Dr. Neil Turok - "From zero to infinity, and beyond!"

good evening everyone welcome here to our origins Institute public lecture series and my name is Ralph PUD it's the director of the Institute and it's great to see you all here on this pleasant spring evening so welcome it's a real treat for me to introduce this evening speaker professor Neil Turok who's the director of the perimeter Institute of which I'm sure most of you have heard a lot of what real great success story in Canadian physics and if not international physics as well just a few words other about Neil's background in addition to your program notes Neil received his PhD in 1983 from Imperial College in London but he migrated there Neil is originally from South Africa an important point that dictates how he's developing science in that continent actually after his PhD and at the time in Fermilab he moved to Princeton if I became a professor of physics at that department and in 1997 moved to take the chair of mathematical physics at Cambridge University you know the one over there on the other side of the Atlantic he became very fortunate for Canada this region Canada and an international scene he accepted being the Perimeter Institute director in 2008 and has done great work there in developing into the premier Institute into a really awesome force in theoretical physics in Canada and beyond the national scene neil also has a deep interest excuse me and commitment to public outreach he as an example initiated and the very important new system of education for African students the so-called African Institute for mathematical sciences which is based in Cape Town that has now several offshoots around the African continent and which is very successful training a new generation and perhaps the first generation of African physicists and will Canada has helped through the Perimeter Institute invested this and this is a really important effort that the really strongly applauded the scientifically Neil as developed some of the very interesting and important ideas about the early state of our universe as you hear about tonight he is the architect of ideas along with Paul Steinhardt on the multiverse and as one of the world's leaders in thinking about the Big Bang as an example as again you'll hear about later in this evening's lecture so Neil and the Perimeter Institute we are also deeply connected with McMaster McMaster in my own department physics and astronomy we have three professors who are associate of the perimeter Institute program so they have an overlap point between perimeter and us and this has allowed us to build up here particle physics and our own Studies on the universe and with with these appointees I've done excellent work in our department and in the origins Institute so we have many deep links that we like to celebrate in this lecture tonight and without further ado I'd like to introduce Neil Turok thank you very much Ralph it's a huge pleasure to be here I've only been in Canada for just over three years but I've never regretted moving here it's amazingly friendly country for people from all around the world and I've been made to feel incredibly welcome as well as incredibly lucky I honestly believe Canada can become intellectual hub for the world use that one I I've got two on I guess neither of them working okay I'm happy to use this one can it can you hear me okay so very happy to be here in Canada I I believe this country has incredible potential as a as a place that attracts people from all over the world and Perimeter Institute is just an amazing place it may be unprecedented in history that level of investment in very basic theoretical physics and I encourage any of you here to come and visit us and see what we do so the topic of my lecture is kind of crazily ambitious I have been for the last decade studying theories of the Big Bang singularity what happened at the very beginning of the universe these are very ambitious theories but what I hope to give you today is in some kind of insight as to why we think we may be able to say something about that very mysterious event 13.7 billion years ago which gave rise to everything we see now but I'm not going to stop there our past is very mysterious but our future is equally mysterious just about just over 10 years ago it was discovered that empty space has and this was a big surprise to physicist that empty space isn't really empty it has some energy it has the effect of causing the universe to expand even faster and ultimately this stuff we call dark energy will or vacuum energy will dominate over everything else will matter like the matter we are made of is really just the froth on the surface of the universe there's much more important stuff beneath it and that will dominate the future and so at the very end of my talk I'm going to talk about some speculations about what happens after that let me begin with this this is the origin of mathematical science and physics in ancient Greece and essentially this is a picture of what we're trying to do at Perimeter Institute you'll find the place not not too different than this there are a few more women that's one of the things the Greeks didn't do very well but over here I want to draw your attention to a couple of interesting people there's Plato and Socrates in the middle Plato in the figure of Leonardo da Vinci this is Raphael School of Athens one of the most famous paintings of the Italian Renaissance but over here on the left you can see the person writing in the big book that's Pythagoras and so he's proving some mathematical theorems he invented the word mathematics and the notion of proving things mathematically over on the right you'll see Euclid doing a demonstration with compasses of mathematics and so mathematics was sort of really part of the whole firmament of ancient Greek life which extended to philosophy and ethics and politics and literature and art and so on but right from the beginning mathematics was sort of a magical piece of this picture and in fact we we still don't understand why it is that the world is described by mathematics mathematics is the most effective piece of knowledge we have and that's still a very deep mystery but everything I'll tell you will be based on mathematics and unfortunately I have left in a few equations in the talk so please forgive me for that and those of you who are not interested in those equations just ignore them you should be able to understand everything without them but but I'm sorry I have left some equations in the talk if you look at the person just behind Pythagoras there's a odd individual who's kind of peering over Pythagoras's shoulder I'm not pointing my hands are here I'm not pointing so if you he's looking over Pythagoras's shoulder he's in the orange robe and it looks like he's cheating ah that is an axe Amanda is the world's first scientist and he is in a sense cheating what he's doing is looking at Pythagoras's mathematical formulae which are the most you know reliable form of knowledge we have I mean two plus two is four and there's no debate about that but