Hidden Realities: Parallel Universes and the Deep Laws of the Cosmos, Dr. Brian Greene, Columbia

thank you thank you it's always a pleasure to come to Portland and lecture here thank you shocking view up there and and thank you for that um the warm introduction indeed when I was five year old or five years old I could multiply 30 digit numbers on a calculator so what I'd like to spend some time here tonight is talking about this possibility of other universes and you know it's a it's a confusing idea at first sight because you know in the old days which means you know about two and a half years ago universe meant everything right the whole shebang the totality so the very notion of more than one universe would seem to be almost a contradiction in terms but as we will discuss tonight there has been work in the last few decades and some very active research even in the last few years which has suggested from the mathematical analysis that what we have long thought to be everything may in fact be a small part of something much much bigger and that much bigger expanse as I'll describe may include realms that should rightly be called universes of their own and thereby giving us this notion of multiple universes the multiverse now there's a way in which however strange that idea may sound it actually fits very well into the history of science right we have gone through over the last 500 years what might be called the series of cosmic demotions right we once thought that we were the center of everything the earth was the center and of course there were very brave and courageous individuals who were willing literally to risk life and limb to note that their mathematical investigations suggested that the earth is not the center that the Sun is the center and then of course even when that idea finally was accepted we learned that the Sun is really not that special there are many other stars there are at least a hundred billion stars in our galaxy and then we learned that our galaxy is not that special there are hundreds of billions of other galaxies out there each with hundreds of billions of stars so if you follow that progression the notion that our universe may not be special that there may be other universes out there perhaps is not all that surprising and as we'll see tonight we'll see very concrete ways in which our mathematical investigations and I really emphasize this none of what I'll be talking about here tonight involves data or observational proof of these ideas but I hope to convince you that the mathematical investigations under the assumptions that I'll lay out are compelling enough that these ideas need to be taken seriously and investigated to their fullest the possibility that our universe is one of many universities you know universes yes now before we get in to the heart of the matter perhaps it's worth noting because I suspect that there are many other authors in the audience and you know when you spend a long time on a project like this writing a book one of the things that many authors put as a primary concern is is their family to protect the family from all of the time and effort and all of the difficulties that it takes to complete a significant project of this sort and I thought I had done a pretty good job of that until about three weeks ago when I was holding my little three daughter and you know I was hoping I said you know Sofia I love you more than anything in the universe and she turned to me and said universe or multiverse yep there there she is right there take no prisoners Sofia yeah okay so into into the subject so what I'm going to do is describe to you a number of multiverse proposals in fact by the end of the evening we'll have covered three different but related multiverse proposals the book actually covers nine variations on the theme but I'm gonna do a little sub tour through these possibilities and what we'll see underlying all of them will be the belief that mathematics can provide insight it can provide a window onto realms that observation and experiment have not yet been able to penetrate and perhaps may never so that will be in some sense the central thread that runs through everything that we discuss and the ones that will focus on all come out of thinking about the universe in a cosmological context thinking about the origin of the universe thinking about the nature of the universe on its grandest of scales so to launch into the first one requires thinking about the following question if you were to get into a spaceship and say travel out into space and just kept on going never turn the steering wheel what would happen would you at some point you know hit a brick wall that would be the end of the universe possible many of us don't think that's the case would you keep going for a while and then notice that you return to your starting point much as would happen if you took a journey of a similar sort on the surface of the earth that's or would you simply keep on going and space would extend infinitely far and you would just carry on never returning to your starting point just getting ever further away from your point of origin that possibility is certainly the one that has received the most attention in the scientific community and we're here to take a poll of most physicists and cosmologists pretty much that would be the model that they would lean toward in describing the overall shape of the universe just goes on forever and if that's the case there is a pretty startling conclusion that you can draw with very simple analysis and the conclusion relies upon recognizing the following fact if the universe goes on infinitely far we don't have access to most of space because if you think about it we can only see things that are close enough to us so that the light they've emitted has enough time to have reached us since the beginning since the Big Bang Big Bang roughly 14 billion years ago so roughly speaking objects that are any further than 14 billion light years away the light they emit will not have had time to reach us so we won't see them so just to sort of give a little picture if you can go back to the screen thank you so just to give a picture imagine that we on earth are that little dot in the center the circle that surrounds us is delineating all those points in space where we can see and any point beyond that are points in space that are simply too far away for us to have seen and it's not just a matter of seeing right because Einstein taught us that nothing can go through space faster than the speed of light so if regions outside that circle are so far away that light they emitted could not have yet reached us then no influence at all that they may be able to exert would have reached us either so we are completely in some sense isolated any region outside of that circle so if space goes on infinitely far you can imagine dividing up space into this kind of pattern each of those circles represents those points in space that can communicate with the center of each circle and those circles themselves are so far apart that they can't see each other they can't communicate they are completely isolated now here is the pretty startling fact in any given finite region of space such as within any one of these circles matter can only arrange itself in finitely many distinct configurations now what does that mean well I like to use an analogy with a deck of cards if you have a deck of cards you begin to shuffle the deck the cards will come out different orders you shuffle again the cards come out a different order still but you know that there are only finitely many different possible orders of the cards in a deck which means if you shuffle that deck of cards enough times infinitely many times you know that the order of the cards sooner or later has to repeat no way around it similarly if space goes on infinitely far the configuration of particles region by region by region must repeat too there simply aren't enough distinct possible configurations to go around now what does that mean well I am just a configuration of particles as are all of you as is the earth as is the Sun if the configuration of particles that we show in evidence here repeat somewhere else in the cosmos as it must by that little argument that I just gave you then that means that out there in the cosmos there are copies of you and the earth the Sun and everything else reality as we know it has parallel versions parallel realities parallel universes out there in an infinite cosmos and in fact if you think about it it's even easier for the particles in some region to almost replicate the configuration that we see here so in some of those other universes some decision that you may have made which amounts to particles in your brain and vocal cords having move one way or another they would have moved in a different configuration you would have made a different decision all possible realities would be out there as long as they are compatible with the laws of physics a startling conclusion now I was asked recently does that mean that there's a universe out there where Sarah Palin is president and to answer that question I just had to re-emphasize that realities have to be compatible with the laws of physics so this this is the simplest example of how there could be universes out there whose realities are really running in a very definite way parallel to ours but now let me turn to a second example the second way in which there could be other universes out there which will have a somewhat different flavor from the one that I just described and this one relies