WEBVTT 00:00:00.000 --> 00:00:02.450 align:middle line:90% [SQUEAKING, RUSTLING, CLICKING] 00:00:02.450 --> 00:00:12.250 align:middle line:90% 00:00:12.250 --> 00:00:15.130 align:middle line:84% DAVID KAISER: If there are no immediate questions, 00:00:15.130 --> 00:00:16.000 align:middle line:90% that's good. 00:00:16.000 --> 00:00:18.670 align:middle line:84% And if so, then I'll go ahead and share screen. 00:00:18.670 --> 00:00:22.120 align:middle line:84% And we'll launch into our continuing adventure 00:00:22.120 --> 00:00:23.810 align:middle line:84% with quantum theory, which is, frankly, 00:00:23.810 --> 00:00:27.730 align:middle line:84% one of my favorite adventures ever, speaking just for myself. 00:00:27.730 --> 00:00:31.990 align:middle line:84% OK, so you will hopefully remember on our previous class 00:00:31.990 --> 00:00:36.490 align:middle line:84% session, we looked at Werner Heisenberg's introduction 00:00:36.490 --> 00:00:39.520 align:middle line:84% of what came to be called matrix mechanics 00:00:39.520 --> 00:00:44.410 align:middle line:84% in spring-summer 1925, and what brought him 00:00:44.410 --> 00:00:46.180 align:middle line:84% to it, what was he reacting against, 00:00:46.180 --> 00:00:49.030 align:middle line:84% and a little taste of what people thought it might all 00:00:49.030 --> 00:00:49.535 align:middle line:90% add up to. 00:00:49.535 --> 00:00:51.160 align:middle line:84% And today, we're going to look actually 00:00:51.160 --> 00:00:54.340 align:middle line:84% at a kind of complementary set of developments that 00:00:54.340 --> 00:00:57.970 align:middle line:84% were unfolding very close in time, very rapid periods 00:00:57.970 --> 00:00:59.210 align:middle line:90% of period of development. 00:00:59.210 --> 00:01:00.760 align:middle line:84% But now looking at what became known 00:01:00.760 --> 00:01:03.940 align:middle line:84% as wave mechanics and some of its features 00:01:03.940 --> 00:01:06.790 align:middle line:84% that people began to really puzzle about. 00:01:06.790 --> 00:01:10.570 align:middle line:84% So for today, we'll look at some of Erwin Schrodinger's 00:01:10.570 --> 00:01:11.665 align:middle line:90% most famous work. 00:01:11.665 --> 00:01:13.040 align:middle line:84% Again, some of this might already 00:01:13.040 --> 00:01:15.560 align:middle line:84% be familiar to some of you, but probably not to all. 00:01:15.560 --> 00:01:19.810 align:middle line:84% And I think it's fun to just go back through and zoom out a bit 00:01:19.810 --> 00:01:23.560 align:middle line:84% and say, what did Schrodinger think he was doing and why? 00:01:23.560 --> 00:01:25.900 align:middle line:84% Let alone, what's the form of the equation 00:01:25.900 --> 00:01:28.250 align:middle line:90% that he put together? 00:01:28.250 --> 00:01:29.590 align:middle line:90% So that's the part one. 00:01:29.590 --> 00:01:32.370 align:middle line:84% Then, we're going to look in parts two, and very briefly, 00:01:32.370 --> 00:01:36.340 align:middle line:84% a shorter part three, at some of the implications 00:01:36.340 --> 00:01:39.700 align:middle line:84% that physicists began already to grapple with implications 00:01:39.700 --> 00:01:42.400 align:middle line:84% of Schrodinger's wave mechanics really pretty quickly. 00:01:42.400 --> 00:01:46.440 align:middle line:84% And for both part two and part three, 00:01:46.440 --> 00:01:48.460 align:middle line:84% as often happens for class session, 00:01:48.460 --> 00:01:51.310 align:middle line:84% I'll try to cover some of the main highlights, some 00:01:51.310 --> 00:01:52.510 align:middle line:90% of the most-- 00:01:52.510 --> 00:01:54.948 align:middle line:84% what I think, most interesting or salient points. 00:01:54.948 --> 00:01:57.490 align:middle line:84% And then, some of the details, some of the extra derivations, 00:01:57.490 --> 00:01:59.980 align:middle line:84% and so on are in those optional lecture notes. 00:01:59.980 --> 00:02:00.910 align:middle line:90% Strictly optional. 00:02:00.910 --> 00:02:02.350 align:middle line:90% They are available on Canvas. 00:02:02.350 --> 00:02:04.150 align:middle line:84% But if something goes by too quickly 00:02:04.150 --> 00:02:07.530 align:middle line:84% or I just had to skim over some of the intervening steps 00:02:07.530 --> 00:02:09.280 align:middle line:84% as sometimes happens, then hopefully those 00:02:09.280 --> 00:02:10.655 align:middle line:84% lecture notes will help fill that 00:02:10.655 --> 00:02:13.550 align:middle line:84% in for those of you who want to dig in a bit more. 00:02:13.550 --> 00:02:15.710 align:middle line:90% So that's our plan for today. 00:02:15.710 --> 00:02:18.200 align:middle line:84% So just to remind ourselves again-- 00:02:18.200 --> 00:02:21.170 align:middle line:84% looking back to the previous class session-- 00:02:21.170 --> 00:02:26.510 align:middle line:84% starting in the spring of 1925, after that bout of severe hay 00:02:26.510 --> 00:02:30.230 align:middle line:84% fever that chased Werner Heisenberg temporarily out 00:02:30.230 --> 00:02:34.100 align:middle line:84% of Copenhagen and to this really quite lovely-looking island 00:02:34.100 --> 00:02:39.200 align:middle line:84% of Heligoland in the North Sea during that span of spring 00:02:39.200 --> 00:02:43.790 align:middle line:84% and summer '25 Heisenberg introduced a whole new way 00:02:43.790 --> 00:02:46.130 align:middle line:84% of trying to think about quantum theory. 00:02:46.130 --> 00:02:50.930 align:middle line:84% This was now something like 25 years into various physicists 00:02:50.930 --> 00:02:53.780 align:middle line:84% grappling with something having to do with quantum theory, 00:02:53.780 --> 00:02:56.720 align:middle line:84% going back to Max Planck's work that 00:02:56.720 --> 00:02:58.520 align:middle line:90% was first published in 1900. 00:02:58.520 --> 00:03:01.040 align:middle line:84% We saw through our several moments 00:03:01.040 --> 00:03:03.680 align:middle line:84% of sitting with what was called "the old quantum theory" 00:03:03.680 --> 00:03:07.460 align:middle line:84% that it wasn't quite so obvious that that collection of ideas 00:03:07.460 --> 00:03:09.680 align:middle line:84% was adding up to any one new thing 00:03:09.680 --> 00:03:11.390 align:middle line:84% or that they'd even fit together. 00:03:11.390 --> 00:03:13.910 align:middle line:84% And that was a concern that people like Heisenberg 00:03:13.910 --> 00:03:18.020 align:middle line:84% and some of his young colleagues really sought to tackle. 00:03:18.020 --> 00:03:21.020 align:middle line:84% They wanted to have a first-principles approach 00:03:21.020 --> 00:03:23.180 align:middle line:84% to quantum theory-- a quantum mechanics-- 00:03:23.180 --> 00:03:26.810 align:middle line:84% rather than what looked already to them, as well 00:03:26.810 --> 00:03:31.280 align:middle line:84% as to many of us today, this grab bag 00:03:31.280 --> 00:03:33.650 align:middle line:84% which had characterized the so-called "old quantum 00:03:33.650 --> 00:03:36.890 align:middle line:84% theory" where people would begin with quite 00:03:36.890 --> 00:03:42.770 align:middle line:84% traditional expressions for the energy of this or momentum 00:03:42.770 --> 00:03:47.300 align:middle line:84% of that, take either Newtonian or Maxwellian expressions 00:03:47.300 --> 00:03:50.210 align:middle line:84% and then just kind of staple on at the end 00:03:50.210 --> 00:03:53.120 align:middle line:84% some new, usually not very well explained, 00:03:53.120 --> 00:03:56.210 align:middle line:84% quantum conditions and kind of ad hoc new rule. 00:03:56.210 --> 00:03:58.580 align:middle line:84% And Heisenberg and his very good friend 00:03:58.580 --> 00:04:00.980 align:middle line:84% from grad school days, Wolfgang Pauli, and a lot 00:04:00.980 --> 00:04:03.110 align:middle line:90% of these younger folks were-- 00:04:03.110 --> 00:04:06.720 align:middle line:84% by the mid-1920s-- were looking to do something different. 00:04:06.720 --> 00:04:11.090 align:middle line:84% They wanted to have a first principles theory all its own 00:04:11.090 --> 00:04:15.560 align:middle line:84% that might account for phenomena at the atomic scale or smaller. 00:04:15.560 --> 00:04:18.410 align:middle line:84% And we saw last time Heisenberg, in particular, 00:04:18.410 --> 00:04:24.680 align:middle line:84% was guided by a kind of approach that 00:04:24.680 --> 00:04:27.830 align:middle line:84% sounded very much like what Albert Einstein had announced 00:04:27.830 --> 00:04:31.850 align:middle line:84% back in 1905, in thinking about the electrodynamics of moving 00:04:31.850 --> 00:04:32.630 align:middle line:90% bodies. 00:04:32.630 --> 00:04:37.580 align:middle line:84% Heisenberg starts sounding a lot like a acolyte of the physicist 00:04:37.580 --> 00:04:38.960 align:middle line:90% and philosopher, Ernst Mach. 00:04:38.960 --> 00:04:42.740 align:middle line:84% So we saw in the opening pages of Heisenberg's article-- 00:04:42.740 --> 00:04:45.320 align:middle line:84% though we had it in the English translation in our reader-- 00:04:45.320 --> 00:04:47.090 align:middle line:84% but even in the opening paragraph he says, 00:04:47.090 --> 00:04:50.720 align:middle line:84% we're going to keep fooling ourselves or chasing 00:04:50.720 --> 00:04:53.420 align:middle line:84% our own tails, basically, if we keep 00:04:53.420 --> 00:04:55.970 align:middle line:84% trying to talk about things that are not even, in principle, 00:04:55.970 --> 00:04:57.278 align:middle line:90% observable. 00:04:57.278 --> 00:04:58.820 align:middle line:84% Examples of which he mentioned, would 00:04:58.820 --> 00:05:00.987 align:middle line:84% be things like the orbit of an electron and an atom. 00:05:00.987 --> 00:05:02.780 align:middle line:84% We don't watch the electrons zooming around 00:05:02.780 --> 00:05:04.620 align:middle line:84% like a planet in the solar system. 00:05:04.620 --> 00:05:07.370 align:middle line:84% Let's stop trying to calculate those features 00:05:07.370 --> 00:05:10.070 align:middle line:84% and focus instead on things that really are objects 00:05:10.070 --> 00:05:12.560 align:middle line:84% of positive experience like the emission 00:05:12.560 --> 00:05:14.420 align:middle line:84% lines, these spectral lines that come out 00:05:14.420 --> 00:05:17.970 align:middle line:84% when certain gases of atoms are excited. 00:05:17.970 --> 00:05:19.790 align:middle line:84% So Heisenberg began looking at things 00:05:19.790 --> 00:05:22.670 align:middle line:84% like the observable features of these spectral lines. 00:05:22.670 --> 00:05:25.520 align:middle line:84% OK, so he reasoned then, we saw in particular 00:05:25.520 --> 00:05:28.040 align:middle line:84% that since the frequencies of these emission lines, 00:05:28.040 --> 00:05:31.340 align:middle line:84% especially for very simple spectra-like for a hydrogen 00:05:31.340 --> 00:05:35.480 align:middle line:84% atom, the frequencies obey this law of addition, 00:05:35.480 --> 00:05:38.300 align:middle line:84% that one line in the spectrum could 00:05:38.300 --> 00:05:41.300 align:middle line:84% be written the actual numerical frequency, the number of cycles 00:05:41.300 --> 00:05:44.780 align:middle line:84% per second, obey these kinds of relationships. 00:05:44.780 --> 00:05:47.420 align:middle line:84% Where there are two other distinct emission lines, 00:05:47.420 --> 00:05:50.160 align:middle line:84% the sum of whose frequencies would add up to this third one 00:05:50.160 --> 00:05:52.550 align:middle line:84% and it could be it could be extended beyond just pairs, 00:05:52.550 --> 00:05:53.840 align:middle line:90% 3's, 4's, 5's. 00:05:53.840 --> 00:05:57.170 align:middle line:84% That there were these addition relationships 00:05:57.170 --> 00:05:59.840 align:middle line:84% between the frequencies of light that really genuinely 00:05:59.840 --> 00:06:02.130 align:middle line:84% was emitted by these excited hydrogen atoms. 00:06:02.130 --> 00:06:06.950 align:middle line:84% And then Heisenberg reasoned that when we characterize 00:06:06.950 --> 00:06:10.460 align:middle line:84% lights, Maxwellian or otherwise, the frequency 00:06:10.460 --> 00:06:13.070 align:middle line:84% appears in the exponent, which suggested 00:06:13.070 --> 00:06:15.710 align:middle line:84% to Heisenberg that the amplitude should multiply. 00:06:15.710 --> 00:06:18.490 align:middle line:84% If the frequencies are adding, according 00:06:18.490 --> 00:06:20.350 align:middle line:84% to this law of addition, and the frequencies 00:06:20.350 --> 00:06:23.500 align:middle line:84% are one way of characterizing the light that comes out, 00:06:23.500 --> 00:06:25.960 align:middle line:84% then shouldn't the amplitudes of those associated 00:06:25.960 --> 00:06:27.370 align:middle line:90% light waves multiply? 00:06:27.370 --> 00:06:29.890 align:middle line:84% And that's what he found, to his great surprise, 00:06:29.890 --> 00:06:32.170 align:middle line:84% alone on the island of Heligoland, 00:06:32.170 --> 00:06:35.140 align:middle line:84% that these amplitudes didn't behave 00:06:35.140 --> 00:06:36.910 align:middle line:90% the way he expected them to. 00:06:36.910 --> 00:06:40.570 align:middle line:84% In fact, the outcome of multiplying two of those things 00:06:40.570 --> 00:06:44.020 align:middle line:84% together depended on the order in which they were multiplied. 00:06:44.020 --> 00:06:46.270 align:middle line:84% And so he returned, or started very soon 00:06:46.270 --> 00:06:48.460 align:middle line:84% afterwards, a position in Gottingen. 00:06:48.460 --> 00:06:51.340 align:middle line:84% And his senior advisor there, Max Born, clarified these 00:06:51.340 --> 00:06:52.000 align:middle line:90% are matrices. 00:06:52.000 --> 00:06:54.760 align:middle line:84% The fact that the outcome of the multiplication 00:06:54.760 --> 00:06:58.270 align:middle line:84% depends on the order is a generic feature of matrices, 00:06:58.270 --> 00:07:01.550 align:middle line:84% whereas mathematicians would say, matrices do not commute. 00:07:01.550 --> 00:07:03.610 align:middle line:84% And so soon after that, his work became 00:07:03.610 --> 00:07:06.370 align:middle line:90% known as matrix mechanics. 00:07:06.370 --> 00:07:08.770 align:middle line:84% And then Heisenberg continued working on that, 00:07:08.770 --> 00:07:10.630 align:middle line:84% sharpening the formalism, working directly 00:07:10.630 --> 00:07:12.730 align:middle line:84% with Max Born and some other colleagues. 00:07:12.730 --> 00:07:14.560 align:middle line:84% But also trying to figure out conceptually, 00:07:14.560 --> 00:07:17.840 align:middle line:84% what might it mean if the world is characterized, 00:07:17.840 --> 00:07:19.460 align:middle line:84% the atomic world is characterized, 00:07:19.460 --> 00:07:22.010 align:middle line:84% by these strange arrays of numbers 00:07:22.010 --> 00:07:23.870 align:middle line:84% whose mathematics was, at least to him, 00:07:23.870 --> 00:07:25.850 align:middle line:90% rather unexpected and foreign? 00:07:25.850 --> 00:07:27.950 align:middle line:84% And where it seemed to be like the outcome 00:07:27.950 --> 00:07:30.140 align:middle line:84% would depend on the order in which you did stuff. 00:07:30.140 --> 00:07:33.530 align:middle line:84% Could it be that our operations on the quantum realm 00:07:33.530 --> 00:07:36.410 align:middle line:84% could have an impact on what we could ever see or measure? 00:07:36.410 --> 00:07:39.080 align:middle line:84% And in thinking along those lines, about what would 00:07:39.080 --> 00:07:41.840 align:middle line:84% it take to perform certain kinds of measurements of things 00:07:41.840 --> 00:07:45.930 align:middle line:84% like an electron scattering high-energy light off of it 00:07:45.930 --> 00:07:50.030 align:middle line:84% and so on, that Heisenberg began to articulate his uncertainty 00:07:50.030 --> 00:07:55.250 align:middle line:84% principle that there seemed to be a consequence of the fact 00:07:55.250 --> 00:07:59.070 align:middle line:84% that these matrices don't commune with each other. 00:07:59.070 --> 00:08:01.730 align:middle line:84% There was an irreducible uncertainty 00:08:01.730 --> 00:08:05.090 align:middle line:84% in the sharpness, the accuracy, or precision 00:08:05.090 --> 00:08:08.180 align:middle line:84% with which we could ever specify at the same moment 00:08:08.180 --> 00:08:10.490 align:middle line:84% the position of, say, an electron 00:08:10.490 --> 00:08:13.850 align:middle line:84% and its simultaneous momentum along the x direction, 00:08:13.850 --> 00:08:16.490 align:middle line:84% that there was a trade off whose scale, like so 00:08:16.490 --> 00:08:19.470 align:middle line:84% many of these things, was set by Planck's constant. 00:08:19.470 --> 00:08:22.010 align:middle line:84% So that was what we mostly looked at last time. 00:08:22.010 --> 00:08:25.010 align:middle line:84% And as I gave a kind of foreshadowing for 00:08:25.010 --> 00:08:27.440 align:middle line:84% today, right around that same time, 00:08:27.440 --> 00:08:32.150 align:middle line:84% just a remarkably close span of weeks and months, 00:08:32.150 --> 00:08:34.669 align:middle line:84% there was a really quite different approach 00:08:34.669 --> 00:08:37.309 align:middle line:84% to some of those very same questions being worked out 00:08:37.309 --> 00:08:38.600 align:middle line:90% by Werner Heisenberg. 00:08:38.600 --> 00:08:41.270 align:middle line:84% And we had an excerpt from this really quite wonderful 00:08:41.270 --> 00:08:43.520 align:middle line:90% biography by Walter Moore. 00:08:43.520 --> 00:08:46.453 align:middle line:84% A part of today's readings was a little section of Moore's book, 00:08:46.453 --> 00:08:48.620 align:middle line:84% talking through how did Schrodinger think about what 00:08:48.620 --> 00:08:49.940 align:middle line:90% became known as wave mechanics? 00:08:49.940 --> 00:08:52.170 align:middle line:84% I want to talk a little bit about that. 00:08:52.170 --> 00:08:55.820 align:middle line:84% So this was happening not in the spring summer of '25 00:08:55.820 --> 00:09:01.370 align:middle line:84% but in winter/spring '26, but really just a few months later. 00:09:01.370 --> 00:09:03.650 align:middle line:84% Aaron Schrodinger began introducing 00:09:03.650 --> 00:09:06.410 align:middle line:84% a different first-principles approach 00:09:06.410 --> 00:09:09.440 align:middle line:84% to quantum theory, much like Heisenberg and Pauli 00:09:09.440 --> 00:09:13.220 align:middle line:84% and these other kind of young researchers. 00:09:13.220 --> 00:09:14.870 align:middle line:84% Schrodinger also thought there should 00:09:14.870 --> 00:09:18.980 align:middle line:84% be a kind of way of building a new theory from the ground up 00:09:18.980 --> 00:09:21.950 align:middle line:84% to treat the behavior of atoms and parts of atoms. 00:09:21.950 --> 00:09:24.493 align:middle line:84% But he followed a different conceptual path. 00:09:24.493 --> 00:09:25.910 align:middle line:84% He was working quite independently 00:09:25.910 --> 00:09:28.230 align:middle line:84% of Heisenberg in these early steps. 00:09:28.230 --> 00:09:32.630 align:middle line:84% So Heisenberg had built upon these ideas about discreteness. 00:09:32.630 --> 00:09:35.210 align:middle line:84% He was influenced by Bohr's work and ultimately 00:09:35.210 --> 00:09:38.420 align:middle line:84% tried to extract away from Bohr's work. 00:09:38.420 --> 00:09:40.430 align:middle line:84% But Schrodinger actually went a different way. 00:09:40.430 --> 00:09:43.520 align:middle line:84% He was most directly inspired, his work, 00:09:43.520 --> 00:09:46.280 align:middle line:84% not by the kind of Bohr atom or this notion 00:09:46.280 --> 00:09:50.120 align:middle line:84% of very rigid, discrete quantum jumps 00:09:50.120 --> 00:09:55.020 align:middle line:84% but rather by Louis de Broglie's very suggestive idea from 1924 00:09:55.020 --> 00:09:56.108 align:middle line:90% about matter waves. 