Renate Loll on the Quantum Origins of Space and Time

it's an incredible privilege visiting a community where a talk on the quantum structure of space and time fills an audience of this size Wow so it will be my task for the next hour to give you my view on space and time and the micro structure of it and well as any good lecturer I give you the punchline to start with so you can rot off happily so basically I'll be treating kind of three different subjects here first I'll start to explain to you why we physicists also interested in space and time in empty space and type in nothing really so what's so fascinating about this so now we'll try to explain a bit that if you're really interested in kind of getting a handle on space and try and possibly manipulating space and time you actually need to understand the quantum structure that underlies kind of the classical space and time we are surrounded by and we'll also as part of this adventure we'll take a trip down the wormhole as you'll see and then I'll also tell you how much we actually know about the quantum structure of space and time and what we can actually hope to understand now I always like as a warm-up to start kind of outlining the vastness of physical scales we are interested in in physics and then more specifically kind of what I'll be zooming in on tonight now here you see this yellow line it gives the rate of scales we are typically interested in in physics now in order to fit it all on one line we use a special scale which is given in powers of 10 so what does that mean if I advanced kind of one little unit along the scale I always multiply by a factor of ten and you could imagine you know sitting down with your microscope he also you turn up the resolution by another factor of ten by another factor of ten so now if you look at our entire universe the phenomena we'd be interested in would be ranging from all the way from ten to the twenty six meters and I've spelled it out for you there it's the one with 26 zeros behind and that in meters all the way down around one meter that is ten to zero to incredibly small units where you subdivide one meter and you get two units the minimal unit looking at is 10 to the minus 35 meters and there you have a zero dot and then you have thirty four zeros and one one so this is kind of the vastness of physical scales we are interested in now physics or what we're interested in physics can often be characterized by a specific scarier looking at so a specific scale is associated with specific physical phenomena and there are sets of laws that are adapted to that scale in which you want to describe so what characterizes the biggest scale of 10 to the minus 26 meters it's the scale of our visible universe so that's kind of as far as you can ever hope to look with our eyes with our instruments and what you see there on the far right at the top is just a picture rendering of the the micro as a Cosmic Microwave Background now you go to small somewhat smaller scales and of course you see all the Galactic kind of the phenomena we see in our universe as two physical ones so you go through kind of spiral galaxy smaller galaxies and all the way till you come to the size of the solar system our own earth and down there that's us 10 to 0 meters that cute little baby and then we go to the centimeter millimeter scale and then we come at about 10 to the minus 10 meters that's the scale of atoms atoms of course have a sub structure so you zoom in onto the nucleus of the atom and the particles that make up the nucleus then you get to the structure of kind of protons neutrons as illustrated here and their constituents which are quarks and gluons that want them together and to about 10 to the minus 90 meters which is a scale which we can probe directly with our most powerful particle accelerators like the Large Hadron colliders LHC's that's being built in Switzerland currently now what I'm interested in is yet far beyond that scale that's the so-called plan scale and what it happens there so that's really the scale of 10 to the minus 35 meters you could also characterize it as a scale for which is two can apply for funding with your average funding agency so that's really what I'm interested in now to rephrase the question about what happens on very short scales you could say well if I I know roughly what the world of my elementary particles is about this is very well described by the so called standard model now I could kind of zoom in there with my microscope and I could really ask now what's in the empty space in between those elementary particles is that nothing or is there a structure still is there something I mean there must be something I mean the nothing is all so far as physicists is an anathema so what is there and we already really know from good old 20 century physics that well nothing kind of empty space contains much more than meets the eye even if you don't go quite to as small scales as I want to do today so this nothingness it's known to have already an intricate and interesting structure from the point of view of both quantum theory and the theory of space and time now of course again to claim to be doing to be working on the structure of nothing doesn't quite sound so fancy so of course he immediately gives us a much better sounding nary causes the back heel now we study the structure of the vacuum and as part of set and to give you a kind of a review of how our understanding of empty space and time has developed I'll give you a very condensed introduction of space and time empty space and time and it's really the briefest history you get anywhere so we are hot in pursuit of a theory describing the quantum structure of that empty space time and again what we believe is behind this I mean the series are to describe it on these smaller scales will be a theory of quantum gravity now how come quantum and how come gravity I mean I was just talking about space and time how are these things connected okay let us backtrack a little bit to the world of classical physics so this this is a world of Newton and really the world of cluster mechanics and it very much accords also with our intuitive view of what space and time is all about so here you see Newton and well the great thing one of the many great things that Newton realized was that there is a connection between the Apple falling from the tree so what makes the earth attract the Apple so it falls down and what's behind a planet like the moon surrounding the earth so what the two things that are kept together in orbit both of these happens through kind of gravitational forces that act between all objects that have a mass so here it's the earth attracting the Apple and really the very same fundamental laws underlie the motion of the Moon around the earth now what was Newton's worldview and what was the prevalent worldview also within physics for many hundred years following Newton well the universe is made up of space and time space is just there it's like a continuum it just happens to be there it just sits there like a big vessel or a stage and what ever ever interesting phenomena there are in physics like gravitational attraction happens in that space but space itself doesn't take part in the action time is something that's separate from space