upon thinking a little bit more closely about the big bang theory now the big bang theory I think we're all are roughly familiar with it but let me just give you a little bit of history because it's quite interesting these are the individuals that are really responsible for the Big Bang Theory no doubt that fella on the right and the second photograph everybody recognizes him up on the left hand side anybody know who that is George we met I think I did hear somebody say that up on the right who's that I hear a mumble mumble mumble but I'll interpret that as Alexander Friedmann absolutely absolutely right so these individuals studied Einstein's equations from his so called general theory of relativity Einstein in the early part of the 20th century rewrote the rules of how gravity works and these individuals limit and Friedman studied the mathematical equations that Einstein wrote down and came to a surprising conclusion at the time because at that time Einstein and everybody else thought that the universe was static eternal unchanging on the largest of scales you know not a not a surprising conclusion to draw when you look out at the night sky you know on the largest of scales the stars don't move so it certainly stands to reason that you might conclude that the universe has just always been in the way that you see it has always been that way but these fellas studying Einstein's mathematics showed that the mathematics would not allow the universe to be static the math required according them that the fabric of space the actual environment within which we are immersed would necessarily be changing its size in fact expanding over time Einstein himself did not by this conclusion even though it came from his own mathematics but these individuals pressed on with it and came to a picture that we now call the Big Bang let me just show you a quick visual of what their theory would look like and for this if you don't mind if there's anybody in the booth listening if you can bring the lights down it looks a little bit better and dark thank you so if we consider their version of cosmology they imagine that way back in the beginning universe was really small dense compressed and it went through this Big Bang expansion where space swelled and as space got larger and larger it cooled down allowing structures to coalesce the stars and galaxies that dot the night sky that of course we are all familiar with now this picture is of course an artist's rendition of what the Big Bang Theory says you can bring the lights back up and you know it came from the mathematics Einstein didn't believe it but ultimately the way in which you judge a conclusion is by observation by experiment that is the ultimate judge and in 1929 an individual can bring back to the screen if you would Edwin Hubble this fella right here an American astronomer working with the telescope at Mount Wilson Observatory looked at the distant galaxies and found that the distant galaxies were actually not static they were not standing still he found that the distant galaxies were all moving away all moving away just as the theory that the Met and Friedman using Einsteins mathematics suggested if the universe swelled outward there'd be a residual swelling today with the galaxies rushing away Einstein learned at this data around 1929 1930 and changed his tune he said I see this is in my opinion the best description of how our universe began and evolved so the Big Bang became one of the accepted ideas from that point forward but there is a little secret about the Big Bang Theory that perhaps we don't emphasize enough when we speak about these ideas in general context and let me tell you what that little secret is the Big Bang Theory leaves something out it leaves out the bank it leaves out what happened at time zero to cause the outward swelling of space to happen in the first place it doesn't tell banged or how it banged her Wyatt banged her frankly if it even banged at all that's a pretty vital missing piece to the story and just to get a feel for why it is that the theory is silent about what happened at time zero it comes down to the fact that if indeed the Big Bang Theory is correct as you examine the universe at ever earlier moments it's ever more dense and extreme and at some point way back toward the beginning it's so fantastically extreme that Einstein's mathematics actually can't cope breaks down let me just show you quickly what that would look like so if you can bring the lights down again that would be great so if we consider the Big Bang in Reverse they use Einstein's mathematics to run the cosmic film from today back toward the beginning in Reverse everything that today is rushing apart it all comes back together so the galaxies get closer and closer together ultimately the Stars get closer and closer together the universe kind of implodes in on itself getting hotter denser ever more extreme and the point is you can use Einstein's math to turn the film back to here this is a fraction of a second after the beginning but you try to push any further back and Einstein's math says I just can't cope and that is what you get noise static a complete lack of understanding about what happened at time zero which means a complete lack of understanding it can be more let's back up about what caused the outward swelling to happen in the first place now if you think about it the issue of what caused the outward swelling is a pretty formidable challenge because what force could it be the electromagnetic force the you know that's the force that you know causes magnets north and south pole to attract now north and north they would repel but the universe doesn't have a magnetic charge so that wouldn't do it the nuclear forces no they don't operate over the appropriate scales could it be the gravitational force could that be there's no gravity pulls things together it doesn't push things apart you know you drop something it falls it doesn't rush upwards so what would be the force that would push the universe apart and a number of people took up this challenge let me just show you those who are responsible for what we believe now to be the answer on the left that's Alan Guth on the right that's andrei linde also paul steinhardt would be part of the trio that discovered what I'm about to describe and perhaps it's worth just by comparison bringing Friedman into this picture here for no other reason than to illustrate just how modern cosmologists have gotten so happy you know Friedman looks like the guy that does my taxes I mean you know so why why are these guys so happy well here is the idea that they came up with and remarkably the answer that we've come to for what pushed the universe apart goes back to Einstein himself it's amazing how so many trails lead back to his thinking because when Einstein rewrote the rules of gravity as I mentioned a little moment to go he found surprisingly that unlike what Newton thought Newton thought gravity is always attractive but Einstein said gravity is attractive when you're talking about the gravity exerted by familiar objects the Sun's gravity the Earth's gravity the moon's gravity as those are all attractive but inside Einstein's equation the inside Einstein's general relativity is the following fact if there's another source for gravity not a planet not a star but a uniform energy that fills space think of a a Turkish bath or a sauna that's filled with steam if that energy uniformly fills space Einstein's math shows that it can yield repulsive gravity and outward pushing gravity and these guys found that there's a way of realizing that idea where the very early universe would have been filled with this energy an energy that would push everything apart putting the bang into the Big Bang Theory it's called inflationary cosmology and again we believe these ideas not just because they're interesting not because they're creative but because of data so let me just give you a feel for the data that supports this collection of ideas first I will show you data that has to do with the Big Bang Theory itself which is something I think you may be familiar with but I mentioned that the universe is very hot when it's little and then it expanded and it cooled it did not cool all the way to zero there is a residual heat left over from the Big Bang that is all around us right now heat in the form of photons that are in the microwave part of the spectrum right now in every cubic metre of space there are about 400 million photons coming to us from the Big Bang if you have an old-fashioned television set go home tonight unplug the cable turn it to channel 69 if you can do that and one of the old ones and you'll get a lot of static on this screen especially if you if there's a show there go between the channels there'll be a lot of static on the screen one percent of that static is from the heat left over from the Big Bang so this stuff is out there and astronomers have measured it and I want to show you the relationship between the theoretical predictions for what this heat should be like the intensity of the heat as a function of the wavelength of the light versus the observation so if you can switch over this curve over here is the theoretical curve of what the heat should be like today as a function of the wavelength of the light and then the observations look like this that's pretty good folks won the Nobel Prize for that but we're inflationary cosmology comes into the story is a refinement of this picture you see because if the universe underwent this inflationary outward swelling coming from a pulse