WEBVTT 00:00:00.140 --> 00:00:04.500 The following content is provided under a Creative Commons license. Your support will 00:00:04.500 --> 00:00:10.100 help MIT OpenCourseWare continue to offer high-quality educational resources for free. 00:00:10.100 --> 00:00:14.860 To make a donation or to view additional materials from hundreds of MIT courses, 00:00:14.860 --> 00:00:19.500 visit MIT OpenCourseWare at ocw.mit.edu. 00:00:25.120 --> 00:00:31.740 PROFESSOR: All right. So today's task is going to be to outline some of the basic experimental 00:00:31.740 --> 00:00:37.900 facts that we will both have to deal with and that our aim should be to understand and 00:00:37.910 --> 00:00:41.210 model through the rest of the course. 00:00:41.210 --> 00:00:46.019 Physics doesn't tell you some abstract truth about why the universe is the way it is. Physics 00:00:46.019 --> 00:00:51.280 gives you models to understand how things work and predict what will happen next. And 00:00:51.280 --> 00:00:55.309 what we will be aiming to do is develop models that give us an intuition for the phenomena 00:00:55.309 --> 00:00:58.859 and allow us to make predictions. And these are going to be the experimental facts I would 00:00:58.859 --> 00:01:05.930 like to both explain, develop an intuition for, and be able to predict consequences of. 00:01:05.930 --> 00:01:15.530 So we'll start off with-- so let me just outline them. So, first fact, atoms exist. I'll go 00:01:15.530 --> 00:01:19.750 over some of the arguments for that. Randomness, definitely present in the world. Atomic spectre 00:01:19.750 --> 00:01:25.420 are discrete and structured. We have a photoelectric effect, which I'll describe in some detail. 00:01:25.420 --> 00:01:31.009 Electrons do some funny things. In particular electron diffraction. And sixth and finally, 00:01:31.009 --> 00:01:34.950 Bell's Inequality. Something that we will come back to at the very end of the class, 00:01:34.950 --> 00:01:41.520 which I like to think of as a sort of a frame for the entirety of 8.04. 00:01:41.530 --> 00:01:47.600 So... we'll stick with this for the moment. 00:01:47.600 --> 00:01:55.200 So everyone in here knows that atoms are made of electrons and nuclei. In particular, you 00:01:55.200 --> 00:01:59.340 know that electrons exist because you've seen a cathode ray tube. I used to be able to say 00:01:59.340 --> 00:02:03.119 you've seen a TV, but you all have flat panel TVs, so this is useless. So a cathode ray 00:02:03.119 --> 00:02:08.598 tube is a gun that shoots electrons at a phosphorescent screen. And every time the electron hits the 00:02:08.600 --> 00:02:13.140 screen it induces a little phosphorescence, a little glow. And that's how you see on a 00:02:13.140 --> 00:02:15.300 CRT. 00:02:15.300 --> 00:02:23.220 And so as was pithily stated long ago by a very famous physicist, if you can spray them, 00:02:23.220 --> 00:02:30.140 they exist. Pretty good argument. There's a better argument for the existence of electrons, 00:02:30.150 --> 00:02:32.879 which is that we can actually see them individually. 00:02:32.879 --> 00:02:37.480 And this is one of the most famous images in high-energy physics. It's from an experiment 00:02:37.480 --> 00:02:47.950 called Gargamelle, which was a 30-cubic meter tank of liquid freon pulsing just at its vapor 00:02:47.950 --> 00:02:53.340 pressure 60 times a second. And what this image is is, apart from all the schmut, you're 00:02:53.340 --> 00:02:58.079 watching a trail of bubbles in this de-pressurizing freon that wants to create bubbles but you 00:02:58.079 --> 00:03:02.159 have to nucleate bubbles. What you're seeing there in that central line that goes up and 00:03:02.159 --> 00:03:07.790 then curls around is a single electron that was nailed by a neutrino incident from a beam 00:03:07.790 --> 00:03:11.599 at CERN where currently the LHC is running. 00:03:11.599 --> 00:03:16.590 And this experiment revealed two things. First, to us it will reveal that you can see individual 00:03:16.590 --> 00:03:21.019 electrons and by studying the images of them moving through fluids and leaving a disturbing 00:03:21.019 --> 00:03:25.709 wake of bubbles behind them. We can study their properties in some considerable detail. 00:03:25.709 --> 00:03:28.760 The second thing it taught us is something new-- we're not going to talk about it in 00:03:28.760 --> 00:03:33.989 detail-- is that it's possible for a neutrino to hit an electron. And that process is called 00:03:33.989 --> 00:03:38.099 a weak neutral current for sort of stupid historical reasons. It's actually a really 00:03:38.099 --> 00:03:44.829 good name. And that was awesome and surprising and so this picture is both a monument to 00:03:44.829 --> 00:03:48.790 the technology of the experiment, but also to the physics of weak neutral currents and 00:03:48.790 --> 00:03:53.420 electrons. They exist if you can discover neutrinos by watching them. OK. 00:03:53.420 --> 00:03:58.220 Secondly, nuclei. We know that nuclei exist because you can shoot alpha particles, which 00:03:58.220 --> 00:04:04.620 come from radioactive decay, at atoms. And you have your atom which is some sort of vague 00:04:04.620 --> 00:04:08.430 thing, and I'm gonna make the-- I'm gonna find the atom by making a sheet of atoms. 00:04:08.430 --> 00:04:13.459 Maybe a foil. A very thin foil of stuff. And then I'm gonna shoot very high-energy alpha 00:04:13.459 --> 00:04:15.390 particles incident of this. 00:04:15.390 --> 00:04:19.470 Probably everyone has heard of this experiment, it was done by Rutherford and Geiger and Marsden, 00:04:19.470 --> 00:04:23.660 in particular his students at the time or post-docs. I don't recall-- and you shoot 00:04:23.660 --> 00:04:27.080 these alpha particles in. And if you think of these guys as some sort of jelly-ish lump 00:04:27.080 --> 00:04:31.000 then maybe they'll deflect a little bit, but if you shoot a bullet through Jello it just 00:04:31.000 --> 00:04:34.390 sort of maybe gets deflected a little bit. But Jello, I mean, come on. 00:04:34.390 --> 00:04:36.790 And I think what was shocking is that you should these alpha particles in and every 00:04:36.790 --> 00:04:41.940 once in a while, they bounce back at, you know, 180, 160 degrees. Rutherford likened 00:04:41.940 --> 00:04:49.630 this to rolling a bowling ball against a piece of paper and having it bounce back. Kind of 00:04:49.630 --> 00:04:53.470 surprising. And the explanation here that people eventually came up upon is that atoms 00:04:53.470 --> 00:05:00.170 are mostly zero density. Except they have very, very high density cores, which are many 00:05:00.170 --> 00:05:04.430 times smaller than the size of the atom but where most of the mass is concentrated. And 00:05:04.430 --> 00:05:06.700 as a consequence, most of the inertia. 00:05:06.700 --> 00:05:10.920 And so we know that atoms have substructure, and the picture we have is that well if you 00:05:10.920 --> 00:05:15.860 scrape this pile of metal, you can pull off the electrons, leaving behind nuclei which 00:05:15.860 --> 00:05:19.440 have positive charge because you've scraped off the electrons that have negative charge. 00:05:19.440 --> 00:05:23.720 So we have a picture from these experiments that there are electrons and there are nuclei-- 00:05:23.720 --> 00:05:29.650 which, I'll just write N and plus-- which are the constituents of atoms. 00:05:29.650 --> 00:05:33.820 Now this leads to a very natural picture of what an atom is. If you're a 19th-century 00:05:33.820 --> 00:05:37.990 physicist, or even an early 20th-century physicist, it's very natural to say, aha, well if I know 00:05:37.990 --> 00:05:42.840 if I have a positive charge and I have a negative charge, then they attract each other with 00:05:42.840 --> 00:05:49.530 a 1 over r minus q1 q2-- sorry, q1 q2 over r potential. This is just like gravity, right. 00:05:49.530 --> 00:05:54.030 The earth and the sun are attracted with an inverse-r potential. This leads to Keplerian 00:05:54.030 --> 00:05:59.880 orbits. And so maybe an atom is just some sort of orbiting classical combination of 00:05:59.880 --> 00:06:03.290 an electron and a nucleus, positively charged nucleus. 00:06:03.290 --> 00:06:07.840 The problem with this picture, as you explore in detail in your first problem on the problem 00:06:07.840 --> 00:06:13.790 set, is that it doesn't work. What happens when you accelerate a charge? It radiates. 00:06:13.790 --> 00:06:17.600 Exactly. So if it's radiating, it's gotta lose energy. It's dumping energy into this-- 00:06:17.600 --> 00:06:22.040 out of the system. So it's gotta fall lower into the potential. Well it falls lower, it 00:06:22.040 --> 00:06:25.930 speeds up. It radiates more. Because it's accelerating more to stay in a circular orbit. 00:06:25.930 --> 00:06:28.380 All right, it radiates more, it has to fall further down. 00:06:28.380 --> 00:06:32.520 So on the problem set you're going to calculate how long that takes. And it's not very long. 00:06:32.520 --> 00:06:37.120 And so the fact that we persist for more than a few picoseconds tells you that it's not 00:06:37.120 --> 00:06:42.220 that-- this is not a correct picture of an atom. OK. 00:06:42.220 --> 00:06:47.870 So in classical mechanics, atoms could not exist. And yet, atoms exist. So we have to 00:06:47.870 --> 00:06:56.880 explain that. That's gonna be our first challenge. Now interestingly Geiger who is this collaborator 00:06:56.880 --> 00:07:01.380 of Rutherford, a young junior collaborator of Rutherford, went on to develop a really 00:07:01.380 --> 00:07:06.190 neat instrument. So suppose you want to see radiation. We do this all the time. I'm looking 00:07:06.190 --> 00:07:09.570 at you and I'm seeing radiation, seeing light. But I'm not seeing ultra high energy radiation, 00:07:09.570 --> 00:07:13.540 I'm seeing energy radiation in the electromagnetic waves in the optical spectrum. 00:07:13.540 --> 00:07:19.370 Meanwhile I'm also not seeing alpha particles. So what Geiger wanted was a way to detect 00:07:19.370 --> 00:07:24.860 without using your eyes radiation that's hard to see. So the way he did this is he took 00:07:24.860 --> 00:07:29.470 a capacitor and he filled the-- surrounded the capacitor with some noble gas. It doesn't 00:07:29.470 --> 00:07:36.190 interact. There's no-- it's very hard to ionize. And if you crank up the potential across this 00:07:36.190 --> 00:07:43.409 capacitor plate high enough, what do you get? A spark. You all know this, if you crank up 00:07:43.409 --> 00:07:46.600 a capacitor it eventually breaks down because the dielectric in between breaks down, you 00:07:46.600 --> 00:07:48.080 get a spontaneous sparking. 00:07:48.080 --> 00:07:51.840 So what do you figure it would look if I take a capacitor plate and I charge it up, but 00:07:51.840 --> 00:07:57.050 not quite to breakdown. Just a good potential. And another charged particle comes flying 00:07:57.050 --> 00:08:00.950 through, like an alpha particle, which carries a charge of plus 2, that positive charge will 00:08:00.950 --> 00:08:06.620 disturb things and will add extra field effectively. And lead to the nucleation of a spark. 00:08:06.620 --> 00:08:10.830 So the presence of a spark when this potential is not strong enough to induce a spark spontaneously 00:08:10.830 --> 00:08:17.200 indicates the passage of a charged particle. Geiger worked later with-- Marsden? Muller. 00:08:17.200 --> 00:08:24.270 Heck. I don't even remember. And developed this into a device now known as the Geiger 00:08:24.270 --> 00:08:31.210 counter. And so you've probably all seen or heard Geiger counters going off in movies, 00:08:31.210 --> 00:08:36.880 right. They go ping ping ping ping ping ping ping ping ping, right. They bounce off randomly. 00:08:36.880 --> 00:08:40.860 This is an extremely important lesson, which is tantamount to the lesson of our second 00:08:40.860 --> 00:08:45.520 experiment yesterday. The 50-50, when we didn't expect it. The white electrons into the harness 00:08:45.520 --> 00:08:49.150 box then into a color box again, would come out 50-50, not 100 percent. And they come 00:08:49.150 --> 00:08:54.030 out in a way that's unpredictable. We have no ability to our knowledge-- and more than 00:08:54.030 --> 00:08:56.400 our knowledge, we'll come back to that with Bell's Inequality-- but we have no ability 00:08:56.400 --> 00:09:02.000 to predict which electron will come out of that third box, white or black, right. 