time is a universal clock that just ticks away for every observer no matter where they are no matter how fast they move this is called as a universal time of classical physics and then there is yet something completely different apart from these two aspects of nature which is gravity the rotational laws that describe the phenomena I just described so what is important to remember here is really that space and time they're just they're the universal there forever unchanging now this changed very radically in the last century with what I'll call an Stein's double revolution now the first part of the revolution goes back to 1905 and with what deliberately I've chosen here a picture of Einstein as he was then he was 26 years old when he came up with the theory of special relativity now what does that say it says well you cannot really consider space and time as two phenomena that have nothing to do with each other on the contrary you cannot draw a sharp distinction between what is time and what is space what's the ultimate reason for that the ultimate reason is really that the speed of light is constant and finite now what does it immediately imply this seemingly well trivial the null observation it implies that two observers will in general not agree on what it means for two things to have happened simultaneously because imagine you know you have like two light bulbs you stand in the middle and two light bulbs they go on at the same time now for you but you see them as going lighting up at the same time but for an observer who stands over there she will see that light bulb lighting up slightly earlier because the light has had to travel a shorter distance to hers and the light coming from that lamp so already the two laws will not even if it's just a tiny tiny difference not agree on what it was that happened simultaneously and if you spin this further well you come to the conclusion that you have to talk about space-time a four-dimensional entity that contains both space and time on the other hand another aspect has not very much changed compared to the Newtonian point of view namely this is still a kind of an unchanging entity now you don't have separate space and time you have one space-time but again it's something that just sits there it's a stage and it doesn't take part in the dynamics of the theory of physical phenomena now this changed very very radically with 90 the advent of so-called general relativity in 1915 now we see is still very youngest looking Einstein his tongue is still red ought to be very ordered hairstyle and one should of course also say you see the age at which he came up there was a theory of special relativity that is like you know in nowadays terminology during his first postdoc and it's amazing physics for part of it she was awarded a Nobel Prize later what he did in that year now what is general relativity all about it really it takes a radically new and different view of space and time now it unifies space time and gravity what it in fact says is that that is space-time comes with a structure the structure we call curvature and that structure is a local structure so it can change from point to point in space and time and we feel this structure as gravitational forces so we encode gravitational forces that massive object objects with mass and energy exert on each other we encode those in the structure of space-time itself now why can one do this one can do it because gravity is universal so nothing and no one can escape the forces of gravity you cannot cheat yourself away from gravity so there's not no escape so if you have a mass or an energy then you will exert gravitational forces on your surroundings and conversely whatever is in your surroundings and has mass or energy will exert gravitational forces gravitational pull on you and since it happens for for everything and everyone in the same way you can ascribe this property to space-time and what you say is well space-time therefore is not just a structuralist continuum that just sits there and doesn't do anything but it itself becomes conversa actor it's no longer just a stage on which things happen but it becomes part of the physical dynamics the physical process now this is all just academic ideas no the real world really seems to be like that so how do we know how do we understand that our very own space time space and time is curved and not just flat and structureless well you start with a little exercise you come back to that also later imagine now for the purpose of illustration you are a two-dimensional being so your little ant but your plat flat so you cannot see the third dimension you live on this two-dimensional surface now how can you distinguish between sitting on a flat surface two-dimensional like a two-dimensional sheet of paper and on the surface of a round sphere by not stepping outside into the third dimension and seeing aha well this is a sphere now how can you when you're just living inside this two-dimensional surface how can you make measurements that would tell you how I must be secretly on a curved space it's very straightforward really you draw a large triangle like indicated here so you connect three edges by straight lines and then you go away and measure the angles between each pair of lines and if those are add up to 180 degrees for each triangle you can draw on the space then you can be sure that you're sitting on a flat space so that's a picture on the left however the result is different when you're sitting on a sphere because then the angles will be larger than 60 degrees each and then that you can recognize just by making measurements within that space being that little and in 2-dimensional flatland you can conclude that you're sitting in a curved space in the very same way it works in our own four-dimensional space-time by just making measurements of length and sending light rays and see how long they travel in in there straight lines we can make come to similar conclusions and this picture here on the right illustrates is effect again in a kind of cartoon like way reducing everything to two dimensions so what you see here on the right is kind of an image an artist's image of deformed space-time through the presence of a very heavy object say a heavy star so this object sits in the center it it curves space in time and as a result any object that could be a comet or in this case a light rays that passes close to it will get will deviate from its straight path and the result you get here it's something phone calls and gravitational lens so actually the situation that's depicted there is imagine you have a very bright object that sits somewhere in the universe and the light which is you which is your eye from very far away now imagine that there is a very heavy object somewhere on the way in that path of light say a heavy galaxy now what will happen is that the light the light rays had come from that bright object will get focused around this heavy galaxy and they will appear to your eye as coming from different locations and this is exactly kind of what what's what's drawn in this picture there on the right as image one at image two and this is not just mere theory down there you see a picture taken by the Hubble telescope of a gravitational lens well it's a specific