of gravity space would have swelled so quickly and become so large so fast that little tiny quantum processes little tiny quantum jitters in space in the early universe would have been stretched out across the sky yielding tiny temperature variations from point to point in space you can calculate what those temperature variations should look like and let me show you a little picture of what they should look like this is a map of the sky where the colors indicate the temperature at any given location and the different colors represent tiny temperature differences not much like one part in 10,000 degrees so the temperature is pretty uniform with these tiny quantum jitters yielding small temperature variations and you can do a statistical analysis of what these temperature variations look like as a function of the angular separation on the sky and I'm going to show you the theoretical curve that comes from this inflationary idea versus the observations of it so here is the curve coming from the theory and I'm just gonna sit back and let the data speak for itself now is that beautiful or what that is illustrating quantum processes that happened 14 billion years ago stretched out by this huge swelling of space giving rise to temperature differences that we can measure today one part in 10,000 and as you saw a moment ago the agreement between the theory and the observation is really really compelling so this is why we take this notion this version of cosmology this refined version of the Big Bang seriously now why am i bringing this up in tonight's discussion I'm bringing it up for the following reason when you study this rapid swelling of space you still need to connect that swelling of space that happened a long time ago with the universe that we live in today and people have worked very hard on bridging the gap between what happened a long time ago and what we now witness and I've found that the process is pretty straight forward this energy that's fills space it causes space to rapidly swell but the energy pocket by pocket by pocket in space begins to degrade over time it's sort of like if you go back to that image I asked you to have in mind of a sauna imagine that the Sun is uniformly filled with steam but then their various regions that cool down and the steam turns into water droplets so you have an opening in the steam that gets filled with little droplets as opposed to the uniform steam that was originally there and that kind of idea happens in this cosmological picture as well so if the light regions are the energy the steam if you will the steam opens up in various regions allowing those areas in this wider cosmos to take the energy that was in the steam not turn it into water droplets but take the energy that was there and turn it into ordinary particles electrons quarks the things that make up stars and galaxies allowing stars and galaxies to form in those darker region each of those darker regions then would correspond if you will to a universe our universe would be one of those regions that the energy degrades allowing particles to form and galaxies and stars to then coalesce from those particles but there are other regions out there where the same kind of process would happen and moreover because the energy between these universes the steam still exerts this repulsive push all of these universes are being pushed apart rapidly and new regions are opening up opening up opening up again universe upon universe upon universe is created via this mechanism of trying to fill in the bang in the Big Bang let me show you a little video of that to make that a little bit more visceral so if you can bring the lights all the way down again that would be good so here is what this would look like here is the beginning the rapid swelling from the repulsive gravity space is rapidly growing bigger and bigger and in various places the energy degrades allowing a little universe to open up each of these black spheres each of these openings is a universe in which particles would be produced from the decaying energy and from those particles various structures could form for instance our universe if we focus in on one of these dark spheres if we penetrate into it the properties in our universe would be evident by virtue of the familiar picture of stars and galaxies but if we were to look in one of the other universes the environmental conditions can be very different from ours and because of that the physical processes will be different and the universe won't look like this it won't look like our familiar universe let's do that take the bird's-eye view all of these other universes out there but let's go into this one coming up here and because of the physical differences you don't have stars and galaxies instead you have like greeny tenderly thingies that are that are that are forming so each of these universes can have very different physical features many of them will not be hospitable to life or at least our form of life but this is the picture that we get by trying to fill in that missing piece in the Big Bang Theory we get not a single universe we get many universes so the picture then would look something like this in still form our universe is that one on the left that's just cut off hanging off the left side of the image these other universes expanding realms but the details of what's inside those realms can be very different from the details of what's inside our realm so that's another very concrete way in which the mathematics leads us to this profound shift in thinking this possibility that there are other swelling realms out there other universes out there now again you might say well how could you test this you know how would you ever know if it's right well there a number of answers let me just give one concrete one if you can print that image back up for a second each of these universes is expanding as I said the space between them is forcing them apart but if they form sufficiently close their rate of expansion can be larger than the rate at which they're pushed apart which means they can collide universes can smash into each other in this framework and if our universe had been hit by another universe how would we know that well if we did have a kind of fender-bender of this sort with another universe the impact would send ripples going through that heat left over from our Big Bang the cosmic microwave background radiation yielding yet more subtle variations in the temperature that we should measure today and astronomers astrophysicists are looking for those kinds of ripples those patterns in the microwave background radiation none yet have been found but this is a very concrete way where at least in principle there's a chance that through observations we'd get this evidence of our universe having been hit by another evidence that there are other universes out there okay so what I want to turn to now is an approach to multi universe theory that comes out of itself a speculative theory namely string theory so I'd like to try to give you a feel for how string theory has weighed in on this possibility of multiple universes and how that has had a fairly profound effect on the way we deal with certain puzzles and problems that we've encountered in the last decade or two in trying to analyze string theory and to motivate what I'm going to talk about I'll begin with something that's non string theoretic I'll begin with an observation an observation that really rocked the foundations of physics in the last decade some of you no doubt have heard of it it's the observation of the so called dark energy just wondering how many people have some familiarity with what dark energy is not a bad fraction and how many of you who know about dark energy I'm like the clap at least one of you up there that's good that know that that's good um so what is what is this story well as I mentioned Hubble in 1929 turned this giant telescope toward the sky and looked at the distant galaxies and found that they're rushing away from us ever since then everybody thought that yes the galaxies are rushing away but they must be rushing away slower and slower over time because you know just like if I take a baseball and I throw it up it moves away from me but it moves away from me slower and slower because the Earth's gravity pulls it back similarly everybody thought that the galaxies are moving away but the gravitational pull of all the other stars and all the other galaxies must be pulling everything back together so like the baseball going slower and slower the guy should be moving away slower and slower to teams of astronomers in the 1990s set out to measure the rate at which the expansion the motion of these galaxies is slowing over time and by the end of their exploration they came to a very unexpected result they found that the galaxies are not slowing down in their recession from us they're speeding up which is if I took that baseball and I threw it up and it went up faster and faster and faster now if I did that with a baseball and you saw it go up faster and faster you would conclude no doubt that something must be pushing the ball upward to counteract the pull of the Earth's gravity similarly with the galaxies rushing away faster and faster everybody concluded that something must be pushing them away counteracting the usual attractive pull of gravity what could that outward push be well I've actually given you the answer earlier in what we discussed sometimes gravity can be repulsive when if it's filled with a uniform energy that uniform energy can give repulsive gravity I use that