Quantum Geometry and Strings
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Formal Metadata
Title 
Quantum Geometry and Strings

Title of Series  
Number of Parts 
06

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2015

Language 
English

Content Metadata
Subject Area 
00:00
Standard deviation
Theory of relativity
Multiplication sign
Closed set
String theory
Mass
Perspective (visual)
Theory
Perspective (visual)
Mathematics
Sign (mathematics)
Lattice (order)
Meeting/Interview
Right angle
Quantum
Resultant
02:03
Group action
Mass flow rate
Lorentz group
Dirac equation
Group representation
Maxima and minima
Invariant (mathematics)
Euclidean space
Dark energy
Invertierbare Matrix
Geometry
Regulator gene
Block (periodic table)
Witt algebra
Gradient
Interior (topology)
Mass
Median
Food energy
EinsteinFeldgleichungen
Riemann surface
Category of being
Divergence
Green's function
Mathematical singularity
Theorem
Mathematician
Spacetime
Directed graph
Point (geometry)
Spectrum (functional analysis)
Momentum
Transformation (genetics)
String theory
Perturbation theory
Point cloud
Dreizehn
Mass
Regular graph
Scattering
Element (mathematics)
Number
Frequency
Carry (arithmetic)
Degrees of freedom (physics and chemistry)
Term (mathematics)
Boundary value problem
Equation
Normal (geometry)
Quantum
Dean number
Series (mathematics)
Pairwise comparison
Standard deviation
Scaling (geometry)
Image resolution
Surface
Classical physics
State of matter
Paradox
Theory
Line (geometry)
Mathematical model
Group action
Quadratic form
Mathematics
Calculation
Function (mathematics)
Universe (mathematics)
Game theory
Quantum field theory
Family
Vacuum
Entropy
Musical ensemble
Beta function
State of matter
Standard Model
Multiplication sign
Decision theory
Direction (geometry)
Mathematical singularity
1 (number)
Mathematical model
Insertion loss
Horizon
Parameter (computer programming)
Mereology
Food energy
Quantum state
Mathematics
Tensor
Matrix (mathematics)
Manysorted logic
Gravitation
Gradientenfluss
Quantum field theory
Planck constant
Renormalization
Sigmaalgebra
Quantum fluctuation
Moment (mathematics)
Physicalism
String theory
Twodimensional space
Price index
Bilinear form
Functional (mathematics)
Metric tensor
Quantum mechanics
Equation
Normal (geometry)
Quantum
Convex hull
Right angle
Classical physics
Geometry
Finitismus
Conformal map
Observational study
Sigmaalgebra
Paradox
Theory
Regular graph
Thermodynamisches System
Symmetry (physics)
Theorem
Gamma function
Field (mathematics)
Conservation of energy
Consistency
Projective plane
Mathematical analysis
Mathematical physics
Incidence algebra
Transformation (genetics)
Entropy
Physicist
Physics
Gravitation
Finite set
Coefficient
Local ring
Spectrum (functional analysis)
20:11
Dynamical system
Correspondence (mathematics)
Analogy
Dimensional analysis
Dirac equation
Abelsche Gruppe
Hausdorff dimension
Physical law
Local ring
Descriptive statistics
Flux
Compact space
Spacetime
Conic section
Basis (linear algebra)
Mass
Parameter (computer programming)
Manifold
Divergence
Order (biology)
Mathematical singularity
Stability theory
Spacetime
Directed graph
Design of experiments
Point (geometry)
Metrischer Raum
Classical electromagnetism
Transformation (genetics)
String theory
Translation (relic)
Event horizon
Frequency
Goodness of fit
Degrees of freedom (physics and chemistry)
Arithmetic mean
Equation
Units of measurement
Initial value problem
Series (mathematics)
Cone penetration test
Image resolution
Surface
Theory
Line (geometry)
Differentiable manifold
Supersymmetry
Network topology
Universe (mathematics)
Gastropod shell
Quantum field theory
Family
Vacuum
Quantum gravity
Spacetime
State of matter
Multiplication sign
Mathematical singularity
Kontraktion <Mathematik>
Parameter (computer programming)
Mereology
Food energy
Quintic function
Junction (traffic)
Rotation
Manysorted logic
Gravitation
Quantum field theory
Circle
Geometric quantization
Area
Process (computing)
Point (geometry)
Moment (mathematics)
Process capability index
Thermal expansion
Measurement
Connected space
Maxima and minima
Hausdorff dimension
Equation
Condition number
Identical particles
Flux
Geometry
Ocean current
Image resolution
Metric tensor
Theory
Supergravity
Gastropod shell
Spacetime
Subtraction
Field (mathematics)
Absolute value
Condition number
Element (mathematics)
Event horizon
Physicist
Factory (trading post)
Gravitation
Momentum
Object (grammar)
Units of measurement
Local ring
37:44
Group action
Mass flow rate
Latin square
Correspondence (mathematics)
Hyperbolische Gruppe
Summation
Maxima and minima
Vector space
Physical law
Homologiegruppe
Thermodynamics
Physical system
Compact space
Invertierbare Matrix
Geometry
Spacetime
Trail
Mass
Staff (military)
Asymptote
Thermodynamischer Zustand
Hand fan
Graph coloring
Phase transition
Mathematical singularity
Theorem
Cycle (graph theory)
Annihilator (ring theory)
Supremum
Spacetime
Directed graph
Point (geometry)
Momentum
Feldtheorie
String theory
Similarity (geometry)
Mass
Regular graph
Counterexample
Number
Renormalization group
Term (mathematics)
Glattheit <Mathematik>
Equation
Devolution (biology)
Stationary state
Units of measurement
Compact space
Scale (map)
Series (mathematics)
Supergravity
State of matter
Theory
Counting
Set (mathematics)
Existence
Equivalence relation
Mathematics
General relativity
Network topology
Field (mathematics)
Game theory
Family
Entropy
State of matter
Interior (topology)
Multiplication sign
Direction (geometry)
Mathematical singularity
Sheaf (mathematics)
Horizon
Parameter (computer programming)
Quantum state
Duality (mathematics)
Order (biology)
Mathematics
Manysorted logic
Scalar field
Lattice (order)
Gravitation
Planck constant
Circle
Stability theory
Area
Process (computing)
Closed set
Point cloud
String theory
Perturbation theory
Term (mathematics)
Bilinear form
Metric tensor
Maxima and minima
Hausdorff dimension
Equation
Right angle
Fourdimensional space
Fundamental theorem of algebra
Resultant
Field (mathematics)
Geometry
Computer programming
Topology
Existence
IsingModell
Image resolution
Modulform
Distance
Theory
Power (physics)
Supergravity
Prime ideal
General relativity
Regular graph
Causality
Wellformed formula
Operator (mathematics)
Theorem
Gamma function
Field (mathematics)
Subtraction
Horizon
Voting
Scalar field
Factory (trading post)
Sheaf (mathematics)
Gravitation
Conservation law
Pressure
Units of measurement
Matching (graph theory)
53:58
Geometry
Spacetime
State of matter
Conformal field theory
Multiplication sign
Correspondence (mathematics)
Mathematical singularity
Horizon
Mereology
Focus (optics)
Equivalence relation
Quantum field theory
Diagram
Right angle
Units of measurement
Condition number
Series (mathematics)
Focus (optics)
Standard deviation
Unitäre Gruppe
Geometry
Spacetime
Process (computing)
Sine
Correspondence (mathematics)
Closed set
State of matter
Theory
Infinity
Perturbation theory
Density of states
Asymptote
General relativity
Mathematical singularity
Conformal field theory
Condition number
Boundary value problem
Quantum gravity
Randbedingung <Mathematik>
56:45
Group action
Greatest element
Curvature
State of matter
Conformal field theory
Wave equation
Multiplication sign
Mathematical singularity
Thermodynamic equilibrium
Horizon
Parameter (computer programming)
Mereology
Food energy
Nominal number
Maxima and minima
Exclusive or
Plane (geometry)
Manysorted logic
Quantum field theory
Moving average
Thermal radiation
Cuboid
Diagram
Descriptive statistics
Physical system
Area
Spacetime
Repetition
Point (geometry)
Physicalism
Infinity
Mass
Food energy
String theory
Functional (mathematics)
Thermodynamic equilibrium
Measurement
Category of being
Graph coloring
Hausdorff dimension
Mathematical singularity
Quantum
Fourdimensional space
Block (periodic table)
Arithmetic progression
Conformal map
Spacetime
Geometry
Point (geometry)
Color confinement
Free group
EinsteinFeldgleichungen
Conformal map
Momentum
Vacuum
Level of measurement
Divisor
Algebraic structure
Feldtheorie
Limit (category theory)
Rule of inference
Theory
Number
Measurement
Frequency
Causality
Operator (mathematics)
Energy level
Right angle
Free group
Field (mathematics)
Condition number
Multiplication sign
Shift operator
Slide rule
Schmelze <Betrieb>
State of matter
Operator (mathematics)
Limit (category theory)
Existence
Sphere
1 (number)
Mathematics
Field extension
Causality