00:09:56.108 --> 00:09:58.650 align:middle line:84% And here's this, again, kind of cartoon version of the bottom 00:09:58.650 --> 00:10:02.580 align:middle line:84% here, trying to show de Broglie's suggestion for why 00:10:02.580 --> 00:10:05.820 align:middle line:84% these very discrete orbits that Niels Bohr had identified 00:10:05.820 --> 00:10:09.900 align:middle line:84% of, say, the behavior of an electron in a hydrogen atom. 00:10:09.900 --> 00:10:13.440 align:middle line:84% Why might those special orbits be picked out as stable? 00:10:13.440 --> 00:10:16.260 align:middle line:84% Maybe there was an inherent waviness of the electron 00:10:16.260 --> 00:10:19.020 align:middle line:84% and you had to have a constructive interference 00:10:19.020 --> 00:10:20.070 align:middle line:90% for a stable orbit. 00:10:20.070 --> 00:10:21.810 align:middle line:84% Anything else would suffer destructive interference. 00:10:21.810 --> 00:10:23.810 align:middle line:84% Those are the kinds of things that really caught 00:10:23.810 --> 00:10:27.480 align:middle line:84% Schrodinger's imagination very soon after de Broglie 00:10:27.480 --> 00:10:29.560 align:middle line:90% himself had introduced them. 00:10:29.560 --> 00:10:32.380 align:middle line:84% So Schrodinger was coming from a bit of a different community. 00:10:32.380 --> 00:10:34.163 align:middle line:90% He was originally from Vienna. 00:10:34.163 --> 00:10:35.830 align:middle line:84% He was, at the time, teaching in Zurich. 00:10:35.830 --> 00:10:38.020 align:middle line:84% He wasn't from Copenhagen. He wasn't 00:10:38.020 --> 00:10:40.360 align:middle line:84% working in Gottingen. It was a little bit 00:10:40.360 --> 00:10:42.160 align:middle line:90% kind of different network. 00:10:42.160 --> 00:10:45.250 align:middle line:84% Perhaps more important, he was also a generation older 00:10:45.250 --> 00:10:46.420 align:middle line:90% than Heisenberg and Pauli. 00:10:46.420 --> 00:10:49.900 align:middle line:84% He was basically very nearly the same age as Albert Einstein. 00:10:49.900 --> 00:10:53.170 align:middle line:84% They became very close friends, closer in age to Niels Bohr. 00:10:53.170 --> 00:10:55.720 align:middle line:84% He'd been working as a professional theoretical 00:10:55.720 --> 00:10:59.110 align:middle line:84% physicist for decades by the time this stuff came up, 00:10:59.110 --> 00:11:03.190 align:middle line:84% unlike Heisenberg and Pauli, who were working 00:11:03.190 --> 00:11:05.200 align:middle line:90% very soon after their own PhDs. 00:11:05.200 --> 00:11:08.950 align:middle line:84% Schrodinger was a established researcher. 00:11:08.950 --> 00:11:13.540 align:middle line:84% And his approach to this question, I think, shows that. 00:11:13.540 --> 00:11:15.220 align:middle line:84% We could characterize his approach 00:11:15.220 --> 00:11:18.010 align:middle line:84% to the new quantum mechanics, the new quantum realm, 00:11:18.010 --> 00:11:22.390 align:middle line:84% as an effort to retain as much of the kind of look 00:11:22.390 --> 00:11:25.300 align:middle line:84% and feel of the toolkit of time-tested physics 00:11:25.300 --> 00:11:26.408 align:middle line:90% as he could. 00:11:26.408 --> 00:11:28.450 align:middle line:84% And I'm just going to pause briefly and mention-- 00:11:28.450 --> 00:11:30.170 align:middle line:90% some of you might know-- 00:11:30.170 --> 00:11:32.810 align:middle line:84% so for the tool kits, Heisenberg and Schrodinger 00:11:32.810 --> 00:11:35.180 align:middle line:84% look very distinct with Schrodinger seeming 00:11:35.180 --> 00:11:37.340 align:middle line:84% to be a little bit more, almost, conservative, 00:11:37.340 --> 00:11:39.810 align:middle line:84% in the sense of let's retain as much as possible. 00:11:39.810 --> 00:11:42.320 align:middle line:84% And Heisenberg saying, it's a new world. 00:11:42.320 --> 00:11:43.700 align:middle line:90% We need a conceptual revolution. 00:11:43.700 --> 00:11:45.530 align:middle line:90% We'll use new techniques. 00:11:45.530 --> 00:11:48.170 align:middle line:84% And yet socially and personally, they were almost inverted. 00:11:48.170 --> 00:11:54.800 align:middle line:84% So Schrodinger, even in his day, was known as a remarkably 00:11:54.800 --> 00:11:59.540 align:middle line:84% Bohemian, leading a Bohemian lifestyle, not 00:11:59.540 --> 00:12:01.820 align:middle line:84% the kind of traditional family values. 00:12:01.820 --> 00:12:04.730 align:middle line:84% He had open relationships with multiple women at a time. 00:12:04.730 --> 00:12:07.910 align:middle line:84% He raised children that he had with one person, 00:12:07.910 --> 00:12:09.680 align:middle line:90% he raised them with his wife. 00:12:09.680 --> 00:12:11.600 align:middle line:84% And it was a really unusual arrangement 00:12:11.600 --> 00:12:13.680 align:middle line:84% that, actually, his own contemporaries 00:12:13.680 --> 00:12:14.570 align:middle line:90% would talk about. 00:12:14.570 --> 00:12:15.380 align:middle line:90% It stood out. 00:12:15.380 --> 00:12:18.170 align:middle line:84% And Heisenberg, as we know, was pursuing, actually, 00:12:18.170 --> 00:12:22.350 align:middle line:84% a very fairly traditional, stereotypical personal family 00:12:22.350 --> 00:12:22.850 align:middle line:90% life. 00:12:22.850 --> 00:12:25.130 align:middle line:84% So who's conservative and who's radical actually, 00:12:25.130 --> 00:12:28.463 align:middle line:84% different about what kinds of aspects of their life and work 00:12:28.463 --> 00:12:29.630 align:middle line:90% were trying to characterize. 00:12:29.630 --> 00:12:31.430 align:middle line:84% And, again, Moore's biography, I think, 00:12:31.430 --> 00:12:34.160 align:middle line:84% is really quite astonishing for this 00:12:34.160 --> 00:12:36.140 align:middle line:84% rounded view of Schrodinger, not only 00:12:36.140 --> 00:12:37.560 align:middle line:90% how he got to a few equations. 00:12:37.560 --> 00:12:38.517 align:middle line:90% So I recommend that-- 00:12:38.517 --> 00:12:40.850 align:middle line:84% more of the book you might enjoy beyond just the excerpt 00:12:40.850 --> 00:12:41.390 align:middle line:90% that I gave. 00:12:41.390 --> 00:12:42.980 align:middle line:90% OK, what did Schrodinger do? 00:12:42.980 --> 00:12:45.890 align:middle line:84% So we know from his own private notebooks 00:12:45.890 --> 00:12:51.470 align:middle line:84% that have survived, this work was happening in December 1925, 00:12:51.470 --> 00:12:55.220 align:middle line:84% January, 1926, really just roughly half a year 00:12:55.220 --> 00:12:57.110 align:middle line:84% after Schrodinger's first publications. 00:12:57.110 --> 00:13:00.320 align:middle line:84% Schrodinger began with the usual expression for energy, just 00:13:00.320 --> 00:13:03.620 align:middle line:84% the Newtonian expression for the kinetic energy 00:13:03.620 --> 00:13:05.610 align:middle line:90% and the potential energy. 00:13:05.610 --> 00:13:07.910 align:middle line:84% But then he immediately, immediately tried 00:13:07.910 --> 00:13:11.150 align:middle line:84% to pick up on what de Broglie had suggested 00:13:11.150 --> 00:13:12.793 align:middle line:90% about these matter waves. 00:13:12.793 --> 00:13:14.210 align:middle line:84% And so Schrodinger, who was again, 00:13:14.210 --> 00:13:17.450 align:middle line:84% very senior, very seasoned mathematical physicist 00:13:17.450 --> 00:13:22.190 align:middle line:84% by this point, reasoned that if something about matter waves 00:13:22.190 --> 00:13:24.410 align:middle line:84% is going to be so important moving forward, 00:13:24.410 --> 00:13:28.460 align:middle line:84% let's use what we know about how to quantitatively characterize 00:13:28.460 --> 00:13:29.560 align:middle line:90% the behavior of waves. 00:13:29.560 --> 00:13:30.060 align:middle line:90% So he did. 00:13:30.060 --> 00:13:32.570 align:middle line:84% He went in a kind of wranglerish way 00:13:32.570 --> 00:13:34.850 align:middle line:84% and said, well, let's consider a wave equation. 00:13:34.850 --> 00:13:37.430 align:middle line:84% How would we characterize, for example, the behavior 00:13:37.430 --> 00:13:39.860 align:middle line:90% of a standing wave? 00:13:39.860 --> 00:13:42.440 align:middle line:84% And we would write down this very simple-looking expression 00:13:42.440 --> 00:13:44.942 align:middle line:84% simple certainly to someone like Schrodinger, very familiar. 00:13:44.942 --> 00:13:47.150 align:middle line:84% And as many of you probably know-- and we saw briefly 00:13:47.150 --> 00:13:51.110 align:middle line:84% in some earlier lectures-- this parameter K here 00:13:51.110 --> 00:13:52.490 align:middle line:90% is called the wave number. 00:13:52.490 --> 00:13:55.370 align:middle line:84% It's inversely proportional to the wavelength. 00:13:55.370 --> 00:13:58.670 align:middle line:84% So we can characterize the behavior of any kind of wave 00:13:58.670 --> 00:14:00.260 align:middle line:84% in terms of a wavelength and ask, 00:14:00.260 --> 00:14:05.840 align:middle line:84% how is the amplitude of that wave changing across space? 00:14:05.840 --> 00:14:10.558 align:middle line:84% How is the wave behaving as we move from one position 00:14:10.558 --> 00:14:11.100 align:middle line:90% to the other? 00:14:11.100 --> 00:14:13.790 align:middle line:84% And that's what this expression is quantifying. 00:14:13.790 --> 00:14:15.650 align:middle line:84% But now de Broglie had said that there 00:14:15.650 --> 00:14:18.530 align:middle line:84% was something very specific about a wavelength for matter, 00:14:18.530 --> 00:14:19.910 align:middle line:90% the de Broglie wavelength. 00:14:19.910 --> 00:14:22.460 align:middle line:84% It should be proportional, de Broglie suggested, 00:14:22.460 --> 00:14:25.550 align:middle line:84% to Planck's constant and inversely proportional 00:14:25.550 --> 00:14:28.010 align:middle line:84% to the momentum of that particle, of that quantum 00:14:28.010 --> 00:14:28.770 align:middle line:90% object. 00:14:28.770 --> 00:14:32.060 align:middle line:84% So now if the wave number is related to a wavelength 00:14:32.060 --> 00:14:34.640 align:middle line:84% and de Broglie's wavelength is related to a momentum, 00:14:34.640 --> 00:14:38.420 align:middle line:84% it was actually not a very difficult series 00:14:38.420 --> 00:14:42.050 align:middle line:84% of steps for Schrodinger to say, maybe this k, this wave number 00:14:42.050 --> 00:14:45.440 align:middle line:84% that appears in any old wave equation for classical waves 00:14:45.440 --> 00:14:47.840 align:middle line:84% of a guitar or ocean waves in the water, 00:14:47.840 --> 00:14:50.360 align:middle line:84% maybe that k is actually deeply related 00:14:50.360 --> 00:14:52.640 align:middle line:84% to the momentum in a way that actually 00:14:52.640 --> 00:14:56.450 align:middle line:84% is new, that comes straight from de Broglie's suggestion. 00:14:56.450 --> 00:15:00.290 align:middle line:84% And if so, if we can relate K to the momentum as usual, 00:15:00.290 --> 00:15:02.270 align:middle line:84% scaled by Planck's constant here, 00:15:02.270 --> 00:15:05.240 align:middle line:84% then we go back to this quite standard equation 00:15:05.240 --> 00:15:07.520 align:middle line:90% for a standing wave of any kind. 00:15:07.520 --> 00:15:10.040 align:middle line:84% And now we want to characterize something specifically 00:15:10.040 --> 00:15:12.590 align:middle line:84% quantum theoretic then we can substitute 00:15:12.590 --> 00:15:16.910 align:middle line:84% the k for the momentum with keeping track of our h bar. 00:15:16.910 --> 00:15:18.320 align:middle line:84% And now it looks like we actually 00:15:18.320 --> 00:15:20.870 align:middle line:84% have a whole new way of thinking about the momentum 00:15:20.870 --> 00:15:22.790 align:middle line:90% of any quantum object. 00:15:22.790 --> 00:15:25.280 align:middle line:84% Maybe the momentum is just a measure 00:15:25.280 --> 00:15:29.610 align:middle line:84% of the kind of spatial gradients of some of associated matter 00:15:29.610 --> 00:15:30.750 align:middle line:90% wave. 00:15:30.750 --> 00:15:33.270 align:middle line:84% So maybe there's a whole new operator. 00:15:33.270 --> 00:15:35.130 align:middle line:84% Maybe there's a new object that tells 00:15:35.130 --> 00:15:39.510 align:middle line:84% us that relates the momentum of some object 00:15:39.510 --> 00:15:44.400 align:middle line:84% to the gradient of its associated matter wave with, 00:15:44.400 --> 00:15:47.070 align:middle line:84% as usual, the scaling, the kind of sense of scale 00:15:47.070 --> 00:15:51.120 align:middle line:84% or a sense of proportion provided by Planck's constant. 00:15:51.120 --> 00:15:52.560 align:middle line:84% So what Schrodinger was doing here 00:15:52.560 --> 00:15:57.810 align:middle line:84% was trying to build up an equation where 00:15:57.810 --> 00:16:00.060 align:middle line:84% Planck's constant was kind of built in from the start, 00:16:00.060 --> 00:16:01.680 align:middle line:90% not appended at the end. 00:16:01.680 --> 00:16:03.450 align:middle line:84% Not, let's solve for some solutions 00:16:03.450 --> 00:16:05.700 align:middle line:84% and then smack on some new constraint 00:16:05.700 --> 00:16:08.670 align:middle line:84% but trying to build a first principles equation that 00:16:08.670 --> 00:16:11.730 align:middle line:84% would describe how matter behaves where Planck's constant 00:16:11.730 --> 00:16:14.560 align:middle line:84% is immediately setting the scale from the start. 00:16:14.560 --> 00:16:21.510 align:middle line:84% And so, with that series of reasonings, Schrodinger, 00:16:21.510 --> 00:16:24.390 align:middle line:84% arrived what we would now call the time-independent 00:16:24.390 --> 00:16:25.680 align:middle line:90% Schrodinger equation. 00:16:25.680 --> 00:16:26.457 align:middle line:90% And it really was. 00:16:26.457 --> 00:16:27.790 align:middle line:90% You can see where it comes from. 00:16:27.790 --> 00:16:29.920 align:middle line:84% It's starting from the typical relation 00:16:29.920 --> 00:16:31.870 align:middle line:84% between kinetic and potential energy 00:16:31.870 --> 00:16:34.090 align:middle line:84% but trying to plug-in these insights 00:16:34.090 --> 00:16:38.350 align:middle line:84% and quantify these insights from de Broglie right 00:16:38.350 --> 00:16:39.460 align:middle line:90% from the start. 00:16:39.460 --> 00:16:42.640 align:middle line:84% OK, so many of you have probably seen this before, 00:16:42.640 --> 00:16:44.860 align:middle line:84% that we still call it the Schrodinger wave equation. 00:16:44.860 --> 00:16:48.130 align:middle line:84% And let's just talk for a few minutes about the nature 00:16:48.130 --> 00:16:49.180 align:middle line:90% of that expression. 00:16:49.180 --> 00:16:51.190 align:middle line:84% First of all, it's all continuum. 00:16:51.190 --> 00:16:55.840 align:middle line:84% This wave function PSI seems to behave just like any other wave 00:16:55.840 --> 00:16:56.340 align:middle line:90% quantity. 00:16:56.340 --> 00:16:57.923 align:middle line:84% At least there's no reason to think it 00:16:57.923 --> 00:16:59.230 align:middle line:90% wouldn't from this expression. 00:16:59.230 --> 00:17:02.740 align:middle line:84% It should be varying continuously across space, 00:17:02.740 --> 00:17:06.130 align:middle line:84% gently having a slightly different value here 00:17:06.130 --> 00:17:07.030 align:middle line:90% than there. 00:17:07.030 --> 00:17:11.260 align:middle line:84% There's nothing of a kind of inherent radical discreteness 00:17:11.260 --> 00:17:16.210 align:middle line:84% that faces us when we look at Schrodinger's equation. 00:17:16.210 --> 00:17:20.950 align:middle line:84% It looks like, other than the presence of Planck's constant, 00:17:20.950 --> 00:17:23.980 align:middle line:84% the form of the equation the mathematical form, 00:17:23.980 --> 00:17:25.240 align:middle line:90% looks quite familiar. 00:17:25.240 --> 00:17:28.240 align:middle line:84% It's a differential equation for how some quantity is 00:17:28.240 --> 00:17:29.950 align:middle line:90% going to change over space. 00:17:29.950 --> 00:17:32.522 align:middle line:84% And he later, as many of you know, 00:17:32.522 --> 00:17:34.510 align:middle line:84% he introduced a time-varying version 00:17:34.510 --> 00:17:36.700 align:middle line:84% where the same quantity PSI could 00:17:36.700 --> 00:17:40.810 align:middle line:84% be continuously smoothly varying over time, as well 00:17:40.810 --> 00:17:42.370 align:middle line:90% as across space. 00:17:42.370 --> 00:17:45.370 align:middle line:84% So it's, again, retaining the look and feel 00:17:45.370 --> 00:17:48.260 align:middle line:84% of continuum-based differential equations. 00:17:48.260 --> 00:17:54.820 align:middle line:84% It doesn't have these ad hoc discreteness features 00:17:54.820 --> 00:17:57.880 align:middle line:84% that seem to be put in by hand by someone like Bohr 00:17:57.880 --> 00:18:00.010 align:middle line:90% in the Bohr model. 00:18:00.010 --> 00:18:01.760 align:middle line:84% So one of his first tasks-- and, again, we 00:18:01.760 --> 00:18:03.830 align:middle line:84% know this from his own private notebook-- 00:18:03.830 --> 00:18:06.170 align:middle line:84% he was having a ski skiing vacation 00:18:06.170 --> 00:18:10.135 align:middle line:84% with, not his wife, but with two very much younger twin women. 00:18:10.135 --> 00:18:12.260 align:middle line:84% And in the midst of this he would take these breaks 00:18:12.260 --> 00:18:13.135 align:middle line:90% and try to calculate. 00:18:13.135 --> 00:18:14.270 align:middle line:90% It's quite astonishing. 00:18:14.270 --> 00:18:15.812 align:middle line:84% And so one of the first tests he knew 00:18:15.812 --> 00:18:19.250 align:middle line:84% he had to apply this formula to was the now time-honored 00:18:19.250 --> 00:18:20.130 align:middle line:90% hydrogen atoms. 00:18:20.130 --> 00:18:22.430 align:middle line:84% So he said, what if the potential energy is not 00:18:22.430 --> 00:18:24.800 align:middle line:84% any old form but is the specific form 00:18:24.800 --> 00:18:27.710 align:middle line:84% he'd need to characterize the mutual attraction 00:18:27.710 --> 00:18:30.920 align:middle line:84% between an electron and a proton in a hydrogen atom put 00:18:30.920 --> 00:18:32.570 align:middle line:90% in the Coulomb potential? 00:18:32.570 --> 00:18:35.120 align:middle line:84% And then he found, again, just on his own 00:18:35.120 --> 00:18:38.150 align:middle line:84% in this kind of ski chalet right around the holiday-- 00:18:38.150 --> 00:18:39.620 align:middle line:90% right around New Year's-- 00:18:39.620 --> 00:18:42.290 align:middle line:84% that solutions to this equation will 00:18:42.290 --> 00:18:45.430 align:middle line:84% correspond to very specific values for the energy. 00:18:45.430 --> 00:18:48.770 align:middle line:84% You notice here, the first in this whole series of articles 00:18:48.770 --> 00:18:52.360 align:middle line:84% that he wrote were called "Quantization as an Eigenvalue 00:18:52.360 --> 00:18:52.860 align:middle line:90% Problem." 00:18:52.860 --> 00:18:54.090 align:middle line:90% And, again, that's a hint. 00:18:54.090 --> 00:18:56.780 align:middle line:84% He wants to work with familiar differential equations. 00:18:56.780 --> 00:18:59.690 align:middle line:84% What he's done here is he has some differential 00:18:59.690 --> 00:19:03.500 align:middle line:84% operators, some combination of terms 00:19:03.500 --> 00:19:07.040 align:middle line:84% that quantify the rates of change 00:19:07.040 --> 00:19:08.390 align:middle line:90% of some continuous property. 00:19:08.390 --> 00:19:09.500 align:middle line:90% That's this side. 00:19:09.500 --> 00:19:11.810 align:middle line:84% And there should be some eigenvalues 00:19:11.810 --> 00:19:16.940 align:middle line:84% of that differential operator, some allowable numerical kind 00:19:16.940 --> 00:19:21.020 align:middle line:84% of coefficients, that will characterize the changing 00:19:21.020 --> 00:19:22.460 align:middle line:90% across space of that quantity. 