to give the bang to the big bang but the suggestion now is maybe there still is some energy suffusing space that is a residual repulsive gravity responsible for the observation of the distant galaxies rushing away now that's a reasonable explanation this is one that most physicists have warmed to many believe that it's correct the bizarreness of the explanation is in the details when we work out the amount of dark energy the amount of energy doesn't give off light so we call it dark the amount of dark energy that must be filling space in order to account for the rate at which those distant galaxies are rushing away the number we get is odd let me show you what the number is here is the amount of energy that must be filling every cubic centimeter of space a decimal point followed by a hundred and twenty two zeros and a one I've seen it's one three eight we don't usually encounter numbers like that when we are thinking about the cosmos and the strangeness of this number from the perspective of a theorist like me is when we try to imagine explaining that number actually calculating from our fundamental equations doing some calculations and having a number like that pop out at the end it seems virtually hopeless that we will ever succeed I mean our equations the fundamental equations of Einstein the fundamental equations of any of the approaches that are taken seriously the numbers that appear in those equations are numbers like one square root of two pi in a 3.14 you know e you know numbers like that how do you start with equations with those kinds of numbers do some mathematical manipulations and wind up with a number that looks like that it seems hopeless and because of that physicists have been warming to a new approach to trying to address this question and a class of similar questions and to give you a feel for what that approach is let me just tell you a little story that will at the same time get me out of trouble because I mentioned my daughter earlier and if I don't mention my son too I'll go home and have to sleep on the couch so I was my son is six now I went to the shoe store with him about two two and a half years ago and we'd gone to his shoe store you know a number of times before but this is the first time when he was really taking in the environment thinking about what was going on so the shoe guy comes over measured his foot goes in the back comes out with a pair of shoes tries it on it fits we bought him he walked out and my son said to me wow isn't it lucky that they had my shoe size and asked him what exactly he meant by that you know and he said well how did how did they know I mean how did they know that I was going to come in and how do they have a shoe that fit my foot you know and if you think about it there's kind of a mystery there if you don't really know how a shoe store works I mean how do they have the one that that fits your foot now of course we all know what the explanation is the misconception that my son had was that the shoe store had one unique shoe size and that fitting his foot that would be strange strange coincidence but when I explained to him that back in the stockroom when the guy disappeared he went out back he had every shoe size back there and he just picked out the one that he'd measured to fit his foot the mystery went away so what we learn is something can seem mysterious if you think it's unique if you think there's a one of it if there's one single number that you're trying to explain but if you realize that that perspective is wrong that a uniqueness view is incorrect that you should think about there being multiple sizes multiple examples of the thing you're trying to explain mysteries can simply evaporate by that change of perspective the belief the possibility is that that notion may apply here if you try to explain that number assuming that it's unique one unique universe trying to explain just that number very very difficult but if you imagine that there are many many universes each with a different amount of dark energy stuff using it then you're kind of in the same situation as the shoe store is it a mystery that our universe has that particular amount of dark energy no every possible value is out there why do we live in a universe with this particular number much for the same reason that the guy brought out a particular shoe for my son's foot it was compatible with the size of his foot this number is compatible with our existence you see this number dictates how strong the repulsive pushes if it were much bigger as it's a would be in this way of thinking about things in other universes the repulsive push there would be so that so strong that clumps of matter would never come together it always be blown apart so stars and galaxies wouldn't form planets wouldn't form in our form of life wouldn't form those other universities so we see a universe with this value of the dark energy because it fits us like the shoe fit my son's foot we can't exist in the other universes that's the basic framework that people are pursuing to try to explain this very strange and unfamiliar observation and what I'd like to do in the time that I have remaining here is put a little bit of flesh on that idea by showing you how it actually very naturally emerges from string theory and to get there there's one fact that I want you to have in the back of your mind over the next 10 12 minutes I'll call upon it when we get to the appropriate point but I want to explain it right here if I try to use this kind of reasoning certainly you would need to ensure that just as the shoe store has many many many many different shoe sizes we have to ensure that there are enough universes to exhaust the possible values of the dark energy little analysis shows that it can very say between zero and one our value seems to be quite small but you need to exhaust all of the possibilities to get rid of the mystery just as you need all possible shoe sizes to get rid of my son's mystery now let's think that through for a second in a more simple context imagine that you all are casting for a movie and you don't know how tall you want the main character to be so you tell your production assistant look at the audition have every possible height represented between say 1 meter and 2 meter so that I can look at all the different actors different heights and I can pick the one that I feel is correct now of course you can't have every possible height so the PA says well - what accuracy do you measure how you say well - a centimeters accuracy so how many actors does the production assistant need to bring into the audition to ensure that every possible height between 1 meter and 2 meter is realized well you know there are a hundred different heights separated by a centimeter this is a 101 centimeters 102 centimeters you know up to 199 centimeters up to 200 centimeters to meters so you'd need at least a hundred actors in order to have a chance that every height is represented but of course some of them may have the same height so you should probably bring in a few hundred actors maybe a thousand actors to ensure that every height is represented in this case with this example if you can go back to that number up there if the dark energy can say vary from 0 to 1 and we can measure it not to a centimeters accuracy as in that little analogy but to an accuracy of about 10 to the minus 124 that's the accuracy that we can measure it how many universes would you need in order to assure that every possible value of the dark energy is out there if you're measuring them to an accuracy of 10 to the minus 120 for anybody well let me lead you through it right so in the case with the actors you are measuring the accuracy of the height to 10 to the minus 2 meters and you needed a hundred because they're a hundred different possibilities you just invert the number 10 to the minus 2 10 to the 200 different actors is the minimum that you need but having duplicates requires that you have more so here with an accuracy of 10 to the minus 124 play the same game you exactly thank you 10 to the 124 thank you whoever said that I appreciate that very good whoever sounded like a young kid which is what I would have expected so so you need at least for this idea to hold water you need at least 10 to the 124 different universes wow it's a lot of universes is it possible that there's some natural way to get that many different universes well let me now show you how string theory comes to a conclusion that's positive on that so to give it a little bit of background I'm going to spend about four minutes giving you a little background on string theory itself so to do that what is string theory well I've lectured on it here before some of you may have been here but let me just give you the rough idea it's an attempt to realize I'm Stein's dream of a unified theory of physics where everything would be described using one basic idea one key notion that would apply to everything and how does string theory accomplish this well it changes the way we think about matter on its most fundamental scale so the ancient Greeks you know 2,500 years ago they asked what is matter made of and we've been trying to answer it ever since in essence we've been saying you know take a piece of wood any piece of matter cut it in half keep on cutting it in half every smaller pieces what's the finest uncuttable indivisible elementary constituent that you come to with that kind of cutting process we know of course in our age that we've come upon molecules and atoms as the ingredients that you'll come to in that kind of