we got everybody here who's coming I guess but I see somebody who isn't here how do you like that now there's an old philosophical question isn't it whether you can see somebody that isn't here I remember arguing in Princeton with the graduate students for hours and hours the philosophy students as to whether what you were talking about when you said there was no chicken in the icebox yeah this philosophy that's wise yeah I have nothing to do with philosophers urticae huh we thought that it was probable that there's still people who don't appreciate the difficulty of this this thing with the boxes and so we'd like to divide you into two groups those who are perfectly confident about it and don't want me to go over at 16 more times and those would like me to go over it well at least two more times so can we we're going to divide this system this thing up and we'd like to know how many want me to go over a couple more times till they really fully feel a difficulty all right we have two three customers something like that so what we'll do is that Ralph over there who is an expert on my assistant guru will take care of you in the meantime the guys who've been asking me very technical questions about perturbation theory calculations and other matters of this kind will have a chance to talk to me because we have such a difference in the backgrounds of people we're going to separate temporarily so the ones who are having trouble before will of coral catch up and see why it's in to us because that's the whole purpose of this is to understand that if you don't understand that we're not going to understand anything else I mean we don't there's no problems so that's essential thing after that it's very easy it's going to be easier it's just like climbing a mountain and from there now it's the kind of view you see the view and now you climb around down on the ground and have fun so that's what it is but we have to get you up to the mountain right so round for client help your client the top of the mountain meantime these guys you think they're there already will waste time by answering the technical things and complicate things so which the others will be addressing anyway all right so can we do it that way so he's over there all right how about that so those who are having you're not going to miss anything in other words because it's just going to be some yeah so we'll just take care of that and the other ones will be we'll talk about other things please then I'll come back when they were all back all on the mountain then we'll go back to the top of the mountain and show what the views are from there on okay so that present questions would perhaps be best if they're not directly a thoughts attached to this question of the 2/3 they will delay those until the friends come back from the mountain okay Oh Brownian motion that is course is fun it's an integer you mean what do you want me to do about it you know about it in terms of what you said yesterday uh reason came up to mind whereas you said well the atom doesn't have to actually we had yeah time aside because of different scale and I was thinking well where would randomness be in the cell I was thinking of living cells you mean in Libya Yeah right biological processes ie of diffusion right and we formulated the question of that by saying talk about Brownian motion yes there's a kind of randomness which is but that randomness is not involved in quantum mechanical randon is you're quite aware and it's due to the complexity of things that there's so much stuff in there all of atoms are bouncing and against each other and it in a kind of chaotic manner so that in for example a liquid like water the molecules are we can take a normal view of molecules as little balls or little shapes of different kinds and all the same kind actuator or water molecule and that there a pile together and jiggling all the time next to each other and this perpetual jiggling is a molecular motion Brownian motion is observable so it's possible to see this jiggling if you put a small particle very fine particle dirt as a matter of fact I did with toothpaste that's it it's rather nice with toothpaste if you haven't got a very powerful Mike good microscope it's easy to see if you put something like toothpaste or something that's a little powder in it then the very fine particles keep jiggling about all the time under the microscope perpetually in the case of the toothpaste they are flat the one that I happen to have were very good because there was some kind of flat little crystals and my microscope wasn't even big enough to see them but because they would turn and the light would come just right it would reflect and be these little flashes all over so it's kind of but it's easy with a good microscope and it's very much like I always hadn't seen this for years but there used to be sometimes a tremendous push balls that they had enormous ball great big thing and they put it on a few with people trying to push it to some direction the other team is trying to push it the other way and the whole ball moves and there's this crowd of people underneath all pushing one way or the other ball just jiggles and if you look at it from a distance you could imagine you was so far away you couldn't see the individual people but could still make out the little ball and then see this little ball jiggling from which you can infer that the people at jiggling so in the same way what you're looking at is a very large mass of atoms when you look at a particle that you can see because a particle you can see even in the microscope is a billion atoms or so it's a great big thing but it doesn't stay put because it's being bombarded all this time by the little atoms and therefore jiggles a little bit and that's called Brownian motion it was discovered by Robert Brown a biologist that when he looked through microscope he saw this jiggling motion maybe being a biologist you would think that he would decide that this motion that he saw must be a form of