Eva Silverstein | Horizon Physics: Cosmology, Black Holes, and String Theory - 1 of 2

[Music] Stanford University bring everybody problem the spring water addiction of dualism the core of our when you are SI TV physics where are reading everything theoretical physicist to tell you what they're basically what they Bromley blister with their cited time what because it's gold are the level was largely been some ways between Scientific American and because it's colloquium what I basically fell make sure I get from you don't Trece procurable I think I do it to our cages very hot but in any case the very we have to go to the solar sorry 25 years ago I think ok must know you for almost 25 years 25 years ago evil is one of the young people who became very excited enthusiastic inspired by string theory and she very quickly became one of the leaders were revealed she's produced a singular body of accomplishments and work in the field almost every area of it and well beyond her field of string theory in fact she's on occupies a rather unique place in that a few years ago she recognized the possibilities and Harriet instinct theory and asking and answering some of the very hard questions about cosmology and today people all over the world are working to find out how to test some of her ideas beaver is a spectacular solid revealed theoretical physics of remain areas and I if I had to guess only guess that's not what we won't talk about tonight inflationary cosmology but I'm not sure it's an air crew of the bacteria the main point is neither tell sodapeta society money that incredible introduction credibly kind introduction I'm very glad to be here I've admired Lenny's efforts at what we like to call night school which is not a pejorative at all it's a wonderful thing and I'm glad to finally participate myself in this I do find inflationary cosmology exciting is and it will be part of part of the story but the theme of these lectures will be unified by the notion of a horizon this is probably something everybody's heard of it's basically a boundary of a region from which not even light can escape and what I'll do is I'll start by describing how this comes about in our classical theories of space-time physics I'm going to start with the Pythagorean theorem and then hope to get to the origin of all structure in the universe in these lectures so we'll see how how well it goes by the way please stop me with questions at any point I'm only using PowerPoint because as you'll see shortly by røde writing is atrocious but I am very happy to write on the board and engage in discussions that's that's a large part of the point so the plan as you can see is to start from the basics to explain what this notion of a horizon is in our classical theory and then move to our goal which is to discuss two very important examples of this in in real physics which are also very interesting and challenging still to us theoretical synthesis and this concerns the two I have in mind are the horizons that arise in cosmology in inflationary cosmology where we get from them first of all a beautifully simple theory of the origin of structure in the universe but even given that if you dig a bit deeper you find that it's sensitive to what we call quantum gravity in a way that I want to lay out very carefully for you in these lectures and discuss some of the very interesting consequences of that which include Believe It or Not a role for string theory and really it's spin off is impaired Oracle science which may surprise some of you depending on what you've heard and sort of the public discourse about string theory but one of my goals here is to explain that carefully and the other place which continues to amaze and puzzle us theorists is in the context of black holes so both of these as I say are observed in nature somewhat indirectly but spectacularly and also challenged us in theoretical physics so let's get started so before I get to the Pythagorean theorem let me just flash what probably many of you have seen at least at this cartoon level that we have a theory of classical gravity due to Einstein that's now over 100 years old in which there's a set of equations that basically relate the geometry of space-time and we'll discuss more about what that means to matter sources matter and light energy and pressure so to speak so there's some what set of equations that roughly speaking in quotations we would write as curvature equals energy and the two targets for our investigation are these extreme situations where you have matter that's so dense that according to this equation a curved space into a black hole with a event horizon beyond which classically nothing can escape the other case where horizons come in importantly is in cosmology where you where the where the right hand side of this equation is a homogeneous source of energy that it's homogeneous in space and nearly homogeneous in time as well and that turns out the source and an expansion of space that accelerates and in that context also we obtain a situation where different observers lose causal contact with each other but let's go back to some basics that will help us understand what this means so some of the principles that we start with in space-time physics classically are the following so nothing moves faster than light particles that aren't subject to any non gravitational forces will they're going from A to B they'll go straight from A to B they'll take the shortest path so we're going to start discussing even though we're interested in these curved geometries which have this property of generating horizons let's start more simply with flat space-time so there's no matter or radiation causing any curvature to begin with but actually let's start with just space and let me indeed start with this equation that I think everybody knows that the square of the length of the hypotenuse of a triangle in flat space is equal to the sum of the squares of the other two sides now let's also notice that we can take this this picture in this equation and we can rotate it we could we can shift it around in space and it just it won't change this relationship right if I rotate the triangle is still true that the length of the hypotenuse is given by this equation okay now let's include time and what we're going to do for reasons that I'll lay out slowly in the next few slides is to take this interval that I that was so far in space just labeling the length of the hypotenuse of the triangle and let's do that add also some other dimensions of space with three three total dimensions of space but also add in time and we're going to include a negative sign there when we write the analog of the Pythagorean theorem for space time in these equations I've written the speed of light C which which in natural units take this this value and one of the important principles of physics is that this speed of light is constant it's invariant it looks the same no matter how what frame of reference you move in so if I boost so to speak this picture mouth of particles will start moving at different velocities but light will always move at the same same velocity and we can understand the reason for this minus sign as related to that in the way I want to explain next but the basic picture here is space and time and light is along this 45 degree line with a velocity that is C the speed of light and massive particles move more slowly than that and they move along straight lines if they're not acted on by some force okay so let's unpack this this idea of a boost which means to move relative to the original frame of reference and let's work with this so-called line element so I've written a delta here as different like we had in the Pythagorean theorem I'm now I'm going to start to use some of the notation that we use in physics normally which is to place up with it's by a de little D but is the same idea so we have we just keep track of one direction of space as well as time one way to think about this is to write this displacement this des this so-called line element in this way so just complete the square and you see that this is the same as that if you just use high school algebra multiply it out and you get the same thing but then you can group it into this DX plus and DX minus and there's an invariance of this equation of the right-hand side that we can immediately see once we write it like this which is that we can stretch X plus by some amount land that we can just multiply it by some number lambda and if at the same time we multiply X minus the thing it multiplies in the line element by the inverse of lambda then the line element D s squared is invariant because we just took it and multiplied lambda times 1 over lambda which is 1 and we get the same thing back so we'll see in the next slide why this has to do with boosting moving relative to the original frame of reference right now it's just a little mathematical invariance that you can see from these equations that fix is this this this generalized distance D s squared so the so this D s squared is invariant as we just saw under this operation and also the light cone which in this language is either X minus equals 0 or X plus equals 0 or both is invariant and remember that was the thing we wanted from our theory the principle we started with was the speed of light is invariant everybody sees it as the same same value and the the analog of the rotations of the triangle in this original picture and so on turns into the invariance under the operation that I just described which in particular fixes the light cone ok so far so good are there any questions Jesus differential yes derivative it is differential just think of it as a little tiny difference thanks any any more questions please do ask ok ok so let's play with this a little bit more let's take the ratio of DX plus 2 DX minus and DX plus so just by dividing the top and bottom here by C DT we get this is the following thing which we now recognize as 1 plus DX DT which is the velocity divided by the speed of light on top and on the bottom one minus the velocity