process but we know that they're not the end of the line because atoms they can be split they can be divided up further electrons going around the nucleus with neutrons and protons and inside the neutrons and protons are smaller particles known as quarks it's sort of like sequence of Russian dolls every time you look at a particle there's something else but the conventional framework before string theory says electrons quarks few other exotic species of particle that's it they are little tiny dots with no internal mechanism nothing further to be found inside the idea of string theory is to challenge that and suggest that there is some thing inside at least one more layer of sub structure and the layer of sub structure would be a little tiny filament little tiny filament look string like I'm sorry called string theory and these little filaments of energy can vibrate in different patterns different vibrational patterns much like the different vibrational patterns on a violin produce different notes these little tiny strings they're different vibrational patterns don't produce different music they produce different particles an electron is a string in this approach vibrating in one way like a G a cork is a string vibrating in a different way a C sharp so in this way all of the particles are united under one idea vibrating strings so let me just show you quickly what that would look like so if you can bring the lights down again to dark that would be good so here is an ordinary piece of matter it's just a candle in a holder and what I want to do is examine the structure of this piece of matter on very very small scales so to do that I dive in I go smaller and smaller and smaller I encounter the molecules and atoms if I go small enough let me focus in on one atom there you schematically see the electrons going around the nucleus with the neutrons and protons inside neutrons and protons you told me there are quarks there they are this is where the conventional framework stops the new idea of string to you that I was mentioning is that inside these particles there are these little tiny vibrating filaments and again there's not a different species of string for the electron or the cork it's one species that can vibrate in different ways so in this way all of the richness of the world around us is reduced to one kind of ingredient that can simply vibrate in a great many different ways so that is you bring the lights back up the basic idea of string theory you know as I mentioned early on string theory is speculative it's not by any means of proven theory just as a footnote you might say why I mean there seems from that little video sequence a very direct way to test the theory grab hold of an electron you know look at it really closely and do you see the stringer don't you see this dream and that's really what it comes down to and that's a perfectly fine way of going about it the problem is that video sequence I just showed you was not to scale those little strings inside these particles according to the conventional math of string theory about 10 to the minus 35 meters across again such a small number that it's hard to envision that tiny scale just to give you an analogy that helps bring it to life so if I were to take an atom one atom and magnify it to be as big as the observable universe huge scale of magnification under that same scale of magnification a string would become roughly the size of a tree a tree is two the entire observable universe as a string is to an atom makes it hard to see them not impossible there are indirect ways of probing this theory that I won't go into now is it'll take us a little bit off-course but we're hopeful that for instance Large Hadron Collider might give us some insight into whether this approach is correct but instead what I want to focus on here is what string theory potentially has to say about the dark energy and other universes and to get there I need to tell you what I consider the strangest maybe the most wondrous feature of string theory of all which is this when you study the math of string theory yes you do find that at least on paper it unifies everything together into one framework but the math itself the math itself doesn't quite work the math has internal inconsistencies if the world only has three dimensions of space if left-right back-forth and up-down are the only dimensions of space the ones that we can see if they are the only ones then the math breaks down theory doesn't work if there were four dimensions it doesn't work five six still doesn't work seven eight nine nope but at ten dimensions all of the mathematical problems evaporate the math holds together if there are ten dimensions now how do you respond to that well you could say well that's nice but that just is a piece of mathematics clearly it can't describe our world our universe our universe has three dimensions look around that's all that there are but there is the possibility that our universe really does have more than three dimensions and we just can't see them or haven't yet seen them the idea is this and it's easiest to work by analogy imagine forget about strings and extra dimensions for a moment think of something simpler like you know just this flat surface right here so just think of this flat surface say this is two-dimensional right flat on the surface you've got left right you've got up down flat on the surface now imagine I take this guy and I roll it up into a tube still has two dimensions on its surface right haven't destroyed a dimension by rolling it up have changed the character of one of them still have left right as before of it up down it's now a circular clockwise counterclockwise dimension and in fact if I could do this and I certainly can't do this with a magazine even it's hard with a single piece of paper but in your mind's eye imagine I wind that tube up thinner and thinner and thinner at some point will be so skinny that you won't even see the circular part at all so if you're say way up and the upper tier in the back looking at this it'll look like one dimensional you only see the left right part so much so that you know if I told you a little ant we're living on it's life on this tube you'd say poor little fellow if you cared about it see they say poor little fella it can only move left and right right that's the only dimension that it has access to that's all there is but if from the back you take a pair of binoculars and you zoom in you see well actually it's not so bad for a little ant because now you can see the circular part of the tube you really the ant can move left and right but can also move clockwise and counter-clockwise the lesson of that little example is that dimensions come in two flavors two varieties they can be big and easy to see they can be curled up and tiny more difficult to detect maybe that lesson applies not just to a piece of paper but to space left-right back-forth up-down maybe those are the big dimensions that we can easily see maybe there are additionally curled up dimensions like the circular part of the tube curled up all around us so small that we haven't seen them that's the idea that we come to is string theory let me just show you a visual bring the lights down if you would so let me give you a version of that analogy not with a piece of paper or magazine but with a cable supporting a traffic light look at that kay but looks one-dimensional from a distant vantage point you don't have the visual acuity to really see the circular part that wraps around it but if you zoom in and take the perspective of little ants the ants are small enough that they can walk along the cable but also around the cable and and I do hope you appreciate this visual because it took so long to get the ants that this but there you have it big dimensions easy to see curled up ones harder to detect now keep the lights down if you will because I want to apply that lesson that idea to space itself so space itself three big dimensions I can only put two on the screen of course but now let's go into space go smaller and smaller and smaller and the idea according to string theory is that if you go small enough you will encounter additional curled up dimensions you see right here additional small ones that we haven't seen too small for us to yet have detected if there's an ultra microscopic ant walking around it can walk in the big dimensions the grid like you and I but as you see here it can also walk in the curled up dimensions it's small enough to access them directly now string theory doesn't say that the extra dimensions look really like little circles and said it says that they're more complicated geometrical shapes they have a name they're called khalaby out shapes after two mathematicians who discovered them they're complex scalar manifolds advantage and first churn class they vanishing Ricci tensor but if any of that language offends you just look at the picture there you have the form for what the extra dimensions could look like one of these khalaby eye shapes curled up six dimensional spaces if these ideas are correct this is what the microscopic fibers of space itself looks like if you could examine it on sufficiently small scales so that's how string theory makes sense main lines back up of this possibility of extra dimensions but the key point for us here tonight is this it's not just a matter of hiding away the extra dimensions because we haven't seen them and the theory predicts it so how do you reconcile observation with theory it's more than that the extra dimensions profoundly affect their shape profoundly