he's also got one eye on the real world and so he's trying to look at the world look at mathematics and try to reconcile the two because he knows if you succeed in doing that you have a real powerful science so Anaximander was the first scientist that we know of he did many things he invented the concept of infinity he thought the universe was Infinite he thought that living creatures like us arose from fish in the sea so he seems to have some I had some ideas about evolution he and then for this talk what's import is that he invented the map concept of a map so whenever use a map that's due to MX Amanda and here's the first map the map of the world in the you know in his time and that's what they knew of the world so this was a very very important concept that you could represent space and the universe on a piece of paper and and that was the beginning of the idea that we should map the universe and we should visualize the universe in this way Anaximander also introduced an instrument called the genome on which was which basically a stick in the sand and you use it as a sundial and so he accurately measured the time introduced the notion that time is something we should measure and record various events using this primitive clock so Anaximander was really the person who introduced the notion of measuring space and time and that in in due course gave rise to all of our theories of of the universe so these were you know very important discoveries and was the beginning of of everything that we do now fast forward to the 19th and early 20th centuries and at that point newton's laws were in place but the person on the right is James Clerk Maxwell who discovered the theory of electromagnetism and the equations behind electromagnetism and in fact Maxwell himself was the product of an era rather similar to that in ancient Greece called the Scottish enlightenment and the Scottish enlightenment was a consequence of investments by the Scottish government in public education and universities and a creation of a whole climate which encouraged intellectual thought and philosophy and economics and literature as well as physics so Maxwell came from that background and he was the person who mathematize electricity and magnetism and in so doing made I think the greatest discovery ever in science which is he understood what light is light is a wave consisting of electrical and magnetic fields traveling through space and so Maxwell's discovery really set the scene for 20th century physics because it took a while for people to realize that Maxwell's theory of electricity and magnetism was actually inconsistent at a deep level with Newton's theory of mechanics and so one or the other had to give and in the end it was Newton Newton lost out and Einstein came along and transformed Newton's theory into a mathematical form which would be consistent with method with Maxwell's theory of light and that was the beginning of relativity and and that's the basis for our description of the universe Maxwell's theory also was in conflict with another great theory in physics theory of heat the theory which people use to describe steam engines and you know the motors of the time and in that case Maxwell lost Maxwell's theory of electromagnetic waves turned out to be inconsistent with the theory of heat the reason being is that Maxwell's theory is spectacularly powerful it describes waves of any wavelength so light has wavelengths of a micron a fraction of a micron radio waves you know have have have much longer wavelengths going up to many kilometers but all of these are described by exactly the same theory the problem with that is that these electromagnetic waves have in capacity in that in the way max will describe them have an infinite capacity to take up eat that if you have a hot body it can give off its energy into electromagnetic waves of all wavelengths an analogy I like to draw is imagine you imagine we had some money in this room and we wanted to throw it around okay so I'm going to throw coins at you and you'll throw coins at your neighbor and we'll all share the money okay so we all understand we're going to catch some money and throw it this bill be some rules and at certain point this will all be you know we'll all be just exchanging money all the time so everybody will have some money now let's introduce some smaller people okay and there'll be more of them okay and there will be people of all sizes and they will go down to zero size so the room will contain an infinite number of these little people now if we allow them to share the money money is energy by the way I like radio waves and light waves take energy from something and transmit it somewhere else so the money is the electromagnetic waves we have all these small people around the problem is that they will soak up all the money because there's just so many of them and there will it will not be possible to have a world where larger people exist and have any money because the little people will just take all of it and that catastrophe in Maxwell's theory is called the ultraviolet catastrophe because ultraviolet waves are very short wavelength waves and the problem was there's just too many of them and they would take all the energy and the world could not exist if Maxwell's theory was right and we'll come back to this at the end but the resolution of that was something called quantum theory that the that basically you had to rig the market okay you couldn't let these little people take money because they take all of it so the rule is you tell the little people okay depending on your size you can only take money in very large amounts okay so somebody half as small as you can only take energy in amount that is double the amount so they can only take two if you can take $1 they can only take two somebody a million times your science can only take a million dollars somebody a billion can only take a billion dollars so these little people are everywhere which is not allowed to take money unless it arrives all together in a sum of a billion dollars and and that's the way quantum theory works short wavelength waves can only carry energy in very large amounts and so by kind of rigging the rules of the market Planck who invented the idea of quantization enabled the world to exist in a sensible way where the little guys don't get all the money or the energy and so that was the beginnings of quantum theory and and as you may know quantum theory is the basis of all of 20th century physics and here here is all of physics that's it there is nothing else so if you want to study physics the your task is to understand what the hell this formula means okay and this summarizes everything we know about physics it's written in the language of mathematics it's a lot of the symbols are Greek in homage to the ancient Greeks sai is the wavefunction it tells you how probable different things are I won't talk you through all of it but want to point out a few sort of interesting things e is a number you may have heard of when people talk about exponential growth like inflation will lead to exponential