A Fork in the Road to Reality, Dr. Roger Penrose. Oxford University, UK

[Music] [Music] and in 1994 he was knighted for his service services to science and was appointed to the order of merit in 2000 please help me welcome Sir Roger Penrose [Applause] well it's a great pleasure to be here and thank you very much now this talk mentions before the Big Bang now I should explain that if somebody had asked me the question what happens before the Big Bang about six months ago I would have given the conventional answer to that question and if you want to know what the conventional answer to that question is well you should have heard Stephen Hawking in what we in our country we have a thing called the Richard and Judy show you've probably never heard of that but what you have heard of is is the analog that you over here which is the Opera Winfrey Show I think that's about as close we get to it and he gave the answer well the Big Bang that there's a singularity and the whole notion of space and time ceases to have meaning at that stage and so it makes no sense to ask the question of course so you must have prepared that answer because it takes him about 20 minutes to just say something that long but let me whoops I hope this is going to go on we're in trouble right yeah yeah OOP is that on perhaps it just takes a while it doesn't look very on to me I know there's another battle bin here but maybe it just takes a while I'll use this one to begin with let me first describe the what were the original cosmological models according to Einstein's theory of general relativity these models were produced by a russian mathematician or mathematical physicist called friedman and there were basically three versions depending upon the value of a think a which tells you the spatial curvature you see what I in all these pictures time goes up from the bottom to the top and at the beginning we have this red splodge here which stands for the Big Bang and you see the universe goes on expanding as time increases as you go out the page and basically the difference between these three models oh the elements looking good now the difference between these three models is the curvature of the spatial part of the geometry so it is space-time pictures so time's going up the page and going across we have the nature of space at any one time so we think of the geometry of this case here k equals 0 that means the curvature of space that's the spatial part of space-time is 0 in other words we have ordinary Euclidean spaces of course I can only draw two dimensions when there really you've got to think of this as three dimensional but don't worry too much about that here we have the positive curvature cases where these will just look like a circle around there but it's you must think of this is really a three-dimensional version of that which is a three-dimensional sphere which starts at the Big Bang of zero size expands up to a maximum and then contracts down until we have at the end what's called the Big Crunch that everything has come back together again the third example this is the negative curvature case and I want to say a little bit more about that this is what's called hyperbolic geometry like this one the universe starts from the singular state where everything is all scratched up together expands outwards indefinitely the difference here is that this one just sort of hangs on never quite collapses this one expands with this of definite speed and it just keeps on going but let me say something about this hyperbolic geometry which is the spatial geometry there and what I'm going to show you is something well this is I ought to have had an Escher picture here to show you but I somehow I've lost my picture and this will do instead it's a very close to a national picture as you had things very much like this these are slight mathematical variants on what I should produce anyway the point about this geometry is you can see well a lot of fish black fish and white fish and they seem to get smaller as you get over to the edge but you have to think that these ones near the edge are really just the same size as the ones in the middle I've depicted them here in such a way that I've had to squash down the ones at the outside in order to fit them into the picture but this is a very accurate representation of hyperbolic geometry it's geometry in which you could have parallel lots of parallels to one line that you have to think of these are straight lines these circular arcs which meet the boundary at right angles and that one never meets this one because this is the boundary here that's infinity you see so you have to think that if you were that little fish down there you'd really be you'd think you were just the same as this one thinks it is they're all the same and any this representation is what's called a conformal representation so if you look at very small shapes you find they are accurately represented in this picture you had to squash them down in scale to get them in the picture but they're all supposed to be I know they're putting it as the angles are correctly represented but the thing I want to emphasize about this picture is that this circle around the outside of course it should really be three-dimensional on yuto sphere around the outside but let's think about the circle around the outside that represents infinity for the geometry which is inhabited by these fish so if they were swimming away it would take them an infinite time to get up to what looks like this boundary here the thing about this picture them and I'm emphasizing is that you can represent infinity for the whole universe this is this whole hyperbolic universe at a perfectly good finite place and as far as the what's called the conformal geometry that is the geometry in which angles are correctly represented distances get squashed down that the conformal geometry is represented accurately in this picture so bear that in mind I want to say something about that later on but for the moment that's just a nice way of representing the geometry that is in this picture here okay so those are the three original standard models in these particular models there's a thing here called lambda that's a capital lambda that thing lambda is zero what is lambda where lambda is what's called the cosmological constant it's something that was introduced by Einstein in 1917 for the wrong reason he wanted a universe that was static there are various reasons but it turned out that was wrong and he needed to put this thing not equal to zero it was ahead of positive value in order to have a universe that could be the same for all time but then it was discovered the universe expanded and he or at least is said to have considered that this was his greatest mistake because he otherwise might have predicted that the universe was expanding anyway that is a thing that could be there and I'll say a good deal about that later on for the moment I'd like you to look at this model here the one with the positive curvature and it starts from the Big Bang and goes on to a Big Crunch now I have over here a number of suggestions for what might have happened before the Big Bang now these are very there is crazy ideas and I should say even though they're crazy all the people who have put them forward are very respectable scientists cosmologists and you need something a bit crazy now say something about why that is the case now this curve here is what's called a cycloid you can actually draw it by rolling a circle you mark a point on the circumference of the circle and roll the circle all along this line and it describes that curve this curve this in this picture time is going that way this curve represents the radius of the universe it's the size if you like of the of the whole universe in this picture and you see in this picture have started with the Big Bang it ends at the Big Crunch but according to this curve it just keeps on going so it was suggested in fact when this model was first put forward it was very often called the cyclic model of the universe and it comes and it produces this singular state here where all matter is condensed into a single point and somehow you have to imagine that it just bounces back out again and so it keeps on doing that it can't do that with the ordinary laws of physics it just goes singular here but you sort of picture that maybe it's somewhere getting around some new law comes in or perhaps it gets very complicated and swishes around and comes out again or something like that so there is people who suggested models of that kind in particularly cosmologists Tolman suggested that these cycles might change and get bigger I think it was as time progresses that was supposed to express something about the second law of thermodynamics I'm gonna have to say something about that but just sort of bear in mind I think I just throw this picture at you for the moment you can see various ideas here we have the wheeler idea which is that somehow it's like this but then they're all the constants of nature get churned up again each time and he wants to have them have different values at different phases of the cycle Lee Smolin has an idea where black holes form and new universes are born out of the black holes and there's an idea due to tear Arkin Steinhardt and various other people in which you have some collision between things called d-branes I'll have to say a little bit about things like this later on but there are all various crazy models about the Big Bang where you might not have you might not say that's the beginning of the universe there was something going on before it okay now we now know that these models are not really that good at representations of what's going on because this thing that Einstein introduced and then retracted this cosmological constant seems not actually to be zero it has a positive value it's all of these things that rightly puzzles me because people cosmologists for a long time we're trying to find out what the value I think I'll put this one over here because it's it's better what the value of this cosmological constant was and I remember going to conferences when people said well maybe at the next meeting we'll know what the value of the cosmological constant is well eventually it's found out what it is and it's not zero and as soon as it's found people started calling it not the cosmological constants anymore they call it the mysterious dark energy and that's what it's now called well it's called dark energy but it's usually called the mysterious dark energy I suppose this is because they didn't expect it I'm Lesley I didn't expect it either but I was quite prepared for it to be there I've written papers in which it was allowed to be there so the fact that it's discovered seems just a fact and I don't quite see why one so puzzled about it I think people are puzzled because they expected it not to have well if it was going to have such a small value as it had to have then it ought to be zero that's not a very good argument really it seems to mean the argument that people have used now I want to stress a point which is one of the main points that I want to make in this talk which has to do with the question okay not why we believe there's a cosmological constant that comes from various different observations but why we believe that there was a big bang at all and one of the most impressive they're a lot of different pieces of evidence which go together to make us have this expectation but one of the most convincing arguments comes from the microwave background this is radiation which is coming to us from or some people call it the the flash of the Big Bang which you can actually see in a sense you can't quite see it because it's radiation which is very low frequency corresponding to a temperature which is about three degrees or two point seven degrees above absolute zero that's very cold but what is rather striking about it is that it has a very very well-defined temperature if I have a curve which is called a plank curve or blackbody curve and going up this way we have the intensity that there is frequencies the frequency is plotted this way and what one finds well there's a curve which was predicted or explained by Max Planck which started off quantum theory in 1900 and this curve he had a very exact formula for it and this curve represents thermal equilibrium so if you have some radiation and matter and stuff all