00:19:22.460 --> 00:19:26.240 align:middle line:84% And so he finds just by putting in the coulomb potential 00:19:26.240 --> 00:19:31.640 align:middle line:84% for the hydrogen atom that this very kind of generic looking 00:19:31.640 --> 00:19:34.550 align:middle line:84% or familiar kind of format of a differential equation 00:19:34.550 --> 00:19:38.900 align:middle line:84% will yield exactly the same energy spectrum, exactly 00:19:38.900 --> 00:19:42.680 align:middle line:84% the same allowable values for the eigenvalues of the energy, 00:19:42.680 --> 00:19:45.620 align:middle line:84% the same coefficients here that will satisfy 00:19:45.620 --> 00:19:48.200 align:middle line:84% the equation, exactly the same series 00:19:48.200 --> 00:19:52.020 align:middle line:84% as what Bohr had found from very different starting points. 00:19:52.020 --> 00:19:54.590 align:middle line:84% So therefore Schrodinger's equation, as well, 00:19:54.590 --> 00:19:57.260 align:middle line:84% would reproduce the successes like the Balmer spectrum. 00:19:57.260 --> 00:20:00.210 align:middle line:84% It should predict precisely the same frequencies 00:20:00.210 --> 00:20:02.903 align:middle line:84% of those emission lines from excited hydrogen atoms. 00:20:02.903 --> 00:20:04.320 align:middle line:84% So Schrodinger, again, had a sense 00:20:04.320 --> 00:20:07.410 align:middle line:84% that he was maybe on to something important here. 00:20:07.410 --> 00:20:08.470 align:middle line:90% How does that work? 00:20:08.470 --> 00:20:10.290 align:middle line:84% And, again, many of you have probably 00:20:10.290 --> 00:20:11.945 align:middle line:84% done this calculation in problem sets 00:20:11.945 --> 00:20:13.320 align:middle line:84% or seen it done in lecture class. 00:20:13.320 --> 00:20:15.420 align:middle line:84% For others of you, it's an exciting thing 00:20:15.420 --> 00:20:16.662 align:middle line:90% to look forward to. 00:20:16.662 --> 00:20:18.870 align:middle line:84% So I'm not going to go through the whole calculation. 00:20:18.870 --> 00:20:21.540 align:middle line:84% But I just want to make sure we understand the kinds of steps 00:20:21.540 --> 00:20:22.832 align:middle line:90% that Schrodinger was following. 00:20:22.832 --> 00:20:27.000 align:middle line:84% How does this continuum-based equation, this differential 00:20:27.000 --> 00:20:31.200 align:middle line:84% equation for some smoothly varying quantity PSI, 00:20:31.200 --> 00:20:35.490 align:middle line:84% how would that ever give us a discrete energy spectrum? 00:20:35.490 --> 00:20:38.717 align:middle line:84% What would this integer n that Bohr 00:20:38.717 --> 00:20:40.800 align:middle line:84% had argued came from some fundamental discreteness 00:20:40.800 --> 00:20:42.930 align:middle line:84% in the behavior of electrons, how does that come 00:20:42.930 --> 00:20:44.470 align:middle line:90% from Schrodinger's equation? 00:20:44.470 --> 00:20:46.800 align:middle line:84% So let's step back and think about a simpler case 00:20:46.800 --> 00:20:48.330 align:middle line:90% involving standing waves. 00:20:48.330 --> 00:20:52.050 align:middle line:84% Let's just consider motion in one direction, so the x-axis. 00:20:52.050 --> 00:20:55.020 align:middle line:84% And let's imagine we have a guitar string or a violin 00:20:55.020 --> 00:20:57.690 align:middle line:84% string where the endpoints are anchored. 00:20:57.690 --> 00:20:59.670 align:middle line:84% So whatever the legitimate solutions 00:20:59.670 --> 00:21:01.820 align:middle line:84% are for this wave equation, PSI being 00:21:01.820 --> 00:21:05.010 align:middle line:84% sort of the amplitude of the wave in this case, 00:21:05.010 --> 00:21:08.840 align:middle line:84% the wave has to vanish at the origin and at the length L, 00:21:08.840 --> 00:21:13.430 align:middle line:84% where the other end of the rope or the string is anchored. 00:21:13.430 --> 00:21:17.570 align:middle line:84% So how do we combine that with the general solutions 00:21:17.570 --> 00:21:19.190 align:middle line:90% for this differential equation? 00:21:19.190 --> 00:21:21.980 align:middle line:84% Again, here's our differential operator, so to speak. 00:21:21.980 --> 00:21:24.830 align:middle line:84% Well, if we ignore the boundary conditions, 00:21:24.830 --> 00:21:27.050 align:middle line:84% if we ignore the fact that this string is anchored 00:21:27.050 --> 00:21:29.270 align:middle line:84% at both ends, then we can very quickly 00:21:29.270 --> 00:21:31.910 align:middle line:84% write down the most general series of solutions 00:21:31.910 --> 00:21:33.090 align:middle line:90% of this wave equation. 00:21:33.090 --> 00:21:38.450 align:middle line:84% It will oscillate across space like sines and cosines, 00:21:38.450 --> 00:21:41.150 align:middle line:84% with some characteristic wave number 00:21:41.150 --> 00:21:42.930 align:middle line:90% and different coefficients. 00:21:42.930 --> 00:21:44.900 align:middle line:84% But now, if we apply the boundary conditions, 00:21:44.900 --> 00:21:47.910 align:middle line:84% then not all of these solutions are viable anymore. 00:21:47.910 --> 00:21:52.280 align:middle line:84% Some of them no longer solve the relevant equation. 00:21:52.280 --> 00:21:55.760 align:middle line:84% And in fact, if we apply these particular boundary conditions 00:21:55.760 --> 00:21:59.090 align:middle line:84% to this very general equation, differential equation, 00:21:59.090 --> 00:22:02.400 align:middle line:84% then the allowable solutions have a discrete set 00:22:02.400 --> 00:22:03.750 align:middle line:90% of eigenvalues. 00:22:03.750 --> 00:22:09.240 align:middle line:84% The wave number k, in this case, becomes not any old continuous 00:22:09.240 --> 00:22:12.420 align:middle line:84% value but, in fact, kind of snaps into place 00:22:12.420 --> 00:22:17.830 align:middle line:84% with only integer allowed, a series of allowable wave 00:22:17.830 --> 00:22:18.330 align:middle line:90% numbers. 00:22:18.330 --> 00:22:20.400 align:middle line:84% So the wave number could be 1 times 00:22:20.400 --> 00:22:23.730 align:middle line:84% some basic reference wave number, or 2 times 00:22:23.730 --> 00:22:25.380 align:middle line:90% that, but not 1.8 times that. 00:22:25.380 --> 00:22:29.250 align:middle line:84% We get a quantum discrete spectrum 00:22:29.250 --> 00:22:32.580 align:middle line:84% by solving a continuum-based differential equation 00:22:32.580 --> 00:22:34.750 align:middle line:84% and applying the appropriate boundary conditions. 00:22:34.750 --> 00:22:38.100 align:middle line:84% And so for the hydrogen atom, Schrodinger reasons similarly. 00:22:38.100 --> 00:22:40.860 align:middle line:84% It wasn't that the electron was somehow glued in space 00:22:40.860 --> 00:22:42.720 align:middle line:84% and could only be here versus there, 00:22:42.720 --> 00:22:46.260 align:middle line:84% like Bohr had suggested in this kind of ad hoc way. 00:22:46.260 --> 00:22:47.910 align:middle line:84% But, rather, Schrodinger said, well, 00:22:47.910 --> 00:22:49.493 align:middle line:84% we're going to solve this differential 00:22:49.493 --> 00:22:53.070 align:middle line:84% equation for some general smoothly varying quantity PSI. 00:22:53.070 --> 00:22:55.590 align:middle line:84% And let's apply some reasonable boundary conditions 00:22:55.590 --> 00:22:59.000 align:middle line:84% that the amplitude should vanish at the origin. 00:22:59.000 --> 00:23:02.520 align:middle line:84% The electron should not be found in the nucleus. 00:23:02.520 --> 00:23:05.630 align:middle line:84% So the wave function somehow describing 00:23:05.630 --> 00:23:09.260 align:middle line:84% the electrons' motion will vanish at the origin. 00:23:09.260 --> 00:23:11.780 align:middle line:84% And the electron shouldn't be found infinitely 00:23:11.780 --> 00:23:13.770 align:middle line:90% far away from its host nucleus. 00:23:13.770 --> 00:23:17.607 align:middle line:84% So the amplitude for whatever's waving, whatever kind of de 00:23:17.607 --> 00:23:19.190 align:middle line:84% Broglie-like matter wave is associated 00:23:19.190 --> 00:23:22.280 align:middle line:84% with the electron, that should have vanishing amplitude when 00:23:22.280 --> 00:23:26.330 align:middle line:84% you're arbitrarily far away from the rest of the atom. 00:23:26.330 --> 00:23:29.060 align:middle line:84% If you impose those boundary conditions, 00:23:29.060 --> 00:23:30.260 align:middle line:90% a little more complicated. 00:23:30.260 --> 00:23:32.150 align:middle line:84% But, conceptually, it's like this kind 00:23:32.150 --> 00:23:35.480 align:middle line:84% of standing wave on the string of fixed endpoints. 00:23:35.480 --> 00:23:37.850 align:middle line:84% That's what forces a discrete spectrum 00:23:37.850 --> 00:23:42.200 align:middle line:84% for the allowable energies, not restricting the kind of motion 00:23:42.200 --> 00:23:45.020 align:middle line:90% of the electron per se. 00:23:45.020 --> 00:23:48.650 align:middle line:84% So Schrodinger now has retained the look and feel 00:23:48.650 --> 00:23:50.750 align:middle line:84% of manipulating differential equations 00:23:50.750 --> 00:23:54.770 align:middle line:84% familiar for a long time by that point. 00:23:54.770 --> 00:23:58.980 align:middle line:84% He has a way of reproducing this kind of inherent discreteness 00:23:58.980 --> 00:24:01.470 align:middle line:84% for things like the emission of these spectral lines 00:24:01.470 --> 00:24:06.840 align:middle line:84% but by building up this kind of waviness of nature 00:24:06.840 --> 00:24:09.060 align:middle line:84% from the start, rather than imposing a kind of ad 00:24:09.060 --> 00:24:10.680 align:middle line:90% hoc quantum condition. 00:24:10.680 --> 00:24:14.550 align:middle line:84% That's what Schrodinger was working toward in that winter 00:24:14.550 --> 00:24:16.350 align:middle line:90% of '25-'26. 00:24:16.350 --> 00:24:19.830 align:middle line:84% He also then quickly realizes that solutions to his equation 00:24:19.830 --> 00:24:21.720 align:middle line:90% are wave functions. 00:24:21.720 --> 00:24:25.240 align:middle line:84% They should obey something called superposition, 00:24:25.240 --> 00:24:29.130 align:middle line:84% which we've seen briefly in previous class sessions, even 00:24:29.130 --> 00:24:30.000 align:middle line:90% this term. 00:24:30.000 --> 00:24:33.180 align:middle line:84% If there was one solution to that equation 00:24:33.180 --> 00:24:36.085 align:middle line:84% and a separate solution, then the sum of them 00:24:36.085 --> 00:24:38.460 align:middle line:84% will also be a solution, for that matter, the difference. 00:24:38.460 --> 00:24:43.290 align:middle line:84% That you can take legitimate solutions to the wave equation 00:24:43.290 --> 00:24:47.968 align:middle line:84% and add them and the resulting sum will also be a solution. 00:24:47.968 --> 00:24:50.010 align:middle line:84% And that means that these wave functions could do 00:24:50.010 --> 00:24:51.480 align:middle line:90% all the things that waves do. 00:24:51.480 --> 00:24:54.413 align:middle line:84% They could undergo interference, for example. 00:24:54.413 --> 00:24:56.080 align:middle line:84% And, again, here's just a quick example. 00:24:56.080 --> 00:24:59.580 align:middle line:84% If you have two waves of the same amplitude but different 00:24:59.580 --> 00:25:03.180 align:middle line:84% wavelength, then in places where the amplitudes happen 00:25:03.180 --> 00:25:05.890 align:middle line:84% to line up, where crest is near crest 00:25:05.890 --> 00:25:07.990 align:middle line:84% and you add those waves together, 00:25:07.990 --> 00:25:09.690 align:middle line:84% we'll get constructive interference. 00:25:09.690 --> 00:25:12.930 align:middle line:84% The resulting wave will have a height nearly twice as 00:25:12.930 --> 00:25:14.910 align:middle line:90% tall as either wave alone. 00:25:14.910 --> 00:25:16.920 align:middle line:84% On the other hand, in other locations 00:25:16.920 --> 00:25:19.260 align:middle line:84% where a crest is nearly lined up with a trough, 00:25:19.260 --> 00:25:20.998 align:middle line:84% they'll just about cancel each other out. 00:25:20.998 --> 00:25:23.040 align:middle line:84% And the resulting amplitude will be much smaller. 00:25:23.040 --> 00:25:24.300 align:middle line:84% You can have destructive interference. 00:25:24.300 --> 00:25:26.760 align:middle line:84% All those things that are familiar from water waves, 00:25:26.760 --> 00:25:30.660 align:middle line:84% from sound waves, from light waves in a Maxwellian context, 00:25:30.660 --> 00:25:33.000 align:middle line:84% all those things seem to carry over 00:25:33.000 --> 00:25:35.280 align:middle line:84% to solutions of Schrodinger's wave equation 00:25:35.280 --> 00:25:38.010 align:middle line:84% as well, even though it's seemingly describing something 00:25:38.010 --> 00:25:40.310 align:middle line:90% like an electron. 00:25:40.310 --> 00:25:44.030 align:middle line:84% So that really forced the question, 00:25:44.030 --> 00:25:48.080 align:middle line:84% if this wave function PSI has definite wave-like properties, 00:25:48.080 --> 00:25:48.980 align:middle line:90% what was it? 00:25:48.980 --> 00:25:51.050 align:middle line:90% What was it a wave of or in? 00:25:51.050 --> 00:25:53.420 align:middle line:84% It starts to sound like the questions about light 00:25:53.420 --> 00:25:56.170 align:middle line:90% that we began this class with. 00:25:56.170 --> 00:26:00.448 align:middle line:84% So what is doing the waving if PSI behaves like a wave? 00:26:00.448 --> 00:26:01.990 align:middle line:84% And then it became even more bizarre. 00:26:01.990 --> 00:26:06.490 align:middle line:84% Here's when it began to break from just the familiar physics 00:26:06.490 --> 00:26:08.202 align:middle line:90% of classical waves. 00:26:08.202 --> 00:26:09.910 align:middle line:84% And, again, Schrodinger-- to his credit-- 00:26:09.910 --> 00:26:11.530 align:middle line:84% was very quick to notice this himself 00:26:11.530 --> 00:26:13.210 align:middle line:84% and really point it out and begin 00:26:13.210 --> 00:26:15.640 align:middle line:90% to try to puzzle it through. 00:26:15.640 --> 00:26:18.350 align:middle line:84% If you consider a system with more than one electron, 00:26:18.350 --> 00:26:21.740 align:middle line:84% let's say as simple as just two electrons, not just one, 00:26:21.740 --> 00:26:23.830 align:middle line:84% then the equation suddenly depends 00:26:23.830 --> 00:26:25.780 align:middle line:90% on many, many coordinates. 00:26:25.780 --> 00:26:29.260 align:middle line:84% The interaction potential, that key portion 00:26:29.260 --> 00:26:31.960 align:middle line:84% within the Schrodinger equation, will now, in general, 00:26:31.960 --> 00:26:36.970 align:middle line:84% depend on the location of both electron one and electron two. 00:26:36.970 --> 00:26:40.690 align:middle line:84% They're each existing in three dimensional space, x, y, and z. 00:26:40.690 --> 00:26:43.150 align:middle line:84% They could be at different locations. 00:26:43.150 --> 00:26:46.810 align:middle line:84% So the potential energy of that two-body system 00:26:46.810 --> 00:26:51.790 align:middle line:84% will now, in general, depend on six spatial coordinates, not 00:26:51.790 --> 00:26:52.840 align:middle line:90% just three. 00:26:52.840 --> 00:26:57.140 align:middle line:84% So now solutions PSI, solutions to Schrodinger's wave equation, 00:26:57.140 --> 00:27:00.860 align:middle line:84% will themselves depend on six dimensions, six coordinates 00:27:00.860 --> 00:27:03.260 align:middle line:90% of space, not just three. 00:27:03.260 --> 00:27:07.910 align:middle line:84% That's not like a water wave, or a sound wave, or a light wave. 00:27:07.910 --> 00:27:10.820 align:middle line:84% So even though the mathematics was, in many ways, 00:27:10.820 --> 00:27:13.820 align:middle line:84% very familiar and Schrodinger used that to great effect 00:27:13.820 --> 00:27:15.620 align:middle line:84% to find solutions, to figure out why 00:27:15.620 --> 00:27:18.200 align:middle line:84% there was a seemingly quantized or discrete spectrum 00:27:18.200 --> 00:27:21.080 align:middle line:84% of eigenvalues and all that, it wasn't actually 00:27:21.080 --> 00:27:23.180 align:middle line:90% just classical waves. 00:27:23.180 --> 00:27:24.740 align:middle line:84% And there were even, mathematically, 00:27:24.740 --> 00:27:28.040 align:middle line:84% some unexpected features that Schrodinger himself began 00:27:28.040 --> 00:27:30.950 align:middle line:84% to elucidate, that PSI, whatever it was, 00:27:30.950 --> 00:27:32.700 align:middle line:90% was not just like a water wave. 00:27:32.700 --> 00:27:35.300 align:middle line:84% In fact, it seemed to live in some higher dimensional 00:27:35.300 --> 00:27:38.150 align:middle line:84% abstract mathematical space that would quickly 00:27:38.150 --> 00:27:40.520 align:middle line:84% become known as configuration space 00:27:40.520 --> 00:27:42.620 align:middle line:84% rather than the space in which we 00:27:42.620 --> 00:27:45.300 align:middle line:90% seem to move around every day. 00:27:45.300 --> 00:27:47.690 align:middle line:84% So that was what Schrodinger began publishing 00:27:47.690 --> 00:27:50.150 align:middle line:90% as early as January 1926. 00:27:50.150 --> 00:27:52.230 align:middle line:84% He wrote a series of papers very, 00:27:52.230 --> 00:27:56.300 align:middle line:84% very quickly, one after the other in a four-part series 00:27:56.300 --> 00:27:59.180 align:middle line:84% throughout that winter and spring of 1926. 00:27:59.180 --> 00:28:02.960 align:middle line:84% And so before long, both Schrodinger and Heisenberg 00:28:02.960 --> 00:28:04.430 align:middle line:84% themselves, and soon many members 00:28:04.430 --> 00:28:07.040 align:middle line:84% of this kind of tight-knit community, 00:28:07.040 --> 00:28:10.760 align:middle line:84% were beginning to do a kind of compare and contrast exercise. 00:28:10.760 --> 00:28:12.920 align:middle line:84% There were now two quite different 00:28:12.920 --> 00:28:19.070 align:middle line:84% looking first approaches to a new quantum theory on offer. 00:28:19.070 --> 00:28:22.730 align:middle line:84% Heisenberg's matrix mechanics, Schrodinger's wave mechanics, 00:28:22.730 --> 00:28:24.500 align:middle line:90% they looked nothing alike. 00:28:24.500 --> 00:28:27.770 align:middle line:84% They seemed to make very different starting assumptions. 00:28:27.770 --> 00:28:31.130 align:middle line:84% And they had different kinds of strange features. 00:28:31.130 --> 00:28:33.600 align:middle line:84% They were strange in different ways. 00:28:33.600 --> 00:28:35.365 align:middle line:84% So Schrodinger eventually caught up 00:28:35.365 --> 00:28:36.740 align:middle line:84% with some of Heisenberg's papers. 00:28:36.740 --> 00:28:40.010 align:middle line:84% And he added a footnote into one of Schrodinger's own follow-up 00:28:40.010 --> 00:28:42.350 align:middle line:90% articles in that first series. 00:28:42.350 --> 00:28:45.120 align:middle line:84% I think this was not in his very first article but some time 00:28:45.120 --> 00:28:47.160 align:middle line:90% later that spring in a footnote. 00:28:47.160 --> 00:28:49.320 align:middle line:84% He writes, as you see here, my theory 00:28:49.320 --> 00:28:53.130 align:middle line:84% was inspired by Louis de Broglie and by short, but incomplete, 00:28:53.130 --> 00:28:54.810 align:middle line:90% remarks by Albert Einstein. 00:28:54.810 --> 00:28:58.870 align:middle line:84% No genetic relation whatever with Heisenberg is known to me. 00:28:58.870 --> 00:29:01.980 align:middle line:84% I knew of his theory, of course, but felt discouraged, not 00:29:01.980 --> 00:29:05.640 align:middle line:84% to say repelled by the methods of transcendental algebra, what 00:29:05.640 --> 00:29:08.850 align:middle line:84% we now call matrices, which appeared very difficult to me, 00:29:08.850 --> 00:29:11.070 align:middle line:84% and by the lack of visualizability. 