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Cosmology  Lecture 7
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Laos Steiger university let's assured
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begin on just just to go back very briefly over what we said last week on what I said was that the the best way to go about trying to estimate the wrath parameters of the expanding universe is begin with a model and then calculate its consequences for what they'll tell you your moment and if that doesn't work so well with just the parameters of the model and keep adjusting until you a reviewer hit pay dirt you agree with data on the new Delaware you configure data and tried of backwards using the the same equations but it's often hard to do do that data not today the model that would put in basically consists of 2 things it consists all a time history for the scale factor of TV end a specification of whether we're talking about a negative weaker positively curved 0 0 occurred numerous on food aid until we get to the properties of the cosmic microwave background and some of the detail contained in the cosmic microwave background which coming to today but until we get to those details on we really typically don't really see deep enough and former mouth that constant a positive curvature negative curvature of 0 curvature is really very critical of the analysis on the site saying if you're on the surface of the earth and you look out the thousand miles well curvature count but it really doesn't it really is not that strong effect if your Everything else that you doing it not too precise hard to tell what liquor theaters could scaled a thousand miles off course you have high precision than you could tell but we're you doing is looking mirror of working out relatively nearby relatively nearby the coverage was much the same is true of negative curvature and so cannot be counting galaxies camping near supernova and things like that which add not such a large red shifts red shifts that never get bigger than 4 5 6 7 or something like that you don't really have not really terribly sensitive to the curvature that both good and bad bad because doesn't allow you to deduce from Riyadh campaign of supernova so for with good precision what the curvature is were 0 plus or minus the other hand since it doesn't matter too much it means that if you don't have to vote too well curvature To make conclusions about other things and the other thing counters the curvature history or on the history of the scale factor however varies with time off so you start with a model which is overtures scale factor as a function of time I want to calculate 2 things you could try calculator and try to calculate these red shift has gone these are the intensity as a function of redshift Uribe's where's the brightness of Standard sources standard camps candles as a function of that's roughly speaking calculating Hubble or relation between velocity armor and you can count and you can calculate from model the number of objects that you see in the sky of a given friendship the another was the density of things out there is a function of of the 2 2 things which you could calculate from wild marble and pinned down parameters as best you can be New York just from recount you do now as well as if you know the curvature with great precision which you which takes c and b data to get at but still a tendency toward 80 fairly flat universe fairly flat our worth a no indication of either positive or negative curvature consistent with 0 curvature end a expansion history which is consistent with the existence other cosmological constant which contains about 70 % of dark energy which contains about 2 % of the energy in the space so that's what you learn from our character supernova standard can it take the other end of things looking very very deep much deeper than where there are galaxies or much deeper than where there are supernova or anything of recognizable standard candles looking deep into the microwave background to do better today we started but Michael A. Background on 4 more generally or we won't talk about it temperature history of the universe the temperature history of the universe temperature 1st always temperature temperature EU Olmaliq temperatures to put a hand on a hot plane you know water heaters feels bad to Frewsburg whatever your taste but
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on strictly speaking temperature is a feature of thermal equilibrium thermal equilibrium as a condition for a system are that is established after a period of time basically by scattering the kinds of systems were thinking about things made up of particles what particles well what particles are present of the University of photons there are electrons protons in nuclei forget neutrons they became very quickly but there on nuclei and simple purposes let's just say there are electrons protons and 4 times those of the particles of make up the universe may present times and firmly equilibrium is what happens if you put particles together and allow them to to collide with each other for a relatively long period of time how long longer by comparison with the time scales it takes for actual collisions that take place particles collide with each other and microscopic amount of time a acquired own mean free pads between particles so the various time scales the time scales are not associated typically with Our with gray cosmological features of the universe that just associated with the nature of the gas Sowerby deaths all fluid or whatever it is we're talking about a fluid matters will be here in a laboratory in the various time scales have to do with the microscopic aspects of fluid and when the fluid sits around or I say fluid I mean whatever happens to be a just use the the term fluid because to comply our free fluid have left To itself for a period of time will establish thermal equilibrium it will establish thermal equilibrium as long as the expansion whatever expansion might exist as long as the expansion is much lower than these kind scales are for which these collisions taking place that will establish a thermal equilibrium but that careful about fat what cause strings to become more used to become the thermal equilibrium I have a box but figures are model again mythical box of stick on ethical box and let's give it perfectly reflecting walls as usual Silverwood after worry about heating walls energy being absorbed by the walls and so forth perfectly reflecting walls and put photons and let's put photons and do it in by shining a laser into a box of China laser into a box to a radiation is in the box and we close up the hall and the radiation of bounces off the walls of the box if this is just pure photons with no interaction between and the interactions between photons is extremely weak photons do not readily scatter of each other ordinarily all think the box will not come the Rick with all will happen is the post of radiation will bounce back and forth and back and forth and back and forth and back and forth forever and ever almost forever and ever without anything interesting happening or maybe you could say that interesting but but without the without the energy being spread through the system without the energy be becoming thermal water takes some scattering takes some form of collisions scatter photons by and caused a system that come from Mariquilla photons dues scatter a little bit is some cross section for the interaction of 4 times but for times of Waverly comparable what we have in the universe today the cross section for scattering work probability for twophoton Saskatchewan is so negligible that these photons would not equilibrate it would not from the thermal equilibrium what it takes to make things come the thermal equilibrium maker of photons come the thermal equilibrium equilibrium is charged particles charged particles scatter very very efficiently off radiation electron assault on or electromagnetic waves of electromagnetic waves was passed electric field causes electron vibrate the vibrating electric field vibrating electron Vincenzo more radiation scattering very efficient if his box contained some density of electrons which column he minus minus from reflected electrons negative charge the box had some population of electrons in it and scattering would be efficient and the boxer very quickly come thermal equilibrium of course the I'm with the distance between electrons are but down with a fleet but a reasonable density electrons in them then photons scattered electrons scattered electrons in the photons all common form eventually of formal soap and under those circumstances we would say that the box has a temperature now the universe it appears there's good reason for this but we are going to get to a tonight is good reason for the universe appears to be electrically neutral art here on a large lumps of positive charge and a large number of negative charge in the universe certainly on
