I expect this is the first time you have been addressed by a real computer. You may have seen science fiction films like 2001 for Blake 7 in which there were computers that spoke. But his films are really cheats. The computer parts were spoken by humans. The reason was that computerized speech synthesizers were not sufficiently good to be used in films or TV programs. But this speech synthesizer is a great Improvement. It's very easy intonation and gives me a voice that sounds Almost Human Instead of like a Dalek. The only trouble is that it gives me an accent that has been variously described as American Scandinavian or Irish. The speech synthesizer is controlled by a small portable computer on the back of the wheelchair. The screen of the computer has been taken off and mounted on the arm of the wheelchair. On the screen. I have a menu which I can scan by pressing a slips in my hand. In this way, I can select Words which are printed out on the lower part of the screen. When I have written what I want I can send it to just leap synthesizer. I can write scientific papers on the system. I write equations in words. Alpha plus beta over 2 equals gamma. I have a program called Tech which translates the equations into symbols and sets the paper. No prototype. I have also used it to write a popular book, which has been translated into 22 languages. I realized it was going to be a success when I sold the rights and serbo-croat. So much for my computer system. Note for my lecture. Nothing puzzles me more than time and space wrote Charles laminate E12. And yet nothing troubles me less as I never think about them. I guess it is the same for most of us. We measure distance or tell the time without bothering to think of what we are really doing. But we would be hard-pressed to say what they mean. Space is not so bad. At least it stays around and you can point it out to someone else. But time is much more mysterious and ephemeral. I mean it slips by and we can never come back to it. So what is the nature of time? There are poetic answers to this but I will concentrate here on how time is treated in scientific theories. I take a positivist view of science. Lettuce, I regard a scientific theory to be just a mathematical model. That describes what we observe. It exists only in our minds and does not have any other reality. Whatever that may mean. Positivism is out of favor with philosophers at the moment. I think principally because it was yesterday's fashion. But it seems the only consistent approach for a scientist. I shall Endeavor to describe what answers our present theories give to questions like What can one do to slow time down or speed it up? Is it possible to travel back in time? Does time have a beginning and an end? And what is beyond these limits? How real is time? Newton was the first person to formulate a complete mathematical model of the universe. This model Incorporated the idea of absolute time. This meant that one could label events in a unique way with a number called time. I'll let surface would agree on us are two events in different places happened at the same time. By contrast the Newton's Theory position in space was not absolute. In other words different observers would not necessarily agree on whether events at two different times took place at the same point of space. This was because there was no standard of absolute rest in Newton's Theory. We do not notice that the Earth is going around the Sun at about 20 miles a second for that. The sun is going around the Galaxy and the Galaxy itself is moving relative to distant galaxies. The reason is that Newton's laws are exactly the same for different observers moving at constant speeds relative to each other. Two events that happened at the same point on the rivers would appear to occur in different places to an observer on the sun because of the distance the Earth will have moved between events. The Newton's Theory time was a thing on its own completely separate from space. This meant that time had to be like a lion. Did my it has a beginning if there was a creation as Newton believed. And that might happen and if there was going to be an apocalypse as Newton also believed. But it was just a straight run from beginning to end. time couldn't do anything fancy in the middle like looking back on itself for dividing into More interesting possibilities for a time where opened up however when Einstein formulated the theory of relativity. The Newton's Theory the laws of mechanics had been the same for different observers moving relative to each other. However, Einstein's theory said that in addition all Observer should miss her light to have the same speed. One can measure the speed of light by sending a pulse of light from one event to another. Linda speed of light is the distance between the two events divided by the time interval between the events. But observers moving at different speeds will not agree on the distance between two events because position in space is not absolute. For example an observer on the Earth would not agree with an observer on the sun on the distance between the two events because the Earth will have moved between them. This is a tulip server site. I calculate the same value for the speed of light. This means that they must also differ on the time interval that they think elapses between events. Last time cannot be absolute in the sense that events cannot be labeled by time in a unique way. Instead each Observer has his own measure of time and clocks carried by different observers will not necessarily agree. the sleep study the so-called winds paradox one twins days on earth and the other twin goes off in a spaceship. When he comes back the stay-at-home twin will be an old man, but he astronaut twin will only be a few years older. All this may sound very well. But most of us don't happen to have a spaceship we can use the try it out. However, one can actually observe this effect by flying an accurate clock on the commercial airline. Still it would take an awful lot of frequent flyer miles to prolong one's life by a day this way. The theory of relativity alter our concept of time by changing it from a thing on its own two part of a construction called