Einstein's Famous Blunder - Sixty Symbols

this is 2015 the century has gone since general relativity was first introduced and I thought it'd be worth just talking a little bit about how Einstein was really quite resistant to the idea that the universe is expanding and he worked very hard to stop it it ultimately failed and he ultimately accepted that it failed but it's quite interesting to see the effort he put in to actually make the universe static and then the consequence of that today and the term that he introduced to make the universe static looks like it it's around today and driving the acceleration of the universe which is a kind of it I really get any quieter and provide I don't you know around 1915 if you what was astronomy telling us well astronomy you'd look out in the night sky and you'd see night after night the Stars and you might see the Andromeda with your are kind of understandably to me it seems that Einstein thought the universe was static he also had reasons for wanting it to be static he believed the universe on large scales had to be homogeneous and isotropic it kind of it looked the same every in all directions and we were in no special place in the universe Albert Einstein wasn't a caveman like he did up at the stars and think there were little points of light he saw beyond skin deep so surely he didn't look up at the nice guy I think I has to always be the same but people didn't know what the universe looked like beyond our Milky Way why would you have the universe expanding if you don't see it if you don't see any evidence of it in fact his beautiful equations it must have been a nightmare for him when he began to look at them and other people quickly began to look at them in 1915 it must have been a nightmare for him when he discovered actually he can't have it static he'd written it down it just would not stay a static what do the equations do the left-hand side of the equations will relate the curvature of space and to the matter content of the universe and so you have you have this situation where the two are intrinsically connected so that if the matter evolves it will affect the curvature of the space-time in which it's evolving as the curvature of space-time evolves it actually determines the trajectory that the matter takes so let me draw two galaxies so here's two galaxies okay I'm going to give them a separation and to make life simple this is this should be a of T right so a is known as the scale factor and it tells me about the the rate at which the space-time is about is evolving right and it's this that Einstein didn't want to evolve because he didn't think that this there was any movement in the space-time itself he just thought that the the universe was nice and static so if you've got a of T then just let me let's just define a couple of terms for us if I call it a dot the rate of change of a let me call it a velocity type term right it's telling me about how this scale factor is changing the time that's how does distance change with time that's a velocity and if I introduce an a double dot then that's like the acceleration term okay that's telling me how the rate of change of the velocity what would a static universe mean a static universe would be one that where a is a constant a dot would equal a double dot which would equal zero there'd be no acceleration because if there was acceleration it would generate a velocity so why does this not work why did Einstein realize this in fact think the metric pointed out it wasn't going to work there are two major equations that you can write down from main Stein's a theory of relativity that apply to cosmology to really needs equation so I'll write down the the first the first of these which is useful is called the acceleration equation so it tells me how a double dot divided by a and it's given in terms of funnily enough Newton's constant so there's four pi gigi is Newton's constant over three and then it has these two contributions it's got a term which I'll call Rho and then it has another term which I'll call P and in fact C squared is the speed of light okay Rho is the density of matter the energy density of matter so any matter in the universe will contribute some energy density Rho so as long as the universe has got matter in there then Rho is nonzero P is the pressure of that and further for the a universe made up of particles like you and I that are not moving very rapidly if you just think about how particles you know pressure is the force per unit area these particles hardly do anything so the pressures effectively zero but the key thing is Rho is nonzero so if I have a universe with matter then it tells me that Rho is not equal to zero and that then immediately tells me because it means to let the right-hand side of here is nonzero so a double dot is not equal to zero and Einstein's had it the universe is going to evolve when I Stan was looking at this he knew the universe was mainly made up of matter you know you could look at the Stars we knew matter was dominating so it's the leading term here in fact radiation can only add to this you'll just make it even worse so it was clear that the the universe had this had this problem it seems as if it was going to evolve and so what Einstein did was he real he decided that there was another term where he knew there was another term which he he hadn't been adding to his equations but if he added them to his equations he could actually sort this issue out but it isn't this a bit like if I always want Brazil to win games of soccer and they lose three nil I just invented u-turn where Brazil always get an extra four goals right at the game as long as your new term was consistent with what your original rules were right that's the key thing he his this term is going to add this cosmological constant term is perfectly consistent with the underlying principles that he had which had that developed developed into general relativity he didn't just take a number on the you know known okay and let's put - April I know I think he just thought for reasons which I mean I don't know they presumed that it wasn't their religion when he was written originally thinking how it was zero for some reason in fact he probably have no right to think that he probably should be thinking all the time why don't I include it so he did include it actually it affects this equation but I'll do that in a second let