Topics in String Theory  Lecture 9
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Title 
Topics in String Theory  Lecture 9

Title of Series  
Part Number 
9

Number of Parts 
9

Author 

License 
CC Attribution 3.0 Germany:
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 
Stanford University

Release Date 
2011

Language 
English

Content Metadata
Subject Area  
Abstract 
(March 14, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses on the mechanisms that make the universe hot. 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.

00:00
Theory of relativity
Hot working
Speed of light
Schreibkreide
Day
Year
Cosmic distance ladder
Profil <Bauelement>
Meeting/Interview
Radiation
Temperature
Gamma ray
Atmosphere of Earth
Cantina Ferrari
Redshift
Photon
Minute
Black
Finger protocol
Black hole
Quantum fluctuation
Excited state
Audio frequency
Computer animation
Gamma ray
Wood
Photonics
Fahrgeschwindigkeit
Plant (control theory)
Mass
Theodolite
Lineofsight propagation
08:24
Prozessleittechnik
Capital ship
Effects unit
Scale (map)
Order and disorder (physics)
Cosmic distance ladder
Light
Particle
Bird vocalization
Roll forming
Continuous track
Transformer
Cylinder block
Hull (watercraft)
Augustus, Count Palatine of Sulzbach
Photon
Virtuelles Photon
Ground station
Paper
FACTS (newspaper)
Focus (optics)
Quantum fluctuation
Autumn
Particle physics
Remote control
Cartridge (firearms)
Wear
Mass
Mintmade errors
Plane (tool)
Lineofsight propagation
Ruler
Hubble's law
Hot working
Trajectory
Willo'thewisp
Spaceflight
Transmission line
Year
Emissionsvermögen
Crystal structure
Interval (mathematics)
Weather front
Alcohol proof
Radiation
Temperature
Material
Cylinder head
Pooltype reactor
Stagecoach
White
Map
Black hole
Angle of attack
Standard cell
Photonics
Plant (control theory)
Last
24:49
Girl (band)
Weapon
Capital ship
Patch antenna
Hot working
Roman calendar
Geokorona
Scale (map)
Year
Force
Automated teller machine
Global warming
Foot (unit)
Interval (mathematics)
Cosmic distance ladder
Mitsubishi A6M Zero
Particle
Bird vocalization
Separation process
Pattern (sewing)
Roll forming
Meeting/Interview
Alcohol proof
Automobile
Ship class
Transformer
Water vapor
Hall effect
Minute
Single (music)
Source (album)
FACTS (newspaper)
Yacht
Kopfstütze
Metre
Black hole
Angle of attack
Motion capture
Weight
Standard cell
Series and parallel circuits
Universe
Lineofsight propagation
38:14
Theory of relativity
Oncotic pressure
Leyden jar
Order and disorder (physics)
Global warming
Cosmic distance ladder
Thermodynamic equilibrium
Light
Particle
Wavelength
Roll forming
Continuous track
Crossover (music)
Thermometer
Astronomer
Worm drive
Water vapor
Electric power distribution
Fur clothing
Textile
Photon
Season
Dipole
Source (album)
FACTS (newspaper)
Switcher
Density
Pufferlager
Signal (electrical engineering)
Newtonsche Flüssigkeit
Cartridge (firearms)
Mass
Lineofsight propagation
Measurement
Gas turbine
Noise figure
Near field communication
Microwave
Hot working
Transmission line
Breitbandkabel
Day
Short circuit
Year
Measurement
Differential (mechanical device)
Galaxy
Summer (George Winston album)
Force
Crystal structure
Foot (unit)
Basis (linear algebra)
Rocket engine
Band gap
Lecture/Conference
Automobile
Radiation
Spare part
Temperature
Hose coupling
Material
Kontraktion
Redshift
Cosmic microwave background radiation
Vakuumphysik
Suitcase
Microscope
Map
Classical mechanics
Kopfstütze
Spant
Black hole
Potenzialausgleich
Photonics
Strangeness
Hour
Plant (control theory)
Universe
56:11
Theory of relativity
Hubble's law
Hot working
Acceleration
Speed of light
Scale (map)
Year
Measurement
Force
Galaxy
Andromeda (play)
Thermodynamic equilibrium
Cosmic distance ladder
Meeting/Interview
Ship class
Automobile
Barrage (dam)
Limiter
Video
Mass distribution
Magnetic moment
Water vapor
Pressure vessel
Fundamental frequency
Kleinwaffe
Vakuumphysik
Season
Electronics
FACTS (newspaper)
Kopfstütze
Metre
Quantum fluctuation
Sizing
Plant (control theory)
Mass
Electric current
Universe
Measurement
Lineofsight propagation
Miner
Model building
1:04:40
Weapon
Hubble's law
Hot working
Year
Measurement
Galaxy
Automated teller machine
Aircraft carrier
Northrop Grumman B2 Spirit
Astronomer
Star
Speckle imaging
Cylinder head
Redshift
Ground station
Vakuumphysik
Cosmic microwave background radiation
Twoway radio
FACTS (newspaper)
Finger protocol
Book design
Lineofsight propagation
Universe
Switch
Natürliche Radioaktivität
Ground (electricity)
1:10:39
Weapon
Solar System
Scale (map)
Thermodynamic equilibrium
Cosmic distance ladder
Light
Bird vocalization
Roll forming
Meeting/Interview
Continuous track
Cardinal direction
Tool
Tape recorder
Artillery battery
Water vapor
DVD player
Shoring
Ground station
Single (music)
FACTS (newspaper)
Pair production
Cosmic microwave background radiation
Quantum fluctuation
Signal (electrical engineering)
Vortex
Measurement
Lineofsight propagation
Containment building
Noise figure
Acoustic membrane
Storm
Microwave
Hauptsatz der Thermodynamik 2
Ruler
Speed of light
Bomb
Day
Year
Measurement
Galaxy
Summer (George Winston album)
Force
Rocket engine
Spare part
Radiation
Orbital period
Temperature
Optical cavity
Star
Planet
Typesetting
Big Bang
Redshift
Flat engine
Gas
Heat
Yacht
Classical mechanics
Sizing
Plant (control theory)
Ford Explorer
Hour
Universe
Miner
1:27:18
Ruler
Cylinder head
Mechanic
Ausreißer <Messtechnik>
Transmission line
Day
Bubble chamber
Commandline interface
Crystal structure
FACTS (newspaper)
Specific weight
Generation
Rootstype supercharger
Standard cell
Meeting/Interview
Ship class
Cartridge (firearms)
Steering wheel
Universe
Noise figure
Leistungsanpassung
Hose coupling
Flip (form)
Coin
1:36:02
Theory of relativity
Patch antenna
Effects unit
Bubble chamber
AMHerculisStern
Sommerreifen
Bird vocalization
Pattern (sewing)
Wavelength
Visibility
Meeting/Interview
Limiter
Atmosphere of Earth
Water vapor
Progressive lens
Sky
Sensor
Electronics
Source (album)
FACTS (newspaper)
Excited state
Missile
Direct current
Series and parallel circuits
Cartridge (firearms)
Wear
Empennage
Satellite
Measurement
Book design
Noise figure
Morning
Orbit
Hot working
Transmission line
Day
Year
Measurement
Basis (linear algebra)
Cell (biology)
Generation
Band gap
String theory
Spare part
Astrophysics
Temperature
Negation
Pink
Pressure
Collision
Cylinder head
Bending (metalworking)
Cosmic microwave background radiation
White
Domäne <Kristallographie>
Yacht
Forging
Game
Kraftfahrzeugzulieferindustrie
Paint
RRS Discovery
Universe
1:55:31
Capital ship
Combined cycle
Field strength
Crystal structure
Force
Basis (linear algebra)
Black hole
Bird vocalization
Remote control
String theory
Cardinal direction
Spare part
Orbital period
Tool
Throttle
Orbit
1:59:49
Ruler
Ship breaking
Capital ship
Prozessleittechnik
Hot working
Ground station
Crystal structure
Paper
Telescopic sight
Silvering
Meeting/Interview
String theory
Spare part
2:03:38
Ruler
Spant
Cylinder head
Hot working
Computer animation
Brickyard
Meeting/Interview
Hull (watercraft)
String theory
Rail transport operations
Cosmic microwave background radiation
00:05
Steiger University OK we have
00:09
10 minutes Ferrari is schmoozing but those days you are over the age of earlier work out a lot you mean how hard is it Bob I what the that is not exactly the same as the black Alderson help you just Berg Brooks black hole at bad time you know that's it pretty much exactly what I was spotted the lecture tour tonight so make sure I start but I'm deferred and until 7 because that was about where I was and begin that's the shot put on a plot build up your juice and debate that way we would that be precise enter whose energy this temperature or the state is still stay on of that after the photon falls into the horizon are on the horizon of you want to call it the entropy won't be hidden information if you like the information that's inaccessible to you because it's either inside the black called our from your perspective very very close the horizon and would take forever for time to go on the information that's hidden is 1 more bit so every time you drop a single photon the entropy increases but warn you can see that yes yes yes the question about the temperature of horizons let me answer it now the horizon is always hard on the back of the horizon there's always hot lower among the barren you would always detect a very high temperatures you get close our eyes so you could think of it as the horizon being a place or surface are extremely high temperature which is constantly in bidding and we absorbing both times are they really quantum fluctuations and there really nothing for them the highfrequency quantum fluctuations that taking place in a small volume of space of small region of space off the horizon makes them real a way which up come which to bridge regard to talk about makes some real thermal fluctuations in a rather interesting way but every horizon always has the property that temperature the actual temperature from real from lower down the horizon would recorded temperature which would be 1 divided by 2 Piney times the distance of the horizon a distance of a horizon nominate every horizon whether it's a black hole horizon and other kind always has their property From U.S. near question I can't remember exactly what's his life the rate that yacht but of the photon came in the buildup of Sokolov the photons Archer being made it why would you stay far from the horizon the horizon not for does the radiation that hits you why isn't it is very high frequency radiation magazine made it very close the horizon that come from Ahmad that you discover that the region near the horizon socalled New Horizon region is very very hot why isn't it hot far away I can assure you we created a blank wall over there about war and we heated up some very very high temperature but suppose it was a very very big Wall we heated up to some temperature I don't think it would make much sense to say that as we moved away from the black out from the wall temperature went down like 1 over the year the distance it would you would be blinded by a highfrequency photons pretty much no matter how far you got from a wall highfrequency photons it came out of the gamma rays super gammarays everything else a came out of the woods blind you no matter pretty much no matter how far you got from from me from this very very large war why is it that that doesn't happen with a horizon of a black or white when you step back from it and get a good deal of distance between you and the horizon why don't you get blinded by these very high frequency folk and the answer was red chip redshift red shift is another way of saying that as the photons propagate away from the horizon they lose energy and they lose energy for exactly the same reason kinetic energy whose energy for exactly the same reason that this piece of chalk up when you throw up in the air here is doing work for you have In North it you have to do work against the gravitational field and don't do work to keep it moving with the same velocity then the velocity was slowed down well with thought of them think about velocity velocities wrong think think about think about energy from nonrelativistic piece of chalk there's a close relationship between velocity and energy but was really happening is losing energy for profile time the relation between velocity and energy different namely the velocity is always a speed of light and energy is the energy but still true that as the photon Klein all of these gravitational influence of the black hole it loses energy so in their transit between verizon near the horizon which very and far away photon loses amount of energy such that a distant observer doesn't see the black coal was being very high seas having the Hawking temperature and the Hawking temperature decreases with mass of a black hole Hawking temperature of black hole and you could think of it as it temperatures as seen by somebody looking at the photons or being exposed to the photons very far from black hole temperatures T hawking is equal our right the precise formula for no particular reason 1 over a plans a mass of a black hole there is an age Borrelia plants constant and some members