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average universe appears to be electrically neutral so it's not just electrons in addition to electrons there are protons and others atomic nuclei with positive charge let's simplify and just say there are but turns in the box but call in Gamma Gamma for gammaray but they're not necessarily gamma views as gamma for photos and there are protons Pete that's what's in the box gamma electrons and protons the number of electrons number of electrons of In a money this is the same as the number of protons and that's why it's electrically neutral well that's not why it's electrically neutral Hawaii of whites electrically neutral more complicated it simply states that the boxes electrically neutral because use the fact that electric charge of electrons is equal and opposite to the charge of proton experimental facts that when I tried to explain tonight 50 electrons and protons are freely moving in the box and other words if not better known to situation 1 situation that you could imagine Is electrons and protons are tied together into hydrogen nuclei hydrogen nuclei are electrically neutral electrically neutral objects are not efficient scatter it is ruled that they do scattering mediation a little bit but on the whole this such week scatter that these varies very small by Luke density of hydrogen The universe today has so little effect on the photons moving through it that it would take forever and try to calculate but I'm very very long time much longer than the age of the universe clause the year of the photons to come from all equilibrium and so could I the universe is not thermal equilibrium that's not thermal equilibrium it doesn't have a proper temperature for another way of saying it is that the various kinds of particles are not in equilibrium with each other atomic nuclei that are out there if you want to characterized them by a temperature How do you characterized by temperature roughly speaking temperatures the kinetic energy of a particle huitre calculate them as if you were to describe them as it by having a temperature the temperature would be much much lower than the temperature of the Qatar characterizes the photo sounds bit so they would marry particles electrons and protons are not in equilibrium with a photon is simply not enough scattering for that happen on the other hand it these electrons and protons work freely moving and not bound to Adams then they would be efficient scatters and they would come to equilibrium together with the photons expected to be characterized by a single temperature the temperature of the electron temperature protons temperature the photons all the same temperature and in that circumstance is a welldefined notion of temperature What does it take to make sure that the electrons don't fall into the protons and former Adam well it takes a high in the temperature when the temperature is high enough be energies Of the photons the energies of electrons and energy protons are large enough that I'm not collisions take place that they keep busting up the idea of a hydrogen atom they us some hydrogen atoms where temperatures height but there are also plenty Free Electron free brought on the scattered radiation and that maintains the thermal equilibrium so if we're in there zenith temperatures with temperatures really meaningful doors were things a thermal equilibrium then at the box of gas is described by a number of electrons and protons or better yet a density of electrons and protons with the density of electrons and protons being equal and a temperature GE Capital treat them the radiation in the box every component of the radiation a referral time if you like every year every bit of radiation is also characterized by a wavelength there are many many different wavelengths in the box the boxes not have a single wavelength wants to thermal equilibrium and the distribution of wavelength is determined by the thermal properties of box of we could also characterized radiation that just by by wavelength but equivalently by frequency and the relationship between frequency and wavelength is the product of a frequency in the wavelength is equal to the speed of light saw you the wavelength off frequency and Aziz said there are many many different frequencies as a whole spectrum of frequencies inside the box that characterized by a functional characterized by function called me intensity intensity on T and the intensity of is basically an energy density basically an energy density but I'll function both did temperatures and the wavelength or the frequency away all the frequency and defined in such a way that your multiplied by the volume of a box or just a small differential volume in the box TV and you multiply it by a small differential of frequency that tells you how much energy is stored in the volume of 80 in a band of frequencies between frequency New and new plus Dino that's the meaning of the intensity of awards the energy density per unit frequency and a function of the temperature the higher the temperature the higher the intensity no we're not going to work at 4 o the fury of this intensity function but pop we can actually work out the behavior of the intensity function as it would have been worked out before 1900 before 1900 only parameter the only constant nature which appeared in the theory of life in the theory of radiation was the speed of light so that's all it was worth city and now you can use simple 0 LONDON dimensional analysis to ask what must be the formula for the intensity as a function of tea and no and yet it's really understood dimensional analysis you just say days of February the dimensional announces the 1st question is what is the dimension of intensity well its
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energy per unit volume per unit of frequency was a unit of frequency insolently In 1st time right so don't consider years it has newly units are energy art for you time sorry energy per unit frequency energy per unit frequency which means energy times time per unit volume now you can ask what kind of quantity can you make what kind of quantities can you make out of the camp which all the other question was it was 1 of what about temperature where the units of temperature was units of intensity energy times time all over our volume for the units of temperature is as temperatures Bob basically unit of energy is a historical glitch definition of temperature temperature was not originally defined it was known that it wasn't an energy it was just defined in terms of boiling water and freezing water and providing a gap in the 100 segments in the socalled degrees disintegrated bots modern theories of what temperatures as temperature is is just basically energy of a the average energy of a molecule or particle against energies temperature temperature is energy the conversion factor numerical conversion factor between energy units and conventional temperature units like centigrade is certain constant called Boltzmann's constant so you often see formulas in which some energy or another whatever it happens to be his written as being proportional to some temperature times a constant K Baltimore the Boltzmann constant is as just a conversion factor I'll keep it around but so are real purposes temperature is an energy and has units of energy and K Boltzmann's just some historical relic we could easily said equal to 1 and not lose everything up people around just because uh traditional to keep it around OK so far from the cables month temperature has unit of energy and so we can a and what kind of all the paintings can I have which has certain units on temperature and frequency frequency as units of 1 over time temperature has units of energy and I Hestand units of energy times time although volumes attacked a few minutes just work at our with the general formula has to be a former I equals temperature times frequency squared off over the speed of light square if if we keep a speed of life but only thing around that we have as the temperature the frequency and the speed of light and the only formula which has the right units of course it's not the only formula has the right units there could be other formulas like for example twice that has no units in fact that's basically the right and twice the temperature frequency square Over the speed of light squared that's as a whole not quite I said I would keep keep both around but the rulers always the same whenever you see a temperature and a formula multiplied cable money and think of temperature Time's cable to mom a single thing with units of energy right so that's a that's a formula for the energy per unit of volume per unit frequency now this formula is a disaster this formula was a disaster was known to people in 18 a early part of the year parts of 19th century that this was a disaster if we plot this as a function of new war it we see that grows parabolic and therefore the total amount of energy contained in this box is going to be infinite more and more and more energy per unit volume and higher and higher frequency so you know the story of course the story was that a new confidence was necessary Ole experimentally experimentally and for the life of me I have never been able to figure out How the experiments were really done discovered that any details of this curve I don't know how they would because I don't know how physicist at that time could have measured the intensity as a function of Waverly and I've looked it up but try to find a can I don't know I'm not even sure that they did do it which guessing Barrett but this is the