say that Dirac is honored in his home city this is Bristol and this is the Dirac monument you can see it reflected there it's a spike anyone that knows about the Dirac Delta function will know that this is a very very fitting tribute to Dirac much better than a statue this is a good description and if you go to bristol city center to the Science Museum you can just see the sign there and it's opposite the cathedral you can see the cathedral in the windows you can see the deduct Dirac Memorial and also you can go visit the Science Museum at the same time ok so this was all sort of happy in the 1920s was this amazing time for the developers of quantum theory and it's sort of summarized by this this is called in various texts the most intelligent photograph ever taken nice Italian photograph ever taken it was taken the 1927 Solvay conference which should have put finishing touches on on the quantum theory as it was developing show you some of the reasons it's so good there's Dirac there is there's Bohr there's Einstein that's Mary Curie and there's Max Planck and there's a whole ton of other people there as well the collective IQ and that photograph is pretty awesome Oh de Broglie there and where's Heisenberg oh there Schrodinger that's Heisenberg I think over that credible photograph bit of a wobble who's heard of Schrodinger's cat most of you I think yes so what Schrodinger's cat so this came a little bit late in 1937 Schrodinger imagined that you had a cat in the box there we are and that box unlike this one will be sealed and a radioactive something would decay that will cause poison to be emitted and would kill the cat but because the poison is given by some sarandon process you don't know and so inside that box is a cat and the cat is both simultaneously alive and dead and that Schrodinger's cat and it's a paradox and it's a paradox about how the way the world of the microscopic and the world of the microscopic seemed to somewhat untidily fit together if anyone watches The Big Bang Theory there was a nice quote by penny on the Big Bang Theory and she said we had a cat once in a box but we didn't need to open the box to know it was dead which is actually quite profound in its own way so that was surely yeah okay and quantum theory up-to-date well let's bring you up to date now with with where things are and then I can tell you about the technology so after the war we had richard fineman who came along and he developed quantum field theory which combined unified quantum theory with optics and the way light interacted with things and was able to show that the electromagnetic force was all to do with the exchange of protons no our photons so the photons these electrons here exchanging photons will give that force and this is the wonderful explanation that we have not only of the way electrons and electromagnetic they're so charged particles interact but also how at an atomic level you have forces inc interacting there then we came out with action at a distance and this is something i want to talk about quite a bit because it's going to relate to our technologies and this is wonderful this shows you again how science works Einstein didn't believe in quantum theory I know he was one of the people that founded it we didn't really believe this this is a quote from him it's very imposing but he never like this uncertainty and very famously he says God does not throw dice God does not throw dice he didn't like this a probabilistic way of looking things he thought everything should be deterministic his theory of T is a deterministic theory and in order to kind of show that this vaunted theory must be wrong here in a couple of others Einstein Podolsky and and with us came up with the thing called the EPR experiment which to say if you create two particles at the same time they have the same wave function that Schrodinger's equation predicts and that means that if you operate a one function and you observe it and it kind of goes into one of its states the other particle must instantly going to the same state these two particles were linked together this was obviously wrong completely contradictory to determinism as he saw it and therefore constant theory must be wrong this was einstein's approach there was a slight problem with that it was a really really good idea and then when they went to look for it in experiments rather than finding that Einstein was right was well rather than finding it the they couldn't do this and therefore quantum theory was wrong they found that they actually existed that it actually happens that if two particles are created together and become entangled they kind of form a coherent consummate theoretical state and if you separate them into a large distance if you do something to one it immediately affects the other bonkers but it works and it's been observed to give you sort of some indication that's why this might be true suppose I'm someone I have a white ball on the black ball and I turn my back and someone puts a white ball in one box and the black bull and the other and then seals the box and then I take one box with me to the other side of the universe and I open it and if I see it's a black ball I instantly know the other box has a white ball in it okay so that's it's not quite the same but it gives you some idea as to why this is true okay so let's talk about the role of quantum physics in technology and there's been sort of two phases in this and this is phase one so at the end of the up to the end of the war all electronics was done with these wonderful things which are cool valves if you haven't met them some of the older people in the jet in the room might have met them I'm old enough to have used them quite a lot that's how big a valve is it's big it uses a lot of power it's not particularly reliable and the valves are now completely replaced in virtually all applications by much smaller devices like transistors or nitro chips here which are much smaller involve much less power and a far more reliable and were infinitely about even if they don't glow in the same way okay and whereas this technology come from it's come from quantum theory it's come from quantum theory now it's all to do with electrons going through outer vacuums which was reasonably well described by classical theory these things are to do with electrons going through semiconductors and electrons go through semiconductors in a funny way some of them just move around like you would expect them to but none of those of them hop from one of these sort of orbits that ball predicted to another leaving holes as they hop and the holes themselves move around as though they were particles and you can only understand electricity conduction in semiconductors if you understand the way holes and electrons move around these wonderful things here are the equations for those I put them down there because I work with these a lot this is part of my job to understand these N and electrons because they're negative peer holes they're positive these are the equations for semiconductors these are what are used to design chips and using these sort of equations in 1947 Shockley at Bell Labs designed the transistor and from the transistor we got the microchip from the microchip you get the computer from the computer we get all the problems of the modern world so that's that the other great technology which came out of a quantum theory to start with was the laser what is how do