00:29:11.070 --> 00:29:13.500 align:middle line:84% So that's about as rude as you can 00:29:13.500 --> 00:29:16.560 align:middle line:84% get in a footnote in a physics journal, at least at that time. 00:29:16.560 --> 00:29:21.270 align:middle line:84% I was discouraged and repelled by my colleagues' work. 00:29:21.270 --> 00:29:23.405 align:middle line:84% Heisenberg was a little less restrained. 00:29:23.405 --> 00:29:24.780 align:middle line:84% He wrote just in a private letter 00:29:24.780 --> 00:29:27.850 align:middle line:84% to his friend, Wolfgang Pauli, around that same time, just 00:29:27.850 --> 00:29:30.720 align:middle line:84% a little correspondence exchange. 00:29:30.720 --> 00:29:32.370 align:middle line:84% Heisenberg said, the more I reflect 00:29:32.370 --> 00:29:34.370 align:middle line:84% on the physical portion of Schrodinger's theory, 00:29:34.370 --> 00:29:36.180 align:middle line:90% the more disgusting I find it. 00:29:36.180 --> 00:29:39.150 align:middle line:84% Where Schrodinger writes on the visual ability of his theory, 00:29:39.150 --> 00:29:40.260 align:middle line:90% I consider it trash. 00:29:40.260 --> 00:29:43.530 align:middle line:84% After all, these waves live in six or more dimensional space. 00:29:43.530 --> 00:29:46.660 align:middle line:84% That seems no more visualizable than these abstract matrices. 00:29:46.660 --> 00:29:49.080 align:middle line:84% So this is really a remarkable clash 00:29:49.080 --> 00:29:51.570 align:middle line:84% between two people working on very similar topics 00:29:51.570 --> 00:29:55.080 align:middle line:84% at the same time and finding each other's work clearly 00:29:55.080 --> 00:29:58.470 align:middle line:84% lacking, not just, say, repulsive, disgusting. 00:29:58.470 --> 00:30:00.840 align:middle line:84% And so it was all the more surprising 00:30:00.840 --> 00:30:04.380 align:middle line:84% and really unexpected when several other physicists, 00:30:04.380 --> 00:30:07.170 align:middle line:84% actually Schrodinger himself and then two others, Pascual 00:30:07.170 --> 00:30:10.080 align:middle line:84% Jordan, who was another young physicist about the same age 00:30:10.080 --> 00:30:11.460 align:middle line:90% as Heisenberg and Pauli. 00:30:11.460 --> 00:30:14.580 align:middle line:84% Jordan was also a young physicist in Gottingen. 00:30:14.580 --> 00:30:17.010 align:middle line:84% So he began working directly with Heisenberg 00:30:17.010 --> 00:30:19.080 align:middle line:90% to elaborate matrix mechanics. 00:30:19.080 --> 00:30:21.930 align:middle line:84% And then separately still, Paul Dirac, 00:30:21.930 --> 00:30:24.900 align:middle line:84% a young British physicist who at this point 00:30:24.900 --> 00:30:27.300 align:middle line:84% was on a fellowship in Cambridge, England. 00:30:27.300 --> 00:30:30.640 align:middle line:84% All independently within a very short span of time, 00:30:30.640 --> 00:30:33.390 align:middle line:84% all three of those physicists demonstrated 00:30:33.390 --> 00:30:37.710 align:middle line:84% by the summer of 1926 that these two quite different-looking 00:30:37.710 --> 00:30:40.800 align:middle line:84% approaches, Heisenberg's matrix mechanics, Schrodinger's wave 00:30:40.800 --> 00:30:43.350 align:middle line:84% mechanics, were actually mathematically equivalent. 00:30:43.350 --> 00:30:45.690 align:middle line:84% You could actually build a mathematical kind 00:30:45.690 --> 00:30:48.900 align:middle line:84% of one-to-one mapping to any expression 00:30:48.900 --> 00:30:51.330 align:middle line:84% you might try to formulate in matrix mechanics 00:30:51.330 --> 00:30:53.620 align:middle line:84% and put that in wave mechanics or vice versa. 00:30:53.620 --> 00:30:58.170 align:middle line:84% So it looks disgusting, and repulsive, and un visualizable, 00:30:58.170 --> 00:31:00.780 align:middle line:84% one to the other, between Schrodinger and Heisenberg. 00:31:00.780 --> 00:31:02.640 align:middle line:84% It looked like these were really just 00:31:02.640 --> 00:31:05.430 align:middle line:84% remarkably different ways of trying to carve up the world. 00:31:05.430 --> 00:31:09.000 align:middle line:84% And yet, again, within just a matter of a few months, 00:31:09.000 --> 00:31:11.340 align:middle line:84% people had found at least a mathematical bridge 00:31:11.340 --> 00:31:12.340 align:middle line:90% between them. 00:31:12.340 --> 00:31:15.990 align:middle line:84% And it was that last work that really 00:31:15.990 --> 00:31:20.670 align:middle line:84% made a kind of a map between matrix and wave mechanics 00:31:20.670 --> 00:31:24.960 align:middle line:84% that really convinced people already by 1926 to begin 00:31:24.960 --> 00:31:28.380 align:middle line:84% referring to a new single thing, a new thing called quantum 00:31:28.380 --> 00:31:32.100 align:middle line:84% mechanics, not just matrix mechanics, not just wave 00:31:32.100 --> 00:31:35.400 align:middle line:84% mechanics, but now one thing called quantum mechanics 00:31:35.400 --> 00:31:38.160 align:middle line:84% and to then start using the phrase, "old quantum 00:31:38.160 --> 00:31:41.400 align:middle line:84% theory" to refer to that kind of grab bag of techniques 00:31:41.400 --> 00:31:46.230 align:middle line:84% that we looked at that had come before 1925-1926. 00:31:46.230 --> 00:31:48.990 align:middle line:84% So the new quantum mechanics was heralded, really, 00:31:48.990 --> 00:31:51.420 align:middle line:84% by that name almost in real time, 00:31:51.420 --> 00:31:54.210 align:middle line:84% just remarkable kind of convergence 00:31:54.210 --> 00:31:56.953 align:middle line:90% by summer and fall of 1926. 00:31:56.953 --> 00:31:58.120 align:middle line:90% So I'm going to pause there. 00:31:58.120 --> 00:32:00.178 align:middle line:84% I see a couple of questions come up in the chat. 00:32:00.178 --> 00:32:01.470 align:middle line:90% Time for some other discussion. 00:32:01.470 --> 00:32:02.670 align:middle line:90% Any questions on that stuff? 00:32:02.670 --> 00:32:06.240 align:middle line:90% 00:32:06.240 --> 00:32:08.647 align:middle line:84% So Alex asks, is this is Heligoland 00:32:08.647 --> 00:32:10.980 align:middle line:84% the same island the British tried to blow up after World 00:32:10.980 --> 00:32:11.480 align:middle line:90% War II? 00:32:11.480 --> 00:32:12.480 align:middle line:90% I have no idea. 00:32:12.480 --> 00:32:13.920 align:middle line:90% Well, that's news to me. 00:32:13.920 --> 00:32:14.910 align:middle line:90% It might be. 00:32:14.910 --> 00:32:16.560 align:middle line:84% Wikipedia at least could inform us. 00:32:16.560 --> 00:32:18.270 align:middle line:90% I don't know. 00:32:18.270 --> 00:32:19.860 align:middle line:84% Did configuration space ever become 00:32:19.860 --> 00:32:21.630 align:middle line:84% generalized to Hilbert space, Fisher asks. 00:32:21.630 --> 00:32:24.330 align:middle line:90% 00:32:24.330 --> 00:32:28.470 align:middle line:84% Yes, I'm not sure I'd say generalized to separately, 00:32:28.470 --> 00:32:31.050 align:middle line:84% and also actually pretty soon afterwards, by people 00:32:31.050 --> 00:32:36.390 align:middle line:84% like Paul Dirac began trying to formulate this new quantum 00:32:36.390 --> 00:32:41.250 align:middle line:84% mechanics in a more mathematically first principles 00:32:41.250 --> 00:32:44.500 align:middle line:84% way, thinking about vectors and vector spaces and so on. 00:32:44.500 --> 00:32:46.405 align:middle line:84% And that comes not only from Dirac 00:32:46.405 --> 00:32:48.780 align:middle line:84% but people like Dirac and John von Neumann, among others. 00:32:48.780 --> 00:32:52.170 align:middle line:84% So they weren't replacing configuration space per se. 00:32:52.170 --> 00:32:54.420 align:middle line:84% But they were certainly trying to think more carefully 00:32:54.420 --> 00:32:58.620 align:middle line:84% about the kinds of spaces, the kinds of mathematical spaces 00:32:58.620 --> 00:33:02.530 align:middle line:84% in which something like a quantum state might reside. 00:33:02.530 --> 00:33:04.800 align:middle line:84% So if you're thinking about a wave function, 00:33:04.800 --> 00:33:06.540 align:middle line:90% that's in configuration space. 00:33:06.540 --> 00:33:09.270 align:middle line:84% If you're thinking about a quantum state 00:33:09.270 --> 00:33:14.160 align:middle line:84% as a kind of eigenvector in some abstract Hilbert space, 00:33:14.160 --> 00:33:16.950 align:middle line:84% then that's the direction that Dirac especially 00:33:16.950 --> 00:33:18.000 align:middle line:90% starts to formalize. 00:33:18.000 --> 00:33:20.417 align:middle line:84% He writes an extraordinarily influential textbook. 00:33:20.417 --> 00:33:22.500 align:middle line:84% In fact, I showed its cover on the previous slide. 00:33:22.500 --> 00:33:24.690 align:middle line:84% First edition 1930, that's pretty quick 00:33:24.690 --> 00:33:27.000 align:middle line:84% to have a textbook on stuff that was really 00:33:27.000 --> 00:33:28.200 align:middle line:90% just a few years old. 00:33:28.200 --> 00:33:30.060 align:middle line:84% And then with the Hilbert spaces, 00:33:30.060 --> 00:33:32.250 align:middle line:84% people began to realize these could be 00:33:32.250 --> 00:33:34.770 align:middle line:90% of almost arbitrary dimension. 00:33:34.770 --> 00:33:36.870 align:middle line:84% So Hilbert spaces could be two dimensions. 00:33:36.870 --> 00:33:38.520 align:middle line:90% They could be 10,000 dimensions. 00:33:38.520 --> 00:33:40.360 align:middle line:84% They could be infinite dimensional. 00:33:40.360 --> 00:33:43.020 align:middle line:84% And so, in that sense, they're similar to configuration space 00:33:43.020 --> 00:33:45.190 align:middle line:84% in not being limited to only x, y, and z. 00:33:45.190 --> 00:33:47.770 align:middle line:84% But they're not exactly the same kind of thing. 00:33:47.770 --> 00:33:49.530 align:middle line:84% It's really people like Paul Dirac, 00:33:49.530 --> 00:33:52.955 align:middle line:84% who started pushing very heavily in that direction. 00:33:52.955 --> 00:33:55.080 align:middle line:84% Silu asked, did their opinions on each other's work 00:33:55.080 --> 00:33:56.790 align:middle line:90% ever change? 00:33:56.790 --> 00:33:57.940 align:middle line:90% That's a good question. 00:33:57.940 --> 00:33:59.940 align:middle line:84% I think they stopped calling each other's work 00:33:59.940 --> 00:34:01.060 align:middle line:90% disgusting in print. 00:34:01.060 --> 00:34:02.770 align:middle line:90% So that's a plus. 00:34:02.770 --> 00:34:04.560 align:middle line:84% And I think Schrodinger himself-- 00:34:04.560 --> 00:34:06.060 align:middle line:84% since he was one of the people who 00:34:06.060 --> 00:34:09.550 align:middle line:84% did find this mathematical bridge, a kind of equivalence 00:34:09.550 --> 00:34:10.927 align:middle line:90% between the two approaches-- 00:34:10.927 --> 00:34:12.969 align:middle line:84% Schrodinger, I think, after that began to realize 00:34:12.969 --> 00:34:18.199 align:middle line:84% there are kind of conveniences of either approach. 00:34:18.199 --> 00:34:19.960 align:middle line:84% So it's not one versus the other, 00:34:19.960 --> 00:34:22.190 align:middle line:84% since they could be mathematically mapped. 00:34:22.190 --> 00:34:24.940 align:middle line:84% But as each of you have probably learned just from your problem 00:34:24.940 --> 00:34:26.739 align:middle line:84% sets, for certain kinds of questions 00:34:26.739 --> 00:34:29.980 align:middle line:84% we might choose to ask, for certain kinds of calculations, 00:34:29.980 --> 00:34:33.880 align:middle line:84% one starting approach, one coordinate system, one 00:34:33.880 --> 00:34:37.030 align:middle line:84% way of characterizing the balance of forces and all that, 00:34:37.030 --> 00:34:39.133 align:middle line:84% that's often more convenient than others, 00:34:39.133 --> 00:34:41.050 align:middle line:84% even if, in principle, we could have mapped it 00:34:41.050 --> 00:34:42.400 align:middle line:90% into a different format. 00:34:42.400 --> 00:34:44.920 align:middle line:84% That's how people begin to talk more and more 00:34:44.920 --> 00:34:49.719 align:middle line:84% about the compare-and-contrast exercise between wave mechanics 00:34:49.719 --> 00:34:50.620 align:middle line:90% and matrix mechanics. 00:34:50.620 --> 00:34:53.530 align:middle line:84% If they are fundamentally mappable, 00:34:53.530 --> 00:34:56.050 align:middle line:84% then use whichever makes the most sense for a given 00:34:56.050 --> 00:34:59.300 align:middle line:84% problem, as opposed to say, choose one versus the other. 00:34:59.300 --> 00:35:02.375 align:middle line:84% So Lucas helpfully tells us that Heligoland 00:35:02.375 --> 00:35:04.750 align:middle line:84% was the site of one of the largest non-nuclear explosions 00:35:04.750 --> 00:35:05.590 align:middle line:90% ever. 00:35:05.590 --> 00:35:06.640 align:middle line:90% I had no idea. 00:35:06.640 --> 00:35:08.028 align:middle line:90% My goodness, thank you. 00:35:08.028 --> 00:35:08.820 align:middle line:90% I didn't know that. 00:35:08.820 --> 00:35:11.310 align:middle line:84% Thank you both to Alex and to Lucas. 00:35:11.310 --> 00:35:13.950 align:middle line:84% I've never been to Heligoland, obviously hard to travel now, 00:35:13.950 --> 00:35:14.860 align:middle line:90% to put it mildly. 00:35:14.860 --> 00:35:16.940 align:middle line:84% That would be an awesome field trip that we-- 00:35:16.940 --> 00:35:19.160 align:middle line:84% we should at least take a virtual field trip. 00:35:19.160 --> 00:35:20.850 align:middle line:90% We can look into that. 00:35:20.850 --> 00:35:24.150 align:middle line:84% Good, so my understanding is Heligoland, 00:35:24.150 --> 00:35:26.370 align:middle line:90% it has been contested territory. 00:35:26.370 --> 00:35:28.890 align:middle line:84% Again, Wikipedia can tell us who. 00:35:28.890 --> 00:35:30.630 align:middle line:84% It's a territory of what nation has 00:35:30.630 --> 00:35:33.450 align:middle line:84% been an unstable question, Germany, Denmark, probably 00:35:33.450 --> 00:35:33.960 align:middle line:90% others. 00:35:33.960 --> 00:35:37.710 align:middle line:84% It seems to sit in the North Sea pretty close to the coasts 00:35:37.710 --> 00:35:40.200 align:middle line:90% of both Germany and Denmark. 00:35:40.200 --> 00:35:42.150 align:middle line:90% So I knew it's been contested. 00:35:42.150 --> 00:35:45.270 align:middle line:84% And I thought it was also a lovely kind of vacation spot 00:35:45.270 --> 00:35:46.860 align:middle line:90% for much of the 19th century. 00:35:46.860 --> 00:35:51.150 align:middle line:84% I didn't realize it was subject to such a bombardment. 00:35:51.150 --> 00:35:52.410 align:middle line:90% So that's a preview. 00:35:52.410 --> 00:35:54.090 align:middle line:84% As you may have guessed, we're going 00:35:54.090 --> 00:35:56.190 align:middle line:84% to be coming to the Second World War in this class 00:35:56.190 --> 00:35:57.180 align:middle line:90% pretty soon, actually. 00:35:57.180 --> 00:36:01.080 align:middle line:84% So we'll be getting to similar kinds of themes, 00:36:01.080 --> 00:36:02.980 align:middle line:84% actually, within about two classes. 00:36:02.980 --> 00:36:05.130 align:middle line:84% So keep that theme in mind, I guess. 00:36:05.130 --> 00:36:07.770 align:middle line:84% Any other questions about Schrodinger, the wave equation, 00:36:07.770 --> 00:36:13.040 align:middle line:84% superposition, discrete eigenvalue spectra? 00:36:13.040 --> 00:36:15.980 align:middle line:90% They're fun. 00:36:15.980 --> 00:36:18.080 align:middle line:84% If not, then I think I'll press on. 00:36:18.080 --> 00:36:20.840 align:middle line:84% We can look at the next part of class. 00:36:20.840 --> 00:36:23.090 align:middle line:84% Of course, obviously please keep the questions coming, 00:36:23.090 --> 00:36:26.840 align:middle line:90% if more questions come up. 00:36:26.840 --> 00:36:28.990 align:middle line:84% So let's look now at the second part for today. 00:36:28.990 --> 00:36:30.730 align:middle line:84% And again here, I just remind you there 00:36:30.730 --> 00:36:33.940 align:middle line:84% is the optional lecture notes that go into this a little bit 00:36:33.940 --> 00:36:35.560 align:middle line:90% more explicitly, as well. 00:36:35.560 --> 00:36:37.060 align:middle line:84% So let's talk about something called 00:36:37.060 --> 00:36:39.280 align:middle line:84% the double-slit experiment which, 00:36:39.280 --> 00:36:41.740 align:middle line:84% again, might be something that at least some of you 00:36:41.740 --> 00:36:42.832 align:middle line:90% have heard about before. 00:36:42.832 --> 00:36:45.040 align:middle line:84% Some of you might have even been able to do a version 00:36:45.040 --> 00:36:46.600 align:middle line:90% in junior lab, for that matter. 00:36:46.600 --> 00:36:47.770 align:middle line:90% I'm not sure. 00:36:47.770 --> 00:36:53.050 align:middle line:84% This is just a remarkably fruitful experiment. 00:36:53.050 --> 00:36:56.108 align:middle line:84% It's the pedagogical gift that keeps on giving. 00:36:56.108 --> 00:36:57.400 align:middle line:90% It's not just me who thinks so. 00:36:57.400 --> 00:37:00.280 align:middle line:84% Look at this remarkable series of people 00:37:00.280 --> 00:37:04.000 align:middle line:84% who have come back time and time again to the double slit. 00:37:04.000 --> 00:37:07.673 align:middle line:84% So Heisenberg lectured on it as early as 1929, perhaps earlier. 00:37:07.673 --> 00:37:09.340 align:middle line:84% But that's the first case we know about. 00:37:09.340 --> 00:37:12.400 align:middle line:84% Schrodinger was lecturing on this as early as 1936 00:37:12.400 --> 00:37:13.330 align:middle line:90% and maybe earlier. 00:37:13.330 --> 00:37:15.190 align:middle line:84% But we have summer school lecture notes 00:37:15.190 --> 00:37:18.040 align:middle line:84% from as early as 1936, where Schrodinger featured it, 00:37:18.040 --> 00:37:18.970 align:middle line:90% as well. 00:37:18.970 --> 00:37:24.220 align:middle line:84% Niels Bohr featured this very famously in his very well known 00:37:24.220 --> 00:37:26.997 align:middle line:84% discussion of his long debate with Albert Einstein 00:37:26.997 --> 00:37:27.830 align:middle line:90% over quantum theory. 00:37:27.830 --> 00:37:29.788 align:middle line:84% That was another one of the readings for today, 00:37:29.788 --> 00:37:31.730 align:middle line:84% was an excerpt, a kind of shortened version 00:37:31.730 --> 00:37:33.620 align:middle line:84% of Bohr's very famous characterization 00:37:33.620 --> 00:37:35.690 align:middle line:84% of his long debate with Einstein. 00:37:35.690 --> 00:37:40.440 align:middle line:84% Coming closer to our own time in the 1960s, 00:37:40.440 --> 00:37:42.710 align:middle line:84% Richard Feynman declared that the double slit 00:37:42.710 --> 00:37:44.665 align:middle line:84% has in it the very heart of quantum mechanics. 00:37:44.665 --> 00:37:46.040 align:middle line:84% He said this is basically all you 00:37:46.040 --> 00:37:47.457 align:middle line:84% need to need to know, practically, 00:37:47.457 --> 00:37:48.920 align:middle line:90% about quantum theory. 00:37:48.920 --> 00:37:50.900 align:middle line:84% And even really much more recently, 00:37:50.900 --> 00:37:52.580 align:middle line:84% readers of Physics World magazine, 00:37:52.580 --> 00:37:56.480 align:middle line:84% which as you may know, is the kind of physics today of the UK 00:37:56.480 --> 00:37:59.870 align:middle line:84% physics society, they voted this double-slit experiment 00:37:59.870 --> 00:38:02.870 align:middle line:84% the single most beautiful experiment in the history 00:38:02.870 --> 00:38:05.180 align:middle line:84% of all of physics-- not the history of 20th century 00:38:05.180 --> 00:38:05.840 align:middle line:90% physics-- 00:38:05.840 --> 00:38:07.670 align:middle line:90% since the Earth cooled. 00:38:07.670 --> 00:38:10.880 align:middle line:84% And humans have done experiments to learn about nature. 