08:25
of factors of C which I can never remember CQ over Karadzic was bounced as far as age His at 3 4 5 8 5 times a mess black hole of the bigger the black called the cooler white doesn't look cooler for a big black while fall that was created very near the horizon has a more difficult time getting away from the big black hole a smaller black holes and other words it has to do what has to do more work it loses more energy in escaping from a big black hole from the New horizon region that does for small black hole so the effect the temperature the effect of temperature seen by an observer far away decreases with the mass of the black hole but if you take this formula you interpreted in terms on energy typical photon was in fact temperature of blackbody radiation the temperature of thermal radiation is approximately the same as a typical energy of any given photon so this just says the photons typically have energy 1 over the mass of black hole of you then Tracy said inward toward the horizon and say how much energy to the photon halfback here when it started out in order to escape and have this much energy when it got out you find the energy is always the same it's always about this 1 over To times the distance from the horizon how Close could you get to the horizon and meaningful well the plot distance the plant distance sets scale for all quantum mechanical systems and so you might say then that these photons originated in the layer as the way they behave the way the system behaves in later perhaps of plant that year the horizon all right at the horizon and it is continuously emitting photons and absorbing photons admitting absorbing them our the energy of the photons as high as you can imagine the block energy now most of those photons don't get out most of those times get out what happens stormed the fullback here's a horizon of a large black or and if the horizon is hot it's continuously emitting photons but also some of those photons the radially out but very very few of them most of them go office mangled the ones that go off and tangled up pretty much guaranteed the full backing of the horizon of the black hole it's only a trainee call angles here that that photons escape so in fact the emission of photons is a very slow process of a slow process because most of them don't come out at an angle which is appropriate for them to escape and most of them simply just fall back verizon fall back because of gravitation the ones that are coming out can bang into the ones falling in and guess what happens they collide very energetic make electronpositron pairs and make everything we could think about and they make this thin layer of very very hot material like no material that we ordinarily encountered much much harder than the surface others continuously emitting photons which we see as having much much lower energy and their mission that's the mathematical theory works the consequence of a mathematical theory of arrived is another way think about it withdrawn pictures of black holes the outside of a black hole was out here inside a black hole was hear and somebody a given distance from the black hole is moving along a trajectory which like this now there are quantum fluctuations that take place without trying to get into the depths of quantum field theory let's just you the rough metaphor of quantum fluctuations being closed loops of virtual particles virtual particles are constantly being created and violated an observer far away just sees those particles created doesn't see them actually all happened too fast years here are the lines of constant wait out is people's infinity what somebody out here a little fluctuation like that playing in the view that they can be detected they can be detected by over highprecision quantum electrodynamics and the properties of a Adams and so forth but there also fluctuations that take place over here now both fluctuations appear To be emitted from the horizon and the horizon is a place very close it was like all year and they appeared to be made and full back into the horizon that is exactly what these things are They are the quantum fluctuations which take Place behind the horizon half in front of eyes and looked at somebody and outside as something emitted from the horizon reabsorb some 20 fractional removed have enough energy to get out we call Hawking radiation he has also where possible all out well OK so it's not the classical horizon which really looks like it but it's always convenient and we all do this all the time we draw surface warned want away from that arrived to the surface 1 1 point away from the right 1 plant gleaned from here on 1 here or plant here it's a surface like if we want to drove us a different way say he is the horizon and 1 plant playing away a fatal error and then the point here of course it is the the horizon is not really accurately defined to within the plant where quantum fluctuations not only of ordinary particles of gravitation and structure of the horizon take place they aren't you really should think of the horizon is slightly thickened and you think it's ever thickened like that the fluctuation takes place in this fluctuation doesn't occur at a time like this beat their careers at some time in the remote Castro sometime in the past it seem it out and falls back into the horizon over here so somebody outside would say Look I see some photons look is they wer e from some very close
16:40
to the horizon with very very high energy they pop out and a full backing that's the that's what mathematics end it got is saying no matter what the the horizon what the horizon it cosmic arising now forecast we August will begin it would have been dead and if there for spent more time on the resort we would farright well aware and good let's talk about cosmic horizons in the same vein there are many ways to draw visitors that based based which exponentially expanding 1 way to draw there's just a draw a time axis which goes to infinity draw the blackboard and keep track of the fact of our heads distance between any pair of neighboring coordinate lines here is exponentially increasing with time that's 1 way to draw another later dry it is squash all future time fall of future time bound by quarter transformation we did the cordon transformation last time so that future infinity is a horizontal line like that corresponds the equals and Inc I think I wrote down the metric for you in a form which maps he equals infinity pool finite place just rewrite it for you all our original method was Iast squared physical minus D squared the usual things plus E to H T B X squared we are getting yet scores and BX square must be why square was easy square and this each of the 2 wage CD vastly exponential expansion of the space White is a common with 2 beers is really just square right distance between points it is increasing Mikey BHP until a given the X corresponds to a growing distance which grows To add Ito BHP and the metric see to it that made a transformation just in order we made a transformation of the time variable we wrote that kind variable T I think How was age right H is the Hubble constant space right it's also the expansion rate wherever he is equal I believe the 1 age E Martinez D . minors Minor surplus of rumors minus stage capital capital C goes for minus infinity restraint when change things To be right the yup capital T goes From minus infinity deep in the past what happens to this they went she goes the minus infinity because big eater minus gets bigger 20 goes awareness but it's bigger negative focus of a remote past people's minds infinity is also capital people's minds but the remote future when this he gets very big flat happened this way in what but was right I paper peppers right me so still tour when Misty is so large and negative this she is also larger negative but now what happens when this he is large and positive when this is large and positive they this gets small and capital T goes ghosts 0 equals infinity is also capital people 0 and this is just a trekked it's a trip forgetting the whole geometry or not the whole geometry but the power interested in the remote future in this case onto the blackboard now what happens if we re write this metric In terms of she'd just remind you that becomes Martinez plus minus he squared plus B X school at all times worn over T square over square each where the exact noticed that when she gets very small distance between points gets very just as it did on this side over here is just a rewriting of this and he goes 0 is the remote future the nice thing about writing the metric this way is that In these coordinates light His move on 45 degree angles that's very helpful in thinking about this geometry and asking who could communicate with cocaine senior why the light rays over 45 degrees in this trachea while the rule of light is that matter should be 0 at the interval should be 0 bt square by square plus the X squared equals 0 to save his DP equals BX indeed Siegel's DX is just a 45 degree of 45 deg why if the library was moving in the plane would be 45 degrees in the plane if only out of the plane with 3 45 degrees at the place was always trip visualize twodimensional but OK Sasser set up that's what that's what space time in this kind of inflating exponentially increasing world looks like areas ballots imagined here's somebody you need a friend the real world of course people only get the lived for a certain kind but right now and pretend we can live forever and so use the world line of some observer and that worldwide it I was really end no it doesn't really end because as an infinite amount of time between any finite point here but on the blackboard we draw these observers as just ending on that point over here that's the remote future what can that observers see well you look back and sees light rays coming out from distant places a light rays more 45 degrees I could a 1 more dimension I think mentioned burning the rewrite Rice receives light is coming but I take it back into another dimension that's too many would like Y Z to you but at least I can get