divided by the speed of light so what happens when we do that operation that I just described is that this ratio goes to lambda squared times itself and so the new ratio 1 plus B prime over C over 1 minus B prime over C the prime just meaning the result of doing this operation is given by this and I think to notice about this is so we said that the speed of light is going to look the same in every reference frame and that means we can't just add up velocities the intuitive way and this tells us how this transformation two moving frames really works now if the velocities are small compared to the speed of light so if this ratio V over C is tiny then we can simplify this formula simplifies and if I just fur it's not essential but we can take this rescaling number lambda that I introduced and write it as the exponential of something that's small so this land is very close to 1 we did very little to the system then then this thing does boil down to the prime the new velocity is just the old one plus some shift but if you go to speeds close to the speed of light you see that it it's very far from that and the speed of light is a limiting speed so nothing moves faster than light these equations reduce to the intuitive addition of velocities when they should but but they generalize that to a system of transformations that make sense and that that that realizes this principle that the speed of light is is invariant okay the reason I'm dwelling on this aside from the fact is beautiful physics and it's basically looks learning this at an impressionable age that got me into physics originally so I always share it when I can the other reason to dwell on this is is the fact that these horizons that we're going to be interested in have have a lot to do with the finite and constant speed of light so do ask if you have any any questions it is called special relativity okay should I suppose I should I should yes okay so now we're going to go toward our goal of thinking about these curved spacetimes but you know ultimately related to this theory of gravity where the curvature is related to the energy and so on and what we're going to do then is is take this line element this D s and and allow it to have so in write it in terms of the differentials these small displacements in the various coordinates time and space but allow the coefficients in that to vary with time ins and with space so we write the names don't matter what we write well we write this line element with with such coefficients that are allowed to vary I've drawn here a patch of a curved space where one of the tools we can use is to think about it both globally but also locally where it looks approximately flat and by patching together approximately flat local patches which which work like in special relativity we can obtain the more general theory of what's called general relativity to deal with these varying coefficients now one of the important features that we've just discussed of special relativity is the invariance of physics under the laws of physics under boosts and rotations and so on and also in general we don't the physics is invariant under exactly how we parameterize the the directions in space-time this T and X and so on so we can change our parameterization of those directions without changing physics okay so in a locally flat frame we just go from A to B in a straight line and there is a theory of minimizing our distance in a curved space-time by basically tracking these flat spaced regions that appear locally and within each of those the system goes in a straight line altogether the motion is on what we call a geodesic which is the shortest distance in the curved space-time geometry is essentially taking this line element and finding an extremum of it so we minimize the distance basically no discussion of special relativity and it's passing to general relativity would be complete without the equation e equals MC squared which sits here so the energy is related to the momentum in the mass in this way locally and the momentum which in classical physics that you might have learned in high school would just be MV has this extra piece that that blows up as the speed of light is reached and similarly for the energy okay so just a little tangent on what what we mean by curvature a little more formally so one thing to keep in mind is that although it's convenient in our minds to think about some surface as embedded in a higher dimensional space the notion of curvature that we are using that we're interested in is an intrinsic one it doesn't depend on an embedding into entire dimensions so for example if you take it's basically a measure of how if you have one of these line elements with these general coefficients as you move around the length change and and it's basically how the change in the length change it's a so-called second derivative of these coefficients that describe how the line element varies in in space and time here I've just written it in a two-dimensional space but the idea is more general and in space-time bringing time back in a nice way to think about it is that curvature can take to initially parallel trajectories which would just always stay stay separate from each other in flat space-time and cause them to move apart or move together and will be particularly interested in this picture I flashed earlier where the space-time is undergoing an exponential expansion and the trajectories move apart so dramatically that they lose contact with each other okay so that's the kind of distinction that we want to get to in flat space-time if you think about it an observer that's life script for observer oh if they wait long enough they can capture signals in light labeled by this label gamma from from anywhere if they wait long enough so like if this observer only waits up to this time time is running upward in this picture then they don't see what what's out here that's a bit longer they do and you can easily convince yourself that everything is in causal contact in flat space-time however if you if you inject an infinite amount of energy and accelerate some observer forever then they can actually lose contact with with light rays from other parts of the space-time that's a bit artificial because it does take an infinite amount of energy to do that but it's worth keeping in mind as I say well we'll be interested in the situation where the curvature of space-time which is sourced by matter and energy does that for us it's not an artificial thing it's it's automatic and probably the easiest geometry to think of that does it is in the case of actually real-world interest in cosmology very early universe cosmology where the space expands exponentially okay and here's I've been saying that inwards but here's the line element the DS corresponding to that we write d s squared as minus DT squared I'm dropping the C now this is something we we professionals do because we're lazy but we remember how to put it back in and and and then we have the part that comes from the three directions of space but the coefficient function is growing exponentially in time okay so that's a relatively simple version of this thing where we can sprinkle in these space time-dependent coefficients and this exponential function means you multiply by a certain number every have you shift in time and by a certain amount you multiply by a number greater than one each time so it's exponential growth which i think is probably familiar to everyone but ask otherwise so in that situation the observer just gets moved along in the space-time if they just sit there they and I should have drawn another one nearby say this one goes that way this one goes that way they're just sitting there in this in the space in the space but but they get pulled apart by this exponential expansion of the space and the function of time and so they they lose contact that this ray of light just can't get there by the way I should probably emphasize that you know this question of whether there's a horizon actually depends on what happens in the asymptotically far future which none of us know so it can be a notion that kind of arises approximately or for a finite time it's a little bit mathematically it's only really well-defined if you know it's going to happen arbitrarily far in the future but it's still a useful notion even in the real world where we measure things you know over finite time periods and so on and I'll I'll try and make that clear as we go on okay so this is this is the first and probably easiest example are there any questions - oh good thank you for asking so this is just a parameter it's called Hubble and you can think of it as well let me actually there's this there's a slightly more general way that we write this kind of vinyl that so let me Utley do that so the s squared equals minus C squared DT squared plus a of T squared DX squared plus dy squared plus DZ squared right now what I took here is a of T equals e to the HT and H is here meant to be a constant when it comes to the this early universe inflationary theory and beyond we will discuss what we know about this but for now just take it to be a constant has units of energy or inverse time or inverse inverse time and in the in so just anticipate a little bit we have a lot of evidence that there was a phase like this in the early universe and this parameter H could be as high as the so-called grand unified scale which is you know 14 orders of magnitude higher than the scale of particle physics that we measure directly but it that's what I'm saying yes in the very early universe we don't know how big it was there's a there's a range so I'm going to get I'm going to discuss this quite a bit but for now it's just a parameter in fact pretty soon we'll get to one of those Einstein equations that got determined that they'll write that down for you and since we're on the topic I could I could also say that there's a more general version of this where where there's a function H as a function of T which is the time derivative of a divided by a or in our normal notation a dot means