00:38:10.880 --> 00:38:12.410 align:middle line:84% Readers of Physics World magazine 00:38:12.410 --> 00:38:15.440 align:middle line:84% concluded the single most beautiful effort of any kind 00:38:15.440 --> 00:38:17.550 align:middle line:84% ever was a double-slit experiment. 00:38:17.550 --> 00:38:19.130 align:middle line:84% So let's spend at least a few minutes 00:38:19.130 --> 00:38:24.260 align:middle line:84% giving proper, well-deserved attention to a double slit. 00:38:24.260 --> 00:38:27.230 align:middle line:84% So here's my very bad cartoon version of the double slit. 00:38:27.230 --> 00:38:30.110 align:middle line:84% I'm going to really follow what Richard Feynman's approach 00:38:30.110 --> 00:38:33.673 align:middle line:84% in what became in the canonical way of introducing 00:38:33.673 --> 00:38:34.340 align:middle line:90% the double slit. 00:38:34.340 --> 00:38:36.980 align:middle line:84% I've really lifted much of this from Feynman's very famous 00:38:36.980 --> 00:38:39.943 align:middle line:84% version of this in the Feynman lectures from the early '60s. 00:38:39.943 --> 00:38:41.360 align:middle line:84% He would have had better pictures. 00:38:41.360 --> 00:38:42.735 align:middle line:84% But the ideas are pretty similar. 00:38:42.735 --> 00:38:45.080 align:middle line:84% So let's imagine, first, the behavior 00:38:45.080 --> 00:38:46.730 align:middle line:90% of classical particles. 00:38:46.730 --> 00:38:50.090 align:middle line:84% These could be baseballs, or basketballs, or bullets 00:38:50.090 --> 00:38:56.920 align:middle line:84% fired from a gun, or any kind of projectile. 00:38:56.920 --> 00:38:58.690 align:middle line:84% So let's imagine we're firing bullets 00:38:58.690 --> 00:39:01.550 align:middle line:84% one at a time toward a bulletproof wall. 00:39:01.550 --> 00:39:03.400 align:middle line:84% So this wall here, this thick wall, 00:39:03.400 --> 00:39:05.560 align:middle line:84% is meant to be bulletproof, sorry. 00:39:05.560 --> 00:39:08.270 align:middle line:84% And yet there are two narrow slits in the wall. 00:39:08.270 --> 00:39:09.970 align:middle line:84% We'll just label those slits, this space 00:39:09.970 --> 00:39:13.060 align:middle line:84% here is slit A, this slit, B. The slits are a distance 00:39:13.060 --> 00:39:14.870 align:middle line:90% D apart. 00:39:14.870 --> 00:39:17.500 align:middle line:84% And then we have some backstop here 00:39:17.500 --> 00:39:19.360 align:middle line:90% where the bullets will lodge. 00:39:19.360 --> 00:39:22.690 align:middle line:84% And then, when it's safe to, and the gun's put away, 00:39:22.690 --> 00:39:26.830 align:middle line:84% we can go out and count up the number of bullets that landed 00:39:26.830 --> 00:39:28.490 align:middle line:90% here versus here versus here. 00:39:28.490 --> 00:39:30.280 align:middle line:84% So we're to ultimately try to add up. 00:39:30.280 --> 00:39:32.350 align:middle line:84% We're going to make a kind of histogram 00:39:32.350 --> 00:39:36.220 align:middle line:84% and plot the number of bullets per location 00:39:36.220 --> 00:39:39.980 align:middle line:84% as we march up in this direction of the backstop. 00:39:39.980 --> 00:39:43.450 align:middle line:84% So we want to then figure out, in a sense, the probability 00:39:43.450 --> 00:39:47.590 align:middle line:84% distribution where our bullet's most likely to wind up 00:39:47.590 --> 00:39:51.610 align:middle line:84% on this backdrop when, either, one slot is open, 00:39:51.610 --> 00:39:54.220 align:middle line:84% the other slot is open, or both are open. 00:39:54.220 --> 00:39:57.080 align:middle line:84% That's our exercise here with classical objects 00:39:57.080 --> 00:40:01.370 align:middle line:84% like baseballs, or in this case bullets fired from a gun. 00:40:01.370 --> 00:40:04.580 align:middle line:84% So let's first imagine that slit A is open but slit 00:40:04.580 --> 00:40:08.210 align:middle line:84% B is closed with some firm bullet-proof kind of shielding. 00:40:08.210 --> 00:40:10.650 align:middle line:84% So then our number of bullets will look like this. 00:40:10.650 --> 00:40:12.020 align:middle line:90% It's been smoothed out. 00:40:12.020 --> 00:40:14.540 align:middle line:84% Let's say if we shot 10,000 bullets, 00:40:14.540 --> 00:40:16.820 align:middle line:84% then it would actually be a pretty smooth curve. 00:40:16.820 --> 00:40:18.260 align:middle line:84% It would be basically a Gaussian. 00:40:18.260 --> 00:40:21.800 align:middle line:84% It would look like a kind of bell-shaped curve centered 00:40:21.800 --> 00:40:23.510 align:middle line:90% around the open slit. 00:40:23.510 --> 00:40:26.330 align:middle line:84% Most bullets would be found directly behind the open slit. 00:40:26.330 --> 00:40:28.370 align:middle line:84% But there'd be some modest scatter, 00:40:28.370 --> 00:40:31.880 align:middle line:84% some width to the distribution, so to speak. 00:40:31.880 --> 00:40:33.800 align:middle line:84% Likewise, if we then sealed up slit A 00:40:33.800 --> 00:40:35.930 align:middle line:84% with some bullet-proof shielding, 00:40:35.930 --> 00:40:38.210 align:middle line:84% and opened only slit B, and performed and shot 00:40:38.210 --> 00:40:41.030 align:middle line:84% another 10,000 bullets at it one at a time, 00:40:41.030 --> 00:40:43.280 align:middle line:84% and then did the same counting exercise, 00:40:43.280 --> 00:40:44.990 align:middle line:84% we could make a separate histogram. 00:40:44.990 --> 00:40:47.550 align:middle line:84% It looks remarkably similar, not surprising. 00:40:47.550 --> 00:40:49.140 align:middle line:90% It's a symmetrical problem. 00:40:49.140 --> 00:40:53.360 align:middle line:84% So if only slit B is open, then the vast majority of bullets 00:40:53.360 --> 00:40:56.060 align:middle line:84% are found directly behind that open slit. 00:40:56.060 --> 00:40:58.610 align:middle line:84% And there'll be some kind of bell-shaped curve, basically 00:40:58.610 --> 00:41:00.380 align:middle line:90% kind of Gaussian distribution. 00:41:00.380 --> 00:41:02.990 align:middle line:84% On either side there'll be some modest scatter. 00:41:02.990 --> 00:41:05.450 align:middle line:84% And then, if we then open both slits, 00:41:05.450 --> 00:41:09.230 align:middle line:84% fire another 10,000 bullets at the bulletproof wall 00:41:09.230 --> 00:41:13.050 align:middle line:84% with both slits A and B open, do the same exercise 00:41:13.050 --> 00:41:15.710 align:middle line:84% and make our histogram, the resulting distribution 00:41:15.710 --> 00:41:18.300 align:middle line:84% is just the sum of the previous two. 00:41:18.300 --> 00:41:20.390 align:middle line:84% So now there are a fair number of bullets 00:41:20.390 --> 00:41:22.340 align:middle line:84% that wind up in the middle because some 00:41:22.340 --> 00:41:24.305 align:middle line:84% are coming from the tail of this distribution. 00:41:24.305 --> 00:41:26.430 align:middle line:84% Some are coming from the tail of this distribution. 00:41:26.430 --> 00:41:28.520 align:middle line:84% And so some of them wind up in the middle. 00:41:28.520 --> 00:41:29.833 align:middle line:90% It's the sum of those two. 00:41:29.833 --> 00:41:31.250 align:middle line:84% But, nonetheless, the distribution 00:41:31.250 --> 00:41:34.790 align:middle line:84% is clearly still peaked in the positions directly 00:41:34.790 --> 00:41:36.530 align:middle line:90% behind the two open slits. 00:41:36.530 --> 00:41:39.530 align:middle line:84% So we have the resulting probability distribution. 00:41:39.530 --> 00:41:42.350 align:middle line:84% The histogram, when we add up when both slits are open, 00:41:42.350 --> 00:41:45.380 align:middle line:84% really is just the sum of those two separate ones. 00:41:45.380 --> 00:41:49.040 align:middle line:84% And so for classical particles, these probability distributions 00:41:49.040 --> 00:41:51.290 align:middle line:90% are of independent events. 00:41:51.290 --> 00:41:54.110 align:middle line:84% And therefore the probabilities in this case simply add. . 00:41:54.110 --> 00:41:57.470 align:middle line:84% We can get the probability distribution for the combined 00:41:57.470 --> 00:41:59.930 align:middle line:84% series, slits A and B open, simply 00:41:59.930 --> 00:42:02.640 align:middle line:84% by adding two independent possibilities. 00:42:02.640 --> 00:42:04.940 align:middle line:84% Each bullet either went through slit A, in which case 00:42:04.940 --> 00:42:06.590 align:middle line:90% it followed this distribution. 00:42:06.590 --> 00:42:10.400 align:middle line:84% Or each bullet, or an individual bullet, went through slit B. 00:42:10.400 --> 00:42:11.810 align:middle line:90% Add up those two options. 00:42:11.810 --> 00:42:13.310 align:middle line:84% Here's our resulting distribution, 00:42:13.310 --> 00:42:15.560 align:middle line:90% not too surprising. 00:42:15.560 --> 00:42:18.110 align:middle line:84% Now let's try a second version with waves. 00:42:18.110 --> 00:42:20.220 align:middle line:84% And this could be macroscopic waves, 00:42:20.220 --> 00:42:22.190 align:middle line:90% for example, ocean waves. 00:42:22.190 --> 00:42:24.380 align:middle line:84% In my little write up, I talk about doing 00:42:24.380 --> 00:42:27.140 align:middle line:84% this near the coast of Australia with waves approaching 00:42:27.140 --> 00:42:28.430 align:middle line:90% the Great Barrier Reef. 00:42:28.430 --> 00:42:30.500 align:middle line:84% But it could be even in an artificial wave 00:42:30.500 --> 00:42:32.630 align:middle line:90% pool with some barrier. 00:42:32.630 --> 00:42:36.110 align:middle line:84% So now we have some reef or some structure 00:42:36.110 --> 00:42:38.997 align:middle line:84% that can block waves that are coming from further away. 00:42:38.997 --> 00:42:39.830 align:middle line:90% They're approaching. 00:42:39.830 --> 00:42:41.210 align:middle line:90% Here's the shore. 00:42:41.210 --> 00:42:43.187 align:middle line:84% And we have some barrier that will block waves 00:42:43.187 --> 00:42:44.270 align:middle line:90% from passing through here. 00:42:44.270 --> 00:42:46.832 align:middle line:84% But the barrier has these two narrow slits 00:42:46.832 --> 00:42:48.290 align:middle line:84% which, again, we can label A and B. 00:42:48.290 --> 00:42:50.640 align:middle line:90% And they're a distance D apart. 00:42:50.640 --> 00:42:53.240 align:middle line:84% So now what we want to do is measure 00:42:53.240 --> 00:42:57.710 align:middle line:84% the intensity of the waves that lap up on shore. 00:42:57.710 --> 00:43:00.290 align:middle line:84% Clearly some water gets through slits A and B. 00:43:00.290 --> 00:43:03.770 align:middle line:84% So what's the pattern of waves that we find on the shoreline? 00:43:03.770 --> 00:43:05.900 align:middle line:84% And how does the intensity of that wave 00:43:05.900 --> 00:43:09.410 align:middle line:84% vary as we march along in location? 00:43:09.410 --> 00:43:14.360 align:middle line:84% And, again, we'll project the positions of slits A and B 00:43:14.360 --> 00:43:17.120 align:middle line:84% on the shore and ask about the varying intensity 00:43:17.120 --> 00:43:19.610 align:middle line:84% of the resulting wave as a function of distance 00:43:19.610 --> 00:43:21.300 align:middle line:90% or location. 00:43:21.300 --> 00:43:24.410 align:middle line:84% So once again, let's start with only one of those slits open. 00:43:24.410 --> 00:43:27.290 align:middle line:84% So we're going to close slit B with some kind of dam. 00:43:27.290 --> 00:43:29.180 align:middle line:84% We're going to block one of those slits 00:43:29.180 --> 00:43:32.510 align:middle line:84% so water can only get through that one narrow slit bay. 00:43:32.510 --> 00:43:35.840 align:middle line:84% And therefore we'll have a clearly peaked distribution. 00:43:35.840 --> 00:43:39.740 align:middle line:84% The wave that results, that we find on shore, is virtually 00:43:39.740 --> 00:43:43.520 align:middle line:84% zero, far away from that location 00:43:43.520 --> 00:43:46.820 align:middle line:84% of slit A, the projection onto the shore of the open slit. 00:43:46.820 --> 00:43:51.140 align:middle line:84% It's very clearly peaked, right directly behind the open slit. 00:43:51.140 --> 00:43:53.750 align:middle line:84% In fact, we can characterize the intensity of the wave 00:43:53.750 --> 00:43:55.400 align:middle line:90% as the square of some amplitude. 00:43:55.400 --> 00:43:55.940 align:middle line:90% It's a wave. 00:43:55.940 --> 00:43:57.740 align:middle line:84% It has some amplitude and some phase. 00:43:57.740 --> 00:44:03.050 align:middle line:84% And the intensity goes clearly as the square of this height, 00:44:03.050 --> 00:44:04.550 align:middle line:90% of this amplitude. 00:44:04.550 --> 00:44:06.980 align:middle line:84% And it basically is very clearly dramatically 00:44:06.980 --> 00:44:08.730 align:middle line:90% peaked behind the open slit. 00:44:08.730 --> 00:44:11.540 align:middle line:84% Now we place the dam in front of slit A, 00:44:11.540 --> 00:44:14.670 align:middle line:90% open slit B, same kind of story. 00:44:14.670 --> 00:44:16.595 align:middle line:84% But as many of you probably know, 00:44:16.595 --> 00:44:19.040 align:middle line:84% once we open both slits A and B, we 00:44:19.040 --> 00:44:21.440 align:middle line:90% get a totally different story. 00:44:21.440 --> 00:44:24.410 align:middle line:84% Now we get one of these characteristic interference 00:44:24.410 --> 00:44:28.310 align:middle line:84% patterns on the shore, not merely the sum of these two 00:44:28.310 --> 00:44:29.850 align:middle line:90% distributions together. 00:44:29.850 --> 00:44:32.150 align:middle line:84% And if we do a little more work, we 00:44:32.150 --> 00:44:34.610 align:middle line:84% can realize we can still characterize the resulting 00:44:34.610 --> 00:44:37.070 align:middle line:84% intensity by summing something together, 00:44:37.070 --> 00:44:40.190 align:middle line:84% not by summing the two intensities, actually 00:44:40.190 --> 00:44:44.790 align:middle line:84% by summing the two amplitudes first and then squaring that. 00:44:44.790 --> 00:44:47.960 align:middle line:84% And that's what allows for these interference patterns, 00:44:47.960 --> 00:44:50.720 align:middle line:84% much like we saw with the standing waves earlier. 00:44:50.720 --> 00:44:53.870 align:middle line:84% In regions where two crests happen to align, 00:44:53.870 --> 00:44:57.330 align:middle line:84% we'll get a sharp constructive interference, a heightened 00:44:57.330 --> 00:45:00.240 align:middle line:84% peak, in regions where there might have been one large peak. 00:45:00.240 --> 00:45:03.510 align:middle line:84% But a very small trough on the other side 00:45:03.510 --> 00:45:05.590 align:middle line:84% will get destructive interference. 00:45:05.590 --> 00:45:10.050 align:middle line:84% So in fact, when we add the amplitudes and then square, 00:45:10.050 --> 00:45:12.150 align:middle line:84% the resulting intensity looks nothing 00:45:12.150 --> 00:45:13.920 align:middle line:84% like the sum of the two intensities 00:45:13.920 --> 00:45:15.300 align:middle line:84% because that would overlook, that 00:45:15.300 --> 00:45:18.330 align:middle line:84% would discount all these ways that the waves can actually 00:45:18.330 --> 00:45:19.560 align:middle line:90% interfere with each other. 00:45:19.560 --> 00:45:23.400 align:middle line:84% And one indication of that is this characteristic feature 00:45:23.400 --> 00:45:24.660 align:middle line:90% of the interference pattern. 00:45:24.660 --> 00:45:28.290 align:middle line:84% The point on the shore with the largest intensity 00:45:28.290 --> 00:45:30.600 align:middle line:84% is a point between either two slits, 00:45:30.600 --> 00:45:32.980 align:middle line:84% whereas when either slit is open alone, 00:45:32.980 --> 00:45:36.300 align:middle line:84% that's a point of actually virtually vanishing intensity. 00:45:36.300 --> 00:45:38.580 align:middle line:84% So the greatest intensity is at a spot 00:45:38.580 --> 00:45:43.060 align:middle line:84% where neither scenario on its own had much power at all. 00:45:43.060 --> 00:45:45.240 align:middle line:84% And so, again, this is a characteristic 00:45:45.240 --> 00:45:48.570 align:middle line:84% of classical wave behavior, that the intensity 00:45:48.570 --> 00:45:52.470 align:middle line:84% goes as the square of the sum, not the sum of the squares. 00:45:52.470 --> 00:45:55.980 align:middle line:84% And since the amplitudes can be both positive and negative, 00:45:55.980 --> 00:45:57.780 align:middle line:84% they can even be complex numbers. 00:45:57.780 --> 00:45:59.340 align:middle line:84% They can be all kinds of situations 00:45:59.340 --> 00:46:05.010 align:middle line:84% in which the sum in which the square of the sum 00:46:05.010 --> 00:46:07.090 align:middle line:84% is quite different than the sum of the squares 00:46:07.090 --> 00:46:10.200 align:middle line:84% and, in particular, has this characteristic wave-like 00:46:10.200 --> 00:46:11.400 align:middle line:90% interference pattern. 00:46:11.400 --> 00:46:13.150 align:middle line:90% Again, probably pretty familiar. 00:46:13.150 --> 00:46:17.790 align:middle line:84% So now what happens when we now move to the quantum realm? 00:46:17.790 --> 00:46:21.420 align:middle line:84% Now let's imagine some cathode ray like JJ Thomson had, 00:46:21.420 --> 00:46:24.960 align:middle line:84% or of a sort that was by this point quite familiar, 00:46:24.960 --> 00:46:27.060 align:middle line:90% even by the 1920s. 00:46:27.060 --> 00:46:30.240 align:middle line:84% Things like what Germer and Davisson 00:46:30.240 --> 00:46:33.810 align:middle line:84% used in 1927 to think about de Broglie waves. 00:46:33.810 --> 00:46:36.330 align:middle line:84% This was already literally a feasible experiment 00:46:36.330 --> 00:46:37.800 align:middle line:90% as early as the mid 1920s. 00:46:37.800 --> 00:46:39.430 align:middle line:90% And people tried to do it. 00:46:39.430 --> 00:46:42.600 align:middle line:84% So let's imagine shooting out single electrons 00:46:42.600 --> 00:46:45.720 align:middle line:84% one at a time from some source, some cathode ray, let's say, 00:46:45.720 --> 00:46:47.048 align:middle line:90% some electron gun. 00:46:47.048 --> 00:46:48.840 align:middle line:84% We're going to send one electron at a time. 00:46:48.840 --> 00:46:51.000 align:middle line:84% We're not going to have a continuous spray of them. 00:46:51.000 --> 00:46:53.890 align:middle line:84% We'll send one, shut down the device. 00:46:53.890 --> 00:46:54.480 align:middle line:90% Let it cool. 00:46:54.480 --> 00:46:55.500 align:middle line:90% Go out for a coffee. 00:46:55.500 --> 00:46:58.290 align:middle line:84% Come back an hour later, send out one more electron. 00:46:58.290 --> 00:47:00.150 align:middle line:90% We can really take our time. 00:47:00.150 --> 00:47:02.800 align:middle line:84% So at any given moment, there's only one electron 00:47:02.800 --> 00:47:05.830 align:middle line:90% in play in the device. 00:47:05.830 --> 00:47:07.480 align:middle line:84% We're going to aim those one-at-a time 00:47:07.480 --> 00:47:08.893 align:middle line:90% electrons at a device. 00:47:08.893 --> 00:47:10.810 align:middle line:84% This is, by the way, taken-- this illustration 00:47:10.810 --> 00:47:14.290 align:middle line:84% is taken from Bohr's essay about his debates with Einstein. 00:47:14.290 --> 00:47:16.140 align:middle line:84% You hopefully recognize it from your reader. 00:47:16.140 --> 00:47:17.890 align:middle line:84% So we're going to send these electrons one 00:47:17.890 --> 00:47:20.740 align:middle line:84% at a time toward a device that has two slits. 00:47:20.740 --> 00:47:23.350 align:middle line:84% The electrons will be blocked if they hit anywhere here. 00:47:23.350 --> 00:47:26.890 align:middle line:84% But they can get through either this slit or that slit. 00:47:26.890 --> 00:47:28.990 align:middle line:84% And we have the opportunity to open or close 00:47:28.990 --> 00:47:31.120 align:middle line:90% each slit independently. 