formula from classical physics and of course experimentally the formula was quite different it turned over and went back down to 0 so that the total energy contained the boxes finite this fact for video of section of the energy the boxes infinite because of this formula was called the ultraviolet catastrophe in order that it can also like that it was necessary that this formula have another constant this was only formula that you could make that only involved the constant state necessary to have a constant constant was of course plant constant plants constant reformulate you couldn't Liuka and Redding can't plant constant you could make up may formulas but let me give you the right 1 to precise formula for also some interesting things about it off he is equals misses the black formula is his black body formula of plant formula plant constant anybody nor the unit's appoints constant energy times time energy charge time of course were unit of energy while you reduce everything Tolley distance distance time and we're and movies squared and reuse over and square the and times when square Times could now and then to get HU multiply by times Woods and links with over over time but whatever there definite very units times new cubed divided by square Thailand's a crazy function and crazy function was 1 divided by E the plants constant frequency divided by Katie again that's money goes together with temperatures or is mightiest warrior I just a look at it as fund was the question of what does this formula have to do with this formula well with this formulas
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are the point is formulas others say lowenergy low frequency for lowfrequency the exponential is an exponential of a small quantity year frequency is very small frequency is close to 0 you can expand that this exponential and use the fact of exponential eagerly X small Exs Jews 1 applause X and subtract after 1 Italy X minus 1 is just X what's a nominated he uses worn over a each room provided by C but that means Katie endorse that's what they complicated function is for small known and multiplied by mayors who twice a new cubed overseas squared Norris 1st of all plant constant disappeared so in 1st approximation for small no 0 plant constant has canceled 1 power of the frequency cancels if I didn't make a mistake in writing these things down prices he KEB rice KEB squared overseas Querida figured out right theory of self that the point of course it is that this becomes important when you get a lot small move formula has written by the classical physicists of the 19th century Jane genes of people that was correct but as new start getting large what happened to the exponential here the exponential starts to give very big stores no becomes large in particular when H. newly Orlic 18 starts to become bigger than 1 this exponential starts to get large and factor becomes so large that the 1 isn't even important here in this whole factor just become exponentially small suburb is a crossover point is a crossover point where each overcame is about equal to 1 instead on this curve continuing up not for the parabola the rather suddenly turns over goes exponentially 0 Russ solving all trade pilot problem the ultraviolet catastrophe that this provides another interesting connection it says that for every temperature taking this formula see more confused time and temperature off this can be written on a motorway cement link with the threat of rate instead of new Oh let's remember that no 1 is equal to steal land room equals see Orlando we plug that in here and as says H although I am there is bigger than 1 that I get that right or that land is less than HC rickety so high frequencies or small wavelengths are strongly affected by quantum mechanics and the spectrum was driven very quickly 0 hour visit crossover point across the point is exactly at Lambeau but for peak woes H see that's crossover point and was in that that's where most of the power it is most of the power most of these energy density hardly see received the largest part of it is contained in a wavelengths Murphy are proportionally to mourn over the temperature that allows us to establish a connection if few between when the temperature can we sort of lose that connection between 1 and then temperature even when the system was not strict thermal equilibrium just to get our wrath and sometimes if we know that we have a bunch of our times whose average Waverly is some particular wavering only 1 how potent they are doing various things to assist them we can roughly speaking of replace it by the question Our hope call would be radiation at corresponding temperature our so we could look at the Photon that we see today and from the bulk of the photons it received numerous be overwhelming majority of them have a particular wavelength wavelength is about a millimeter and that allows us to associate it with a temperature at temperature is about 3 degrees from from back but that does not and it's not terribly we should not tempered that in itself as saying anything is in thermal equilibrium that is the rough correspondents turns out to be much better than that prefer reasonable come down that we're going but kill but nor on about plant was doing a combination of 2 things used to be a combination of curve fitting on a case so various things will not be a factor that the wavelength of the central wavelength year shift with temperature that was known I was cortical means displacement loss the displacement of the central peak as a function of temperature was a physicist of the 19th century and the plant them very well and he was able to read off the displacement law he was able to read off a constant H Our K was nothing no everybody knows Acadian temperature together by that time speed of light was not and so the displacement law which said that when the goes as 1 of the temperature was parameterized but no constant called so that these most important part of plant was just like defied this constant or identify the comes the source that is it that much deeper than exams he also we recognize that had something to do with harmonic oscillators he recognized that he had the wrong idea he didn't realize had to do with the radiation and being described by oscillators he thought they had to do With the walls of a box containing harmonic oscillators some sort oscillating system was before Adams were known for sure molecules were really understood that he had the idea the something vibrating in the walls of of the box and the walls of the boxer remaining had right ideas some wrong ideas it was Einstein of course were pulled derived we derived this formula in detail from a set of principles but when I that's so abroad today showcase sorrow from them all of us that OK how
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our Hey reorder of heroic but you want to do it at home Peter K. Botswana's energy Young hours or here your or get out we can do it for us they now but that will off a all it so the units of the RIA With 2 units of part energy per unit volume per unit frequency or assess what better be . Herrera wrong times energy strive fuel yet I say has units of energy provided by a frequency energy per unit frequencies per unit volume and that is energy what's what's units of energy what energy was translates mass times velocity squared IMF handling square over Times Square energy What about frequency frequency is 1 over over time so that would put tying upstairs and volume downstairs revealing Q but I was sure we get that may have provided by a Wang 1st time divided by late times time and now we have to go over with the right hand side probably made a mistake and substituting for the energy there since the energy ready appears on the side withstood still it anyway on that's that's a unit of intensity units on the right hand side Oregon energy misses the right hand side right hand side Garth energy which is again vast translate squared or prime squared frequencies squared is 1 over Times Square echoed the words were out of those from divided by sea square see squares links with overtime squared that's Times Square overlaid square Is that more good does it what's going on on how much a wee off by yes I looks I grew up by about a factor C but L squared cancel yacht were off by a factor of Cecil times trying is laid over time squared time although which means a C were up by a factor of Cesar was upstairs and downstairs what happened see Cuban embargo are my guess is that the definition of intensity has a extra factors of scenes that I know about because I remember this well I mean of remembered the formula wrong Mayor remembered the speed of light that along the speed of light of courses gal case so we will arrive formula CCube downstairs CQ downstairs looks like and now you can also ask about this exponential here is that dimensionless it should be dimensionless because it has to be compared with 1 that I'm sure is that 5 H. Newell that's an energy equals H. know everybody knows at farright energy no intake is also an energy so weren't good shape part about but apart from the speed of light cube which I move for its really worry that no effect on this relationship between frequencies a wavelength and temperatures are given a temperature this wavelength