00:09:02.000 --> 00:09:05.270 Similarly with a Geiger counter you hear that atoms decay, but they decay randomly. The 00:09:05.270 --> 00:09:09.510 radiation comes out of a pile of radioactive material totally at random. We know the probabilistic 00:09:09.510 --> 00:09:13.710 description of that. We're going to develop that, but we don't know exactly when. And 00:09:13.710 --> 00:09:18.510 that's a really powerful example-- both of those experiments are powerful examples of 00:09:18.510 --> 00:09:19.190 randomness. 00:09:19.190 --> 00:09:22.890 And so we're going to have to incorporate that into our laws of physics into our model 00:09:22.890 --> 00:09:29.800 of quantum phenomena as well. Questions? I usually have a Geiger counter at this point, 00:09:29.800 --> 00:09:34.700 which is totally awesome, so I'll try to produce the Geiger counter demo later. But the person 00:09:34.700 --> 00:09:41.700 with the Geiger counter turns out to have left the continent, so made it a little challenging. 00:09:41.700 --> 00:09:48.630 OK. Just sort of since we're at MIT, an interesting side note. This strategy of so-called hard 00:09:48.630 --> 00:09:54.010 scattering, of taking some object and sending it at very high velocity at some other object 00:09:54.010 --> 00:09:58.760 and looking for the rare events when they bounce off at some large angle, so-called 00:09:58.760 --> 00:10:05.070 hard scattering. Which is used to detect dense cores of objects. It didn't stop with Rutherford. 00:10:05.070 --> 00:10:06.680 People didn't just give up at that point. 00:10:06.680 --> 00:10:12.360 Similar experience in the '60s and '70s which are conducted at Slack, were involved not 00:10:12.360 --> 00:10:19.140 alpha particles incident on atoms but individual electrons incident on protons. So not shooting 00:10:19.140 --> 00:10:22.510 into the nucleus, but shooting and looking for the effect of hitting individual protons 00:10:22.510 --> 00:10:28.250 inside the nucleus. And through this process it was discovered that in fact-- so this was 00:10:28.250 --> 00:10:33.630 done in the '60s and '70s, that in fact the proton itself is also not a fundamental particle. 00:10:33.630 --> 00:10:39.170 The proton is itself composite. 00:10:39.170 --> 00:10:44.140 And in particular, it's made out of-- eventually people understood that it's made out of, morally 00:10:44.140 --> 00:10:47.210 speaking, and I'm gonna put this in quotation marks-- ask me about it in office hours-- 00:10:47.210 --> 00:10:54.400 three quarks, which are some particles. And the reason we-- all this tells you is that 00:10:54.400 --> 00:10:57.570 it's some object and we've given it the name quark. But indeed there are three point-like 00:10:57.570 --> 00:11:01.590 particles that in some sense make up a proton. It's actually much more complicated than that, 00:11:01.590 --> 00:11:05.230 but these quarks, among other things, have very strange properties. Like they have fractional 00:11:05.230 --> 00:11:10.220 charge. 00:11:10.220 --> 00:11:16.320 And this was discovered by a large group of people, in particular led by Kendall and Friedman 00:11:16.320 --> 00:11:21.600 and also Richard Taylor. Kendall and Friedman were at MIT, Richard Taylor was at Stanford. 00:11:21.600 --> 00:11:26.660 And in 1990 they shared the Nobel Prize for the discovery of the partonic structure out 00:11:26.660 --> 00:11:31.140 of the nucleons. So these sorts of techniques that people have been using for a very long 00:11:31.140 --> 00:11:33.190 time continue to be useful and awesome. 00:11:33.190 --> 00:11:36.700 And in particular the experiment, the experimental version of this that's currently going on, 00:11:36.700 --> 00:11:40.240 that I particularly love is something called the relativistic heavy ion collider, which 00:11:40.240 --> 00:11:43.640 is going on at Brookhaven. So here what you're doing is you take two protons and you blow 00:11:43.640 --> 00:11:48.320 them into each other at ultra high energy. Two protons, collide them and see what happens. 00:11:48.320 --> 00:11:54.610 And that's what happens. You get massive shrapnel coming flying out. So instead of having a 00:11:54.610 --> 00:11:57.720 simple thing where one of the protons just bounces because there's some hard quark, instead 00:11:57.720 --> 00:12:03.750 what happens is just shrapnel everywhere, right. So you might think, well, how do we 00:12:03.750 --> 00:12:08.700 interpret that at all. How do you make sense out of 14,000 particles coming out of two 00:12:08.700 --> 00:12:13.440 protons bouncing into each other. How does that make any sense? And the answer turns 00:12:13.440 --> 00:12:14.480 out to be kind of awesome. 00:12:14.480 --> 00:12:20.110 And so this touches on my research. So I want to make a quick comment on it just for color. 00:12:20.110 --> 00:12:24.370 The answer turns out to be really interesting. First off, the interior constituents of protons 00:12:24.370 --> 00:12:29.850 interact very strongly with each other. But at the brief moment when protons collide with 00:12:29.850 --> 00:12:35.130 each other, what you actually form is not a point-like quirk and another point-like 00:12:35.130 --> 00:12:38.470 quark. In fact, protons aren't made out of point-like quarks at all. Protons are big 00:12:38.470 --> 00:12:42.690 bags with quarks and gluons and all sorts of particles fluctuating in and out of existence 00:12:42.690 --> 00:12:44.130 in a complicated fashion. 00:12:44.130 --> 00:12:50.910 And what you actually get is, amazingly, a liquid. For a brief, brief moment of time 00:12:50.910 --> 00:12:54.290 the parts of those protons that overlap-- think of them as two spheres and they overlap 00:12:54.290 --> 00:12:57.960 in some sort of almond-shaped region. The parts of those protons that overlap form a 00:12:57.960 --> 00:13:03.380 liquid at ultra high temperature and at ultra high density. It's called the RHIC fireball 00:13:03.380 --> 00:13:07.000 or the quark-gluon plasma, although it's not actually a plasma. But it's a liquid like 00:13:07.000 --> 00:13:11.380 water. And what I mean by saying it's a liquid like water, if you push it, it spreads in 00:13:11.380 --> 00:13:15.400 waves. And like water, it's dissipative. Those waves dissipate. 00:13:15.400 --> 00:13:18.620 But it's a really funny bit of liquid. 00:13:18.620 --> 00:13:22.200 Imagine you take your cup of coffee. You drink it, you're drinking your coffee as I am wont 00:13:22.200 --> 00:13:25.790 to do, and it cools down over time. This is very frustrating. So you pour in a little 00:13:25.790 --> 00:13:29.730 bit of hot coffee and when you pour in that hot coffee, the system is out of equilibrium. 00:13:29.730 --> 00:13:34.300 It hasn't thermalized. So what you want is you want to wait for all of the system to 00:13:34.300 --> 00:13:37.660 wait until it's come to equilibrium so you don't get a swig of hot or swig of cold. You 00:13:37.660 --> 00:13:39.620 want some sort of Goldilocks-ean in between. 00:13:39.620 --> 00:13:44.710 So you can ask how long does it take for this coffee to come to thermal equilibrium. Well 00:13:44.710 --> 00:13:47.990 it takes a while. You know, a few seconds, a few minutes, depending on exactly how you 00:13:47.990 --> 00:13:51.850 mess with it. But let me ask you a quick question. How does that time scale compare to the time 00:13:51.850 --> 00:14:00.250 it takes for light to cross your mug? Much, much, much slower, right? By orders of magnitude. 00:14:00.250 --> 00:14:05.190 For this liquid that's formed in the ultra high energy collision of two protons, the 00:14:05.190 --> 00:14:09.779 time it takes for the system-- which starts out crazy out of equilibrium with all sorts 00:14:09.779 --> 00:14:14.350 of quarks here and gluons there and stuff flying about-- the time it takes for it to 00:14:14.350 --> 00:14:19.990 come to thermal equilibrium is of order the time it takes for light to cross the little 00:14:19.990 --> 00:14:25.430 puddle of liquid. This is a crazy liquid, it's called a quantum liquid. And it has all 00:14:25.430 --> 00:14:29.040 sorts of wonderful properties. And the best thing about it to my mind is that it's very 00:14:29.040 --> 00:14:35.660 well modeled by black holes. Which is totally separate issue, but it's a fun example. So 00:14:35.660 --> 00:14:41.880 from these sorts of collisions, we know a great deal about the existence of atoms and 00:14:41.880 --> 00:14:45.160 randomness, as you can see. That's a fairly random sorting. 00:14:45.160 --> 00:14:51.150 OK so moving on to more 8.04 things. Back to atoms. So let's look at specifics of that. 00:14:51.150 --> 00:14:58.630 I'm not kidding, they really are related to black holes. I get paid for this. So here's 00:14:58.630 --> 00:15:03.720 a nice fact, so let's get to atomic spectra. So to study atomic spectra, here's the experiment 00:15:03.720 --> 00:15:08.670 I want to run. The experiment I want to run starts out with some sort of power plant. 00:15:08.670 --> 00:15:13.970 And out of the power plant come two wires. And I'm going to run these wires across a 00:15:13.970 --> 00:15:19.380 spark gap, you know, a piece of metal here, a piece of metal here, and put them inside 00:15:19.380 --> 00:15:25.230 a container, which has some gas. Like H2 or neon or whatever you want. But some simple 00:15:25.230 --> 00:15:28.130 gas inside here. 00:15:28.130 --> 00:15:32.339 So we've got an electric potential established across it. Again, we don't want so much potential 00:15:32.339 --> 00:15:38.070 that it sparks, but we do want to excite the H2. So we can even make it spark, it doesn't 00:15:38.070 --> 00:15:41.730 really matter too much. The important thing is that we're going to excite the hydrogen, 00:15:41.730 --> 00:15:48.210 and in exciting the hydrogen the excited hydrogen is going to send out light. And then I'm going 00:15:48.210 --> 00:15:56.850 to take this light-- we take the light, and I'm gonna shine this on a prism, something 00:15:56.850 --> 00:16:05.930 I was taught to do by Newton. And-- metaphorically speaking-- and look at the image of this light 00:16:05.930 --> 00:16:08.610 having passed through the prism. 00:16:08.610 --> 00:16:14.330 And what you find is you find a very distinct set of patterns. You do not get a continuous 00:16:14.330 --> 00:16:17.480 band. In fact what you get-- I'm going to have a hard time drawing this so let me draw 00:16:17.480 --> 00:16:22.740 down here. I'm now going to draw the intensity of the light incident on the screen on this 00:16:22.740 --> 00:16:27.600 piece of paper-- people really used to use pieces of paper for this, which is kind of 00:16:27.600 --> 00:16:30.300 awesome-- as a function of the wavelength, and I'll measure it in angstroms. 00:16:30.300 --> 00:16:39.690 And what you discover is-- here's around 1,000 angstroms-- you get a bunch of lines. Get 00:16:39.690 --> 00:16:43.860 these spikes. And they start to spread out, and then there aren't so many. And then at 00:16:43.860 --> 00:17:01.120 around 3,000, you get another set. And then at around 10,000, you get another set. 00:17:01.120 --> 00:17:06.819 This is around 10,000. 00:17:06.819 --> 00:17:10.220 And here's the interesting thing about these. So the discovery of these lines-- these are 00:17:10.220 --> 00:17:19.020 named after a guy named Lyman, these are-- these are named after a guy named-- Ballmer. 00:17:19.020 --> 00:17:29.400 Thank you. Steve Ballmer. And these are passion, like passion fruit. So. Everyone needs a mnemonic, 00:17:29.400 --> 00:17:36.679 OK. And so these people identified these lines and explained various things about them. 00:17:36.679 --> 00:17:39.900 But here's an interesting fact. If you replace this nuclear power plant with a coal plant, 00:17:39.900 --> 00:17:43.890 it makes no difference. If you replace this prism by a different prism, it makes no difference 00:17:43.890 --> 00:17:49.670 to where the lines are. If you change this mechanism of exciting the hydrogen, it makes 00:17:49.670 --> 00:17:52.910 no difference. As long as it's hydrogen-- as long as it's hydrogen in here you get the 00:17:52.910 --> 00:17:56.190 same lines, mainly with different intensities depending upon how exactly you do the experiment. 00:17:56.190 --> 00:18:02.350 But you get the same position of the lines. And that's a really striking thing. 00:18:02.350 --> 00:18:06.790 Now if you use a different chemical, a different gas in here, like neon, you get a very different 00:18:06.790 --> 00:18:10.900 set of lines. And a very different effective color now when you eyeball this thing. So 00:18:10.900 --> 00:18:18.630 Ballmer, incidentally-- and I think this is actually why he got blamed for that particular 00:18:18.630 --> 00:18:22.929 series, although I don't know the history-- Ballmer noticed by being-- depending on which 00:18:22.929 --> 00:18:28.500 biography you read-- very clever or very obsessed that these guys, this particular set, could 00:18:28.500 --> 00:18:31.250 be-- they're wavelengths. If you wrote their wavelengths and labeled them by an integer 00:18:31.250 --> 00:18:37.110 n, where n ran from 3 to any positive integer above 3, could be written as 36. So this is 00:18:37.110 --> 00:18:44.020 pure numerology. 