a time derivative so more generally there's a function Hubble that describes a more general time evolutions of this expanding space and and we often see H of T which means a dot over a now you see why I'm using slides but I hope that that helped are there any question yes oh well the light just it follows when it does the correct statement of what the light does is that it it always has this D s equals zero so it's possible that I didn't draw it correctly in this in this diagram we often make a transformation in which it's always going at 45 degrees but the equation that solved this D s equals zero any other questions okay okay so we were already doing this please I just went yes I'm struck by the fact that there's the regular horizon which requires infinite energy yeah we're in an expensive expensive extending universe you don't need people as long as you do because then it's just distributed over all of space so it's infinite because you ultimately have an infinite volume you might always have in it I mean it depends on the topology of space also but um right well one way to say it I think to get better at your question is suppose you we're trying to work in flat space-time but then you injected all this energy to make this observer accelerate well then you better at some point you better include the effect of that on the geometry itself for example so you have to be careful about things like that having said that there's a sense in which the the horizon very near a black hole you know is like a Rindler horizon in a sense that for an observer to stay outside of it they have to they would have to accelerate but the curvature of the geometry makes a difference and we'll we'll get to not in fact we were coming to this on the next slide which I can now show you so so here I'm just trying to share with you a little bit more of the of the detail of this curvature equals energy type equation it's a it's actually a set of equations but one of them is is one that determines this functions H of T with that being the left hand side related to the curvature and the right hand side is the energy density in units of a fundamental constant called the Planck plunk mass which putting in all the constants back in their full glory is it squared is is inversely related to the Newton concept the thing that determines the gravitational force in terms of energy scales it's it's gigantic you can also think of it as the mass of the lightest black hole and I'll say more about that later but anyway the equation that generates a of T through this this equation how it does have this exponential solution a is some constant times e to the HT if the right hand side is constant if it doesn't vary in time or in space which i've assumed here that it doesn't vary in space then we get this exponential as a solution so this is kind of a global picture of that space again light razor have 0df and you can ask what how to think about the physics just in a patch of the space-time that an observer has full access to now I'm not going to answer that on this slide but but what I want to show you and this I haven't derived this for you I'm just writing yet another formula for a displacement DF and you'll see you'll see the pattern as we go but it turns out that if you take them before remember I emphasize that with these with these formulas for D s like this one it doesn't matter how you parameterize the space and time Direction you can you can redefine them and still get the same physics out and and there's a redefinition which I'm not explaining so don't don't feel like this should be this formula should should be clear to you I'm just going to tell you that we can make such a redefinition of variables that we use to describe the system and and characterize the patch that a single observer can see in this way and it has a certain so the direction R is horizontal in this picture basically and the direction T is the time direction and you can see that the coefficient here goes to zero at some finite value and that is where the horizon fits and I'll say more about that momentarily after flashing for you a similar line element a similar formula for this DS that applies to to a black to the black hole case and again there's a there's a radial direction away from the object with these coefficients that depend on the position in front of the coordinate displacements and again in this case there's there's a coefficient of this time direction which which goes to zero at a special all you and that turns out to correspond to the horizons I'm going to say more about that shortly but for now I hope this at least fits within the framework that I've been trying to introduce to you with these these formulas for D F and this is just a nice way of characterizing the horizon in a set of variables that are kind of natural for an external observer okay so for black holes there's a lot to say and we will not be able to say all there is to say about them and even if we did say all that we could say about them there are huge puzzles that remain but let me just make a few comments these black holes are formed again by matter coming together into a very dense region so small that a horizon forms and light cannot escape and one funny feature of them which you can sort of see from this formula that I that I am flashing for you is that it the result of that doesn't depend on the details of what the matter was that went in it just had to be dense enough and then you get this very simple geometry so but there's a lot of evidence that this is just a very macroscopic a kind of coarse-grained description and there's a lot of facets to that but just just at the level of the fact that you could have formed it in many ways so you should clue you in to that and we're going to start when we get to applications with the cosmological case but we'll come back to the black holes given time later on okay so this so we saw this pattern when I wrote for you these formulas for des near horizons let me flash again briefly there was the one in an observer patch in cosmology with this funny coefficient and the one in black holes and with yet another simple coordinate change we can actually write it near the horizon in a simple way as a displacement in time times some function that goes to there at the horizon but goes well actually in these very yeah well it goes to one for outside plus just a simple the displacement in the radial direction and one thing you can see from this is is that there are different notions of time so if you count time with a clock corresponding to this variable little T and you compare it to the time counted on a clock carried by say somebody who falls into the black hole who's whose radial displacement is zero because they just are at their own position then there's an infinite factor an infinite ratio of those two notions of time so one way to say this is that the clock of an observer far outside ticks infinitely many times as some some somebody falls into the horizon another feature of these horizons is you know as you could guess from the fact that light doesn't escape from within them is that the escape velocity for anything is the speed of light at different isin so this is all very dramatic but on the other hand the curvature is turns out rather mild or can be rather mild in our horizon so here's a picture of that let me start with space again so well actually let me start with what well the space-time so I had these coefficients in the line element and I said it went to zero at the horizon if you work it out it goes to zero like a quadratic function it goes to zero in a fairly simple way and this line element describes a geometry which actually doesn't have any curvature the corrections to this that that pertain further away from the horizon contained the curvature and the problem and affect how things fall into the horizon in a big way but when you get close enough to the and it might as well have been Riddler space and it's not curved now there's a spatial version of that that's maybe a little bit easier to understand if you take a sphere like what I've done here the line element for that is simply D of theta the angular direction of this in this direction starting from the North Pole plus a coefficient that's just a trigonometric sine function squared multiplying the displacement in the Phi direction this angle now it's just a simple feature of this don't worry if you don't remember your high school trig but basically this sine function goes to theta itself as theta becomes small and what that describes is simply that these circles in the Phi direction are getting smaller and smaller so even though there's this vanishing of this coefficient in the spatial case this theta this coefficient of D Phi is getting small as theta goes to zero you can see in this picture all that's happening is you've you parameterize things with these circles that are getting smaller and smaller but it's a flat space is nothing really funny is happening there and and the thing with horizons is quite like that just in the space-time okay are there any questions enough yes okay so these this is a great subject because it has it all it's very interesting theoretically I hope that's already clear in the classical theory that I have tried to outline and it gets much more so when we include more aspects of modern physics like quantum theory but another very important feature is that these are real these things are seen in the universe so black holes are now seen in a variety of ways it's always indirect by definition nothing can come out of the black hole so the top thing I'm not going to belabor this too much but I think it's I mean I'm not an observer and it would be a stretch for me to tell you all about it the details of these things but they're beautiful measurements so this toplin is a picture of orbits of various bodies in the vicinity of what is thought to be a black hole in the center of our galaxy and these guys studied that for over a decade and it's all in all fits with it being a black hole recently there was a spectacular