is called the thermal wavering with thermal wavering resources with that temperature novice something else helpful for simplifying about this formula but as take the formula and get rid of everything that irrelevant for my purposes right now To what agency are constant so let me think out here just say this is a proportionality Mr. proportionality is proportional no Q. transistor over here notice what in only here is a function of newly divided by temperature which in here that contains constants KNH but its dependence on the frequency is through the ratio of new 0 the temperature well let's let's divide despite temperatures Q and now multiplied at a temperature what I'm interested in is the shape of the curve the shape of the curve here and for the moment at the height of the curve I'm interested for the moment all only In this tape Of this particular curve and the shape of the curve as a function of new is not influenced by whether I do would multiply by cube multiplying by CCube simply changes the overall normalization height of the curve but it doesn't change its shape here is which determines its universal shape and notice that only a function of the ratio of Lulu temperature other was a shape the curve dropping the fact that TQ is just a function of the ratio of new temperature that means that if I change in temperature all the happens is the curve Reese scales the frequency Reese for example supposing I change of temperature by a factor of 2 what happened to this curve it's simply Reese gales by a factor of 2 along the new axis here I just stretch it by a factor of 2 tool if I want to change the temperature by a factor of 2 of I want to change the temperature by a factor of 100 I just stretch the curve by a factor of a hundred in terms of wavelengths I do the same thing remember that is proportional to 1 over the wavelength could right this way everyone did 1 over way if I change the temperature than as a function of wavelength I just squeeze the curve lots of versatile
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behavior to the shape of the blackbody spectrum entered if you know it and 1 temperature and you want to get another temperature you simply rescale rescale the frequency proportional to the the rescheduling of the temperature and that's important point is gonna come up there was a very important birth fact sensor simplifying track OK as I said neutral atoms and fact today's most of electrons and protons the universe of bound up in Adams and furthermore the vary by looter on many of them per unit volume may more photons in there are protons neutrons scattered and the scanners I don't really available for scattering bound up in these nuclei so universe today is not In thermal equilibrium the fact that there is at a temperature associated with the black body radiation is a kind of actually took overcome OK so when they when the temperature is too low in the box From this eat riyadh radiation did couples the right kind be couples from the charged particles with temperatures to the charged particles formed Adams b Adams a poor scatters and for the most part these photons of the box the radiation the box doesn't even see the charged particles it is goes right past be couples from that's the right now let's imagine starting with this box and for whatever reason let's suppose it starts and a height temperature but suppose supposedly starts alike temperature so high that electrons and protons in it are ionized not bound into Adams or least all of them abound Adams so it does have a temperature it does have a thermal equilibrium and the radiation spectrum looks like a black body radiation spectrum now let's start to expand the box as we expand the box just expanded physically as we expand the box it cools it cause because of various particles the work on the box and the work Her deplete the energy inside the box about pulls the temperature goes down of course and eventually it gets so cold in the box b electrons and protons combined Adams and they just aren't enough sources of scattering there aren't enough high energy photons there aren't the only thing they have to work lure ionized really II Adam so what happens they radiation these couples From Adams the Adams go their own way would also happens to them their temperature also go down the temperature of the radiation goes down but it doesn't really stay in thermal equilibrium the States and thermal equilibrium means the temperature of every part of the system is the same system falls out of thermal equilibrium at some point it falls out of thermal equilibrium but nevertheless as we continued to expand the shape of the blackbody spectrum here is so frozen in its frozen in for the simple reason that when you expand the size of the box every single photon just has it's wavelength stretched by the same factor every photon stretched by the same factor as we saw stretching the wavelengths by a factor of 2 for example in this formula in this formula here is equivalent to just changing the temperature by a factor of 2 Class a box expands every wavelength doubled worked very it in mimics In mimics the effect of just lowering the temperature by a factor of 2 but only for the radiation what happens to the other particles only do whatever they do but they don't couple over much of the radiation so in general happened is he is the molecules was Adams and there will have a different temperature in the radiation they walk the thermal equilibrium because amount of fish scatters but the radiation will have exactly the same form the blackbody spectrum will not change except in so far as it Reese gales according to the change in volume of a change in leadership dimension of the box leave the mention the box doubles the effect of temperature goes down by a factor of 2 quadrupoles the effect of temperature rose them by a factor of 4 and so forth that's why they were universes bottle cold for it to be in thermal equilibrium radiation with matter nevertheless the spectrum of radiation the universe has the black body former again I emphasize it's not because the radiation is in equilibrium with anything it's just because it had the shape frozen even some very early time and maintain that shit now how we note that it had that shape at a very early time we know because we measure the shape of the blackbody spectrum of measure the shape of the photon spectrum nearest with this of course lots of different kinds of folk answers gamma rays in the universe when Mary light Starlight nor kind of stuff but they although Wyoming majority of photons are in the wavelength range of about everything else it is just more or less incidental carries very little energy and this fully accounted for by mechanisms that we understand dominant form of radiation but analysts say that both by energy and by counting number of photons the dominant form by a long shot is the black body microwave cosmic background radiation that was discovered 1960 our batteries and has studied the death and of course it does have the shape of a blackbody spectrum of very high precision Vieira borrowers by now on very very tiny and nurture exactly how big they are source more a deviation From a black body a much much smaller than the Arab properly small Mira bars or because we have many many different frequencies we study it at the end of statistically be curve fits the blackbody spectrum of very high precision sold what we see today is a uterus filled with radiation that appears for all practical purposes to be the remnant of a thermal distribution that must had become so wise at a much higher temperatures where the electrons and protons where I am I at a cost a best guess as to what they history thermal history of the uterus waters Bergoo what's expand bomber but what can we
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say all our 1st or other facts factory were we know that for a while but holding for them some what's the use the faces a photon market price that is a a loaded question our assumptions the has no signs of all but does have a quantum mechanical spread units in the course probability distribution arm I I must say that 2 prizes size roughly equal to it puts wavelength the inverse temperature I think that's that's a over photons of a floating around not only have a wave about his big but the wave packets that described them also roughly about that big storm mm mm characteristics size scale of a part of the folk on a wave packets wavelengths about millimeter in today's the sitin yeah but the peak the peak years today the peak here today is about 1 millimeter there is no welders no universal welldefined notion of how big a particle several different several different things that you could call the size of the sort that attracted select OK that is another formula that Iowa right down which will come back through the did let's call this phenomenon where you go through all this situation where you start with ionized lower the temperature and come out the other side would lower temperature with With the Adam that's phenomenon of vote combination could call recombination combination where the electrons and protons combining Adams that's the point at which scattering stops that's Colby coupling and characterized by a certain temperature it's characterized by a