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extra more played diagram so this observer looks back and as time goes on gets to see more and more but never gets to see more of the space time is in the back like cars here so in particular never gets to see anything out here for here at least doesn't get to see it in any sort of usual standards so the region most of space and time almost everything is totally inaccessible to those observed now course may be another observer over here however observers something else that some overlap OK but this person gets to see everything in here this person gets to see everything over here works so simplified just that you want observer of the time for all practical purposes is universe spacetime universe is backward like cars here now what is busy busy see things a world which seems to depend on time you would think sell you might think well everything seems to be exponentially expanding but let's just below us a very simple exercise let's consider it this distance and compare it with Mr. spends and assistants and assistants and this basically this distance drawing year is the distance from the observer to his horizon let's see how the changes would partner looks like a shrinking will assist checker here is a metric electric and let's put this point over here at T equals minus 1 but but this point over here he equals minus hat this 1 over here if people's minds of quarter incidentally that corresponds to uniformed picking off proper time each you look proper time would correspond to dividing this interval by half that's the way this transformation work as 1 of his innings the amount of time in here and now calculate this districts to calculate that and we just look at the metric system at and all these 2 points are separated by a spatial distance but no time so they still pouring are separated by Zero time interval that means in this former here should be equal sign the should be equal R D do all it really out there was no time separation of all between these 2 points so let's write now finally formed not differential form the square of the distance scholar from AT the beat what is that no time separation what is the dealt that X between these 2 points you tell me this is a 45 degree angle this distances capital T. distances also capital In fact onsite bother writing Misty was minus 1 wanted to speak T letters be this distance here the horizontal distance is also the same as the vertical distance we've 0 from here from here we get plus and Delta X it is the same squared but now divided but he squared age what's the answer 1 over each squares another distance from here to here Is as war age as the actual Rio
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physical distance that you would measure where measuring devices but not as he answered doesn't depend on the distance between here and here is exactly the same as the distance between here and here the X is smaller but the tea is also small so when you right at the he I got the ax gets shrunk by a factor of 2 but he also destroyed by a factor of 2 so the distance of the observer from the horizon is always the same observer sees a horizon around him a source for years and that's here doesn't change with time the fact you might suspect but if you use coordinates that were appropriate told The Observer inside 1 horizon you might discover that the metric had no kind after all the distance the horizon doesn't have any timedependent it's always the same and in fact many things don't change with time it just looks like they do not expect that maybe this some weight to rewrite this geometry and went on not burger tell and or worker micro organized detailed but using call wouldn't it's like there's spatial coordinates which are appropriate to the absolute interior of the horizon region there is another way of writing the metric only good for this region it doesn't capture what's going on the outside but captures everything on the inside show you what it is and you look at 4 minutes and may look somewhat familiar familiar but not these are coordinates but a Soros built on the pattern but described here another words that coordinates in which we coordinate distance between here and here is the same as the coordinates distance between here and here is coordinate distance in the accord next will be the same as this will be the same as as that of Australia with what the medical yes squared equals DP squared as no surprise that actually proper time actual proper time and then the rest of it is class but all not on sorry wrong I apologize mistakes but these mistakes happen when I haven't had my cookies at markets quota if rest global sugar 1 might h squared are squared PT squared plus 1 all 1 of my biggest H. are scored squared last are square feet alternate yet 2 squared and remember what Omega is right when you're sitting at the center and you look around you you see em angular sphere you and this is just 1 way are not riding out the full circle just simplifying it is is real familiar at what to look like dollars meters remind you short show works like exactly the same except H there telerate square is replaced by twice MG and then divided by are rating is exactly the same if you take the parentheses Ferguson here likewise over here as the same kind of form and fact looks awfully different about each square supporters but the important thing was for Where is the horizon and a short but the rights but the horizon is where this thing is equal to 0 as a place where Clark slow down as places where distances are infinitely contracted and it's also the place which separates the inside of a black or the outside of a black hole you could also write in a form on minus 2 Ng are doesn't matter how you write it be real importance of this term is the place where managers were equals 0 that is where the horizon likewise here saying idea of the place where this thing vanishes which is are are equals 1 already age oracle's 1 age that's the distance of rice so this is another way of writing exactly the same geometry accept something really breaks down if you try to make bigger than 1 over age something goes loser Kia you really don't get out past the hall metric gets a little bit so a space journey and the time difference in terms space we don't need to worry about that right now you let go from 0 to 1 over age and this geometry covers the entire cold everything that's inside a call and is Everything that can be seen by observers single observer yacht have slowed because you are here to begin with because we're talking about an exponentially expanding universe right eaten with scale factors age series blood over all water over these now others all here a horizontal bars only 1 over age and therefore they elected distance the horizon here From Oracle 0 2 1 0 foreigner takes a little bit of mathematical trickery to rewrite this metric a few chord changes a transformations recorded security and when done most for coordinate transformations to find that this patch called sometimes called patch static hatch and 1 thing you notice about the matter the most interesting thing about many interesting things about it 1st of all a horizon but 2nd of all none of the coefficients year depend on time they do depend on arms but they don't depend on time and that's sent in this form the metric is completely time independent that's another way of saying that were observed the seas around him just doesn't change with time it's static is always looks the same distance the horizon was always the same wherever the observer does it want time if he does the same thing at a later time will see the same fact now it is true that it takes 2 particles but ignore any forces between but suppose it takes 2 particles and some girls will happen Spain the Bloomberg a many attractive forces that space between them expands and go flying off to say at I'm independent but the
38:17
point is if it does the same experiment at a later time you'll see exactly the same thing they could do particles on goal and they will slowly accelerate apart from each other take the particles at a later time do exactly the same experiment they will slowly accelerate away from each other as part of this article that done once we get to this point here we can kind of see that a black hole horizon and the space horizon are very very close relatives on the fact that Everything that you can say about the near horizon region of which what black hole it is pretty much the same for the armed affably de Sitter space I'm going to try to prove that the similarity of the Magic's a pretty clear and they fact near the horizon almost identical very close to eyes but the whole global picture of things it's quite different wears a black hole is something that we stand on the outside and look at and amid talking addition the whole picture here is quite the opposite we are only inside the black staffers on the outside the stuff we can't say and yes there is Hawking radiation being emitted From a horizon for the same reason admitted an absorbing absorbed some times a photon gets to us but can also ask the question What is energy of a photon by the time it gets from near the horizon plots and then there is a big redshift factor this metric just like a short film metric has associated with of gravitational potential this metric also has a gravitational potential a foot before all draw for you as a function of art as a function of ah is gravitational potential Tiverton and drug upside down which like the meaning of that Is it takes work to pull something from the horizon equivalently an object emitted from the center as it makes its way toward the center will moves energy potential energy pasta climb up out of this potential lose energy another way of talking about redshift Yukon work out the redshift easily enough from metric and do it now but a photon emitted near the horizon will lose energy on the way out he said that the Hawking temperature temperatures seen over here is of water but see orders it but somewhat over the distance from the horizon war was over distance from the horizon in plant units how they use our horizons how big the horizon Our our eyes our horizons