life it was a good biologist and made the necessary experiments and ultimately discovered that the motions to even existed in the water that was enclosed in a quartz crystal that you could get from the ground that been there for millions and millions of years and he looked in it was still jiggling inside there so he concluded that couldn't be life that that was a universal phenomenon of of nature and it is that we look very calm we look at things that they're permanent they're stationary but as a matter of fact of course they're made out of piles of atoms which are always jiggling our eyes can see that delicate jiggling but that is a way that you could make a random generator you could amplify such jiggling electrons and wires jiggle - everything's jiggling and that's yes that's right and so they make it electrical voltages fluctuating so if you have a good amplifier you get a Russian oil Shh all the time it's easy to measure and so on as a matter of fact the first determinations of the sizes of atoms was made by measuring how much jiggling there was because you can imagine you can see that how much this thing Wiggles depends upon how big the molecules on so on how many there are so and of course in the beginning when there was a theory of atoms there was a lot of evidence for it but there was no way of measuring or estimating how big they were at first the first estimate was made I think by the intensity of the blue of the sky which I was curious but the more accurate one is the 1:1 the jiggling Einstein made a lot of mathematics for the theory of Brownian motion is jiggling and these equations were used to compare to experimental time in the sizes of atoms since then there are much better ways of measuring the size of that what else can we say about the jiggling have any other points yes I mean I don't wanna get to take me here and now because we've got all the untechnical people like when I was a student yes experiment I was to set up a fork to do a little stuff of you know wave and particle how that is today it's a two-slit but you know you you have one slit chance I know I want to discuss the two slit experiment in detail later on a few days from now but I want the choice sitting up the counters okay yeah when we're going to describe that very experiment but therefore if you don't mind that I keep P seemed it always every one of your questions I always seem to put off but let's say it this way they're very relevant to what we're talking about and I had planned to talk about that that's not I'm not going to leave you off at the end I'm not cheating death is but clearly why gender diagrams should actually manifest when we look for them just because I because you know the exact solution isn't something we can't do right right right in theories of why in nature do we find the terms because we're finding the answer so to something let me show you something okay suppose that the right answer to a mathematical problem is one divided by one minus one 100 and suppose I don't know how to divide because it's very difficult this is imaginary this is analogy the analogy is that have very complicated equations I can solve directly but there are certain other operations that I know how to do more or less easily so yes now we could say that this would be equal to 1 plus 0.01 plus 0.01 times 0.01 plus 0.01 times 0.01 times 0.01 which we write is the 3 you know that's the cube and so on now the fact that and then and so on forever it's never correct if I stop anywhere but if I keep on going let's say it goes oh 1 x o1 x o1 x on 1 for x or you know what this cube means I presume four times and then if there's five times and so forth okay now if I wanted to see whether my theory agreed with experiment so I measured something that the theory says is this big all right but I can't really calculate that because I don't know how to divide you understand it's an analogy of course I know how to give up but I do know how to multiply and add and so I would measure this let's say I'd measure this and I'd find out the result was 100 103 or something whatever I want to know if it's agrees with experiment I mean the theory let's say it one per here that many places that's not a decimal point that's that's me that means I got it that accurate okay uh accurate yeah and I'm these are significant I measure it again and again and it always agrees with that now we want to find out if it's correct then we could do it this way we'd say well if it was a sloppy measurement the answers 1 that means I drop all this stuff but I could do better by adding another piece which is the first piece but the next piece turns out if you multiply it out to be double double double one and the next one if you're worked it out there's no every one times old one four four zero six zero its five zero zero one and so on now maybe to make the analogy better it gets harder and harder to calculate the I'm hot it's hard for me to multiply it takes a lot of work you have to do more multiplying and more multiplying okay so I can only do a few of these terms nevertheless you see if I do a few of them I get an excellent approximation to the answer so you say why is it valid it's valid for the following that to do to leave out some terms when really the correct answers are sum of all the terms the answer is that the higher terms are contributing less and less we hope anyway we can't calculate exact we're not going to compute them exactly that we're going to stop somewhere but by a mathematical argument or by guessing or by noticing how each one is going down so well we suppose that the higher ones are smaller and smaller so if we forget some the first for say then we would we would get an answer that was presumably about rather accurate we can estimate that the next one is a hundred times smaller than that perhaps of course all these estimating is and so on are unnecessary we actually can carry it out in this example but it's by analogy we imagined it's hard to do all the arithmetic then we would