Computer animation
Function (mathematics)
Field (mathematics)
Gravitation
Boundary value problem
Cuboid
Local ring
1:04:29
Spacetime
State of matter
Conformal field theory
Multiplication sign
Decision theory
Mathematical singularity
1 (number)
Insertion loss
Horizon
Weight
Food energy
Summation
Physical system
Geometry
Spacetime
Product (category theory)
Block (periodic table)
Point (geometry)
Mass
Term (mathematics)
Law of large numbers
Measurement
Maxima and minima
Density matrix
RWE Dea
Figurate number
Resultant
Geometry
Point (geometry)
Level of measurement
Line (geometry)
Algebraic structure
Infinity
Measurement
Degree (graph theory)
Causality
Term (mathematics)
Wellformed formula
Operator (mathematics)
Selectivity (electronic)
Lie group
Field (mathematics)
Initial value problem
Multiplication sign
State of matter
Horizon
Theory
Independence (probability theory)
Division (mathematics)
Existence
Inclusion map
Causality
Function (mathematics)
Game theory
Boundary value problem
Family
Vacuum
Perfect group
1:11:39
Point (geometry)
Geometry
Group action
State of matter
Multiplication sign
Image resolution
Feldtheorie
String theory
Horizon
Mereology
Frequency
Meeting/Interview
Transverse wave
Descriptive statistics
State of matter
Theory
Food energy
Set (mathematics)
Mathematics
Calculation
Causality
Logic
Universe (mathematics)
Mathematical singularity
Resultant
00:07
the on and on and on and on and on on and on and on and thank you very much for the invitation to this closing day and actually even tho I was not a very systematic by the soup and the police said of the mass there yeah I really enjoyed it because it's the way I hadn't spent much time in my life thinking about the quality of water and sewer but I think I learned many things now the 1st signs of the change should they go from here all so fast disclaimer you might think I was asked by mobile pollution the right but meeting I think I was asked by these 3 gentlemen the organizers to talk about stink COD in a way that enormous specialists would get at least something out of the picture even I some of my strength theory friends in the audience I condemn them right away that they will not learn much from this stock it but hopefully I will convey a little bit of the others people that haven't been watching you the subject and way with this in mind where I'm not going to speak about my results from a recent results I would just put in perspective the fuel I think wellestablished facts by my standards of mathematical rigor and comment a little bit on the recently that shoring up relations with the issues that were raised in I want them master so it's some kind of pulled pork for months a version of book by tea same amount and there for general
02:04
were by team I was surfing 1 idea have anything but a low surfing with a family friend make federalism blonde from a younger man American mathematician who happened it was a she and she wasn't invited 1 of the movement of police than she had the ball the world a sending out should drop by but she didn't speak French so she says something interesting happens when you are really lost you know at this stage that otherwise might not that just for example a notice there was only 1 of the women in the crowd and the about 40 depressed people From the picture on the left you can also see that the median age is probably what 50 or so it's apparently OK before the sleep and the singing and would like to hear from let's holds here will be no feel free this last year are his very brief outline of what I would like to try write to say here I was spent very little time 5 minutes hopefully just to say a few generalities about string theory of course there's no chance I kind the way justice to the subjects I would just make some general remarks then held token little bit about singularities the game the way in which singularities have been consider think the audience here I'm talking about mostly singularities of spacetime the ran in the last 2 parts 2 hours trying to talk to you about 4 eyes arms and entropy and above the muds and geometry and against some of my friends here I you see I will probably have much more to land it we can see us things goal through the end now so some generalities 1st of all let me just the right to set To put the setting somewhere the local Wolfson whatever I say you know past knew that things are usually the Wolverines to the satisfaction of the physicist motive in mathematician on mathematical physicist but this statement usually are considered the most efficient solid so as not to pose questions so as you all know here is the story would have would have it elected this quantum field theory that's the standard model it's but the defined you can put it in some grand unified school Peterson politically for initial again for a physicist this means that it can be defined in principle opposed this from status on the way to the deep the violence then is leaves in a classical among around them the classical background is indeed there are described by the Einstein's but Classical Action and blue herons clouds this morning I don't think twice about quantum field theory and classical geometry and I think of this doesn't found employment in their next clash at dawn with presentday observational studies geometry classical the it's the quantum field theory in the background of course there is a lot of you know already good that can going through the use and that this was explained this morning but a priori from the point of view of a physicist you know thinks simple worked perfectly fine now of course many things may hide in the sky but again there are 3 aptly citizens why this story is not satisfactory there is an optional problem because some people think the solution is outside physics in metaphysics of are the wives of dark energy right that's the 1 thing no 1 has been good beginning of the feeling of understanding then there are all these conceptual problems conceptually incomplete you should should 1 think of John successful here and mix quantum states and what about the information paradox of black callers and finally anyway this series of a mathematical incomplete and there is on singularity so durability so you know you cannot simply shown that Einstein's theories the end of the story because the theory has a generic singularities and that's where you have to do something people boundary conditions say something more do something more so could I think everyone agrees that something should be done at the latest at the Bronx and actually you know people have tried all sorts of things for years and most indeed ideas I'm very quickly and the difficulties you know that most of the real idea would be to say Well let's former Einstein's theory to make it to normalize the room it's OK for you create gravity but this has go when you try go to Lawrence and signature so this doesn't work the then I think the idea was by probably Shahada affairs who said Well you know maybe gravity some kind of hydrodynamics it sense in marriage From quantum field theory In the same way that hydrodynamics emerges from atomic or molecular physics and actually have tasting a simple version this was ruled out by the socalled Weinberg with fear and this is a very simple kind of and it's a theorem that had in the autumn by my standards but Europe for many of the people in the audience it's a statement that says that there there cannot be a massless spin to state In a theory that has a conserved management's intention and they're optimistic and violence and the theorem is a really sort of thing hour or you have to do is show that there is a matrix elements off the average American comparison between 2 states that has to be nonzero it has to be 0 because the energy is a course of quantity chief integrate the 0 0 you should get he and there is a further more sensitive items you can check quickly forcing people write down these as the answer but this is obviously inconsistent is there you have JSP bigger than 1 particles simply because these quantity on the left does not have consistent transformation properties if you to update by a mindless feet around the momentum of the spin projection of the particles being deprived separate 3 reinstatement simply if this is the wrecks the representation of the Lawrence Group and its Jay's begin unwanted you cannot make this work because you change of the have at least 