you know growth in the cost of anything well e the number E is named after Euler mathematician who discovered it in the 18th century and this this this formula for all the laws of physics involves this number e at a very fundamental level and even more peculiar number in this formulas I you'll see that e to the power I over H what is that I well the I is the square root of -1 I times I is minus 1 that's a very very counterintuitive fact that you can take a number and square it and you get minus 1 but as I'll explain again towards the end of this talk that I is the basis of quantum mechanics and it does describe the world you may think the world you may think you can picture the world in your mind you may think the world is a place with objects in it and maybe waves traveling through it well that that's a wrong picture that's a picture of a classical world that's the picture the Greeks developed it involves geometry and oceans of space and objects existing in space and time and it's it's max will have the same picture an Einstein had the same picture but that pictures just wrong the world is not a definite thing the world is described by this formula which includes a square root of minus 1 which certainly doesn't have any place in any definite world we can picture but we know the world works this way and there are experiments you can do that show that there just isn't a classical world the world is quantum and by the way the future is quantum we have quantum computers around the corner I mean in 10 or 20 years we may have quantum computers and they'll be a lot more fun than your laptop's ok because quantum theory is very exploratory and creative and it's totally different than classical it's trying out everything at once all the time so much more interesting you'll see under the eye is H which is Planck's constant and that was the number Planck introduced to kind of rig this economy of energy and to make sure that the little the little the short wavelength waves didn't steal all the energy and it's still there in 20th century physics as as a a number and then we have Einstein's theory of gravity Newton only survives in the formula as a constant okay G Newton's constant so that's the end of all the rest of Newton's laws are irrelevant we don't use them anymore at in fundamental physics use them in engineering a very good approximation but they're not they're only an approximation on the left of the formula you see Einstein are Einstein's theory of gravity so that's a theory describing space and time and how space can expand how the universe can expand how black holes form how planets attracted to two stars and so on and then we have Maxwell's theory theory the strong and the weak interactions as well as the same form and this is rather compact notation but it's basically everything is there we have Dirac's theory which describes electrons and all the other particles that were made of all the matter particles and then the Japanese have a kind of stranglehold on the next term which is the term explaining how particles get their mass and it involves Phi Phi is the Higgs field and you've probably heard of the Large Hadron Collider the greatest experiment of all time currently underway and one of its main goals is to find this Higgs field in fact to find the particle associated with things field and so that's the last term in this equation which is still not verified but it is possible that this year later this year the Large Hadron Collider will announce the discovery of the Higgs and that will be the final piece in the puzzle there a few few little loose ends apart from this but it'll essentially be the final piece in the the great puzzle of 20th century physics and how that what's called the standard model works now I'll talk about the little pieces that are missing later but even within this formula as beautiful as it is incredibly powerful this formula it has a number of free parameters is 18 numbers buried in this formula but it explains a countless number of observations it explains every single experiment as and some some quantities that can be calculated one partner trillion using this formula and the answer is right like the magnetic moment of the electron is computed at one partner trillion from this formula formula and the answer agrees so this is a really well tested formula but it has problems one of the problems is on the left with gravity that when we take this formula seriously and calculate processes involving gravity we find infinities one example is the Big Bang singularity that the singularity in the Big Bang is the place where the description of space and time fails and so the density of the universe is infinity the curvature of space and time become infinite and the theory just fails and and this is seen in in many calculations involving Einstein's theory you get infinities and you can't make a sensible prediction at the other end of the formula is something denoted V okay the very last term over there is a V and V means a potential energy but it's also V for vacuum energy and so that that term in this equation describes the energy in empty space and again that's one of the great mysteries and that will dominate that's beginning to do it has already dominated in the universe and will totally control our future and we don't know what it is we we see its effect and we really don't understand what is going on in the vacuum and so you have these two the two ends of the formula formula represent a problem at very tiny length scales with singularities and a problem at very large length scales with the whole universe and its future and both of them are very mysterious and that's exactly where we focus because as as versus we want to we want to fix these problems and because they will they will lead us to new discoveries so here's the Large Hadron Collider in CERN the most powerful microscope ever built which is looking for the Higgs particle and all of this relates to the history of the universe because as far as we know the universe started in a hot Big Bang 13.7 billion years ago and so the Large Hadron colliders recreating those conditions in the very early universe about a 110 billion of a second after the Bang itself that's the time being probed that's a conditions being probed by the Large Hadron Collider so this picture of the universe has been remarkably successful we understand how energy came out of the Big Bang how particles condensed into atomic nuclei we can compute the abundances of the different elements like hydrogen helium lithium the light elements we can follow the way in which matter clumped to form galaxies and stars and then the heavier elements were produced in the stars and objects like black holes and and the universe around us so we have a remarkably consistent and complete history of the universe but it traces back to this crazy moment called the Big Bang singularity and that's what I'm going to talk about the equation which describes the universe is Einsteins equation and it connects the curvature of space-time - the energy contained in the space-time here's one