36, 46 angstroms times the function n squared over n squared minus 4, 00:18:44.020 --> 00:18:48.679 where N is equal to 3, 4, dot dot dot-- an integer. 00:18:48.679 --> 00:18:51.270 And it turns out if you just plug in these integers, you get a pretty good approximation 00:18:51.270 --> 00:18:58.020 to this series of lines. This is a hallowed tradition, a phenomenological fit to some 00:18:58.020 --> 00:19:02.760 data. Where did it come from? It came from his creative or obsessed mind. So this was 00:19:02.760 --> 00:19:10.510 Ballmer. And this is specifically for hydrogen gas, H2. 00:19:10.510 --> 00:19:16.750 So Rydberg and Ritz, R and R, said, well actually we can do one better. Now that they realized 00:19:16.750 --> 00:19:19.720 that this is true, they looked at the whole sequence. And they found a really neat little 00:19:19.720 --> 00:19:24.750 expression, which is that 1 over the wavelength is equal to a single constant parameter. Not 00:19:24.750 --> 00:19:30.559 just for all these, but for all of them. One single numerical coefficient times 1 over 00:19:30.559 --> 00:19:36.460 m squared minus 1 over n squared-- n is an integer greater than zero and greater in particular 00:19:36.460 --> 00:19:41.450 than m. And if you plug in any value of n and any value of m, for sufficiently reasonable-- 00:19:41.450 --> 00:19:43.770 I mean, if you put in 10 million integers you're not going to see it because it's way 00:19:43.770 --> 00:19:52.750 out there, but if you put in or-- rather, in here-- if you put any value of n and m, 00:19:52.750 --> 00:20:03.390 you will get one of these lines. So again, why? You know, as it's said, who ordered that. 00:20:03.390 --> 00:20:06.030 So this is experimental result three that we're going to have to deal with. When you 00:20:06.030 --> 00:20:09.530 look at atoms and you look at the specter of light coming off of them, their spectra 00:20:09.530 --> 00:20:14.799 are discrete. But they're not just stupidly discrete, they're discrete with real structure. 00:20:14.799 --> 00:20:19.559 Something that begs for an explanation. This is obviously more than numerology, because 00:20:19.559 --> 00:20:25.179 it explains with one tunable coefficient a tremendous number of spectral lines. And there's 00:20:25.179 --> 00:20:29.760 a difference-- and crucially, these both work specifically for hydrogen. For different atoms 00:20:29.760 --> 00:20:31.450 you need a totally different formula. 00:20:31.450 --> 00:20:44.740 But again, there's always some formula that nails those spectral lines. Why? Questions? 00:20:44.740 --> 00:21:00.120 OK. So speaking of atomic spectra-- whoops, I went one too far-- here's a different experiment. 00:21:00.120 --> 00:21:07.470 So people notice the following thing. People notice that if you take a piece of metal and 00:21:07.470 --> 00:21:12.660 you shine a light at it, by taking the sun or better yet, you know, these days we'd use 00:21:12.660 --> 00:21:17.840 a laser, but you shine light on this piece of metal. Something that is done all the time 00:21:17.840 --> 00:21:21.640 in condensed matter labs, it's a very useful technique. We really do use lasers not the 00:21:21.640 --> 00:21:24.390 sun, but still it continues to be useful in fact to this day. 00:21:24.390 --> 00:21:27.630 You shine light on a piece of metal and every once in a while what happens is electrons 00:21:27.630 --> 00:21:35.049 come flying off. And the more light and the stronger the light you shine, you see changes 00:21:35.049 --> 00:21:39.920 in the way that electrons bounce off. So we'd like to measure that. I'd like to make that 00:21:39.920 --> 00:21:43.429 precise. And this was done in a really lovely experiment. Here's the experiment. The basic 00:21:43.429 --> 00:21:47.510 idea of the experiment is I want to check to see, as I change the features of the light, 00:21:47.510 --> 00:21:50.660 the intensity, the frequency, whatever, I want to see how that changes the properties 00:21:50.660 --> 00:21:52.059 of the electrons that bounce off. 00:21:52.059 --> 00:21:55.690 Now one obvious way-- one obvious feature of an electron that flew off a piece of metal 00:21:55.690 --> 00:21:59.890 is how fast is it going, how much energy does it have. What's its kinetic energy. So I'd 00:21:59.890 --> 00:22:03.540 like to build an experiment that measures the kinetic energy of an electron that's been 00:22:03.540 --> 00:22:09.400 excited through this photoelectric effect. Through emission after shining light on a 00:22:09.400 --> 00:22:10.280 piece of metal. Cool? 00:22:10.280 --> 00:22:14.590 So I want to build that experiment. So here's how that experiment goes. Well if this electron 00:22:14.590 --> 00:22:20.809 comes flying off with some kinetic energy and I want to measure that kinetic energy, 00:22:20.809 --> 00:22:26.390 imagine the following circuit. OK first off imagine I just take a second piece of metal 00:22:26.390 --> 00:22:33.000 over here, and I'm going to put a little current meter here, an ammeter. And here's what this 00:22:33.000 --> 00:22:36.370 circuit does. When you shine light on this piece of metal-- we'll put a screen to protect 00:22:36.370 --> 00:22:40.020 the other piece of metal-- the electrons come flying off, they get over here. And now I've 00:22:40.020 --> 00:22:43.230 got a bunch of extra electrons over here and I'm missing electrons over here. So this is 00:22:43.230 --> 00:22:47.170 negative, this is positive. And the electrons will not flow along this wire back here to 00:22:47.170 --> 00:22:48.330 neutralize the system. 00:22:48.330 --> 00:22:52.870 The more light I shine, the more electrons will go through this circuit. And as a consequence, 00:22:52.870 --> 00:22:58.030 there will be a current running through this current meter. That cool with everyone? OK. 00:22:58.030 --> 00:23:01.299 So we haven't yet measured the kinetic energy, though. How do we measure the kinetic energy? 00:23:01.299 --> 00:23:04.929 I want to know how much energy, with how much energy, were these electrons ejected. 00:23:04.929 --> 00:23:10.210 Well I can do that by the following clever trick. I'm going to put now a voltage source 00:23:10.210 --> 00:23:15.370 here, which I can tune the voltage of, with the voltage V. And what that's going to do 00:23:15.370 --> 00:23:19.960 is set up a potential difference across these and the energy in that is the charge times 00:23:19.960 --> 00:23:24.770 the potential difference. So I know that the potential difference it takes, so the amount 00:23:24.770 --> 00:23:31.020 of energy it takes to overcome this potential difference, is q times V. That cool? 00:23:31.020 --> 00:23:35.990 So now imagine I send in an electron-- I send in light and it leads an electron to jump 00:23:35.990 --> 00:23:41.660 across, and it has kinetic energy, kE. Well if the kinetic energy is less than this, will 00:23:41.660 --> 00:23:46.320 it get across? Not so much. It'll just fall back. But if the kinetic energy is greater 00:23:46.320 --> 00:23:51.360 than the energy it takes to cross, it'll cross and induce a current. 00:23:51.360 --> 00:23:58.780 So the upshot is that, as a function of the voltage, what I should see is that there is 00:23:58.780 --> 00:24:04.030 some critical minimum voltage. And depending on how you set up the sign, the sign could 00:24:04.030 --> 00:24:11.260 be the other way, but there's some critical minimal voltage where, for less voltage, the 00:24:11.260 --> 00:24:18.500 electron doesn't get across. And for any greater voltage-- or, sorry, for any closer to zero 00:24:18.500 --> 00:24:24.020 voltage, the electron has enough kinetic energy to get across. And so the current should increase. 00:24:24.020 --> 00:24:28.740 So there's a critical voltage, V-critical, where the current running through the system 00:24:28.740 --> 00:24:35.030 runs to zero. You make it harder for the electrons by making the voltage in magnitude even larger. 00:24:35.030 --> 00:24:38.390 You make it harder for the electrons to get across. None will get across. Make it a little 00:24:38.390 --> 00:24:45.470 easier, more and more will get across. And the current will go up. So what you want to 00:24:45.470 --> 00:24:49.830 do to measure this kinetic energy is you want to measure the critical voltage at which the 00:24:49.830 --> 00:24:57.440 current goes to zero. 00:24:57.440 --> 00:25:01.210 So now the question is what do we expect to see. And remember that things we can tune 00:25:01.210 --> 00:25:08.530 in this experiment are the intensity of the light, which is like e squared plus b squared. 00:25:08.530 --> 00:25:14.130 And we can tune the frequency of the light. We can vary that. Now does the total energy, 00:25:14.130 --> 00:25:18.919 does that frequency show up in the total energy of a classical electromagnetic wave? No. If 00:25:18.919 --> 00:25:25.950 it's an electromagnetic wave, it cancels out. You just get the total intensity, which is 00:25:25.950 --> 00:25:33.880 a square of the fields. So this is just like a harmonic oscillator. The energy is in the 00:25:33.880 --> 00:25:36.919 amplitude. The frequency of the oscillator doesn't matter. You push the swing harder, 00:25:36.919 --> 00:25:43.440 it gets more kinetic energy. It's got more energy. OK. 00:25:43.440 --> 00:25:48.740 So what do we expect to see as we vary, for example, the intensity? So here's a natural 00:25:48.740 --> 00:25:53.220 gas. If you take-- so you can think about the light here as getting a person literally, 00:25:53.220 --> 00:25:57.559 like get the person next to you to take a bat and hit a piece of metal. If they hit 00:25:57.559 --> 00:25:59.970 it really lightly they're probably not going to excite electrons with a lot of energy. 00:25:59.970 --> 00:26:03.840 If they just whack the heck out of it, then it wouldn't be too surprising if you get much 00:26:03.840 --> 00:26:06.860 more energy in the particles that come flying off. Hit it hard enough, things are just gonna 00:26:06.860 --> 00:26:09.980 shrapnel and disintegrate. 00:26:09.980 --> 00:26:20.900 The expectation here is the following. That if you have a more intense beam, then you 00:26:20.910 --> 00:26:25.510 should get more-- the electrons coming off should be more energetic. Because you're hitting 00:26:25.510 --> 00:26:37.370 them harder. And remember that the potential, which I will call V0, the stopping voltage. 00:26:37.370 --> 00:26:44.230 So therefore V0 should be greater in magnitude. 00:26:44.230 --> 00:26:49.850 So this anticipates that the way this curve should look as we vary the current as a function 00:26:49.850 --> 00:26:57.250 of v, if we have a low voltage-- sorry, if we have a low-intensity beam-- it shouldn't 00:26:57.250 --> 00:27:01.990 take too much potential just to impede the motion. 00:27:01.990 --> 00:27:04.880 But if we have a-- so this is a low intensity. 00:27:04.880 --> 00:27:09.960 But if we have a high-intensity beam, it should take a really large voltage to impede the 00:27:09.960 --> 00:27:14.250 electric flow, the electric current, because high-intensity beam you're just whacking those 00:27:14.250 --> 00:27:19.870 electrons really hard and they're coming off with a lot of kinetic energy. So this is high 00:27:19.870 --> 00:27:28.070 intensity. Everyone down with that intuition? This is what you get from Maxwell's electrodynamics. 00:27:28.070 --> 00:27:31.990 This is what you'd expect. 00:27:31.990 --> 00:27:40.660 And in particular, as we vary-- so this is our predictions-- in particular as we vary-- 00:27:40.660 --> 00:27:50.820 so this is 1, 2, with greater intensity. And the second prediction is that V-naught should 00:27:50.830 --> 00:27:55.169 be independent of frequency. Because the energy density and electromagnetic wave is independent 00:27:55.169 --> 00:28:04.600 of the frequency. It just depends on the amplitude. And I will use nu to denote the frequency. 00:28:04.600 --> 00:28:15.020 So those are the predictions that come from 8.02 and 8.03. But this is 8.04. And here's what 00:28:15.020 --> 00:28:21.880 the experimental results actually look like. So here's the intensity, here's the potential. 00:28:21.880 --> 00:28:26.230 And if we look at high potential, it turns out that-- if we look, sorry, if we look at 00:28:26.230 --> 00:28:32.770 intermediate potentials, it's true that the high intensity leads to a larger current and 00:28:32.770 --> 00:28:36.690 the low intensity leads to a lower current. 