Olbers' Paradox - A Level Physics

hello today we're continuing in our a level physics revision series looking at the subject of Olbers paradox the paradox is named after Heinrich Wilhelm Olbers who lived from 1758 to 1840 and essentially he asked the question why is the sky dark at night now you may say that the answer is obvious here is the earth spinning on its axis and here am i standing on the surface of the earth and here is the sun shining and during the day the sun's light is refracted and that's what makes the sky blue and bright but at nighttime the earth has spun around on its axis and I am now here on the earth the Sun of course is still here shining but I can't see it because I am essentially in the shadow caused by the earth and all I can see are the stars in the sky and possibly the moon there is very little light coming from these stars and the moon so consequently there's very little in the way of refraction and so the rest of the sky is dark that must be the obvious answer but Olbers says no that's not obvious at all because he lived in an age where he was told that the universe was fixed and infinite that is to say it had always been there from time immemorial it had never been created it had always just existed and that there was no end to it it was infinite so all the said well if that is true then when I stand on the surface of the earth at nighttime so there's no Sun in the sky every direction that I look must eventually end in a star it might be a near star or it might be a distant star but the point is if there are an infinite number of stars then everywhere you look eventually you will reach a star and that means that every single line of sight that you look if there are an infinite number of stars then eventually you're going to see a star and Alba says on that basis the entire sky should be covered in stars because eventually every single line of sight that you tend to look at will end in a star so the whole of the sky should be completely covered with stars so the whole of the sky should be white at night now we might reply to that to say our but Olbers you've forgotten a very important point and that is that the intensity of the light from a star is proportional to one over R squared in other words the distance from me to the star is the distance are the intensity falls off as the square of the distance so the further away the star is the less intense it will be so maybe if you're looking at stars that are a long long long way away they are so faint that they will barely be visible and therefore you can't really see them but over says no no no that can't be right either let's take this is the earth here let's assume that the universe is homogeneous and isotropic that is the same everywhere and that means that we can say that there are n galaxies per unit volume whatever volume you want to take wherever you go there are the same number of galaxies per particular volume in the universe so let's construct a shell around the earth and we'll have a shell this is the shell it's bit like an orange peel around an orange the shell is a distance R from the earth and its thickness is Delta R and the point is that Delta R is very much smaller then our now the volume of that shell just the shell is equal to the surface area of the shell times its thickness it's not strictly absolutely true but it's near enough for what we need so the volume of that shell is equal to V is volume here the surface area of a sphere well the surface area of a sphere is 4 PI R squared multiplied by the thickness that's the surface area to get the volume you multiply by the thickness which is Delta R so that's the volume just of the shell just of the orange-peel as it were now if there are n galaxies per unit volume then in this volume there will be the number of galaxies will be let's pull it galaxies the number of galaxies will equal the volume 4 PI R squared Delta R times the number of galaxies per unit volume so that's the total number of galaxies that you will find in this shell around the earth now what is the intensity of all of those galaxies intensity of all the galaxies in this shell will be proportional to the number of galaxies which is 4 PI R squared Delta R n divided by R squared because we've already said that the intensity falls off as one over R squared so the intensity of all the galaxies in this shell will be proportional to 4 PI R squared Delta R which is the volume of the shell times n which is the number of galaxies per unit volume divided by R squared and you'll notice that the R Squared's cancel so the intensity is 4 pi Delta R n that's the intensity of light coming from a shell but not look there is no R term in this as a delta R which is the thickness of the shell but what this says is that the intensity of radiation from the galaxy's inner shell is independent of the distance of that shell from the earth why is this well the reason is that if you've got a shell that's close to the earth then there will be fewer total galaxies in that shell because it will have a smaller volume but it's close to the earth and therefore the intensity will be large whereas if you go a long way away from the earth then there's going to be a much larger volume of the shell so there are going to be more galaxies but they're further away and the two just compensate for one another so every shell generates the same amount of intensity this shell here of thickness Delta R will generate the same intensity of radiation as this shell here because of this formula here now says olders I'm told that there's an infinite universe so there's an infinite number of shells reaching right out to infinity and if there's an infinite number of shells then what we have to do is to add the intensity of the radiation from this shell to the intensity of radiation from the next shell and the next shell and the next shell and the next shell and the next shell and the next shell and the next shell in the next shell right the way out and that means that the total intensity of all the radiation coming from all the galaxies is infinite and if the total intensity reaching the earth from all the shells is infinite then not only should the sky be white at night but the earth wouldn't exist because it would of course be completely frazzled by the intensity of the radiation that was hitting it it would just vaporize now we can do an experiment we simply need to go outside at night and look up at the sky and what do we see it isn't white it's substantially dark and there are some stars sometimes the moon is out but if it's not then there are just some stars generally speaking the naked I can see about 3,000 stars why is that the case when Albers has shown that the sky should be white at night well remember Olbers lived from 1758 to 1840 long before anybody had thought about the Big Bang long before the modern thinking on cosmology had taken place indeed Albers was one of the people who started the thinking that has led to the Big Bang Theory so the conclusions that you can draw from oldest paradox are either firstly that the universe is not infinite if the universe is not infinite then you can argue that it would be possible for although you might look up and see a star in that direction it may be the case that there is a line of sight that goes up and never sees a star and that might be the explanation why you see some stars but not others because it's not an infinite universe and therefore there will be some lines of sight that never end on a star the trouble with that argument is that although the universe might not be infinite it's still going to be pretty big and so most lines of sight will end on a star even if not all do and