of these equations which I'm just going to skip over unless anybody asks and and this is all I want to say about it is that there's the universe has a size we call it the scale factor it's as if you take the universe at one moment with all the galaxies distributed and then just stretch it okay and we call the stretch factor the scale factor the universe is just scaling up objects like planets and stars and galaxies are not scaling up they have a fixed size but the distance between them is scaling up and some galaxies are actually orbit around each other so they are not scaling up but the distance between that pair of galaxies orbiting and another pair will be scaling up so the overall scale of the universe is this quantity called a and if you want to understand how a changes in time then this is basically the picture so you can imagine it that a is really the position of a ball you see I know that if I take a ball here in this room and I throw it vertically if I throw it up it's going to come down well that's only true if I do if I throw it below a certain speed if I'm able to throw it at enough speed bigger than the escape velocity from the earth then the ball will make it out of the Earth's gravitational field just like when we launch a rocket and the ball will sail off to infinity so it's as if you were throwing a ball in a hill or rolling a ball up a hill of the shape of that yellow curve okay so I start off at small scale factor and I've got to throw that ball the little red ball over the hill the first part of the hill is a steep part pushing you back to a equals zero that is the matter and radiation density that's the the stuff in the universe which self gravitates so you throw the universe out and the gravity of this stuff pulls it back okay so if you roll that ball up the hill it's going to come back to zero if you do make it too large enough scale factor there's another term it dominates called lambda that's the vacuum energy it's another name for it's like the V but upside down but we we use the names interchangeably lambda is that vacuum energy and so if you made it over that hill if you threw the ball hard enough that you roll the ball fast enough that it went over the hill it would go down the other side and once it's going down the other side a just gets bigger and bigger and that's the effect of the dark energy or vacuum energy driving an exponential expansion of the universe and that's where we are now we've made it over the hill the matter and radiation have failed to recal apps' the universe and now the vacuum energy is taking over and it's just going to drive us to infinity so here's a picture of dark energy made it great expense so this is a Hubble telescope image cost billions and the strange thing about dark I just want to emphasize how odd dark energy is this is the energy of empty space it's unlike any other form of energy you ever thought of okay most other forms of energy are gravitationally attractive you have so we I think we intuitively know the earth is a huge lump of matter and it's pulling us down and that's the gravity that it's exerting dark energy the opposite it's repulsive it repels itself and this follows from Einstein's equations and this dark energy has also has other mysterious properties one of which is that you know with ordinary matter if it's traveling that gives it more energy we call that kinetic energy you know the truck is coming at you faster that's worse because it's going to hit you with even more energy but vacuum energy doesn't matter how fast you travel it's always the same I can travel however fast you like the vacuum is the vacuum it doesn't change at all this is its fundamental feature and and and and this is the reason mathematically why it is gravitationally repulsive whereas ordinary matter is not so this stuff is taking over but as I emphasized we really don't know what it is we have theories we have ideas and models none of them are really very good so this is the composition of the universe as it is today if you look at all the energy in the universe it's a fraction of a percent in radiation light radio waves microwave radiation left over from the Big Bang so microwaves just like in your microwave oven are actually the most important form of radiation in the universe most of the energy in the radiation is in microwaves just like in your oven and they that was discovered in the 60s then you have ordinary matter like the stuff we're made of nuclei electrons atoms molecules that is all together only 5% of the energy in the universe and then you have dark matter which is something not described by that formula I wrote down but which we can see is there by its gravitational effect and it's still a huge mystery and one of the hopes is that the Large Hadron Collider if we're very fortunate may actually be able to make the stuff in some theories that would be true so dark matter is five times more important than ordinary matter in the energy budget of the universe and then this dark energy is the most important thing of all as well as this the universe is not completely uniform as you may have noticed in this room we the density varies its higher in me than it is in in the air okay and the origin of the density variations in the universe go back to the beginning when the universe came out of the Big Bang it wasn't perfectly smooth it was almost perfectly smooth but the density varied very slightly from place to place by about one part in a hundred thousand so these very tiny variations in the density of the universe are what gave rise to galaxies and stars and planets and people and all the interesting stuff we see now so these variations are very important that they're there but they were at a tiny level and what one of the goals of theory is to explain why did the universe come out of the Big Bang with these variations it's a very strange and puzzling mix I mean the the universe that came out these numbers we don't have any good explanation for why these numbers are the values they are in 2001 the satellite was launched to map the whole universe called Wilkinson map Wilkinson was a famous cosmologists who who was one of the pioneers of measuring the radiation from the Big Bang and so here's the satellite it mapped the sky there was actually an earlier satellite called Kobe in 1992 which made the first map so you can see the Kobe map is fairly blurry not not a lot of detail the W map picture was much finer and those little variations so this is the whole sky just projected onto an ellipse on an oval and the reddish areas are slightly denser the bluer areas of slightly less dense and the variations are just a part in a hundred thousand so those are our those density variations are our ancestors those variations then seeded the formation of galaxies and stars so places which are slightly more dense would clump under gravity places which are slightly less dense would expand without clumping and and that was the beginning of structure in the universe so now I'll show you a graph and the this is the kind of thing which theory is able to predict the red