4 they don't they've had with the Montemayor this is very aggressively for the 1st time around here that there has been this has recently told Moss as far as many there is no concern there is a moment in time for the Commission to reduce the probability it shouldn't so this seemed the bands you that if you had a facility like she did With only sorry I'm sorry the stands me in that if I have a feeling like she did write the theory that has a lockout conserved their regiment pencil this theory cannot have stage with speed bigger than 1 I must Kate cannot have Marsalis graphic terms unilaterally there just so if you take a regular quantum field theory there is no way you will ever constructed masses bound state before too so of course if you start with the unionized gravity you know that's a different story but then the answer is that the news of the and actually you know basically I don't want to go into details you have to to define gauging violent obviously want states and that's the way the just out of this contradiction so also is on the all the milking you 0 in Mecosta spacetime that's all it was was this is about as we call Mickelson's face fines it will take until missed because of their lower loses Europe lies along with all the those decisions yes yes yes because I'm using actually Iran's compliance for the argument you need both things in local conservative management pencil and Lawrence Korb and then they series get away from the list because of digital file
11:25
there is no concern local cotton now this you know people have tried all sorts of things for his son's 1 way to evade the theorems to break Lawrence seems to be either explicitly or spontaneously the autumn I think didn't 1st many other things many other people died but all of the switched from the extreme to compare arrived and they don't think it's everyone's very far it has been revived over the years including more recently by the whole of but I don't think these manages to go all the way and of course the most Bronson was thing that people have been saying is that when if you're going to have a gravity marriage as a bond state then probably spacetime should be matched to these are words that sound like a the words but they amazing thing in some ways and that's the only a point where I work for the word amazingly items that somehow but there was a think theory has it made this 1st stumbling blocks in a much more conventional weighed in with a circumvented this origin memorable statements in a very conventional way actually and 1 may say that the act is really the father of theory both because she wrote is marvelous little paper were supplied to compute the mass of the new ones as the 1st excited state of membrane and loss of course because she never believed in any normalization analysis so that there should be some welldefined serially UV and once and never taken Phoenix selling it's where take now so again the words about clear and unwilling to explain of course for the mathematical days but essentially 1 way states it is the foreign invaders the formation of geometry of classical geometry that 1 may call the effort behind the formation of the signal model the formation so the starting point is twodimensional Hadfield fearing this is the quantum mechanics for a simple thing that propagates in some background metric and extra fields and this is called the deal me for consistency 1 has to actually as shown environs these the twodimensional signal model basically there are 2 dimensional the Auxiliary Medical has to completely get out of the picture because it's not part of the degrees of freedom of the propagating strength note 1 of the most beautiful discovery setting starting with the faces is the fact that invades the beta function equations for these 2 dimensional sigma model give gradient fuel the arrive from some action or C functions and have written down the 1st hit their arms Of these function which stands out to play their role of the classic the formation of the Einstein's too but the history has the Einstein them and then she has a series of higher character of corrections was very well defined coefficients people compute them and that this simply the bait the function of sigma model information which math language if you want visited to back court acted by the appropriate higher from the firm's in there is the absolute of all of this is that geometry for classical lines find is in sensitive placed by conformal invariant Sigma modems and I think of this is an example of the formation where you come from some other directions 1 price to the foreign consistently Einstein's theory that information involves all sorts of thinks it has no boss and this can be shown it always has the speed to Marsalis estate in the respect movies thanks from sense at this advanced stage but a lot of a finite set a number of quantum fields but the from something here and by the way the fact that this should be Marsalis users Vedic Shelley quantum mechanics namely the fact that when you compute the massive parade before this thing it starts out as minus 1 that's due to quantum fluctuations of this thing is over there is some kind of Kazimiyah mosque and if it went for these minus 1 you will never get the Marsalis spin book about the grew out of fracturing things was use all his you also heard the news he said up to the stage that is glossed but if you something infinite series and of course you are not doing it like this you basically go directly to the spectrum Of the stink and then you can check that there is no loss of seats in the incidence of chronic is really the only indication for the size of this review we already frayed sold regulation because of incident the last of the Is it where you have to some so that cost up to disorder would that be a and the scale of a prime distinct starting with a furious sounding thing it's serious it goes away university that were work with the people of services used to yes because that's what how you do it but you can't do it differently you just quantifies the same calculate its matrix and so on and then you see that the estimated from the whole thing is that we 1 "quotation mark so amazing is that if the war and the 1st thing you is use of shouldn't fast this is time adoption up fast where if you are going to talk about things after the scale of this thing so anyway this is clearly a fascinating the formation of classical Jonathan has given a prize for sort of beautiful mathematics from the University that became 1 of these known genetic backgrounds things that have absolutely no geometric counterparts also sometimes called last met the before its have come out of this and there is clearly a very rich mathematical subjects and it's also something that allows them to go on and computer the things that In naive quantum field theory squandered the controlled things like 1 or 2 look scattering of gravity forms that give you a finite period of service would not be you at this time and again this has not been developed by many people in particular Kevin Haller Michael Green Seal of our beautiful mathematics and that Clinton was this and the that's essentially where I was stopped about generous theory I just want to make 1 Marmora market but it is a seniority were no external sources that allowed them because only on sale quantities have known they Virgin of finite fashion as you type of goal off said were put some external sources you don't know anymore how to calculate police finite things so in a sense that much of quantum mechanics at the above mentioned the other day he is also enormous of string theory is so that finally we hold that the have original forum Friday nite this during the we're aware so you know the claim is that if the if you find any divergent 6 can always be converted 24 added that sentence he fretted insists we had used useful we have mocked where it buys them the Simplot sailors who don't understand something about the ground state and we don't understand many things about the the ground states now I don't think there is more often and this is something you can't evolve by your hands you for months surfaces and show that the dangers comefrombehind there's so much like face of the immense efforts and those consolidating their interpreted as infrared problems and you know it wisdom has slightly indeed what I've done very carefully they don't
20:12