space-time. SpaceTime is the collection of all events. Event can be labeled by for number 3 for the position in space and one for the position in time. Time was no longer Universal an absolute as in the tolian theory, but it depended on the motion of the Observer like position in space. The crawl space time properly. I would need an overhead projector with a four dimensional screen. This means that I will have to use diagrams in which I leave out two of the space directions. I will draw the position of an event and time in the vertical Direction and the position in space in the horizontal Direction. In the absence of strong gravitational fields, the history of a ray of light will be represented by a diagonal line which moves to the right and space while it moves upwards in time. In this case time simply moves forward from the bottom of the diagram to the top. The most one can do is the slow down once personal time with respect to that of another Observer by moving at a high speed relative to him. The situation is much more interesting. However, if one takes into account strong gravitational fields. In this case space-time is no longer flat, but it is distorted and curved by the presence of matter and energy. The histories of rays of light are no longer straight lines, but are bent by gravity. We can actually detect such spending by observing Stars ghost light passes close to the Sun on its way to us. Look position of the Stirrup here slightly different because the light is deflected through a small angle. The spending opens up new possibilities such as black holes. These are regions like a collapsing star where the gravitational field becomes so strong that no further light can escape but it's bent back into the region. Light emitted from the region just before it became a black hole would almost be bent back by the gravitational field. That means it will take a long time to get away from the region. Lost someone at a distance watching a star collapse to form a black hole would never see the star actually disappear. Instead it would just become dimmer and dimmer and redder and redder until it was invisible for practical purposes. It would be similar if you were watching an astronaut who was foolhardy enough to jump into a black hole. At some time on his watch say 11 o'clock. He would enter the black hole the region from which it is not possible for light or anything else to escape. But no matter how long someone outside the black hole waited. They would never see the astronauts watch reach 11 o'clock. Instead each second on the what would appear to take longer and longer until the last second before 11 o'clock would take forever. Lost by jumping into a black hole one could ensure that once image lasted forever. At least for those that stayed behind outside the black hole. But the picture would fade very rapidly and grow so dim that no one could see it. People who stay outside the black hole will never see the astronauts history reach 11 o'clock. But he astronaut himself wouldn't notice anything special when his watch reads 11 o'clock and he goes inside the black hole. Inside the black hole. There will be a singularity a place where space and time come to an end. There are solutions of the equations of general relativity in which the astronaut could fall into a black hole avoid hitting the singularity, but go instead through a small passage and come out of the white hole. A white hole is the time reverse of a black hole. That is an object. That one can come out of but not fall into. The Whitehall might be in another universe or another part of our universe. In the latter case one good news black holes for travel to distant galaxies. Indeed one would need something like that if Intergalactic travel is Tamiya practical possibility. Otherwise the distances are so vast that it would take millions of years ago to the next galaxy and return. But if you could go through black holes you could be back in time for tea. The trouble is there would be nothing to stop you getting back before you set out. You couldn't make sure that you never said out. Or even worse someone else might use a black hole to travel back in time and kill your parents before you were born. Fortunately for our survival, it seems that space times in which one can travel back to the past or unstable. The least disturbance such as a spaceship going through will cause the passage between a black hole and a white hole to pinch off. The history of the spaceship would come to an end as it was torn apart and crushed out of existence at the singularity the end of space and time. According to the theory of relativity there would also be another singularity in our past called The Big Bang which would be the beginning of the universe. NASA history of time would be rather dull. It would begin at the big bang and it would come to an end inside a black hole for when the whole universe reap collapsed. In fact in relativity time leader has to behave this way or go around in a circle. This is because the direction in space time in which time increases is very different from the directions that correspond to changing position in space. Thus although relativity combines time and space into space time. That does not fully unify time with space. Time is still really on its own and it's like a lion. In a minute, I will tell you how we may be able fully to unify time with space and get away from this line like character of time. Please wait while I load the rest of my lecture. I will continue it is only in the last 15 years that we have realized. It may be possible to used 1. Mm Theory to fully unify time. Which base? This would mean that one could get away from this one-dimensional line like behavior of time. Quantum theory was invented in the 1920s by Erwin Schrodinger and Werner Heisenberg to describe the behavior of very small systems like atoms or Elementary particles. That depended in an essential way on the use of a new kind of number called complex numbers. A complex number can be regarded as a shorthand way of writing a pair of ordinary numbers. It can be represented as a point in the plane with the two numbers corresponding to the positions of the point in the horizontal and vertical