gun it has a name from codename there and what it is it's really light of a quasar that is eight billion light years away from us and it's being focused by a galaxy that sits in between the light way the pathway of the light and you see multiple images and of course the geometry of these images depends on the mass distribution and the shape of this intermittent galaxy but here you see directly gravitational forces at play and how they can be translated in curvature of space-time so curved space-time geometry is being reinterpreted as gravitational force so this brings me kind of to the end kind of the first part of my talk which is you know let us summarize so we've discovered that empty space and time is actually an entity that's of intrinsic interest to us especially to us physicists because it has intricate local properties and we can probe these properties for example by traveling light rays or studying objects that move in such a curved background now how a piece of space-time curves and moves depends of course on what kind of objects massive and energetic objects sit in it and where they sit in it and it is described quantitatively by the equations of the classical theory of general relativity said was first written down about Einstein so that's what we call the classical theory of gravity in order to distinguish it from quantum theory which we'll be getting to and what you see here is this beautiful illustration of course that's not real space but you see this is a picture of a simulation where to very heavy stars circle each other kind of before they fall into each other and they give off kind of a gravitational wave and that is a dynamical phenomenon that is also described by general relativity and we're looking currently with gravitational wave detectors they're trying to pick up such signals they haven't quite managed to yet because they extremely extremely weak but everyone believes they're there and where you should be seeing them any day now but that's not that's not not my wife that's not my that's not my length scale so of course this is not the end of the story because otherwise I wouldn't be standing here in front of you now why is this not the answer Einstein's classical theory is really in a specific way incomplete so it cannot in principle answer all questions we can ask about space and time about space-time rather so which questions can it not answer let us go back to the in image I started off with the image of the vastness of the physical scales now where do we know that general relativity gives a very very good description we know that this is true for the very large scales so there's Astrophysical the cosmological scales so that was on the right branch of my of my length scale and really their gr general relativity I should rather say is very very well tested and we can even test the theory or at least aspect of the theory down to about a millimeter range now what happens below that well of course then we run into phenomena that are on an atomic and subatomic scale now what about gravity their gravitational forces well seemingly they are entirely unimportant in that range of length scales why is that well because there are other fundamental forces namely electromagnetic force and then the weak and the strong nuclear forces which are so much stronger than gravity that well gravity gravitational forces are seemingly totally unimportant there so and this holds really all the way to kind of particle accelerator scales and for some scales beyond that so there is apparently no real trace of gravity and we don't have to worry seemingly about gravity however of course you can ask yourself now the the gravitational forces are so much weaker now how how does the story continue when we go to even shorter scales and now one has to backtrack a little bit and say well all these other fundamental interaction I've just mentioned they are in their essence they are not classical series or not described by classical equations of motion but that quantum series so that's kind of a general rule which we seem to understand about physics is that any self-respecting theory is really a quantum theory now what means a quantum Zee what's the difference between a quantum theory and a classical theory well I Ellis traited here why this picture these two kind of sketches that pertain to atomic structure I've taken a helium atom so that's a very simple atom so it has two protons and two neutrons in its core and you see it has two electrons so the electrons are of course electrically a negatively charged the protons inside are positively charged so overall the thing is neutral and there is something one will call the classical model of a helium atom where you have this positively charged core and then you have your two little electrons they zoom around you know like planets on orbits around this core now unfortunately that doesn't give one a very good in the accurate description of the helium atom or any other kind of atom for that purpose now why is this well because exactly you come to very very small scales where you cannot apply any more kind of the intuition you have developed on much much larger scales of things being in a precise place with a precise velocity you know at any given point in time quantum simply doesn't work like this so a much more accurate and better description it turns out is the one that's given there on the right so you still have two electrons now what is now what is now drawn around this nucleus is what one calls a cloud kind of a probability cloud for these two electrons what does it mean the darker the shade of grey is the greater the probability to find one of the two electrons in the region of space and that turns out just to give you a much better description of how this electron actually sorry how how this atom actually behaves so we get substituted exact kind of classical looking orbits where everything is just in you know in a specific place at a specific time with a specific speed to such probability clouds of things and that's an idea we'll also meet again later when we're talking about the quantum structure of space and time because you have an idea of what it what the classical structure of space and time is all about but when it comes to the quantum structure you'll expect that well it will become kind of quantum fuzzy so space-time will not be in a specific state of having a specific curvature but it will kind of quantum fluctuate just like the position of the electrons in this atom a quantum fluctuates so this is what we are after now the reason why quantum effects for gravity are expected to occur at a much much much smaller scale than those say for electromagnetism and the nuclear forces is exactly because gravity is just so much weaker so you expect really kind of quantum effects to become relevant on a much much much smaller scale and this is exactly what gets you to this exotic and ridiculously small Planck scale so this is what everyone's been looking for for the better part of the last 50 years a quantum theory of gravity and just rephrasing what I just said it must capture something like the famous Heisenberg uncertainty relations that exactly for the case of a particle say I cannot measure with arbitrary precision its position and its