mediators say the horizon that we think we know about on the basis of known expansion properties of the universe this distance 1 of H 1 of 8 each is about 20 times tent 7 9 light years 20 billion light years these red shift of a folk art from the horizon so where we are it is by this factor of 1 all over 20 times can overnight at a lot of photons it we see coming from the horizon hour of incredibly basically the answer is that the photons that we see Havel wave point which is about 10 billion light years so those are not very energetic photon we're not likely to to see what kind of experiment would we do see them while you do the same kind of experiment with black all except we do it from the inside Alice takes over a fishing pole and the end of a fishing pole worms you have the Mama and cast about recovery long line fishing cast about be expansion of the universe polls on these thermometer or tends to be accelerated out away from her and she waits 10 billion years of there's also a year it's not just a fishing line it happens to be a cop coaxial cable or something that she can read off the temperature as she waits 10 billion light years in Ernst & Young put some money spitting real to stop at 2 dozen look through the horizon stops over here and she waits until the signal comes back that's another 10 billion years and she reads off the temperature and the temperature should read office height the other hand if she just sits fewer with amount the temperature that she sees his red shifted and is very very very well so far lower than anything that could be produced laboratory it's not in particular are microwave background temperature is nothing to do with that it's the sitter temperature that's properties of the world that we live in the as it will be a couple of hundred billion years empty apart from our sitting at the center of everything else having passed out of the horizon some amount of stuff gravitationally bound together Farrar galaxy a couple of other galaxies that happened beaten not being dragged away with the euro ambient expansion and everything else will be essentially and except for those very very very feeble of radiation radiation from the horizon soso grimmer prospect of various people noted astronomers at that time will be confused we understand why along a very big universe in fact elaborate hard time measuring how big the universe it won't be anything out look at Seoul will be and the possibility of measuring this radiation were happening after that it way well yet we are exactly the same as a black hole is a black hole from our perspective and classical analysis we would see things getting closer and closer and closer and closer to her eyes you could say exactly the same thing only a draw it is our observer somebody bolster the horizon Our observer here never gets the see them for the horizon triangles on fraud observers here you look back as far as he can tell as time goes on longer and longer Bob says Alice is getting flat against horizon now so it's exactly the same as is fade away the bag that so what to see that OK classically classically just without warning mannequins that season ABA of wrong terms since the wavelengths of radiation that they send so long see it but he reserved mathematical description of jar is our eyes and hair and here is wasn't Alice
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Alice still 1 day alleging Alice Falls over verizon get squashed Jane gets closer and started get squashed how's gets closer Jane also another where kind of sedimentary structure Forms New horizon but is gradually gets closer and closer and hair skin here now that's a classical description of what actually happens quantum mechanically is more complicated and walls this interaction with be emitted radiation and what which that's all over the place the ionized isn't Cookson does terrible things but the classical prospective you would just lose track of them as they get squashed closer and closer and you lose track of them because the radiation from them we get more and more and more Richard closed ever at a day case the residents or 2 they city clothes don't cross over Alice has no problem of arrived shows perfectly happily real Bob just lose track of buffer tries to do an experiment which sees what happened we come back to this very strange situation as Heisenberg um microscope situation where the only way to do an experiment Mr. shined some highfrequency light on ours and theirs Alice gets closer and closer to the horizon the wavelength of our life gets more and more Soviets to ensure whenever you know is that you can't look at cook car yes we can say was also acts as a black hole gravitational well let's hear whether it is a bit is a gravitational are good pilots Bilal exercise fur any kind of a gravitating material which would usually call mass could could lose the energy for any kind of distribution of energy or mess there is around it torrents neighborhood some orders there's a gravitational potential gravitational potential is usually called 5 fight is such that its derivative its gradient is the gravitational force of object on the unit next summer Test match the unit now find satisfies in equation on the lefthand side of the equation is something involving 5 and the righthand side of the equation is the mass density is the Newtonian physics with plutonium physics what some righthand side with just say the mass density which role and function position in general it might just be a point source said there was still left different 5 of course quite right anybody know there right but the beverages because you close something called Dell squares which is basically the 2nd derivative with respect respect to the Palm these 2nd by Dr squared of Pfeiffer a radially symmetric distribution of mass is equal to Rome this would give us for example for a point mass it would give us the usual Coolong usual Newtonian potential energy now vacuum energy is an interesting possible candidates put on the righthand side not do sell the as my sign right still squared fired minus role plus I can't remember the microchip figure it out for the other Bond but gerdes' fought what would happen if they were vacuum energy in addition to the pockets of ordinary energy that's it well Europe but constant on the righthand side with a constant beat the constant would be a constant vacuum energy sometimes called cosmological constant other times it's just called H square and basically portal squared factors for each contract so he is a formula for the gravitational potential of a space which is filled with a uniform distribution of maps it's a vacuum energy absolutely uniform only doesn't change with position it doesn't even change with time I was a solution of this equation the year no easier than that it's fine Eagles plus or minus 4 figure out the sign later 8 squared Our squares let's differentiate but maybe there's a factor of 2 was a 1st derivative of this respect Wayne are was the 2nd derivative a squared Justice think so like that a uniform absolutely uniform distribution of energy and this should be a minus gap should be a minus here we do it right so we see that as a potential gravitational potential you could think of it as being due to this uniform distribution of energy distributed all office space and was a look like it looks like there's a minus 8 square are squared off too was asleep this means at what don't follow that that's the potential energy that I a I at the center of my geometry I'm special I'm at the center of my geometry special units and your geometry and that's fine with me but I know that I'm special might I make measurements and make measurements on test masses are finding move in various ways of finding move and ear they were In a potential which went like this incidentally was a force due due to this potential nor the force is derivative Of the potential price so do River the potential others are so this is a forest which increases into repulsive but minus pushes Darren and the 4th increases linearly with distance so any kill objects if you just start an hour at rest they will start to accelerate away from each other and they'll eventually start picking up some speed how long taken the pick up any appreciable speed that depends on a beach basically 10 billion years that pick up any significant speed but it's awakened billion years it will be moving like a rocket OK so no not like a rocket by a photon closed thought so where are those mean supposing you start an object right up to the top literally of the top what happened is stays right it's at a point of unstable equilibrium will last another way of saying that meet in my own frame of reference if I take an
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object which is located right where I am it'll stay there you have to be to a sophisticated about it I am my own object and I don't move away from myself well about sometimes but not that usually have now lads and I think an object a little bit away from land and again we're ignoring all other forces we can take into account the forces were ignoring so I start somebody out at rest 400 meters away from me that's over here what happened some going away and factor in this kind of potential they will move with an accelerated motion that that will be if we take into account relativity and everything will be exponential expansion felt that just a statement that the space in between things is expanding exponentially so this kind of picture is a kind told me in a description of the scene physics as the exponential expansion of the universe as the was No. 1 a uniform distribution of matter a rare meat and number 2 0 gravitational potential energy which is pushing everything away now we certainly don't works that young fraud so if I took bullet the potential energy between you and me only gravity for simplicity there's another contribution I'm standing at the center and I'm thinking about you and I see that you haven't would never gravitational Tony and potential energy relative to meet in addition to that at 1st told your ordinary gravitational potential energy look like right back polling me the Sept calling you would my said look like at 1 will our potential artifact is that to this look something like that subpart class enough from close enough that I get pulled you get full taught me online at this this what you arrive at this distance in a kind of unstable equilibrium of his slightly farther away than populace the new get pushed away so this is exactly the situation that the Andromeda galaxy appears to be in here somewhere was falling toward us a few galaxies away their accelerating out away from it's while you're there is a lot of talk about what an aide said that their Witcher which aboard a normal normal not there's 1 thing you could call a vacuum energy court cosmological constant is only 1 thing and if you want to