curve is the theoretical prediction and what the shows is the fluctuation level in the temperature of the sky from place to place versus the angular scale on the sky so in the left of the horizontal axis our big big angular scales the whole sky and on the right very small angular scales and you'll see that red curve is has bumps a whole series of bumps all of the theory of this was essentially worked out in the early 1970s this just involves plasma physics Einstein's equations it's classical well-known physics which was worked out in the 70s long before the measurements were made and the measurements came in and they just lined up absolutely beautifully with theory it's quite shocking that you know theoretical physics all of the basic ingredients needed to make this computation were there in the 1920s in in theoretical physics nobody even at that time thought it might apply to the whole universe but it absolutely does and the whole universe a Bayes these laws of physics these laws are unbelievably powerful much more than we appreciate so the the the second graph is of the polarization and here I played a small role we did the first calculations of polarization of the sky and how it would correlate with the temperature and in that calculation they actually no free parameters at all I mean you just take the measurements of the temperature from the sky you use standard Theory you you turn the handle and you predict exactly what the polarization should be of the light coming from the Big Bang and it fits perfectly so it's quite a weird feeling very disappointing actually because because you know we were just the mice in the machine working out the consequences of some equations there was no creativity creativity involved at all but I'll make up for that now so here's the picture that is emerged it's called a concordance inflationary model it's the most popular picture of the big bang left to right is time you see the W map satellite on the right of the picture looking out at the sky seeing galaxies and looking back to the Big Bang I mean as we measure distances further and further out in space we're seeing the universe as it was at earlier in earlier times because light takes a take some time to reach us and so W map is looking out seeing the sky that blue pale blue oval on the left of the picture we're seeing the hot plasma of the early universe as it emerged from the Big Bang but we can't see the Big Bang itself we can't see the most interesting event the singularity just because the early universe is opaque you see currently in the universe space is transparent we can look out and see galaxies and stars and stuff but in the early universe the plasma was so dense that light can't get through it and so when we look back we can look all the way back to about 400,000 years after the bang and we can't see any further with light but we can see further with other with other means and I'll describe them at the end of the talk so this is the part of the universe we can see the history we can see it fits extremely well with a fairly simple description and this is really this concordance has developed in the last less than 15 years so if you asked 15 years ago what was the history of the universe cosmologists were in huge disagreement there were many different models nobody could you know people had many different points if you all that went away the data came in almost all the models were ruled out and one survived and and this is it it's still a puzzling model but there's incredible consensus that this Theory's got to explain this because it works really well now this period of inflation is a bit mysterious it's a hypothesized period in the very early universe so the idea is that there was this bang which which has infinite density of matter and that somehow the universe blew itself up to the huge thing we see now and this blowing up is is is called inflation and I'm going to talk a little bit about it because it is the most popular paradigm what came before the inflation is most people don't dare to go there I will but what came before it is in my view is the most interesting thing of all I mean what happened at the singularity where did all this stuff come from so let's talk a little bit about inflation so inflation is driven by this V that I talked about v is the vacuum energy and it's weird stuff that is gravitationally repulsive so it causes the universe to blow up so we see currently it is there and it's blowing up the universe but currently the vacuum energy is very tiny the idea of inflation is that to assume that in the very early universe the vacuum energy was much bigger okay and then it would be much more repulsive and it would blow the universe up into this great big thing so that's it that's the idea of inflation in a nutshell and so I've graphed V against Phi and you start the universe off that's the red ball with a very high V and as the red ball rolls down the hill the V will decrease the vacuum energy will decrease this repulsive gravity will switch off and ultimately the red ball will SAP settle at the bottom of the valley where there's a tiny little vacuum energy and and that will be the universe we live in so that's the theory of inflation now the trouble is for me from my point of view I've always been critical of it that it it assumes the answer in many ways so it assumes that somebody started the universe or something started the universe with this enormous vacuum energy there was no need for that that is just an assumption it Tunes this V of fire turns out you have to dial it very carefully to agree with to get the one part in 100,000 number I mentioned and and finally you have to make sure that the vacuum energy today is really really small so there's lots of sort of by hand fitting of numbers in the formula and these are very serious fitting of numbers so for example you have to adjust the lambda lower vacuum energy we see today two point zero zero zero zero with a hundred and twenty zeros one accuracy okay otherwise you won't get a universe looking like ours so that we call fine-tuning it's a it's on the scale of theories it's incredibly ugly okay what you look for in a theory is something where for a small number of input parameters you get lots of predictions out but this theory there are lots of tunable parameters and essentially every time you make an observation you have to tune the theory to agree with the observation many puzzling features of inflation one is the beginning leave no idea what is this beginning what is the inflation it's it's ad hoc you introduce things to make it happen in an ad hoc way the Dark Matter we don't we still don't understand the dark energy or vacuum energy we we don't understand and the end it's pretty peculiar or we go really going into this phase of vacuum domination which will take everything over and last an eternity is that the way the universe is going to end that's that's very strange and finally this fine-tuning problem that we find ourselves dialing the parameters in the theory - kind of ridiculous accuracy and many scientists have many good