you get lasers from again you've got these Bohr atoms here Bohr orbits here an electron might or be orbiting here you pump in a whole ton of energy the the electrons jump up to what we call an excited state and then they start jumping back down to the original state as they jump down according to the quanta theory they give off radiation the radiation has to be at a prescribed frequency so you get a lot of radiation at an exactly prescribed frequency and it's all coherent and that gives us the laser once an example there's an example there's a nice coherence laser light when this is discovered people said ah right well jolly good well done and lasers were described as a problem an answer looking for a problem and then what happened well here's one use for them there's James Bond Goldfinger being about to be cut in half by laser and of course lasers are used to cut things very much so but here are all the many other applications of lasers so your CD player your DVDs all of these things laser printers rely on the laser of course including pointers over there okay so that's the laser so the laser understand the transistor are all products of quantum theory and I would say the original quantum theory as we were kind of evolving through but now we're into what's called quantum technology - so this is the new generation of quantum theory and this relies on these kind of spooky spooky types of quantum theory that I've been hinting up so one of the spooky things is that a particle of something can exist in two states at once simultaneously now in a computer in your you know computer energy information is stored in bits it's a 0 or 1 it's on or off ok in a quantum information something can be simultaneously on and off okay and that's called a qubit a quantum bit a quantum bit it's simultaneously on and off that means if you have n qubits rather than storing n amounts of information you can store 2 to the power of n so if you have three one you can score one two you can score two two two two four eight sixteen and so on very rapidly you can store exponentially large amounts of information still vastly more information with allowing these simultaneous things than you could so this immediately opens the possibility of storing far more information with quantum theoretical things than you could and then you operate on these using things called quantum gates so until for a long time these were thought to be theoretical properties you can never do this but now people are building them so for example an Oxford here's a direct quote from from the independent actually it's a recent article in the independent using trapped ions so using ions and atoms you can start storing things in exactly this way so this idea of things exactly seeing existing in many states at once is a reality it's a reality and this is sort of various sort of interesting issues about this one of the things about quantum information is that the theory says it can be neither created or destroyed and again until recently there was a problem here with black holes because black holes were thought of things which would destroy information and now we understand that if you look at a wavefunction which includes not only the black hole but also the other possibilities you can resolve this and information can exist in many states at once and not be resolved not being destroyed where's this going well the big application of these qubits is in the field of quantum computing so some of you may have heard this is going to be the thing which changes all our lives I predict so various people including phiman predicted or came up with the idea of quantum computing a quantum computer would with its power totally dwarf the power of modern computers it would just be completely out of this world different operating at speeds almost inconceivable today so these are the things if we can get them working will utterly change things your computer will modern computer you know the great terabyte terahertz or whatever thing that you've got will look like a stone-age ax in comparison with these things I can't really describe how the work but basically the way they work is that they have these qubits the things which can be in several states simultaneously if something can be in several states simultaneously it means that you can do loads and loads of things all at the same time they are what we call the ultimate in parallel computers that every single atom almost becomes a computer and it can do all its operations simultaneously so it's block that we have in computers of time and memory essentially goes away with quantum computers the reason we haven't gotten them yet means a bit like Schrodinger's cat so Schrodinger's cat simultaneously exists in the state of being alive and dead but of course it doesn't that cat is either alive or it's dead and the reason the cat is like that is that at a large scale this sort of property of and coherence quantum theory has sort of dissipates away and the difficulty is keeping these qubits which can exist in all the states possible in this state for long enough to do all your algorithms on that that's the basic and that's the problem we have with this size at the moment but just to say many governments of funding content computing to develop them for all these sort of things and there is one chord if you want to play with a content computer there's one online you can play with which is a 20 cubic computer which IBM have put together so you can actually go onto the website and ever play with this thing and there it is that's what it looks like why we worried about these things well why are we excited about these things well the security for our banking system essentially relies on the fact that two numbers when you multiply them together it's very hard to factorize what you've got so here's a challenge for you see by the end of today whether you can factorize these numbers okay it's very very hard and the cost of factorizing numbers increases exponentially with the number of digits the number and that means that if you have a number which is say a thousand digits long no computer nowadays can factorize that and that is the security of our banking system all our codes rely on this property that you can't factorize a number except you can with a quantum computer so by the way these are the prime numbers so a cons of computer using a thing called short factorization are can factorize numbers so if we can get a contact computer to work banking systems which rely on factorization become vulnerable and therefore bankers start worrying but at the moment that's the record for it until recently the record was 15 so we dumped a bit better than that okay I'm running out of time so I'll just whizz through the next bit and get on to the last bit so just to say the quantum theory is hugely successful with enormous applications still lots of things around we don't understand we certainly don't understand the way that quantum theory and general relativity interact although their various efforts at doing this but the key message I want you to take away from this is at the end of the 19th century physicists were pretty sure they sorted everything out at the beginning of the cent when T first century we haven't got really much idea what's going on out there thank you very much you

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Id: IEmlSRL4QCU

Length: 58min 2sec (3482 seconds)

Published: Thu Mar 15 2018