directions. Thus for example, the complex number that is a shorthand for the pair of numbers 1 and 2 would be represented by a point one unit to the right of the center and two units up. one can write this complex number as 1 + 2 I here I is a so-called imaginary number. It is not really a number in the usual sense of the word. One cannot have I apples in a bag for having a perfect Wing. I pounce. Whether it is a bookkeeping device. That just means that the number that multiplies it. Is that right angles to ordinary real numbers. But complex numbers behave like ordinary numbers in the sense that one can give formal rules for adding subtracting multiplying and dividing them. Multiplying by Lee imaginary number I is really a shorthand for rotating points through a right angle about the central point. Multiplying by again rotates toilets through no you're right angle about the central point. Thus multiplying twice my I will take a point to a new position on the opposite side of the central point, but at the same distance from the center. This point will correspond to a complex number which is minus the complex number of the original point. Thus for example, if one multiplies the complex number 1 plus 2i twice by i1 rotates it through two right angles to the complex number minus 1 minus 2i which is on the opposite side of the central point. One can therefore say that in a sense. I times I equals minus one. However, one should remember that I is really a shorthand for rotation through a right angle. There is no number which when multiplied by itself equals -1 in quantum theory one cannot predict events precisely as one could in Newton's and Einstein's theories. Instead one can predict only the probabilities that events occur and there is an element of uncertainty or Randomness in what happens. Einstein objected strongly to this Randomness saying that God does not play dice. But all the evidence points to God being an inveterate Gambler and throwing the dice to determine the outcome of every observation. A good way to describe the uncertainty introduced by quantum theory is the idea of a sum over histories put forward by Richard Feynman. In this mathematical model of reality a particle does not have a single well-defined history. Instead that can be regarded as moving through space-time on all possible pass. We'll each path is associated a complex number which depends on the shape of the path. the probability of a particle getting from a point a to a point B is given by adding up the complex numbers for all the possible paths from A to B and then back to a One could regard to sum over histories as just a mathematical trick that happens to give predictions that agree with experiment but which doesn't reflect the underlying reality. However, if one adopts a positivist Viewpoint as I do and Schrodinger dead, it is meaningless to talk about an underlying reality. How could one determine what reality was? Instead one can just build mathematical models of the universe and the best model is one that accurately describes the observations and assess elegant as possible. On that basis the sum over histories has a strong claim to be accepted as a model of how the universe behaves. You may we'll ask what has London theory in the sum over histories not to do with the nature of time. The answer is that adding up the complex numbers associated with each path doesn't give a well-defined some if one uses the histories of particles in ordinary time. S1 includes more passion the some the answer fluctuates wildly and doesn't tend to a well-defined value. However, one can get a well-defined answer if one supposes that the time label of an event is not just an ordinary number as we normally think but it can be a complex number. In that case, there is another direction of time called imaginary time at right angles to ordinary time. One can consider histories of particles that take place in this imaginary time Direction instead of in the ordinary real-time Direction. If one adds of the complex numbers associated with each of these histories in imaginary time one gets a well-defined answer. From the sensor one can calculate the probabilities for different things happening in ordinary time. Again, one could regardless use of imaginary time as just a mathematical trick which tells us nothing about reality. But from a positivist point of view it is not useful to ask what reality is. Instead the value of the concept like imaginary time depends on whether it enables us to formulate mathematical models that describe what we observe and to predict new phenomena, which can be tested by observation. In this case great new possibilities open up. If one combines the concept of imaginary time coming from quantum theory with the idea of the theory of relativity that space and time are joined together in space-time. One can then have the space-time in which events are labeled by three numbers for position in space and one number four position in imaginary time rather than ordinary time. In such a space time the distinction between directions in space when an imaginary time disappears. The space-time is said to be euclidean because it is like ordinary space in which One Direction is not distinguished from another. Quantum theory was originally invented to deal with very small systems. However, if one is to have a consistent and unified theory one has to apply quantum theory to the whole universe. The best way of doing this seems to me to use the sum over histories idea. In this case, the sum is over histories of the entire universe not just over the possible histories of a particle in space-time. That is the sum is over curved spacetimes which represent the history of the whole universe and everything in it. The new orders at the some good the well-defined answer that is necessary to use euclidean space X that is space times in which events are labeled by imaginary time rather than ordinary time. One has to specify how the space-time start off in the past. If one were dealing with events in ordinary time time would be like a line. It was either gold back infinitely in the past or it would have a beginning in the finite past at a singularity which would form a boundary to space-time. before