discovery of a gravitational wave signature of a pair of of colliding black holes at least again the measurements are quite consistent with the general relativistic predictions for that process in a lot of detail for some black holes that that are inferred to have masses that are 30 times the solar mass there's another project going on called the event horizon telescope which involves emission from black holes which have matter around them more like the one in the centre of the galaxy and so on and so it's just a beautiful subject at the observational level in cosmology we also have spectacular evidence for the kind of accelerated expansion that I introduced just it's thought to occur both in the late universe the phase were getting to now and the early universe which I'll focus on in the cosmological part of the Steve lectures and so in the late new verse it was a spectacular discovery around 1998 where a bunch of different probes including supernovae observed at at far back in the universe and also measurements of something we'll talk a lot about the microwave background radiation and other probes which all fit with a with a geometry for the evolution of the universe that requires a nonzero constant Hubble in the light universe a very small value in that case in the early universe we'll talk a lot about this radiation which comes from the time when atoms forms and we'll see how their it fits also with a period of exponential expansion at a much in a much higher rate in the early universe so these are just kind of pretty pictures which all I'll get to explain a bit a bit of of this one as we go for those of you who came to Leonardo sanatoriums lectures I think this should build from them and I think you if you were there you have learned a lot about this already but I won't to assume that either so okay so so far what I've tried to share with you is the classical theory of special and general relativity it's an introduction to how that works and with an eye toward how these horizons develop and what they mean we're going to be interested in as I said it's beginning in these systems as you know probes of higher energy physics and before moving on I what I would like to do next is explain a very basic feature of modern physics that that will come into our discussion which has to do with when it is that very high energy physics like like the theory of quantum gravity or just additional particles that might be in the universe's higher math skills and we have observed how that fits into our way of organizing physics and observations and theories so there's something I want to go through very slowly and and some definitely ask many questions if any of it is unclear let me start with a cartoon of the energy scales in some aspects of particle physics and gravity that we know about so we have this very low energy density that is a of the order of the source of accelerating expansion that that I mentioned that we know about in the late universe so this energy scale is like 10 to the minus 4 electron volts compared to the 10 to the 19th electron volts or sorry times 10 to the 9 of the Planck scale so there's a gigantic ratio of energy scales that we talk about in physics what we've measured in particle physics kind of goes up to 100 of these Giga electron volts which is 10 to the 9 and you know that's been beautifully measured I think sava simopoulos may have given some lectures on that subject earlier in this series if we go up to the Planck scale we start to get into a mass scale or an energy scale at which we can get these black hole solutions in relativity and then as we go up in in mass or energy the solutions actually get larger they get larger in size to the point where we can start to measure them using the tools that I described just a few slides ago so in some times we measure down here we measure up there we don't know what we have in the middle so clearly so there's very interesting but still speculative conjectures for what kind of physics might complete our picture of particles and gravity involving thing ideas like grand unification or string theory which is going to be one of the tools we'll use in these lectures and and again as we go to higher energies we go we go up in this plot for for a while as we do that until we get to this Planck scale we're also going to shorter distance scales it's like waves of higher energy have shorter wavelength but eventually we cross over to where we go again to longer distance scales we start to have some some handle on it but anyway we clearly have ignorant of this wide intermediate range in this plot of energy scales in this plot okay so that might make it seem like how do we ever do anything we have so much ignorance of physics over a range of energy scales that that might matter for the observations and series that we deal with well there's a simple way of understanding why most of the time that's not a problem which is known as the names that don't matter again but this is known as well so effective field theory and you can formulate this in a variety of ways it really came out of condensed matter physics but I'm going to describe it in the following way which is a little more tied to observables we might consider in gravity or particle physics so basically the idea is you can take any physical quantity that we that we think about measure for example the force between two masses or scatter a probability for scattering of different particles and we can parameterize our ignorant of the physics at relatively high energies in the previous plot in a in a very systematic way so we can take the formula you probably know from high school physics which is the force is minus G Newton times the mass of the first thing times the mass of the second divided by R squared right this is everybody learns in high school physics but for all we know it's just the first in a series of contributions to the force that that could come in with coefficients that go inversely with this huge plunk mass scale for example or really any of the similar comments would apply if there's there's other scales of physics such as grand unification scale or the scale of the tension of a fundamental string etc today but if we just put in the scale we we infer from gravity we would still expect with coefficient c1 c2 etc that we don't know that there could be corrections to this expression for the force and the point is we wouldn't know one way or the other if they're there we our observations are not sensitive to that at at long range or low energies so but we can be there's something called dimensional analysis where we can parameterize these Corrections we can simplify the form that these Corrections can take by noticing that they better not have any net powers of lengths or energies in them and that's why we get ratios of the Newton constant to the radius of separation of these two objects in my expression with coefficients that are constant so there's if you think about there's an infinite sequence of terms like this so we know nothing about but it's okay because much of the time our observations are limited to long distance scales large values of this this are the separation that appears in this system and so we don't know these but we don't need to know these so these these terms are hence called irrelevant in the parlance of this this idea of effective field theory so in and for many purposes that's Dutch this perfectly perfectly good and it's a great way of organizing our understanding of physics starting from low energies and parameterizing carefully are ignorant of higher energy scales and the effects that that have okay it you know there's a caveat here which is several versions of the caveat here which is really interesting and comes in in early universe cosmology and also we think in black hole physics in a certain way so again I want to go on this let me start so the idea is that that although there's this this expansion in these infinite sequence of terms which are typically very small at low energies if we wait long enough if we have a process that goes on for long enough time and or we have enough enough data then we could be sensitive to those things even though we don't directly excite anything at those energies so a classic example of this again I'm not sure if for those who went to Savas talks if you imagine you might have talked about this I'm just going to say it very qualitatively there's this idea of grand unification which if it happened happened at a very high energy scale and you know just a couple of orders of magnitude below the Planck scale this theory in that simplest form predicts that there are particles at that scale very heavy particles and these are not things we've produced in accelerators however and it but they could participate in particle interactions and the theory predicts that they do and in fact that they would cause the proton to decay so when experimentalist did as they said okay well if the proton decays I could see it if I assemble a huge amount of material containing protons and and monitor it for a long time and you know even though the processes is small it's one of these things that appears in this sequence of suppressed terms if you have enough chances for it to happen you it could happen and conversely if you don't see it you can put about an experimental bound on that and that that happened and so the simplest versions of this idea of grand unification were excluded based on based on this even though nobody's exciting particle you know nobody is directly exciting energies at that scale now there's a there's a variant that evades these balance but it is very very useful null result on a parameter in a very interesting theory of physics okay here's another example of a slightly different form suppose that I take a an electric field I permeate space with an electric field but let me stipulate that it's very very weak so the energy it carries locally is tiny and I stick some charges in the system which also have massive energies that are that are small not nowhere near these high energy