temperature and is characterized by a wave through the connection between wavelengths temperatures OK what about the wavelength Of the radiation today the wavelength of the radiation today it's formula trivial formula the Waverly Of the radiation that we see today even rendered radiation from the blackbody spectrum of court today and now we need the average wavelength between me and way link at the top of the peak wavelength they don't buy it by the wavelength and coupling is bigger than sworn 1 was questioned the big number of small number and the number the ways that stretched think whether they get stretched by the gets stretched by the expansion of the universe so we can write this is just the ratio of the scale factor today provided by a the scale factor at the time that D coupling took place they find the coupling the place is not an absolutely rigorously sharply defined kind it happened over some period of time but the characteristic kind that happened over is relatively short and so we can talk about the ratio of the scale factor in other words this race is erased fueled by which the universe expanded all over that period of time between 2 coupling phenomenon and today so it's interesting as we know about it it is also equal since the wavelengths are inversely proportional to the characteristic temperature it's also equal to the ratio of the temperature a D coupling the the temperature Teddy she'd today landed today 0 0 ended coupling TV coupling or what he said was temperature but the temperature was wrong about the temperature even in outer space if you are out there floating around that would be most of the temperature you actually feel would probably have a lot more to do with it temperature of these molecules and atoms they're not we're talking about the temperature all right the microwave radiation microwave background radiation eyes and this is a race out the temperature today that the temperature of this it is about 3 degrees 3 degrees at the graph 3 degrees Kelvin but the temperature today is about 3 degrees and interesting question or what can we say about temperature at be coupling always a temperature at which hydrogen recombined Orbadiah's he went in the other direction what will be the temperature at which hydrogen would love with ionized 1 simple answer to it when the temperature it is not that the photons have enough energy I ICM that's when the photon would ignore the energy of ionization unanimous that dying of 13 electron volts if the photons of the characteristic photons and energy of 15 electron volts then they would have plenty of energy keep the hell out of a hydrogen atoms and an organizer that's a temperature a but Street where does a much bigger temperature than the Bibby coupling temperature property wire anemometer OK but that is what a simple theory of the temperature coupling it's the temperature at which they average photon has an energy comparable the 13 . 4 it electron volts Peru organize a matter OK but is another element of the other element it that it is all a lot of photons out there the number of the ratio of the number of fulltime number protons is very large and that the number of photons the number Proton cars or the number of Adams while the number of electrons of the same thing but the number of of electrons the ratio is about entity a now we're that number comes from how it's so many photons get this is something we try to talk about how did it get to be this is an observable fact this is a fact that we know by looking at the matter in the universe we know honey protons a Romney electrons Iraq measure normally photons are often blackbody spectrum and we know that the ratio of the number 4 times the number of electrons is about and 3 outlets posed that the temperature was just called to take temperature T what is the probability that a photon have given energy the answer is at
1:05:55
a temperature T a probability for fulltime staff different energies is over form e doubleAminus correctly the energy of the photon scholar epsilon for the energy of the photon energy photons divided by Katie is a standard formula as the Boltzmann distribution to a minus energy over overcame This is the probability that the photon have an energy Exel fund but a forward soon I can as the question what the probability that a photon have the ionization energy the ionization energy being 13 . 5 0 electron volts let's just substitute that in Epsilon ionization epsilon since energy epsilon ionization is just good old 13 . 5 0 electron volts that's the probability the given photon haven't energy which is big enough to ionized hydrogen atoms if epsilon is very much smaller indicates he this is a small small number exponentially small on the other hand there are a lot of folk so instead of asking the question was the probability that given photo Harris hour an energy big enough time we could ask how many photons aren't they can organize via the Internet we have multiplied this no budget per annum Hyundai photons are they they can do the job and the answer is this number kind to so in other words were actually operating in the details of the distribution here where the multiply this by tenderly if this combination of numbers is order 1 is roughly 1 or bigger then there are simply enough photons ionized electron so it will be 1 photon if this is what 1 that says they will be roughly 1 photon per Adam with juice ionized I tend to be a is approximately 20 for some like that at work at at young but don't forget spectrum falls off quickly so it's mostly ought to be pretty much in the vicinity of that energy but guessed that energy or energy about full pleasure With that these features way back when we were not know nor as far as foreigners the ratio of these numbers go back was frozen in was no no mechanism within this box for changing either the number of photons or the number of electrons or the number per car at least not until the temperatures are very very much higher than we're talking about these uh history back 2 d coupling is a history of of pretty much construed number of particles and the number of photons considered number of electrons considered number of protons and tool not the calculate that to requires some calculation but that's that that's a bomb lined that the number of particles of any given species really didn't change very much OK Back to be coupling and probably well back before that fight so we have each of the 20 times 8 of them minors ionization energy of a cake he should be wanted and that we can write that then that they ionization ionization court Katie should be on bigger than or equal tool about what 20 Porter are another words we can write this turned over over it says that case TV is about 1 in 20 years Of the ionization energy lower the adjust spell out what this means in these arrests only photons around that you don't actually have beat the system up to the ionization temperature before this is significant population of photons that can ionize gas at a temperature we want 20th the ionization temperature there are enough photons around because of a large population of booked exist and the AD after there are enough high energy
1:11:21
photons high energy photons now means above 13 . 5 electron volts there are enough of them around the make sure that a significant population of the atoms are ionized that happens when the temperature of the characteristic temperatures only 1 point RVR organizations of Charlie 3 but what's that the root of all of us have resources it and that Will shit Nova Irving these population of 4 cards very very photons it came out of stars they learn even around at that time so we don't care about them at all and that even if we did the population of them tiny tiny fraction of the year population overall for not only capping the photons that are in the microwave background the remnants on the relics of that early thermal equilibrium Bozo ones accounted for her concerns OK so we know now the so a couple illegal but problems Brooks that combined but said at lot of 60 Mark gets says why that was lot of reached what time was alarmed the process is happening slowly enough it will stay in thermal equilibrium and stays in thermal equilibrium in the curve will be the right occur if the expansion takes place a little faster and there will be a kind of bomb at a 13 . 5 electron also happens slowly on the balance will maintain itself and the population in the population will conform to the video there equilibrium sold technically if the expansion slow enough that the processes 80 abatic do we mean thermal equilibrium role times after field until the point where this simply aren't enough for were charged particles to keep equilibrium but what the OK that temperatures above 5 thousand 4 thousand degrees 1 20th could plug in the ionization energy corresponds to research a wavelength away right some angstrom or whatever it is plugged in energy out and the temperature is the temperature at which the ionization happens over recombination happens as about 20 of because of the large population that brings it down to about 4 thousand degrees 4 thousand degrees is much lower than the ionization temperature by work toward the magnitude now left 20 5th you had won him over 1 quarter of the whatever set right turnout was but I want to if the case or for me were William from Sudan young Over alpha Alpha was awful 0 OK did she was almost the best Is better they could be effective 40 diamond this is this is very rough this very rough is now our yard detailed calculation has to be done their detailed calculations detailed calculation have been done I haven't done them love but this is the basic physics the important thing is that it's a good deal lower than the ionization temperature by about a factor 20 may be a factor 40 our kids are right cell recombination happens I'll be coupling happens at a temperature of 4 thousand degrees the temperature of the current radiation is 3 degrees 4 thousand degrees of 3 degrees it is about a thousand 2 thousand 200 or some 1300 that OK so that tells us that the temperature would be coupling provided by the temperature