00:28:36.690 --> 00:28:44.330 But here's the funny thing that happens. As you go down to the critical voltage, their 00:28:44.330 --> 00:28:52.440 critical voltages are the same. What that tells you is that the kinetic energy kicked 00:28:52.440 --> 00:28:57.010 out-- or the kinetic energy of an electron kicked out of this piece of metal by the light 00:28:57.010 --> 00:29:03.530 is independent of how intense that beam is. No matter how intense that beam is, no matter 00:29:03.530 --> 00:29:09.120 how strong the light you shine on the material, the electrons all come out with the same energy. 00:29:09.120 --> 00:29:15.600 This would be like taking a baseball and hitting it with a really powerful swing or a really 00:29:15.600 --> 00:29:19.450 weak swing and seeing that the electron dribbles away with the same amount of energy. This 00:29:19.450 --> 00:29:25.140 is very counter-intuitive. 00:29:25.140 --> 00:29:32.690 But more surprisingly, V-naught is actually independent of intensity. But here's the real 00:29:32.690 --> 00:29:41.770 shocker. V-naught varies linearly in the frequency. What does change V-naught is changing the 00:29:41.770 --> 00:29:45.960 frequency of the light in this incident. That means that if you take an incredibly diffuse 00:29:45.960 --> 00:29:51.090 light-- incredibly diffuse light, you can barely see it-- of a very high frequency, 00:29:51.090 --> 00:29:56.710 then it takes a lot of energy to impede the electrons that come popping off. 00:29:56.710 --> 00:30:01.900 The electrons that come popping off have a large energy. But if you take a low-frequency 00:30:01.900 --> 00:30:07.720 light with extremely high intensity, then those electrons are really easy to stop. Powerful 00:30:07.720 --> 00:30:11.539 beam but low frequency, it's easy to stop those electrons. Weak little tiny beam at 00:30:11.539 --> 00:30:16.530 high frequency, very hard to stop the electrons that do come off. So this is very counter-intuitive 00:30:16.530 --> 00:30:23.730 and it doesn't fit at all with the Maxwellian picture. Questions about that? 00:30:23.730 --> 00:30:34.340 So this led Einstein to make a prediction. This was his 1905 result. One of his many 00:30:34.340 --> 00:30:38.679 totally breathtaking papers of that year. And he didn't really propose a model or a 00:30:38.679 --> 00:30:42.720 detailed theoretical understanding of this, but he proposed a very simple idea. And he 00:30:42.720 --> 00:30:47.990 said, look, if you want to fit this-- if you want to fit this experiment with some simple 00:30:47.990 --> 00:30:53.850 equations, here's the way to explain it. I claim-- I here means Einstein, not me-- I 00:30:53.850 --> 00:31:09.539 claim that light comes in packets or chunks with definite energy. And the energy is linearly 00:31:09.539 --> 00:31:14.120 proportional to the frequency. And our energy is equal to something times nu, and we'll 00:31:14.120 --> 00:31:18.780 call the coefficient h. 00:31:18.780 --> 00:31:31.820 The intensity of light, or the amplitude squared, the intensity is like the number of packets. 00:31:31.820 --> 00:31:36.580 So if you have a more intense beam at the same frequency, the energy of each individual 00:31:36.580 --> 00:31:44.070 chunk of light is the same. There are just a lot more chunks flying around. And so to 00:31:44.070 --> 00:31:48.350 explain the photoelectric effect, Einstein observed the following. Look, he said, the 00:31:48.350 --> 00:31:52.860 electrons are stuck under the metal. And it takes some work to pull them off. So now what's 00:31:52.860 --> 00:31:59.159 the kinetic energy of an electron that comes flying off-- whoops, k3. Bart might have a 00:31:59.159 --> 00:32:03.470 laugh about that one. Kinetic, kE, not 3. 00:32:03.470 --> 00:32:07.780 So the kinetic energy of electron that comes flying off, well, it's the energy deposited 00:32:07.780 --> 00:32:13.580 by the photon, the chunk of light, h-nu well we have to subtract off the work it took. 00:32:13.580 --> 00:32:18.070 Minus the work to extract the electron from the material. And you can think of this as 00:32:18.070 --> 00:32:24.820 how much energy does it take to suck it off the surface. And the consequence of this is 00:32:24.820 --> 00:32:34.809 that the kinetic energy of an electron should be-- look, if h-nu is too small, if the frequency 00:32:34.809 --> 00:32:37.850 is too low, then the kinetic energy would be negative. 00:32:37.850 --> 00:32:41.090 But that doesn't make any sense. You can't have negative kinetic energy. It's a strictly 00:32:41.090 --> 00:32:45.679 positive quantity. So it just doesn't work until you have a critical value where the 00:32:45.679 --> 00:32:50.460 frequency times h-- this coefficient-- is equal to the work it takes to extract. And 00:32:50.460 --> 00:32:55.960 after that, the kinetic energy rises with the frequency with a slope equal to h. And 00:32:55.960 --> 00:33:04.000 that fits the data like a champ. 00:33:04.000 --> 00:33:08.650 So no matter-- let's think about what this is saying again. No matter what you do, if 00:33:08.650 --> 00:33:13.130 your light is very low-frequency and you pick some definite piece of metal that has a very 00:33:13.130 --> 00:33:17.049 definite work function, very definite amount of energy it takes to extract electrons from 00:33:17.049 --> 00:33:23.610 the surface. No matter how intense your beam, if the frequency is insufficiently high, no 00:33:23.610 --> 00:33:26.799 electrons come off. None. 00:33:26.799 --> 00:33:30.840 So it turns out none is maybe a little overstatement because what you can have is two photon processes, 00:33:30.840 --> 00:33:34.309 where two chunks hit one electron at the right, just at the same time. Roughly speaking the 00:33:34.309 --> 00:33:37.950 same time. And they have twice the energy, but you can imagine that the probability of 00:33:37.950 --> 00:33:41.850 two photon hitting one electron at the same time of pretty low. So the intensity has to 00:33:41.850 --> 00:33:45.450 be preposterously high. And you see those sorts of multi-photon effects. But as long 00:33:45.450 --> 00:33:52.730 as we're not talking about insanely high intensities, this is an absolutely fantastic probe of the 00:33:52.730 --> 00:33:53.450 physics. 00:33:53.450 --> 00:33:57.650 Now there's a whole long subsequent story in the development of quantum mechanics about 00:33:57.650 --> 00:34:00.320 this particular effect. And it turns out that the photoelectric effect is a little more 00:34:00.320 --> 00:34:07.440 complicated than this. But the story line is a very useful one for organizing your understanding 00:34:07.440 --> 00:34:12.460 of the photoelectric effect. And in particular, this relation that Einstein proposed out of 00:34:12.460 --> 00:34:16.940 the blue, with no other basis. No one else had ever seen this sort of statement that 00:34:16.940 --> 00:34:22.699 the electrons, or that the energy of a beam of light should be made up of some number 00:34:22.699 --> 00:34:27.909 of chunks, each of which has a definite minimum amount of energy. 00:34:27.909 --> 00:34:33.859 So you can take what you've learned from 8.02 and 8.03 and extract a little bit more information 00:34:33.859 --> 00:34:39.639 out of this. So here's something you learned from 8.02. In 8.02 you learned that the energy 00:34:39.639 --> 00:34:44.239 of an electromagnetic wave is equal to c times the momentum carried by that wave-- whoops, 00:34:44.239 --> 00:34:51.509 over two. And in 8.03 you should have learned that the wavelength of an electromagnetic 00:34:51.509 --> 00:34:59.099 wave times the frequency is equal to the speed of light, C. 00:34:59.099 --> 00:35:07.539 And we just had Einstein tell us-- or declare, without further evidence, just saying, look 00:35:07.539 --> 00:35:13.809 this fits-- that the energy of a chunk of light should be h times the frequency. So 00:35:13.809 --> 00:35:16.960 if you combine these together, you get another nice relation that's similar to this one, 00:35:16.960 --> 00:35:25.269 which says that the momentum of a chunk of light is equal to h over lambda. So these 00:35:25.269 --> 00:35:29.789 are two enormously influential expressions which come out of this argument from the photoelectric 00:35:29.789 --> 00:35:33.279 effect from Einstein. And they're going to be-- their legacy will be with us throughout 00:35:33.279 --> 00:35:36.789 the rest of the semester. 00:35:36.789 --> 00:35:51.989 Now this coefficient has a name, and it was named after Planck. It's called Planck's Constant. 00:35:51.989 --> 00:35:55.339 And the reason that it's called Planck's Constant has nothing to do with the photoelectric effect. 00:35:55.339 --> 00:36:03.489 It was first this idea that an electromagnetic wave, that light, has an energy which is linearly 00:36:03.489 --> 00:36:07.469 proportional not to its intensity squared, none of that, but just linearly proportional 00:36:07.469 --> 00:36:13.339 to the frequency. First came up an analysis of black body radiation by Planck. And you'll 00:36:13.339 --> 00:36:16.690 understand, you'll go through this in some detail in 8.044 later in the semester. So I'm 00:36:16.690 --> 00:36:20.660 not going to dwell on it now, but I do want to give you a little bit of perspective on it. 00:36:20.660 --> 00:36:28.710 So Planck ran across this idea that E is equal to h/nu. Through the process of trying to 00:36:28.710 --> 00:36:34.829 fit an experimental curve. There was a theory of how much energy should be emitted by an 00:36:34.829 --> 00:36:39.329 object that's hot and glowing as a function of frequency. And that theory turned out to 00:36:39.329 --> 00:36:44.019 be in total disagreement with experiment. Spectacular disagreement. The curve for the 00:36:44.019 --> 00:36:48.109 theory went up, the curve for the experiment went down. They were totally different. 00:36:48.109 --> 00:36:52.819 So Planck set about writing down a function that described the data. Literally curve-fitting, 00:36:52.819 --> 00:36:58.069 that's all he was doing. And this is the depths of desperation to which he was led, was curve-fitting. 00:36:58.069 --> 00:37:02.749 He's an adult. He shouldn't be doing this, but he was curve-fitting. And so he fits the 00:37:02.749 --> 00:37:07.339 curve, and in order to get it to fit the only thing that he can get to work even vaguely 00:37:07.339 --> 00:37:13.299 well is if he puts in this calculation of h/nu. He says, well, maybe when I sum over 00:37:13.299 --> 00:37:17.569 all the possible energies I should restrict the energies which were proportional to the 00:37:17.569 --> 00:37:20.759 frequency. 00:37:20.759 --> 00:37:24.979 And it was forced on him because it fit from the function. Just functional analysis. Hated 00:37:24.979 --> 00:37:30.910 it. Hated it, he completely hated it. He was really frustrated by this. It fit perfectly, 00:37:30.910 --> 00:37:34.950 he became very famous. He was already famous, but he became ridiculously famous. Just totally 00:37:34.950 --> 00:37:40.539 loathed this idea. OK. So it's now become a cornerstone of quantum mechanics. But he 00:37:40.539 --> 00:37:41.549 wasn't so happy about it. 00:37:41.549 --> 00:37:46.579 And to give you a sense for how bold and punchy this paper by Einstein was that said, look, 00:37:46.579 --> 00:37:52.269 seriously. Seriously guys. e equals h/nu. Here's what Planck had to say when he wrote 00:37:52.269 --> 00:37:55.910 a letter of recommendation to get Einstein into the Prussian Academy of Sciences in 1917, 00:37:55.910 --> 00:38:01.170 or 1913. So he said, there is hardly one among the great problems in physics to which Einstein 00:38:01.170 --> 00:38:05.670 has not made an important contribution. That he may sometimes have missed the target in 00:38:05.670 --> 00:38:11.479 his speculations as in his hypothesis of photons cannot really be held too much against him. 00:38:11.479 --> 00:38:18.249 It's not possible to introduce new ideas without occasionally taking a risk. 00:38:18.249 --> 00:38:22.680 Einstein who subsequently went on to develop special relativity and general relativity 00:38:22.680 --> 00:38:28.559 and prove the existence of atoms and the best measurement of Avogadro's Constant, subsequently 00:38:28.559 --> 00:38:33.180 got the Nobel Prize. Not for Avogadro's Constant, not for proving the existence of atoms, not 00:38:33.180 --> 00:38:39.380 for relativity, but for photons. Because of guys like Planck, right. This is crazy. 