scales that we're talking about clearly if I wait long enough so an electric field accelerates a charge and if I wait long enough the system will develop an arbitrarily high energy locally the energy carried by the electric field is infinite when you integrate over all the volume coming back to your point from before but locally it's small so it's a weak field and yet over a long enough time you can you could in principle access arbitrarily high energy physics clear or any questions ok there's a similar thing in weakly curved geometries with a horizon where the role of the electric field is played by the curvature of the geometry and one of the one of the features that were interested in these days occurs specifically in the case of say a black hole horizon in which you drop a couple of observers so say so this is a picture as a schematic picture of a black hole this is the same line element I was referring to earlier and then I wrote it in a way that's useful new or the horizon where as we discovered earlier it looks like flat space and what we're doing here is dropping in two objects at different times but otherwise in the same way and the conversion from these courts of mathematically I'll say this in two ways but mathematically you can write this DF in the second way by making a change of variables and the change of variables that's involved in this case is this exponential relationship so X plus or minus some pre factor that I haven't written times and exponential in the time T in units I should have said before that this R sub s is my notation for the radial position of the event horizon so there's this exponential relation and that means that as one and two drop in exactly the same way but just at different times they they end up with an energy in this near horizon region which is a completely well-defined thing it's a patch of flat space-time and and the energy and this in the center-of-mass of the two of these systems is exponentially large in the time difference of their info so this is took a little more explanation but really it's it's a glorified version it's a space-time geometry or curvature version of this electric field in fact I mentioned here and it's something we'll return to it's again a situation where the curvature is weak locally but over long enough time you get a big energy involved in this case I just say the energy is distributed quite not locally but that will be interested interesting in this case of string theory long way okay so in early universe cosmology so by the way this whole thing and I love this term until I say it too much is known as dangerous dangerously irrelevant Corrections so these I said before that the way we parameterize our ignorance is this type of expansion and and these terms that are small at large at large distance scales or low energies are called irrelevant for obvious reasons but when you have this situation with long times and/or large excursions and or a lot of data you can get access to higher energy physics and that basically is called dangerous irrelevance so in the early universe such corrections it turns out there exists Corrections of this kind in some cases in the case where this Hubble that we talked about earlier is on the high end in some cases an infinite amount of dangerous the irrelevant terms that matter for the process so this is kind of a spoiler alert I'm going to explain all of this but there are sort of two ways that this comes in in the early universe one is that we will see that there's motivation for there having been a phase of accelerated expansion in the early universe and that is sourced according to these Einstein equations with energy generating the curvature in this case the expansion of the universe requiring a nearly constant source of energy so as we as we discussed back here actually so we found that if this right-hand side was constant then we got an exponential expansion and it will turn out that we there's a lot of reasons to think that that is what happened in the early universe and that it was nearly constant for a large period I'll explain very carefully what I mean by the largeness of this of this time period the actual time is a fraction of a second but the but the universe expands by some 10 to the 26 a factor of 10 to the 26 during the process and there's a field that goes over a long range and so there's a important sense in which this is a long process and hence subject to this this this issue of dangerous irrelevant sensitivity to higher energy physics the other thing about the early universe is we're getting amazing data more and more and that's enough as it turns out to to make tests of various interesting ideas for for high energy physics interaction new degrees of freedom and interactions that might have been going on during this phase of accelerated expansion including at you know rather high mass scale scales that are two orders of magnitude higher than the scale Hubble Hubble believe it or not that we we can you know constrain potentially detect but at least constrain using the prodigious amount of data that observers are providing so for these two reasons in the early years vers cosmology version of the physics that we're talking about you know in addition to a very simple theory of the origin of structure that I'll explain it has this added feature of some sensitivity to high-energy physics okay so I'm going to move on to that case Lenny what is the time scale of this lecture I wasn't totally sure okay okay okay now I mean I please ask questions if you yes yes yeah you had a slide where sugar is going up yes and the disc is going to China then at some point maybe yes like that it goes up again it goes up again yes yes well this is a very deep thing which let me just say a little bit more about it although I didn't I didn't derive it for you but what what happens when you solve these Einstein equations in the situation where you accumulate a lot of mass together to form a black hole is that the more math you you congregate together the larger the object ends up being it's a linear relationship so the this this short chilled radius that I wrote is basically the mass times G Newton or the mass of the black hole divided by the Planck scale squared again I'm setting C to once and it's I'll get into this more in the in the next lecture but there's just a beautiful property that this has well maybe I shouldn't go in here but at the level we're discussing it right now it's just a fact about these equations that the more mass you congregate eventually these black holes get larger the solution gets gets larger and so yeah it is kind of fun that we measure down here we measure up there but not in the middle yes I do oh absolutely yeah so when I discussed this wilsonian effective field theory it applies all across the board so any system you can organize them out in that way I mean I wouldn't say so although one thing that happened before the discovery of the Higgs was something like this where there were some of these these correction terms were very consistent with her being a Higgs boson even though we hadn't directly observed the Higgs boson so at the moment we don't have any we don't have a situation like that where we can we can easily expect another particle but as we went up in energy that did happen in the past and in particle physics so that's a great question anymore okay okay so let's get started with cosmology so I want to give you the you know the the basic theory first that's that's crucial and again some of you saw that beautifully from Leonardo earlier so I'm going to probably focus on you know slightly different aspects of it involving this dangerous irrelevance and so on but they all this is related it's a beautiful subject because there are different approaches to it that all intersect in the early universe but anyway I'll start with the basics we'll talk about the expansion of the universe this idea of cosmic inflation and a huge spin-off that it has involving quantum mechanics and this theory that I alluded to of the origin of structure in the universe before moving on to new tests for other things that might be going on there beyond this minimal theory including the role of quantum gravity for reasons that I alluded to and again this leads to one of you know one of the most interesting developments over the last decade which we've been very into here and you know has developed in a number of different ways has to do with this role that string theory has been playing in empirical science and I want to explain that carefully so one direct role that it plays just to spell it out before we get into details or back into the basics is that it's a theory we don't know if it's the right or wrong theory of quantum gravity but it has a lot going for it and as a theory of quantum gravity it accounts for these dangerously irrelevant effects so it's it's interesting to model physics that sensitive to those in a theory that has some account of them and this turns out to mesh very beautifully with ongoing observations involving primordial gravitational waves but beyond just thinking of it taking it sort of literally it's had a spin offs effects which is to destroy the mathematical structure of the theory has taught us about mechanisms for cosmology that we're just harder to think about in other ways they had they didn't occur to us previously and then you know that gets incorporated in a more systematic low-energy description of cosmology including the observable signatures and the analysis of the data that comes in so I'll try to get this across but let's again start from oops start from the beginning okay so what's the logic first of all we have strong evidence that universe is expanding and let me go back to the beginning again by before we get to that just reminding you about a neat feature of light and also sound waves and so on that is called red shifting or blue shifting the Doppler effect which is that you know if you if you this is a picture of an eye and if you look at some object that's moving towards you the pulses of light come