mixed up together in thermal equilibrium and I'll say a little bit more about that then it's the frequency and the intensity at any given frequency follows a curve like this depending on the temperature this curve may be moved over one way or the other but the shape of it is always exactly this shape and what you find these little boxes represent the limits of observation and I should say this transparency is an old one if I had shown you a new transparency you would have seen these little boxes is much smaller than this well they start to get a bit bigger down here but then if you look carefully at what it says about it it's magnified by a factor of about 500 so in fact although the boxes here give you the error and roundabout here they're about the same size as these boxes they're too big by a factor of about 500 so that means they're so tight these measurements are so tight on the curve that you just wouldn't see that any off at all it's an incredibly precise observation you find that this theoretical curve fits the data to an enormous precision and what does this tell us this tells us that to an incredible precision the early universe was in thermal equilibrium now that is a paradox in a certain sense it's a very good indication that the early universe was sort of hearts just great big hot mess and that is if you like a piece of evidence for the Big Bang I should explain this picture over here these are where we actually allow a positive cosmological constant and what you see is that rather having things rika lapsing they all do more or less the same thing all these models start off up to about there they look very much like the ones we had before but then they start to accelerate away and there's this exponential increase so they start accelerating moving away faster and faster and faster and it doesn't make much difference what the spatial curvature is the universe has this acceleration accelerating expansion and this is due to the presence of this cosmological constant or the mysterious dark energy whichever term you prefer now why is it a paradox that this curve should be telling us that the early universe was in thermal equilibrium well let me say something about the second law of thermodynamics the second law of thermodynamics is a crucial feature of what I want to say and it's illustrated by this cartoon at the top here which well okay we have three pictures and you have to put them in the right order here we have a glass sitting on the edge of a table a glass of wine here we have it falling through the air here we have it and the wine splashing out and here we have it smashed on the carpet at the bottom and the correct order is this 1 2 3 now that's the way I've got them you see time going that way we can't cover this up for the moment now you see according to the Newtonian dynamics that is about sufficient for the description of this what's going on here the Newtonian laws are completely reversible in time so that means it would equally be possible according to Newtonian dynamics for this to be first then that then that there's nothing to choose between the two except that we never see this we never see broken glasses with wine or spilt into the carpet suddenly jumping up in the air and the wine going into the glass and then landing itself delicately on the edge of table that just doesn't happen so the way we describe what in addition to the Newtonian dynamics is going on here we say that there's a thing called entropy and this entropy has to increase in time we're certainly not decreased in time and in these pictures that's exactly what's happening what is entropy we're roughly speaking entropy is a measure of disorder so it's telling you the disorder is increasing as time goes on it's a sort of depressing a law if you like it's telling you things getting worse and worse well I'll say a little bit more about that it's not quite as bad as you might think but at first it's what it's telling us and we can actually make this a bit more precise because entropy if I say disorder that's not much used to you I mean how do you measure that well there's a very wonderful formula due to the man physicist Ludwig Boltzmann Austrian physicist and here's the formula s is the entropy aren't quite sure why s is the entropy but it is and s is K times the logarithm of V well you have to know what V is what is V well to explain that I need to describe what's called phase space here we have a picture of phase space what is phase space well to describe phase space let me start by describing something a little easier namely a configuration space so you have to imagine some system consisting of lots and lots of bits and here I've got lots and lots of bits and for every location of the bits and that can mean where the bits are what where the center of mass is if you like and where how its oriented and so on so all the parameters which are needed to describe where the bits are give you lots and lots of numbers you'd need in order to specify that and what you do is you use those numbers as coordinates in some space that's called configuration space so that means each point in this space it has a huge number of dimensions each point here represents exactly one location of all these bits so as these things move around this point will move around in here now face space it's just a bit more than that face space the first place we need to know not just where the bits are but how the bits are moving so we need to know the velocities if you like of the bits strictly speaking it's the momenta that's just the velocities time the mass really don't worry too much about that distinction so I put a little arrows here to tell you where they're moving and this dimension of this space is not twice as I haven't change the picture but then if it's hardly adequate anyway but the number of dimensions has just gone up by a factor of two so if it was a zillion before it's now to Zelena so this is now face face I've crossed off the configuration and don't worry about all this this is just some nice mathematics which I'm not going to worry about the point that I do want to stress is that now if you know any one point there the dynamics is completely fixes the system so that there's a curve which goes through that line the whole thing is got curves drawn up and that tells you how the evolution progresses once you know where that is the dynamics is determined it tells you where that point moves so that's that's all I'm going to use here and that's what we've got here this is face face of this let's imagine there's a box in which all that sitting and the location of all the particles in the situation is encompassed in this phase space here and they're also the motions of all the particles now what are these bubbles here that I've drawn those are what are called coarse graining boxes coarse graining regions what does that mean that means if I take two points in the same bubble I can't tell them apart as far as macroscopic coordinates are concerned you see there are lots of air molecules and wine molecules whatever they are running around in here and I may not care exactly where all those molecules are and what might care on the other hand what the pressure is what the temperature is there is overall parameters but I don't care about the exact fine detail of where all the little particles are so I love together in one of these boxes one of these bubbles all the different configurations which look just the same so these everything in there would be pretty well indistinguishable from the point of view of macroscopic measurements it's a little bit vague but entropy is a little bit vague that'll do and what you do then is you say what if the particle was here what is the volume of that bubble well that's V and then you supposed to take the logarithm of that and then you put this number here that's called Boltzmann's constant in fact the only thing in this formula that was not due to Botsman is the K which is both it's constant but everything else was Boltzmann's so I don't think he was interested in you know how big things actually were he was interested in there in the general principles okay so this is a coarse-grained phase space now and we have now the measure of entropy because that's the size the logarithm basically of the size of this bubble now why does entropy increase with time well you see one thing I should explain is that these volumes tend to be absolutely stupendously different from each other so if you happen to be in this one here and that's the next one this one would be so much bigger than that that if you find your way into this there's no chance of you finding that one back again well when I say no chance I mean absolutely teeny-weeny chance so if you happen to be in one of these little bubbles at one time and you wander around then you find yourself in a bigger one there's no chance of finding the little one again so this tells you that wherever you're you are in this picture the entropy has some value the entropy is going to get bigger and bigger and bigger and bigger well you say that's all the rest of the second law is pretty pretty simple isn't it the only trouble is let me ask it slightly different question how is it that the glass got there on the edge of the table well you might use the same argument but this time you're using it backwards in time and you find that the most likely way that this glass to have got on the corner of the table there is that it started a great mess on the ground there the wine all sort of wetting the grass assembled itself the one jumped into it jumped on the that's the right answer if that's the right answer if all you know is the argument I just gave you before so if you use the Boltzmann argument instead of into the future which is the user where but if used in the past you get that the entropy went up in the past - of course it didn't that isn't how the glass got there it's because somebody put it there and in fact that started for something with an actual lower entropy like this so the way the actual universe behaves is indeed in accordance with the second law but you can't argue in the past direction like this to get the right answer instead there seems to have been something pulling it down in the past well let's go and work our way backwards in time and see what happens there we have that curve and you go back and there is the Big Bang you go on right back and back and back until you get to the Big Bang so to ensure that the entropy continues to go down in the past we need an enormous constraint on the space-time well I why space-time geometry you see I said there was a paradox here I said there was something strange about this incredible curve here what is strange is that this tells us that the early universe was in thermal equilibrium where where is thermal equilibrium in this picture remember this picture I didn't actually I heard the right way around too before which is that way the biggest box of all and in fact this box is likely to be even bigger than all the rest put together the biggest box of all is what's called thermal equilibrium that's the maximum entropy maximum entropy so we go back to the Big Bang we find we're at thermal equilibrium if this is maximum entropy because thoroughly libram why on earth is it the smallest value so there's a paradox how is it that the universe started off at maximum entropy and has been going up ever since that's I'm glad to hear you see that's a little strange well you see the answer to it lots of people predict presented wrong answers to this question for a long time the correct answer I won't worry over the wrong answers the correct answer is that as far as matter is concerned indeed it is true that it was in thermal equipment that tells us this wonderful curve tells us yes indeed the matter was in thermal equilibrium but the matter is not the whole story the whole story involves the space-time geometry of the universe and the space-time geometry involves gravity according to Einstein's general theory of relativity what about gravity why is that something a bit different well I also show you another picture here this is the sort of the one at the top it's the sort of thing that people often use as an example of how entropy might look increasing here we have a gas in a box and we might have a little smaller box where we have the gas to start with and then we open the door there and the gas