00:38:39.380 --> 00:38:45.089 So this was a pretty bold idea. And here, to get a sense for why-- we're gonna leave 00:38:45.089 --> 00:38:51.599 that up because it's just sort of fun to see these guys scowling and smiling-- there is, 00:38:51.599 --> 00:38:57.339 incidentally there's a great book about Einstein's years in Berlin by Tom Levenson, who's a professor 00:38:57.339 --> 00:39:04.539 here. A great writer and a sort of historian of science. You should take a class from him, 00:39:04.539 --> 00:39:08.549 which is really great. But I encourage you to read this book. It talks about why Planck 00:39:08.549 --> 00:39:14.650 is not looking so pleased right there, among many other things. It's a great story. 00:39:14.650 --> 00:39:18.630 So let's step back for a second. Why was Planck so upset by this, and why was in fact everyone 00:39:18.630 --> 00:39:24.529 so flustered by this idea that it led to the best prize you can give a physicist. Apart 00:39:24.529 --> 00:39:36.450 from a happy home and, you know. I've got that one. That's the one that matters to me. 00:39:36.450 --> 00:39:42.529 So why is this so surprising? And the answer is really simple. We know that it's false. 00:39:42.529 --> 00:39:47.700 We know empirically, we've known for two hundred and some years that light is a wave. Empirically. 00:39:47.700 --> 00:39:52.069 This isn't like people are like, oh I think it'd be nice if it was a wave. It's a wave. 00:39:52.069 --> 00:39:56.799 So how do we know that? So this goes back to the double-slit experiment from Young. 00:39:56.799 --> 00:40:04.489 Young's performance of this was in 1803. Intimations of it come much earlier. But this is really 00:40:04.489 --> 00:40:09.609 where it hits nails to the wall. And here's the experiment. 00:40:09.609 --> 00:40:15.700 So how many people in here have not seen a double-slit experiment described? Yeah, exactly. 00:40:15.700 --> 00:40:18.880 OK. So I'm just going to quickly remind you of how this goes. 00:40:18.880 --> 00:40:23.339 So we have a source for waves. We let the waves get big until they're basically plane 00:40:23.339 --> 00:40:29.459 waves. And then we take a barrier. And we poke two slits in it. And these plane waves 00:40:29.459 --> 00:40:35.680 induce-- they act like sources at the slits and we get nu. And you get crests and troughs. 00:40:35.680 --> 00:40:38.579 And you look at some distant screen and you look at the pattern, and the pattern you get 00:40:38.579 --> 00:40:45.509 has a maximum. But then it falls off, and it has these wiggles, these interference fringes. 00:40:45.509 --> 00:40:49.799 These interference fringes are, of course, extremely important. And what's going on here 00:40:49.799 --> 00:40:55.579 is that the waves sometimes add in-- so the amplitude of the wave, the height of the wave, 00:40:55.579 --> 00:41:01.160 sometimes adds constructively and sometimes destructively. So that sometimes you get twice 00:41:01.160 --> 00:41:06.369 the height and sometimes you get nothing. 00:41:06.369 --> 00:41:11.859 So just because it's fun to see this, here's Young's actual diagram from his original note 00:41:11.859 --> 00:41:18.640 on the double-slit experiment. So a and b are the slits, and c, d and f are the [INAUDIBLE] 00:41:18.640 --> 00:41:27.690 on the screen, the distant screen. He drew it by hand. It's pretty good. 00:41:27.690 --> 00:41:32.039 So we've known for a very long time that light, because of the double-slit experiment, light 00:41:32.039 --> 00:41:35.119 is clearly wavy, it behaves like a wave. And what are the senses in which it behaves like 00:41:35.119 --> 00:41:44.940 a wave? There are two important senses here. The first is answered by the question, where 00:41:44.940 --> 00:41:55.430 did the wave hit the screen? So when we send in a wave, you know, I drop a stone, one big 00:41:55.430 --> 00:41:59.900 pulsive wave comes out. It splits into-- it leads to new waves being instigated here and 00:41:59.900 --> 00:42:07.700 over here. Where did that wave hit the screen? Anyone? 00:42:07.700 --> 00:42:09.040 AUDIENCE: Everywhere. 00:42:09.040 --> 00:42:12.259 PROFESSOR: Yeah, exactly. It didn't hit this wave-- the screen in any one spot. But some 00:42:12.259 --> 00:42:15.890 amplitude shows up everywhere. The wave is a distributed object, it does not exist at 00:42:15.890 --> 00:42:20.420 one spot, and it's by virtue of the fact that it is not a localized object-- it is not a 00:42:20.420 --> 00:42:27.910 point-like object-- that it can interfere with itself. The wave is a big large phenomena 00:42:27.910 --> 00:42:31.519 in a liquid, in some thing. 00:42:31.519 --> 00:42:37.299 So it's sort of essential that it's not a localized object. So not localized. The answer 00:42:37.299 --> 00:42:45.569 is not localized. And let's contrast this with what happens if you take this double-slit 00:42:45.569 --> 00:42:56.120 experiment and you do it with, you know, I don't know, take-- who. Hmm. Tim Wakefield. 00:42:56.120 --> 00:42:57.979 Let's give some love to that guy. 00:42:57.979 --> 00:43:03.729 So, baseball player. And have him throw baseballs at a screen with two slits in it. OK? Now 00:43:03.729 --> 00:43:10.650 he's got pretty good-- well, he's got terrible accuracy, actually. So every once in a while 00:43:10.650 --> 00:43:15.150 he'll make it through the slits. So let's imagine first blocking off-- what, he's a 00:43:15.150 --> 00:43:18.670 knuckle-baller, right-- so every once in a while it goes, the baseball will go through 00:43:18.670 --> 00:43:19.930 the slit. 00:43:19.930 --> 00:43:22.719 And let's think about what happens, so let's cover one slit. And what we expect to happen 00:43:22.719 --> 00:43:26.759 is, well, it'll go through more or less straight, but sometimes it'll scrape the edge, it'll 00:43:26.759 --> 00:43:30.769 go off to the side, and sometimes it'll come over here. But if you take a whole bunch of 00:43:30.769 --> 00:43:39.309 baseballs, and-- so any one baseball, where does it hit? Some spot. Right? One spot. Not 00:43:39.309 --> 00:43:40.519 distributed. One spot. 00:43:40.519 --> 00:43:44.739 And as a consequence, you know, one goes here, one goes there, one goes there. And now, there's 00:43:44.739 --> 00:43:50.059 nothing like interference effects, but what happens is as it sort of doesn't-- you get 00:43:50.059 --> 00:43:54.309 some distribution if you look at where they all hit. Yeah? Everyone cool with that? And 00:43:54.309 --> 00:43:59.839 if we had covered over this slot, or slit, and let the baseballs go through this one, 00:43:59.839 --> 00:44:00.729 same thing would have happened. 00:44:00.729 --> 00:44:04.650 Now if we leave them both open, what happens is sometimes it goes here, sometimes it goes 00:44:04.650 --> 00:44:07.670 here. So now it's pretty useful that we've got a knuckle-baller. And what you actually 00:44:07.670 --> 00:44:12.989 get is the total distribution looks like this. It's the sum of the two. But at any given 00:44:12.989 --> 00:44:16.200 time, any one baseball, you say, aha, the baseball either went through the top slit, 00:44:16.200 --> 00:44:18.650 and more or less goes up here. Or it went through the bottom slit and more or less goes 00:44:18.650 --> 00:44:28.219 down here. So for chunks-- so this is for waves-- for chunks or localized particles, 00:44:28.219 --> 00:44:43.190 they are localized. And as a consequence, we get no interference. 00:44:43.190 --> 00:44:55.509 So for waves, they are not localized, and we do get interference. Yes, interference. 00:44:55.509 --> 00:45:01.849 OK. So on your problem set, you're going to deal with some calculations involving these 00:45:01.849 --> 00:45:05.509 interference effects. And I'm going to brush over them. 00:45:05.509 --> 00:45:13.599 Anyway the point of the double-slit experiment is that whatever else you want to say about 00:45:13.599 --> 00:45:19.769 baseballs or anything else, light, as we've learned since 1803 in Young's double-slit 00:45:19.769 --> 00:45:23.569 experiment, light behaves like a wave. It is not localized, it hits the screen over 00:45:23.569 --> 00:45:28.369 its entire extent. And as a consequence, we get interference. The amplitudes add. The 00:45:28.369 --> 00:45:34.519 intensity is the square of the amplitude. If the intensities add-- so sorry, if the 00:45:34.519 --> 00:45:39.559 amplitudes add-- amplitude total is equal to a1 plus a2, the intensity, which is the 00:45:39.559 --> 00:45:57.920 square of a1 plus a2 squared, has interference terms, the cross terms, from this square. 00:45:57.920 --> 00:46:02.900 So light, from this point of view, is an electromagnetic wave. It interferes with itself. It's made 00:46:02.900 --> 00:46:08.700 of chunks. And I can't help but think about it this way, this is literally the metaphor 00:46:08.700 --> 00:46:18.160 I use in my head-- light is creamy and smooth like a wave. Chunks are very different. But 00:46:18.160 --> 00:46:25.089 here's the funny thing. Light is both smooth like a wave, it is also chunky. It is super 00:46:25.089 --> 00:46:31.900 chunky, as we have learned from the photoelectric effect. So light is both at once. So it's 00:46:31.900 --> 00:46:36.400 the best of both worlds. Everyone will be satisfied, unless you're not from the US, 00:46:36.400 --> 00:46:45.400 in which case this is deeply disturbing. So of course the original Superchunk is a band. 00:46:45.400 --> 00:46:49.309 So we've learned now from Young that light is a wave. We've learned from the photoelectric 00:46:49.309 --> 00:46:58.430 effect that light is a bunch of chunks. OK. Most experimental results are true. So how 00:46:58.430 --> 00:47:02.759 does that work? Well, we're gonna have to deal with that. 00:47:02.759 --> 00:47:07.339 But enough about light. If this is true of light, if light, depending on what experiment 00:47:07.339 --> 00:47:10.739 you do and how you do the experiment, sometimes it seems like it's a wave, sometimes it seems 00:47:10.739 --> 00:47:17.180 like it's a chunk or particle, which is true? Which is the better description? 00:47:17.180 --> 00:47:21.739 So it's actually worthwhile to not think about light all the time. Let's think about something 00:47:21.739 --> 00:47:27.099 more general. Let's stick to electrons. So as we saw from yesterday's lecture, you probably 00:47:27.099 --> 00:47:30.589 want to be a little bit wary when thinking about individual electrons. Things could be 00:47:30.589 --> 00:47:34.999 a little bit different than your classical intuition. But here's a crucial thing. Before 00:47:34.999 --> 00:47:38.449 doing anything else, we can just think, which one of these two is more likely to describe 00:47:38.449 --> 00:47:39.799 electrons well. 00:47:39.799 --> 00:47:46.190 Well electrons are localized. When you throw an electron at a CRT, it does not hit the 00:47:46.190 --> 00:47:49.199 whole CRT with a wavy distribution. When you take a single electron and you throw it at 00:47:49.199 --> 00:47:54.699 a CRT, it goes ping and there's a little glowing spot. Electrons are localized. And we know 00:47:54.699 --> 00:48:02.940 that localized things don't lead to interference. 00:48:02.940 --> 00:48:06.279 Some guys at Hitachi, really good scientists and engineers, developed some really awesome 00:48:06.279 --> 00:48:10.019 technology a couple of decades ago. They were trying to figure out a good way to demonstrate 00:48:10.019 --> 00:48:13.680 their technology. And they decided that you know what would be really awesome, this thought 00:48:13.680 --> 00:48:16.579 experiment that people have always talked about that's never been done really well, 00:48:16.579 --> 00:48:20.499 of sending an electron through a two-slitted experiment. In this case it was like ten slits 00:48:20.499 --> 00:48:24.910 effectively, it was a grading. Send an electron, a bunch of electrons, one at a time, throw 00:48:24.910 --> 00:48:28.529 the electron, wait. Throw the electron, wait. Like our French guy with the boat. 00:48:28.529 --> 00:48:34.349 So do this experiment with our technology and let's see what happens. And this really 00:48:34.349 --> 00:48:42.269 is one of my favorite-- let's see, how we close these screens-- aha. OK. This is going 00:48:42.269 --> 00:48:50.180 to take a little bit of-- and it's broken. No, no. Oh that's so sad. 00:48:50.180 --> 00:48:57.620 AUDIENCE: [LAUGHTER] 00:48:57.620 --> 00:49:07.440 PROFESSOR: Come on. I'm just gonna let-- let's see if we can, we'll get part of the way. 00:49:07.440 --> 00:49:11.729 I don't want to destroy it. So what they actually did is they said, look, let's-- we want to 00:49:11.729 --> 00:49:15.839 see what happens. We want to actually do this experiment because we're so awesome at Hitachi 00:49:15.839 --> 00:49:22.289 Research Labs, so let's do it. So here's what they did. And I'm going to turn off the light. 