consequently you would still expect the sky to be a lot brighter than it is it might not be completely white but it ought to be substantially white on the basis of that argument because the universe is sufficiently big that quite a lot of the lines of sight will end in a star even if not all do the second response you can make two oldest paradoxes to say well maybe the universe isn't infinitely old maybe the reason that the skies of white at night is that the light which of course is traveling at the speed of light from stars hasn't reached us yet so for example this star here the light has had time to reach us and we see that star in the sky but maybe this star or this galaxy in the universe the light is on its way from the beginning of the universe the light which is traveling at a finite speed although it's very fast three times ten to the eighth meters per second the light hasn't yet got to us so when we look up in this direction when we look in this line-of-sight we don't see that star because the light hasn't got to us yet maybe that's the explanation that we only see the Stars given the amount of time that the light has had to get to us so maybe a much smaller sphere of stars and anything outside that sphere the light hasn't got to us yet maybe that's the explanation because the universe is not infinitely old it only had a starting point and that starting point means that the light has only had a finite amount of time to travel to reach us and maybe it just hasn't got there yet well once again that's not a complete answer because the implication of that at its face value would simply be that once upon a time there was nothing and then suddenly a universe appeared where there was a star and here's the earth and the light started traveling towards the Earth but how does the universe suddenly form out of nothing how does a big universe just suddenly appear not an immediate answer to that question what is now accepted and Olbers paradox pointed the way to this conclusion is that the universe is not infinite and unchanging as was thought to be the case and indeed thought to be the case right up to the time of Einstein at the beginning of the 20th century but rather that it started 13.7 billion years ago with a Big Bang and has been expanding ever since now how does that help us to explain all those paradox here we have a universe that is constantly expanding from the Big Bang well there are several things that follow from that firstly we know that light that comes from stars that are that are moving away from us is what's called redshifted that's called the Doppler effect and I deal with that in another one of my videos but the Doppler effect is something that you experience all the time when you see an ambulance go past as it goes past you and then starts traveling away from you the sound of the siren will go down in pitch it will go something like Dada Dada Dada Dada Dada Dada a much lower pitch as it goes past you and the reason for that is that as the ambulance moves away so the sound waves that are reaching you are stretched out they get a longer wavelength and a lower frequency and that lower frequency is the lower pitch and it's exactly the same with stars that are moving away from you the light which is traveling towards you will because of this expansion be stretched the wavelength of the light is longer the frequency is shorter and that means it's what's called red shifted it moves in the direction of the red end of the spectrum the red end has a longer wavelength and a shorter or smaller frequency and the further away the star is from us the faster it is traveling away from us that's known as Hubble's law and I've dealt with that in a separate video so you can get to a point where the speed of the star moving away from us stretches the light so much that it is now no longer in the visible part of the spectrum it's gone beyond the red into the infrared and of course your eyes can't see infrared so that's one reason why you might not be able to see stars in the sky the second reason is that at a certain point in the expansion of the universe and just to make this point the universe can expand at any rate it likes including greater than the speed of light some people think that nothing can go faster than the speed of light that is true with the one exception that universe expansion can travel at any speed including more than the speed of light so there may be a star that is traveling outwards at a relative speed to us of more than the speed of light because it is traveling with the expansion of the universe and consequently the light that it emits can never reach us so that's another reason why we won't see the star in the sky so it is now accepted that it is the expansion of the universe that means that the sky is not light at night so when you go out at night and you look up and you see a dark sky with a few scattered stars but predominantly a dark sky you are actually looking at evidence of the expanding universe now you might argue that if the universe is expanding there must have been a time in the past when it was much much smaller and therefore all these arguments about stretching the light or the stars being travelling with the universe at more than the speed of light didn't apply because the universe would have been very very very small and surely you would argue but at that point the sky would have been light at night and you'd be absolutely right in those days the whole universe would have been covered in light but where has that light gone it's must still be in the universe you can't get outside the universe all that light must still be there where is it and the answer is yes that light which made the sky as it were bright at night in the very early days of the universe is still roaming around the universe but as the universe has expanded so the wavelength of that light has been stretched and stretched and stretched to the point where now this light which once billions of years ago would have been visible and would have lit the sky if the earth had existed has now been stretched not just beyond the visible light range but beyond the infrared range and is now in the microwave range of the spectrum and that is called cosmic microwave background radiation and that is pretty much uniform across the sky wherever you look every single direction that you look from Earth there is cosmic microwave background radiation hitting us so in that sense the sky is light at night but not light in visible colors light in microwaves so actually there is radiation covering the entire sky every direction has cosmic microwave background radiation but it's now of course because it's frequency has gone down you may remember from another of my videos we said that the energy of radiation is equal to Planck's constant times its frequency the frequency of microwave radiation is very low consequently the energy is very low and the radiation which hits us now this cosmic microwave background radiation is about Sirmon so low such low energy that it has no material effect on us but it can be detected if you've got the right kind of detectors and that is the remnant of the visible light in the very early days of the universe when the entire universe would have been filled with light all of it is as it were a consequence of or can be developed from Olbers paradox simply standing outside at night and wondering why the sky is dark rather than light

Channel: DrPhysicsA

Views: 386,540

Rating: 4.8362422 out of 5

Keywords: Olbers, Paradox, sky, dark, night, big, bang, intensity, shell, infinite, static, expanding, universe, red, shift, CMBR

Id: yQz0VgMNGPQ

Length: 19min 48sec (1188 seconds)

Published: Thu Jun 14 2012