affects the physics that we do observe in the world around us in string theory and the reason is quite simple in string theory all of the physical properties can be weird to how strings vibrate now a string is so small that when it vibrates it doesn't just vibrate into the big dimensions that we can see strings also vibrate into these curled up dimensions and the shape of the curled up dimensions affects that profoundly how the strings can vibrate I mean if you consider the air streams going through a French horn the air streams have vibrational patterns that are dictated by the twists and turns in the geometry of the instrument similarly the vibrational patterns of strings are influenced by the twists and turns in the geometry of the extra dimensions so if we knew exactly what the extra dimensions look like we would calculate how strings vibrate we calculate the physical properties that string theory gives rise to so let me just show you what that again looks like visually going down to black again would be nice thank you so just to give you a sense with the analogy here's a French horn look at the air the air streams are it's all vibrating but it's determined by the precise shape of the instrument precise shape of the path that the air follows if we now segue to the real interest these extra dimensional shapes these khalaby out shapes the precise way in which the geometry folds in on itself twists back on itself affects how a string in this environment would vibrate so to show that let me just bring in a couple of strings you see them here and as they're vibrating the environment has a very direct influence a very direct effect on how they vibrate look you've all experienced this in the shower when you sing in the shower the vibrations are influenced by the shape of the stall the vibrations of the strings are affected by the shape of the extra dimensions you can bring the lights back up now the natural thing then to do would be to take a given shape for the extra dimensions calculate the Associated physics loud vibrations and in that way make some predictions that might be tested in fact in 1986 when I was a graduate student my dissertation my dissertation taking one of the shapes for the extra dimensions and doing that analysis the result that we found did not agree with observations but it was just a test case the natural thing would be to move on to some of the other shapes that were known I've showed you a picture of one possible shape one colaba shape but they're actually in 1986 there were five known shapes that fit the mathematical criterion that I rattled off to you candidate shapes for the extra dimensions so natural thing would be to go and look at the second shape after analyzing the first and not find a success the problem with that program is it rapidly became much more challenging because within a few months mathematicians and physicists found hundreds of more candidate shapes for the extra dimension so they started to build a catalog of possible shapes for the extra dimensions and within a year or two the number of possibilities is up to five ten thousand possible shapes now ten thousand is big but you could still imagine analyzing them one by one I mean after all graduate students have to have something to do but very quickly ten thousand grew to a hundred thousand grew to a million known shapes a billion known shapes through the 2000s as of today the number of known distinct shapes for the extra dimensions is about ten to the five hundred ten to the five hundred different shapes in this catalog of possible shapes for the extra dimensions so what do you do with that sort of a development well some string theorists looked at that and said ten to the five hundred possible shapes for the extra dimensions each one affects physics we're never going to make any predictions we are done and they moved on to other fields within physics which is a completely reasonable response to that kind of development other group of physicists including me have taken the perspective look we've been at this for twenty thirty years yeah but on cosmic terms that's not a long time and we're trying to answer some pretty deep questions let's keep going maybe we will find an equation that picks out one page in the khalaby I'll catalog says that's the shape for the extra dimensions and then we'll do the analysis and if the physics agrees with what we see great if it doesn't we'll throw it away and be done and move on to another subject we've not yet been able to find that mathematical equation a third group of physicists have suggested something far more radical they've said look we have been trying for all these years to pin down the exact shape of the extra dimensions and we have failed maybe we should listen to that failure maybe that failure is telling us that we can't pick out one particular shape for the extra dimensions much as there's not one particular shoe size in the shoe store maybe there are many many universes each with a different shape for the extra dimensions and we simply live in that universe where the shape of the extra dimensions gives rise to physics compatible with what we see and the fact that we are able to exist and in fact there's something quite wonderful about aligning that idea with the observations of the dark energy that I mentioned a few minutes ago you may recall that we discussed how many distinct universes you would need to ensure that the explanation for the dark energy using this multiple universe approach would make sense do you remember I told you to try to remember the idea we need at least how many universes 10 to the 120 for how many different shapes for the khalaby eye shapes are there 10 to the 500 is 10 to the 500 bigger than 10 to the 124 yeah it is much much bigger if I took 10 to the 500 and subtracted 10 to the 124 what would I get 10 to the 500 it wouldn't make a dent that's how big 10 to the 500 is and in fact when you analyze these shapes I'll show you a little picture over here the altitude in this little schematic is telling us the amount of energy stuff using ordinary three dimensions the grid part if the extra dimensions have one shape or another or another still the altitude represents the amount of energy that those shapes would contribute to the energy stuff using ordinary three-dimensional space as you can see different shapes contribute different amounts of energy which means if you had 10 to the 500 universes each with a different shape for the extra dimensions you would fill out all of these nooks and cracks and crannies inside this landscape and you would effectively be guaranteed that many of these universes have a dark energy value compatible with what we have observed so the picture that you would come to is you'd have universes inside of universes so the sphere inside the sphere on the right hand side is an expanding universe inside another expanding universe with different shapes for the extra dimensions different amounts of this energy there's dark energy and if you then allow these kinds of processes to run their course the ultimate view of the universe would be universe upon universe upon universe each with a different shape for the extra dimensions with our universe just being one of those the one or the collection of those compatible with our existence just like my son shoot was the one that the guy pulled out that was compatible with the size of his foot so then the picture that we would come to and if you can bring the lights down I'm going to reprise this video sequence and now overlay it with our new insights this is what the picture of cosmology would look like universe begins with the repulsive gravity driving space to swell very very very quickly in regions throughout this expanding realm the energy would degrade allowing a more ordinary universe a more ordinary expanding realm to form and in the string theoretic perspective each of these expanding realms would have a different shape for the extra dimensions if we have a universe where the extra dimensional shape gives rise to physics compatible with what we see going into that universe would yield this kind of an environment the extra dimensions give rise to electrons and quarks all the familiar particles that then coalesce into stars and galaxies but again if we pull out from our universe look at the wider expanse there will be other universes out there with different shapes for the extra dimensions and if we go into one of those the extra dimension shape gives rise to different physics different properties of the particles different amounts of dark energy and so that universe doesn't look like ours that has properties perhaps incompatible with our form of life and the reason why we're not there is that we simply could not have evolved there so rather than trying to explain that dark energy by a unique calculation we say all of the possible values of the dark energy are realized universe by universe and we just happen to live where we can exist so then this is the ultimate picture where now we recognize that in the string theory version of this story each of those different universes different shape for the extra dimensions different physical features different amount of dark energy and the ultimate explanation of why we're in one universe and not another is simply one of survival I mean the lights back up so that's where we've gotten in our search to understand the deep laws whether or not there are other universes out there ultimately it'll have to come down to observation I've suggested some ways that observations could clarify