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Topics in String Theory | Lecture 5

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never so you had homework Writer homework build a black hole a brilliant to the lump still not recur Berg said it won't hold the for a full name that has a population of what it is that a Buhl broker right it a work force of about that but he never bomb suppose you didn't know answer the driver estimated we do this last time that black coldest temperatures and 3 degrees wife 3 degrees well 3 degrees the temperature of empty space are due to these cosmic Baquiran background radiation so if we had a black hole which was 3 degrees it would be in equilibrium with surroundings now would that be particularly interesting no because little bit harder by accident that you know just a CPA get harder and that the Devil will be cooler by accident by emitting Khamenei photons suddenly cooler so there's no real equilibrium but nevertheless just it is to try out some members of freedom degree black hole 3 there 3 degrees Kelvin black or white does anybody know the wavelength of light which is about 3 degrees you know it tell me otherwise I'll have to look for work it out fast centimeter not know don't know it's 21 she's yet microbar Michael background OK so what as but Oh no it's not 10 leaders No no no no no no no 10 meters normal but that you want at the His capital centimeters so let's just say that state act the yacht as got a fever money came up asserted that could point so it's gotta be less than thought L and now but they Eds centimeter of sorrow OK now is a factor to haven't noticed it already column that the way the ruling Our light at the temperature of the black hole is about the same size as the radius of a black hole that's the committee there aren't too many parameters around the given shuffle around and the radius the wavelength of light emitted by a black hole of size all are better wavelength is about so we can read off From an what they radius of a black hole which he made 1 centimeter light and the answer was a set at so renowned for its what you radius now was a question again how big was it a massive I met our case have massive there's 1 centimeter How many centimeters Iberia kilometer a thousand times a hundred a hundred thousand right so this 10 the 5 centimeters a kilometer and a solemn black hole is about a kilometer big Armitage to Khan maybe it's a little bit bigger but a few kilometers they'd saw me with thinking about is a 100 thousand times smaller in radius about amassed romance and the radius of proportional which of 2 ng so a 100 thousand times a lighter then firms sub but massive a 100 thousand times like in sun it's about their at roughly order of magnitude the earth the massive
years so if the mass of the Earth compressed to a black hole would be roughly a Our Love that's so but why did did that Camara procure remember somebody asked about possibly possess agree with what will from says if a the newly ramps does a little small Khamenei Moon sounds a little bit small but there but the point is it's not a thing a hole in your pocket by her case it's pretty heavy I'm surprised moon there are White a bucket withstood factor wife no not only is about a quarter of the radius of the area that dozens of rookie Mozart apparently with succulent we want build ourselves a black coal now we have some moving parts of working part you may remind you what working are the 1st to working products are the pillars diagrams for flat face and Forest Watch black holes woods draw that will we don't want do any real calculations calculation too hard draw pictures and get the basic mathematical fact from pictures at let's start with flat face 1st of all we're here just to remind you were Penrose diagram looks like college or flat space over here says time now the other then the problem is that be exit could be radial distance so it never those negative radius is that never never negative radius goes this way seemed to remove negative over a year ago that worrying and every point at tea and are also the angular direction so am I. for corn that's a polar coordinates included me I'm right over here I also have a clocks are moving vertically my clock is ticking off time and at different distances from me that correspond to different all are but every are theirs a sphere false points so an object there could be at any point I'll be able to suppress that at the draw we just couldn't drawn to light that move toward the origin commit along 45 like erasable out from the origin go out at 45 degrees and so for right the Penrose diagram the colors with this is just gotten by watching it switching his mathematical operations worker will Wolfram Wolfram wishing that we schmo this way and that way until we get a on finite plane do sorrow and is more than 1 way to do it incidentally but they all look the same as more than 1 functional form that you could use for the coordinate transformations but all look very much the same as the point over here as the origin of both space and time is nothing is nothing special about this Point vs . vs. this point just a different time but but take a origin of tying him for a ride over here this is time equals infinity and it corresponds to a these location the described location off the people at different radio we're just stand still if we just stand still but just warning of vertically obeche equals infinity but I figured they also wind-up at what looks like a point but of course that point is not points is the factor which pushed Schwartz squarish it is only and they get things 7 dancers you go out here because after all there is an infinite distance out to infinity and absorbing plotted on this Penrose diagram of the vertical lines which become crime of hyperbole is not necessarily exactly hyperbole was moving hyperbolic issue they accumulate mean say they get closer and closer over here here and that's through vertical warns the horizontal lines which are lines of constant well the