1:16:51
today putting everything together that we know it is about a factor of but that's also the ratio of the scale factor and the temperatures scales inversely with scare factor and so this is also equaled the scale factor today divided by the scale factor had Bacup like that 3rd let's have an amazing piece of information and know that the universe expanded by a factor of a thousand from the time that it was opaque opaque means that was ionized and therefore light could not readily travel through it but last 1 a landmark service because of warm where morgue going back with a time of course still a lot of landmarks story backward in time overlooked in thinking about the history of the universe gone backward after I haven't talked of a galaxy formation I haven't talked about black hole forming also 2 things and come back to those things we don't have enough information to think about where was it would led to galaxies that performance full but 3rd but jumping back in ignoring that we come to the 1st landmark which is b copper Mark 2nd landmark in going backwards a 2nd important things that happened in need gone backward is the universe went from being matter dominated being radiation dominated or to put correctly the universe work from radiation dominated being matters dominated the level of radiation dominated the matter dominated means BET equation state for radiation and the equation of state for matter led to 2 different formulas for the energy density and took kind of of energy use the energy density in the matter scaled like some constant political role divided by the scale factor Q that's just that the evolution of particles as universe expand whereas role of radiation went like some other role summer role 1 recalls will matter of Radiation This is the number provided by 84 off as we go forward in time radiation becomes less important well of course it's less important today it's much less important today because we go backward in time we come to a time when this becomes bigger than that today he and throw almost the entire observable period of the universe universe was matter dominated meaning that the matter contribution was much bigger the radiation that affected the way the universe
1:20:16
expanded expect them like Tito the twothirds instead of Tetovo onehalf or whatever but if we go back early enough where the scale factors small enough we come to the point where there's crossover between here and here let's see if we can estimate where cross over happened what Peace Dale factors were where you have happened 1st let's see what we know about the the race here all day with sector race today of Rice's formula or refuse to make things here but said the race today Of the energy density in radiation for the energy density of matter they yesterday's studied do it well 1st of all you know From the blackbody spectrum you know how much energy density is present in the form of fourpart basically you could use the following facts that for every for every Proton offer every hydrogen atoms this tend to be a fulltime tenderly peril proton 2nd of all we know energy of each photon energy of each photon is about can a minus for electron volts that's C 3 degrees that will correspond to 3 degrees and what about the energy of a proton as you approach it a billion electron volts 1 GV 1 billion electron volts sold there's a factor of 10 20 84 per cent of the mine error tantalum Reyes 8 times I guess 10 the 13th 10 to the 10th of a minus 8 is the ratio of the number of protons number of photons and then 10 to the 13th is a ratio of energy per photon poprock Proton the energy per photon anyway straight to work out and he answers about 10 to the 5 100 thousand the ratio of matter radiation today it about a 10th of a fight OK now how they behave in the past in the past as extrapolate backward roll matter scales with Wheat powers of the scale factor whereas role radiation scales with 4 factors of this scale factor that means the race she'll here in time scaled white 1 factor of the scale factor How far back Oh this is incorrect Wise is incorrect and made a mistake 11 of dark matter forgot about our daughter matter has about 10 times as much nets as the ordinary luminous matter protons so this actually becomes the 6th and 6th ratio a romantic tour radiation right now the way that they scale as you go backward in time differs by 1 factor of the scale factor nor that tells you what that tells you is that in the past at a time when the scale factor was a million times smaller than it is today but the energy density of matter and energy density in radiation were the same as go backward when the scale factor is a million times smaller than it is today and other words when the temperature is a million times larger than the 3 degrees but well well above that of the roughly a thousand times a thousand times the temperature of the D coupling period when the temperature was another factor of thousand larger universe another factor thousands more then it was a class over man University dominated by radiation the radiation energy became larger In the matter energy and as you go even further and further back universe becomes more and more and more radiation dominated at that tells us that if you go to the very very early universe that matters never meaning massive particles protons electrons but they basically protons nuclei were very unimportant to the energy balance and Friedman equation was basically just be equations coming from radiation Griselda's very early and we don't easily see directly back that time so in fact we don't easily see back to a time when the universe was radiation dominated several theory tells us it must radiation dominated with temperatures were forecast if acknowledging that he recounted a process at the end of the world all of this would be a now seen his fast yes there not honestly to talk starlight starlight is daytoday it wasn't there Israel and incidentally all of these things are happening long before they were stars in temperature was with a web that long before they were stars galaxies himself or his death the although the freeelectron OK images that got all see not you did a game he NCAA get and chief part so what's the name of the ADDS any change was
1:27:31
in working order carburet that's SSA still would become that ratio that's an important ratio from it hopefully tonight OK cell without landmarks D coupling I would say about how that add up house here is that they can remember at a depth dealer a magnet to assure a carrier member 5 what's it creating enter soil or a magnitude from a couple hundred thousand years about 5 for 1 as at work 13 and 13 . 1 Everton building at the time the time I until the day coupling is negligible except kind time and and cosmological scales and then that's right expanded from what you normally think of is the big bang expanded by a factor of thousand volume expanded by a factor over a thousand times a thousand years million 800 thousand a billion gap yes but that that's correct that's the lesson is that over the period that we usually associated with after the Big Bang universe that depends on what did the find to be the big bang define the Big Bang beaded coupling era when universe became transparent expanded by a factor of a thousand now before that presumably expanded by a much bigger factor or fact we go back if we go back to the point where this crossover took place between radiation and matter that's a factor million when your back before that you go back earlier than that the next important landmark the next 1 likened think of is aware market where the temperature was however not harm To create positron or if it were waiting for the a that not what we are related to show a 0 0 was a memo yard then I have a warning letters before space is pretty close to being flat when space flat only radios of aides have meaning you take a flat plain in U.S. what the radius of curvature of it it doesn't mean anything radius of curvature infinite but if the plane stretches by a factor of tools so that the grid that's embedded in the plane stretches by a factor of 2 that's welldefined so to the extent that the uterus he is and what is close to being slapped a dozen willingness to the radius of every race yields of aII that is an expansion of so bad at the twoday dash books whose were we have had my eye today but I think that incorrectly and look at depends on whether Keyes plus 1 minus 1 0 0 if Keyes plus 1 that means a close