velocity the two things together cannot be cannot be determined with arbitrary precision now you might ask yourself okay what is our expectation kind of qualitatively what will space and time look like when I now zoom in with my imaginary microscope to this tiny tiny scales netted near the plant scale well people have been waving their hands like in just the manner I'm doing now for 50 years and they have been drawing little cartoons like the one you see here on the screen so one says well obviously space and time cannot be a structureless continuum like we see it you know on everyday scales so it will start quantum fluctuating and since I told you what is the structure of space and time what its curvature kind of the way its bend and curved well we expected to become subject to quantum fluctuations so what might happen on very short scales well first you might see some ripples when you zoom in with your microscope and when you then really really get close to the Planck scale well anything might happen so people say oh space and time are ripped apart or they you know they they they develop not say develop little little wormholes and all manner of things that might happen well and a name for that that has been coined in the 70s I believe is space-time foam and well this is an artistic impression drawn by one of my students now obviously we are physicists and we don't are not contend with just drawing little pictures like that you would really like to understand things quantitatively so we really want to write down sets of laws that pertain to whatever structure sits there it's a plumb scale from which we can then derive other things maybe make predictions on what happens on larger scales and we are also really driven by some fundamental questions that a theory of quantum gravity would hopefully help us answer now here are some assorted questions that keep us awake at night occasionally now of course physics has worked one thing that has worked extremely well in physics is reductionism you could say it's sometimes used as a pejorative but well this is really a lot of physics works so you try to reduce something you see on a larger scale some phenomenon physical phenomena - you try to explain it from smaller constituents and how they interact on a smaller scale and really what one would also dearly like to do for space and time is to say aha well actually space and time on the smallest scale imaginable let's say that the Planck scale consists of little let me call them atoms of space-time for lack of a better word now let let them interact in some simple manner according to quantum laws of motion and then let's see whether that can explain what we see and perceive on larger scales so is this possible so can we really reduce the problem like of why our universe has the shape and structure it has can be really derive this from more fundamental ingredients laws of motion so that's really the search for the microstructure of space and time and so can we explain something like the shape of our own universe that is so called digital universe I get back to what this is later on in the talk of course another interesting question is to say well maybe we are just made of course we our humans our human intuition is just made to understand and interact with things that are on our scale like okay one meter millimeter okay we can grasp easily with our intuition but maybe when I go to something as short as a Planck scale well there is no notion of space and time it just been substituted by something completely different which I find difficult to imagine so it said true do we have our maybe space and time and the notion like causality as is just emerging properties that only are meaningful on everyday scales and maybe still it and it see scales but not when you go down all the way to the Planck length now I've singled out the partial space and times this notion of causality causality is really something that is a principle that's intricately woven into all of physics in stately briefly it just means that course precedes effect so for anything that happens now there was a course and that course was in the past so there is a definite notion of past present and future and we we know nothing in physics that violates his principle but of course again that could be just something that happens to be true on the large macroscopic scales we are able to probe with current technology maybe if you go to much much shorter scales that will no longer be true maybe they can have a causal things happening at the Planck scale of course and the difficulty would be if you have a model that works like that to show that nevertheless what comes out on macroscopic scales is still well in tune with what we know to be true which is causal kind of macroscopic and physics now more intriguingly for the lovers of science fiction among you of course I might also be interested in perhaps manipulating a space and time and as it will turn out one really needs to understand quantum structure of space and time in order to be able to do this so this would in in specifically cover a notion like a wormhole or space-time foam which I have already drawn now this cartoons on the right again illustrates kind of our qualitative expectations of what might happen to a piece of empty space and time when we zoom into it as a plan of scale there a busser you see a little portion of quantum foam now to be something more somewhat more specific let us talk about wormholes now what's the wormhole wormhole is a structure of empty space time so let me define it for you that's not straight taken from Wikipedia has some input for myself so I give you two I give you two possible definitions a more technical one that says it's a solution to the classical Einstein equations so it's something that is in principle described by Einstein's theory of classical general relativity and it describes something like a shortcut it can describe a shortcut in space-time that is and a situation like it is illustrated by this figure down here at the bottom so again we already practice a little bit becoming two-dimensional so our universe our three-dimensional spatial universe is here just described by a two-dimensional sheet of paper again it's flat well you can figure out for yourselves why this bends there on the right is actually not detectable not visible for the two-dimensional little arms that crawls along there but that's a different story altogether now this illustrates kind of a region in the universe close to the earth so the earth is LZ on this other part of this machine and 26 light years away sits Vega no Vega is a very bright star on the night sky one of the ones it's closest to us to our solar system and and well one of the closest a mere 26 light years away and of course if you travel there by conventional means it would take you a very considerable time to get there now a wormhole is an ingenious thing it's a shortcut of course we don't know it's it's not know to exist but theoretically possible imagine there was not a little throat which you could travel down very close to earth which was much much much shorter than those 26 light years and you came out and oops says Vega just in front of you now that's a wormhole and well there's a named wormhole is there for