1 people 0 that's pretty obvious that starts here and it goes out to be the 1 at tea equals 1 also goes out to meeting like that is not necessarily a factor not straight lines as a rule and again they get closer and closer and closer and closer as you get up toward the Yarra infinite time saying things lower part of the diagram which won't draw right if you join it correctly them light rays more 140 degree lines said but we just definition of the way you draw and somebody's pointed out last time Have I draw accurately light gray with then moved well apparently I didn't driver accurately because it's warned the ball here that it just put a mother warning bird and so forth that's a light rays from the origin our life from out back to the origin is that way you can have a light rays started later and origin later and backed out that's fine your much same except 1 later the other you could also imagine light which don't hit the origin so again I'm the origin you fleshy laser Anthony and goes by me add meters from the point of view of radial distance it comes from a long distance away and it sure looks like it's aimed toward me so if I could tell them the radio White wave but that as it gets closer instead of getting the Oracle 0 it gets a certain minimum distance Lagos backed out of pray that this is the origin is another 1 and this is the origin of drugs from bolder and bold comes in pretty much the same and then goes back out I did draw with any great accuracy but you get the idea they all look the same incidentally far away every light the matter how much it misses me by this far enough away it looks like seems toward me OK that's lab space that have Our as 1 of the moving part or 1 of the ticket or elements that will put together build are black or build the black now I mean at least mathematically are imagination create a black hole as opposed to just take the mathematical structure examined how would you go about creating 1 in the laboratory well we need a pretty big laboratory right next it was pen rose diagrams bullish what over by calls I do it for you last time around we draw now it is a little bit on you the way you drive you begin by drawing a square but on the diagonal of a dying in the square diamonds that they join other square diamond next of the same size and then from the top of his diamond wittily lying top of this diamonds from the bottom of this diamond you draw a really lying about that that the Willie lines are the singularity futures singularity Of course singularity plus singularity minus people outside the black although there over here this side with a fine that doesn't really mean anything so don't obsess about the size don't even asked me about it for the moment we find out what happened to it here in here are somewhat on physical but this region over here far away from the black hole it ought to look like flat space of the black hole or a million miles away and live far away from the north to like flat look like what flat face looks like How beyond a certain distance here but not a lot of magic his articles city that matches the point over here 5 years he calls affinity minus infinity light rays coming from he a light rays go here lonely of constant all are connected me the Schwartz still are all rural with doesn't matter proper distance all articles to Angie right here if you can't along a line like that you get articles to right over there may draw that line a different color if this is blind T equals 0 legal 0 starts far away and comes in and it comes into the horizon right at articles for to ng articles here's a later time is later time and so forth
earlier time earlier that this is Oracle's to about articles 3 G farther from the horizon that's going to look something like this are equals Agunos 6 MG mushers everywhere would be Styron as Oracle's 6 articles or 100 ng far from a black hole and so forth and so on and so as you could see this figure and this figure look Free similar as long as far away from the black hole but this figure looks quite different than this 1 does new articles 0 Oracle 0 light rays bounce off that there is no article 0 the light rays bounced off here instead a array just move right through the horizon and the singularity solve nearly black hole a different far from the black hole with similar want in here as we talk about before you cannot escape your don't you like to singularity OK now 1 more ingredient because the theorem I call that our broadcast is called Kravis and their policy is a generalization of Newton's steered remind you about new say no but these elements together and then it notice theorem let me 1st express it in a general way if you have a spherically symmetric distribution of maps merge its isotropic the same in every direction areas that doesn't have to be a shell it could be a lot it could be a shell it could be a solid CEO with uniform density like durable Eurydice that quite uniform density or it could be a sphere like a like Jupiter with varying density more dense in the sent there to you get out of the outer boundary where it has almost no density art it doesn't even have to come to an end just the Justice Veracruz symmetric distribution that when no Stevens says and they also will discuss Vermont when this fears as if that any fear that the gravitational force of our test Messer a point at that distance on the sphere is exactly the same as the the gravitational field of the same amount of mass not that total amount the but the Maersk contained within as if were located right at the center of a force on the particle he is best if the entire Mass inside the Sphere will concentrate the center and the Mets outside this year has no effect on the gravitational force on particle role as 0 I love these special cases are be interest Entiat what about the story supposing distribution terminates at some radius so that out Beyond that radius there is no matter but not theorem says the out beyond that mess the entire of objects gravitates as far as your concern exactly as if the entire mess with the center now let's take a case of show supply that Rochelle supply that show how the Blue Line is shell of man Bruce circle for the most feared accurate it is a symmetric shell of mass arms if we want to think really mathematically with too much precision about we would imagine there was an infinitely thin shell but we have to do that but it has a certain mess and and the gravitational field of a particle on the inside well refined did we take that point with put it on a sphere I would say that the gravitational force on that point is exactly the same as the gravitational mass all gravitational force of solar masses inside the Sphere but is no man's inside the Sphere so the gravitational field of gravitational force on something inside the Sphere 0 interior of the spheres exactly the same as if there had been no show ministerial about outside the sphere outside the sphere it behaves exactly as if the same amount the mast was concentrated at the center OK now let's take a after version of this year b mine or KOF KDH OF per Bond but Garcia very similar things says yeah will will take the case of a show of mass but it doesn't really have to be a show you considered very similar things in the distribution of a special case Michelle it says that the metric tensor metric tensor is the gravitational field or better yet geometry of space time geometry inside the shell is exactly the same as if nothing was there another words it was good old flat space-time Minkowski space-time the simplest thing with no curvature of black called just and B flat space and outside the show of man and the metric is exactly the same as if it were a black hole near the center here of mess and so it's a big let's take for example we mess of the earth nonagon maker black elaborate is take the mess of a black hole the rest of Europe and leave it as a massive gonna and is smooth out of the perfectly symmetric perfectly symmetric their that if Europe outside the surface of the earth geometry is exactly the same as the Schwartz that their corresponding to exact group and that's another word it behaves exactly the same way of the gravitational field you will feel the gravitational field that you would feel would be the same as that little 1 centimeter nugget form the black hole of saying man OK so that's Burke fear now will put together we want we would like to create souls a black hole and this is the simplest of all ways to create a black hole simplest always create a black hole what your imagine you tell us a little more but I don't think it would work more you know they have these lasers but there are