faster than if it's moving away or sitting still and we can also tell how far some object is using the fact that whatever it admits spreads out in space and so we can relate the intensity that reaches us to where it came from so this is what led basically to a distance redshift relation the fact that galaxies by observation galaxies farthest away from us appear to be moving the fastest and despite modern political theory I could call that let's refrain from placing ourselves at the center of the universe and if we if we refrain from that then we get a picture we're just all of space is expanding now I mentioned this Doppler effect a moment ago I should say next that the expansion of space in itself causes the wavelengths of light to stretch out and that's a somewhat different effect but it's similar and that the wavelengths of light change so more than that as I've now alluded to a number of times there's strong evidence for their having been not just expansion but accelerated expansion expansion that gets faster and faster with time in the early universe so I'm going to start by explaining some of the early motivations that people have and actually this is the logic of this is a bit debatable but it's a very interesting argument and we'll see that there's a lot of reasons for this hypothesis and it has incredible observable consequences so let me start from the early motivations again this is a picture of the universe expanding this time slice of time is moving upward the time slice is meant to indicate the present day where our eye is looking as we go back in time things good things get squished together there's a particular time slice that's really important for observations which is the time at which atoms first formed in the universe meaning and electrons and neutrons came together to form atoms if after that that light could just stream toward us relatively freely before that it scattered off these charges and so we see this the famous microwave background radiation from from this time now if we if we were to extrapolate expansion but not accelerated expansion further back in time then you know the matter in the universe gets denser and denser and you find if you just follow those equations that the densest matter that we understand meaning we don't go past the gut scale or Planck scale or take your favorite unknown physical scale and and we just we shut up about what happened before that because we have no idea so the the confusion that comes up is the following this radiation that I'm been mentioning an important thing about it is that it comes to us from all angles on the sky at almost the same temperature will be very interested in the fact that it's only almost the same but it's really it really is almost the same up to Corrections of order 10 to the minus 5 so problem is if you take this picture and again we're using the fact that you know nothing moves faster than light if you if you imagine that the light coming to us from one side of the sky versus the other side of the sky is it not the same temperature it's confusing because if you track this back it looks like whatever the source of this light is it was never in causal contact with in the phase of the universe that we understand using using the regular physics we know that's not a contradiction there could be a theory of gravity that just from on high dictates that that that's true but it's it's we wish to do better and really provide an explanation the cartoon way of saying why that's confusing is you know nor normal physics if if two parts of the system are the same temperatures usually because you know they've mixed up so if we have a cold tap and a hot tap you know they need to mix together to become the same temperature to become warm and it's confusing if we're seeing things at the same temperature that never could have equilibrated in this kind of obviously so a resolution of this possible puzzle is a period of instead of just assuming that what we're seeing evolves back without modification we could postulate that instead there there is an early period in which the expansion the universe was getting faster with time if you think about that means the universe actually is older because if we fix the expansion rate now that means that it was it was slower back here because it's getting faster and in the same kind of picture we wouldn't run into the same confusion there would have been causal contact between the sources of this radiation now there's quite a heuristic argument but this among other things like high energy physical theories with lots of particles that could have been around in the early universe that we don't see the possibility that the the base on which matter is homogeneous could be quite curved and yet we see it as relatively flat all those issues would be also resolved by a process in which the size of space just expanded exponentially in the early universe another sort of more prosaic motivation is just that when we write down the possible dynamics that physical theories can have this source of energy that drives expansion it's actually kind of a leading thing you would write down in our this Wilsonian expansion in in terms of higher and higher inverse plunk masses say so it's it's it's the most relevant term that we can write down in physics so it makes perfect sense that we should entertain we should think very hard about the possibility that there was such a phase of accelerating expansion source by by energy that doesn't dilute simply for that reason that it's the most relevant term in in the expansion of our Einstein equations okay so we already had this cartoon okay and next there's there's a very beautiful there's a very beautiful spin off of this that that I want explained so we know that if this is even if this is true it can't go on forever because the universe that we observe in you know that Hubble observes and so on is not accelerating so there's a between what I'm calling the early universe and late universe there's there's a period in which the expansion is not accelerating that we observe so whatever drove that the collaborated expansion has to end and so the source of energy that's driving the expansion needs to be there at first and then it needs to go away so that means it can't just be some extra fundamental constant it has to be a dynamical thing and so the way we understand that the simplest way that can work in physics is for this energy that drives inflation to be the potential energy of some new field we with great creativity call this field the in photon field five and the simplest sort of scenario for for this process would be one in which it has potential energy that drives this inflationary faith that's what the early universe accelerated expansion is called and then this potential energy dies away and what's left is among other things the kinetic energy or energy of motion of the field just like a high school civics problem with potential and kinetic energy this field also carries potential energy and kinetic energy and it needs a nearly constant potential energy for a sufficient period to do the job of this inflation but then it needs to end so we had to introduce a new degree of freedom the reason I am harping on that is because this once we do that the moment we add another field we were interested in it because it's it could sort of homogenious Li roll down the potential hill that I drew in the previous slide and and source the early universe inflation which then ended but as a new field it it has the possibility of a fluctuating of varying in both space and time and in fact in quantum theory it it has to it can't help but let's luck shoe it and I'll get to that momentarily but the idea will be that those essential quantum fluctuations that are an automatic outcome of this hypothesis of having had early universe inflation that ends will get fluctuations due to quantum theory that are perfect I mean they they are this seed structure in a way that is the spitting image of the results we get from data so it's um it's worth because I think that's before we get to the fancier stuff okay so I haven't said anything about quantum mechanics yet really but let me the beautiful thing about this stuff is it uses really the essential thing about climbing cases that I think people have at least heard of and again ask questions nobody's asking questions but the the Heisenberg uncertainty principle says that if you have some degree of freedom so let me back up and we're talking about this field sigh but but you can also think about just a particle moving around in some space so for example consider a particle that's moving around in a potential well like this this parabola or whatever some potential well or just you know in it in any system there's an essential principle in cloud mechanics that says that we can't know its position and momentum simultaneously so heuristic aliy are the uncertainty in position times the uncertainty of momentum is some fundamental constants plunk constant which is non zero and that applies not just the particles moving around and potential Wells which is the quantum mechanics upgrade of the thing you learned in high school physics but it applies also to any physical degree of freedom more abstractly like this this info in photon field it applies to you like a magnetic field and so on so so the input time we can't specify what its field value is and what its field momentum is how rapidly it's changing at the same time the best we can do is a kind of minimal uncertainty thing where where it takes a normal distribution so I don't want at this late hour I don't want to bother people with too many equations but you know probably everyone turn the bell curve and a normal distribution basically the simplest theory of these perturbations in quantum theory in a system which will turn out to be relevant for this inflationary stuff where it lives in a in a you know parabolic potential landscape the best we can do is a minimal uncertainty in position and momentum which still gives us some probability to sign the field