me write down the second equation which is known as the Freedman equation and that tells me about the house of Allah evolves okay so this is called the Hubble parameter by the way that a dot over a so this is actually given by the following it's given by that energy density again with Newton's constant in there and then I can add in a new term which is this most this is my cosmological constant lambda these factors of three are just to make life simpler and then there is another term which is going to be important and this tells me about the curvature of my universe this is the a by the way this this scale factor okay this is known as the Friedman equation there are three terms this is my energy density the of them of the matter that I'm thinking about this is my cosmological constant term lambda is a constant and this term K represents the curvature of the special curvature of the universe because it turned out there are three possibilities that that are consistent with Einstein's original idea that the universe is homogeneous and isotropic one is if K is positive and that's known as a closed universe so the universe is finite in special extent it grows to a big to fixed size and then collapses again the second which is what it looks like the universe looks like is flat this is especially infinite universe if I was on a 2d plane it would just look like this and go on and on and on forever and the third is if K is negative and this is known as an open universe which you can think of it's it's it's a bit like a saddle and it's also infinite so we have these three types of universe all consistent and I'd just wrap them all up in this general K oh and by the way this term the K doesn't appear in the acceleration equation including the lambda term then the acceleration equation now becomes what it was before minus four PI G upon three into Rho plus m3p over C squared and then finally I ate this lambda term is there it appears in this acceleration now remember what I need what Albert wanted was he wanted a dot and a double dot to be zero so I just set the left hand side of this equation and this equation to be 0 so if I do it here remember I'm saying that P equals zero for because we're thinking of this is a universe dominated by matter so not in particular nonrelativistic matter like like you are now made of so if I set a double dot to be equal to zero then I have a simple equation the threes cancel and I have an equation for lambda it just tells me that lambda is equal to 4pi G times the energy density in the matter divided by C squared if H you tunes lambda sitting exactly matches the energy density then it will give a universe that doesn't accelerate what does it mean for the if you like the velocity the Friedman equation so I also need a dot to equal zero so I go back to my Friedman equation and I substitute in you can can you see that I can substitute in for the lambda term here replace the row with lambda and I get the following expression 2 over 3 lambda C squared from for the from Disick's from this term plus lambda C squared upon 3 from that minus KC squared over a squared equals 0 so I now have a solution that tells me that lambda minus K over s squared equals 0 and so that's telling me that a static universe requires K which is equal to lambda s squared to be positive because lambda is positive the energy density is positive so this must be positive so this is telling me so Einstein for Einsteins solution to work for him to stop the universe from expanding he had to make it a positively curved universe with a cosmological constant I think bread is going to stop me doing any more maths but I've got one more professor Copeland before we start at said can I do equations I'll just do two very simple one this is what we're on so so I won't go into three I won't go into the stability but here's that here's the neat thing we've got the universe which we've made it static he did this in 1917 right as far as I can tell it predated any of the cosmology related papers which demonstrated the universe was expanding the the papers of I think the sitter may have written one before that but Lemaitre and Friedman they all came later with their papers and yet they were coming in saying there there are all these other solutions which we're not going to go into with but you we saw it right at the beginning there if we if we don't have that cause module cousin and we don't have the curvature to balance it then the universe will evolve so there were all these evolving universe solutions out there and he just didn't like them he just said he initially he thought there was some mistakes made in some of the papers the Friedman solution he thought was wrong but then he realized it was right but he said basically he said it's a correct solution but I think it's just part of your you know it's one of these with wonderful solutions which this beautiful system of equations has but is irrelevant Lemaitre had a solution which Einstein said your solutions correct what your physics is rubbish effectively and so he just wouldn't buy it but you know at the same time as all of this was happening astronomers like slifer we're doing observations of distant nebulae and they were beginning to see evidence of the light from these distant nebulae being redshifted Einstein didn't accept this as part of an evidence that the universe must be doing something on these very large scales then of course in the 20s Hubble turned his attention to this and he started looking at distant galaxies and he realized the distant galaxies are moving apart the a of T that we're talking about here that these galaxies are moving apart on very large scales and he came up with this lor wishes that basically the velocity of that they were moving apart was proportion to their separation so the further away they were the faster they were moving after than looking at the night sky hmm what was Einstein basing this assumption on we famously always get told never to never assume anything for him the underlying criteria which he was using to sort of come up with that the thought that the universe is homogeneous and isotropic on those scales there's known as Marx principle which was a principle that sort of suggests that features on large scales determine what we see on small scales is one way of thinking about it and on small scales we weren't seeing anything evolving and so the features on