showed off all simultaneously and radiation shell of radiation comes in it's something squeezes it but I have no idea whether it level work on really don't know what they want do but if you imagine our aid much more symmetric field of lasers here where you really fill this thing up and made very very smooth shell of lasers and then did your flashed thing with the lasers it would create a shell of life coming it I salute would begin then works but on draw the lasers and only draw the sphere of light coming in a sphere of light is coming in with the velocity city propagating in with velocities light has entered how much energy does light wave of whatever happens which cause he in fact from a outside we would say it has met E equals M C squared where the energy of it is divided by sea squared that's the mass of this object as seen from Earth so far away but that distinguish energy and maps equals and on to lose object girl it is a collapse shown on they asked collapsing with the speed of light and off or Newton's heroes per 0 applies to it was it saying it says all incidentally What I I should have told you are talking about member cast there it doesn't matter whether the masses moving as long as it stays spherically symmetric the fear the correct so here the masses moving inward and what we can say is the interior of the sale at any given time of course what may have been the interior of the shell at 1 o'clock maybe the exterior of the shell at 2 o'clock but take the interior of the show at any time in the interior of the shell and any time the geometry metric gravitational field is just empty space as if nothing was their army outside where you have the short shows that the girl black hole might see a piecing them together where imagining taking a retail space with nothing in it and sewing it together with the region's based on the outside and we are now seeing the place with us together it is the mass distribution let's try to draw up pen rose diagram for that let's start with a and B flats face begin joined with empty flat basically Yiddish a and B flat space and a 70 flats base where throw a show of white so I would begin by drawing empty flat base it is over here doesn't get rid of some the lines with needles lines are so here's R & B flat Urich just a trial malformed followed lady we're going to a in the shell of light instead of only from Livermore let's throw in from infinity so I comes in from very very far away a lot of things shell that was never replied that looks something like a red line here is going to be the trajectory of light ray of light shall remember each point in the diagram is really a two-dimensional so every point on the diagram represents a two-dimensional surface in every point along the light gray year really represents a shelf life of this point the shows very big far away and moving toward more and more are and when it gets to the center of the show has shrunk to a point I saw a lot of energy that we put into a small volume where the energy is if we squeezed into nothing volume we've created a huge energy density would create a lot of energy with a small volume might think we make by call repair and you'd right OK let's begin let's take a first-half Our but costs 0 it says inside the shell space-time is perfectly flat where is inside a shell but imagine drawing 1 of these surfaces along the surface the radius is increasing where the inside of the shell not be insiders shelf that's the outside the show right is inside from here to here packed with major all the places which correspond to the interior of the shelves of all of this all of that is the interior of the shelves the interior of the show Brookoff tells us is just flat space-time this diagram here was all flat space it means I got the picture right inside the ship just by joined flat space-time inside the shell I got it right outside shell I don't get it right what does the Tommy outside the shell is outside the Shelby the metric should be the metric of the Black also looks to older black home accurate stroll the black or metrics bro here it is again by going to simplify it that get was throwing in a light ray from infinity starts out here and it comes in and boom has a singularity where are now is inside a shallow and wearers outside the shell inside a show is to lower left outside the show is to the upper right so where that I get the metric right on this by with Our outside but Our here as well it should look like outside shelf and this that's wrong also this is wrong so it's sick 1st polls but
draft tells us as the wrong thing year and this wrong that among other things I'm throwing away all this problematic region with another universe summer left all white hole in the singularity in the past and I'm left with only that's that's the portion of the black hole metric outside do you of black also is a light ray intersects hits singularity right over here as light rain comes in and it's Oracle 0 0 right over there these 2 points must be the same point in the the library trajectory if I want to know what I would do is our tormented taking this and simply tasting it on top of this pasting the 2 together and here replied How here that's the the swatch of electric and erased the the rest of it but here it is it's everything above red line as goes here everything below the red line that's here that's the simplest but that's the simplest formation of a black hole and the reason that I spent some time it was to show you among other things what happens to these crazy regions the other half of the the wormhole beyond the worry and what happened to the Whitehall finals now back the worm holes there but there is a singularity their singularities there having established what any questions a permanent was off Ali having talked about the trauma horizon of this geometry a revered do have minute but glad Odessa question and that there were clear other these here are there was a every year yet career right now at the singularity Aura's equal to 0 Eric but that a worthwhile point now members you go back to the short showed that the singularity was exactly where that will shrunk 0 away on went 0 so