obvious reasons and the big question is now well this is allowed by I've stated to you that this is allowed by the classical equations of Einstein's theory but we are not really aware of such wormholes kind of popping up here and there and having been around for the modern space traveler now of course now if you want to convince say the head of your Institute that wormholes are a really really cool and useful thing to work on of course a promotional video can say more than a thousand words so I will now take a couple of minutes to show you the beautiful uses of a wormhole in almost real life the wormhole in the video that follows in order for you to appreciate what's being shown I need to introduce a few elements that are shown in this little movie so what you'll see is a wormhole so this actually is essential kind of ball in the middle there and the green yellow orange lines they are only there to guide our understanding of how space is curved in this specific curved speed of space-time that makes up a wormhole so you'll travel down the wormhole and these lines given by these this yellow and greens straight we're almost straight lines they are the shortest lines so web light will travel in the space and since it's a very very curved space the shortest lines really have completely different properties from what we're used from from straight shortest lines in flat space so what you actually see in in your travel we'll move into the wormhole and we follow the green lines if this was flat space of course the green lines they would meet exactly at the center of this yellow cube but this is a wormhole so you'll actually see that there will be a sequence of three cubes nested in each other so the outermost is a yellow one then the throat of the wormhole is a cube where you see already its edges are also deformed when you look at it from the outside and then there will be yet another cube the nested inside that orange cube which is blue but once you get to the blue one you'll see ya at the other end of the wormhole and things look entirely symmetric there so from there it would appear that the origin the yellow cube are actually nested inside each other now these bizarre properties of course only possible because this is a space that is just extremely curved so it differs just very very much from flat space geometry you're used to okay now ready go now the purpose of this is imagine you're a member of the as a physics group in tubing and universities that's where this movie was made and while you're thinking of it's lunchtime and you think oh wouldn't it be lovely to go to the beach say in northern France ah here's our wormhole here it is and you can already see inside the wormhole you get already a distant view kind of of the sand dunes on the coast but you know let's have a look around this drag campus like there are many here's our wormhole as I said you really the wormhole itself is this thing in the center what you see there is kind of the distortions of the light these rings they really originate from the very very strong curvature that this thing has now you're falling into the wormhole you're following the straight green lines and the orange cube you see it's also very much deformed already now it's the slow descent of the wormhole now you're following it even further you see the green the green ends they sit perpendicularly on yet another cube and now when we exit this cube we see we've reached the other end of the wormhole so this was an extremely short trip very handy for lunch breaks and now we are exiting the wormhole and looking at it from the outside well the beautiful cells use obviously now get out your lunch packet and looking back we see again it's a place where we started from so the University campus now we're flying back and you see now the blue cube is the outermost cube you're now going back through the wormhole and you'll stop a little bit now in the plane of the throat and you see the bizarre thing is that the cube the orange cube now fills lies in a plane and how can that be is the three-dimensional object well this can just be because this geometry is so curved now you're already looking back at two billion well the ground you're having you're looking having a little look around here's the building so we are making a little circle above the throat of the wormhole so you see again the outer cubes and on the on the German end and the distortions and this upside down view originated again because of strong curvature properties this wormhole has okay one last tour and back we are now if that doesn't convince the head of your school then I don't know what does and of the desirability to be able you know to mold space and time like this now here's our little one more of course this raises not a number of questions so since well I presume none of you has recently come across such a nice contraction the question is why why as it is so which part here is fact and which is fiction so it's a fact part I already mentioned to you so the geometry by this is really described as a solution to the classical theory now we're now where's the snack well first of all the classical theory doesn't describe the birth of wormholes I mean how could they come about if they we're not maybe born back at the beginnings of the universe where could they come from we have no idea the classical theory doesn't describe this process for you secondly it turns out that in order to keep such a wormhole open you need something very very exotic you need a very exotic form of energy called negative energy and you need larger well relatively large amount of it and it's if if so it's negative energy so that's not a substance we know of and it needs to have a density that's the billion times higher than that of a neutron star so the neutron star is really kind of the densest material we know of in our universe so very very highly compressed kind of neutrons now here you are asked for a substance that has negative energy it has a density that a billion times larger than this I mean this is just forget it it does it doesn't exist and also of course this energy needs to have also another non-trivial property it must be such that it doesn't interact with you try to travel through the wormhole because if it does and so therefore what we can already see a couple of reasons for why we haven't seen many of those around now there is a very very interesting question that poses itself to physicist so even if one is much less ambitious so one might ask okay maybe such a you know large sized wormhole is not very realistic let us make it very very very small first of all let us say well that's not worried about where it came from that doesn't zoom it just there let us make it very small and could we make it just so big that some tiny you know light ray or tiny particle Kutcher's flows fly through it and that would be actually a real big problem now why would that be so because as one can show relatively easily this kind of Gedanken experiments the presence of a wormhole usually implies via the ability to travel backward in time and the ability to travel backward in time unfortunately is in conflict with causality so this beloved principle of causality that apparently you know all physics we are aware of obeys now why is it