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# Topics in String Theory | Lecture 7

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back and think we were in the midst of trying to explain to you how string theory gives a rough explanations of the entropy of black holes but doesn't pass if you remember evolves remind you if you did remember on the a slight some equations on the blackboard here which will be useful but I don't know that that things a he is a key hair care was false Richard them as indistinguishable will take them where we treat them indistinguishable if they are identical ahead you can a counter positions within the box yah yah putting them into a box of a certain size namely the argues that soon will be extreme would pick up if we woke there that of the on OK I want to write some equations on the blackboard remind you that simple equations and then I want set target goal for simple little derivation of the entropy of a black hole it's kind indirect minutes very subtle but very easy doesn't doesn't want anything is complicated I don't think it involves even the derivative let alone in the world certainly no infinite some odd it's pretty easy but still it is subtle sometimes Osub listings of the easiest ones in the sense of easy mathematically and this is 1 of the pilots so 1st 1st equation GDR he is Newton's constant we're going to work in units in which C equals age bar equals 1 and that that Newton's constant equal to 1 we believe that flooring so as 1 because for quite see because we measure space and time in the same units the speed of light is 1 constant be equal to 1 that's something go that permissible to do and it's just units which the uncertainty principle says that the product of the uncertainty of position on the uncertainty of momentum is equal to 1 unit 1 unit of something they Nunavut options ROC people 1 but we won't fit along with all traversable Newton's crop comes from more than you at all the results Eagles age follicle toward the loop but you have to specify you can either take it to be all or mass and I'm not cast is in leg man isn't in for does remind you why that is the fact that energy which is the same as last year you will need to do write equations find some equations after energy and look at the various dimensions and see what happens energy for example quantum mechanics energy is given by plants can't stand are divided by the wavelength times well
and that is the way photon for example this would be a connection between the energy of a photon adds wavering using it for anything except to to say what relationship between energy Our between these units In units are now this is not the romance To make a massive think we have abided by squares right ER overseas squared is equal and lots of people who know that you overseas Quaid was a Quebec em but it took a genius of Einstein to realize it and people to see squared price would Chloromycetin Yancey downstairs not only a cad novices I don't they can wear overseas our because we're a cervical but so the only point of this was to say the U.S. ask what we said Siegel born on the same as a unit of upon constant over land but also said plants constant equaled 1 now a unit of mass on 1 the key never mind mass is 1 Lowery Europe's Unit 1 day now what about a unit of GE not said called 1 gene has units set to hide the figure would be units of a G R we just take again equation that has G in it and those look at who what's assemblers equation contains G which he gets acceleration equals GE and also our square now bereft inside what's the units of the left-hand side of is overtime squares and time at the same units whimsy is equal more this is just following squared which is 108 right what a square of course it is laying square costly squared and now we can multiply both sides of the equation by laying squared his becomes line upstairs where we know that before it in ways that sphere radius ish children 80 years or proportional radius of black hole but now on is late in the 1st length and on we can ride a mass is 1 of our main transferred to the other side we discover that in these units GE has units of an area what area His only area around a bit could be the plant area I too GE is in fact not only an area that's also the a plug area square it's important equation and the fact that helps us understand why it is that the entropy of a black hole is an earlier divided by 4 Heinz G. forget before a seat it a divided by GE at sea area in plant so whose we're OK so that's 1 inquiries and now there's is another factor and that's that jail of course also has not just owing squared it does have to do with the strength of gravity so let's think about it in the context of string theory as having to do with the force of gravity What does the force of gravity come from the force of gravity and no explanation of this tonight this is not for tonight we talked about before this is justified cartoon The 1st of gravity between 2 objects this could be the a communal not he is due to the exchange a rabbit out as happens string well everything is made up of strings of string breaks off funds of often takes off when the stream courses itself there is a probability that won a string of the CB strain wears core boy no
turned this there and keep that he and stick out when the stream classes itself that can be arranged the string closes it's also could rearrange that probability of the square root of that probably would restrict speaking square root of it is cold we amplitude for rearrangement Austrian breaking or whatever but some breaking its rearrangement of Squire little Judy with talk about before Fuji remained about it is it a problem at square the probability a probability has no Unix dimensionless His G which is the probability that we're straying crosses itself it breaks off a little piece that OPEC jumps across 4 other things really Rangers again the shooting jump from 1 side to the other that in string theory is the diagram of the analog of fighting diagram which has to do with the forces between the 2 sides and but the thing is proportional to powers of this Jew you want to limit total for those to absorb liberal Stern that tells us the force of gravity is proportional Judy square so what must tell them is that Lucy squared must be proportional the notice CoreStates known as constant as the strength of gravity liturgy is the probability for break a string breaking but this can't be right laughter insiders dimensionless has no dimensions is just a probability the right-hand side has units of so other Huston something Ellison hero for make up the units give you and is on the left side was that that has to do with the fundamental link scale of theories it's not a punk like it's the fundamentally length scale of string theory is basically if you look at a lot of illegally staying you'll discover inevitably consists of little wiggle at random walks but as with and is basically the size of Lulu with the basic size of Art and it's cold strength with talk about before founders reminding you it's all other