have informed 1st the measure of official from 1 July the they I don't believe there is a pool of last with revision even for me there no growth but it sounds like a great areas of it is also a due to define some of the most topical and of course matter yes the hands of the claims that the ambiguities have yet to gage fixing vouchers and let's not get you know in a sense if you had said to some 140 years ago computer to gavekal scattering amplitude and you will get the final answer if physicists would be perfectly happy with these might even that you will never see anything beyond the will to win but the it's so that's not something that has to be but over time and this would be a great achievement if there is finally approved but funeral for someone again economy reminded like me may say OK all this is marvelous why haven't we done you know what what's the story would have organized formation of geometry it seems to do all sorts of mothers village things where there is a pragmatic and the foundation and they should know the answer to is the pragmatic 1 I think it's clear the connection between the observed lawyers world is incomplete and this raises very hard problems supersymmetry is essential when you break it is the David Justice ,comma 3 this season space doesn't paralyze naturally accelerating universe doesn't arise naturally and the seemed indeed problems of how to select the Viking that the stable and the resembles a writer's work sooner says this spinoff for a physicist clearly the problems if 1 wants to 1 day make contracts with there 1 essentially event but from a more foundation for my foot blisters on where reality is so you know this is a serious offense dimensions are world looks for dimensional you have therefore find some compact money for language in How will you find there In is clear of yet showed yes sir or minds way would be something that looks like me cause the empty space or fair this seat there was an extremely larger of care what you it again I'm not going to talk about this because there is a more foundational problem which Steinman sensing the arrest of the talk I think of him was to talk about this show to you what immunity but you know since Slav unmentioned so this great physicist were and I'm going to care for their should find some good he and in a the fast guys that try to do with phenomenology of time 1 the priests practical and that is marvelous sanctions if Iraq was the basic earlier notice phenomena Roger things about time that I absolutely find flaws and there are no closed unlike geodesic and that this is the Greek translation for they were the phrase that you never get in the same Maleeva twice I know that it's not obvious a yes said "quotation mark enemies seek peace scenery invention it that at that you that they PET which means sort of you think you're getting the same Stanley replies but the what arms you have changed right so that some it's so there are as many as 10 times on back in so now so does the summarized most theory I think avoid some of them 1st perhaps a little too field of quantum gravity but as I will not thrive while you issues with spying "quotation mark shell and not at all and the conditional so if you start to see the light of the sanctioning no sourcing theory has been very successful new but is ordering singularities I will give you a few examples of these are places where the geometry the geometric lines signed description breaks down it and AGR 1 will have to supplement and the quantum field theory that leaves of the only 1 will have to supplement the Serie by and talk about their conditions for instance here is or before it is simply RN muddied out by Sandis capable of patient will it has a conical tip singularity and they should try to do general at the miscreant U.S. Steel needs you need to give some call prescription for what happened here there's only 1 the these aren't exactly yes announced series all of this and the way it does is that it gives you a very precise set of socalled twisted the states basically stated that go around the United States Yukon quantized them they leave near the singularity because it takes a lot of energy or must forget that way so there are these localized degrees of freedom they can be Marsalis and so the singularities that you think you get are completely resolved because of this new Marsalis states that you didn't see in general that favored the and if you do and scrapping or anything else he may excite them and again remember them what is that if you use to singularities via infrared it's because you for what some must listing 400 degrees of freedom and that's exactly what happened was already here as officials units is assisting walls is the views is worried "quotation mark U.S. sales this year of security In the years since all of which was we're not in the sense that in the space I can't calculate for dual unambiguously say has made 6 elements even if the incoming particles seemed to provide it to the people of the call my father was the state of the art book is included in the sale also state which is used during the overgrown was Commission problems particularly because of the yes it see of course had you the foreign currency that there is nothing being alone is not that signal that's what space and spaces they just how close enough to the factory in you see if I was doing quantum field theory I would have to round off this thing and then defined my story but there would be a total ambiguity on how do you rounded off and get different answers for the difference warnings some source theory gives you a prescription that's what 1 means his or basically it did you want to do at this point I know there are various other examples maybe I won't describe them on 1 of the most famous ones such socalled the brains and the said again singularities in spacetime but were instead of his localized boosted molds you get opens things that's the thing that sticks to the spacetime defects in which something singular spacetime it is characterized by the fact that some opens things fixedrate Dobbins thinks so can be must listen the again that's how you resolve is the brain singularities in a very precise waiting by the union countries scattering and you get the exact answers if you allow for the possibility that opens things can also get excited about there is something called the corner for maybe our state please it is the enormity of the conifer that simply some singular beyond money for at the moment is that the muscle is the good news of freedom are not stinks as in the previous 2 examples but perhaps membranes from the 2 brings some of the various things have been checked sources here but here is an example of that probably anyone that has worked from
28:58
Jonathan knowledge it is the socalled Tobin not connected to so this is 1 of the very nice it medics in 4 dimensions With the topology of our 3 cross circle it and that there news met the QC it was only beaten don't see any here is the explicit method and if you think of the 8th by dimensionality simple threedimensional so before you get to this compact Sarah actually the money for the looks like a cigar 1 says that's how it looks where a X acquires zeros that people missing .period there's no singularity that it's in simply localities are for it but if you try to dimensionality use this from what you would find exactly is essentially the the 1 4 some senior of solutions it offer their fate the dimensionality of comedians geometry but of course in 1 onedimensional there is no singularity at all this perfectly smooth manifold and what part of the Marsalis molds localized modes of singularity here there simply current subprime loans from modes that was used in this way we can for the easier it is also those where is the justice and you really have to go to court is so city working with holdings of the it's like you know what time found for this small area said but is asking a lot of things you know if this is what it is also the basis for the whole of Europe collegiate wait still huge easy here is whether yeah that's that's a good point so of course in this example the answer is no you might think that the brain example the answer is yes yes you can get care which was diverged if you'd just be naive the gravity of surprise rather distinguished universities would be with you I don't passed down to the east also those think you hear accused