at a non-zero value so so this is a little quick but the the upshot which I may be able to unpack a little more for you next time is that these fluctuations in the field automatically happen to be closed because of quantum mechanics the probability distribution the probability for finding the field at a certain value is basically a normal distribution with a width that is of order this this constant Hubble that we have in in our theory that drove the expansion the universe and as a result of that we will get seeds for structure so I put back in the numbers that we sometimes set to 1 this is a quantum effect it's a very beautiful essential clime effect one way to describe how strange it is is that the mean value of the fluctuation the field is 0 in this picture but the mean square value is nonzero ok so this is the the basic picture it assumes that the interactions that this field undergoes with it amongst you know it so in the particles that it creates by itself or with other fields that might be around are negligible and you know that's something we can push on a lot more we can test for interaction effects and effects of other fields that might have been around on this probability distribution but the leaving behavior of this fluctuation is is as in this this normal distribution another way to yes so I would just bump you'll that other eigenstate subjects to be measurably well in a certain sense we measure we measure of the I'm actually getting getting to that we don't you know we're not back at that time we're not directly measuring it but it actually I'm about to say something about that it's this it this gives a theory of the seeds for structure of the sort of the initial conditions by initial I mean say the conditions at the time when Adams first four were this light streams to us the theory will give us initial conditions on on the fluctuations in density and not medium that that then effect that the light that we see so that that's what we measure but it fits with a theory in which those initial conditions were set by such a field which I'm actually about to cartoon sketch for you here let me see yeah okay so so again the picture is we have the field that has potential energy and eventually just kinetic energy it has fluctuations that we're now concerned with and it's living it's a it's a field that lives in this exponentially expanding geometry so let's look at a patch of that geometry of characteristic size of corresponding to the parameter Hubble H that we talked a lot about earlier so again Hubble has units of inverse time and it it's a characteristic scale in the problem and what happens is a more physical way of describing life it's a scale that matters is the following so if you think about some fluctuations of this new field that we've introduced over a wavelength that's very small compared to this the scale of Hubble inverse then you might as well be in flat space it doesn't the field doesn't know anything about the accelerated expansion to first approximation it just behaves as in flat space-time cereal fields which you can imagine we understand pretty well but as the universe inflates the wavelength of this of this fluctuation you know accidentally expands to the point where it's quickly pulled outside of this constant nearly constant let say Hubble inverse patch so it's nearly clean it's actually decreasing a little bit with time as in this picture but basically it's the Hubble is nearly constant and this wavelength stretches out outside of the so called Hubble horizon which is a bit of a abuse of language but this is this is the picture and once it freezes out it you know it stops it might as well be constant from the point of view of this patch and the value at which it freezes out is dictated you know on average in quantum mechanics is dictated by the uncertainty principle and that's the thing that gives us a root mean squared excursion of the field of order Hubble I think I I think this is a good place to stop what we'll do well do next time is to finish the development of this inflationary theory in these perturbations and get into this business with the sensitivity to quantum gravity and then also come back to black hole physics in the role that form gravity and string theory plays there so let me stop here [Applause] even for ironing of depression 70s detective to sort of elevate the new movie texture okay there's all bunch of things that you obviously saw and the same things I will be solely and the same things of the environments in fact including us the same things that cosmologists appear either a physicist experimental physicist all over the world and yet when it passes through the media the screen can be compared and now it turns out almost as badly as climate science I feel there's elements yeah how many people believe is one of them contentious could you can you make anything about varying a series of articles well I mean should we explain what you mean more or there's the public discourse on this subject as well as on string theory which we haven't really gotten to is often grossly inaccurate I think is what Lenny is saying inches from the other side of the horizon maybe right so so right I haven't really gotten quite to the evidence for this inflationary theory but there it's substantial and there are those who quite reasonably explore the possibility of alternative explanations of the early universe physics and that's you know that's a perfectly valid endeavor but the the status of that is it it's it's it's a very challenging problem and you know these alternate theories tend to involve physics that is is very strongly curved in the sense that I started to explain and and very difficult to understand theoretically but that has led certain practitioners - I don't know - as Lenny is living to write Scientific American perfect holes which which which which are not very accurate and part of the thing we'll learn a bit you know pretty soon in the next part of these lectures is the the evidence that there really is for this inflationary scenario III do actually have more pointed comments to that to that question that that come a bit later after we've got develop things further I feel free to say what you have to say about the elephant in the rainbow but I I'm not sure everybody's read this article and maybe we shouldn't not contentious though so that's the topic yeah now climate science is a great analogy it's George your drawing is so clear and so good no idea what the math means that they could just find you up in position just like is not the kind of thing to say it's not it's not the reason we we believe inflation is is the right there's a universe but thank you yeah I'm sorry I feel free to say what you I just want to point out there is a whole bunch of stuff you find in Arlo pretty much the whole community pretty much takes long for graduates I haven't every day my way I'm in Seoul so I'm really trying to clean a little better what Lea is saying based on something I did show already which is and I think I've shared it okay so I flashed this this thing now this looks like a rather messy plot when it when it is is a picture of these fluctuations at a variety of scales the structure that you see this plot actually has to do with Soundwave in the plasma that was there when atoms were first forming which is very well understood physics and the model of cosmology that we get that that fits with this data the red curve in these figures actually depends on only six parameters it's incredibly simple if and and that is quite consistent with the simplest theory of inflation on the one hand in contrast to what you would get if you just threw a dart at possible ways that the fluctuations could come out so if we don't know anything about say quantum gravity we took the picture with the which I had here somewhere where things got very dense and we and we didn't postulate inflation but we tried to model what happened in the early universe in some way that involved this this dense and highly curved slice of time you know we we don't know anything about that and without a theory we would you know we would have to entertain the possibility that they're just wild variations in the fluctuations of the function of scale and so on the inflationary theory its simplest versions is very clear that that shouldn't happen this is also in contrast to certain other well-defined scenarios like cosmic strings of sources of structure that were were viable before this data came in and and that's just the fact that to good approximation it boils down to these six parameters is strong evidence for this inflationary paradigm in a sense it's you know it's a function that could have had wild variation depending on many many many parameters and instead you know many as a result of that you can think of it as you know many parameters have been constrained down to a simple curve that fits with inflation so it's you can think of it as a functions worth of tests really and so there's reasons why you know we don't just assume it it is a nice idea but we don't just assume and it has it has a lot of evidence in its favor of course you never prove a scientific theory you just get better and better evidence and so far inflation has has survived these massive tests extremely well despite what you might see in the Scientific American level literature which tries to type it sometimes appears as if there's a sort of 50/50 probability between this and some other scenario which is you know much more challenging to develop and has not had such successes if that's why do so shelly yang Oh [Music] yeah that's a wonderful question yeah there I'm glad you asked because I'm going to get to that more next time but these let's see so so the we've gotten to these fluctuations and we discussed how if you assume there's only one field in it and it has no no no interactions that really matter it's just a bell curve but we can do tests on the light that we see eventually that that has imprinted on it the the size and the statistics of these perturbations and we can check for much