starts spreading out through the whole region and this represents an increase in entropy so this is high entropy middle of size entropy pretty low entropy now let's suppose this is not just a gas in the box but a lot of gravitating bodies so these are feel like a stars or something like that or running around and they are attracting each other gravitationally what you find is that they start clumping together like this and eventually clump into black holes I have to say a bit more about black holes later on but well yes I said bit more about them later on but what I want to emphasize here is that in both sets of pictures entropy is increasing this way it's just they look different in the case of just the gas the thing gets more and more uniform when there's gravity involved it starts off uniform and it gets less and less uniform what we find in the actual universe is this and this we find a great uniformity in the universe as far as the matter is concerned indeed we find maximum entropy that curve tells us this as far as gravity is concerned it's low entropy now you see as I think I said before it's a pretty if you like boring law the second law of thermodynamics it tells us things are getting more and more boring well that's only true if you like if you just have this picture but in this picture it's the other way around and in fact we're the actual universe it's a mixture of these and so you but it doesn't tell you it could be interesting it could be boring it could be all sorts of things so we have progression in both directions here I mean in this direction in both cases but here it represents say things getting more uniform in here less uniform so what we find in the universe is it's this and this as far as gravity is concerned it's very low entropy in fact I can give you an illustration of how important this is to us it's the very thing we rely on lets me talk about the Sun the Sun is a hot spot in the otherwise dark sky and you see people often say well we get energy from the Sun but that's not quite right what we get from the Sun is not energy because the earth receives from the Sun just about as much as it spews out again ok at night if you like we have this radiation going back out again if the earth simply got energy from the Sun it would just get hotter and hotter and hotter but in fact we get just about the same amount of energy from the Sun as we give back again well with global warming it's actually maybe we're actually giving a bit more away but let's not talk about that here the this picture is a pretty good approximation and you see I've got somebody here having a good meal and you see what's really you see the plants here are taking advantage of a certain fact you see the Sun is hotter than the background what does that mean that means that the photons from the Sun are individually more energetic they have a higher frequency and according to Planck's famous formula e equals H nu that means the energy is proportional to proportional to the frequency here we have a higher frequency than there that means the energy per photon is higher for those which come from the Sun than from those which go away again so you get a few relatively few photons coming from the Sun and the energy mean carried away with loads and loads and loads of photons now loads and loads and loads of photons have many more degrees of freedom than these more degrees of freedom means larger phase space volume means higher entropy so the entropy is high there and low here so really what the Sun is giving us is a source of low entropy the plants the clever plants where their photosynthesis are able to convert the photons into lower frequency photons and thereby build up their substance animals eat plants and they live on on the reservoir of low entropy we eat either plants or animals and we take advantage again ultimately of the plants in their cleverness in reducing the reducing the frequency of the photons from high to low and thereby reducing the entropy okay well it's a complicated story in detail but the key point is that the Sun is a hot spot in a dark sky or what is the key point there what it why is the Sun a hot spot in that eye so why is the Sun there at all well it's there okay there all sorts of things like thermonuclear reactions and so on taking place but that's not the important thing the important thing is that the Sun is there and it's there because it's held together by gravity and the gravity is the key thing previously the Sun was just a lot of gas and this convinced by gravity and produced a hot thing and it's this hot spot in a dark sky which we take advantage of okay so that is you see it's gravity is the key thing and it's the fact that we have gravity clumping in this case just to get stars and that's what we live off well what about black holes that's the ultimate if you like in what stars do you have a nice picture of a black hole doesn't help us too much for what I want to say I just thought I'd show it to you now the key point really is that inside there you can't see it inside there is a singularity and it's a bit like the Big Bang in that respect the Big Bang was a nasty old singularity and we have the in this cause of black holes also a singularity now I've got to find the right transparency here it's one we had before what I want to do now is improve upon this picture okay I could improve the artistry but that's not what I'm trying to do I'm going to improve it because this is a uniform model where the material is completely isotropic and homogeneous there's no irregularity in the matter content of the universe that's the sort of models that you can actually solve the equations for and so that's what people did but we know that the universe isn't completely uniform otherwise there'd be nothing interesting going on in it and if we introduce your regularities the pictures have to be changed somewhat these red lines which I've now introduced are basically the black hole singularities so you don't just have the singular state at the beginning where curvatures of space-time diverge to infinity we've now got singular States at the end representing the singularities of black holes I'll draw you some other pictures of black holes which are a little bit more to the point of what I want to say but these ones have black holes it's even worse for the Big Crunch of the model here because it's a horrendous mess of all these black hole singularities coming together and that's a more accurate picture if you like then the one that we had before now we also might have the cosmological constant and put thee with the singularities on that one if I haven't gone and lost them it looks just the same as the other one except we don't have a Big Crunch where's it gone oh yeah [Applause] so I put the black hole singularities on okay oh yeah now I have to say a bit more about Einstein's general theory of relativity the basic ingredient the first ingredient of Einstein's theory is any principle of equivalence together they understand principle equivalence which roughly speaking is just telling you that well here's old Galileo whether or not he actually did this we can imagine he did dropping a big rock and a little rock from the top of the Leaning Tower and as we all now know they would fall together like this at least they would if there were no air resistance now suppose you imagine that you're an insect sitting on the big rock say having a look at the little one because they fall together it would look as though the little one hovers before the insect and there doesn't seem to be any gravity as far as the insect is concerned as the dropping takes place across something will happen at the end but astronauts know how to do it better by being in orbit but it's the same thing here is an astronaut and there is some futuristic Space Station like Stanley Kubrick's thing and the astronaut is looking at the space station and it seems to hover in front of him it's just like the rock in front of the insect so somehow despite the fact that the earth is right there and you can see it there gravity seems to have been cancelled out simply by falling freely that's the principle of equivalence well there's a bit more to it than just that because you might think if it was just that why is there any effect of gravity at all you could just get rid of it by falling freely well you can't quite do that and here I've shown why because the earth isn't really quite an infinity here we have an astronaut and let's imagine that astronaut is surrounded by a sphere of particles now the astronaut is accelerating to the Earth's center I mean could be an orbit but so the acceleration of the Earth's center at a certain rate particles a little bit closer to the Earth's center will accelerate a bit more so relative to the astronaut there will be a little bit a second away from the astronaut here the acceleration is a little less so relative to the astronaut it would be away from the astronaut where is it the sides you see the acceleration is slightly inwards because the Earth's center is not as infinity and so relative to the astronaut there will be slight inward acceleration so this ellipsoid sorry this sphere we started with starts at rest relative to the astronaut and in a moment it will be stretched into this ellipsoid now this is what in general relativity will refer to what it's the tidal effect it's called the viol part of the curvature I'll have to say a bit more about that if there was this is this occurs when there's no matter inside here and what you actually find it's an expression of the inverse square law is that the sphere and the ellipse which it gets distorted into actually have the same volume that's an expression of the inverse square law but if there's matter inside then the volume gets reduced and these are two parts of the curvature according to Einstein's theory the rock vial and the Ricci part of the curvature I've drawn this in space-time terms these represent the world lines of these particles so the distortion of the sphere into an ellipsoid is represented here we have a sphere as time progresses becomes more stretched out this case where it's accelerating into the earth that the volume gets reduced okay this is a picture take a little while to get used to those things but really what I wanted to show you is that it's called space-time curvature why is it called space-time curvature well you see it's very like this here we have surfaces this one is a positively curved surface this is a negatively curved surface look like a saddle you see the positively curved surface if you start as straight lines as you can draw they're called geodesics they even if they're parallel to begin where that corresponds you see two these lines here being parallel to begin where that is at rest to begin with here they start to come together that's just what's happening here whereas in the negative curve of this view apart and that's what's happening to these other ones here okay it's complicated in in all the dimension in infor space-time dimensions which is what you've got in general theory of relativity these curvature things have got lots and lots of components I'm not going to worry about all that I just got to giving you the general idea here but what you find is that the whole curvature which is measured in this kind of way is splits into these two parts this is the empty space part and that's the part where there's matter around I'm sorry this is a little bit it's a little bit of getting used to but it just illustrates how the curvature splits into these two pieces in fact if you want to be a little bit more accurate you can do it with light rays and in fact it's quite nice you can here I've just drawn the analog of the pictures at the bottom over there with light rays and this is the bending of light and this is what's called the lensing effect here we imagine the Sun it seemed as you could see through it and the star field gets distorted circular patterns gets stretched into ellipses outside here and that's the vile part in the middle you've got the Ricci part and Einstein's theory tells you it's the Ricci part which you equate to the density of matter the viol part measures gravity that measures free gravity these things you can actually see it's very remarkable there are many many observations now where you can see effects like the ones in this picture here just by looking at distant galaxies