of bloated Georgian generals at his spot about the only world also uses the euro over in search of those in the industry should not ongoing expansion that's what I'm trying to say United diet exercise that's what's the feeling that you don't do I'm expansion and that's the whole point but hold your question and maybe we can discuss it because it's the thing I want to say is what is the border said all of the singularity sometimes like actually will never resort singularity instincts fewer times I'm idle spectator it is so these things are things that you know stay there for a long time and with space like all light like singularities string theory has had a remarkably less success actually I might even say no success and it's not because people haven't died you know people have tried all sorts of things for instance or be before but where you just moved out by Lawrence transformation indefinite metric spaces it or simply weaker facing state found that solutions or things I will mention them in a moment .period this brains or more recently the socalled dissidents if the correspondence nothing seems to work at least in any reasonable manner so clearly there is a problem serious accent amusing a marriage it was shown to you a little bit what I mean we're all these little totally Leonel to stop the crew smokin on probably will stay here just think about brothers onedimensional look for dynamics and define source to the Yankee identity you know this is the effort cost 0 usually but let's put the chores that plays the order of the day 1 reported in the press 1 dimensions so if I was in the press 1 on time was a spectator here there would be a more but I am going to press 1 that's crucial to know you may say What is this that's something singular for the act monopolist we'll know how to resolve the singularity by going for instance the some Mona be inferior analyzing down India a call from 1 . is called the point of morning .period but how about the simple Fiore well 1st of all if you think about what the source does it does the following thing we call the family event it's simply depots GE units of magnetic flux at some spacetime .period out that this of course for the free equations and simply expands in your life ,comma and there is the act by event where you basically full cost a beam of light in surprise 1 dimensions to a spacetime .period very disappears show madam say well hamstring theories on this kind of thing the answer is it does but it doesn't very bizarre 1 in American version was 1st of all you can you can check with the little paper that's the essential nontrivial statement there that there is some monolog of the IOC conversation condition what you can do is try to calculate simple then what happens to a charged particles in the presence of the event and there is a topological answered doesn't depend on the details of the event here only on the longerrange fields and that the biological and citizens a particular 5 signed a lamented Edwards is over to buy and the is quantized can fish and G has for so they be quantities but he chief counsel is not the accident here it comes from a very different arguments In a way ahead so sink theories or is this a singularity as follows and you see the difference it is or is it with the help of an next Sunday mentioned so that's exactly what happens there is this object they quantity to brain and the equations on brains are precisely the equations for twoplus onedimensional look them and makes themselves we believe for this but some of this is that the brain leaders in some higher dimensional space and actually magnetic flax called find outside the but can be carried by a particle let's call department growth and therefore the process I just showed will corresponds to some of the particle coming in from outside the Fluxus confined its cannot spread cheats the surface of it spreads by the way you can actually tried to do this in an experiment in Josephson junctions in all of the the words have exactly the same individuals from 1 of the history of mother good convincing experimental mainly you know someone should but I'm a bit to convince them to do this experiment I can't tell you more about the point that I want to stress here is that in this example singular events have genetic Millard the particle conceit it while I events require absolute finetuning data it went there is a generalized is too high and dimensions but the main point is that there is solution I like that define Reich singularities it is a very different view it's time like singularity here would be resolved by embedding memorabilia of the Audi A which does the resolution of the monopolist but this doesn't help steer the country the resolution depends on the initial conditions in Annex and then mentioned so how to transplant list of gravity the theory and does it make any wiser I'm not sure but this is the kind of problem that people that tried to talk about this brains and experiences some those sorts of things are facing 1 of the the resolution since the depends on initial conditions in Ontario man this show the
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summarized this string theory is also sort of time like similarities but spacelike forms a different challenge so before a long and happy opened the fundamentals of the sort of thing the latest phase of the use of coal which is the last day of the people of this year's articles because it's a bit of right I'm I'm going to come to the show maybe loosen this guy was is so overloaded with the leaders of undone by many of course this season but let's discuss it and I'm going on this year it now precisely I want to come out .period items so this singularity say talks about that now have nobody generosity namely sense there is there are not many quantum states in and 1 way to say is that all of these localized molds and talked about that generically the ground states or if more than just escaped the efficiency and that your by control and on degenerates Latin so what happens to the alliances among the simplest examples are the socalled extreme out to charge black hole so I'm going to come to where you see is pointing a series an example so suppose you take a stake in its happens to be anecdote extinct here it wines around some compact Circle a number of times quality W but it also has some momentum In the same direction which is quantized in units of the same views because the way faction has to be single valued so the momentum is an over and and undoubtedly 1 of the 2 charges dash to here so this is not some kind of staying has this school charges that that all this should concern you cannot handle the winding you cannot destroy movement a conserved quantity it and why can't say that the mass of this thing is bigger require them some lowest possible values for the extreme value which is another top to out of the winding number of times the tension of this strings and no 1 can also use it to check that Aziz has there are a number of the janitor quantum states of the system under the act of being in the extreme of case is exactly given into the large MW limited by 4 squirreled them up so that simply general bonfires in the furthest thing was due the sunset show the number of states girls as the charges become larger and larger no when we say we're here is a particle that has spent opium to charges let's think about the corresponding gravity solution in this case I already had the compact SerbCroat Simon ninemonth compact dimensions so there there because it's always there for convenience instinct fury otherwise things get timely but don't get to too and you I down program solutions and they happened to be singular naturally and there is a way their singular is that it's not only automatic unfortunately serial fortunately there are many other fields including scalar fields like many agents of competitive occasionally this cannot be of course a constant it's a fielding gravity unchanged from 1 point to the other day and that the Latham is another 1 of the things out there who's in charge is you can never equilibrated this generous to finite values just understand why think of this system if there was only winding it would tend to shrink the circle to if there was only momentum with them will always find a Asian pressure but both of them managed to stabilize it somewhat more value sure there it is to stablize