scientists even having my view taken a huge step backwards by saying that by adopting anthropocentric reasoning which is to say the universe is the way it is because because of us to say there's some things about the universe we will never explain it's just that if they were very different than this they would kill us then nature would kill us that's the eye it's called the anthropic principle and I won't talk much about it but it's it's not really a very predictive principle it's more of a rationalization of just saying they're these really difficult things to understand and maybe they just have to be that way and in my point of view at least that's more or less giving up on scientific explanation so theorists are really pulling the hair out over this model ok I want to give you this impression we have a great model it fits the data but we look at it we think there's no rhyme or reason behind it I mean it's it's really just it's it's incredibly contrived it's a we'd say Heath Robinson I don't have use Heath Robinson in Canada there's another one in the u.s. I know honey you know you know Heath Robinson gadget is lots of strings and pulleys and I know there's there's an American but I don't know what can eat Canadian safer Heath Robinson Rube Goldberg thank you it's a Rube Goldberg model now the best theory we have which attempts to unify all of physics is called m-theory and it's the most complicated theory anybody ever dreamt of it's a very mathematical and very abstract so I'm going to just give you a cartoon picture of it but I'll describe why it too has run into problems in facing up to the unit the idea REM theory is that particles in the universe are really strings and they vibrate so I've pictured a photon a photon is a particle of light and in string theory that's just a little straight piece of string which is spinning end over end with its ends moving spinning around at the speed of light and the two polarizations of the photon are that particle spinning to the right or spinning to the left it always has to be aligned perpendicular to its direction of motion a graviton is just two photons stuck together okay graviton is a spin-2 particle it's the particle of the gravitational field and just two of those photons stuck together so at least even in that picture you see that string theory has the capacity to unify electromagnetism and light with gravity that's really how it works then you have membranes and then we think about three-dimensional space that we live in as another kind of membrane it's an extended object that we happen to be embedded in and on top of this you have seven extra dimensions of space so here here is a sort of picture the seventh one is a little bit more peculiar describe it in a moment but the six extra dimension looks like a little ball so you should think that every point in this room they're not if you sat at any of you if you're at any particular point you can travel in three different directions north south east west up down okay but there are actually six more directions you could travel in which are not obvious but if you if you were able to point yourself in the direction of the extra dimension you could zoom off into the extra dimension at any point in in this room so it's a bit like a pile carpet I mean you should think of space is not really being simple but it looks like every point has this little pile that you can run run along and string theory is sort of very beautiful size and shape of these extra mentions fix the pattern of elementary particles and the forces that we see in our three-dimensional world the big problem is that there are at least 10 to the power one thousand different possibilities for the way in the sexes in which these extra dimensions are curled up and those ways determine what we would see around us which laws we would see so this is called the multiverse string theory turned out not to be a theory of everything turned out to be a theory of anything okay and it predicts universes with you know 10 to the 1,000 different possible universes with different physical laws and so on so this is actually a disaster and I in my view this is the modern version of Planck's ultraviolet catastrophe it's just this theory just isn't right there's too much stuff going on and it makes predictions impossible so some people are trying to resolve this problem with the anthropic principle but to my mind that's not going to get anywhere well what so the key is you see you have to figure out why did the universe come out in the form it did why did it come out with these laws every universe that we know of comes out of a singularity and so for me it's evident that we're not going to solve this problem until we understand the singularity so let's now assume that the bigger the sinc the singularity at the beginning of the universe was not arbitrary so all all of the theories I've talked about just assume the universe came into existence just after the singularity we can't deal with singularity so we'll just make some assumption about what how it emerged just after the singularity but what if the singularity really was was a bounce it was a gateway to universe before and so that's something I've been studying and it turns out if it was a gateway to a previous universe then this whole theory of inflation isn't needed you can you can create a big smooth universe much more easily if you have time before the singularity to do it and so here's a little movie which which shows how this works and I hope it will show how it works sorry the movie is a bit temperamental here we go so these are two three-dimensional universes actually moving in this seventh dimension I mentioned which is most mysterious dimension the the gap between them is actually very very tiny so it's just been exaggerated so you can see it but it's much smaller than the size of a atomic nucleus you have these through two three-dimensional worlds and they contain one of them contains our universe but what happens is that from time to time the other one comes along and collides with our world releases a whole lot of energy that's the Big Bang that energy then forms itself into galaxies and stars then we have dark energy coming along and expanding everything away making it flat and smooth again and the universe goes into another cycle so there's a mathematician just a movie there's a mathematical description underlying this is a model underlying it and that is a possible cyclic universe that there's Big Bang after Big Bang after Big Bang now so now I'm going to get a little bit too mathematical so I apologize but this is our recent work which shows that so we're able to study the equations for the singularity and what they show I won't attempt to describe what these quantities me but what they show is that when these objects collide at a big crunch there's a big crunch and then a big bang what we've discovered is that in between the big crunch in the big bang is actually a phase called an anti-gravity phase it's a phase where Newton's constant flip sign so gravity goes from being attractive to repulsive briefly