00:47:31.120 --> 00:47:34.450 align:middle line:84% And then behind the wall with two slits, 00:47:34.450 --> 00:47:37.630 align:middle line:84% we have an array of very closely-spaced detectors, 00:47:37.630 --> 00:47:39.610 align:middle line:90% electron detectors. 00:47:39.610 --> 00:47:42.400 align:middle line:84% And so we can measure with very good resolution 00:47:42.400 --> 00:47:46.720 align:middle line:84% where electrons are detected as a function of position 00:47:46.720 --> 00:47:50.230 align:middle line:84% along this kind of backstop, as array of detectors. 00:47:50.230 --> 00:47:52.600 align:middle line:84% We also can arrange things So that the distance 00:47:52.600 --> 00:47:55.720 align:middle line:84% between the two slits, the distance little D, 00:47:55.720 --> 00:48:00.850 align:middle line:84% is 10,000 times larger than the characteristic waviness 00:48:00.850 --> 00:48:03.740 align:middle line:84% scale, the de Broglie wavelength of those electrons. 00:48:03.740 --> 00:48:06.850 align:middle line:84% So the electron, if it's approaching, if it's anywhere 00:48:06.850 --> 00:48:11.590 align:middle line:84% near this slit, it should be 10,000 electron distances away 00:48:11.590 --> 00:48:14.740 align:middle line:90% from that slit and vice versa. 00:48:14.740 --> 00:48:17.110 align:middle line:84% It should have a localized behavior 00:48:17.110 --> 00:48:18.430 align:middle line:90% as it encounters the slits. 00:48:18.430 --> 00:48:20.860 align:middle line:84% Moreover, each of the detectors is 00:48:20.860 --> 00:48:22.570 align:middle line:84% going to detect the location of electron 00:48:22.570 --> 00:48:26.060 align:middle line:84% with a very, very small region of space. 00:48:26.060 --> 00:48:29.110 align:middle line:84% So we're not going to expect to find a splayed out wave 00:48:29.110 --> 00:48:29.740 align:middle line:90% of electrons. 00:48:29.740 --> 00:48:33.430 align:middle line:84% Each one is detected as a point-like discrete particulate 00:48:33.430 --> 00:48:35.830 align:middle line:84% detection because we've these very high resolution 00:48:35.830 --> 00:48:37.310 align:middle line:90% detectors in the back. 00:48:37.310 --> 00:48:39.460 align:middle line:84% So we're going to release one electron at a time. 00:48:39.460 --> 00:48:42.618 align:middle line:84% Wait one hour between and do that 10,000 times. 00:48:42.618 --> 00:48:44.410 align:middle line:84% Which, as I like to say, is why we actually 00:48:44.410 --> 00:48:45.510 align:middle line:90% have graduate students. 00:48:45.510 --> 00:48:47.093 align:middle line:84% Who's going to have patience for that, 00:48:47.093 --> 00:48:48.880 align:middle line:84% with many thanks to our teaching systems. 00:48:48.880 --> 00:48:51.640 align:middle line:90% So this is going to take months. 00:48:51.640 --> 00:48:54.290 align:middle line:84% But we care about the nature of the universe. 00:48:54.290 --> 00:48:57.100 align:middle line:84% And so we're going to just go plow through and do this. 00:48:57.100 --> 00:49:00.230 align:middle line:84% Now we're going to do the same kind of accounting exercise 00:49:00.230 --> 00:49:03.040 align:middle line:84% as we've done with both the classical particles 00:49:03.040 --> 00:49:04.490 align:middle line:90% and with the classical waves. 00:49:04.490 --> 00:49:06.250 align:middle line:84% We're going to make a kind of histogram 00:49:06.250 --> 00:49:08.800 align:middle line:84% of the number of electrons that are found in each 00:49:08.800 --> 00:49:11.890 align:middle line:84% of these bins, each of these detector bins, 00:49:11.890 --> 00:49:14.390 align:middle line:90% as a function of location. 00:49:14.390 --> 00:49:16.180 align:middle line:84% So once again, we'll start by keeping 00:49:16.180 --> 00:49:18.490 align:middle line:84% one slit closed so the electrons can only 00:49:18.490 --> 00:49:19.900 align:middle line:90% pass through the other slit. 00:49:19.900 --> 00:49:22.990 align:middle line:84% So if only slit A is open, we get this very strongly 00:49:22.990 --> 00:49:25.390 align:middle line:84% peaked distribution directly behind the open slit, 00:49:25.390 --> 00:49:26.800 align:middle line:90% just like with the bullets. 00:49:26.800 --> 00:49:30.010 align:middle line:84% If slit A is closed but only slit B is open, 00:49:30.010 --> 00:49:32.690 align:middle line:84% again, a very strongly peaked distribution. 00:49:32.690 --> 00:49:36.070 align:middle line:84% And so it looks a lot like the classical particles. 00:49:36.070 --> 00:49:38.320 align:middle line:84% In fact, if you've taken junior lab, 00:49:38.320 --> 00:49:40.660 align:middle line:84% you probably would learn to say those little wiggles 00:49:40.660 --> 00:49:44.560 align:middle line:84% are clearly instrumental error, that statistical 00:49:44.560 --> 00:49:45.730 align:middle line:90% insignificance. 00:49:45.730 --> 00:49:48.880 align:middle line:84% They never rise above about 1% of the central peak. 00:49:48.880 --> 00:49:51.280 align:middle line:84% It really looks like electrons are behaving like bullets. 00:49:51.280 --> 00:49:54.790 align:middle line:84% They're each emitted like a tiny little discrete particle. 00:49:54.790 --> 00:49:56.632 align:middle line:84% They're encountering one slit or the other 00:49:56.632 --> 00:49:58.840 align:middle line:84% because we've arranged the distance to be so extreme. 00:49:58.840 --> 00:50:01.990 align:middle line:84% They're all being detected as one little blip 00:50:01.990 --> 00:50:03.280 align:middle line:90% on that detector screen. 00:50:03.280 --> 00:50:06.100 align:middle line:84% They look like little baseballs or bullets. 00:50:06.100 --> 00:50:10.180 align:middle line:84% And yet, when we then look at the pattern 00:50:10.180 --> 00:50:12.520 align:middle line:84% when both slits are open but only one electron 00:50:12.520 --> 00:50:15.640 align:middle line:84% went through at a time, we get right back 00:50:15.640 --> 00:50:19.870 align:middle line:84% to this very familiar wave pattern. 00:50:19.870 --> 00:50:22.900 align:middle line:84% How this can happen has kept people up at night 00:50:22.900 --> 00:50:25.930 align:middle line:90% for, now, very nearly 100 years. 00:50:25.930 --> 00:50:29.960 align:middle line:84% And I hope we're not too blase about it even today. 00:50:29.960 --> 00:50:32.540 align:middle line:84% It looks like particles when only one slit's open. 00:50:32.540 --> 00:50:34.490 align:middle line:84% It looks like waves when both slits are open. 00:50:34.490 --> 00:50:39.440 align:middle line:84% And yet we've been super careful to only send 00:50:39.440 --> 00:50:41.220 align:middle line:90% one electron through at a time. 00:50:41.220 --> 00:50:44.990 align:middle line:84% Unlike a water wave is clearly an extended continuous object, 00:50:44.990 --> 00:50:46.880 align:middle line:84% clearly the wave can interfere with itself. 00:50:46.880 --> 00:50:48.500 align:middle line:84% It is literally an extended object 00:50:48.500 --> 00:50:50.150 align:middle line:90% which has many moving parts. 00:50:50.150 --> 00:50:52.190 align:middle line:84% These electrons are tiny little pellets. 00:50:52.190 --> 00:50:56.210 align:middle line:84% We emit them as little discrete bundles. 00:50:56.210 --> 00:50:58.105 align:middle line:84% We only have one in play at a time. 00:50:58.105 --> 00:50:59.480 align:middle line:84% It's not like two electrons could 00:50:59.480 --> 00:51:01.680 align:middle line:84% have influenced each other by repelling each other 00:51:01.680 --> 00:51:03.893 align:middle line:84% and made some kind of characteristic pattern 00:51:03.893 --> 00:51:05.810 align:middle line:84% because they were interacting with each other. 00:51:05.810 --> 00:51:07.250 align:middle line:84% We sent only one through at a time 00:51:07.250 --> 00:51:09.530 align:middle line:84% and waited a whole hour in between. 00:51:09.530 --> 00:51:12.500 align:middle line:84% We've done that 10,000 individual times. 00:51:12.500 --> 00:51:14.660 align:middle line:84% And yet the pattern that builds up, 00:51:14.660 --> 00:51:17.570 align:middle line:84% one individual point-like detection at a time, 00:51:17.570 --> 00:51:20.600 align:middle line:84% is this undeniable, very familiar wave pattern 00:51:20.600 --> 00:51:24.380 align:middle line:84% where, much as we would expect now from the ocean waves, 00:51:24.380 --> 00:51:26.780 align:middle line:84% the resulting probability distribution 00:51:26.780 --> 00:51:30.450 align:middle line:84% goes like the square of the sum and definitely not 00:51:30.450 --> 00:51:31.890 align:middle line:90% like the sum of the squares. 00:51:31.890 --> 00:51:34.860 align:middle line:84% It is not the sum of this distribution plus that one. 00:51:34.860 --> 00:51:36.960 align:middle line:84% It is absolutely emphatically not 00:51:36.960 --> 00:51:40.830 align:middle line:84% like 10,000 baseballs thrown at a wall with two holes, 00:51:40.830 --> 00:51:43.350 align:middle line:90% or bullets shot at some barrier. 00:51:43.350 --> 00:51:45.300 align:middle line:84% It looks just like the water wave, 00:51:45.300 --> 00:51:47.280 align:middle line:84% even though this built up over time 00:51:47.280 --> 00:51:52.360 align:middle line:90% from 10,000 independent events. 00:51:52.360 --> 00:51:54.870 align:middle line:84% Now, if I were to unmute you all, 00:51:54.870 --> 00:51:58.380 align:middle line:84% I should hear you screaming with either joy and ecstasy 00:51:58.380 --> 00:51:59.970 align:middle line:90% or real deep despair. 00:51:59.970 --> 00:52:02.950 align:middle line:84% Either way this should not be an emotionally neutral statement. 00:52:02.950 --> 00:52:05.760 align:middle line:84% So what comes from all this is Max 00:52:05.760 --> 00:52:08.820 align:middle line:84% Born, the Gottingen theorist, a contemporary of Einstein 00:52:08.820 --> 00:52:11.010 align:middle line:84% and Schrodinger, Heisenberg's mentor 00:52:11.010 --> 00:52:13.560 align:middle line:84% who taught mentor that these were matrices, 00:52:13.560 --> 00:52:15.630 align:middle line:84% Max Born then suggests from exactly 00:52:15.630 --> 00:52:21.510 align:middle line:84% these kinds of reasoning as early as the summer of 1926 00:52:21.510 --> 00:52:23.730 align:middle line:84% that what is this wave PSI, the thing 00:52:23.730 --> 00:52:26.590 align:middle line:84% that is a solution to Schrodinger's wave equation? 00:52:26.590 --> 00:52:29.550 align:middle line:84% It seems to be not a physical bit of the electron. 00:52:29.550 --> 00:52:33.900 align:middle line:84% It's not some electron density that's spread out in space. 00:52:33.900 --> 00:52:36.900 align:middle line:84% It seems to be related to the likely behavior 00:52:36.900 --> 00:52:39.870 align:middle line:90% of the associated particle. 00:52:39.870 --> 00:52:42.370 align:middle line:84% It's not a physical bit of the particle. 00:52:42.370 --> 00:52:45.000 align:middle line:84% It's a description of the way that particle 00:52:45.000 --> 00:52:47.250 align:middle line:90% is likely to behave. 00:52:47.250 --> 00:52:50.550 align:middle line:84% In particular, it's what comes to be called a probability 00:52:50.550 --> 00:52:54.850 align:middle line:84% amplitude, not the probability, not the peak that 00:52:54.850 --> 00:52:57.160 align:middle line:84% has this value on our histogram but actually 00:52:57.160 --> 00:53:00.340 align:middle line:84% the object whose absolute square gives rise 00:53:00.340 --> 00:53:02.780 align:middle line:84% to this thick black-line pattern. 00:53:02.780 --> 00:53:04.900 align:middle line:84% So the probability, Born says-- we now 00:53:04.900 --> 00:53:06.730 align:middle line:84% call this Born's interpretation-- 00:53:06.730 --> 00:53:10.480 align:middle line:84% the probability to find an electron here versus here 00:53:10.480 --> 00:53:13.300 align:middle line:84% versus here goes like the absolute square 00:53:13.300 --> 00:53:16.390 align:middle line:84% of this wave-like quantity, Schrodinger's wave function. 00:53:16.390 --> 00:53:19.780 align:middle line:84% That's what gets worked out within six months 00:53:19.780 --> 00:53:22.480 align:middle line:84% of Schrodinger's first publication on this 00:53:22.480 --> 00:53:24.820 align:middle line:84% by thinking about what is actually 00:53:24.820 --> 00:53:27.010 align:middle line:84% observable in experiments involving 00:53:27.010 --> 00:53:29.060 align:middle line:90% these wave-like features. 00:53:29.060 --> 00:53:32.950 align:middle line:84% So, again, that was a thought experiment in 1926. 00:53:32.950 --> 00:53:35.770 align:middle line:84% By 1920-- literally by 1927, there 00:53:35.770 --> 00:53:38.170 align:middle line:84% were efforts to try to do this experimentally. 00:53:38.170 --> 00:53:40.420 align:middle line:84% Nowadays we have very fancy equipment 00:53:40.420 --> 00:53:43.460 align:middle line:84% with high-precision sources and detectors. 00:53:43.460 --> 00:53:45.040 align:middle line:84% So here's a series of images courtesy 00:53:45.040 --> 00:53:48.112 align:middle line:84% from my colleagues, Robert Austin and Lyman Page 00:53:48.112 --> 00:53:49.570 align:middle line:84% at Princeton, this is not something 00:53:49.570 --> 00:53:53.410 align:middle line:84% we can do as an in-class demo or as an undergraduate laboratory. 00:53:53.410 --> 00:53:54.340 align:middle line:90% So this is real data. 00:53:54.340 --> 00:53:55.690 align:middle line:90% This isn't simulated. 00:53:55.690 --> 00:54:01.930 align:middle line:84% These are snapshots of the kind of fluorescent screen 00:54:01.930 --> 00:54:04.360 align:middle line:84% of an actual double-slit experiment done 00:54:04.360 --> 00:54:07.900 align:middle line:84% at different moments in time as the pattern builds up. 00:54:07.900 --> 00:54:10.720 align:middle line:84% So individual photons were fired out of a screen 00:54:10.720 --> 00:54:12.490 align:middle line:84% with two slits, literally one at a time. 00:54:12.490 --> 00:54:14.600 align:middle line:84% And now we can do single photon experiments, 00:54:14.600 --> 00:54:16.190 align:middle line:90% which is quite extraordinary. 00:54:16.190 --> 00:54:19.540 align:middle line:84% And then you can detect where each individual photon 00:54:19.540 --> 00:54:21.410 align:middle line:90% was detected. 00:54:21.410 --> 00:54:24.550 align:middle line:84% So these are little pinpricks of light 00:54:24.550 --> 00:54:26.920 align:middle line:84% where an individual photon interacted 00:54:26.920 --> 00:54:29.680 align:middle line:84% with the fluorescent photo detector. 00:54:29.680 --> 00:54:31.713 align:middle line:84% So you have a mostly blackened screen 00:54:31.713 --> 00:54:33.880 align:middle line:84% because we've only sent a couple of photons through, 00:54:33.880 --> 00:54:37.870 align:middle line:84% one at a time so far, very localized individual detections 00:54:37.870 --> 00:54:39.490 align:middle line:90% here and here, but not here. 00:54:39.490 --> 00:54:42.310 align:middle line:84% That's after the first 1/30 of a second that's 00:54:42.310 --> 00:54:45.370 align:middle line:84% shooting rapidly one photon at a time and only one at a time. 00:54:45.370 --> 00:54:47.965 align:middle line:84% After a whole second has gone by, 00:54:47.965 --> 00:54:49.840 align:middle line:90% you have accumulating pattern. 00:54:49.840 --> 00:54:53.580 align:middle line:84% Now you have several hundred photons individually detected. 00:54:53.580 --> 00:54:56.550 align:middle line:84% Wait 100 seconds and you see very clearly 00:54:56.550 --> 00:54:59.400 align:middle line:84% this wave-like interference pattern, exactly the pattern 00:54:59.400 --> 00:55:02.370 align:middle line:84% described by that Born interpretation 00:55:02.370 --> 00:55:05.280 align:middle line:84% even though this is built from thousands 00:55:05.280 --> 00:55:09.600 align:middle line:84% of otherwise independents located in time and space 00:55:09.600 --> 00:55:12.450 align:middle line:90% detections of individual quanta. 00:55:12.450 --> 00:55:16.440 align:middle line:84% So we shoot out individual quanta, particulate-like. 00:55:16.440 --> 00:55:19.873 align:middle line:84% We detect individual quanta, particulate-like. 00:55:19.873 --> 00:55:21.540 align:middle line:84% And they can't interfere with each other 00:55:21.540 --> 00:55:23.220 align:middle line:84% because we make sure only one's sort of in the device 00:55:23.220 --> 00:55:24.030 align:middle line:90% at a time. 00:55:24.030 --> 00:55:27.030 align:middle line:84% And yet, over time, they somehow build up 00:55:27.030 --> 00:55:30.360 align:middle line:84% this very characteristic wave-like interference pattern. 00:55:30.360 --> 00:55:33.340 align:middle line:84% That is what's called the double-slit experiment. 00:55:33.340 --> 00:55:35.380 align:middle line:90% So let pause there. 00:55:35.380 --> 00:55:38.890 align:middle line:84% How do we go from one electron every hour to 100 every second? 00:55:38.890 --> 00:55:39.390 align:middle line:90% Oh, good. 00:55:39.390 --> 00:55:40.600 align:middle line:90% So, Alex, good. 00:55:40.600 --> 00:55:44.550 align:middle line:84% So the data I just showed you is actually with photons, 00:55:44.550 --> 00:55:45.630 align:middle line:90% the Princeton group. 00:55:45.630 --> 00:55:47.760 align:middle line:84% One can do it with electrons, as well. 00:55:47.760 --> 00:55:53.250 align:middle line:84% They were using, let's say, a photon source that 00:55:53.250 --> 00:55:55.660 align:middle line:90% emits single photons rapidly. 00:55:55.660 --> 00:55:58.730 align:middle line:84% So they really were shooting out only one photon at a time. 00:55:58.730 --> 00:56:01.340 align:middle line:84% But they can produce many photons per second. 00:56:01.340 --> 00:56:04.480 align:middle line:84% So the timing when we're dealing with that particular source 00:56:04.480 --> 00:56:07.250 align:middle line:84% of individual quanta, just what's called the duty cycle 00:56:07.250 --> 00:56:07.990 align:middle line:90% is shorter. 00:56:07.990 --> 00:56:11.630 align:middle line:84% We also have very rapid electronics now, unlike 1927. 00:56:11.630 --> 00:56:15.430 align:middle line:84% So the electronics can actually resolve individual detections 00:56:15.430 --> 00:56:17.030 align:middle line:90% in a tiny fraction of a second. 00:56:17.030 --> 00:56:20.650 align:middle line:84% So, conceptually, it's as if we had gone back to my cartoon, 00:56:20.650 --> 00:56:22.990 align:middle line:84% turned on our machine, shot out one particle, 00:56:22.990 --> 00:56:24.280 align:middle line:90% turn it off, went away. 00:56:24.280 --> 00:56:27.970 align:middle line:84% It's just now we can do that with the kind of high-duty 00:56:27.970 --> 00:56:29.320 align:middle line:90% cycle rapid electronics. 00:56:29.320 --> 00:56:33.760 align:middle line:84% But, conceptually, it to my mind is quite similar. 00:56:33.760 --> 00:56:35.980 align:middle line:84% Vittorio asks, as you do the experiment 00:56:35.980 --> 00:56:38.412 align:middle line:84% with progressively heavier particles-- oh, good question-- 00:56:38.412 --> 00:56:40.870 align:middle line:84% is there a certain point where the resulting pattern begins 00:56:40.870 --> 00:56:43.000 align:middle line:84% to look like what you'd expect from two bullets? 00:56:43.000 --> 00:56:44.260 align:middle line:90% Oh, thank you, Vittorio. 00:56:44.260 --> 00:56:46.630 align:middle line:90% What a wonderful question. 00:56:46.630 --> 00:56:50.223 align:middle line:84% That is a question that is still occupying, 00:56:50.223 --> 00:56:51.890 align:middle line:84% literally, many of my friends, let along 00:56:51.890 --> 00:56:53.340 align:middle line:90% colleagues around the world. 00:56:53.340 --> 00:56:54.990 align:middle line:90% The short answer is yes. 00:56:54.990 --> 00:56:58.770 align:middle line:84% The longer answer is why and how. 00:56:58.770 --> 00:57:00.180 align:middle line:90% And Jade's quite right. 