but that the them is not bearish Charles solutions and actually it's 30 we force In that several people including at the age of the world have succeeded in doing precisely that 20 games where managed to sum up this powerful prime court actions in a precise way to show that even tho it's a singular solution find find fury if these in most singular solution of these efficiently corrected ceiling by these higherorder terms and not only this but by using what is generalization of the entropy formula Yukon match exactly this fall by squirrels and by just calculating the whole arise in area of his black holes so these are sometimes called smaller that cost here and there of course very interesting In a sense but I don't want to say wanting them yes you the good news is that the formula causes our own yes there is an not for all quantities but for the entropy of an extreme on hold Blackwater will you do the issue of whether the call was made as a result of history of operations each and all you are here you know you can see that the I think on squarecornered from suffices to school the solution in the sense of creating a horse rides on it you know if you put the 1st 2 terms but then you know the whole point is currently exactly calculated the Eddie our actually that warned the equivalent of the area In the system and that's what these people have done and if you do if you find but the overall results will be used to describe any kind of In this failed British stated above all of this is that would where will it with the girl who yet some quarters so you know you only singularity it's the use of solution of Einstein's theory and that in very closeness in United States changes and this creates a polarizing that's what is the the case is suitable all high and don't want to go behind the time and I'm not sure because you would see that's going behind his unusual but what I'm trying to say is that it here is a singularity you know that that's the summaries of singularity that has the Genesis has hasn't opened it is apparently being the Azores based in theory but it's all happening a gain of this thing called the Bronx in a very very short distances so it's you know a better version on a its version of the resolutions we have already seen it but nothing drastic when it's something you know is also way that that's sure actually made me think I'm like I think it's fine like beyond the goes it's extremely stable it was the beginning of the new leadership of the advantage of Inter but what about the large black and now that's where things start becoming more interesting because if we now repeat this thing but a
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system where the 4 eyes on Grolsch 2 very large size then why on earth would Einstein's theory breakdown or if it does what happens with the serious it breaks down the cost of much of some large but in a very large black on the care much several most desirable qualities so that's where things start becoming more interesting the famously charge example is the strong giraffe a black hole doesn't matter you know how you make it up here is in a sense a kind envisioned for the Ising model is Holy has defied Bahrain's the 1 brains because it's a crime worlds that move up and down and the whole thing is happening if 5 golds affordable and under the fate of the number of 5 brings the number of the and the number of collegiate molds for the momentum out the city charges and again believe you sure of this Super Gravitt equations there is now a big macroscopic for rise and fall of charges and is now it make inside Haugen formula area over 4 units Bob which is given by these charges and that this is an example where you can count the fates of the court so there is that athletes for their microscopic picture cannot be totally crazy now this kind of bright colors Suriname going to get close to it you see the same it this is a really basically a generalization of the charge black called in fourdimensional Einstein Prize much with the here is the metrics breaks for jobs brother according to looks like the swatches met this cave factories or the Red Sea factory has it's somewhat different form you should quite dramatically in 1 hour if there are 2 places where values they are called out there and in organisms they are given by the my son the charge intentional this formulae and again there is a mantelpiece the area over the horizon G and the temperature which is the difference of this tool but show the question is 0 is the extreme cases where the mosque is equal to the challenge and the squirt land seized and that in a sense the guards faith of this system "quotation mark now here is indeed a very interesting proposal on Yusuf is 1 of the people that has worked a lot on this which has altered by people for almost 10 years now and 1 proposal which goes by the name of fast bowlers used to say the following so you know I showed some of the brains and the do some counting that measures exactly the number of micro states of the system but all these micro states be simply called the vivid geometry now this goes against 4 parole theorem scored no hair the Orange which are basically divided in 4 dimensions and which stated that outside the hall rise of black or once it has settled down to the ground states there's not much you see the electromagnetic fields that kind of Chancellor coupled the charge it but nothing it now this folklore theorem clearly favors naturally high and dimensions so the folklore says that there are no gravitational solely from southern that cause there are many many visa windows and pitfalls with the very last prehistory apparently this is the only other wrong paper of policy and on the Parlier wrote it paper fans find the nonexistence before regular stationary solutions of relativistic field equations in 40 fearing they had in mind the kinds of client fielding 5 dimensions and they just told you right before then there are 1 of the solutions the Feldman method the started all of this is small and that among black holes you just regular solutions sorry bunch of current applying theory now the arguments the reason why the argument was wrong because that's the EU's summerlong scathing argument you Yukon overlooking the paper which is or was some amazing really for to know that even these people can make a mistake there but that has to be shelved yes which is also home Bloomberg has absolutely now the TT based cannot topology and there is a very nice innocent paper of the devolution Warner that puts the votes from the eyes In the past it's like this for 5 dimensional super gravity to suppress saying face the I'm not sure how I'm doing find who's come to kind of them I want to make this keeps proved that essentially way what they're showing a very general setting is that it if you concede there 5 dimensions of gravity theory was supported gravity has some extra staff it and that is find a stationary or Sephardic solutions this means that you should find like to invoke the cup then the existence of Fremont the 2nd home mortgages from Ontario to cycles or the special sections is enough give your stable source funds and then they exhibit a large number of them and basically you can avoid the simple noble theorem because of some chance I understand you can look at the people who afterward so 1 can avoid the and a lot of hard work has gone into trying to generate the enough of the solutions to account for the end of each of the 3 charge black hole now and the end of my thought maybe Youssouf with planting Jamaica comments there Lisbon just make the following statement ignoring member of this would be now solutions that through benefits the like black callers but when you get close to the horizon space will lend some some small so in a sense there is neither horizon ordered the interior of the the corn in the usual sense no of course it would be a grave mathematical achievements the entropy of these things could be accounted for by small 11 dimensional geometry supra granted geometries and personally skeptical can indeed be closed and military engineers the area ,comma will you saved in a sense a baby version of these are my dissent that stalled last John with Sinn Fein dimension is a benefit to small solutions of 5 dimensional consequent fearing the new extreme of fourdimensional charged calls from far away there is no doubt about the use it but does the civilian prior breakdown effects of field theory for some new foreign observer that should normally see very flat on the stand before I as Geritol activity usually fences no my take is that in most of these had elected to field or statements 1 always make some assumptions January 16 has fought for more than 1 mix and things that happened here look extremely known genetic another way