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mimic make it all my new Tony in physics you model it by a uniform mass distribution there was 1 thing it's not vacuum energy cosmological constant barrage of dark energy all the same thing and they all correspondence if you Weiser said if you want a model it the in context you simply imagine a uniform a but I can't think of a buyer EU commuters at the consequence of rural you of course the go together at this good it said and for and sitting in said this season as less to hear well the origin the dark energy the cosmological constant vacuum energy is most likely quantum mechanical Georgia old wants its it's just energy in fact I mean you know the mass of the electron has a contribution to it which is car quantum mechanical our but once we know what the mayor we simply use it in classical physics were just an ordinary man sold large quite true that the dark energy cosmological constant May ultimately be due the quantum fluctuations nevertheless by the time we average over those quantum fluctuations what we see is a uniform distribution of energy very small to be sure if wasn't small men now we be rocketing away from each other it's very very small arms in natural units and plant units something like hint of miners a 120 3 very very small number compared to any of the natural scale and physics art and it sets the scale for and the reason it moments is the reason that in the sober while the will be like effect cosmological constant was much larger the words of each was much larger here is this the distance the horizon sorry Waroway age was much much bigger than we be surrounded by our small for years we will be living in what effectively looked like a much smaller universe even those even know what it was being big right age is being that cost means more rapid expansion but also means of small horizon so would be sitting in the small horizon but with a much larger repulsion between things H for larger repulsion would be larger and the size of the horizon would be much smaller so we be much more tightly restricted but will also be subject to a force which would be course in everything to explore so there is a limit to how big the Hubble current video of cosmological constant of dark energy could be and we still be able to measure it there we would be able it talk about it now there is a place yes insects whose relationship this language the language to users not plants constant plant constant is a thing which carries dimension always good to talk about dimensionless if you work don't plunked units you're automatically talking about prevention was saying armed and of course knowing what the plant unit is doesn't belong in ordinary a measure Europe's doesn't knowing what age bars but dumb yes there the answer is and plant units that means everything is dimension in means that the Newton constant as 1 it means the plant constant is 1 the speed of light is 1 in those units were all the fundamental constants of physics most fundamental constants of physics Citicorp water In those units be cosmological constant energy dark
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energy is a 123 orders of magnitude smaller so that's 1 of the great puzzles physics watch the origin of the carrier's small numbers not all right here that has Hugo out the world about asking people occurred ladders man by 40 per cent of Americans don't know that and I don't think the situation is is well below the charitable works is not quite yeah but there are some serious physicist who work question but 11 and 10 years ago you might have reasonably question Head of 15 years ago you might reasonably question on the bounce from experiment get tighter and tighter and tighter what they mean by saying that the cosmological constant is the constant is is the hypothesis that basically that age varies with time and decreases of decreases decreases and will eventually settled down to learn 0 the idea that the vacuum energy whatever it is temporary transient thing which was settled prior arm and eventually not be there he said it will be at the Art of ourselves that we would know that EXE galaxies you may not tell her telescopic can yet there also father firmly young without a telescope yet so you do not appear that the plan is a Kurdish writer always all it sold you're a it's a very interesting question I've thought about myself and some of the people about how old would astronomers of that distant time in the future the earth is still here there still here you to do this some questions and problems but nevertheless were all still here and we have our telescopes lost our history books the Internet Is failed we've lost our history books we don't know how might we become aware of the fact that there was a finite horizon out there that it was a dark energy that things are accelerating away from each other and it's very very harmful imagine and I can't think of any way that maybe it would tell be cosmic microwave background what would happen to it a red shifts the point where it's completely undetectable or about the galaxies that we cannot ignore the measure the Hubble constant and so forth out
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there more and it just becomes a very very difficult to imagine how they could reconstruct them out here galaxies and born from empty space they no dark energy those world prequel actually before we are got there was some people lose their wrapped in English that hats that will there wouldn't be would be spies out there is no law nearly all bears paradox we remind your all Parra box were of infinite uniform density of stars out to infinity if you just take the stars from within our galaxy how much like they give we know how much like gift all this paradox was a paradox of what happens if the universe it is filled with stars out to infinity and they're not D didn't know about the about expansion of just sitting there is no less galaxies so they will just look at each stop ever they but they would see it into the stars who would see the galaxy have received island universe that a astronomers before Hubble believe will a he said if that they are not images they would be on the right this galaxy these spirit gets right rights no no no no that just speeches where they are now will be aware of how far because the galaxy but a thousand light years right small 20 microscopic sorry I think the right each he was born a shrink it verizon bowls ensuring yes are view of the year but we're talking about yes yes and how they will it be in 20 of 30 billion years no no no no honorable if you galactic radio it will be about 20 billion light years from the dark energy that we know is there from the measurements of
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everything we know about the cosmological constant is a certain number of how big big enough to put the horizon about 20 billion light years away now tomorrow basically forever so they'll be sitting in his big containers by 20 billion light years crossed with 100 thousand light years era galaxy a vacancy everything else having been swept clean and how they detect the fact that there is maybe I wouldn't have boundary which court there is a great start rejected that yacht guts stars are stars in a rejected who got your full of brought track in track for a while but you won't be a track America Cosmo odd jobs as as well as how I that storms repertoire Miguel Back at a news tip Inter when I see it we can see it and see if we can we can see we can the measure young the expansion rate and reconstruct reconstructed With his enough for stuff around To be able to reconstruct at the person per year just outside this is about us now would be quite yesterday they gave us that that would that was a good but it's not be at the horizon is not going to shrinking horizons it's going to be at the place where a from be acts with the number that we have today With the numbers that we have today well measured checked many different ways prediction for the future is that the horizon will be at about 20 billion light years that's worth a for another Lawrence H. is constant touring bearing is kind of expansion and the distance the way you have to go to where it was be we've seen speed of light that could be cut off if they had a bye North Shore said that a guy we can see that part that's out beyond the horizon as I'll be on the horizon that will not be visible us what through our future editions now what it is true there is something which is show our record point Carey occurrences of player Hungary recurrences 1st of all you picture on that's the inside of picture should be that this summer temperatures of very low temperature from our point of view of a high temperature of the boundary but you should think of it as thermal system in fact has an entropy the entropy is just be area of the horizon and plant unit president could be fined finite B a c could think of the toll large extent as a cavity with a finite amount of effort the rule the thermal gasses mainly out near the horizon because of this effect and retain out here it is constantly fluctuating now thermal system with talk about the thermal systems on box a box of guests water molecules after a comes a thermal equilibrium and in fact what will happen is everything will come thermal equilibrium when everything passes out to the horizon it will be in thermal equilibrium was a gas a boxer guests like 1 of thermal equilibrium was like nothing amiss a big double box of uniform density nothing much happens it just sits there and sits there forever and ever right then that its radiation and there it's a black body of molecules in the other molecules and fairly against that apart from tiny little populations nothing ever happened without depends on time scales there are times skills basically statistically anything can happen there are no rules there are no rules is only statistics only probabilities but although our probabilities it could really is what he is the probability that all the molecules suddenly come together in such a way that they all warning that in the corner of the room is an entity that is of about the proverb Yuri is basically E miners enter B of the get the entropy is roughly the number of molecules we get so we have a box would conclude 25th molecules eat them a and the 20 New Wave that kind of audit Ito the tent the 25th at called upon current and basically the Ponca recurrence time is the timescale for extremely rare and unusual populations place extremely rare and than usual fluctuation might be all molecules called off and or it might be the will assemble themselves into an elephant whatever I love that time scale is of what's called a potpourri recurrence and it's normally extremely huge on that time scale is constantly things going on fluctuations taking place which taking of thermal equilibrium so far at a thermal equilibrium that a new returned the thermal equilibrium all sorts of complicated vortices and other things might form and a half before return of thermal equilibrium is is also thought to be true for this airspace that you really wait long enough for how long he can have a 120 what units it doesn't matter where you with me it doesn't matter reduce its ABU Mister could think of will take he did attend the 120 of those units they years for a recurrence of workers and on that time scale all kinds of things will take place so or are among other things but no short of such impossibly long time scales nothing will happen just be heat that the same kind of heat that the takes place in here when everything comes to equilibrium was more interesting things well a a more wild fluctuations could have fluctuations could happen I'll give you an example fluctuation that can happen we can even give a rough estimate of how long between such fluctuations instead of the whole world