and you see they get stretched out this is because in the middle there's there's some lensing object like the Sun in this picture here which is stretched out the images around and if you look at this sort of squint a bit perhaps you can see it's as though there's some lens in the middle there having this effect and this is now a very often use aspect of of observational cosmology you can sort of tell how much mass there is in the middle by looking at the distortion outside very striking now okay I just telling you all that really because I wanted to give some idea of these two parts of curvature the Ricci part which is what Einstein says that is is due to directly due to matter and the viol part which is free gravity now I have to tell you that because otherwise I can't explain the idea I'm trying to give you here but okay let's stock our cosmological models now I should have had my black holes on them I suppose so let's bring the black holes back yeah now you see in this picture you've got singularity singularities at the beginning and singularities in the black holes which is sort of the ends as far as anybody who falls into one is concerned no what's special about the Big Bang one is I said that what is special about the Big Bang which is explaining why the entropy can be low despite the fact that it seems to be thermal equilibrium as far as matter is concerned what is special is that the viol curvature seems to be zero or very very small and that's very special so let me draw that here the Big Bang singularity was enormous Li constrained and you can even give a measure of this to one part in much greater than something like 10 to the power 10 to the power 123 let me give you some feeling for how precise that is how big is that number well you see suppose I wanted to write it down 1 0 0 0 0 with 10 to 123 zeroes well I wouldn't be able to write that down even if I put 1 0 and every proton in the observable universe it's not nearly enough room to write it down of course I've written it down here but then and then I cheated by using double exponents but of course that's mathematics that's not cheating you have to you never know X isn't cheating okay what is I'm gonna call the vial curvature hypothesis this is just a hypothesis I'm saying this seems to be true of the universe as we know it that there are these singularities in the universe as I've indicated here some of them in the future the black hole ones some of them in the past were the Big Bang but the Big Bang seems to have been enormous ly constrained in this sort of way that the VAR curvature was pretty well zero now I'm not saying why that was true well I'm going to try and say why that might have been true that's the crazy idea I want to give you I have to get there first let me first just I'll just flash this one up you see people tend to think well the theory we need to explain singularity structure is quantum gravity and troubles we don't have a quantum gravity theory trouble with quantum gravity is that the all the quantum gravity theories we know at the moment are time symmetrical and that doesn't explain the difference between the singularities at the past in the future why is the past one the past one so it's special to be constrained in this a normal way now who lost my universes I've just got the singularities well that's good and that's really what we're talking about isn't it why is it that the initial ones are so constrained and the final ones don't seem to be it tells us that whatever theory we should have is asymmetrical in time but we don't have the theory well I've got to say even a little bit more about general relativity I'm sorry about that but I really should which is the Lycans light cones are an important part of relativity theory this is time going up the picture here and this describes a theoretical flash of light you imagine in the center here there's a flash of light and I've written a space picture here there it is and then it starts spreading out like this concentric spheres around this point we have the past comb which is concentric spheres converging on that point so that's the light cone and it's the most important we don't leave the bottom thing here it's the most important aspect of relativity really because it tells you our causal effects can propagate light signals go like this particles with mass go within the cone they're restricted by the speed of light special relativity that's minkovski spaces it's called looks like this that is to say the light cones are all arranged nicely uniformly Einstein's general relativity they're all all over the place well they could be that's the difference now you see Young's general relativity allows us to do all sorts of things like draw pictures of black holes and here we do have the collapse to a black hole with the light cones behaving in this rather odd way which is what prevents signals from escaping outside this is the horizon here is time going up the picture collapsing material here there's the singularity in the middle and if you're unfortunate enough to fall in there's no way you can get back out again because the light codes are tipping over like this and they're forcing you into this terrible place in the middle we're curvatures go to infinity and so on okay that's what the light cones are good for I want to tell you something else about the light cones I think I'll tell you on this one here remember the picture I showed you about the hyperbolic geometry which was a conformal picture and that conformal picture there was a scale involved which could be greater or smaller but I didn't want to change the angles small shapes were accurately represented in the in the pictures which you had before just trying to find that one again it doesn't matter now in the kind of geometry that you have in relativity you have the light cones those are the crucial things yes I should put a light cone back for you light cones are the crucial things but the light cones are most of the geometry in a certain sense they're nine-tenths of the geometry you see the metric according to relativity has ten components but nine of them tell you where the light cone is the other one tells you this Gaelle so here I have a light cone drawn and I have certain surfaces here which represent the ticking of a clock if you like suppose we have a clock at worldline as a clock and these represent successive ticks that that clock makes and you see that these surfaces here they're actually defined by the light cone the only thing that's not defined is the scale so the metric is ten components and it measures time I don't worry too much about these pictures you could if you have a clock going along you see it's the metric the clock has a world line that's this curve and the time that this clock measures is the interval according to its this formula here don't worry too much about the formula but it's the metric of space-time which determines the clock rates and the light cone is most of that information but not quite all of it the scaling is the remainder of that information now I want to describe to you two mathematical tricks which we've been using in the subject of relativity for a long time these mathematical tricks whether it's one of them is sort of the opposite of the other one and the first one in a finite place this trick even reused in relativity theory it's been used for a long time to describe infinity for gravitational radiation you see what's this picture mean here I have two bodies going around each other and as they go run each other they spew out these gravitational waves those as ripples and space-time which go out and you want to know how what happens to the Mazda infinity and there's a trick here where you make infinity you squash it down until it looks like a finite region so there's the trick you shrink infinity down to a finite place by taking this Omega well it's only good thing is a scale factor so you let it go to zero that's the idea now the opposite trick is you can take a cosmological singularity like the ones I've just been talking about and you stretch it out so here I squash down to make infinity finite here I stretch out to make a singularity into a nice smooth place it's the same more almost the same trick but it's just the other way around you see it's a it's it's the inverse of the trick my colleague Paul Todd has used this as a formulation of the vial curvature hypothesis it's a very nice way of doing it what does he mean you see instead of saying the vial curvature goes to zero okay you can say that but what he says is another way of saying it which is much nicer you say that the Big Bang is such that as far as it's conformal geometry is concerned infinity is just a nice smooth place okay to get the singularity just squash it down as I said most of the information is in the light cones the light cones are all nice and regular here that you squash them down and you'll get the singularity of the Big Bang so Todd's form of the viol curvature hypothesis is that this trick works the trick works in the past that's to say you can find a nice smooth surface to represent the Big Bang the future trick well when there is a cosmological constant you see I told you that lots of people didn't like it or didn't expect it I didn't like it for a while but I've come to love it now you see this is the thing you have to change your attitude in and find out what's true and then you learn to like it so I found that actually the cosmological constant is a good thing and it makes this trick work in some respects much better than if it wasn't there in fact at one crucial respect it makes something work which would never work otherwise I think I'm going to do quit I probably shouldn't waste time doing all these things but let me show you something which is helps me describe the things I want to describe a little more precisely than otherwise this is just what's called a strict conformal diagram conformal diagram is a nice way of representing a whole universe in it on the back of an envelope so you have certain conventions this brown dotted line means a symmetry axis a purple straight line represents infinity the squiggly line represents singularity the point represents a point a little circle represents a fear is that's the key what you got to do is you draw some diagram like this picture here okay there's infinity there's infinity there's an axis each point in the diagram you've got imagine rotating around the axis so it rotates around the only strike catches that here your your imagination will probably take this round in a circle yeah but you've got to take it round in the whole two-dimensional sphere okay that's just a piece of mathematics but if you can do that you can represent all these cosmologies which i've been flashing up at you in these nice little pictures here you can represent the black hole which is this picture here there's the black hole you can even represent what Stephen Hawking tells us to expect of a black hole if you wait an awful long time here is a collapse to a black hole there's its horizon you wait and you wait and you wait and you wait and you wait and you wait and you wait until we see Hawking tells us that the black hole has a temperature it's not completely black it's not completely cold it has a very very tiny temperature the tiny temperature is so tiny that for the hottest black holes we have any reason to believe in in the universe that temperature is sort of comparable with the coldest temperatures that's ever made being made on the earth so pretty cold but the universe as it keeps on expanding is going to get colder and colder and colder and colder and ultimately particularly because of this accelerated expansion ultimately it will get colder than the black hole when it's colder than the black hole the black hole will start to radiate away will lose some of its heat and as it radiates away it loses energy and therefore it loses mass by a equals MC squared ian's energy and mass equivalent and therefore it gets smaller and smaller and smaller and smaller and smaller and finally disappears with a pop now why do I say pop or not bang well because it's not very big by cosmological standards it'd be a bit nasty I mean very nasty I should say if if it went off in this Hall here but that's pretty small beer when you consider cosmology and so on so that's why it's pop and here is a picture of the thing doing it well don't