say the answers 1 on 100 or one it could conclude for example 1 let's say it could conclude from this example that is disagrees with experiment only if the agrees depends on what the experimental result is it could it be agree that they could agree the point is we don't have to calculate mathematical quantity exactly if the theory is complicated we have all the mathematical rearrangements which your equivalent that's all it is and the perturbation Theory so-called with the diagrams is simply a way of circulating the successive terms of a series like that specific terms manifest because we started with something that we know yeah a formula that produces these turn that's what the theory is Oh each one of those terms has a final diagram and he's asking why should the individuals manifest as physical processes they're all the terms of that like the particular one of those terms might even take a kind of scattering No a particular kind of scattering is the sum of all the terms all the things are happening when there's a scattering you've broken it up into elementary sub parts to a now analyze it each diagram represents a piece of an analysis you could say in this case if you wanted to you could say this is called ash lanka s-- okay now the theory is complicated says not any number of schlock asses can occur I can analyze it by saying either there are no strong cases the product that the contribution will no schlump this effect is one the contribution from the ones longest effect is 0.01 and two schlong cases is point all one and so on but in any real situation is an arbitrary number of sri lanka stirs and there in the formula here there's yes yes simple but there are high in turn that's right that means that the formula for the decay of a new plant is a complicated expression which is being expressed as a sequence of approximation the first first-order term yes though is a final diagram and the second-order is so this is a second-order terms that are more complicated fine that's right represents a more complicated looking nature and we find the first order term plus the second-order time plus they thought what it is we point them all ok we find them all as nearly as we can measure if we only measure the six a certain number of figures that I can't be sure that these are here but they were invented because this is what we were trying to express we know this side and we represent it this way and we just say there at these terms and these terms are left out because they were plucks they're so small I don't know what the problem yeah but maybe we can talk together sometime and get it to clear have everybody back or no I see there still somebody work is oh ok so you're all back you mean you've all been educated everything ok oh great well that was easier he said it would take a half an hour but apparently you were closer to understanding it then he thought or he was clever at explaining it that or else he gave up the right okay well now that we all are together on it and see that there's something deeply puzzling about it I review the phenomena for just a moment and say a few words about it and tell you things the idea was we discovered this that if we can get two boxes each of which has three buttons on it there's three buttons which we say one or two or three and we can push a button and it lights a light which is either red or green your mind I change the color from red and black the backlight is a little annoying analogy it doesn't light it no good so here's the measuring light that comes out you pushed yes you could do it many ways you push this in the lights red or your or green this is button one button to button three I like wise on this spot and just to review once finally more goes like this the boxes is set up and I give you charges for them or I give you the boxes of the games I have once they were together they can be taken anywhere now it goes like this if you don't push any button here the light or light up either red or green and it's about 50/50 if you push a button here and then push a different button on the box then the light agrees with the other one only a quarter of the time that is if this one gives red and then you push the other one this will only give red a quarter of the time or it gives black the opposite color three-quarters of the time we said it both ways right and that's very curious if they're worse well we've explained the curiosity of it for too many times now the situation is here that this box has the same prompt that this box will always agree with this one if you push a button on both of them then the buttons will give the same color lights didn't have a light yet so therefore it won't work yet all right I'll put the light on it good now if you push button 2 on both boxes then the lights are both red or both green they always agree with each other no problem and but what's odd is that if you push a button one here and get red and push button 2 here it'll be black three-quarters of the time and after a lot of thought and much study we've discovered that that's very strange okay get 2/3 of the time without any trouble but not 3/4 of the time so I would not like to just to say what whether you answer what the uncertainty principle is I said it once before I'll just say it again to make it clear to everybody who now understands it what balance theorem is and what the einstein-podolsky-rosen paradox were supposed to be okay and a little bit of the history of it the first forget the second box first and think about this first one if when I push this button I get red and green then if I push this one and it agrees or disagrees that said three-quarters of the time that's impossible unless if we imagine there were cards under there or something like that that was set that when we started out that this was going to be red if we pushed it and if we pushed this one let's say it was going to be green and this one green then sometimes when we pushed a pair of buttons like this pair we get them to match and that would