so well one way of phrasing it is to trace the so-called grand follows paradox I don't really like to use the paradox because there's a lot of unnecessary violence in it so what what is the grandfather paradox yeah imagine you have a time machine and such a wormhole can serve as a time machine and you can go back in the past now what can you do when you are back in the past well you take your hand gun which you have you know at your ready and you shoot your grandfather before he meets your grandmother and of course that is a slight problem because it seems that you wouldn't be able to be born you have kind of you have messed up the initial conditions so there is a logical contradiction that arises there if you want to stick to our standard notion of causality so it's really so if what I want to emphasize if there was a possibility to create a wormhole even the tiniest tiniest wormhole which would enable you know like a little particle piece of information to sneak through it immediately most likely be in trouble but very interestingly you could of course asked well is there anything let let us study this problem your closer let us try to study this problem with the help of general relativity because general relativity describes to me how space and time are curved and it describes to me also this solution these wormhole solutions now it turns out no matter which way you're pushing the question you always end up with a question that we that cannot be answered within the classical theory alone because it will involve very very very small scales or energies that become larger and larger and larger and they're well simply is a classical theory is no longer valid and something else must take its place and that is the putative and long sought for theory of quantum gravity so to answer the specific question about is there anything in the nature of time and space that maybe would prevent the existence or generation of such a wormhole we unfortunately well unfortunately for some must turn to a theory of quantum gravity now I've mentioned to you already various reasons why we would really love to have such a theory now what do we know about quantum gravity many many research grants have been written and granted but it has proved really difficult to come up with a consistent and quantitative theory of quantum gravity that would answer some or all of these questions not least of course because of the fact that we cannot really by experiment probe these very very short distances so we definitely unlike in other theories you don't have experiment or observations to guide us to what what the right serie might be and that is really a genuine problem here now on the other hand you might take an optimistic view on this you might say okay I cannot directly look at the Planck scale and probably in the foreseeable future I will never be able to do that great that is that means kind of a free ride free lunch at the Planck scale you know I just invent my theory at the Planck scale and who are you to tell me that it's wrong and you invent your own theory you know you you cook up some ingredients you let them interact in some nice way you know you choose strings you choose little billiard balls and you let them interact in some way and you just claim this is a correct theory of quantum gravity at the Planck scale and I would have a hard time contradicting your journal as long as there are no tools to extract or to extrapolate from some microscopic dynamics your postulating to exist to what happens on a much much much larger scale so the problem is you cook up your quantum theory on very short scales with your favorite ingredients and the problem is then how do you really quantitatively extract what it tells you what happens on much much much larger scales so you have here your piece of quantum fluctuating space-time and what you want to do is then cannot zoom out you know there's a resolution of your microscope and look at it from a distance and then say how's that really reminds me of yeah I was based on continuum which we see around on a large scale so that's of course something you want and unfortunately there are not so many tools available that would enable us to do that so really I would say even I mean the sociology of this subject of scientific inquiry has been to some extent dictated by the lack of direct experimental evidence to guide us and even the lack of being able to predict what your own model or theory predicts to heaven on large scales but unbowed but fortunately we have been introducing and using for about the last 10 years some computational tools that to some extent enable us to extract macroscopic information from microscopic models and well I term that that kind of movement or that kind of set of ideas that people have been following in recent I attended a new conservatism in quantum gravity because the answer is to use really as fuel agreeance as possible so to not introduce kind of large arbitrariness and then kind of try and extract at least kind of two to first approximation what do your microscopic models really predict on large scales and this is it or compatible what we know has to be true say on everyday scales now of course you'd be justified to say well how do you go about constructing the cereal in the first place I mean where you know where do I even start so there's a logic of how one proceeds is as follows or how one ought to proceed in my opinions as follows so of course to start with we have well-established series that are well tested and known to work very well on large scales so first of all I've talked about general relativity comes a classical theory of space-time and how it's curved and then of course we have quantum theory or more accurately speaking quantum field theory so that's what describes the interactions that underlie the interactions of elementary particles so really kind of most of the physics we are ever interested in apart everything apart from quantum gravity so for one can then try and do is with as few extra ingredients as or kind of taking just all the most fundamental principles which we know to hold on large scales and adding as little as possible in terms of postulating new ingredients that that should exist in which we haven't seen new symmetries that should exist and we haven't seen so try to be absolutely minimalist built models at the Planck scale and try to do the building in such a way that it doesn't depend crucially on exactly what ingredients you choose and exactly how you let these ingredients interact so what you want to have you want some robustness to your models in order that not some arbitrary input which of course you have to pull out of a head determines what the cirrie tells you in the end because if you had a very very large choice of initial input say at the plant scale and they all give you kind of equally say internally consistent models of quantum gravity well then you would be lost for choice you know there would be such a vast number of series to choose from then that not by any kind of finite number of experiments you could do in the real world you would be able to discriminate one from the other now so that's kind of the idea keep things simple and what has also been found is that there is a very strong condition imposed