more elaborate functions here that could come from other fields you know it's very natural to expect other fields in physics when we when we complete our theories of particle physics and gravity we know the ways we understand how to do that involve extra fields and one of the things where we're dealing with now in collaboration with Leonardo and others is is exactly that even very heavy fields make an imprint on this picture that change the statistics a bit even if there are two orders of magnitude higher than Hubble that interact within photons and a reasonable strength they lead to effects on this picture that we can either constrain or potentially detect and that is in progress that's a current very current area of research there's there's other versions of this involving multiple field sectors some of others of which could be light and that hasn't that also makes an imprint on this sort of picture so a great question and I'll tell you this I mean I'll definitely get to that next time yeah all right I know it I'm so glad you asked that so so the horizontal axis here is is the field this is a a so the field is some degree of freedom that can have a strength so that's what this Phi refers to you and I should have labeled it but the horizontal axis is is that field fine it's changing with time it's rolling down this potential now if it's true that we can measure time using the field itself as a clock and that is actually a very useful way to think about the problem I'm going to get to that later so let me actually I'm not going to go on but there's since you asked the question there's sort of three ways you might think about measuring the duration of inflation one is how much the universe expands which turns out to be a gigantic factor of 10 to the 26 another is how far does the field go and it's a perfectly good measure of time as well and that turns out to be the way to think about it to understand the connection to quantum gravity best and then you know the time coordinate T that we've been working with in that in that variable it's just a tiny fraction of a second so so all of these statements are true is the same yes I see they're all true it's just different ways of measuring the extent of the process and the top and bottom are kind of the most useful and I think sort of the most faithful ways of thinking about it but they're all true yeah yes yes I've recently been reading a series of trances of by Adam Thomas and when she proposes and revised areas of gravity which inside of a black hole or any collection of objects which is massive enough to have a sports Gerald radius he proposes that inside of a black hole that mass becomes negative oh I'm sorry he proposes that then gravity reverses and becomes repulsive now this doesn't make any sense unto me unless inside the black hole that also massive negative well recently there's an O reportedly and Washington State University to think for reproduce in the lab a fluid with negative mass we apply a positive force to it and it accelerates in the opposite direction does all of this have any relevance to what you're saying I would have to look at what what you're referring to with the experiment I I'm not sure what that might mean to be honest maybe you can explain afterwards there there are these kind of laboratory analogs of black holes called called dumb holes in the sense that it's sound sound waves they can't get out but if you ask the question okay we have this mass parameter when we think about black holes and if you just say it's just a mathematically what happens if you make that that negative it causes a problem there's a certain kind of singularity in the that you get in the solution in that case which is you know very difficult to resolve it probably is not possible to resolve it and the reason we think so is that if you you know well first of all we we don't understand we would don't understand how to resolve the singularity that the Einstein equations would imply but more importantly if you had negative math objects then things would be very unstable in physics general you could pair produce them and decrease the energy you know ad infinitum so it there are good reasons why the negative meshwork shield geometry doesn't make sense yes in the beginning he said that it takes an infinite amount of time for something we get to the horizons but does that mean that singularity never reforms I'm not sure what you mean by infinite amount of time I was but it was nothing about horizons is that nothing gets out of them so you know it is oh sorry yes okay so the matter never reaches the varieties in amount of time a lot like the singularity never actually formed well I think that you're falling in you know it's an arbitrary thing what your clock is doing in some sense and if you're falling in the proper time does not build up at the horizon that just according to the classical theory you just go straight through so the question of how to put together these different observers views is a very interesting one that we deal with but at level you're asking it's you know it's not that the singularity is unimportant for the in faller in the classical theory yes when you're talking about the idea that the in photon field is some sort of exist that some kind of potential and then becomes this energy but then you had a drawing or the deflation slows down again so is the notion that that somehow returns to the energy of the field or is dissipating by some other mechanism well that's another great question so it's a little of both so it if all we had was this in photon field rolling down the potential then the potential energy would basically become kinetic energy that's a that's a little quick because in the expanding universe you know the energy and the v field isn't strictly conserve by itself but you know basically it would go into the kinetic energy of the field so to speak the it's variation in time but in the in you know a complete model of inflation and it's aftermath there's a phase called reheating where you have to excite the particles that we know and love that we're made of and so you know at some level the input on couples couples to those those degrees of freedom and as it rolls down it it impart energy into them and that could work in a wide variety of ways it's an area of modern research in this subject but that's the short answer interesting to experimental results to develop recently in full-scale gravitational waves in the same universe what was your life like before those goals exactly expensive any image you mean the the dark energy the accelerated expansion I'm not quite that old to have lived through the discovery of the expansion itself so I the discovery of the dark energy with gigantic it's a wonderful thing it's a single number so far at least and you know we suspect that's it but it's a single number that that changes you know the fact that it's nonzero and positive means something for the causal structure of the whole space-time so it's it's a it was a huge discovery and there's yeah I may be able to say more about it later was the other one you wanted to I mean I'm not sure we scout gravitational waves yes so that's also a beautiful beautiful thing of course and well I don't know what to say about it's hard to overstate how how exciting it is that this LIGO experiment managed to detect you know this process this event for my own interest in early universe cosmology there's another version of gravitational waves which is very much in play which is the primordial version and that we test for using a slightly more indirect measurement involving this microwave background and I'll be able to talk a bit more about that next time and in that case also there's an interesting threshold that we'll get to either we'll see it by that threshold or we won't and that will tell us whether this in photon field in fact it's right here whether the simpleton field moved over a range that corresponds to bigger or less than this huge Planck scale so that's a wonderful observational constraint to come from gravitational waves of a different sort so yeah and with about the whole inflation turning to a regime that there was some sort of a runway conversion of potential energy into kinetic energy and become what is the physical intuition of why this conversion harmonic well it shouldn't actually run run too far away it just I mean you've got it you've got the right idea it's we have potential energy and then it converts into kinetic energy with the added point that it just the just the potential dropping I mean it's just like a particle on an inclined plane from from exactly.the the field value is a physical degree of freedom that is you know similar to the position of a particle on an inclined plane the kinetic energy tends to increase yeah that was there a long period before this triggered well yes I mean that's what I'm trying to express here so we it's okay in this variable T that we've been talking about it's a fraction of a second but but better there are two better ways to really think about how long or how extensive the process is the first one is how much did the universe expand and it expanded by this ginormous factor of e to the 60 or 10 to the 26th you know that it sort of scales with Hubble and giving you the extent of it on the high end of Hubble and then again we'll get into this next time but another measure of how long it goes is how far the field rolls on this potential and that you know we don't we don't know there there are different ways the process could work in detail that have different answers to that question but in all cases there's a sensitivity to chrome' gravity that I want to get to and you know it's again a better to me it's a more useful measure than the fact that this delta T is something as a fraction of a second for more please visit us at stanford.edu

Channel: Stanford Institute for Theoretical Physics

Views: 15,473

Rating: 4.7658539 out of 5

Keywords: physics, black holes, cosmology

Id: zMz4fX3SShM

Length: 107min 40sec (6460 seconds)

Published: Wed May 17 2017