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to say this is precisely draw the panel's diagram of it charged arising and most the caller ID let me again not explain because I want to go to the last part but the singularities of this geometry are indeed time like they are hiding behind the 2nd eyes are so this is the outofcourt eyes this is the 2nd Clerides releases the originated between and that the fairness and others have shown that company ordered the scoresheet Clerides and called he's completely unstable small perturbation and should collapse space like singularities so I think 1 but I cannot prove it but we're still in a situation where we don't have space flights in like this and 1 would have totally exhibit cases with space likes interests life is to make the final would face more convincing now the dinner
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holding off Houston's probably it been come to this but they want to monitor the last 10 minutes go to the last question which I think poses a very sharp the problem that many people have been pondering in the last 2 or 3 years which is the question of humans Jonathan but they now on this season's come into very sharp focus in the context of the socalled the idiocy of the show with their you exactly what they mean now even if you're not distant fears must have surely hair then there is this conjectural which says that all said quantum gravity With asymptotic acted deceit the bond that conditions at spatially infinity is equivalent to an ordinary relativistic conformal field theory of quantum field theory in 1 as mention all of the bond of the space and the most famous and cited example is quantum gravity made 5 process 5 and 8 . 4 4 and then mentioned earlier this year no young series unit that everyone would have been even again made the it won't be without necessarily using Susan correspondences rides 1 should have states that resemble black hole that's I think all of you so here we have a very would pose problems How does the geometry of the standard is space emerged from a regular performer filled the and by the close of course once to evade with Withernsea M. Weinberg with interferon but this win opened the
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latest in a string note to stop and to see that this is a hard question clearly this is a very hard question but here is what you can do consider 1st empty entered the seat there this is intended deceive it's flat spacetime and 1 the other day mentioned so that things get a little sister Doris and if it does you will uniformly as removing Indian dimension but they now all the this is 1 of the coordinates of the gravity fury but not of the performance with history so the performer filled the arena the has operates as a dependent next let me take 1 of these operators it's a conformal field is so it has some scaling dimensions than that now there is a dictionary that they want described but which allows you to formally I'd done something like if fatigue gravitational field in the box when take this a period of 4 years transforming it then you sound Over the years of solutions of the free wave equation enacted this at the space with appropriate minus related to the scaling mentioned Ushaped II this has 550 because this is entirely defined in quantum field theory there's no gravity however it's easy to shoulder you know that's very simple by just looking at the twopoint function of this superior see if they that this has exacted a property you expect a free quantum field and the system and actually in the limits "quotation mark the number of callers feted this season has already told .period functions that's part of the sludge and factorization straight through to the delight of the fees but now what does it mean to find the locality in the box geometry of
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this theory of what we know about what this means is that the have stated goal of full points practice Of this and this should find the onset of that falls off very rapidly and there is a way bike that he formed coming to the same point and in spacetime of 5 dimensions right so I mean these are free fields non going to make them in facts to leading more than 1 of the but this just the regular with Beijing fury and I want to understand why this interaction with local local melting exclusion usually but postseason nosy was a madeup coordinated didn't appear a priori in the performance of its no that's a very nontrivial question naturally and it hasn't been answered that I know there is really marvelous mathematical progress for calculating exactly the fourpoint functions of super young news for all the values of the copying so disabled answer this question if we had the answer but all of this technology is completely on sale in the conformal field furiously Yukon knowledge take Is the examiner operated to have lifelike momentum and clearly here offset quantities in the call for field theory To calculate also scattering got so and even this simple fact empty that this season has not yet been fully tested but there are very indirect but very convincing arguments that's if the conformal field use of a special kind namely its has a gap in the scaling dimensions for a period of sustained bigger than tall and by just looking at the statue of performance Brock's there is convincing evidence that's this theory gives you a lot of physics in 5 dimensional entered the system even tho it's a fourdimensional safety and of course the statements have been checked and checked in quest for measures for these and other sanctions once you showing them once you pull them and from the stature of performance broke you can essentially convinced yourself the floor palaces there in the vacuum no I used here .period paraquat ordinances is actually for the next question world to global coordinates were the is of boxes confines things in the middle because there's anything and so the bond there is not any more plane but the sphere Feinstein's and this should bite the bullet to the bond there is infinite blue shifts from you come back here and now let's think now about this problem and then done in a few minutes so we still have an answer by young is defined as the times are the delegation and descriptions there is a sense that the Asian is reflected at the bottom of the sits there and if you want to get out there are 2 kinds of black holes in the system there also socalled small black colors that are like a disquieted that holds the community level but there is another kind of record if you put enough energy to the news you dive the temperature very high since then the Asian cannot escape that's a trap you 138 ceremony will you please and for the high enough temperatures this thermal equilibrium geometric states is this socalled large India's Blackwater with it the Arizona it's not simply if a dash of rules it actually got thumbs condition is clear that 14 states physicians so at sufficiently high energy demand and say that it did because state of the quantum field theory made out before their and square operate stores that's the correct energy should resemble a large is but cause and now have a problem with the candidate construct these geometry from normally quantum field theory and this is now a geometry that has accoring on and the space like singularity here is the geometry mothers and all way out here there is a polarizing and you just can't know if you just sort of the Einstein equations that's what you find that's the perils monogram actually this is an experiment black hole this is the exterior of this is the black hole in the area of so if you created the black hole it and then falling said you don't get this fall diagram is useful diagrams sold sense the coastal maximum extension of the and this has a white Holland the America but the main point I want to make is that there is a polarizing and space flights and liked it so what would call former physics theories do about the Vatican on now In a sense we're going to start the problem so since the record does not operates the final singularity gravity is unavoidable but even this is thinks the audio so superior needs 1 must be it must be possible to understand why and how the effects if it's usually breaks down better break down because there cannot be such a singularity in supplying that the heart 14 assumption or things like that would not help here because the symbolizes a conscience