on such models by requiring them to reproduce on sufficiently large scales the physics that's already known to be correct on those scales and that is Einstein's theory of general relativity now the problem usually being that we don't really know how to extrapolate the might the macroscopic from the microscopic but once you're able to do that with certain computational tools when all of a sudden sees oh wow many of the models that I thought they looked great at the Planck scale unfortunately are completely useless because they don't give rise on large scale to the kind of type of space-time we know to be present there now very concretely how would one now go about constructing such a Syria that can only be extremely sketchy and anyway you know I don't want this to be a technical talk I just want to get get you the flavor of things wonders there and of course it's cutting short a history as I said earlier off on the order of 50 years of quantum gravity research women also has learned from many past failures of things that did not work for one reason or other so let me now zoom in on a specific way of thinking about quantum gravity that a group of collaborators and myself have been developing over the last more than 10 years by now and it's a it's a new theory where causality plays a special role and thus a derisive name it's called causal dynamical triangulation so what I mean to indicate here is that we're choosing we are working with kind of sub planking building blocks they are just imagined I mean they don't believe that space is made up from these building blocks but they just help you to construct this curved quantum fluctuating space-time structure so triangles or higher dimensional generalizations of triangles turn out to be very versatile for doing that and as an aside that's of course familiar to anyone working say in the movie industry or with animation one knows that curved surfaces say two-dimensional surfaces are very nicely approximated by gluing together little straight triangles so we're doing the same thing for four dimensional curved spacetimes you glues them together from little flat straight building blocks in such a manner to create all kinds of wildly curved spacetimes now you glue this building blocks together to get curved space sides and then we let them interact a core due to some simple laws but the most have to be quantum laws so they introduce also this kind of quantum fuzziness so you can no longer say well my space-time has this curvature it's not true it has a quantum fluctuation curvature and it's kind of a probability cloud of things happening so that is very much like what I showed you illustrated to you in terms of this cartoon of the helium atom now what's now the great ingredients that helps us to make further progress from this microscopic model is that we have a computer that allows us to extrapolate kind of macros what happens microscopically so we have this many tiny tiny building blocks interacting in a very complex manner although according to very simple laws on small scales but what you really want to understand is their collective behavior on larger scales and it's it's very difficult something you cannot really do with pen and paper so you really need to simulate this system on a computer and the computer is great it cannot do it everything for you but it can give you a very good idea of whether the model you're working with is a complete failure or has perhaps a chance of being true or partially so the big question is if you switch on the dynamics we have these microscopic reeds with switch on the dynamics you let the computer work out what happens microscopically what do we get now let me go back to my wormhole theme because now we have a quantitative way of verifying two different hypotheses one hypothesis is wormholes are allowed to exist microscopic little little wormholes so those are the ones I was interested in I mean can it say what is the nature of space and time like on microscopic on very very short scales maybe can these are these were motor that classical classically kind of forbidden maybe can they exist does it make sense from the point of view of the quantum gravity theory or alternatively does it not make sense so what I do is I set up two experiments well I left my X by experiments I mean I choose the initial conditions I choose initially agreed Ian and I let the computer work out the consequences so experiment a I use microscopic building rules for my little triangular building blocks again there could be there could be squares it could be Pentagon's it doesn't really matter and the building rules are chosen such that wormholes are both allowed to exist and to be formed there can be of any size so it's not that I put the wormholes anybody I make the rules such that the shuttle they are allowed to be there the second alternative experiment I do everything the same but I disallow for the formation of such wormholes and now let quantum fluctuations run their course here on the right hand side these are examples of pieces of space and with were more so it's just these handles and of course the handles can become very complicated you have lots of wormholes they have handles over handles over handles so that's a piece of space and there's many many handles so what happens well what happens is really quite a big surprise so you might have thought well when I allow wormholes that will really make my space time really interesting right not saying we're having the time travel you know at the back of my mind but instead what happens is that only if I forbid the wormhole all together singles to very very dynamically counter fluctuation but they are not allowed to form only in that case do on large scales do I find a space-time that resembles the four-dimensional space-time that we expect to find on the basis well not just on general relativity theory but on what we see around us now and kind of miraculously kind of the collective behavior in that case if I don't allow these wormholes of these building blocks which I have such trouble kind of describing exactly but nevertheless you can hose the computer that tells me about the collective dynamical behaviors that give rise to an extended four dimensional quantum universe now you might of course say well now what goes wrong for the chaos of wormholes well the interesting thing is either one way to think about this is as soon as you allow wormholes really I mean any tiniest piece of space-time wants to curl up and become its own little wormhole so if you add more and more kind of space-time volume more and more and more it doesn't contribute if you allow for the formation of well most to kind of the growth of what I call the mother universe because this extended things that you want to have in the end but on the contrary it will just create a little handle connecting to other handles and all that will happen is you add more and more and more and more spaced on volume and your universe will never grow it just becomes a tightly kind of knotted ball of wormholes over warmers over wormholes it will never grow and this tiny tiny space has a very bizarre property namely you're basically in one step you're everywhere so and that's the property of a space with a very very large dimension so