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returning to the original Big Bang which might happen that would be this time scale here because far modest kind of fluctuation a more modest kind of fluctuation might be of fluctuation happens in which a solar system accident which form the Kowloon elephant form Tadeusz of elephant form and the time scale for elephants performers not eat the minus the entropy of the whole gas it's Ito minus the entropy of an elephant Wojciech appear elephant roughly the number of molecules we are in the same way if you wait long enough by accident but to what thermal fluctuations a solar system might form here that might be the cheapest way of making enough observers the cheapest way probabilistically speaking of making an observer might be for a flocculation happened and to create a solar system but the figure something a little cheaper I can't think are just a form that would be even cheaper the entropy of who my worry will be if there was no sign and new would guarantee warm but word that you might former and already warmer verify that keeps itself warm for some period of time and you say Well maybe a of time the people toe toe toe evolve tho worry that the fluctuations involves the creation of people but even cheaper for for you want as a single observer you could imagine a single observers or just as brain just as bright being look by random fluctuation such things a call Boltzmann brain and Sears physicists worry about computing the relative probability of would observers have reasonable history like us verses both they thought want a universe In which show in which the typical observers is a Boltzmann brain that's not a good thing if when you calculate the properties of the universe that you find out that the old wellmeaning majority observers Our both membranes that appears spontaneously out of nowhere and serious physicist worry about a about whether their cosmology will be dominated by Boltzmann brains instead of Darwinian brains that the fact that I'm mad giving an hour that's a serious business they made us laugh little while but off the here and now you're right I'm going there should qualify restatement statement possible tour it's impossible to do it except on kind scales which are big enough to Explorer such large regions right that's exactly right on these forces are such that they only become appreciable at distance scales of let's say some fraction of a billion light years so yes if you could go out and explore cost you write that much shorter time scale you could go out there and that you're explorers map out the the geometry of a light signals on measured the properties of space on scale of space and time and if you had yourself a few billion years to do it rockets that could get out there and explore that largesized yes yesterday you could definitely tell our brothers few restricted tools if the usual lifetime an experiment well any kind of wooden every time scales you would have a much harder time Russia Hewitt young but they're absolutely right you could imagine sending our explorers about geometry and they would find they would fight this the task very rich while the time scale experiments would be of water over 2 billion light years to say how long the more you a fair fight yes or take much longer to do express leaders it's right the answer by then I think you're right it is as it is a matter of Richard that is the but that's OK in the wake of the bombing just send observers out let that make measurements from light rays of light rays take a billion years to get from 1 place to another took a we have a billion years and just bring observers back in and be right there is a major factor but we face exactly the same richest factor warmly measure today we measure today the cosmological constant by monitoring go go cosmic Makarova background that's been registered factor was Austral sold it was the major qualify readership you don't have to raise shift that much if you want to explore a universe on a scale of like 84 billion light years on size and that's that's enough battery probably a billion light years would be more than enough to detect the expansion the billion light years these there is a small as it is not a big deal it's a small fraction of 1 attend or something like that so you not Ltd by Richard Boomer making these measurements if you or we wouldn't be able to be planets and so stars and galaxies that we see here that we count which form are measured Ronson so for those erupt reform 2 billion light years arms but would not limited by in detecting them by Richard from a pair of dollars based on a novel that there's a conqueror occurrences on can classical bad death base under laws they was she said Jack also that a half probably warned but I guess you can't is well taken but it's also true that they are the most world single robust set of rules that has never been shaken and all of the rules of thermodynamics statistics so if I had the better off Armed which laws would be most likely to survive for a very long time arbitrary time I would guess those which were based on statistics probability theory namely statistical mechanics but we don't know what else to say about but they also lost by serious yes I think we will review our was going to talk about what what what times day it's now or what that I know I know I know what I'm really on time
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I thought I would amuse you with some other things that that that's physicist worry about today's some very bizarre the question is whether it should be you I never quite get to it dawned it is the right time from read you have moved some they will get to have some I was going to tell you about a puzzle that has to do with probability theory that is really so obsessed in a lot of physicists and they worry comes from the 1st thing we which were not talk about tonight is the idea accept this convention is the ideology eternal inflation I'll drew a picture of it for a couple of days and then I'll tell you what the nature of the puzzle for a story of picture on the blackboard picture of the sitters a a expanding the inflating universe looked like back everything below here is the world everything about that doesn't mean anything and the time OK 1 other things that was discovered sometime in 1970 by physicist by the name of Sidney Coleman was that the de Sitter space probably unstable and butts unstable very specific way it's unstable With respect to look leading little bubbles in which the cosmological constant might be smaller understood draw you with the picture looks like bubble nucleated over here in which the cosmological constant was a little bit smaller or maybe a lot smaller what happened a region with Kuralt we've grown and eventually show up a regional space like that this regional space in here this regional space time in here it is itself and the higher you don't ask me why it's a bubble butt of expanding novel and that expanding bubble expands out something infinitely big up here and it corresponds in some sense to leave With time many of these bubbles will form and factor the population of them Whoa exponentially increase why it has to do with the exponential expansion of population will exponentially increase and this is a picture that cosmetologist love to draw these different bubbles could be different from each other that's not really terribly important that might be different from each other things go on in them and processes imagined to keep going and going and going now each 1 of these tiny little bubbles is as big as the original 1 I drew here for the same reason that this line here is as big as that it's just that they occur later and if not all of future infinity here what kind of fractal structure of exponentially increasing population it could be people in Nantucket be whether you like the population's exponentially increase there are some very funny puzzles about probability theory having to do with armed exponentially increasing population and they have really gotten away I'll give you some examples just for fun some examples in an opera house or how it applies a match the following good Donkin world the thought that some experiments show the world in fact it's not about our world it so well in which the population is exponentially increasing unfortunately this is approximately true number 2 0 is a world with finite resources figures but let's take it to be the case that for 1 reason or another nobody really has the vaguest idea what the problem resources Mr. figures not true what's wrong must sit 1 half of Congress anyway I'll write so I would take it these citizens who live in this In this exponentially growing population and they really don't know no idea the resources are but they are interested in them the probability that they want to know what the probabilities are their resources will last for another generation or so how did give alchemy given hints this I don't know what the resources are below and 1 more postulate a normal classes when the wheel always make in science abuse some examples of it and it is that we work doing the experiment typical typical means the foreign it means that if there a great many possible outcomes but they're more but by some large majority b observers who are doing this have a larger problem well let's say it now OK let's talk about let's talk about coin flip but according represent hate the digress but but but didn't declined for we have zillions and zillions of these people are obsessed with calling for thing with a lot to do with they love the flip according million times all these people say an account heads again in the camp bigger with it I don't know but a typical 