and the trajectory of the universe is shown in that curve that with the arrow it heads into the crunch goes into a very short anti-gravity phase and it comes out in the bang now so I want to end by talking about I ok the square root of minus 1 because that's my my most recent work is to is to describe unambiguously exactly how you go through the singularity using quantum effects quantum theory of gravity and that comes down to this I then that in that formula I so let me just tell you the story of I I can't explain these equations to you but at least I can hopefully tell you how I was discovered it's not the iPhone it's a different I ok this is the real I okay except it's called imaginary very very bad name for it we call I an imaginary number and don't think of it as imaginary it's very definite it's more definite than anything else you can think of okay but but we call it I engineers use it all the time in signal processing and so on for the same reason it's used in quantum theory let's begin with equation so imagine you're in the 15th century okay they were playing with equations in the 15th century and they believed in numbers numbers themselves are pretty weird I mean nobody I've never seen the number I've never seen the number 3 ok where is the number 3 where is the number 5 doesn't really exist but there are objects in the universe that look like they're three of them alright all look like they're five them it's an abstraction mathematics is an abstraction from the real world but it's an extremely powerful one as I said nobody doubts that 2+2 is is 4 so in the 15th century they're worrying about these equations and they're trying to find solutions for the equation so let's start with equation 1 in the 15th century they put everything on the left-hand side of the equations that was just the fourth way they wrote equation so you start with X minus 3 equals 0 what's the solution well that one has a solution x equals 3 that's everybody but would agree with that everyone's happy with 3 it's a positive number there can be 3 things ok it seems to make sense but in the 15th century they had a huge debate what if I had an equation X plus 3 is 0 well is minus 3 a number I've never seen anything in minus 3 amount I may have seen 3 objects I've never seen minus 3 objects so this was the department the debate raged and raged and finally they said oh it seems to make sense so we'll we'll stick with negative numbers well it will go with negative numbers so that equation had a solution that X is minus 3 now then they thought over the next equation x squared minus 9 equals 0 well that seemed pretty good because X could be plus or minus 3 that had two solutions and both of them are ok and once you're happy with negative numbers these seem ok but then naturally you write down x squared plus 9 equals 0 what about that one well naively you'd say there has no solutions because x squared is positive and 9 is positive how can the sum be 0 but mathematician is a wonderful story that they used to have math contests in the 1500s and there were big prizes cash prizes and so a mathematician invented claim up with a trick for solving these equations but he kept it a secret and he kept it until he died and then he told his student and then the student had a duel with another mathematician there's a very involved story about the discovery of AI but essentially the notion that there is a number Square is -1 turned out to be really useful when you wrote down equations typically you could write a formula that involves the square root of -1 several times and if you allow that quantity to exist the formula made sense and it gave you a good answer but if you just ruled out the formula because it has square root of -1 in it you wouldn't you would have been stuck so this was discovered and they said ok well let's go along with I I times I is minus 1 and then happen then what happened was something miraculous as soon as you allowed I into the world of numbers that was it you didn't need anything else every single equation you could write down X to the power 15 plus 3 X to the 14th plus 17 X to the 13 and so on all the way down to a constant you write down that equation you can prove it always has a solution that's it that's the end of algebra it's called the fundamental theorem of algebra that the introduction of I into numbers allows you to solve any conceivable equation so this this took a hundred years for people to prove rigorously one of the people who did it was Euler that person I mentioned but he his proof wasn't wasn't correct ultimately and this is an example of jump to universality which is that sometimes when you invent a process then this process goes to infinity an example is the way we write numbers say 1 2 3 up to 10 and then we have decimal points well that's enough to write all the numbers in the Roman numerals they couldn't write all numbers because you know is it just too clumsy machinery but when you invent the right machinery then everything works another example is the genetic code which which we're made of it seems to have this capacity even though it evolved only to develop bacteria microorganisms it somehow had the capability of describing conscious beings like us why did that happen it was an example of a jump to universality once you've got that far the rest is downhill and so it there are these phenomena in the universe and I is one of them this I and and here again ignore the math but I just want to tell you the story of AI this AI allows you to get relativity from Pythagoras's rule pythagoras rule for a triangle says that sum of the squares of two sides the shorter sides is equal to the square of the hypotenuse now if you go to three dimensions take a box it says that the sum of the length width and height each squared is equal to the diagonal squared it's just Pythagoras in 3d if you go to 40 you have four different directions sum of the squares is the length squared still works and so that's the left side of the equation the sum of four quantity squared and now I make what now I say W is I T so W squared is minus or W squared is minus T Square bingo you get the right hand side and and if you've read any popular book on relativity you'll know the right hand side is the foundation of relativity so this introduction of I takes you from space into space-time it's probably this is one way of describing it at the same time it takes you to quantum mechanics that that formula e to the I that I had that this is the last formula on the slide that e to the I something over Planck's constant is actually just the equation from heat where the temperature is Planck's constant that's why things are jittering in the vacuum that's why the quantum vacuum sort of jitters around it's it's because there is a temperature in this fourth dimension and the time to see this analogy you make time imaginary so this is a very powerful trick for making forgetting relativity and quantum mechanics out of classical physics we have this idea of a complex number which is a real part so use of T is complex it's a sum of real part an ordinary