inbounded universe has some meaning must still be only thing we know is that it is race CEOs of 80 we don't know work the other prime ordeals size of the universe was well 1st form if it was a sphere if it is negatively current and started out infinite star ours is infinite hyperbolic measure drawing so yes where were operating now at the level of what the observational cosmology say what they can say is about ratios good let's keep going back in time truck a patient guests are a good bit of observed draw pictures normal now but that that is correct that that's not necessarily with any observations and it's well are observations doing today so looked at work but the discussed right sold last time I drew a picture of board time vs. based plan goes upward space because how example let's imagine us sitting at the origin he and here we are is now later later later and fact Piers today the flying on this surface represents today and we look backward we look backward long white ways in which you various things now U.S. me repeat your question in the yeah that's where are a of the current correct sold in looking back a different time periods we see different distances Wickham plot that by saying we sit at the center of a out only see a thousand years ago we see things of cows light years away Michel a million years ago RIR ever even further out we see things as they were a million years ago we further and further out and eventually we see back looking out received back at which this recombination took place right that's actually looking at some time but from our perspective it's shells corresponding to different times that we see light coming in from different places and that is the subject of astronomy of course but before I'd be coupling took place the universe was
1:34:43
ionized like does not that the whole point of whites scatters a great deal from ionized material fact polite simply didn't make its way very readily through the ionized material before that was there before Bacup that basically means roughly speaking that it was all pick the uterus was optically opaque before pickup so that means we work out With a distance out here that distance Mazzola looking at looking at the microwave background basically telescopes looking at Microrim background effectively looking back there and beyond that I can't see because of now you might have a chance I love seeing other kinds of things coming through that are less affected by whatever it is creating new opacity for example neutrinos neutrinos competitor want more stuff lowenergy neutrinos compares to a lot more stuff than the photons and so principal you concede neutrinos from further our Gravitt times even more subtle so what you could distances to which you concede in principle may not be constrained to the same degree as the things that you could see by optical of optical like me I mean the general sense radiation electromagnetic radiation and electromagnetic radiation the earliest that we concede is coupling period anything else beyond that is is circumstantial evidence to court but some of it we understand very well OK let's let's keep going back in time going out past year well somewheres out here it was v transition from radiation dominated 2 0 radiation dominated side matter dominated here radiation dominated here a matter dominated here here's D coupling coupling and galaxies form some mourners in here here we are today so that that's picture of universal much but more things could be traced back we understand the laws of physics well enough devotee at higher temperatures its initial going higher and higher temperatures scale factors getting ahead despite the fact that it looks like things a getting bigger as we go out of the scale factor itself was getting smaller which means it temperatures increasing something no happens when the temperature gets to be about came the 10th 10th of the tell them that correspond because Bonds drew it a T E a already Of city of about 10 of the 14 0 at that point with the universe was painted the 14 times smaller scale factor was 10 of 14 times smaller than the temperatures will be 10 of the 14 times larger and the characteristic fulltime wavelength of the characteristic photon energy would be about a million electron volts at this point the characteristic energy before Khan is 1 in called epsilon earlier the other juror photon here is about 1 and 1 million electron volts know that happens to be about twice the massive electron BMC square of electron on sorry it's about 2 . 5 they don't correspond to the mess electric cars are mess electron once the temperature gets up La high temperature there are lots of photons around was energy is high enough that yeah they collide when they collide 2 photons they have enough energy that when they collided that they can make a transition to an electron minus and a positively charged electron or positron another words pair production becomes possible that whether it doesn't doesn't happen is a matter of quantum electrodynamics computation but it could not happen when the energies will much lower than the energy of the massive electronic so want to get up above this threshold here the photons have enough energy that they can make electronpositron pairs and they do and they do climb electrodynamics says the 4 kinds of such energy when they collide have a significant probability of creating electronpositron pairs it's also true that electronpositron Paris will collide together and make pairs of photons what happens it is a lecture positrons and folkart comment the thermal equilibrium the electrons and positrons the number of electrons and positrons is no longer a determined by the memory of the future the memory of a future meeting today go backward in time we come to a point where no particles can legitimately be created by simply the energy of collusion of photons and the equilibrium of the number of such show of electrons and positrons is determined not by history but just by the temperature and the track that will equilibrium at that temperatures when you're thermal equilibrium of that temperature the number of electrons is he equal the number of positrons but quite moment but closed number electrons equal to the number positrons is about equal to the number of another where did so consisting of electronic if the war what what happens if the number of electrons and positrons gets too low well the replenished by collision was replaced by collisions and the collisions will tend to simply a resupply them what happens if the number of electrons and positrons ghetto high they will collide and make times so the balance in the balance it is not determined by anything except the temperature and above that temperature 3 species of electrons positrons and photons are all about equally a bond that is set at the process yesterday's like to brokers from North exactly electrical neutral they agreed the that ideology after the top part of course which ones on there which were forward about these are the additional warnings right and remember that this number is about tend to be 8 times larger than a year to year number of electrons today yacht the implication of that something like this the number of electrons minus the number of positrons Betsy excess electrons
1:43:30
positrons that doesn't change that doesn't change the excess of electrons or positrons doesn't change as the universe Coles What does change is a solemn of electron from public trials were collision takes place agreed some electron repository so the electrons plus positrons increased the electrons mind positrons of yours excess of electrons or positrons does not change the number of electrons my the number of positrons basically the number of electrons where number of electrons today is it was originally the number of electrons minus the number of positrons have you divide that by the number of electrons plus the number of positrons while the number of electrons plus the number of positrons is basically of the same order of magnitude as the number of photons but the number of electrons today he radioed the number of photons is 10 to the minus 8 so this number is believed at the time when the universe was kind enough to create lots of electrons and positrons this number it is believed to have been about 10 miners in another words if we forget about today we just as was a lifer like the very very early times when electrons and positrons were as abundant as folk and basically every it can be a electronpositron pairs who was 1 excess electron now that's an extremely odd fact the 2 extremely hard fact ended at Cannes upside down the old question of why there are so many photons the question is lot why there are so many photons as it is why there are so few white excess electrons minus what is different is so much smaller than the total number of electron and positrons question is not how the number of photons get to be large its why is the excess of mine might discharges or plus charges so terribly kind but the question can even be turned around again in the body SK what is it that led me difference between the number of electrons and number of if the universe really started neutral in a moment oppose war no probe would start with the world would know From our no protons there's lots of photons lots of