large scales shouldn't be really evolving either I think that is kind of where this came from I'm not sure there's no value on the cosmological constants not like it's not like a pie or Hubble's calm it's not a value that's coming out of some fundamental theory which says yeah lambda is equal to PI over a or something but you can see from this equation here when you mock my equations but you know can now see that the lambda depends upon whatever the density of matter is in the universe so that's like if you like an observational fact you would measure that density that mean density and you would set that would be what you're learning that's another cosmological constant won't come out as eight yes maybe a number yeah and in some units so you've got this solution right now what you do in college when you when you have a solution is you ask one obvious question to ask about a solution is is it stable right in other words if I have a static solution here for a what happens if I just hit it you know is it with what just perturb it with what well in this case what you're perturbing is the density of the matter you're letting the density of matter vary ever so slightly so in a static universe of course it's a constant because it's not evolving but imagine I just let it vary ever so slightly with time so it's not it's a constant plus a little bit and then you can ask well what does that do to the evolution of this scale factor does it somehow move and yet then go back to its original position so the static universe returns that might be in the analog of a ball going at the bottom of a colander right if so it's stable points you think is at the bottom and then you put you perturb it slightly you push it up and then let it go and then of course what happens is it just oscillates slightly and goes to the bottom however on the other hand imagine that you had a pencil and you were careful enough that you could put the pencil sharp end up and then you you know that if I perturb that slightly just a little it will go it will fall flat that's an unstable situation and what really surprised me it was that it wasn't until 1930 when Eddington published a paper he said what happens if I perturb the matter density ever so slightly what was the consequence it has on this scale factor and he found that a small fluctuation in the matter caused the a of T to act not to simply oscillate around its fixed point and then come back which is a stable search it either grew exponentially fast or it decreased exponentially fast it either went off to infinity or shut down towards zero you've got the evidence coming from Hubble in 1920s from Slifer earlier that the universe is exceeds to be expanding Einstein didn't want to accept it you then have Eddington showing that Einsteins own solution is unstable and then Einstein came and gave a lecture here I don't think it was in German note there's no record of the lecture except we have that wonderful blackboard which he signed on the 30th of June 1930 and that would be still before Eddington have managed to color in and bash him into it saying actually your solutions unstable yeah I just think it's nice that within a few months of a weeks even have been being here he was actually beginning to accept the universe is expanding but it is strange that it's thirteen years after his original work if I could conjure up Einstein and bring him into the room now yes please what would wold you ask him what would you want to know or has science moved on so much that he would be left behind now he'd have to go and read a few books to catch up on what's being built or he'd have used to contribute if he'd be happy to go back and think about gr there's so much we've yet to really understand about general ativy T there's a mass of stuff that is yet to be uncovered as an Einstein would be the guy to ask I'm sure what he not doing at the time then yeah because he died or you know no it's a bit kind of a little bit sad in that after the night that's in this 1931 paper he wrote on with the sitter was his final paper in cosmology and I think soon after that he began to his attention turned to this idea of unifying the forces and he that's where he put cloud and most of his energies I mean it must have been also the fact that he was a major celebrity I mean truly major celebrity right it was all over the place sort of giving talks and being invited to places but his own research seemed to move into this area of unifying the forces and and that as it has with many people led him up dead ends and and so I think it's fair circle that there's not much of that work that has survived today people don't refer to much of that work he did some fantastic things in the 30s on quantum mechanics and that's but actually beginning to come back is that people think about things like quantum information but in terms of gr in terms of those this wonderful set of equations he kind of left them for a while and never came back to them and that's why I say if he comes back and we could persuade him to work on gr yeah it would be wonderful very privileged to see this and to realize that even famous scientists like Einstein couldn't really use the blackboard very clearly and so I might have had difficulty to follow the lecture

Channel: Sixty Symbols

Views: 481,672

Rating: 4.9439812 out of 5

Keywords: sixtysymbols, Albert Einstein (Academic), Physics (Field Of Study), General Relativity (Field Of Study), universe

Id: nJsFsjSWYx0

Length: 18min 47sec (1127 seconds)

Published: Thu Nov 19 2015

Reddit Comments

[u/TheSov]

Brady, stop getting on people's case for showing math there has never been a time where it wasn't fascinating, and most of us are probably subbed to numberphile as well!

[u/Viking_Lordbeast]

I'm not sure how easy it would be to do or explain, but I would love a video with someone explaining the process that Einstein went through to develope these equations. It doesn't have to in depth or anything. I'm just one of those people that's curious about it, but not smart enough to be able to go read about it and comprehend it.

[u/tomsk31]

Great video. Love Ed's explanations, and the equations. Title is a bit click-baity.

[u/Kotsoumpis]

Just one problem at 5:05 the arrow that indicates that the left part of the equation in not zero can confuse people that the denominator is zero. Which cannot be done. None the less a great video! Keep up!