dinner eat I'm began at a singularity as the theory of relativity would predict there would be a number of questions like What happened before the beginning? What determines How the Universe began because one cannot define the laws of physics at a singularity? However, because imaginary time behaves just like directions in space-time. There are new possibilities. What does that space an imaginary time together can form of space-time that is finite an extent, but which doesn't have any boundaries edges or singularities? That would be a bit like the surface of the Earth but with whom or dimensions. The surface of the Earth is finite in size but no one has fallen off the edge of the world since the time of Christopher Columbus. Len imaginary time would begin at the North Pole which is the most Northerly point on the earth and it will end at the South Pole. To ask about events at imaginary times before the beginning would be like asking about places north of the North Pole. They simply are not defined. In 1983 Jim hartle and I proposed that the sum over histories should be taken only over imaginary times base times that are finite an extent, but which don't have boundaries edges or singularities? If it is no boundary proposal is correct the complex number associated with each history would be determined simply by the laws of physics. This would mean that the state of the universe would be determined just by the laws of physics on the other hand if the history sin imaginary time had a boundary such as the singularity one would have to know the probability of that particular form of boundary in order to calculate the probability of that history. The laws of physics would not determine the probability of the boundary because they cannot be defined a singularity. Instead one would have to appeal to some agency outside the universe such as God to determine the probabilities of different possible boundaries. This would mean that the state of the universe would not be determined by the laws of physics alone, but it would also depend on God's choice of the behavior at the edge of space time. However, if the no boundary proposal is correct. God would have had no choice in the state of the universe. How's the universe began at the Big Bang singularity in ordinary time would be determined by its behavior and lack of boundaries in imaginary time. Imaginary time can also provide a means of Escape for a Plex that fall into a black hole. The history of Neil perfect in ordinary time will come to an end at the singularity inside the black hole where the effect will be crushed out of existence. However, one can also consider the history of the object in imaginary time this history cannot come to an end if the no boundary proposal is correct because there will be no boundaries or singularities in imaginary time. Instead it seems that it will pass through a thin tube or wormhole in imaginary time and out into another universe or another part of our universe. This is rather like to go possible scenario in ordinary time mentioned earlier in which one fell into a black hole and came out from a white hole. However, there are important differences. First wormholes in ordinary time cause problems because they will allow one to travel into the past and change it. But it seems that in the wormholes in imaginary time can allow particles to travel into the past they do so in such a way as not to affect what has already happened. Secondly the wormholes in ordinary time contain singularities in earn stable occurring only in very special cases of gravitational collapse. But wormholes in imaginary time don't have any singularities and can occur in any situation. Indeed. It seems there should be a very large number of very small imaginary time wormholes in an apparently empty space. Individual Elementary particles can pass through them going to and coming from other universes. The effect of this will be to make the particles going in and out of a wormhole appear to interact with each other. Not wormholes will change the apparent interactions of particles in ways that still have to be calculated properly. But it does seem that one important interaction is affected in a very significant way. This is the so-called cosmological constant which gives space-time an inbuilt tendency to expand or contract. by observing the motion of distant galaxies, we can determine that this constant is either zero or very small This is very surprising because quantum theory would lead us to expect a value for the cosmological constant. That is very much larger than what we observe. And when I say much larger, I mean at least a billion billion billion billion billion times larger. Up to recently there has been no explanation for why the cosmological constant should be so remarkably small. But if one includes in the sum over histories imaginary time histories containing wormholes one find sadly apparent value of the cosmological constant is exactly zero. most mathematical models of the universe that use the concept of imaginary time can give an explanation of why the universe began in the way it did and why the cosmological constant at 0 If you like you can say that this use of imaginary time is just a mathematical trick. That doesn't tell us anything about reality or the nature of time. But if you take a positivist position as I do westerns about reality don't have any meaning. All one can ask is whether imaginary time is useful in formulating mathematical models that describe what we observe. This it certainly is. Indeed one could even take an extreme position when say that imaginary time was really the fundamental Concept in which the mathematical model should be formulated. Ordinary time would be a derived concept that we invent for psychological reasons. We learned ordinary time so that we can describe the universe as a succession of events in time rather than just as a static picture like a map of the surface of the Earth. Anyway, whether you think that ordinary or imaginary time are the more fundamental I have certainly used up my ordinary time for tonight and probably my imaginary time as well. I will therefore stop before I run into the singularity of the chairman sex. Thank you.