worry too much about that except you can draw pictures of it that's nice but what we do want to what I would do want to emphasize is that it seems to be what's going to happen the universe you see this is the thing that worried me about all the universe that we seem to have to get used to is it's a dreadfully boring place it seems you see it just goes out okay you get these black holes and they sit around and they sit around sit around there wait for the universe to cool down and then finally well they start to shrink takes an age even longer and longer and longer before they evaporate away finally disappear pop okay that's the end of the black holes you've got bigger ones they take longer but they disappear eventually pop they go off at the end like that okay that's what's happening nothing left but this radiation running around seems dreadfully boring that's for eternity but then you have to think what's going to be around in the universe at that time not you or me the only thing left in the universe according to this picture will be radiation rate massless radiation now what about what's so funny about massless radiation well photons you like a photon has the curious property that the moment from it's created to when it's absorbed it doesn't experience any time at all it's that's the way relativity works is no time between creation and destruction so it just well it's even more than that if that photon is going sailing off into the universe eternity to that photon it was no time at all it's no big deal for a photon in fact if there's nothing left in the universe but massless entities there is no way of keeping time that's the point I want to make you can't build a clock and the reason you can't build a clock is that the equations that govern massless entities photons or other things which might be around now here's where the idea that I'm trying to describe needs certain things to be true that we don't know are true what I want to claim is that ultimately everything that's around we'll decay away into massless particles and this requires certain things that we don't know a true that there should be what's called a massless fermions that there's a massless charged particle and so on but if nothing is left but things which have no mass then you find that the geometry they respect is the conformal geometry that I've been talking about the scale is forgotten somehow the universe forgets how to keep time you can't build a clock there's no way it can keep time and so the proposal that I'm making is that it's a bit like this here now the pictures which I showed you for a moment of the various cosmological models there's a point I want to make and that is that when there's a cosmological constant which is zero they look different in the future from the past well this one does because they don't feel worried about that one but these ones you have infinity which is actually what's called null its life it's it's tangent to the light cone whereas if there's a positive cosmological constant these things are called space-like so the light cones poked through them in fright and they look just like the Big Bang but the other way around so I'm making the wild suggestion that in the remote future the universe loses track of time and it's only interested in conformal geometry likewise in the remote past if you go right down to the Big Bang what do you find when you find energies get hotter and hotter and hotter and more and more and more you get very energetic particles and at that point the mass of these particles becomes irrelevant because the energy is so much greater than the mass of the particle that they're more or less massless they're two so I'm saying in the future there's nothing left but massless things in the past there's nothing left but massless things and they don't know anything about the metric all they know is conformal geometry so the proposal is that you match them together and here I've matched it with the conformal diagrams here I've just matched it well it's a sort of conformal diagram I require you can either call these requirements that's a sort of negative thing we can say predictions that's pose to say our theory predicts own sir let's do it that way around then it predicts the existence of a masters Fermi on that means of massless particle like an electron we don't know that there is there could be neutrinos which are masses we don't know if that's the case all we know is that there are massive ones and there could be at most one massless one but there might be a mass this one what's more little alarming is we nearly massless charged particle like an electron but with no mass and the idea is that well this is a thing about quantum mechanics which has to do with well let me show you a very rough sketch of how what I perceive this is meant to be the phase space now you see remember the except just I should get this the rest wake up which is that way up remember that the universe seems to start it out with this tiny region of face space that's because we have a vowel curvature hypothesis according to Todd it's because you can extend through the Big Bang in a conformal way and according to me now I'm saying that glues onto a previous phase of the universe in which you had its maximum expansion expansion and that really means that the whole phase space of the previous universe has to go into the little tiny region representing the Big Bang of the next one so this is a pretty sketchy picture but that's what I'm proposing here that does need some rescaling not only of a metric but also of some of the rules of quantum mechanics and that needs to be looked into quite seriously but nevertheless that's the picture that I'm proposing finally finally finally finally is this something we could make observational tests off well I believe we could and I just want to indicate the observational implications of this idea I think I put this one here there are observational implications and I want to indicate two of them let's suppose that the previous phase of the universe the physics which is just the same as the one we have here there is the possibility that somehow the constants of nature get recouped each time it goes through here that's just not going to be bad news for me because it's hard to make any predictions at all in that case but let's say that the constants of nature don't get changed and here we have in the previous phase of the universe there is black holes there could be great big holes and middles of galaxies which start to spiral into each other they'd be round and as they do this they produce ripples in space-time gravitational radiation now what one finds in this scheme is that on order this matching to work for the conformal geometry to match from one side to the other these gravitational waves actually get through so they get through to the next phase that's one of the striking features about the scheme they actually get through and as they get through they cause certain fluctuations in the density on the other side so there will be density fluctuations and these density fluctuations are the sorts of things that caused the slight variations in the temperature as you look round in the microwave background at different directions okay it's the thermal radiation but the temperature is not exactly the same in all different directions and this is these satellites called W map all sorts of other satellites and earth-based observations and so on have been very interested in measuring these density fluctuations and this model would produce some definite scheme as to what these density fluctuations should be like so we have two forms of observation things like the W map and so on and here I've put down Lisa this is a gravitational wave detection scheme which would consist of some satellites little trailing the earth in its orbit forming this equilateral triangle and you have to try and measure slight changes in the lengths of these paths which would indicate the presence of gravitational radiation and the idea is that Lisa might be able to measure these primordial gravitational waves the thing is that this scheme seems to make pretty clear predictions I haven't gone into it thoroughly yet I have a student looking at it so I don't know fully what the conclusions are but it seems that there should be some quite definite predictions from this model and one would have to see where these predictions are an agreement or not with observations Lisa's not there yet but when it's working it should be able to maybe give us some clues as to what's going on with regard to primordial gravitational radiation okay I think I'd better stop at that point thank you very much what do you think of the big crunch I mean do you think it would exist or would it actually happen after a long time every stable caesarian stable system has to come to a constant stable state right so I expect a brick ranch to happen probably at some point in time well that's not the scheme I have and there's one more question yes if I could complete that okay yeah you said the Big Bang is kind of the start of time so what what happened before start of time is there anything called before sign of time in the first place there has to be something so something exists after that right you see in that sense it keeps on going that's all you see it's it's endless I'm you can map all this into a some other picture to which I could have done for you but the it just keeps on going so there's no initial state it's a bit like steady state model in that sense yes there is no beginning there is no crunch either but but what you have are infinitely dispersed expansion and that then becomes the next new Big Bang and it just keeps on going like that if you have an infinitely expanding system it has to be it has to come to a constant point so you have the next infinite thing coming up right we're not in the scheme you have to have a rescaling all the time you see the the metric gets rescaled and and in a certain sense Planck's constant it gets rescale to each time but but if you need that but it's not at and one point at n equal to infinity probably it will have the rescaling constant being infinity again so don't match up you could talk about where the whole thing came from if you like yeah yes all right sure in fact there are pictures which I don't know whether I brought or not which maybe show you the sort of thing you're asking about oh great yeah okay I asked this question that was concerned me for a while that is it the and you touched on it a little bit when you said that the photon doesn't experience any time for yes okay if that's so does the photon know anything about space or what space also not be existent but it doesn't measure space you see because this space and time are related to each other via the light come but it does know the light comes you see what I was trying to say is that nine out of the ten components of the metric is actually where the light cones are so the photons don't actually measure the scale they know where the light cones are because they're mean they're going along it so the the light cones which is nine tenths of a metric is determined by the photons but not actually space or time because the space and time if you like another way of putting it is that if you know the speed of light and you know a second then you know a light second and vice versa so that so that space measurements and time measurements are coupled once you've got the light cones yeah they're coupled to each other so not knowing time implies not knowing space to if you like yes that's thank you okay over here yeah in your in your picture you've described these arising of gravity all singular T's yes but I have a problem with that when you have the fact you have a gravitational time dilation from the standpoint of external observable observer a black hole will never actually form in the space-time picture it does so so there are ways of looking at it where you think it doesn't happen but if you're thinking of the whole space-time then certainly the it's there so I don't think that gets you out of it if you like but I have to get rid of the black holes by hawking of aberration if the black holes were still there at the end they would have a measure of time as well I mean they they have mass and so my proposal wouldn't work if they were still around it's necessary to get rid of them and this which which fortunately