00:49:22.289 --> 00:49:29.599 And I set this to some music because I like it. 00:49:29.599 --> 00:49:37.529 OK here's what's happening. One at a time, individual photons. 00:49:37.529 --> 00:49:55.280 [MUSIC PLAYING] 00:49:55.280 --> 00:50:05.979 PROFESSOR: So they look pretty localized. There's not a whole lot of structure. Now 00:50:05.979 --> 00:50:13.400 they're going to start speeding it up. It's 100 times the actual speed. 00:50:13.400 --> 00:50:41.240 [MUSIC PLAYING] 00:50:41.240 --> 00:50:43.520 PROFESSOR: Eh? Yeah. 00:50:43.540 --> 00:50:49.280 AUDIENCE: [APPLAUSE] 00:50:49.280 --> 00:50:55.580 PROFESSOR: So those guys know what they're doing. Let's-- there were go. So I think I 00:50:55.589 --> 00:51:00.509 don't know of a more vivid example of electron interference than that one. It's totally obvious. 00:51:00.509 --> 00:51:04.069 You see individual electrons. They run through the apparatus. You wait, they run through 00:51:04.069 --> 00:51:08.529 the apparatus. You wait. One at a time, single electron, like a baseball being pitched through 00:51:08.529 --> 00:51:12.660 two slits, and what you see is an interference effect. But you don't see the interference 00:51:12.660 --> 00:51:16.400 effect like you do from light, from waves on the sea. 00:51:16.400 --> 00:51:20.079 You see the interference effect by looking at the cumulative stacking up of all the electrons 00:51:20.079 --> 00:51:25.680 as they hit. Look at where all the electrons hit one at a time. So is an electron behaving 00:51:25.680 --> 00:51:35.339 like a wave in a pond? No. Does a wave in a pond at a spot? No. It's a distributed beast. 00:51:35.339 --> 00:51:40.650 OK yes, it interferes, but it's not localized. Well is it behaving like a baseball? Well 00:51:40.650 --> 00:51:41.969 it's localized. 00:51:41.969 --> 00:51:47.440 But on-- when I look at a whole bunch of electrons, they do that. They seem to interfere, but 00:51:47.440 --> 00:51:50.079 there's only one electron going through at a time. So in some sense it's interfering 00:51:50.079 --> 00:51:54.239 with itself. How does that work? Is an electron a wave? 00:51:54.239 --> 00:51:56.569 AUDIENCE: Yes. 00:51:56.569 --> 00:52:00.130 PROFESSOR: Does an electron hit at many spots at once? 00:52:00.130 --> 00:52:00.880 AUDIENCE: No. 00:52:00.880 --> 00:52:08.920 PROFESSOR: No. So is an electron a wave. No. Is an electron a baseball? No. It's an electron. 00:52:08.920 --> 00:52:14.029 So this is something you're going to have to deal with, that every once in awhile we 00:52:14.029 --> 00:52:17.150 have these wonderful moments where it's useful to think about an electron as behaving in 00:52:17.150 --> 00:52:21.699 a wave-like sense. Sometimes it's useful to think about it as behaving in a particle-like 00:52:21.699 --> 00:52:25.630 sense. But it is not a particle like you normally conceive of a baseball. And it is not a wave 00:52:25.630 --> 00:52:35.680 like you normally conceive of a wave on the surface of a pond. It's an electron. 00:52:35.680 --> 00:52:41.229 I like to think about this like an elephant. If you're closing your eyes and you walk up 00:52:41.229 --> 00:52:44.670 to an elephant, you might think like I've got a snake and I've got a tree trunk and, 00:52:44.670 --> 00:52:48.739 you know, there's a fan over here. And you wouldn't know, like, maybe it's a wave, maybe 00:52:48.739 --> 00:52:52.650 it's a particle, I can't really tell. But if you could just see the thing the way it 00:52:52.650 --> 00:52:57.569 is, not through the preconceived sort of notions you have, you'd see it's an elephant. Yes, 00:52:57.569 --> 00:53:03.709 that is the Stata Center. So-- look, everything has to happen sometime, right? 00:53:03.709 --> 00:53:06.780 AUDIENCE: [LAUGHTER] 00:53:06.780 --> 00:53:12.600 PROFESSOR: So Heisenberg-- it's often, people often give the false impression in popular 00:53:12.609 --> 00:53:16.369 books on physics, so I want to subvert this, that in the early days of quantum mechanics, 00:53:16.369 --> 00:53:23.609 the early people like Born and Oppenheimer and Heisenberg who invented quantum mechanics, 00:53:23.609 --> 00:53:26.880 they were really tortured about, you know, is it an electron, is it a wave. It's a wave-particle 00:53:26.880 --> 00:53:31.740 duality. It's both. And this is one of the best subversions of that sort of silliness 00:53:31.740 --> 00:53:32.300 that I know of. 00:53:32.319 --> 00:53:36.019 And so what Heisenberg says, the two mental pictures which experiments lead us to form, 00:53:36.019 --> 00:53:41.259 the one of particles the other waves, are both incomplete and have the validity of analogies, 00:53:41.259 --> 00:53:46.099 which are accurate only in limited cases. The apparent duality rises in the limitation 00:53:46.099 --> 00:53:50.390 of our language. And then he goes on to say, look, you developed your intuition by throwing 00:53:50.390 --> 00:53:56.239 rocks and, you know, swimming. And, duh, that's not going to be very good for atoms. 00:53:56.239 --> 00:54:01.609 So this will be posted, it's really wonderful. His whole lecture is really-- the lectures 00:54:01.609 --> 00:54:05.440 are really quite lovely. And by the way, that's him in the middle there, Pauley all the way 00:54:05.440 --> 00:54:12.279 on the right. I guess they were pleased. OK so that's the Hitachi thing. 00:54:12.279 --> 00:54:19.539 So now let's pick up on this, though. Let's pick up on this and think about what happens. 00:54:19.539 --> 00:54:23.599 I want to think in a little more detail about this Hitachi experiment. And I want to think 00:54:23.599 --> 00:54:28.099 about it in the context of a simple two-slit experiment. So here's our source of electrons. 00:54:28.099 --> 00:54:31.690 It's literally a gun, an electron gun. And it's firing off electrons. And here's our 00:54:31.690 --> 00:54:37.259 barrier, and it has two slits in it. 00:54:37.259 --> 00:54:44.049 And we know that any individual electron hits its own spot. But when we take many of them, 00:54:44.049 --> 00:54:48.380 we get an interference effect. We get interference fringes. And so the number that hit a given 00:54:48.380 --> 00:54:57.390 spot fill up, construct this distribution. So then here's the question I want to ask. 00:54:57.390 --> 00:55:01.839 When I take a single electron, I shoot one electron at a time through this experiment, 00:55:01.839 --> 00:55:06.430 one electron. It could go through the top slit, it could go through the bottom slit. 00:55:06.430 --> 00:55:12.960 While it's inside the apparatus, which path does it take? 00:55:12.960 --> 00:55:15.920 AUDIENCE: Superposition. 00:55:15.920 --> 00:55:17.939 PROFESSOR: Good. So did it take the top path? 00:55:17.939 --> 00:55:18.799 AUDIENCE: No. 00:55:18.799 --> 00:55:20.249 PROFESSOR: How do you know? 00:55:20.249 --> 00:55:23.400 [INTERPOSING VOICES] 00:55:23.400 --> 00:55:28.959 PROFESSOR: Good, let's block the bottom, OK, to force it to go through the top slit. So 00:55:28.959 --> 00:55:32.619 we'll block the bottom slit. Now the only electrons that make it through go through 00:55:32.619 --> 00:55:37.839 the top slit. Half of them don't make it through. But those that do make it through give you 00:55:37.839 --> 00:55:43.390 this distribution. No interference. But I didn't tell you these are hundreds of thousands 00:55:43.390 --> 00:55:47.430 of kilometers apart, the person who threw in the electron didn't know whether there 00:55:47.430 --> 00:55:50.599 was a barrier here. The electron, how could it possibly know whether there was a barrier 00:55:50.599 --> 00:55:52.089 here if you went through the top. 00:55:52.089 --> 00:55:57.719 This is exactly like our boxes. It's exactly like our box. Did it go through-- an electron, 00:55:57.719 --> 00:56:03.229 when the slits are both open and we know that ensemble average it will give us an interference 00:56:03.229 --> 00:56:08.329 effect, did the electron inside the apparatus go through the top path? No. Did it go through 00:56:08.329 --> 00:56:13.489 the bottom path? Did it go through both? Because we only see one electron. Did it go through 00:56:13.489 --> 00:56:14.969 neither? It is in a-- 00:56:14.969 --> 00:56:16.360 AUDIENCE: Superposition. 00:56:16.360 --> 00:56:19.140 PROFESSOR: --of having gone through the top and the bottom. Of being along the top half 00:56:19.150 --> 00:56:25.519 and being along the bottom path. This is a classic example of the two-box experiment. 00:56:25.519 --> 00:56:34.529 OK. So you want to tie that together. 00:56:34.529 --> 00:56:37.779 So let's nuance this just a little bit, though, because it's going to have an interesting 00:56:37.779 --> 00:56:47.650 implication for gravity. So here's the nuance I want to pull on this one. Let's cheat. OK. 00:56:47.650 --> 00:56:53.939 Suppose I want to measure which slit the electron actually did go through. How might I do that? 00:56:53.939 --> 00:56:57.630 Well I could do the course thing I've been doing which is I could block it and just catch 00:56:57.630 --> 00:57:02.420 the-- catch electrons that go through in that spot. But that's a little heavy-handed. Probably 00:57:02.420 --> 00:57:03.529 I can do something a little more delicate. 00:57:03.529 --> 00:57:11.979 And so here's the more delicate thing I'm going to do. I want to build a detector that 00:57:11.979 --> 00:57:17.259 uses very, very, very weak light, extremely weak light, to detect whether the particle 00:57:17.259 --> 00:57:20.920 went through here or here. And the way I can do that is I can sort of shine light through 00:57:20.920 --> 00:57:27.380 and-- I'm gonna, you know, bounce-- so here's my source of light. And I'll be able to tell 00:57:27.380 --> 00:57:31.779 whether the electron went through this slit or it went through this slit. Cool? 00:57:31.779 --> 00:57:38.479 So imagine I did that. So obviously I don't want to use some giant, huge, ultra high-energy 00:57:38.479 --> 00:57:41.279 laser because it would just blast the thing out of the way. It would destroy the experiment. 00:57:41.279 --> 00:57:45.979 So I wanna something very diffuse, very low energy, very low intensity electromagnetic 00:57:45.979 --> 00:57:51.209 wave. And the idea here is that, OK, it's true that when I bounce this light off an 00:57:51.209 --> 00:57:56.439 electron, let's say it bounces off an electron here, it's true it's going impart some momentum 00:57:56.439 --> 00:58:00.079 and the electron's gonna change its course. But if it's really, really weak, low energy 00:58:00.079 --> 00:58:03.199 light, then it's-- it's gonna deflect only a little tiny bit. 00:58:03.199 --> 00:58:08.569 So it will change the pattern I get over here. But it will change it in some relatively minor 00:58:08.569 --> 00:58:13.749 way because I've just thrown in very, very low energy light. Yeah? That make sense? So 00:58:13.749 --> 00:58:24.320 this is the experiment I want to do. This experiment doesn't work. Why. 00:58:24.320 --> 00:58:27.160 AUDIENCE: You know which slit it went through. 00:58:27.180 --> 00:58:31.100 PROFESSOR: No. It's true that it turns out that those are correlated facts, but here's 00:58:31.109 --> 00:58:36.089 the problem. I can run this experiment without anyone actually knowing what happens until 00:58:36.089 --> 00:58:42.170 long afterwards. So knowing doesn't seem to play any role in it. It's very tempting often 00:58:42.170 --> 00:58:46.170 to say, no, but it turns out that it's really not about what you know. It's really just 00:58:46.170 --> 00:58:47.499 about the experiment you're doing. 00:58:47.499 --> 00:58:53.140 So what principle that we've already run into today makes it impossible to make this work? 00:58:53.140 --> 00:58:58.269 If I want to shine really low-energy, really diffuse light through, and have it scatter 00:58:58.269 --> 00:59:01.580 weakly. Yeah. 00:59:01.580 --> 00:59:05.400 AUDIENCE: Um, light is chunky. 00:59:05.400 --> 00:59:10.660 PROFESSOR: Yeah, exactly. That's exactly right. So when I say really low-energy light, I don't-- 00:59:10.670 --> 00:59:14.549 I really can't mean, because we've already done this experiment, I cannot possibly mean 00:59:14.549 --> 00:59:20.499 low intensity. Because intensity doesn't control the energy imparted by the light. The thing 00:59:20.499 --> 00:59:25.079 that controls the energy imparted by a collision of the light with the electron is the frequency. 00:59:25.079 --> 00:59:28.999 The energy in a chunk of light is proportional to the frequency. 