the story but the bottom line takeaway message if you will is this all of these ideas are emerging from us following in their tradition laid down by the greats by Newton by Maxwell by Einstein where they showed us that mathematical calculations can be a potent guide a sure-footed guide a gateway if you will into realms that we have not yet been able to probe experimentally is that the case here we don't know yet because you don't know whether the math is right until you test it but I hope that this convinces you that these ideas are sufficiently compelling that it's worth taking seriously the possibility that we are one of many universes and frankly if we in our lifetime are fortunate enough to get experimental or observational confirmation of any of these ideas and we learn that we are part of a multiverse that there are other universes out there I just can't imagine anything more thrilling than that thank you very much okay so I'm told that we have time for some questions in case anything wasn't crystal clear and their mic set of the spotlights on them so just go to those and yep go ahead yeah whoever's that I might go ahead thank you dr. Greene that was I was fascinating I was wondering how the laws of thermodynamics might apply across the multiverse if some universes are winding down and others are spinning up would there ultimately be a so-called you know it's very hard to apply those kinds of laws across the multiverse for instance we don't even have an ocean of time that applies pan universe in this sense each universe has its own notion of space within it each universe has his own notion of time within it but comparing from universe to universe at the moment we don't even have a benchmark to align them in a way where that kind of comparison would be sensible so it may in fact not be sensible maybe that these ideas really need to be studied universe by universe so I don't know if some sort of grand notion of the second law of thermodynamics in terms of some compensating winding up or winding down so I think that's sort of the best answer I could give on them someone on the left yes I'm an eighth grader from Westland and I have two questions my first one is how could the other universes start if this multi universe theory is true like are they all Big Bang's or what good so when I was showing you that video of that steam that energy that was forced in the universe to expand that repulsive gravity and I mentioned that within that expanding that rapidly expanding realm pockets opened up where the energy degraded you can think of that process of the energy degrading and that hole opening up you can think of that as if it's a Big Bang what is the Big Bang the Big Bang is really a region of space that begins to grow and cool off and particles coalesce and that's happening in each of those pockets that are opening so you can really think about that multiverse is basically being big bang upon BIGBANG BIGBANG BIGBANG happening all over the place so another summary of it would be a multiple Big Bang Theory with our universe being the result of just one of those bangs okay my other question is could dark energy increase the energy it puts out yes can dark energy increased energy puts out we don't know but it's certainly possible the version of dark energy that comes to us from Albert Einstein has another name called the cosmological constant that's what he called it and if the cosmological constant is what its name says constant then it strains wouldn't increase over time but some physicists have been investigating the possibility that the intrinsic strength the intrinsic repulsive push of the dark energy might increase over time if it did we would be in for some interesting things in the far future because right now you could say you know why isn't the dark energy pushing the Sun away from the earth the reason is because the pull of the Sun on the earth and the earth on the Sun is so much stronger than the repulsive outward push from the dark energy that the repulsive push isn't effective only on large scales where there's a lot of space and a lot of dark energy is the dark energy strong enough to have observable consequences making the distant galaxies rush apart faster and faster but if the dark energy increases its strength over time then in the far future they repulsive push even between the Sun and the earth we'd go strong enough you know to push them apart if it grew sufficiently strong even the little amount of space between the nucleus of an atom an electron that little space there would be enough of a repulsive push to drive atoms to rip apart which gives rise to the possibility that all matter might be blown apart by the repulsive push of the dark energy in the far future something that physicists call the big rip so this is something that could happen in the far future up on the top speaking of the big rip yes is the universe in your in your mathematical equations expanding at this point inflation in from an inflationary perspective faster than the actual speed of light or is it limited to a speed slower than that no the the universe in terms of the rate at which distant objects are receding from one another from the swelling space between them if objects are sufficiently far apart then they are receding at faster than the speed of light now when you hear that it seems to conflict with this idea that we've all had you know really drilled into our heads that nothing goes faster than the speed of light but you need to be real careful about what Einstein actually said and what special relativity really says it says no object can move through space faster than the speed of light but there is no limitation on how fast space itself can swell thereby pushing objects apart and indeed objects that are far enough apart are moving away from one another at far greater than the speed of light sure so you talked about how there are infinite possibilities of universes right and if one universe if there's infinite possibilities and even if it's like our reality but with a slight twist when there be a reality let's say that some guy has some detonator that will blow up every single reality and but then but then there'd be some other universe that that I got with a different detonator I had one to upload that universe before that kind could detonate it and it'll be like a paradox of universes blowing up each other what's your opinion on that oh it's my opinion cool [Laughter] [Applause] yeah I yeah I'll have to talk to my son about that when I get home I think he and you would get along quite well but um the first thing that I would say and perhaps the only thing I'll say is um you were speaking about a guy with a detonator that could blow up all of the other universes not a guy okay like a transformer maybe uh maybe even just Bionicle maybe something like that maybe even just physical laws that affect other you know like the laws sure the universes that destroy them but another one counteracts that it's like a paradox yeah the key thing to bear in mind is number one these universes again except for the possibility of them banging into each other that what I discuss these universes can't affect each other because they are moving apart so quickly that no signal that any universe emits can reach any of the other universes that's point number one but point number two is and this is a more serious point all of the universe and all of the processes that we're talking about in all those video sequences that I would show you all these other universes of worth all are coming from the coherent logical laws that we are studying the mathematical laws and those laws are carefully constructed so that there aren't any possibilities for paradoxes that is the nature of the analysis that we do that's why we work within the straightjacket of mathematics in order to have the best hope of not encountering those kinds of logical contradictions that you're trying to bring us toward so if indeed we've done our job and I think we have in these theories then we won't encounter any of the logical paradoxes that the wild imaginings of a nine-year-old might take us to twelve-year-old I'm sorry I really do apologize it's so dark I can't see there but thank you it's interesting and crazy idea okay Oh another question mathematical challenge to you another mathematical yes let me get a piece of paper though for this one yeah I'm tell you okay and King when you talk about the little strings vibrating yes this is kind of my theory on that one okay the smallest possible amount of energy or matter I mean be pure energy cuz you can't cut pure energy like Newton's say you can create or destroy energy so what those strings be made up of energy and that kind of solves the problem um which problem where you try this off I mean I'm not sure if it's a problem but like what those strings are made out what the strings are made of or what they are and that would be pure energy cuz you can't clear to destroy it so you can't cut it yes I in fact I would agree with you completely if I were pushed to say what are the strings made of I would use the language that you just did not the guy with the detonator and are looking but um you know I would say the strings are made of pure energy they are energy is really according to Einstein not not Newton per se but Einstein really showed us from e equals mc-squared that energy is the ultimate convertible currency you can take energy and turn it into mass and that formula tells you how much mass you would get so indeed these strings since they can become any kind of particle