in fact Yemeni a matching the Oracle 0 along here with Oracle's here they do match that the construction of black all the way would do it this is the kind of black or we would get so loud let's now ask Where is the horizon wears a horizon of the black or the definition of the horizon now is not Oracle's torn G temporary definition of the horizon and the horizon is the fact that which separated the region say this clearly there of those places where it's possible to send the message out to infinity and tourists alike layout to and if you have enough a fuel a engine you have a chance of escaping their from regions but a particular light rays can escape from certain regions and from other regions they cannot escape me definition of the horizon is the surfaced which separates those 2 regions period surfaced in space and time which separates those 2 regions back from which you can escape the singularity and from that which you came well and very easy to see where that you just brought a light call you back if you're over here and you get out now you'll lined up at best over here where about if you're out here could get out of because the light rail out anywhere is lower right of the green line in a light gray can get out now lightly can also be did you could also arrived late and as sister safe from the outside you can throw things into the black hole you cannot from the inside throw things out of the black hole of the Green Line here is a separator a seperate the places where you can escape from those we can escape the notice something curious when line here is just empty flat space there is no blood that was nothing there was as good big black space a flat space meeting they not only game comedy like Shell had gotten there yet and yet there was a horizon what's going on but just think about somebody who happens to be over here he doesn't know anything at all about the white show which is going to come in the light show he never received no message that the light shows coming in show originated over here a signal cannot get knows nothing about it like shows coming in but he doesn't know it it has no knowledge of it or nevertheless the fact that that lie sales coming amenities trapped cannot escape to infinity that light Shell is going down you could see why don't have Edwards a picture is worth word worth a thousand words yet is behind this line he cannot get out that line without exceeding the speed of light so Is the singularity even tho there has nothing is happening yet geometry it His flats and yet the horizons over here the horizon forms before video light shell gets there was everything really happened anybody see anything somebody moving over here they see something happening now nothing special happens over there but whether they like it or not the doomed by the time they get I give you an example I've used example many times of a drain hole as the euro as a black or the drain a lake a big big lake with the drain hole in the center where the water is being sucked out so fast on that bet that some distance away he may be a drain hole was draining away water so fast that arm roller who's trying out row current came out row it because of velocity in what too fast so imagine that the drain hole a show off if your from plugged up to drink or you're sitting a couple of meters away from where the drain hole is nothing is happening the water isn't moving here
perfectly happy hour if they like that forever you would have no trouble throwing away but now unbeknownst to use somebody pulls the plug from underneath and all of a sudden the war starts rushing toward the center you'll are doomed whether or not you felt anything going on here don't because all of a sudden the velocity of the water as such the 2 came out relate solely as an example of you've Europe your past the point of no return even tho there's no flow of the water at that point saying this show here pulling the plug is analogous to slight she coming here once the lie cheat well but why she comes in and anybody who happens to be in here Ms. trapped what happened to her eyes said above the horizon will forever it is our eyes and number at each point on this diagram there is a two-dimensional sphere so each point along represents a two-dimensional spirit was the the size of this fear over here 0 0 right so we start earlier With 0 size sphere of iterative now we move out along the horizon How big is Verizon well a slightly bigger the horizon has grown even those things happen but has been going on here and the horizon keeps growing up until this point here when How big is at this point to energy ONG whether remember we just taken a black hole geometry and so well over the alarm and the black hole geometry on this side had a horizon whose sizes to Angie sodas grows until it becomes a size 2 Ng and then I just days that way unless somebody throws in some more stuff somebody throws in some more stuff the horizon will grow so that's a picture of the year of the creation of a black hole from an incoming light it's so a shame reason Pol Pot the shipyard but rural that example to show you that even those nothing's happened yet you could nevertheless be beyond the point of no return or you could be like on the edge of a Niagara Falls at a time when Niagara Falls was frozen out there wasn't moving at all and you think it perfectly safe there is no point of no return the world not moving and then all of a sudden the ice gives way in the water starts going you're doing doesn't matter repair nothing seemed to be happening same kind of thing objected so we take a break I've got a fellow that is Sean write us a little bit all of that worries staff see what we got now not being distant observer can see in the distant observers out can't see him there are barriers what can happen on paper singularity he can avoid it the dress the calories right there all of us here well OK sir she got in here somehow Anthony Maine well we lose track of her it could begin begin existence over here may have come from here this particles his particles maybe he was maybe his mother was over here and whose grandfather was over he himself or someone or maybe he just accidentally collected data came to existence saying funny fluctuation Roberto molecules because of molecules with that before Adams or something with their energy was there before him the energy came in here in areas and yes somebody looking back concede his grandfather what followed orders for his particles but can't see him factories she's busy sees these particles just collecting on this horizon which is peculiar because some sense the black hole hasn't even formed yet In Obama is we're doesn't really weird observer up here looked back and see his grandfather falling in the the areas is born over here it looks back and whether the this city he sees grandfather getting closer and closer and closer to something which doesn't exist but can't get but never seasonal past this year the private sector less solidly Brooke 8 were asking what somebody on the outside rescue or measures the deaths warnings figures because abroad so that world where the person he knows that a black hole for it was a black hole formed he sees the light coming from he has no problem knowing that a black all forms taken look back and conceived in so person here wasn't black holes formed the odd thing is that he sees this person over here getting trapped on the horizon even before the show that look back looked through the shell just light see to light you look back through the shell and sees it I everything that a man of merged forever In every or onto black coal evaporate right now we are going to come they really bizarre questions have to do with combination of black holes gravity and quantum mechanics and information abroad less up there till the