00:59:28.999 --> 00:59:33.499 So now if I want to make the effect the energy or the momentum, similarly-- the momentum, 00:59:33.499 --> 00:59:39.229 where did it go-- remember the momentum goes like h over lambda. If I want to make the 00:59:39.229 --> 00:59:42.079 energy really low, I need to make the frequency really low. Or if I want to make the momentum 00:59:42.079 --> 00:59:47.369 really low, I need to make the wavelength what? Really big. Right? So in order to make 00:59:47.369 --> 00:59:51.489 the momentum imparted by this photon really low, I need to make the wavelength really 00:59:51.489 --> 00:59:52.089 long. 00:59:52.089 --> 00:59:58.299 But now here's the problem. If I make the wavelength really long, so if I use a really 00:59:58.299 --> 01:00:03.380 long-wavelengthed wave, like this long of a wavelength, are you ever going to be able 01:00:03.380 --> 01:00:07.369 to tell which slit it went through? No, because the particle could have been anywhere. It 01:00:07.369 --> 01:00:10.739 could have scattered this light if it was here, if it was here, if it was here, right? 01:00:10.739 --> 01:00:15.569 In order to measure where the electron is to some reasonable precision-- so, for example, 01:00:15.569 --> 01:00:19.599 to this sort of wavelength, I need to be able to send in light with a wavelength that's 01:00:19.599 --> 01:00:25.479 comparable to the scale that I want to measure. And it turns out that if you run through and 01:00:25.479 --> 01:00:30.589 just do the calculation, suppose I send in-- and this is done in the books, in I think 01:00:30.589 --> 01:00:37.029 all four, but this is done in the books on the reading list-- if you send in a wave with 01:00:37.029 --> 01:00:41.719 a short enough wavelength to be able to distinguish between these two slits, which slit did it 01:00:41.719 --> 01:00:47.309 go through, the momentum that it imparts precisely watches-- washes out is just enough to wash 01:00:47.309 --> 01:00:52.509 out the interference effect, and break up these fringes so you don't see interference 01:00:52.509 --> 01:00:55.229 effects. 01:00:55.229 --> 01:00:59.880 It's not about what you know. It's about the particulate nature of light and the fact that 01:00:59.880 --> 01:01:06.880 the momentum of a chunk of light goes like h over lambda. OK? But this tells you something 01:01:06.880 --> 01:01:13.979 really interesting. Did I have to use light to do this measurement? I could have sent 01:01:13.979 --> 01:01:17.650 in anything, right? I didn't have to bounce light off these things. 01:01:17.650 --> 01:01:24.519 I could have bounced off gravitational waves. So if I had a gravitational wave detector, 01:01:24.519 --> 01:01:29.939 so-- Matt works on gravitational wave detectors, and so, I didn't tell you this but Matt gave 01:01:29.939 --> 01:01:34.420 me a pretty killer gravitational wave detector. It's, you know, here it is. There's my awesome 01:01:34.420 --> 01:01:38.130 gravitational wave detector. And I'm now going to build supernova. OK. 01:01:38.130 --> 01:01:40.519 And they are creeping under this black hole, and it's going to create giant gravitational 01:01:40.519 --> 01:01:44.369 waves. And we're gonna use those gravitational waves and detect them with the super advanced 01:01:44.369 --> 01:01:48.859 LIGO. And I'm gonna detect which slit it went through. But gravitational waves, those aren't 01:01:48.859 --> 01:01:52.670 photons. So I really can make a low-intensity gravitational wave, and then I can tell which 01:01:52.670 --> 01:01:59.429 slit it went through without destroying the interference effect. That would be awesome. 01:01:59.429 --> 01:02:05.699 What does that tell you about gravitational waves? They must come in chunks. In order 01:02:05.699 --> 01:02:09.679 for this all to fit together logically, you need all the interactions that you could scatter 01:02:09.679 --> 01:02:15.029 off this to satisfy these quantization properties. But the energy is proportional to the frequency. 01:02:15.029 --> 01:02:18.979 The line I just gave you is a heuristic. And making it precise is one of the great challenges 01:02:18.979 --> 01:02:23.890 of modern contemporary high-energy physics, of dealing with the quantum mechanics and 01:02:23.890 --> 01:02:24.839 gravity together. 01:02:24.839 --> 01:02:30.140 But this gives you a strong picture of why we need to treat all forces in all interactions 01:02:30.140 --> 01:02:39.589 quantum-mechanically in order for the world to be consistent. OK. Good. OK, questions 01:02:39.589 --> 01:02:51.679 at this point? OK. So-- oh, I forgot about this one-- so there are actually two more. 01:02:51.679 --> 01:02:55.029 So I want to just quickly show you-- well, OK. 01:02:55.029 --> 01:02:59.549 So, this is a gorgeous experiment. So remember I told you the story of the guy with the boat 01:02:59.549 --> 01:03:05.029 and the opaque wall and it turns out that's a cheat. It turns out that this opaque screen 01:03:05.029 --> 01:03:11.939 doesn't actually give you quantum mechanically isolated photons. They're still, in a very 01:03:11.939 --> 01:03:17.179 important way, classical. So this experiment was done truly with a source that gives you 01:03:17.179 --> 01:03:20.359 quantum mechanically isolated single photons, one at a time. 01:03:20.359 --> 01:03:26.759 So this is the analogue of the Hitachi experiment. And it was done by this pretty awesome Japanese 01:03:26.759 --> 01:03:30.599 group some number of years ago. And I just want to emphasize that it gives you exactly 01:03:30.599 --> 01:03:34.519 the same effects. We see that photons-- this should look essentially identical to what 01:03:34.519 --> 01:03:37.920 we saw at the end of the Hitachi video. And that's because it's exactly the same physics. 01:03:37.920 --> 01:03:42.369 It's a grating with something like 10 slits and individual particles going through one 01:03:42.369 --> 01:03:45.788 at a time and hitting the screen and going, bing. 01:03:45.788 --> 01:03:53.949 So what you see is the light going, bing, on a CCD. It's a pretty spectacular experience. 01:03:53.949 --> 01:03:58.509 So let's get back to electrons. I want another probe of whether electrons are really waves 01:03:58.509 --> 01:04:03.390 or not. So this other experiment-- again, you're going to study this on your problem 01:04:03.390 --> 01:04:11.259 set-- this other experiment was done by a couple of characters named Davisson and Germer. 01:04:11.259 --> 01:04:15.839 And in this experiment, what they did is they took a crystal, and a crystal is just a lattice 01:04:15.840 --> 01:04:25.600 of regularly-located ions, like diamond or something. Yeah? 01:04:25.600 --> 01:04:27.540 AUDIENCE: Before you go on I guess, 01:04:27.540 --> 01:04:33.900 I wanted to ask if the probability of a photon or an electron going through the 10 slits is about the same? 01:04:33.900 --> 01:04:35.560 PROFESSOR: Is what, sorry? 01:04:35.560 --> 01:04:36.839 AUDIENCE: Is exactly the same. 01:04:36.839 --> 01:04:38.549 PROFESSOR: You mean for different electrons? 01:04:38.549 --> 01:04:38.839 AUDIENCE: Yeah. 01:04:38.839 --> 01:04:42.069 PROFESSOR: Well they can be different if the initial conditions are different. But they 01:04:42.069 --> 01:04:46.599 could be-- if the initial conditions are the same, then the probabilities are identical. 01:04:46.599 --> 01:04:50.379 So every electron behaves identically to every other electron in that sense. Is that what 01:04:50.380 --> 01:04:51.380 you were asking? 01:04:51.380 --> 01:04:58.140 AUDIENCE: It is actually like through any [INAUDIBLE] the probability of it going like [INAUDIBLE]? 01:04:58.140 --> 01:05:02.200 PROFESSOR: Sure, absolutely. So the issue there is just a technological one of trying 01:05:02.219 --> 01:05:07.049 to build a beam that's perfectly columnated. And that's just not doable. So there's always 01:05:07.049 --> 01:05:11.880 some dispersion in your beam. So in practice it's very hard to make them identical, but 01:05:11.880 --> 01:05:16.939 in principle they could be if you were infinitely powerful as an experimentalist, which-- again, 01:05:16.939 --> 01:05:19.910 I was banned from the lab, so not me. 01:05:19.910 --> 01:05:23.469 So here's our crystal. You could think of this as diamond or nickel or whatever. I think 01:05:23.469 --> 01:05:32.140 they actually use nickel but I don't remember exactly. And they sent in a beam of electrons. 01:05:32.140 --> 01:05:38.299 So they send in a beam of electrons, and what they discover is that if you send in these 01:05:38.299 --> 01:05:44.390 electrons and watch how they scatter at various different angles-- I'm going to call the angle 01:05:44.390 --> 01:05:54.059 here of scattering theta-- what they discover is that the intensity of the reflected beam, 01:05:54.059 --> 01:06:03.099 as a function of theta, shows interference effects. 01:06:03.099 --> 01:06:06.059 And in particular they gave a whole calculation for this, which I'm not going to go through 01:06:06.059 --> 01:06:09.640 right now because it's not terribly germane for us-- you're going to go through it on 01:06:09.640 --> 01:06:12.679 your problem set, so that'll be good and it's a perfect thing for your recitation instructors 01:06:12.679 --> 01:06:17.660 to go through. But the important thing is the upshot. So if the distance between these 01:06:17.660 --> 01:06:24.630 crystal planes is L-- or, sorry, d-- let me call it d. If the distance between the crystal 01:06:24.630 --> 01:06:31.059 planes is d, what they discover is that the interference effects that they observed, these 01:06:31.059 --> 01:06:40.429 maxima and minima, are consistent with the wavelength of light. Or, sorry, with the electrons 01:06:40.429 --> 01:06:46.288 behaving as if they were waves with a definite wavelength, with a wavelength lambda being 01:06:46.288 --> 01:06:56.239 equal to some integer, n, over 2d sine theta. 01:06:56.239 --> 01:07:01.449 So this is the data-- these are the data they actually saw, data are plural. And these are 01:07:01.449 --> 01:07:06.049 the data they actually saw. And they infer from this that the electrons are behaving 01:07:06.049 --> 01:07:11.079 as if they were wave-like with this wavelength. And what they actually see are individual 01:07:11.079 --> 01:07:13.839 electrons hitting one by one. Although in their experiment, they couldn't resolve individual 01:07:13.839 --> 01:07:15.799 electrons. But that is what they see. 01:07:15.799 --> 01:07:21.538 And so in particular, plugging all of this back into the experiment, you send in the 01:07:21.538 --> 01:07:24.660 electrons with some energy, which corresponds to some definite momentum. This leads us back 01:07:24.660 --> 01:07:29.809 to the same expression as before, that the momentum is equal to h over lambda, with this 01:07:29.809 --> 01:07:35.229 lambda associated. So it turns out that this is correct. 01:07:35.229 --> 01:07:40.420 So the electrons diffract off the crystal as if they have a momentum which comes with 01:07:40.420 --> 01:07:48.759 a definite wavelength corresponding to its momentum. So that's experimental result-- 01:07:48.759 --> 01:07:53.999 oh, I forgot to check off four-- that's experimental result five, that electrons diffract. We already 01:07:53.999 --> 01:07:57.959 saw the electron diffraction. 01:07:57.959 --> 01:08:04.150 So something to emphasize is that-- so these experiments as we've described them were done 01:08:04.150 --> 01:08:09.559 with photons and with electrons, but you can imagine doing the experiments with soccer 01:08:09.559 --> 01:08:14.390 balls. This is of course hard. Quantum effects for macroscopic objects are usually insignificantly 01:08:14.390 --> 01:08:19.830 small. However, this experiment was done with Buckyballs, which are the same shape as soccer 01:08:19.830 --> 01:08:26.189 balls in some sense. But they're huge, they're gigantic objects. So here's the experiment 01:08:26.189 --> 01:08:31.819 in which this was actually done. So these guys are just totally amazing. So this is 01:08:31.819 --> 01:08:38.580 Zellinger's lab. And it doesn't look like all-- I mean it looks kind of, you know. It's 01:08:38.580 --> 01:08:41.420 hideous, right? I mean to a theorist it's like, come on, you've got to be kidding that 01:08:41.420 --> 01:08:42.710 that's-- 01:08:42.710 --> 01:08:47.640 But here's what a theorist is happy about. You know, because it looks simple. We really 01:08:47.640 --> 01:08:52.318 love lying to ourselves about that. So here's an over. We're going to cook up some Buckyballs 01:08:52.318 --> 01:08:57.000 and emit them with some definite known thermal energy. Known to some accuracy. We're going 01:08:57.000 --> 01:08:59.830 to columnate them by sending them through a single slit, and then we're going to send 01:08:59.830 --> 01:09:03.000 them through a diffraction grating which, again, is just a whole bunch of slits. 