be a third of the time because we could pick the buttons of every payer combination there are three out of all of the six different ways of choosing three different ways of choosing pairs one of them match that that one would give a match that would give a not match and that would give a knot nice so if I pick two buttons at random itix pecked they match one-third of the time but actually they only match 1/4 of the time the easy example would be if it they didn't match at all then you would have to say sorry either case that something happens that when you push this button if they were red green green and was a set that they would have made if I had pushed them now when I pushed this one I must change it some abaqus the remaining result as a quarter of the time so when I pushed this the only way to explain that is to have a machine that if I push one button it changes the ones underneath now if we go to nature and look at it and say well what happens if I looked at all the buttons at the same time that I pushed this and got the result push that and push that and found all the results will always repeat for example nothing will ever change then I've been a pickle so but it is true that we're only allowed to push one button at a time and furthermore it does turn out that when we push a button let's say this one and gets read then this one turn is green say and we push this one again it's no longer red so we have experimentally noticed that it is true it's quite possible and perfectly true that we could imagine it this way that when we push the buttons they change the colors of the other light I remind you if you push the same button again and again it always checks out the same color I start out make sure this is red by pushing it eight times then I push this one it's green and it'll stay green all the time say then if i push this it's possible let it be green now okay otherwise I'd never be able to explain this one thing yes yes if you push the same button it never changes the result if you push it again you push the same button again yeah yes it in a particular segment obviously this is set up for a particular measurement yes it can be made so that it doesn't in general doesn't change and you can push it as much as you want there are situation where things change but there are situations where they know yes you can push it as many times as you want in succession and nothing about that button would change if we don't know what's happening in the other one is because we can't see and when you push another one then you see it's changed so you could still imagine that they were sort of potential local cards underneath there or some kind of thing that determines what color is going to be but now we have a new rule that when we push it it changes what's under the other buttons and furthermore we can't assume that it doesn't change because if we assume it doesn't change we're going to get in trouble with the one quarter result so therefore we would have to say that if this theory that well experimentally is Right theory is right but when the early days when it was first discovered that all the experiments weren't done yet but when the theory came out I would predict results like this it was obvious that it was necessary for such results that if there were such a thing as the potential non lights that were going to light I mean the potential cards under that but by pushing buttons you're changing the results that you would get for the other buttons and experimentally it does turn out just like we said it's all right everything's okay if you push this and get red then you push this and get green it is possible when you push that to find it's changed in fact it's necessary that you find it change because if we keep on thinking about this we would get 2/3 otherwise we don't put different 2/3 of the time they would be different they would change and then 1/3 they would be the same but it's rather three corners in 1/4 so we have to have it change in God thank God it does change but that's a very simple view then there's nothing wrong with Apple to say that they were these things were under here but they change at the same there were things under here that is ahead of time there's potentiality to be red or green or green without looking at it yet we can talk about such an idea we're going to call a classical view that means an old-fashioned view and what Heisenberg said was that the old-fashioned view if it's tried to be maintained at all would have to have in it an additional new feature that it shall be impossible to determine what color this one would be without changing the potential color that the other one would be in other words by measuring that by pushing that button number two you've got to change the colors on the number 1 or 3 if you wanted to picture it with color and we see why we have to do that otherwise we would get 1 3 2 we wouldn't get the result today of experiment and at that time of theory historical ly however Heisenberg's statement wasn't measured with this particular box business and he didn't have this nicely which took 40 years of patient thinking to get the simplest possible example he had a more complicated example which was measuring something called a position of a product which is an idea that anybody classically would think a little ball or an electron or a particle would have some kind of position and you can measure what it was it would be a number would tell you how far it is from the east wall but three numbers if you want Plus that wall Plus that well but let's talk about motion just this way there'd be a number which would tell how far particle was from a wall there was another thing one could measure in classical physics which was something like the speed actually it's called the momentum it's the speed times the mass it's a thing that tells you how well it coasts and you could also measure the momentum something obviously you can measure its speed and you can measure it exactly what and the position is act