horizon now a different picture the rise is just a surface there it is where full downward now is our eyes Chile's it's really a great exterior but just like the surface of the Earth is a big let's take a flatter as the approximation of a flat horizon approximation and just perfect on the horizon being over here things fall down this directions for the horizon and let's talk about the properties Of the region near the horizon and what happens the things as they fall toward the horizon through the horizon where happens now 1 of the things we discovered early on was the black holes have temperature black also as temperatures we even discussed the temperature and think we can do our roughly can't do it if they have entropy the entropy is proportional to the horizon area so it's almost as be entropy was carried by things which were so wallpapered onto the horizon maybe not so surprising since from outside everything does look at silent does look like it's plastered on the horizon so maybe it's not all that surprising that the entropy of the black hole is proportional the area we discovered that we try to throw more bits it made the black hole bigger every bit increase the area by 1 plant unit the area of the horizon we went that that's a quantum phenomena involves a spot our soul that and tapping and was also temperature anybody remember what the temperature Hawking temperature of a black hole with the sorrow of security some of his pictures over here and go back there hockey temperature black coal I was caught the was it'll be inducted cheat but you aged bar is a sea killed Co thing CQ CQ over a car a M G which it could also write in interns I'll be Schwartz the radius To MG divided by C squared is the short film radio services also equal I think that age see all over a looks to me like quarter piety all are do I have a right to OMG from slower have to put 2 0 here and divide by 2 0 yacht yes but in end particularly units in Barnes Serie 1 which natural units for us a temperature of the black hole was proportional 1 over the radius of the horizon and the radius of the horizon of a big black hole was big and black holes are cold cold know what exactly does this temperature means a best can't temperature depend on positions this is movie In some sense yes in some sense now our was a sense in which the temperature can depend their position I tell you right now the temperature in New York City is not the same as as the temperature OK but you said the temperature a kid and amount position right that somebody says that would explain yourself but it should empty space in a truly empty space at temperatures 0 in thermal equilibrium temperature is really only accurately defined with infinite precision in equilibrium temperatures thing that has to do with thermal equilibrium thermal equilibrium was what happens with everything gets equilibrated were all the variations in temperature when the heat flows in such a way as to increase entropy to the maximum amount and then temperature and thermal equilibrium is exactly constant now this is a true statement but or has done this stand in the gravitational field exactly what it means it does not mean here the gravitational field it does not mean in thermal and thermal equilibrium does not mean that if you took and ordinary standards thermometers and lowered it down all raised it up the temperature would be the same hour His wife temperature was temperature roughly speaking very roughly speaking in measures to Connecticut and of particles right now suppose it we had our that the surface of the earth was being heated from underneath his flames is a green flames heeding the surface of the Earth from Erminie making the surface of earth end around it was ejected finger thermal molecules into the atmosphere and factors molecules were the atmosphere left go to an extreme situation where the molecules of so rare that they don't bang into each other the mean free path between them is very large all the molecules of a weakly interacting that basically what happens when a molecule gets ejected is it falls back down so this above the surface of the earth molecules gravitation is pulling them back they'll be jumped up depending on the kinetic energy the words they jump up I am out of their which depends on normal fluctuations of the letter got hit with a hot surface here is bombarded vibrating shaking doing whatever the the fluctuating kicker molecule up a molecule will fall back do expect that can then make energy of the molecules to be the same how high you are not not because they Lewis Connecticut Energy may rise up supposing you want if you wanted to know so here's an example where even tho in some very technical standards which had not going to try to describe exactly the temperature resisting the everywhere there is a sense in which that is true but for practical purposes with what we mean by
temperature is that which is measured by a thermometer and what measure but from my mother can make energy of the particles of the hitting the thermometer the temperature would be higher down low that it would be a pipe paid sold or ever Connecticut you're particles would be harder more of the same would be true incidentally is of molecules but we were radiating times but can also be radiated and photons are also subject the gravitational force photons which are radiated will also fall backed down in fact as they they arise they lose energy as they fall Regine energy sources say photon photons of different right now let's suppose you will have we're very very far away you don't get too close to saying but you want to know what the temperature was below what would you do White measure the temperature high up and say Well it's a half a degree temperature up here but you could extrapolate down and say if the camp the typical Connecticut energy of a particle or a photon you see up Our 100 miles from the surface such is such that you could just use straightforward extrapolation and figure out what these were temperatures found near the horizon authorized no new leader near the surface