the Hawking of aberration does Stephen Hawking saves hey go ahead hi I just want to thank you for coming first and I really enjoyed the presentation you said that as the universe cools a black hole will lose its mass because it's losing its yes and eventually will pop when that happens all that we left are protons and therefore time will stop I understand it I said photons yeah I understand time will stop but how does the matter actually get destroyed I thought matter couldn't be created that's right I should say that there is actually a huge question mark related to what happens when the black hole disappears and nobody knows and there are various proposals so I'm just taking the simplest one here I'm taking the one that suits me if you like which is which is you know it's also the one that's most favored I think by people which is that the black hole does disappear and it disappears in an explosion where that explosion that takes the form of radiation so that you have basically photons coming out now there could be other particles as well there could be massive particles like electrons and so on and then those have to decay on my scheme and we don't know that electrons do decay we we don't know that protons decay but all that would be required by my model so this is if you like either a requirement or a prediction depending on which way you want to read it all right well thank you very much ok ok over here good well microscopic black holes at Planck length that are predicted to exist does your theory have an explanation for those you're talking about what a cause of virtual you see the an actual you have to be a little careful cuz in quantum mechanics one has these things called virtual processes and I think you're referring to things that might be there and this is what's called the phone in the in the at the Planck scale that really also depends on on theory one doesn't know whether they're there or not but it's certainly a quite respected view that there could be black holes but they just sort of come and go all the time then they they're evaporating as soon as they appear so according to the Hawking of apparation scale if you had a black hole of a mass plank mass it would disappear at a Planck time which is 10 to the minus 43 seconds which isn't very long I mean that's that's a tiny time so yeah they would appear and disappear in this game but but they would only be there kind of potentially all the time they wouldn't make any difference to the to the scheme that I'm proposing and what about Planck scale universes well again that they would disappear ourselves the same time but one doesn't know you see these things are I'm not really saying much about quantum gravity these these ideas are things which people bring up when they talk about quantum gravity and they're among the ideas which certainly you probably read about and we don't know whether they're true or not because we don't have a consistent theory of quantum gravity it's certainly a possibility but on the scheme that I'm presenting are they're not really playing a role I mean ok they could be there they could if you look it's a small enough scale they could be there but then there's something has to happen when you go from one side to the other because the scales roughly speaking change and so Planck scale in a certain sense gets renormalized when you go across see the plant costs Planck's constant gets renormalized and the metric gets renormalized so I don't know the answer to your question something something funny may happen there yeah thank you when it does thank you for coming to talk to us was a fascinating lecture could you I'm interested in your massless charged part yes I interesting yes yes could you talk a little bit about its nature where we might look for it and why we haven't seen it yet well they would have to be very hard to make they're not part of present-day physical theory certainly not part of the standard model and sometimes people object and they say well if you have a massless particle which is charged then it will produce a sheet of radiation and so on these pictures seem to apply very much when you have a sort of particle picture with regard to the field picture they make perfect good sense now they haven't been seen absolutely and I don't think there's any suggestion that dark matter is anything that but I I would just have to postulate that they're there on this scheme otherwise back to the other ways of getting rid of charge which I haven't gone into which might not require the existence of a massless charged particle and they might be more comfortable I don't think particle physicists are very keen on the idea massless charged particles it just seems to me the most plausible way around the problem I otherwise have you see if you have positive and negative charges in there Niall 8 then you've just got radiation and that's fine but if you get sort of trapped in an event horizon a single charged particle and there's no charged particle of the opposite charge to come around and and neutralize it it's just you're just left with it which is a nuisance now it may be that there are non-local quantum of EPR effects or something which will do the trick for you it needs thinking about seriously but I have no answer to this question and my only the simplest thing to say at this stage is that there will be massless charged particles it might not be the only answer and it might be there are other ways of doing it which you're not so unpleasant for particle physicists thank you no seriously I just want to be sure I understand your new idea yeah correctly starting from where we are in the universe right now yeah if you were to let time run out everything eventually will become just light and it'll be evenly distributed and light itself has no sense of time and no sense of itself so you've got what we would see is a very cool universe what the universe at that point would see as something that's neither hot or cold it's just all the same stuff so is there really a difference between what's really really hot and what's really cold well in this game there has to be no difference in the sense that I that's right because basically the this matter that's that you end up with has no metric doesn't it has no way of measuring the metric and it has I think the idea of temperature I thought all these things through but I think clearly if you're going to be able to match the Big Bang with the remote expanded universe you've got a very low temperature on one side and a very high temperature on the other side and so if they're to be matched yes you have to lose track of temperature as well so that would indeed be part of this proposal yes that's right well for this to be true yeah then also have a universe of no size with no size yes well there's no metric you see so there's no scale yeah so infinity and a singularity become the very same thing that's right yep yep that's that's what this proposal is see when I've drawn these pictures here you may not see the distinction but the purple line here represents in turn is an eternity that's infinity and then that smoothly goes over to the Big Bang so what I'm saying is that the conformal geometry actually is perfectly makes sense here it's just that in normal physics you demand too much you say we need to know certain things you need to know the scale you need to know how to measure time you need to know how to measure space and if you forget that but you keep the light cones you keep those things which are conformally invariant such as electromagnetic fields and other massless entities and if you keep that then you can match this perfectly well provided the viol curvature hypothesis in Todd's form is true because gravity has a particular way of scaling which makes it only work when that is true so it's the only proposal I know of which actually requires the valve curvature hypothesis I think that does very well to bring the reality of imperfection back into the universe you know there's some kind of some kind of evolution well it's it starts all over again in this picture I mean you certainly have imperfections in the sense that you have these little ripples which get through here so it's not exactly a uniform universe at any stage but it enables you to compute what scale these ripples are going to be from the behavior of the universe in the previous size so trying to get my head around the idea that there's no s-- that every place is the center and there's no edge but that's pretty easy I guess not go ahead yes this is a native question you said it a black hole as a singularity at the beginning in a light cannot escape and the universe also has a singularity at the beginning and light cannot escape either saw the question my question is simple is our universe a black hole and if not why not and if yes in what no actually some of the things are not quite what I was saying the singularity in a black hole is in the future you see if you fall into a black hole then you run into that singularity so as far as local observers are concerned the black hole singularities our future singularities the big bang singer there is a past singular you can see that in these conformal diagrams but probably define one's going to be a challenge for me I know here we are you see the black hole singularity is at the top here which means it's a future singularity whereas the Big Bang singularity zap a singularity and the Grau curvature policy is saying that these things actually behave very differently and a black hole has a right horizon you cannot escape from but the the the Big Bang has well the Big Bang has what's called a particle horizon what the black hole has is what called event horizon and these are the opposite way around in time particle horizon is if you like the past version of an event horizon so what you're saying is is appropriate but we have to you know get the terms right that the black hole things are the other way around in time and in fact for a long time people emphasize the similarity between black hole singularities and the Big Bang they said well they're very basically the same thing it's just ones that in the future the others in the past but now what I'm pointing out or stressing here I've pointed out before but I'm stressing again here is that this structure of geometrical is very different it's not just the time reverse and this has to do with the second law it's in fact crucial it's the whole basis of the second law of thermodynamics that what starts is very very constrained and the singularities in the future are quite general completely general and the viol curvature is likely to diverge and oscillate and do completely wild things in the future singularities up here whereas the Big Bang apparently as we as we know from the observations of the universe the the VAR curvature seems to be very small perhaps zero and this scheme is trying to make that into a more global picture thank you okay we're gonna need to cut this off with some print but let's go go ahead I don't think this is really touched onion you're not gonna be like all these questions guys oh sorry go ahead okay um but I was wondering about your twister theory and what the significance would be of being able to map geometric objects in Minkowski space and into a four dimensional complex space and I was wondering whether this would be similar to a Hilbert space used in quantum mechanics probably I should leave I mean it is it's I mean I'd love to answer questions like that but it's about a different subject and so probably I shouldn't the other thing I would say about twister theory is that it is very weird two conformal geometry so it might well be and twister theory and in this cosmological context hasn't been much studied it may well be that it would be an appropriate vehicle for describing some of these things you need to read the book that's as far as I can go it's in road to reality to addresses I mean clearer okay thank you so go ahead one more over here and I think we're gonna this one then you gotta wrap it cuz we're late already alright thank you for your presentation professor Preta knows I was wondering kind of a trivial question could you please explain the time integral for integral from A to B of the function D s I believe yes well if you're familiar with the notion of a metric as applied in relativity theory you have this quantity D s as it was this picture I think