electrons and lot of positron end if you believe in symmetry in particular symmetry between particles and that particles you might guess that the way the world started was with equal number of unequal abundance of electrons and positrons and electrons and positrons to begin with it would very quickly the photons would collide with each other make electrons and positrons with equal numbers so natural explanation naturally expect pensions based on symmetry would be that the number of electrons in number positrons were equal plenty of that this would be 0 that is a question around again given that the number of electrons and positrons are not equal which is on itself the question then becomes why is so small but on the other hand you could say well Pinto the miners say is a lot bigger than 0 so why is it so big wife is so big rises so small was a theory which tells us why why there's an electron positron balance added fully address that what go back you go you address that next time that's the theory of particle in that particle excess axis of particles over and particles let's just go a little bit further back another factor of a 100 to 200 of 300 temperature and something else begins to happen we go back another factor of what certainly by a factor of was certainly by a factor of thousands then the probably would be a lesson that then the photon collisions could make work Olympic works by the time it's a thousand times over Our harder collisions could make protons and pepper prices so if we go back another factor of a thousand universe should be filled with protons and end that broke again in equal abundance the trouble is it still hot for protons and that protons to exist they simply the same way that hydrogen dissociated electrons and protons these protons and neutrons proton secular Will dissociated the quarks so above what would be a lost track of the temperature by about a factor of 10 to the 2 will attend the and the world Is it not soup of electrons and positrons photons quarks and backcourt missing anything no matter how far matter which we don't know exactly what who ones all sorts of things in the population gets more more complicated but this will Turkey how that that that is not important to be earlier it's not that important nearly universal that's not part of the story of the stage on but what is true is that there are some relax some relics offered by France 1 of the things which didn't change since the very earliest time to end its expected or thought that be excess I'm not day and that matters particulary electrons positrons goes way way back CD with the number of quark stand back works number of quirks more quirks today the Niantic works as Mr. protons and Olympic protons among many in times out there and so the others in excess of quirks de works is in excess of electrons over positrons and the question is what is the origin of that why so small was theory that account was what's at 1st tentative goes although they are a factor of 3 because 3 quarks to a proton but Young the excesses of Barry on matters that barrier on which means quirks that works is the same as the excess of electron apart from that keep electrical neutrality young and a that's about the same number roughly the same number end dumb know we can attest what In our experience with the physics would account could could account for about balance we have a serial that's not a detailed theory but that number 10 to the minus it has never been calculated as a hard numbers but charm there is a rough theory of it we more or stand what's more got letters were are not yet but it was not easy for before the vote is worth a try athlete experts we back
1:52:17
much now yet but let let's just let's just let's start with just think about from moment starting with this condition where there's lots of electrons and positrons lots of photons it makes his hot soup it's almost completely balanced between electrons and positrons with tiny accepts and that followed with forward in time as we follow the forward in time and thought to cool down electrons and positrons were annihilated the photons but typically the photons will not that will not have enough energy arm to were collide and make electrons and positrons again so as you Kulik down annihilation becomes the dominant thing that happens annihilation of electrons and positrons and electrons and positrons just annihilate just disappeared and turned defunct the photons scatter when they scattered formalized and their temperature calms below the temperature needed to make electrons and positrons and so if the number of electrons and positrons with equal what would simply happened essentially all electrons and positrons will annihilate them they would be a none left almost none of the what we see is the leftover be costs it it wasn't exactly what we see is the imbalance the Fars weakened tail electrons dominate of positrons everywhere and the university matters if we would just a local local pocket where there's more electrons and positrons a statistical fluctuations our no matter how far out we look what we see appears to be due to to electron and the positrons we see cosmic rays coming in cosmic rays appear to be made the cosmic rays the highest energy ones Our Cosmic Origins very far away nobody has ever seen In a nucleus come in in cosmic rays is there are fuel in Bypro times a comment but that's easy to explain a fine energy particle comes in hits the atmosphere will make that broke but the chances of making an entire nucleus calls helium nucleus that's extremely small the other hand if they were galaxies out there that Orient that galaxies that we should see coming from them in tight nuclei which would be of the same kind of just the opposite charge of the nuclei that we see coming from ordinary matter galaxies so the complete absence and nuclei in cosmic rays are pretty strong indications that everywhere throughout the universe this signed difference hero of this excess electrons or positrons is and of the same order of magnitude in fact is of the same order ah summer summer door explained E. also minute and yes but at this time the protons are still the same protons they are proton pair creation has not happened yet so at this time indeed this is this difference here is the same as the Member proprietors Brooks at this kind of protons was pretty much of proton bill and knocking around the temperature was high enough to keep them around a lot but I wasn't high enough to destroy and it wasn't high enough to create rule proton impact for prime pairs wasn't period when the protons we're just plain old protons and it was a trainee population of them compared to the photon stand minus and the proton number was about the same as the difference between electrons your how she letters but the a 4th variety says that is that all of us she said High Road I think that over I think it was barred LUM be rebound much too large to be a local statistical fluctuations local statistical fluctuations overall volume of Alexei and and white music you all of which have the same kind of imbalance saying order magnitude such a random statistical fluctuations of our matter away and that would be violently on likely so the fact that these 10 million light years of 20 billion light years so that we see is all of the same certainly needs an explanation exploration cannot be a random statistical fluctuations but you're pork is correct we simply can't see out beyond a certain distance of summer kind of reason why there might be a transition for another region where everything is backward respectful electrons America positrons we wouldn't know it easily so the answer is we don't have much information about what's out there beyond 15 20 billion years 1st please at 2 I agree that called yeah we see orders on all actually getting ready for that assessed yes yes for you as that I felt like a gap of 4 that's what gets beat it the case that this is a proper and with the car would be copper Norbert here His today we see back that does us absolutely nothing about whether there are galaxies up here are not today was the doors right now we could not a them because can't get light from them from this great distance we can get life altogether but certainly we can't get light from comparable time so we we knew we'd bestows nothing about were there galaxies out beyond what we do know is up by looking out as far as we can work we see galaxies homogeneously distributed no reason to think that a sharp edge of and the galaxy population uniform job most people would bet that that uniformity extends our beyond this Roberto 3 rule from forward Corkery for 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Computeranimation
Metadaten
Formale Metadaten
Titel  Cosmology  Lecture 7 
Serientitel  Lecture Collection  Cosmology 
Teil  7 
Anzahl der Teile  9 
Autor 
Susskind, Leonard

Lizenz 
CCNamensnennung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/15059 
Herausgeber  Stanford University 
Erscheinungsjahr  2013 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Physik 
Abstract  (February 25, 2013) Leonard Susskind examines one of the fundamental questions in cosmology: why are there more protons than antiprotons in the universe today? The answer lies in theory of baryogenesis in the very early universe. 