of the earth in this case now what is the Hawking temperature the Hawking temperature is temperature seen by F. among other far from the black hole actual temperature over Mama would register were very far from a black hole it would be registering the presence of photons thermal photons black body thermal photons which somehow were rejected from black hole which out there's a kind of atmosphere of far from the black hole which were exciting the amount of violating and temperature is pretty cold but in the same way you can extrapolate downward and ask what the temperature must've been close to the surface of the black hole there actually is a formula we're doing it and I think it's a little bit late now we will go through time how you actually calculate be variations of these actual measured temperature in a gravitational field but other tell you the answer is the 1st of all it is that very far away the temperatures it is the Hawking temperature wears serious right over here as you get closer and closer to the black hole the temperature arises and as you get very close to the black hole you get close to the horizon we will close the Hawking temperature but kind of be extrapolated Hawking temperature would you extrapolate into let's give it a name he world it's temperature measured at a proper distance role from the horizon is 1 over to role 1 divided by 2 pi role the closer you are the higher the temperature now in fact the horizon is a very difficult place to escape from the factors behind the horizon you can escape at all you're right at the horizon or very close to the horizon it's extremely difficult to get away which is another way of saying you lose and water Of energy of photon loses a lot of energy when it tries to escape from very close to the horizon so if you see are fighting temperature a distance above the horizon extremely close to the horizon the kinetic energy very large as what's going on here be actual temperature Of the photons or of the thermometer that would be loaded on a cable Utah experiment returned lower thermometer on a cable to get 20 kind thermometer because forward reserve OF use tiny Fernandez's Booloora 24 Mama on a cable cable wheels send back a signal telling us what temperature recorded on Ammamaria's and as you only and find milder temperatures up up and up local up or 0 well if you really believe this but you would say that the temperature of course for the horizon was very very hot now we have a funny situation now on Web suppose we take an Adam and we it down closer and closer to the horizon what happens to that Adam as it gets close to the horizon would too if forget it forget general Otididae now it's just moving toward very hot region weapons to it becomes excited but a getting hot skiing really really hot but it's it's getting really really hot the nucleus gets a torn to pieces by the high temperatures quirks give liberated this defeated wealth gap right AII that's ripening enough red if we lowered the if we put a cable around you and lowered it down and put your feet of the surface of the black coal you get hot for that's what this picture says and how do you get away from it them a calculation of the legitimate calculation and this is a legitimate calculation the calculation correct and by now would be tested over and over again if you do lower something down on a cable and car then put back up it will be all of the evidence of having been In a very very hot region so services this is not to be questioned but the something funny America's because From this point of view and from this picture over here the horizon is nothing very special adjust the Green Line that I drew the ire but there was nothing there it was just a mathematical line that they drew 2 seperate the region from which you consider the signal out or you can't say no but nothing special was going on the horizon over here the curvature didn't get large the metric near the horizon was closed a flat space we already established that until nothing very dramatic going on this team I expect that if you dropped something through the horizon
and now think about it in the frame of reference of the falling object of falling object doesn't say it took an infinite amount of time to go through years of falling object or in the horizon the clock takes
off 2nd attack exactly 7 seconds to go from here to here in the frame of reference a foreign object the objects as I fell through I felt past the point where originally calculated the was a horizon because they a bomb by just over the horizon but when it was outside the black hole he made a calculation of where the horizon was estimated how long it would take the fall through it fell through it nothing happened From the point of view of somebody who falls through the horizon nothing happens effect point sounds contradictory either here it does get burned up or it doesn't get burned up 2 dozen get burned up how avoid the consequences of his very very high temperature or it could be a pattern of that ionized does get ionized particles gets spread over the entire Verizon by extremely hard heat which causes things to diffuse or of the fall through here there's gotta be the answer is 1 of the other a candy bar Frank Tom sold I think 1 way of trying together this is a think to try to think as much as possible it what I would call a year finally in kind away or maybe it's a Heisenberg kind of way the trial being To try the operation were about to try this luck let's see if we can approve or disapprove this so that by doing an experiment that he is the kind of experiment that you might try to think about the temperature of the Adam Media increases as a forced in fact it gives very high hard before it passes through the horizon it doesn't have to go through the horizon to get good hot hot doesn't have to get analyze a hydrogen atom 13 15 electron volts L 3 thousand degrees of 2000 agrees so at some point it reaches 3 thousand degrees outside the horizon at that point all makes a 2nd it should get a nest before itself through therefore it ought to be able to send the signal back out of somebody station ought to be able to send the signal back Taliban said the Adam unit did or didn't get ionized from 1 point of view we are Adam ought to be able to say nothing happening to me and falling freely to the horizon and within the within a certain distance of the horizon you told me the temperature was gonna be 3 thousand degrees but I don't feel a darn thing and that message to you and tell from the other point of view done a mathematical calculation which says that the temperature gets hot in that conflict real conflict so let's see if we can turned it into an experimental conflict after intact before we do I want to remind you of the Heisenberg uncertainty principle and the reason is the logic goes on here and that is important in understanding that it is very close to the of the logic of world that Heisenberg used when