you're referring to and if you have a curve then the integral of D s this is that you see the D s you'd have some form in a d s squared equals something some expression and if you take the square root of that in other words D s and you integrate that along the curve from A to B that tells you directly the o'clock time as measured by the clock following that worldline so if you have an ideal clock and we now have clocks which are extraordinarily precise now nuclear clocks for instance they actually do measure this metric in a very direct precise way well this is one reason I think for regarding space-time geometry is what some has got chronometry this was a point of view very much emphasized by Bondi and my sing that is best not to think of space-time metric in terms of little rulers you see this is where people tend to think about metric as you think laying a lot of rulers around your space but what's much more direct and physical is to think of timelike curves in other words the paths of possible particles and the time is experienced by that particle between two events on that curve is given precisely by this integral so integral of D s which is the square root of that formula there from A to B and it's a very simple formula directly telling you how the metric gives you some immediate physical quantity simpler level you brought up the depicted the glass falling off the table which brought up the paradox of the direction of the arrow of time ilya prigogine has been it's working and I wondered what the the ordinary physicists nowadays is thinking about Brigid Gene's solution to that based on non equilibrium systems chaos yeah well I'm not an expert on his point of view as far as I'm aware he did take the view that in some sense physics was not actually time symmetrical on the small scale now it's not part of anything I've been saying today but in some sense I would have a view that's not dissimilar from that but it's only it's it is different in detail from what he's saying my view would be that somehow it's the measurement aspect of quantum mechanics which gives you a time which is not reversible in time the physics most of the physics we know at this micro scale is reversible in time and I would take a conventional view with regard to the arrow of time as we call it that is the entropy increase and that that is not a local phenomenon that it's it's governed by boundary conditions so I'm saying it's to do with the very there's special nature of the Big Bang and that that drives it but in addition to that I would expect to see some asymmetry in the quantum state reduction process but that hasn't come in to what I was saying here but it should it ties in with this picture I'm sure but it's it's not been something I've referred to and frayed here I suspect that they're very similar there we go anyway I thank you very much get a run cuz we're late and thank you [Applause] you [Applause] the Coupe de grace of this of this dinner is that now that we have you know poured some wine down him and you know filled him up before he very satisfied he was lean and mean it's a lecture but now we've got him you know sort of vulnerable so you can ask him they're really you know the deep questions and the deeper questions or maybe not so deep resonance so it says it's so Sir Roger if you if you're asking me what I really think I mean that's too strong it's a proposal it's a proposal which I would say has a better chance and when I say it's not it's never meant to be a metaphor or or I mean these these are meant to be theories which might apply to the world I'm not saying that it does you see because what because it could run into some fundamental roadblock which would just show it doesn't work now that's quite possible it's not something which I have as much confidence in as I have in some other ideas that I've suggested but nevertheless I think it's something worth talking about and which is as I think I said the only scheme that I know of which really requires some form of our curvature hypothesis which is in my view a real really fundamental puzzle about the universe it's it's one which hardly anybody talks about if you look at cosmologies and you look at theories of the Big Bang and this and that they hardly ever mention this issue but the very very it's a very very big puzzle how it is that this initial state had this extraordinary precision about it and so this is proposed or at least attacks that question doesn't mean that it's right it could be there are fundamental problems the fact that you require charge massless particle for instances there's a bit of a mouthful or whatever it is but so I'm not saying I believe it there are other schemes which I've been associated with which I'd be more likely to say I believe it than this one on the other hand I think it's got a chance of being okay I mean it has experimental there are things which could at least in principle be tested by experiment and so it could be clearly refuted or it could be that these experiments support the idea it does depend also on the constants of nature not changing from one cycle to the next which raises other issues which people talk about the anthropic principle and other constants of nature especially geared so that life can come about and so on so there are lots of issues it's connected with but I think it's it's something maybe you could treat it as something for discussion I think that's at least one can you do I think it has a chance of being something more serious than that but I'm not saying that it's there's the whole truth or anything like this I mean that would be certainly not what I'm claiming it's not even a theory with based with a good equator I mean like I said I'm sorry relativity has equations you see it's a new contest to see where those equations really are satisfied in the worlds that we that we know whereas this scheme of mine is severely lacking in things like that it needs a lot of work before it even has that kind of foundation so at the moment it's just an idea a purpose of working with people yeah we're on the edge trying to understand the nature of cosmology and I don't know whether I don't know whether I mean I know some cosmologists who rather disappointed me I won't mention names here but there was a cosmologists who I challenged and asked whether why this person was putting forward a certain view we've seen sorry there was no bet no there was no bet I was asking why he put forward a certain viewpoint which seemed like a rather strange one to me and the response was that a viewpoint that he'd be promoting earlier had a chance of being experimentally refuted by some observation and so he had to have something in reserve I thought this was rather shocking you see because it seemed to me when it's trying to find out how the world ticks that's that's what I was trying to do once trying to find out you know how the world is constructed what is it what's going on out there and to have a different theory in reserve in case the observations didn't go the way you hoped originally it doesn't seem to be the right point of view it seemed to me a strange attitude so I mean yeah I'm a few one what one is trying to do is to find out what the world's like what's out there why is it out there why is it doing what it's doing it's it's it's that's that's the aim certainly it's not producing models which might excite might get into the New York Times or something like that it's producing models which one things might have a serious chance of representing reality it's not supposed to be that it's not written to be easy if you like well it is to some degree because I could have written a really difficult book which no the equations are there because they're there I mean these these I'm not you know putting equations in to make the book more difficult I'm putting equations because that's the way to explain certain things and the mathematics is there in the world if one's going to understand how the world ticks one has to relate it to mathematics I mean that's seems to be no escape I mean that we don't know any other way of understanding nature at any kind of deep level so it's not that I put it there like nature did I'm trying to I'm not you know putting all the details it's it's it's supposed to give to give some idea of of how you know the kinds of mathematics that that underlie are at least what we think I understand basic the basis of nature so far so some places where I put bits of mathematics in just because I thought they were fun and not because they were really essential for the book there are a few places like that and but in a sense that's fine because you see mathematics ought to be fun there are other places where Idol skimped on the mathematics where perhaps I could have been a bit more serious about it it was just sometimes I had to make a choice as to which to do and I put in these problems because often it was well it was for two reasons one was I suppose slightly o'the but as I thought that maybe it would be used in courses and I know that people like to have examples in books that are used in courses but there's a more serious reason and that is that in explaining things I often found that okay I could explain this at this point but if I did it would simply detract from the thread of argument and so I said well maybe there's enough information here for somebody to work it out themselves so I would give it as an example and it was just a sort of device for easing the writing that those things the things that a certain problems are almost always things that would be useful to know anyway and I could have put them in the text the knowledge level was enough to explain them but it seemed to me it would be distracting for the reader and that it was better you just put them in a problem not in there you see okay the reader can either ignore them completely or else look at the problem and take it on trust or or do it so in the best possible world yes sure yeah yes yeah that's fine yeah I don't know it's certainly true that when you try to quantize say conformally invariant theory you tend to find that you can't preserve the AMEX this sort of issue of anomalies where the classical theory has certain symmetries and you may find that the quantum theory you're forced into into violating these symmetries so that can't happen but there's also something strange has to happen about quantum mechanics in this scheme I mean the view would be that in the remote future when the densities of these fields become so so feeble so weak so is it small but in fact the quantum nature of the fields becomes less and less relevant so not only does mass some somehow become unimportant but the quantum nature also becomes unimportant because somehow you have to rescale the quantum the quantum scale these rescaling as well mainly because the phase space volume has a natural measure see this is the problem that's I encountered that that the phase space of the of the entire universe if the previous phase roughly speaking has to fit in the region of the Big Bang of the next universe now on conventional physics viewpoint there is a natural measure two phase space which is given if you like my Planck's constant because you have a DP DQ the position momentum thing and there is a natural measure which in terms of h-bar something so in order to be able to put the whole or face space into this small region the universe also has to lose track of the quantum scale so it's not just the metric and this is one of the things that I found a little bit well it needs more thinking about well somehow yes that once the when the when the fields become very dispersed that in effect they become fields and the quantum nature of them is lost but then you've got to see how on the other side this somehow scales fits in with it with a different quantum scale he's thinking about seriously and I don't I wouldn't say I thought all that through but it is an important point you can ask that question and I was if I had a sort of weeding out of transparencies before I gave his talk and I think the one that was going to respond to that question i weeded out because somebody else had asked the question which was very like that one the first question I think and in fact you can it depends up to that point it doesn't make much difference in my scheme which value of the curvature is I mean you can have K positive negative or zero and the picture