really are pure energy that realizes itself as it vibrates and it looks like matter but deep inside its energy there are two sides of the same coin absolutely yet an awesome presentation oh thank you very much so you talked about how there are 10 to the 124th at least we would need that many universities yet and then you talked about how there are at least 10 to the 500 different shapes but how do we know that there are enough universes enough pockets in our sauna to have at least one of every one of those 10 to the 500 shapes yes and it has to do with something that I at the last minute decided not to show you but if you can actually there you go right there so again just for you and anybody else that follows if you know a little bit about quantum physics in quantum physics there's something known as quantum tunneling where say a particle can go through barriers that according to the classical ideas of Newton and Maxwell it can't penetrate but quantum theory says that it can penetrate me do observations it does penetrate that idea that we've studied at the level of electrons can be scaled up to whole universes and the processes that we are studying amount to imagining that there's only one pocket to begin with with one particular shape for the extra dimensions but then quantum processes allow that universe to tunnel and a little region within it to open up with a different shape for the extra dimensions and on and on and on the quantum processes let you tunnel through all of these mountain peaks allowing it to populate all of the possible locations all of the possible values of the dark energy all the possible shapes for the extra dimensions it comes down to those kinds of quantum processes thank you yeah I'm gonna top so do though there being many use of universes could different universes have different amount of dimensions yes in terms of the different amount of large dimensions so within string theory the total dimensions in any given universe would be the same the number and that I'm talking about but you could envision that the picture I'm drawing up here is too limited there could be universes where there are five big dimensions and the rest are all curled up or nine big dimensions and the rest are curled up so I didn't bother talking about those but in the grandeur landscape there's every reason to suspect they would be there too so yes and again the same notion of why don't we live in one of those well it's not hard to establish that our kind of stable physical structures would have a great deal of difficulty existing in more than three large spatial dimensions and four large spatial dimensions you know you could look right into my beating heart and pull it out without having to go through my skin those are the kinds of things that happen in a higher dimensional setup yes absolutely you bore with me for quite a long time so you're talking about how there's like extra mentions and strings vibrate within the nose dimensions and given the characteristics of that extra dimension they vibrate and create certain physical laws and stuff so kind of my question is like people themselves are sort of extra dimensions and thought vibrates within them and gives birth to ideas and different things like that and generate not exactly physical laws and stuff but how would you characterize thought like what is not well I'm a great fan of thought yeah but I don't have a lot to say about it unfortunately and the reason is when you're talking about thought you're talking about processes taking place in a fairly complicated structure you know this great thing inside of our heads and when we do our analysis like when we do our quantum mechanical analysis we typically focus on analyzing the properties of a small number of particles or if we're talking about universes we model the universe as a very homogeneous structure so that we don't have to analyze all of the intricate details simply because we can't at our current level of understanding do so we do not have the mathematical capability today to apply our fundamental understanding of matter to a complex arrangement of matter such as this thing inside of our heads one day I do think that we will understand thought from the basic physical processes of the elementary constituents that make up a brain maybe even will replicate those processes by virtue of that understanding in a machine who knows but as of today there's just no way for us to make any statement with confidence that links together fundamental physics and the workings of the mind now I know that there are many people out there that attempt to make statements of that sort and I appreciate the drive and I think it's wonderful that people want to use fundamental discoveries to understand something that is so vital to life you know thought consciousness but I am enormous ly skeptical that anything of any real lasting value can be said today because our understanding is just two people you want to hold him up to the mic maybe I mean if universes collide and dark energy seeps from universe to universe what will happen if a universe is overcharged with dark energy it won't be pretty and it could happen so you know in these universe collisions or in this process that I was describing our universe forms inside another universe the amount of dark energy typically does vary and so people have done studies as to what happens during the transition phase from a universe that has a certain amount of dark energy when that amount of dark energy transitions to a different value and the impact on a given universe can be quite dramatic the basic physics that we know about can sharply change and all of the processes that give rise to structures that are familiar in that universe can go away so if it were to happen to us what could happen there could be some dramatic changes our universe could start to collapse if the dark energy actually even went negative from its value that we now know about or the things that we know and love in our observational data would go away too so the work that we have in front of us is along the lines of what you are suggesting we need to fully understand the implications and the processes that take us the picture is no longer there but from one universe to another in the kinds of transitions that we were talking about and that's your homework assignment and I'm at Columbia and just send it to me by Monday if if you will last question okay so you were talking about it before like little dimensions inside these that we can't see cuz for too large to see correct yes now I don't know if you read the book flatland but it talks about how like someone the third dimension could pop in second dimension flip stuff around but so someone in the second dimension couldn't fully comprehend the third dimension Trey so how could we comprehend these tiny little it's not that they couldn't fully comprehend the third dimension it's that they'd have to be really smart to comprehend to dimension what I mean by that is as in flatland what happens is these flat beings are living on a flat surface and you know the point that I made before about in higher dimensions you could reach in and grab my heart without passing through my skin you can see if there's a human being that's flat on the surface here their skin is on the surface and I can reach in and grab their internal structure without passing through the skin that was actually the point those making it before it comes right from flatland but in that story what happens is the Flatlanders encounter aspects of this higher dimensional world and through those clues they do begin to understand it they do begin to understand that they are living in a flat world and there's more to of the universe than the flat environment that they are familiar with but can they really comprehend up and down I think they can I think they can just as you know we're struggling I mean you could ask me do I really comprehend do my colleagues really comprehend the other dimensions in the sense of being able to picture them no I can't picture anything in more than three dimensions and I well I was gonna say nobody that I know can but there's a famous story of mathematician Thurston at Princeton is teaching a class about six dimensional geometrical spaces and the class looks all confused and doesn't know why and he goes off into the corner he thinks about for many comings as ah it's so much easier to picture this in twelve dimensions whether it's true or not I don't know but anyway I can't picture more than three dimensions but what I can do and this really speaks to your question when I'm talking about this in a public setting I show pictures I try to use analogies and so forth but I'm doing the analysis I'm running down mathematical equations to describe those extra dimensions just like you might use XY and z to describe three dimensions I use X Y Z and then W P Q R and these other symbols literally I'm not joking and using those other coordinates I and anybody who works on this subject can understand in mathematical terms those extra dimensions and that's how we do our analysis you know do we understand that at the level of intuition that we understand these dimensions No so intuition intuitive understanding maybe not mathematical understanding yeah I think so thank you thank you very much [Applause]

Channel: Linus Pauling Memorial Lecture Series

Views: 70,402

Rating: 4.6458015 out of 5

Keywords: quantum mechanics, cosmology, big bang, parallel universes, multiverse

Id: 6tgMQJSxB5k

Length: 92min 1sec (5521 seconds)

Published: Sat Oct 06 2018