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you're just standing there is not some initial conditions so what can you
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do it again people have tried all sorts of exotic you and that's a fair game you know when you're faced with such a question why not try anything he is aerial exotica for instance it's called The Post's selection quarterfinals state bond airconditioners singularity it is a formula that labs very much this is basically the probability of successive measurements and timely warning to up to weigh on using specific values it wanted to again and this proposal says where we have to stadium loss of some kind of density matrix for the final stage but that's coming in or even I can't swallow this that's catastrophic because you violates the 1 we may want to keep namely that the result of an experiment to find minus1 measurements doesn't depends on the honest measurement you may want to make later in time not only if this was the that also on notion of collided with Gol so says this is an exotic proposal that I find very hard for except well let's take a closer look at you too long after the Black office formed the near the whole arise on the geometry as use 1 looks like empty locally and calls disparities and in terms of the coordinates of falling observers into the Ordinance the Vikings somewhat here looks like a family might you can make this very precise so there are the modes that that defines say at some given time the views Horizon's at a given time the they're there items the left molds that I modes are the only ones that can Stapleton feeding so they are the only ones that propagates the bond where the conformal field defined so if you are going to make an effort to reconstruct the geometry beyond the 4 eyes or you have to say something about the other half of the the more to the left molds these made of operators in the same field but space or not here are 3 ounces you know it is not sense leaving it to the unavoidable conclusion the firewall y where you can see it in the figure if these are both early independent molds "quotation mark there's me that the states has been prepared so carefully that all sorts of wanted don't propagated from this side of the block calling the men 1 I'm falling in from the side of besieged by your from the extreme support avoid the fire water if the animals were completely independent acting in a different but there is only Arnold's would acquired a very big finetuning of the state of the system and we know nothing about this so the I'm the answer is yes but very deceiving if this modes were acting on exactly the same few but space Heredia has the animals he would get in from other problems then the foreign observers and packed with the same here space states as the guy outside and then why can't you send a signal to him right and if he has access to exactly the same Hilbert spaces 3 minutes and the consequent modify thinks there is a consensus signals but remember this support dying here can never fought over communicating 1 the outside so you know both arrived at the time I'm out here is this fair prices probably most division proposal proposed by these 2 young guys it provided Emerson Rajoelina seized papers the answer is yes unity sticks that sends and unfortunately the construction the state's dependence of the what they mean based on this misimpression idea looks promising but it still must overcome I think many many hired those state independence causality and still people wanted terrorists what happens in the final lies but the idea of this be pleased to essentially may make in an approximate weight that dominated the decider construction of observe rose so they say the following let's consider at the peak of highly excited states side Of the performer fits the only the propeller states that has enough energy to be a black hole now the algebra of observer some this is something you would absolutely great it is a very very small arms but you don't want to use any possible parade through because in particular there would be a better says that destroyed the black hole but the only experiments with duo are basically pressed there being little these days so if you think a fund manager but that doesn't not out there out of drastically the states in particular the operators never initiated state of the world this is the state's independence of your potatoes we're going to look at it nondiscriminatory be enlarged by you there and that's where you know morning mathematical stronger people in my opinion can come in and try to settle some of the points in particularly want to avoid and square for products with disappeared a thoroughly because these are precisely the kind of things that would and the original states should another Bender says that you can things but you cannot arbitrarily multiplied and now if you're sure these then by mimicking essentially construction Yukon showing did that 1 may construct a major loss kind break them which commutes with and sets lacked the Oldfield that all operators at exactly the time to the ceremony in the lost the side take it from a sound topological but if there's you this was the worst thing that always news that the you find out the state in 19 states of this parade through find exactly what you expect from a family states so remember your basic political stopped visiting the stated that the frostbite of here here the letter insisted that giving up with me just
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finished and then we can discuss more but in a sense what this says is that you can't try to construct the motive behind the horse rides on which her family and find with the modes of outside it will only be unaffected description and more importantly it would depend on outside so every time changed sides will be different said before period 1st now you may say no point in considering it but in a sense maybe that's what we need to describe in aboveground independent way the geometry of funding for an observer so I'm not I think you know the merit of this is that it helps to sharpen its passes and some very different settings for them in a context where in principle limited technical prowess that would be uncertain but actually extending the early calculations have been very hard to using his debates and some the Steve violently you have been brave enough to try them you know it is a wellknown fact that high images scattering of thinks is known locally understands this thinks that a child plant created thousands of size and many people feel that they should still play a role in the resolution and it doesn't that followed in this part of the demise of houses solution so there I'm not sure what the final stories but I think it's a welldefined problem for once and something should
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come onto the shrinking 1 of the only his fellow remark of his fastball was already wanted for the most personal holds that he's looking for something nothing in the world the hearing established finalized for the 3 charges and are on file with his although a lot of quality results in various university alliances in the battle of freedom because of you the a remark he made in the face of the July last year when your heart is in the U.S. state of mind in light of the articles of the 5 kilometers away from the beaches along for the year singularity is a priority not here in Seoul is regarded him a logical way service to Televisa not the only if I may say Parliament and of course that would be marvelous told president of the then 1 would have to understand why individual effective field theory In approximately Mccoulskey spacetime valued if there is a singularity and undermine the dollar and the other side of the world and that's very initial tightening if 1 gets some understanding of this then it would be marvelous police the me Hi