Eisenberg say said you can measure both the position and velocity of a particle bounce factor in some sense it can't have both position and velocity has 1 or the other you could measure 1 or the other Oregon you're having a certain property means that property could be measured then it has 1 or the other and both and that seems contradictory wives the contradictory if it makes sense to talk about the position of a particle at time and then it makes sense to talk about the sequence of positions of particles it makes sense to talk about the sequence of positions particle then it has a trajectory and that trajectory could be used tool to extrapolate confined the velocity of particle so that's really chose a tip that their particle has a position and every incident Vanhowe could not have a velocity of every step behind him but said I don't care what you say about whether it does it doesn't that asked if we could really measure both simultaneously understood this is a war very quickly remind you of the larger Kia supposing you are have a particle electron and you want to measure its position the high precision your measures position the high-precision how you do it you hit it with a photon you create an image of a timer screen and in all time the resolving hours to see the location of that electron within 80 resolution don't you have to have a full hit with photons of light waves who is wavelength it is no larger less than or equal the dope addicts but they end the wavelength is less than Delta X that says that the momentum is the larger of the photon was going to be larger are equaled the plants constant over Delta X is that punks constant width across a without the across because that means that the particles Gillingham bombarded by a photon in order to measure it you mother said look I believe that particles standing still has created that particle research away the standing absolutely spilled and I want to confirm the stand they have a right confirmed the standing absolutely still happy origin so what I will do what is measured position that quickly and then instantaneously Afterwards measures last week and tried check it was both at the origin and that rest well you know the story in the stone is extremely well just reminding you that if you have to hit it With the particle of momentum P it's going ahead of a recoil particles go go often some direction with the momentum more or less avoid P in what direction somewhat random eyes and sold if you try to measure the velocity
afterward it will not be what you thought it was in the 1st place I'm not the experiment create exactly the condition that it was designed to show wasn't the case the experiment was designed the show that the velocity was 0 level and just experiment itself created the conditions which was the opposite of what it was designed to confirm that Heisenberg logic is deeply of course connected with quantum mechanics each bar appears in arms classical electrodynamics you could make an image with arbitrarily small amount of uh arbitrarily low intensity electromagnetic waves you don't have the have 1 whole quantum in quantum mechanics you can subdivide the energy less quantum so if you want to experiment use stock you where are you going to give that were charred kick OK let's let's analyze would be Heisenberg and analyze the question What happens when and Adam falls on the horizon does it or does it not get our idealized does it does get a really mutilated by the high temperatures above a certain line here said the cost Bowser online use the line role a distance role with temperature T is 1 or 2 Pyro now were interested in it is when meet Adam falls below the line with the temperature has exceeded the ionization temperature when not understood what happens when the Adam is above the region where it's nice and cold where interest in what happens to the Adam when it gets within the within the region where the temperature is of order the ionization temperature but once it gets down at low it's in this huge gravitational field it fell from above the huge gravitational field near the black hole has accelerated its accelerated by that point up to close the speed of light just because the figures the gravitational field so we can't near the horizon so hard to get away the gravitational field things falling down would now with close to the speed of light how much time those affair before it actually falls through the authorized wanted through the horizon it you cannot find anything out about it wanted through her eyes I saw how much time does it have before distant while the answer is wears a rollover see if this distances row the time there has His roll over state which is proportional to sober while the temperature world the ionization temperature behind the ionization temperature was short of the amount of time that the particle fans In region OK now how we going to do an experiment from the outside to determine whether the year before waterfalls it's too late once a fall so the horizon late kink in the information and we want to find out during this the short period of time he also falling in the high temperature region we want to try and find out a suicide how we find out of the we shine some light on him Be a source of light over here that life is gone illuminated bounce off and created image is image over here is either and Adam on ionized or it's gonna be Adam splattered all over the place where we don't know it OK we have a very short amount of time to do the express namely the amount of time that it takes the fall from the region where the temperature 1st got high enough United it would force the horizon short amount of time that means was me in terms of arm of resolution power the latest say it is we have a small distance that we have to resolve we have to see that happen within a small despair at small distances role was means well I mean that that 4 times had had better have a of which is smaller than the distance wrote so I am there possibly smaller than role and that does the energy of that photon vestibule larger I'm with a row of C H bar over land that saying the biodiversity the is current seen this is P. C. right 4 H H the energy has to be larger than the small away when the larger the energy and lenders or a row of energy has to be larger than there so well this is essentially exactly energy that corresponds to this temperature for overall we did were made bottoms a 1 role while rose thing he another words you have hit particle you have to hit the Adam with a photon which is energetic enough time analyzes the North to see it in that period you have to hit it with a 4 which is energetic enough but I am another words you have to create exactly the conditions which the experiment was designed to show do not happen the experiment will organize the year of the year and there is no way to check whether it was the experiment that ionize the Avenue China do it again try to do it again after the experiment the sea of still lionized that's will be stored 18 experiment to do which is designed to prove that the Adam wasn't ionized will ionized an iron ICM uncontrolled way in a way to do that you can't go back and the check was my wife so young lady the whole