1 of them or 1 of them as the question of what they should I make the harmony heads entails where did not exactly but you know within some reasonable bounds on the experiment an experimental physicist all experiments involves statistics is especially inquire mechanics alone will make predictions of making predictions and analogous to the prediction of Corning workers who were offered Corning's what see into the instead is there are some coin flip pros who flipped all heads are some calling for the Brewers who old tales according to the standard theory of probability the overwhelming majority lip about up with a million million flipped a million plus or minus a thousand square root of a man so if you're at all smart and you're good experimental physicist and you know the rules of statistics you will put down your prediction your prediction will be less half a million plus a minus about half that figure probably set off half a million plus or minus a thousand OBU best guests and Aviva very far away from the you probably say there was something you probably won't believe that you are outlier you're more likely to believe that you feel it was just wrong but they're gonna be those people are outliers and they of course will believe it theory is wrong and they'll be Rock will always make the assumption that we are typical soul in this expanding population let's make this option that we are typical we are like the majority of all observers who ever lived then what bet do we make a how long these the resources will is less than half that present time now well not necessarily the last 1 but there won't be more toward 3 generations after us and the reason is in exponentially expanding population like that about
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half these people who ever existed exist now about threequarters of the people who ever existed existed within 2 generations about 780 within 3 regeneration sell with typical in exponentially expanding population we all are near the end of that expansion with nearly end that expansion now that's a very puzzling conclusion it doesn't it that sounds like something wrong with it how could you possibly know that if you don't know what we want the resources are on the other hand it is true that no matter what the resources are most people will be near the end of the recesses right this is I give you and I give you another example of this kind of exponential expansion we've all seen show seen these my favorite drawing I got a comeback over and over again because as Beat mathematical significant its Esher's drawing called limits Circle No. 4 foresees angels and devils mind that trial drawing angels and devils but it has a big game you it's just that restrict us of the Devils preferred that it has made a big devil sent there'd smaller Devils out here have smaller Devils out here and that in fact the geometry is such that they really all identical to to each other there are symmetries of this diagram which moved points which can move this pointing to this point move this point into the something small here it's just a way that is drawn make some things look small and some things were bigger completely symmetric but of course when Esther actually draw it he did have to draw the small things more big things they're not here is the question let's defined In Angel with devil Excuse me a devil which has been drawn with a body part missing but column amputated case definition of epic if the devil was drawn with some body parts missing will call on amputate and his doubles gotta sleep and they wake up in the morning and they wonder and 1 of the missile the unfortunate amputees a reminder 1 the year on the whole Devils up if you look at issues drawing and you extrapolate is drawing past the last visible devil you believe that you can extrapolated we look a CSU was awfully good drawing he did Devils missing body parts so you conclusion would be high probability here and not the name of the other hand Esser had finite resources finite patients finite time finite amount of game and that means as he got tired I knew very very edges surely vary very close to these edges you'll find that almost all of the angels and devils will be slightly Mr. on a course that will be they it won't have their heads and tails or whatever it is the ones out of the band now what it is the ratio of the ones which are adjacent to the boundary of all of them In early intend no there are about as many out near the boundary as there are in the whole thing not obviously do fewer about factor of the and that's B costs the number of them grows exponentially as you make the bigger and bigger said they grow exponentially and so to actually character few if you cut off but say by putting a circle around here now count all the ones that are adjacent to the circle and all the ones on the inside you'll find about equal it's same mathematics as saying about half the population how long into the past the population would be gone for a day about half the population 1 generation constitutes about half the population of anything ever existed in the same way about half of the Devils all right on the edge where Over the edges we don't have to know how much resources Fisher had it doesn't matter how much she had no matter how much she had as he draws more and more and more of them the ones near the edge will always be about half of all of their himself it you wake up in the morning you don't know where the euro whole or have bedeviled the chances are about 50 % but you have a devil deputy this is very puzzling because you state well how can I say that when I don't know how much we sources it water enters a dozen dormitories they now we come back here but but with a hat Oregon facing a problem of exponential our population growth in this case population of little bubble universes bulletriddled Meacham back from a comeback we come back through our through angels and devils connecting doubles before we go 1 2 universes tested they have angels and devils let's ask a different question the different question being when you wake up in the morning are you an angel or a devil 50 percent probability right there are as many angels devils and the mathematics of pressure drawing if away conference means something that would be true but we know that Leicester have finite resources which means we have to draw and the answer for the ratio Our devils through throughout Angels is extremely sensitive the way we draw that line extremely sensitive away we we could draw the line for example every time we come to endanger Let's go around it that way every time we come to a devil we got around it that way and now we push this edge out further and further by a factor of about 3 quarters we will have more devils and Angels at all in the edge at all in air and Soviet assignment of probabilities for Angel Ms. or devil mess is just extremely sensitive to what Escher did just as he was running out of resources it's ridiculous because know you simply don't know anything about his resources you would think they and so was 50 50 but the end he had a little bit less pink paint the white the answer would be many many more White and Pink the same exact thing here you want to know the relative probability of different kinds of bubble universes warning blue ones pink ones and so forth the population exponentially growing how do you decide you try tried decide the same way they let China this offered some time the number of blue ones Rice's Pinkwater but the problem is the answer is super hypersensitive exactly you draw this line and that has led to a problem that cosmologist physicist herself called a major problem measure as in probability measures how do you assign probabilities in a world of exponentially increasing population answer although it is it is extremely sensitive to the way they cut things off the way you and your imagination in the universe misses a very very big problem for cosmologists because they want to be able to use this series in a predictive way make predictive of predictive predictions of the kind of predictions that what best but not predictions at least explanations of things and sold in this kind of world is really true that there's an exponentially increasing population we run into new kinds of questions about probability theory and about how the use of statistics which really just overload baffled really baffled us my guess is of course that were asking the wrong question will probably asking the wrong question but that doesn't help the state that will probably asking the wrong questions doesn't help us to say what the right questions yacht is there any mention normalization of is by me
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but I never thought he told a a word of a number all them him also very well be there are relations with renormalization there are relations with renormalization theory renormalization theory also a situation where Arafat again you start your a picture of the world is having a finite number of degrees of freedom per unit volume and then you double the number of degrees of freedom volume new double it again in double it again you don't double it really in double in your imagination and ask how things converge bowler talking about of course is you start picture in the world as a lattice UK candle continuous infinity of degrees of freedom so you thought the world was alive and you make a calculations are based on 1 degree of freedom per unit Compton wavelength of an electron something or more and you say I want more accuracy of the wider world and every cell in half again and I recalculate Leach case they the same kind of questions what's role that the populations of regions of space with this property that property begins not with respect to real honest time but with respect to move your mathematical sequence of description of the population is exponentially increase again you get infinite answers you have to deal with those in cities and quantum field theory theory techniques for asking questions which are not sensitive to be let's call on the edge effects to be there are techniques for extracting of things which are not sensitive to the details of how to chop this up so young their honor correspondents similarities between questions in quantum field theory and these kind of questions and cosmology people are trying to exploit those similarities but not I must say with a great success which yacht yeah well what's called eternal inflation creating not deeply connected with the inflationary fears if to please enclose the air at it we should see on the skies will funny a patch of sky there are funny patches on the sky and the again very serious physicists astrophysicist trying to sort out the details of what you would see the sky if these bowls collided with novel you'd see a