variable around and the problem is his plunked squared beside strength a beside his gravity gravity tells us that this side is our plant squared off only sensible equation like right but only contains things that have to do with string theory on side is to say that this is Jae squared times l string square and that's the collect equation physical like equation that the plant closed squared which is the same as big G is little D squared times L. string scrimmages thing about them and that means that if we G well over 20 20 number gravity will be very weak and tell us is that was much much more restrained for further fact is school G which appears he could also be thought of as having could do more With the relative size Of the plant length scale length scale it has to do do with gravity and streamlined scaled back we can even take the square root of this equation do so it says that plant is G Times strength cassettes another equation right Darren ya plant is equal to GE Times l strength over equations that we need cut next equation just make a list of them before which I use them and before we tightened arriving next equation and they are they strengthen the entropy of a string X entropy basically counts the number of decisions yes No War up up then owned or left to right decisions that you have to make the describe the system let's just leave it at that that's the number of could finally was a matter of binary it could be trying very hard quaternary some small number number of decisions that you have to make the specified configuration I get a little example all a model for string theory and is it it's a reasonably good model for string theory is well that statistical mechanics people use all the time laughter string theory but other purposes where Place restrained by a series
right frenetic and that will equal I'm not school said Jean Todt square 3rd divided by going right models have not realize this woman who has to be our summer here you'd better be because yeah life please please let me say yes vote less drama OK 1 here Tuesday at the time of her death of but now I think we're right down OK but multiply both sides by no stretch and then we get a lot Jean square hello straying square it is equal to em scholar L string well as Jean Monnet squirt Pennzoil quartered capital Jedi at this pointing at the target point its capital GE at the point where we were trying to investigate the object so we can like this equation and not squared Connors was just Koji not whatever the constant was at this point over here Digital room will be moved here was just a truck about where we thought it was that and stop point over here crimes Telstra what solid year I'm not think pungent spot Citicorp which boast change services where's where's the equation this equation over here that's entropy which doesn't change its the entropy at this point but it's also the entropy over here some particular it's see entropy of interest sorrow a float is the connection between the 2 sets of ideas it's not the subject he thought of as a string and use them use a lot change it until it becomes a strain and off the entropy from the properties Of the string of point and that relates and not squared Jean which is why clear formula all rear someplace relates the bloc also Mueller at that point from stream formula at that point that was the theology of the connection between our understanding the entry fees of black holes and relating it the properties of stray this much more sophisticated versions of its version of it was not powerful enough to determine the numerical constant medical constant one-quarter this was much too crude for that hour why was it too crude among among other reasons as always was a bit of sloppiness in exactly where this transition happened the transition between string end of black hole is not a shot sudden transition and even if just trust transition will not have the power to predict exactly where it is all we can do is Paris bureau of so this
technique was not powerful enough to them the factor were quarter but where was powerful enough for for hours to get the same kinds of formulas for White a wide variety of different kinds of black coal objects different dimensions of space different things called Black things called black a black holes in all different dimensions charged black holes all the whole works the same technique work but not good enough to get a numerical factor the factor was provided by mathematically sophisticated version of which had a great deal of symmetry supersymmetry things when I can do I didn't it did in anything conceptually Avery knew it entered the color of symmetry and make very precise complications and the end result was a factor but was correctly identified OK that's so much slower strings and entropy but I just some it was deemed it doesn't string theory is correct it means that is mathematically consistent description of gravity and quantum mechanics which does contain black holes has within it only framework an explanation of the entropy of black holes YTD is an explanation of entropy black all's well armed entropy as opposed to climb again is an indication of the existence of microscopic substructure which equations are you a rough coarse-grained description may not see so the fact that black clothes hadn't would be woes evidence that there was some underlying small step Tuesday describing whenever a black aware of the horizon of a black hole is an To do that string theory was 1 1 and 1 other thing which is destined to is at the Apollo came out right here in my have come out Kobe
space now it was at the point and then maintained the same quarter positions nevertheless spaces expanding between fixed isn't the time this separating with a velocity which is related to the dissidents by the Hubble constant at that instant of time but that's not what they see when they look at each other what they see when they look at each other as they look back and they see 1 another and earlier part so this fellow over here sees this 1 moving away from him not the velocity that it has the same incident of time velocity that he had earlier and so you have to use a more complicated formula if you want to answer the question what somebody sees but this is what it is true at a distance of foreign elements of the plan that affected show was mayor of hers may not be as interesting as what you could actually be attacked by looking back but the rush is quick OK now 10 the Hubble constant beat constant is something that is capable of really just be a number and not changing with time what was quoted as all before we do what sort of reels but some if this is true a given instant of Prime indeed given instant of time that the velocity is the distance the Hubble constant and spaces Is it delivered the elections us and is a distant scale which is large enough that things are moving away from you with the speed of light and factors a distance which is large enough of them moving away with from you with 10 times the speed of light it is was not a mistake this is a true statement that