yes no frame of the falling object yes yes the Adam why doesn't like what happens if somebody out here what amount to you walk and see whether you could fall through the horizon if they did an experiment to check we will evaporate you voted for but if so nobody does experiment to define the nuclear have you're in trouble but you're draw the letter borrow a black hole radio you have exactly the same problem if you try if you try check the the temperature is rising Our when he checked with about it but let's say you just drop a thermometer Maryland you drop elected a murmur of freely for you wanna find out from commanders gun the Opel bit heavier find out again as the amount of Monaco's falling you've got the gets some radiation back from the thermometer so you have it was some radiation and we'll talk at the look at the thermometer more or something has to interactive Mama anywhere to always find inevitably bad for prevent it will show that it was hot but was show it was hot just acceleration of turning around like a top they all such cash a his long as you could be getting information back that information will be coming back in the form of quanta and those Kwan below either have been emitted by the object of her remains interacted with the object is no way you could get information without getting I want them back from the object is object radiated those quanta and therefore recoiled or you hate it with want there is no way to do it without where influencing the object and the amount of influence is always always exactly what don't have work the temperature about point would have done so what's sort of Catch-22 Liu not do the experiment causing the thing you would try of can so that I can be thought of as a result of yacht what or small time but the they're saying that went out back out of the strictly that tried to get out of a block or a former mentor block or it gets out arrived earlier this week said he or not got it does because Newdale says Bob now that's full-time did not have to be a high energy photon by the time we got out using traveling how would you lose some energy but it did have to be a high energy photon region here His Adam doesn't care what before Parliament you was out here wants to know what the energy that was a world it with the measurement it yet by up to get it doesn't have to be an external photon hitting it could be something that it naturally admitted but Herbert tripped on board black holes of direction he told Europe goes through erasable let's not that at its upper can get a JOB object which is Fawnia me objectives for years it's kinetic images and temperature but interacting with an environment which is getting harder and harder see environment its interacting with which is which is the top you should have look like it's a radiation from a black hole what was said shit Carrara if you you could look you could do an experiment you could imagine next an experiment in a laboratory that's falling with the magnetic fields were wasn't and that experiment as you fall we could be doing the experiment the problem is giving me information back out of the black hole right so whatever happens in the laboratory you'll have to dual you interact laboratory was something external and the information by back out and it will always be the case but these are the energy of the fault the necessary to get that energy that information back out on the scene or at least as big as energy Of the environmental photons and the normal back but that is exactly what really very small and very small errors that that's a point you dark urine dude distance over which the temperature is high is very small and to me the think that you have to have a photon of high spatial resolution or high time resolution you the way you say the photon has a high momentum has a high energy this is what we did to review whose jets yes yes yes so this this parcel about what goes on the high seas surface of a black hole whether it does or doesn't get hunt all mixed up with these questions over of our of quantum uncertainties and so forth and that's the result there's no way answer the question other than to do the experimentally the expanded the experiment will do exactly what you were trying to show didn't happen so now brokered
resolution it at time a holy war or energy the only get worn shot a beach go article forward Verizon His is opposing did the same experiment over and over with many many Adams and use a low-resolution going before about that 1 the travel use less less energetic photons of course each worker question susceptible will question good we oughta be answered back is threat above all right but you don't have to do we are the right a total but you can't beat the uncertainty principle by what you try to do those days we did the 1st volume of now we can only say grab the experiment William itself cause the conditions trying to prove that happen so we can go from this kind of analysis and other words were we to if somebody comes and as work I am convinced that there are that somebody who falls Verizon and nothing happened the will be yes could you do an experiment that shows the Ansel been all you cannot do experiment that shows that Solis is designed to show that level of operational Experimental physics it would be impossible to confirm that the year after the Adam did not experience a high temperature and will come back will book and a couple more good Duncan experiments and try to see what they say is of course there's no way to say what happens is no experiment is done now it's very much like to slit experiment where are you dumped do an experiment is no meaning the question which slipped to 1 you don't do an experiment is no answer the question OK we're sure all Marie work for
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Metadaten

Formale Metadaten

Titel Topics in String Theory | Lecture 5
Serientitel Lecture Collection | Topics in String Theory
Teil 5
Anzahl der Teile 9
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15118
Herausgeber Stanford University
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (February 7, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses again on black holes and how light behaves around a black hole. He uses his own theories to mathematically explain the behavior of a black hole and the area around it. In the last of course of this series, Leonard Susskind continues his exploration of string theory that attempts to reconcile quantum mechanics and general relativity. In particular, the course focuses on string theory with regard to important issues in contemporary physics.

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