00:57:00.180 --> 00:57:02.100 align:middle line:84% Jade puts in the chat, this experiment 00:57:02.100 --> 00:57:04.590 align:middle line:84% has been done, a comparable experiment, with objects 00:57:04.590 --> 00:57:08.610 align:middle line:84% as large as buckyballs, C60, molecules of 60 carbon 00:57:08.610 --> 00:57:12.040 align:middle line:84% atoms in one bound state, not just individual electrons. 00:57:12.040 --> 00:57:15.660 align:middle line:84% So an object as large as a buckyball which is, I think, 00:57:15.660 --> 00:57:18.600 align:middle line:84% not a billion, but several tens of millions of times larger 00:57:18.600 --> 00:57:21.390 align:middle line:84% than an individual electron, we still 00:57:21.390 --> 00:57:24.750 align:middle line:84% find this characteristic quantum interference very clearly. 00:57:24.750 --> 00:57:29.873 align:middle line:84% Again, it's well within statistical significance. 00:57:29.873 --> 00:57:31.290 align:middle line:84% And, in fact, that's an experiment 00:57:31.290 --> 00:57:33.665 align:middle line:84% that one of my colleagues, Anton Zeilinger, and his group 00:57:33.665 --> 00:57:35.590 align:middle line:90% had done quite some time ago. 00:57:35.590 --> 00:57:38.490 align:middle line:84% So the question is, where does that stop? 00:57:38.490 --> 00:57:42.150 align:middle line:84% I had a very beloved physics professor of my own, 00:57:42.150 --> 00:57:43.728 align:middle line:90% when I was an undergraduate. 00:57:43.728 --> 00:57:44.520 align:middle line:90% He was very senior. 00:57:44.520 --> 00:57:45.390 align:middle line:90% He's actually just retired. 00:57:45.390 --> 00:57:47.070 align:middle line:84% He was still teaching just for fun. 00:57:47.070 --> 00:57:49.410 align:middle line:84% And he used to joke that when he was in graduate school, 00:57:49.410 --> 00:57:52.067 align:middle line:84% he and his buddies would wonder, could they get themselves 00:57:52.067 --> 00:57:54.400 align:middle line:84% to interfere if they rode a bicycle through two standing 00:57:54.400 --> 00:57:56.800 align:middle line:84% posts sufficiently quickly, something 00:57:56.800 --> 00:57:59.260 align:middle line:84% when they don't interfere with themselves. 00:57:59.260 --> 00:58:01.030 align:middle line:84% An individual human on a bicycle doesn't 00:58:01.030 --> 00:58:04.180 align:middle line:84% undergo, at least not in any obvious way, 00:58:04.180 --> 00:58:05.560 align:middle line:90% this kind of interference. 00:58:05.560 --> 00:58:09.760 align:middle line:84% It doesn't seem to happen with things 00:58:09.760 --> 00:58:12.010 align:middle line:84% we can shrink down and look at microscopically 00:58:12.010 --> 00:58:15.970 align:middle line:84% at the scale of, say, amoebas, which people have tried. 00:58:15.970 --> 00:58:19.330 align:middle line:84% But it does happen with enormous molecules, 00:58:19.330 --> 00:58:21.800 align:middle line:84% enormous on the size of parts of atoms. 00:58:21.800 --> 00:58:23.540 align:middle line:90% So where is that line? 00:58:23.540 --> 00:58:26.570 align:middle line:84% And what causes the transition in behavior? 00:58:26.570 --> 00:58:29.890 align:middle line:84% If we're all made up of atoms and electrons, and electrons 00:58:29.890 --> 00:58:32.830 align:middle line:84% and atoms behave in this fundamentally quantum 00:58:32.830 --> 00:58:35.560 align:middle line:90% mechanical way, why don't we? 00:58:35.560 --> 00:58:37.480 align:middle line:84% Why didn't my professor on his bicycle 00:58:37.480 --> 00:58:39.550 align:middle line:84% get diffracted when he biked through 00:58:39.550 --> 00:58:41.630 align:middle line:90% between two standing posts? 00:58:41.630 --> 00:58:44.470 align:middle line:84% So that's what's often now called the quantum 00:58:44.470 --> 00:58:46.090 align:middle line:90% to classical transition. 00:58:46.090 --> 00:58:49.643 align:middle line:84% If you have nothing better to do with yourself for the next 17 00:58:49.643 --> 00:58:51.310 align:middle line:84% years, I suggest you start googling that 00:58:51.310 --> 00:58:52.435 align:middle line:90% and read every paper on it. 00:58:52.435 --> 00:58:55.180 align:middle line:84% It's enormously complicated and still very 00:58:55.180 --> 00:58:57.910 align:middle line:84% much on the forefront of the research 00:58:57.910 --> 00:58:59.440 align:middle line:90% frontier for many people. 00:58:59.440 --> 00:59:01.588 align:middle line:84% And we just genuinely, we collectively, 00:59:01.588 --> 00:59:03.130 align:middle line:84% the community genuinely doesn't know. 00:59:03.130 --> 00:59:05.710 align:middle line:84% We're getting better at characterizing 00:59:05.710 --> 00:59:09.160 align:middle line:84% where the break is, where the line is, but not why, 00:59:09.160 --> 00:59:12.670 align:middle line:84% and not what would cause the behavior to transition 00:59:12.670 --> 00:59:17.510 align:middle line:84% from one very specific kind of behavior to the other. 00:59:17.510 --> 00:59:20.570 align:middle line:84% So other colleagues are trying to do this with living objects. 00:59:20.570 --> 00:59:23.560 align:middle line:84% So it turns out viruses, some kinds of viruses, 00:59:23.560 --> 00:59:26.590 align:middle line:84% might be just small enough for this to work 00:59:26.590 --> 00:59:28.810 align:middle line:84% and yet much, much bigger than buckyballs. 00:59:28.810 --> 00:59:30.580 align:middle line:84% So people are trying to get living 00:59:30.580 --> 00:59:33.460 align:middle line:84% things, seemingly living things like viruses, 00:59:33.460 --> 00:59:34.420 align:middle line:90% to quantum interfere. 00:59:34.420 --> 00:59:35.300 align:middle line:90% That's not been done yet. 00:59:35.300 --> 00:59:36.925 align:middle line:84% But that's one thing people are trying. 00:59:36.925 --> 00:59:40.060 align:middle line:84% So this question, how big could it get and still show 00:59:40.060 --> 00:59:41.260 align:middle line:90% this inherent quantumness? 00:59:41.260 --> 00:59:45.310 align:middle line:84% That is still very much a live issue. 00:59:45.310 --> 00:59:47.410 align:middle line:84% And as I said, there's two facets to it. 00:59:47.410 --> 00:59:48.790 align:middle line:90% What's the scale? 00:59:48.790 --> 00:59:52.180 align:middle line:84% But even more subtly, what's the reason why 00:59:52.180 --> 00:59:55.060 align:middle line:84% that stops working as we continue 00:59:55.060 --> 00:59:56.868 align:middle line:90% considering larger objects? 00:59:56.868 --> 00:59:58.160 align:middle line:90% So thank you for that question. 00:59:58.160 --> 00:59:59.610 align:middle line:90% Great question. 00:59:59.610 --> 01:00:01.360 align:middle line:84% Any other questions about the double slit, 01:00:01.360 --> 01:00:04.402 align:middle line:84% about this, what should have been the scream. 01:00:04.402 --> 01:00:05.860 align:middle line:84% I mean, all of you should have just 01:00:05.860 --> 01:00:09.055 align:middle line:84% been unmuted and just howling at the moon. 01:00:09.055 --> 01:00:10.180 align:middle line:90% At least that's how I feel. 01:00:10.180 --> 01:00:11.950 align:middle line:90% And I still think about this. 01:00:11.950 --> 01:00:13.210 align:middle line:90% Maybe that's my problem. 01:00:13.210 --> 01:00:14.902 align:middle line:84% I just find that just astonishing. 01:00:14.902 --> 01:00:16.360 align:middle line:84% It's not just a thought experiment. 01:00:16.360 --> 01:00:18.940 align:middle line:84% We can do that now with individual quanta 01:00:18.940 --> 01:00:22.480 align:middle line:84% with super careful control on our source, on our detectors, 01:00:22.480 --> 01:00:25.480 align:middle line:84% have really extraordinarily high statistical significance on all 01:00:25.480 --> 01:00:30.070 align:middle line:84% the measurements, and fire what looked, for, 01:00:30.070 --> 01:00:33.370 align:middle line:84% all intents and purposes, to be like little tiny baseballs. 01:00:33.370 --> 01:00:35.260 align:middle line:90% And somehow they know. 01:00:35.260 --> 01:00:37.480 align:middle line:84% Somehow their behavior is guided in a way 01:00:37.480 --> 01:00:43.050 align:middle line:84% that baseballs and bullets just aren't, or basketballs. 01:00:43.050 --> 01:00:45.740 align:middle line:84% If that's just OK for all of you then, I mean, come on. 01:00:45.740 --> 01:00:47.750 align:middle line:84% That's just like, that's COVID speaking. 01:00:47.750 --> 01:00:49.400 align:middle line:90% That should just-- 01:00:49.400 --> 01:00:50.633 align:middle line:90% OK, you get the point. 01:00:50.633 --> 01:00:52.550 align:middle line:84% Any other questions on either my mental state, 01:00:52.550 --> 01:00:55.690 align:middle line:84% or emotional state, or on the double-slit experiment? 01:00:55.690 --> 01:00:57.440 align:middle line:84% If not we'll go into one last little part, 01:00:57.440 --> 01:00:59.240 align:middle line:84% one kind of CODA for double slit. 01:00:59.240 --> 01:01:02.930 align:middle line:84% And then we'll have time for questions, as well. 01:01:02.930 --> 01:01:04.707 align:middle line:90% OK, so I'll get it together. 01:01:04.707 --> 01:01:05.790 align:middle line:90% I'll pull myself together. 01:01:05.790 --> 01:01:09.320 align:middle line:84% I'll talk now about this last part, which also started 01:01:09.320 --> 01:01:14.240 align:middle line:84% being thought about very early, even in the late 1920s, 01:01:14.240 --> 01:01:17.960 align:middle line:84% as further ways to try to probe what's going on when we think 01:01:17.960 --> 01:01:19.410 align:middle line:90% about this quantum level. 01:01:19.410 --> 01:01:21.950 align:middle line:84% So, again, this I'm going to do, especially schematically 01:01:21.950 --> 01:01:23.330 align:middle line:90% in the class session. 01:01:23.330 --> 01:01:25.670 align:middle line:84% There is a bit more explicit discussion 01:01:25.670 --> 01:01:29.735 align:middle line:84% in the optional lecture notes on the course site. 01:01:29.735 --> 01:01:31.110 align:middle line:84% Let's go back to that same setup, 01:01:31.110 --> 01:01:32.152 align:middle line:90% the one we just ended on. 01:01:32.152 --> 01:01:34.700 align:middle line:84% Let's say we're sending one electron at a time, 01:01:34.700 --> 01:01:39.440 align:middle line:84% waiting ample time in between, firing them 01:01:39.440 --> 01:01:43.320 align:middle line:84% toward this system where the distance between slits A and B 01:01:43.320 --> 01:01:47.850 align:middle line:84% is much, much larger than the kind of characteristic size 01:01:47.850 --> 01:01:49.840 align:middle line:90% of the particles themselves. 01:01:49.840 --> 01:01:52.560 align:middle line:84% But now we want to say these particles clearly 01:01:52.560 --> 01:01:54.240 align:middle line:84% must have gone through either slit A 01:01:54.240 --> 01:01:58.470 align:middle line:84% or slit B. That seems like a reasonable question to ponder. 01:01:58.470 --> 01:02:02.550 align:middle line:84% Which slit do they pass through on any individual experimental 01:02:02.550 --> 01:02:03.270 align:middle line:90% run? 01:02:03.270 --> 01:02:06.660 align:middle line:84% The distance between the slits is so much larger 01:02:06.660 --> 01:02:10.800 align:middle line:84% than the characteristic size that each particle 01:02:10.800 --> 01:02:12.780 align:middle line:84% must have had to have chosen to go 01:02:12.780 --> 01:02:16.800 align:middle line:84% through either slit A or slit B. So why don't we 01:02:16.800 --> 01:02:17.728 align:middle line:90% try to find out? 01:02:17.728 --> 01:02:19.020 align:middle line:90% And this is a very clever idea. 01:02:19.020 --> 01:02:22.560 align:middle line:84% Heisenberg's lectures on this, even in those 1929 lectures-- 01:02:22.560 --> 01:02:24.420 align:middle line:84% and others have developed it since then. 01:02:24.420 --> 01:02:26.730 align:middle line:84% Let's put a bunch of test particles 01:02:26.730 --> 01:02:29.710 align:middle line:84% behind only one of the slits so now 01:02:29.710 --> 01:02:31.420 align:middle line:90% it'll be like an alarm system. 01:02:31.420 --> 01:02:34.230 align:middle line:84% If an electron happens to go through slit A, 01:02:34.230 --> 01:02:36.660 align:middle line:84% it'll smack into these test particles. 01:02:36.660 --> 01:02:37.620 align:middle line:90% We'll have collisions. 01:02:37.620 --> 01:02:40.050 align:middle line:84% We'll have scattered particles zooming out 01:02:40.050 --> 01:02:42.330 align:middle line:84% of this region of the experiment that we could then 01:02:42.330 --> 01:02:43.590 align:middle line:90% detect and measure. 01:02:43.590 --> 01:02:46.290 align:middle line:84% And if no test particles are scattered, 01:02:46.290 --> 01:02:47.910 align:middle line:84% then we know the electron must have 01:02:47.910 --> 01:02:49.470 align:middle line:90% gone through the other slit. 01:02:49.470 --> 01:02:52.920 align:middle line:84% So we're going to bunch together, get kind of close 01:02:52.920 --> 01:02:58.830 align:middle line:84% in space, some targets behind only one of the two open slits. 01:02:58.830 --> 01:03:01.080 align:middle line:84% And that way, we have what's called a slit detector. 01:03:01.080 --> 01:03:03.960 align:middle line:84% We have some mechanism of determining event 01:03:03.960 --> 01:03:10.030 align:middle line:84% by event through which slit the particle actually passed. 01:03:10.030 --> 01:03:13.090 align:middle line:84% And so now what happens when both slits are open, 01:03:13.090 --> 01:03:16.120 align:middle line:84% but we measure through these slit detectors through which 01:03:16.120 --> 01:03:19.210 align:middle line:84% slit each electron passed, then the distribution, 01:03:19.210 --> 01:03:22.010 align:middle line:84% even for these quantum mechanical electrons, 01:03:22.010 --> 01:03:27.010 align:middle line:84% the distribution reverts back to this thoroughly classical sum 01:03:27.010 --> 01:03:29.090 align:middle line:84% of two independent probabilities. 01:03:29.090 --> 01:03:30.640 align:middle line:90% So we do our usual experiment. 01:03:30.640 --> 01:03:32.350 align:middle line:90% We do this 10,000 times. 01:03:32.350 --> 01:03:35.380 align:middle line:84% Sometimes we see the scattered particles from behind slit A. 01:03:35.380 --> 01:03:37.060 align:middle line:84% Sometimes we see no scattered particles. 01:03:37.060 --> 01:03:38.470 align:middle line:84% It must have gone through slit B. 01:03:38.470 --> 01:03:40.002 align:middle line:84% And then separately from that, we 01:03:40.002 --> 01:03:41.710 align:middle line:84% count up where all the electrons actually 01:03:41.710 --> 01:03:45.790 align:middle line:84% wind up at that backstop with our closely-spaced detectors. 01:03:45.790 --> 01:03:48.370 align:middle line:84% And we get, basically, the classical distribution. 01:03:48.370 --> 01:03:52.390 align:middle line:84% It looks like the sum of two independent classical 01:03:52.390 --> 01:03:54.370 align:middle line:90% particle-like distributions. 01:03:54.370 --> 01:03:58.870 align:middle line:84% When we ask through which slit each individual particle 01:03:58.870 --> 01:04:02.470 align:middle line:84% passed, the particles give us a particle-like answer. 01:04:02.470 --> 01:04:05.680 align:middle line:84% They pass through either slit A or slit B 01:04:05.680 --> 01:04:08.800 align:middle line:84% and had correspondingly no interference pattern 01:04:08.800 --> 01:04:10.598 align:middle line:90% between those two options. 01:04:10.598 --> 01:04:12.140 align:middle line:84% On the other hand, when we don't even 01:04:12.140 --> 01:04:14.330 align:middle line:84% try to ask through which slit did 01:04:14.330 --> 01:04:17.690 align:middle line:84% those individual particles pass, we remove that slit detector 01:04:17.690 --> 01:04:18.560 align:middle line:90% altogether. 01:04:18.560 --> 01:04:21.200 align:middle line:84% Then we get back to the results that we'd already found, 01:04:21.200 --> 01:04:22.850 align:middle line:84% that when both slits are open, we 01:04:22.850 --> 01:04:26.420 align:middle line:84% get this characteristic wave-like interference pattern. 01:04:26.420 --> 01:04:29.840 align:middle line:84% And we only get that when we've given up even the opportunity 01:04:29.840 --> 01:04:35.150 align:middle line:84% to ask this particle-like question about through which 01:04:35.150 --> 01:04:37.160 align:middle line:84% slit had individual particles passed. 01:04:37.160 --> 01:04:38.840 align:middle line:84% So we are allowed to ask the question. 01:04:38.840 --> 01:04:40.160 align:middle line:90% We actually can ask a question. 01:04:40.160 --> 01:04:42.410 align:middle line:84% People have done it with a slightly more sophisticated 01:04:42.410 --> 01:04:44.390 align:middle line:90% version than just that cartoon. 01:04:44.390 --> 01:04:47.180 align:middle line:84% And yet, somehow, the nature of the results 01:04:47.180 --> 01:04:49.580 align:middle line:84% changes very deeply and fundamentally, 01:04:49.580 --> 01:04:52.400 align:middle line:84% based on the nature of the question we asked. 01:04:52.400 --> 01:04:54.710 align:middle line:84% So, again, you can see why that happens. 01:04:54.710 --> 01:04:57.350 align:middle line:84% I'm being pretty schematic and kind of waving my hands. 01:04:57.350 --> 01:04:59.180 align:middle line:84% It's only a couple lines of algebra. 01:04:59.180 --> 01:05:00.763 align:middle line:84% And you might have already guessed it. 01:05:00.763 --> 01:05:02.518 align:middle line:84% If I go back to the cartoon, just 01:05:02.518 --> 01:05:04.310 align:middle line:84% to say quickly what's going to happen here, 01:05:04.310 --> 01:05:07.310 align:middle line:84% in order for this to be a reliable slit detector, 01:05:07.310 --> 01:05:10.580 align:middle line:84% this bundle of particles has to really be behind A and not 01:05:10.580 --> 01:05:14.330 align:middle line:84% behind B. That means that the spread in space 01:05:14.330 --> 01:05:16.130 align:middle line:90% can't be arbitrarily large. 01:05:16.130 --> 01:05:17.720 align:middle line:84% If we call this vertical direction 01:05:17.720 --> 01:05:20.120 align:middle line:84% the y direction, like my arrow here shows, 01:05:20.120 --> 01:05:23.850 align:middle line:84% then the delta y over this distribution can't be too big. 01:05:23.850 --> 01:05:26.510 align:middle line:84% In fact, it has to be much smaller than the distance D. 01:05:26.510 --> 01:05:28.920 align:middle line:84% If the distribution were too big, 01:05:28.920 --> 01:05:32.870 align:middle line:84% then we could see that test particles were scattered into-- 01:05:32.870 --> 01:05:35.300 align:middle line:84% but they would no longer tell us whether the particle had 01:05:35.300 --> 01:05:37.070 align:middle line:90% gone through slit A or slit B. 01:05:37.070 --> 01:05:39.320 align:middle line:84% We would lose the resolution in space 01:05:39.320 --> 01:05:42.590 align:middle line:84% if the bundle of particles was too far spread out 01:05:42.590 --> 01:05:43.830 align:middle line:90% in the y direction. 01:05:43.830 --> 01:05:46.400 align:middle line:84% So we have to contain or compress 01:05:46.400 --> 01:05:47.990 align:middle line:84% the distribution of test particles 01:05:47.990 --> 01:05:50.240 align:middle line:90% within a small region delta y. 01:05:50.240 --> 01:05:52.880 align:middle line:84% But that means they must have a correspondingly large 01:05:52.880 --> 01:05:56.030 align:middle line:84% uncertainty in the momentum because of the uncertainty 01:05:56.030 --> 01:05:56.605 align:middle line:90% principle. 01:05:56.605 --> 01:05:58.730 align:middle line:84% And, therefore, there'll be a correspondingly large 01:05:58.730 --> 01:06:02.660 align:middle line:84% uncertainty in the recoil momentum of the electron after 01:06:02.660 --> 01:06:05.030 align:middle line:84% scattering of exactly the right amount-- 01:06:05.030 --> 01:06:06.410 align:middle line:90% this part is kind of amazing-- 01:06:06.410 --> 01:06:09.920 align:middle line:84% of exactly the right amount needed to perfectly wash out 01:06:09.920 --> 01:06:13.340 align:middle line:84% those very clear interference fringes to get back to two 01:06:13.340 --> 01:06:18.440 align:middle line:84% bell-shaped curves, so that very regular, very narrow peaks 01:06:18.440 --> 01:06:19.740 align:middle line:90% of the interference fringes. 