because biology in an expanding universe like this could to the points can be be moving away from each other with greater than the speed of light the kid has each other with greater than the speed of light some those not you can't could buy you as the speed of light but 2 things sufficient would fall apart can and will be the year of the relationship between the Hubble constant than distance scale in order that you are at the speed of light you would just get pregnancy here see equals distance times age says you see meaning the speed of light the some arbitrary constant let's at the speed of light as we usually do and they say at a distance equal all over the Hubble constant that that instant of time things and not the moving away from you at a speed of light million most instances not because most allergies Ivins scores Montes that we use today means most Cosmo that was that the hairs on the Hubble constant decreased with time the Hubble constant decreased with time as time went on the Hubble constant of smaller and smaller which in the distance outerwear things are moving with the speed of light relative to you get a larger and larger with time you might think if his of our galaxy out there which is only from you with the speed of light on the that you could never see but the Hubble constant is decreasing you wait a little while and you find out that the distance to which you concede is a lodger Hoover was distant store that things are moving with the speed of light is larger and so announced because not allergies only because my orgies it was a case that there that there was no bound them when you could eventually see Bible gets smaller and smaller and smaller some distant outerwear things are moving with the speed of light we get larger and larger and you eventually see their mother because Macias uppercase modern Cosmo the Hubble constant or the Hubble constant thought open the Hubble constant meaning opened in the future appears as if it's becoming comes truly constant from some with foreign our Epsom observational factor I can tell you how we're not getting the observational cosmology here but there is good evidence that we live very strong evidence that we live in a universe where the Hubble constant is pending to a constant true-crime so let's investigate the consequences of the universe In which the Hubble is can't and they what's like if that is the case the bubble constant is a constant vandalism universal distance out which will you look at that distant things will be moving relative to you with the speed of light and that distance won't change with time but so let's investigate that possibility what does it said was a mathematically just spend a couple of minutes ever to might continue next time was says the Hubble constant is 8 . 0 8 already achieved it was age and ask constant now now age is just and constant has some units were due what time right right so only when you specify the Hubble constant Europe specifying applying scale innocuous the relevant time scale is about wild about 15 billion years so other kinds of the very small number but nevertheless appears to be constantly figure the become spent as says tree writers equation as DAY beauty physical the age relative signed that Is that the rate of change of something is proportional proving itself was a solution of equation like that exponential exponential 80 equals a at some fixed tying the matter what kind we don't matter important crimes eagerly H the scale factor increases exponentially with distance between pairs appoints a good increases exponentially Coleman and inflating universe that's called space for this property space with this property with a being before he put 2 H that put to death and see where it is square hazy BHP a square to late in this space has it called the de Sitter space base through beyond our mathematical astronomer physicist 1st discovered it the sooner what will and Willem de Sitter Dutchman but 0 4 4 4 or Swope smoky space sitter exponentially experimental armed I think we are I think we're stop now what the next time it is that the Soto space spaces with this property have event horizon event dozens which are in many respects similar a black hole horizons Our but they're almost like inside out horizon when you think about a black hole outside the black coal and looking at and you see a region where things on the inside are moving away from you faster than the speed of light roughly that's why the kick out our allies of de Sitter space is quite the opposite exactly the opposite of religion out there was large enough distance with things are moving away from you with the speed of light you kind of on the inside of it and things are moving away from you with the speed of light for whatever them and you
will never catch up very passing through that relies and are there were things are moving with the speed of light that as the those system with the passing the horizon of a black-owned the only differences as far as we know this space does not evaporate them with a black hole of her so talk about the city's face the problem at its horizons and will talk about why it that creates a lot of confusion and interest in modern pathology for more please
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Wellenlänge
Target
Direkte Messung
Masse <Physik>
Closed Loop Identification
Stringtheorie
Lichtgeschwindigkeit
Konfektionsgröße
Besprechung/Interview
Minute
Computeranimation
Schwarzes Loch
Regelstrecke
Theke
Jahr
Rangierlokomotive
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Transporttechnik
Passfeder
Wärmeaustauscher
Fahrzeugsitz
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Direkte Messung
Parallelschaltung
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Stringtheorie
Konfektionsgröße
Geokorona
Leistungssteuerung
Leitungstheorie
Photon
Regelstrecke
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VW-Golf GTI
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Tag
Rauschzahl
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Jahr
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Virtuelles Photon
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Stringtheorie
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Blei-209
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Gas
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Leistungssteuerung
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Juni
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Masse <Physik>
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Buick Century
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Target
Summer
Stringtheorie
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Weiß
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Minute
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Schwarzes Loch
Satzspiegel
Jahr
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Initiator <Steuerungstechnik>
Planet
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Jahr
Matrize <Drucktechnik>
Ersatzteil
Schwarzes Loch
Lichtgeschwindigkeit
Computeranimation