number times I plus I times another number and an idea of a complex plane I'm not going to describe this don't worry about it but I just want to tell you the the idea of all my recent work which is that we have this Big Bang singularity which we can call T equals zero when time is zero that's at the center of the diagram and then the idea is to say well we can't go through it if time is real it's singular all the equations don't make any sense but it turns out you can go round it in the complex time plane you just avoid it just sidestep the singularity and it turns out that whether you go below it or above it you get exactly the same answer so if there is a unique way to go through Big Bang singularity z-- by using this complex time method and so finally I wanted to tell you a little bit about a rival hypothesis that obviously there are only two choices either universe had a beginning or it didn't okay so what I described is the idea that it did not but what if it did how are you going to describe the beginning so Stephen Hawking and Jim Hartle have the I think only plausible description of the beginning that we know of currently in physics and the way it works is is again using this I it's exactly the same trick so according to Hartwell and Hawking you see if we trace the universe back to very small size essentially what they do is they trace it back to very small size and then they make time go imaginary meaning it's proportional to I and square root of minus 1 and then they close off the universe to stop there being any earlier time so if I took a piece of space-time like the one I've drawn time is vertical and space goes around the diagram then Harville and Hawking would tell you to stop time on the equator of that space and just continue it onto a round surface where time is imaginary in the complex time plane this means you go back towards T equals zero but it whoops sorry it hasn't come out that slide should show that you go back towards T equals zero which is the center of the diagram and then you go up the imaginary axis so time is proportional to I and then you close off the universe so that's the proposal unfortunate doesn't work but in terms of explaining what we see it produces an empty universe but I'll give you I hope this gives you some impression at least of the things we're playing with what motivates me is is this belief that the universe is is incredibly beautiful and seem certainly seems to be following some very rational principles and John Wheeler who I knew when I was at Princeton he was a colleague of mine there said it very well he said behind it all surely an idea so simple so beautiful that when we grasp it in a decade a century or millennium we'll all say to each other how could it have been otherwise and and I I firmly believe this is true you might say we're just talking about angels on the dancing on the head of a pin is this just mathematics and philosophy absolutely not okay these ideas are observational e testable that's the wonderful thing about the time we live in and the tests of these so we have these two hypotheses one the universe began and the other one it did not the other one is that it there was a pre bang universe which created the bang and it turns out these two hypotheses are distinguishable through observation and the observational probe will be gravitational waves I already explained we can't see through the plasma of the early universe it's too dense and it's opaque but there are not only gravitation and not only electromagnetic waves light in the universe there are gravitational waves gravitational waves are ripples in space space-time in Einstein's theory and it turns out these just go straight through the plasma it's completely transparent to those so if we can measure gravitational waves we will literally be able to see the Big Bang singularity directly just see what happened and that we hope will happen in the in the next decade or two so right now this satellite is flying it's overhead I don't know if it's overhead at the moment but but it's in the sky and it's gathering data it's working beautifully and Stephen Hawking has bet me that this satellite will detect the gravitational wave signal of the inflationary universe and that's the universe which would have started according to his theory would have started at some definite time so he stuck his neck out his record with bets is not that great and so I'm I'm quite encouraged but he he has bet and actually there's another theorist another famous theorist of inflation is also bet me that that this signal will be measurable a signal of inflation of a signal of a universe with a beginning if that signal is seen it will be very strong evidence against a pre bang universe of the time I was exploring so our theory could be ruled out it could be that in a year's time I I have to give up which would be great we would we would be we'd be making progress but but I've bet that this will not detect the signal of inflation we'll see and then what's coming up next is Lisa interferometric interferometric space antenna three satellites a million miles apart in an equilateral triangle and if a gravitational wave goes by it changes the length of the arms and you can measure that by sending a laser beam back and forth across the arm so this is a proposed satellite it's been delayed due to various budget cuts and so on but its feet certainly feasible and this will be even more powerful probe of these gravitational waves so this is testable science as bizarre as it is we will I believe ultimately know what really happened at the Big Bang and then finally in the title of my talk I said and beyond what happens in the future is this vacuum energy going to take over and that's the end and it turns out so this is mathematical I won't describe it but it turns out that it's perfectly possible to go beyond the Infinity into another universe and you can have a universe so this is the size it starts at zero it blows up to infinity then it turns out there is a unique way using complex numbers using this I of coming into universe that is collapsing to another singularity and growing again and so on so this is simply mathematical model that you can play with but it indicates that there may be a future beyond beyond this vacuum energy and Roger Penrose has written in fact a popular book about this topic with a slightly different scenario he has to actually change the laws of physics at each Big Bang which I do not need to do but but his his scenarios is definitely very interesting conclusions there is a unique way to get through the Big Bang singularity surprisingly it involves a brief phase of anti-gravity where gravity is repulsive you get particle production in other words production of stuff like radiation and perhaps in the view of this Institute this is pointing us towards a new picture of our origins so thank you very much you you

Channel: McMasterUTV

Views: 102,358

Rating: 4.7821484 out of 5

Keywords: singularity, dark energy, dark matter

Id: URYOkgbr604

Length: 72min 59sec (4379 seconds)

Published: Fri Oct 19 2012