something to ponder when you're under the shower very bizarre ok now it's very very sad news for the science fiction aficionados and I'm not clearly this is a whitewater tied argument but it turns out to be rather generic so I mean these wormholes I suspect they're just not there so it shows you kind of the usefulness of being able to study these things quantitatively even if you cannot do it pen on paper you use the computer to extract some information without which you would have never been able to understand this it's a phenomenon that's not easily understood it's very far away from classical physics now so the wormholes are ruled out for the moment now what then does the series outwards what does it give me doesn't lead to something sensible and of course the answer is now I call this the self-organized quantum universe just certain circumscribing our ignorance of exactly how it happens that sees fluctuating microscopic building blocks generate this nice large shape now what we find is that the quantum universe we have created very directly in the computer has the shape of again a solution to the classical Einstein equations that is well-known a well-known so-called cosmological solution and it is the descent of space-time that already came up when I talked about classical space times now what is the digital space time does it our space time is really a space time that if you look at any piece of it it expands at an ever-increasing rate so it's kind of expanding universe but the universe expanding accelerated the expanding universe now how can you detect that well if you have stuff sitting in the universe you know like stars galaxies solar systems they will be pushed apart by the seeming force or energy that underlies this process which is often called dark energy so the de sitter space is really the simplest solution to the classical equations of motion which contains a cosmological constant which is kind of interchangeably used for this mysterious dark energy so what comes out of our computer simulations is a macroscopic space-time that has exactly the shade of a digital universe and what is of course in the digital universe really describes our own universe at least in the distant future as far as we can tell very well and also but also kind of closer to the beginning of the Big Bang where you also had a you also had a original time where you got such a accelerated expansion so it's really a very very physical now well that's great news and the first time that this has been derived from nothing but first principles now of course you might ask all right but all you've been doing is kind of read arriving the classical theory you know I told you that it's already a great deal but you probably would like to see more you want to understand the general quantum structure of this object I've created there now we have started making measurements making experiments on this thing that sits in our computer right as a bunch of zeros and ones and one really has to work hard in order to understand what its properties are what its geometric properties are and one thing we've been able to establish is something rather bizarre that if you look at it on very very short scale so that's really was a plank in physics comes in it's no longer a four dimensional object but it's some things that's effectively two-dimensional so it's not a flat sheet of paper or anything like a classical geometry it's more something like resembling a fractal and people you know here who played around with fractals they'll also know that these fractals they are not like classical object so for instance they can have dimensions that are not even an integer one two three but they can have a dimension of one point three eight seven something exists so there are very bizarre spaces that have nothing much to do with classical geometry that have such properties and apparently what we find here on very small scales for our quantum space-time it's just something like this because work is ongoing to establish quantitatively exactly what this stuff is and how we might from understanding its macroscopic structure hopefully derive how say a light ray will behave in such a medium or how a particle will behave in such a medium and pick up possible effects of this quantum structure so that ultimately we'll be able to tie this model to genuine observations or experiments now this brings me almost to the end my talk here's some final thoughts what is maybe most surprising and of course for me as a scientist most rewarding in this subject is said we really have started making quantitative statements and kind of predictions within a specific but was a robust framework and of course we cannot experimentally probe the plant scale but we have kind of a poor woman's substitute which is kind of the phone experimental lab and which are these computer simulations where which are able to extract very non-trivial information about the system which has direct bearing on beautiful and interesting questions like do wormholes and time travel exists of course this comes with a big health warning namely that really all current series of quantum gravity that people are working on currently apart from having to be shown to fit in smoothly with a classical theory still of course have to be corroborated eventually by observation or experiments before they will be accepted as you know part of the physical our physical understanding of the universe now the theory my pet theory my my baby has a very nice property that for the first time it has one has been able to show that from nothing but kind of pure quantum fluctuations one can actually create well in a way kind of explained macroscopic behavior that we are used to that we have seen in the classical macroscopic theory of general relativity and again very rewarding Li that has served as an input for other people to go and look in their own models and series of quantum gravity whether they can really write some of these results and the result of the two dimensionality of short scales for example has been now corroborated with in a number of other approaches and in the best of all worlds it would of course mean we are all on the right path now is it hasn't quite overwhelmed you enough I recommend you a nice popular article on the subject we've written a couple of years ago which has appeared in the Scientific American more stuff you'll find on my website and if you want to travel again through the wormhole and you'll get other really interesting and beautiful visualizations of relativity there is the website I'm giving there and that's me here forever staring through my microscope looking at the structure the quantum structure to be understood of space and time thank you very much for your attention

Channel: TVO Docs

Views: 234,926

Rating: 4.7205129 out of 5

Keywords: TVO, TVOntario, TVOKids, polka, dot, door, polkaroo, education, public, television, Elwy, Yost, Steve, Paikin, big, back, yard, ideas, Canada, quantum theory, Einstein, space and time, physics, science

Id: fv2gBjQ8xIo

Length: 71min 18sec (4278 seconds)

Published: Fri Jun 24 2011

Reddit Comments

[u/eggn00dles]

the wormhole animation is probably the best visualization ive seen of something like this. its also the first.. any other good ones?