01:09:03.000 --> 01:09:09.818 And then we're going to image them using photo ionization and see where they pop through. 01:09:09.818 --> 01:09:16.559 So here is the horizontal position of this wave along the grating, and this is the number 01:09:16.559 --> 01:09:20.660 that come through. This is literally one by one counts because they're going bing, bing, 01:09:20.660 --> 01:09:25.479 bing, as a c60 molecule goes through. So without the grating, you just get a peek. But with 01:09:25.479 --> 01:09:29.540 the grating, you get the side bands. You get interference fringes. 01:09:29.540 --> 01:09:36.910 So these guys, again, they're going through one by one. A single Buckyball, 60 carbons, 01:09:36.910 --> 01:09:41.479 going through one by one is interfering with itself. This is a gigantic object by any sort 01:09:41.479 --> 01:09:47.899 of comparison to single electrons. And we're seeing these interference fringes. 01:09:47.899 --> 01:09:51.160 So this is a pretty tour de force experiment, but I just want to emphasize that if you could 01:09:51.160 --> 01:09:55.910 do this with your neighbor, it would work. You'd just have to isolate the system well 01:09:55.910 --> 01:10:02.559 enough. And that's a technological challenge but not an in-principle one. 01:10:02.559 --> 01:10:16.460 OK. So we have one last experimental facts to deal with. And this is Bell's Inequality, 01:10:16.460 --> 01:10:24.940 and this is my favorite one. So Bell's Inequality for many years languished in obscurity until 01:10:24.940 --> 01:10:28.960 someone realized that it could actually be done beautifully in an experiment that led 01:10:28.960 --> 01:10:32.309 to a very concrete experiment that they could actually do and that they wanted to do. 01:10:32.309 --> 01:10:39.460 And we now think of it as an enormously influential idea which nails the coffin closed for classical 01:10:39.460 --> 01:10:46.110 mechanics. And it starts with a very simple question. I claim that the following inequality 01:10:46.110 --> 01:10:54.720 is true: the number of undergraduate-- of the number of people in the room who are undergraduates, 01:10:54.720 --> 01:11:00.350 which I'll denote as U-- and not blonde, which I will denote as bar B-- so undergraduates 01:11:00.350 --> 01:11:04.840 who are not blonde-- actually let me write this out in English. It's gonna be easier. 01:11:04.840 --> 01:11:18.530 Number who are undergrads and not blonde plus the number of people in the room who are blonde 01:11:18.530 --> 01:11:27.970 but not from Massachusetts is strictly greater than or equal to the number of people in the 01:11:27.980 --> 01:11:36.960 room who are undergraduates and not from Massachusetts. 01:11:36.960 --> 01:11:39.960 I claim that this is true. I haven't checked 01:11:39.960 --> 01:11:41.860 in this room. But I claim that this is true. 01:11:41.860 --> 01:11:47.860 So let's check. How many people are undergraduates who are not blonde? OK this is going to-- 01:11:47.860 --> 01:11:56.110 jeez. OK that's-- so, lots. OK. How many people are blonde but not from Massachusetts? OK. 01:11:56.110 --> 01:12:01.860 A smattering. Oh God, this is actually going to be terrible. 01:12:01.860 --> 01:12:11.860 AUDIENCE: [LAUGHTER] 01:12:11.870 --> 01:12:21.559 PROFESSOR: Shoot. This is a really large class. OK. Small. And how many people are undergraduates 01:12:21.559 --> 01:12:25.520 who are not from Massachusetts? Yeah, this-- oh God. This counting is going to be-- so 01:12:25.520 --> 01:12:28.600 let's-- I'm going to do this just so I can do the counting with the first two rows here. 01:12:28.600 --> 01:12:30.710 OK. My life is going to be easier this way. 01:12:30.710 --> 01:12:34.270 So how many people in the first two rows, in the center section, are undergraduates 01:12:34.270 --> 01:12:40.550 but not blonde? One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, 01:12:40.550 --> 01:12:45.790 thirteen, fourteen. We could dispute some of those, but we'll take it for the moment. 01:12:45.790 --> 01:12:52.110 So, fourteen. You're probably all undergraduates. So blonde and not from Massachusetts. One. 01:12:52.110 --> 01:13:01.180 Awesome. Undergraduates not from Massachusetts. One, two, three, four, five, six, seven, eight, 01:13:01.180 --> 01:13:07.460 nine, ten, eleven, twelve, thirteen, fourteen, fifteen. Equality. 01:13:07.460 --> 01:13:09.030 AUDIENCE: [LAUGHTER] 01:13:09.030 --> 01:13:15.150 PROFESSOR: OK. So that-- you might say well, look, you should have been nervous there. 01:13:15.150 --> 01:13:19.809 You know, and admittedly sometimes there's experimental error. But I want to convince 01:13:19.809 --> 01:13:25.620 you that I should never, ever ever be nervous about this moment in 8.04. And the reason is 01:13:25.620 --> 01:13:28.630 the following. I want to prove this for you. And the way I'm gonna prove it is slightly 01:13:28.630 --> 01:13:33.000 more general, in more generality. And I want to prove to you that the number-- if I have 01:13:33.000 --> 01:13:37.059 a set, or, sorry, if the number of people who are undergraduates and not blonde which, 01:13:37.059 --> 01:13:43.250 all right, is b bar plus the number who are blonde but not from Massachusetts is greater 01:13:43.250 --> 01:13:48.840 than or equal to the number that are undergraduates and not from Massachusetts. 01:13:48.840 --> 01:13:54.040 So how do I prove this? Well if you're an undergraduate and not blonde, you may or you 01:13:54.040 --> 01:13:58.540 may not be from Massachusetts. So this is equal to the number of undergraduates who 01:13:58.540 --> 01:14:03.750 are not blonde and are from Massachusetts plus the number of undergraduates who are 01:14:03.750 --> 01:14:09.920 not blonde and are not from Massachusetts. It could hardly be otherwise. You either are 01:14:09.920 --> 01:14:15.690 or you are not from Massachusetts. Not the sort of thing that you normally see in physics. 01:14:15.690 --> 01:14:19.460 So this is the number of people who are blonde and not from Massachusetts, number of people 01:14:19.460 --> 01:14:23.570 who are blonde, who are-- so if you're blonde and not from Massachusetts, you may or may 01:14:23.570 --> 01:14:27.300 not be an undergraduate. So this is the number of people who are undergraduates, blonde, 01:14:27.300 --> 01:14:32.350 and not from Massachusetts plus the number of people who are not undergraduates, are 01:14:32.350 --> 01:14:36.040 blonde and are not from Massachusetts. 01:14:36.040 --> 01:14:42.330 And on the right hand side-- so, adding these two together gives us plus and plus. On the 01:14:42.330 --> 01:14:45.080 right hand side, the number of people that are undergraduates and not from Massachusetts, 01:14:45.080 --> 01:14:49.720 well each one could be either blonde or not blonde. So this is equal to the number that 01:14:49.720 --> 01:14:53.520 are undergraduates, blonde, and not from Massachusetts, 01:14:53.520 --> 01:14:56.740 plus-- remember that our undergraduates not 01:14:56.750 --> 01:15:00.440 blonde and not from Massachusetts. Agreed? 01:15:00.440 --> 01:15:05.460 I am now going to use the awesome power of-- and so this is what we want to prove, and 01:15:05.460 --> 01:15:12.150 I'm going to use the awesome power of subtraction. And note that U, B, M bar, these guys cancel. 01:15:12.150 --> 01:15:19.380 And U, B bar, M bar, these guys cancel. And we're left with the following proposition: 01:15:19.380 --> 01:15:23.750 the number of undergraduates who are not blonde but are from Massachusetts plus the number 01:15:23.750 --> 01:15:27.809 of undergrad-- of non-undergraduates who are blonde but not from Massachusetts must be 01:15:27.809 --> 01:15:31.570 greater than or equal to zero. 01:15:31.570 --> 01:15:37.800 Can you have a number of people in a room satisfying some condition be less than zero? 01:15:37.800 --> 01:15:44.260 Can minus 3 of you be blonde undergraduates not from Massachusetts? Not so much. This 01:15:44.260 --> 01:15:47.570 is a strictly positive number, because it's a numerative. It's a counting problem. How 01:15:47.570 --> 01:15:53.230 many are undergraduates not blonde and from Massachusetts. Yeah? Everyone cool with that? 01:15:53.230 --> 01:15:56.090 So it could hardly have been otherwise. It had to work out like this. 01:15:56.090 --> 01:16:01.670 And here's the more general statement. The more general statement is that the number 01:16:01.670 --> 01:16:06.410 of people, or the number of elements of any set where each element in that set has binary 01:16:06.410 --> 01:16:12.780 properties a b and c-- a or not a, b or not b, c or not c. Satisfies the following inequality. 01:16:12.780 --> 01:16:19.450 The number who are a but not b plus the number who are b but not c is greater than or equal 01:16:19.450 --> 01:16:27.160 to the number who are a but not c. And this is exactly the same argument. 01:16:27.160 --> 01:16:35.020 And this inequality which is a tautology, really, is called Bell's Inequality. And it's 01:16:35.020 --> 01:16:43.190 obviously true. What did I use to derive this? Logic and integers, right? I mean, that's 01:16:43.190 --> 01:16:46.520 bedrock stuff. 01:16:46.520 --> 01:16:53.390 Here's the problem. I didn't mention this last time, but in fact electrons have a third 01:16:53.390 --> 01:16:58.830 property in addition to-- electrons have a third property in addition to hardness and 01:16:58.830 --> 01:17:05.080 color. The third property is called whimsy, and you can either be whimsical or not whimsical. 01:17:05.080 --> 01:17:08.270 And every electron, when measured, is either whimsical or not whimsical. You never have 01:17:08.270 --> 01:17:14.580 a boring electron. You never have an ambiguous electron. Always whimsical or not whimsical. 01:17:14.580 --> 01:17:20.800 So we have hardness, we have color, we have whimsy. OK. And I can perform the following 01:17:20.800 --> 01:17:31.030 experiment. From a set of electrons, I can measure the number that are hard and not black, 01:17:31.030 --> 01:17:40.960 plus the number that are black but not whimsical. And I can measure the number that are hard 01:17:40.960 --> 01:17:45.520 and not whimsical. OK? 01:17:45.520 --> 01:17:50.460 And I want to just open up the case a little bit and tell you that the hardness here really 01:17:50.460 --> 01:17:56.380 is the angular momentum of the electron along the x-axis. Color is the angular momentum 01:17:56.380 --> 01:18:01.210 of the electron along the y-axis. And whimsy is the angular momentum of the electron along 01:18:01.210 --> 01:18:05.830 the z-axis. These are things I can measure because I can measure angular momentum. 01:18:05.830 --> 01:18:16.559 So I can perform this experiment with electrons and it needn't be satisfied. In particular, 01:18:16.559 --> 01:18:24.080 we will show that the number of electrons, just to be very precise, the number of electrons 01:18:24.080 --> 01:18:30.470 in a given set, which have positive angular momentum along the x-axis and down along the 01:18:30.470 --> 01:18:38.520 y-axis, plus up along the y-axis and down along the z-axis, is less than the number 01:18:38.520 --> 01:18:46.610 that are up. Actually let me do this in a very particular way. Up... zero down at theta. 01:18:46.610 --> 01:18:53.790 Up at theta, down at-- two theta is greater than the number that are up at zero and down at theta. 01:18:53.790 --> 01:18:59.130 Now here's the thing-- two theta. You can't at the moment understand what this equation 01:18:59.130 --> 01:19:06.030 means. But if I just tell you that these are three binary properties of the electron, OK, 01:19:06.030 --> 01:19:11.850 and that it violates this inequality, there is something deeply troubling about this result. 01:19:11.850 --> 01:19:18.770 Bell's Inequality, which we proved-- trivially, using integers, using logic-- is false in 01:19:18.770 --> 01:19:19.830 quantum mechanics. 01:19:19.830 --> 01:19:23.800 And it's not just false in quantum mechanics. We will at the end of the course derive the 01:19:23.800 --> 01:19:27.460 quantum mechanical prediction for this result and show that at least to a predicted violation 01:19:27.460 --> 01:19:33.870 of Bell's Inequality. This experiment has been done, and the real world violates Bell's 01:19:33.870 --> 01:19:39.880 Inequality. Logic and integers and adding probabilities, as we have done, is misguided. 01:19:39.880 --> 01:19:44.460 And our job, which we will begin with the next lecture, is to find a better way to add 01:19:44.460 --> 01:19:49.980 probabilities than classically. And that will be quantum mechanics See you on Tuesday. 01:19:49.980 --> 01:19:56.960 AUDIENCE: [APPLAUSE]