looks very similar but if you want to represent the entire you can represent the entire family of cycles as a part of a conformal you can represent conformally as a part of the what's called the sitter space and and you can then ask ok where does all that come from so there's a sort of second-order question you can ask the cycle goes on and on and on but in some sense you could say is there an origin to the whole thing well it is the sort of tails all the way down question yes that's right but it's but it's not unlike steady state model you see yeah but you're right I mean there is that issue and I don't deny it I mean elsewhere than in the places we know it well I hope it's present in most people here yes yes I know yeah well you could read these things in other directions but I prefer to think of it as that the physical universe is out there and the potential for consciousness is out there it doesn't mean that a rock possesses well you see it depends on you need to have a better theory maybe the conscious rock was that possesses point zero zero zero zero zero something units of consciousness does something I have no idea and that a human being possesses many more units but on the other hand maybe a rock doesn't have any you see on the other hand you could ask questions about well a cat you see well that's relevant to the Schrodinger's cat of course or a mouse or a snail or an amoeba these questions you can ask at all sorts of levels and who knows the answer at the moment well I wouldn't take that view it seems to me that that's somewhat unhelpful view I mean you would say it's floating around in the room somewhere and there's as much of it over there as there is over here or over there or something I find that not very helpful in the sense that the only thing we have the only way we have to relate to consciousness is through we communicating with other people and seeing how they correspond to our own feelings of awareness and so on and we do our best but I would say that there's not much evidence that a rock as much of this quality if any yes but you have to use our present level of understanding you have to use a good measure of common sense I would say so you might be right I mean maybe a rock has no has has just as much consciousness as a as a human being of the same size I'm sorry yeah I think at our present stage of understanding we need to make guesses about this and that's the way it works I mean in in you know there's what philosophers call the problem of other minds I mean how do we know that anybody else has awareness and so on okay you can say that but it's not knowing is too strong you say you guess and the guess is is based it's not a it's not a completely guess plucked out of the skies you know if people react in certain ways which seem to be consistent with the way one acts oneself under certain circumstances when one seems to feel conscious one behaves in certain ways and other people behave in that way sometimes and you think they're probably conscious at that time it seems to be a reasonable it's not a proof of anything I'm not saying this is a demonstration of anything but it's a pretty good guess I would say not yet I would say this is a potential issue that I have a student working on this and I wish it he'd hurry up say I don't know the answer at the moment but my guess is that there are there may be some parameters which have to be sorted out but my guess is that there is a fairly clear prediction that this theory would give one can certainly estimate how many black holes there are hanging around out there and make some crude estimate as to how much radiation would be produced over the whole of history of the universe as we know it and maybe one could relate that to some primordial gravitational radiation and in the next phase and we have to assume that the previous phase was like hours and that the constants of nature haven't radically changed since then so I'm not enthusiastic about these theories in which the constants of nature change because if they do basically all bets are off in the scheme but I think the first thing to try at least is to assume they don't change and to try and make some good estimate on the basis of what we think the rote future would be like but these calculations have not yet been done so I don't know the answer detail and whether they would be anything within the range that Lisa could could find I just don't know I was interested in how information how much cost is from module X yes well that's yes remarkably that's fairly well defined and the reason has to do with what's the sort of curious feature of the transformations which which knows this a long time ago but couldn't quite see what the role was which has to do with how how the VAR curvature scales and how the gravitational radiation scales and what you see is that in the remote future the gravitational radiation the equations that are satisfied by my gravitational radiation if you like are basically conformally invariant but they're conformally invariant with a different scale factor from liz's sense in which the viol curvature is conformally invariant which means that the radiation as it goes out and sort of hits infinity if you like it has a finite value which which is perfectly fine I mean the equations just carry it out and hit it hits it with this finite value but the Warka which are scales to zero at that point and that zero scale has to go over to the other side which gives you the vial coverage hypothesis but the violently gravitation radiation goes right through and and it's it's the mathematics seems to me at least fairly clear and it should all one needs to do is make the right estimates as to how much radiation should be around and the conclusion as to how much radiation should come out the other side is pretty unambiguous also the amount of density fluctuations on the other side it seemed to me to be pretty unambiguous but I'm speaking a little bit I'll just out of turn here because the detail calculations have not yet been done and it remains to be seen questions dude that's it that's it come root even to the next phase after this yeah yes yes it's funny because one of the papers which it's very relevant to this whole subject was written in the 1990s by Freeman Dyson when he was interested in the future of future of intelligence I can't remember what the title was but he was at that time looking at the remote future according to what seemed at that time to be the most promising model for the universe that had a zero cosmological constant but had negative curvature and that was a feature of the low density of matter I think dark matter was known but certainly not what is now called dark energy in other words the cosmological constant that was not known and I did email him at one time and ask him what the president view was and he emailed me back and said well all the conclusions in that paper are wrong look because of the cosmological constant and he said he referred me some other people who had actually done these calculations later on but he was interested in how somehow intelligent life might be able to persist and know what you know even though the density would go right and write down that somehow they could keep themselves going in the remote future a very interesting idea but there may be an extension of this side it was very much like what you're saying you could imagine somehow some remote in future intelligence where they would control the emotions of black black holes and so on and make them spout in ways which encode you know some great piece of music or whatever it is and that's somehow this is out there in the next phase of the universe one could write a science fiction story about that I should imagine but it seems a bit remote possibility but maybe maybe the information will get through to the phase beyond the one that we it's something which I hadn't really thought through that I suppose I had sort of thought that it would get lost somehow in the web but maybe that's not right I don't know yes well yes what do you see there's an interesting question which is where these fluctuations come from and the sort of view that people express they talk about quantum fluctuations and in the inflationary models that's the type of language that's used I have a lot of trouble with this because quantum fluctuations don't actually come about unless you have state reduction see they should all be in superposition all these things and somehow they've got to resolve excuse me you have to resolve one reality out of the potential and and some of these issues aren't addressed properly in any of these models as far as I can see so you need some scheme which actually solves the quantum measurement problem before you can even really talk about that well you can call it that I'm keeping and keeping clear that's a point of view yes well that again actually there's different kinds of versions of multi universes the one which maybe you're referring to is what people sometimes refer to as the many-worlds interpretation of quantum mechanics where you have in that view various different alternatives coexisting the trouble is it's not really what happens in quantum mechanics the in superposition they're not alternatives and so how you I've never quite understood how that's supposed to work but okay it's it's a it's a point of view that's often expressed you also have multi universes and other points of view namely which connected with the anthropic principle you say the constant of nature might have a different value maybe there's a parallel universe out there in which the constants of nature have a different value and one of the ways of coming to terms with the fact that maybe the constants of nature are just right so that life can happen which is the thing that worries many people one solution to that would be well there are lots of different universes all also parallel to each other and we happen to find ourselves in one in which life could exist because we couldn't find ourselves than any of the others so it's a sort of tautology if you like but it does in a sense require these alternative universes somehow to exist out there ah my own view is I don't like any of these multi universes I don't like the quantum mechanical one because I don't think it solves the measurement paradox and it seems to me a very extravagant non solution to the problem because you really need a theory of why conscious being only perceived one universe and so on and that's not part of their theory is it as far as I can see so it doesn't really I solve the measurement paradox as yet maybe a different schema version of it might it doesn't I have a lot of trouble with the other version which is where you have these constants of nature having to have other values particularly it's not such good news for my scheme because it would mean maybe these get changed as each cycle in which case we have a lot of trouble making predictions in the scheme but maybe they do one needs to have a deeper understanding of nature III can't rule them out if you take the anthropic one the arguments tend to be things like if we didn't have the the neutron being slightly more massive than the proton then you might have trouble with having proper chemistry and so on there are things about water if water was simplest parameters were slightly different than ice wouldn't be lighter than water and for some reason that causes problems I'm not quite sure what but Michael tea with all these things is that we really have no idea what the preconditions for conscious beings are if they didn't come out if consciousness didn't come about in the way that we know maybe it could have come about in some completely different way which have which we have no conception whatsoever so it's very hard to argue very strongly about these things you certainly find that people take refuge in the anthropic argument very much they say you know their theories don't predict values of the constants so saying well maybe there are all these different universes and where these different values of the constants hold I'm not very happy with us theories I can't say they're wrong when I'm not happy with you

Channel: Linus Pauling Memorial Lecture Series

Views: 10,925

Keywords: Small and Large, Beauty, Mathematical physics, General Relativity, Quantum Theory

Id: MLw-VcEaEWs

Length: 116min 33sec (6993 seconds)

Published: Sun Sep 30 2018