small patch of sky Richard rooibos colder warmer temperatures are of course you do see patches on the sky with the warm and cold temperature I love but to be more detailed laughter and get really details to see that that's what they are 1 of the details would be the polarization of the microwave background around the interesting it is so patches and sky called cold spot called spot and nobody knows what to do called on the sky called bottoms microwave background called about a candidate for a spot where another bobble collided with Bob it's a candidate what more could you say about it other than the candidate well you could try work out more details of such a patch would look like itself for example you discover that the satellite His polarized figure the direction of polarization around this is a particular characteristic way people doing that working out the consequences of such a bubble collision at cost if should this be confirmed this is the does look like a bubble coercion and detailed does this of course would be a major major revolution because knowledge the discovery and detection of other bubbles which collided Wirraba would be very very majors this is a list that it not part of a vast region typically is expanding faster and our region someone's in here and it had a history of different expansion so source complicated it's a complicated story but it does include this idea I'm exponential population growth so 1 could receive a situation in which we truly confirmed that they were bubble collisions with our world we would have confirmed something like this picture at least a piece of then it becomes a really serious matter To try to get predicted and to ask what the relative probabilities of different kinds of bubbles and that's where we run into this troubled exponential population the cancers would be very dependent on the question whether they will find that resources on was a finite resources at what fiery sausages prosaic comes inside out and the details of the way that it came to an end would be what day determined what wrote probabilities were flag had no it's more complicated than that the place where they call y depending on details however some recall the domain wall which separates them and the domain wall on 1 side has won behavior the only 1 on the other side has another behavior but point is the domain wall would be visible show us all could be visible progress it would a bit of luck here we are here's our observer at the domain of 3 young bobble collides over here bubble collision over here this observer was there to see it but collides over here than it does get a city so there's different scenarios different situations but it does that doesn't steamed partly out of the question with numbers that we know that they could be bubble coalition could be visible bobble collisions and its sorrow they have a particular signature particular behavior that fairly characteristic man if the darkness cold spot it is such a bubble collusion we will not be tire wear white decked out in our pattern or love said that while the course yes 8 8 with good book that made a bombed these bubbles I used to eat negatively current written Robert Walker negative spatial curvature very bubble collision would certainly modified their workers Cher's characteristic worry but would wouldn't turn the world from a world with very negative curvature of positive that could do young but I must say that really credit appear to have lost a lot of 4 that that's a matter of individual opinions which I don't think there's any value in trying to assign a possibility probability and that not and then initialize it means I can't give you a give you an answer given before there is any a mathematical structures and very precise mathematical structures were exists mathematically consistent our mathematicians have 1 big prizes Ferreira offered for approving the year terms that would 1st suggested by on the basis of string theory which
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mathematicians didn't know so the consistency of the internal consistency of it has been extremely well check is a structure the structure has gravity and that has quite a mechanic so in that sense string theory is a welldefined exact not cost as remote possibility that somebody will discover inconsistency in the extremely unlikely mathematical consist on the other hand that part of it which is mathematically precise
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Plateau Court string theory with capital rests with Capitol Records brings theory capital it is supersymmetric it is army its supersymmetric The world is not supersymmetric the world as we see it as not supersymmetric mathematical structure which is well defined and for which we have a lot of confidence that really exist court quantum repair gravity with supersymmetry . it is not the real world so in that sense we know now no question string theory is not the right 100 % we know if assure me breaking the symmetry nobody really knows how to do it is not part of the mathematically precise part of the theory we all expect that this thing that we call capital string theory Areas strength has many many many different versions of a huge number of different possibilities lie within we all expect that contained within something bigger something bigger that we don't know how analyze it more relaxed like the situation where maybe it's like a situation where a physicist at the time preceding might have discovered a formula as sequels in and the formula the force equal pay and aimed 2 dimes G are square but they didn't have the mathematical tools that analyzed anything but the simplest orbit so they said all right we will use symmetry the symmetry of circular orbits we want a little bit of extra information we need to know the acceleration of a circular orbit that's not tool hard to and do on on the basis of some simple symmetries and you can never figure out our kept which 1 of the losses it 1 of the kettle laws which tells you that period is a function of radius you know you know that the theory that you working with the fury of circular orbits is not correct but you just don't have any mathematical power were to be able to go beyond it I don't know if that's what the real situation is but it could be like that so we know that the theory of circular orbits is contained in something bigger don't not analyze if we know that the perfectly idealized supersymmetric string theory the 1 that we really paralyzed is not the real world it looks a little bit like the real world but not the real world and the question is whether it contained in something bigger which we could call string theory with a small west of the answer is we don't know very much about we know a great deal about this this is enough to tell us all sorts of things about the combination of gravity in quantum mechanics things about black holes things about the kinds of things but To say 1 way or
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another what's the probability that string theory contains a or the research and extension of a bigger version of it contains all worldwide over here and of course In some local of course that's true world someplace his theory someplace to hand this mess you get something bigger but that's not how we wanna know whether in some interesting way the fury of the real world is some extrapolation from what we already know that there is no there's no way to know not only capital string it contradict a possibility but says it has a lot of capital string theory doesn't rule out the presence of the doesn't rule out the existence of small stirred but work does say is that nature is not as we know it is not described by capital so we know with certainty that bigger structure has to be found however that big a structure that contains our world will sort of be contiguous with connected to the smaller structure of capital string theory this we don't
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we go make objects to this people arrive loads and loads of papers about the symmetry breaking of string theory the silver symmetry breaking some particular of symmetry breaking of strippers we know a lot about the the mathematics of supersymmetry but we don't know precise version of higher combined the breaking of supersymmetry restraint theory bad debtors outside the scope of what we know that doesn't stop people from you make an approximation here and there and they start rolling and you could do some things the problem is that making approximations but you don't know what those approximations approximations you make some standard approximations that we use all the time and you start calculating but there's no lower backbone your approximate so at the present time I think Garnes I think Our the safest thing to say string theory as we know it and as we can rigors version of it certainly not the real world is in my view lots of reasons the thing that the part of it that we know about it is not the whole thing that could be bigger it probably is almost certainly bigger however say whether the real world as part of that very much a prejudiced different physicist share different proportions that this is a bad they said that the 1st process of a must Noel it really it really does require a special wrote no special relativity can be be violated by by the environment was sitting here in a room where everybody's arrest and the world does not look good Lorentz invariant your presence here violates my over and over and also violates we talk but is less time on our serve you could
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have what physicists call up background which means stuff in it which richer picks out a particular frame of reference the underlying rules Merrimoor rules were of a string theory who will have learned how fast he I wanted to predictions that the most robust but most robust predictions that has gravity is no way for it cannot hire gravity test say is Dad a head of a depth of Young's question about Bagram independence is a confusing warned of long from yard His His background independent up to a point up to a point yet it's hard to change the asymptotic boundary conditions continuously but it should be hard to change the asymptotic boundary conditions continuously at EU change asymptotic boundary conditions continuously you can't do any operation that would change that but short of time boundary conditions changing the background locally in space time string theory and new not take my word for it 3rd so this is something that's been long studied since the 19 eighties works of people like calendar and other people have studied now we're going there was finished OK so photo for
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more please visit and said Steen Ford Dr. Dean