01:06:19.740 --> 01:06:22.100 align:middle line:84% So it's literally the uncertainty principle 01:06:22.100 --> 01:06:26.210 align:middle line:84% that precludes being able to both measure through which 01:06:26.210 --> 01:06:28.100 align:middle line:84% slit an individual particle passed 01:06:28.100 --> 01:06:31.880 align:middle line:84% and also retain these very clear features of the interference 01:06:31.880 --> 01:06:32.600 align:middle line:90% pattern. 01:06:32.600 --> 01:06:34.610 align:middle line:84% I think it's pretty amazing and very beautiful. 01:06:34.610 --> 01:06:36.920 align:middle line:84% And it's only a couple lines of algebra to show. 01:06:36.920 --> 01:06:40.550 align:middle line:84% So if even this most recent hand-waving effort of mine 01:06:40.550 --> 01:06:43.050 align:middle line:84% was too quick, I encourage you to look at the lecture notes. 01:06:43.050 --> 01:06:45.370 align:middle line:90% But that's the upshot. 01:06:45.370 --> 01:06:47.890 align:middle line:84% So what we're really finding conceptually-- 01:06:47.890 --> 01:06:53.020 align:middle line:84% and this is what people began to converge around, 01:06:53.020 --> 01:06:55.510 align:middle line:90% even by the late 1920s-- 01:06:55.510 --> 01:06:59.320 align:middle line:84% was that if we ask a particle-like question such as, 01:06:59.320 --> 01:07:00.400 align:middle line:90% what was your path? 01:07:00.400 --> 01:07:03.580 align:middle line:84% Through which slit did an individual particle pass? 01:07:03.580 --> 01:07:05.260 align:middle line:90% We will get a definite answer. 01:07:05.260 --> 01:07:07.300 align:middle line:84% We will get a particle like answer. 01:07:07.300 --> 01:07:09.760 align:middle line:84% Each particle either went through slit A 01:07:09.760 --> 01:07:13.540 align:middle line:84% or went through slit B with corresponding particle-like 01:07:13.540 --> 01:07:14.170 align:middle line:90% statistics. 01:07:14.170 --> 01:07:15.490 align:middle line:90% It's all consistent. 01:07:15.490 --> 01:07:17.020 align:middle line:90% We'll get a clear answer. 01:07:17.020 --> 01:07:18.400 align:middle line:84% And the whole rest of the problem 01:07:18.400 --> 01:07:20.650 align:middle line:84% will be consistent with particle-like questions 01:07:20.650 --> 01:07:22.090 align:middle line:90% and answers. 01:07:22.090 --> 01:07:25.120 align:middle line:84% On the other hand, if we ask a wave-like question, 01:07:25.120 --> 01:07:27.040 align:middle line:84% how does this wave function evolve 01:07:27.040 --> 01:07:29.200 align:middle line:84% in the region between the slits and the detector, 01:07:29.200 --> 01:07:32.050 align:middle line:84% for example, then we'll get a wave-like answer, 01:07:32.050 --> 01:07:34.660 align:middle line:84% the way the probability amplitude, 01:07:34.660 --> 01:07:38.440 align:middle line:84% the Schrodinger wave function, will spread out in space, 01:07:38.440 --> 01:07:40.840 align:middle line:84% in some regions they'll be constructive interference 01:07:40.840 --> 01:07:43.660 align:middle line:84% and the likelihood to find electron will be higher. 01:07:43.660 --> 01:07:46.340 align:middle line:84% In other regions of space you'll get destructive interference, 01:07:46.340 --> 01:07:48.680 align:middle line:84% corresponding to lower likelihood for an electron 01:07:48.680 --> 01:07:49.400 align:middle line:90% to be found. 01:07:49.400 --> 01:07:51.770 align:middle line:84% But we only get wave-like answers 01:07:51.770 --> 01:07:54.600 align:middle line:90% when we ask wave-like questions. 01:07:54.600 --> 01:07:55.460 align:middle line:90% So let me summarize. 01:07:55.460 --> 01:07:58.500 align:middle line:84% And we'll have a few moments for some discussion and questions. 01:07:58.500 --> 01:08:02.000 align:middle line:84% So in a really quite limited span of time, really 01:08:02.000 --> 01:08:05.900 align:middle line:84% in less than a whole calendar year between spring of 1925 01:08:05.900 --> 01:08:10.280 align:middle line:84% and spring of 1926, both Werner Heisenberg and separately, 01:08:10.280 --> 01:08:13.460 align:middle line:84% Erwin Schrodinger, introduced whole new approaches 01:08:13.460 --> 01:08:16.910 align:middle line:84% to what they were seeking, a kind of first principles theory 01:08:16.910 --> 01:08:20.810 align:middle line:84% of the quantum realm, a quantum mechanics, rather than 01:08:20.810 --> 01:08:24.720 align:middle line:84% this grab bag of ad hoc quantum conditions. 01:08:24.720 --> 01:08:27.260 align:middle line:84% They were looking for this quantitative description 01:08:27.260 --> 01:08:30.680 align:middle line:84% of the atomic realm that had certain quantum ideas built 01:08:30.680 --> 01:08:33.859 align:middle line:84% in from the start, discrete spectral lines from excited 01:08:33.859 --> 01:08:36.890 align:middle line:84% atoms, de Broglie wave, matter waves, and so on, 01:08:36.890 --> 01:08:40.550 align:middle line:84% rather than kind of stapling these on at the end. 01:08:40.550 --> 01:08:43.640 align:middle line:84% Now these approaches looked quite different at first 01:08:43.640 --> 01:08:46.399 align:middle line:84% and even kind of not very encouraging, 01:08:46.399 --> 01:08:49.279 align:middle line:84% to be polite about it, to each other's inventors. 01:08:49.279 --> 01:08:51.319 align:middle line:84% Heisenberg's approach really emphasized 01:08:51.319 --> 01:08:53.090 align:middle line:84% and built upon what he considered a kind 01:08:53.090 --> 01:08:54.410 align:middle line:90% of inherent discreteness. 01:08:54.410 --> 01:08:56.899 align:middle line:84% That was the main lesson of the quantum 01:08:56.899 --> 01:08:58.729 align:middle line:84% as far as Heisenberg was concerned. 01:08:58.729 --> 01:09:01.279 align:middle line:84% Schrodinger, in the meantime, built separately 01:09:01.279 --> 01:09:02.870 align:middle line:90% on de Broglie's suggestion. 01:09:02.870 --> 01:09:06.109 align:middle line:84% The real lesson is a surprising continua, 01:09:06.109 --> 01:09:08.330 align:middle line:84% that even solid matter like electrons 01:09:08.330 --> 01:09:10.310 align:middle line:84% have associated wavelike behavior. 01:09:10.310 --> 01:09:12.800 align:middle line:84% They're building on different kinds of conceptual building 01:09:12.800 --> 01:09:13.550 align:middle line:90% blocks. 01:09:13.550 --> 01:09:17.899 align:middle line:84% And yet, by the summer of 1926, several physicists 01:09:17.899 --> 01:09:21.710 align:middle line:84% had built this mathematical map between these very, very 01:09:21.710 --> 01:09:24.350 align:middle line:90% different looking approaches. 01:09:24.350 --> 01:09:26.990 align:middle line:84% And even though there was now, arguably, 01:09:26.990 --> 01:09:30.680 align:middle line:84% one internally consistent mathematical approach, 01:09:30.680 --> 01:09:32.240 align:middle line:84% what it all meant about the world 01:09:32.240 --> 01:09:36.630 align:middle line:84% was as unclear then, often, as it remains even to this day. 01:09:36.630 --> 01:09:39.920 align:middle line:84% So one question was, what's this wave? 01:09:39.920 --> 01:09:43.250 align:middle line:84% The wave function is now an object 01:09:43.250 --> 01:09:45.852 align:middle line:84% that can be manipulated using familiar techniques. 01:09:45.852 --> 01:09:47.060 align:middle line:90% It's a differential equation. 01:09:47.060 --> 01:09:50.270 align:middle line:84% We can understand the spectrum of allowable eigenvalues. 01:09:50.270 --> 01:09:53.060 align:middle line:84% But what is it actually telling us about the world? 01:09:53.060 --> 01:09:56.630 align:middle line:84% And with Max Born's suggestion in the summer of 1926, 01:09:56.630 --> 01:09:59.073 align:middle line:84% physicists pretty quickly came to the idea 01:09:59.073 --> 01:10:00.740 align:middle line:84% that the wave function is not telling us 01:10:00.740 --> 01:10:04.160 align:middle line:84% about the physical extent of an object in space 01:10:04.160 --> 01:10:06.350 align:middle line:84% but actually about the likelihood for events 01:10:06.350 --> 01:10:07.100 align:middle line:90% to happen. 01:10:07.100 --> 01:10:09.350 align:middle line:84% And in particular, the absolute square 01:10:09.350 --> 01:10:13.730 align:middle line:84% of this wave-like quantity should give us the probability. 01:10:13.730 --> 01:10:16.190 align:middle line:84% Quickly on the heels of that, less than a whole year later 01:10:16.190 --> 01:10:18.950 align:middle line:84% by spring of '27, Heisenberg had derived 01:10:18.950 --> 01:10:21.380 align:middle line:84% his now famous uncertainty principle, that there 01:10:21.380 --> 01:10:25.820 align:middle line:84% are these unavoidable trade offs in the precision with which we 01:10:25.820 --> 01:10:28.340 align:middle line:84% could ever hope to specify characteristics 01:10:28.340 --> 01:10:31.850 align:middle line:84% of the kind of quantum realm, a kind of pairwise 01:10:31.850 --> 01:10:34.820 align:middle line:84% trade off where we can make one quantity really sharp but only 01:10:34.820 --> 01:10:38.960 align:middle line:84% at the expense of making some corresponding or complementary 01:10:38.960 --> 01:10:41.690 align:middle line:90% quantity very imprecise. 01:10:41.690 --> 01:10:43.670 align:middle line:84% And the trade off, the seesaw, again, 01:10:43.670 --> 01:10:46.890 align:middle line:84% being controlled by Planck's constant. 01:10:46.890 --> 01:10:49.760 align:middle line:84% And then these kinds of broader conceptual dualities, 01:10:49.760 --> 01:10:52.820 align:middle line:84% like this wave particle duality we've seen now a few times. 01:10:52.820 --> 01:10:55.880 align:middle line:84% But the type of answer we could ever hope to find 01:10:55.880 --> 01:10:58.340 align:middle line:84% depends on the type of question we ask. 01:10:58.340 --> 01:11:01.970 align:middle line:84% So it's not that the electron really is a particle or a wave, 01:11:01.970 --> 01:11:04.970 align:middle line:84% that it's a kind of contextual question. 01:11:04.970 --> 01:11:08.120 align:middle line:84% Then what kind of properties do we hope to investigate? 01:11:08.120 --> 01:11:10.220 align:middle line:84% Then we're going to foreclose some answers 01:11:10.220 --> 01:11:12.860 align:middle line:84% from ever even being possible, even as we get 01:11:12.860 --> 01:11:14.720 align:middle line:90% other quite definite answers. 01:11:14.720 --> 01:11:18.650 align:middle line:84% So Niels Bohr, partly from his intense discussions 01:11:18.650 --> 01:11:20.600 align:middle line:84% with Heisenberg, with other colleagues, 01:11:20.600 --> 01:11:23.600 align:middle line:84% he used that to enunciate a very general philosophy 01:11:23.600 --> 01:11:27.170 align:middle line:84% of the quantum realm by September of 1927, 01:11:27.170 --> 01:11:28.880 align:middle line:84% right on the heels of this, which he 01:11:28.880 --> 01:11:30.990 align:middle line:90% came to call complementarity. 01:11:30.990 --> 01:11:33.230 align:middle line:90% So it's not an either or world. 01:11:33.230 --> 01:11:34.940 align:middle line:90% It's a both and. 01:11:34.940 --> 01:11:37.790 align:middle line:84% We are required, in this case, to draw 01:11:37.790 --> 01:11:40.940 align:middle line:84% on both ideas and actual mathematical techniques 01:11:40.940 --> 01:11:43.250 align:middle line:84% with which we characterize wave behavior, 01:11:43.250 --> 01:11:47.040 align:middle line:84% and ideas and techniques with which we characterize particle 01:11:47.040 --> 01:11:47.670 align:middle line:90% behavior. 01:11:47.670 --> 01:11:49.230 align:middle line:90% They are mutually exclusive. 01:11:49.230 --> 01:11:51.180 align:middle line:84% We literally can't use them at the same time. 01:11:51.180 --> 01:11:52.620 align:middle line:90% And yet we need both. 01:11:52.620 --> 01:11:54.750 align:middle line:84% A complete description requires both, 01:11:54.750 --> 01:11:56.850 align:middle line:84% even though they don't fit together at once. 01:11:56.850 --> 01:11:59.580 align:middle line:84% And that, to Bohr, was the deepest meaning, the deepest 01:11:59.580 --> 01:12:01.207 align:middle line:90% lesson of quantum theory. 01:12:01.207 --> 01:12:02.040 align:middle line:90% Not everyone agreed. 01:12:02.040 --> 01:12:05.040 align:middle line:84% But that's where Bohr arrived by 1927. 01:12:05.040 --> 01:12:06.980 align:middle line:84% OK, any questions on any of that? 01:12:06.980 --> 01:12:18.440 align:middle line:90% 01:12:18.440 --> 01:12:22.215 align:middle line:84% That is so straightforward, so boringly familiar, 01:12:22.215 --> 01:12:23.840 align:middle line:84% that there's not even a single question 01:12:23.840 --> 01:12:27.100 align:middle line:84% to ask about the fundamental nature of reality. 01:12:27.100 --> 01:12:28.480 align:middle line:90% Boy, holiday weekends. 01:12:28.480 --> 01:12:30.970 align:middle line:90% 01:12:30.970 --> 01:12:31.470 align:middle line:90% No. 01:12:31.470 --> 01:12:34.530 align:middle line:90% 01:12:34.530 --> 01:12:37.698 align:middle line:84% Well, if you'll permit me, on tomorrow's class 01:12:37.698 --> 01:12:39.990 align:middle line:84% I'm going to try to shake your quantum complacency even 01:12:39.990 --> 01:12:40.490 align:middle line:90% further. 01:12:40.490 --> 01:12:42.750 align:middle line:84% So tomorrow we'll explore quantum weirdness 01:12:42.750 --> 01:12:44.920 align:middle line:90% in even more directions. 01:12:44.920 --> 01:12:47.430 align:middle line:84% So if this stuff is humdrum and familiar, 01:12:47.430 --> 01:12:49.210 align:middle line:84% give me one more shot for tomorrow. 01:12:49.210 --> 01:12:51.030 align:middle line:84% So Fisher asks, was Schrodinger's work 01:12:51.030 --> 01:12:54.270 align:middle line:84% more quickly accepted because it was more basic mechanics? 01:12:54.270 --> 01:12:56.490 align:middle line:84% I think that's absolutely right, Fisher. 01:12:56.490 --> 01:12:59.850 align:middle line:84% And I think there was a kind of-- 01:12:59.850 --> 01:13:02.460 align:middle line:90% people could do stuff with it. 01:13:02.460 --> 01:13:06.210 align:middle line:84% So even while the concepts were still very far from clear, 01:13:06.210 --> 01:13:08.520 align:middle line:90% what's the wave function? 01:13:08.520 --> 01:13:09.390 align:middle line:90% What is a wave of? 01:13:09.390 --> 01:13:11.010 align:middle line:90% What is it telling us? 01:13:11.010 --> 01:13:12.660 align:middle line:90% That was by no means clear. 01:13:12.660 --> 01:13:14.910 align:middle line:84% And even after the answers that we would now recognize 01:13:14.910 --> 01:13:19.650 align:middle line:84% were put forward, those didn't claim consensus right away. 01:13:19.650 --> 01:13:22.560 align:middle line:84% And yet, in between, people could still do stuff. 01:13:22.560 --> 01:13:24.870 align:middle line:84% You could train PhD students to look 01:13:24.870 --> 01:13:26.640 align:middle line:84% at this or that specific question 01:13:26.640 --> 01:13:30.050 align:middle line:84% because the apparatus, the mathematical apparatus, 01:13:30.050 --> 01:13:32.550 align:middle line:84% was already something they'd practiced since their youngest, 01:13:32.550 --> 01:13:33.910 align:middle line:90% earliest studies. 01:13:33.910 --> 01:13:35.620 align:middle line:84% So I think that really had a lot to do 01:13:35.620 --> 01:13:41.950 align:middle line:84% with how rapidly Schrodinger's work was really welcomed 01:13:41.950 --> 01:13:43.360 align:middle line:90% and that it helped. 01:13:43.360 --> 01:13:47.380 align:middle line:84% Obviously it helped a lot when Schrodinger, and Jordan, 01:13:47.380 --> 01:13:52.137 align:middle line:84% and Dirac elucidated the kind of mathematical mapping. 01:13:52.137 --> 01:13:54.220 align:middle line:84% So then it really became a question of convenience 01:13:54.220 --> 01:13:54.987 align:middle line:90% and not either/or. 01:13:54.987 --> 01:13:57.070 align:middle line:84% It's not like you had to vote for team Schrodinger 01:13:57.070 --> 01:13:58.480 align:middle line:90% versus team Heisenberg. 01:13:58.480 --> 01:14:00.910 align:middle line:84% Now you could say, oh, this set of techniques 01:14:00.910 --> 01:14:01.660 align:middle line:90% is familiar to me. 01:14:01.660 --> 01:14:03.850 align:middle line:84% I have lots of experience from classical mechanics 01:14:03.850 --> 01:14:05.750 align:middle line:90% or Maxwell or whatever. 01:14:05.750 --> 01:14:09.042 align:middle line:84% And so then it became a kind of tool of choice. 01:14:09.042 --> 01:14:11.500 align:middle line:84% And these tools were much more familiar to many more people 01:14:11.500 --> 01:14:12.000 align:middle line:90% at the time. 01:14:12.000 --> 01:14:16.030 align:middle line:84% That absolutely played a role in hastening 01:14:16.030 --> 01:14:18.730 align:middle line:84% many people's attention to this stuff, good, good point. 01:14:18.730 --> 01:14:22.870 align:middle line:84% Aiden asks, is Heisenberg's principle kind of spiritual? 01:14:22.870 --> 01:14:24.340 align:middle line:90% For some people, yes. 01:14:24.340 --> 01:14:27.610 align:middle line:84% Although that gets-- there's a lot to say about that. 01:14:27.610 --> 01:14:30.183 align:middle line:84% Are there those who think a more literal analysis would 01:14:30.183 --> 01:14:32.350 align:middle line:84% be that we simply need to discover from observation, 01:14:32.350 --> 01:14:33.768 align:middle line:90% not involve test particles? 01:14:33.768 --> 01:14:36.310 align:middle line:84% So, Aiden, I thought you were going a different way at first. 01:14:36.310 --> 01:14:39.160 align:middle line:90% So one topic, which is-- 01:14:39.160 --> 01:14:40.400 align:middle line:90% I'll say controversial. 01:14:40.400 --> 01:14:41.320 align:middle line:90% Some people pursue it. 01:14:41.320 --> 01:14:43.510 align:middle line:84% Other people think it is full of holes. 01:14:43.510 --> 01:14:47.350 align:middle line:84% One idea would be to say, does the uncertainty principle give 01:14:47.350 --> 01:14:49.240 align:middle line:84% us a physical reason why there might 01:14:49.240 --> 01:14:51.820 align:middle line:90% be something like free will-- 01:14:51.820 --> 01:14:55.840 align:middle line:84% consciousness and the experience of free will? 01:14:55.840 --> 01:14:58.210 align:middle line:84% You can see part of the concern, going back 01:14:58.210 --> 01:15:02.770 align:middle line:84% to the days of both Newton and, for that matter, Maxwell. 01:15:02.770 --> 01:15:07.030 align:middle line:84% If we live in a universe in which determinism holds 01:15:07.030 --> 01:15:10.770 align:middle line:84% perfectly, if events in the future 01:15:10.770 --> 01:15:14.190 align:middle line:84% are uniquely determined by events in the past, 01:15:14.190 --> 01:15:18.000 align:middle line:84% and then we turn on our sci-fi imaginations and imagine 01:15:18.000 --> 01:15:22.770 align:middle line:84% we're made of matter, atoms, and molecules. 01:15:22.770 --> 01:15:28.270 align:middle line:84% If atoms and molecules have to obey the laws of nature 01:15:28.270 --> 01:15:30.550 align:middle line:84% then, in principle, they are subject to determinism, 01:15:30.550 --> 01:15:32.440 align:middle line:84% at least in a pre quantum mechanical way. 01:15:32.440 --> 01:15:35.890 align:middle line:84% Then aren't we all just pre-programmed? 01:15:35.890 --> 01:15:39.040 align:middle line:84% Aren't we merely machines with no more free will 01:15:39.040 --> 01:15:41.800 align:middle line:84% than comets who can't help but follow a Keplerian 01:15:41.800 --> 01:15:43.613 align:middle line:90% orbit as they orbit the sun? 01:15:43.613 --> 01:15:45.280 align:middle line:84% And believe it or not, that was a debate 01:15:45.280 --> 01:15:49.410 align:middle line:84% that got people very excited and exorcized and mad 01:15:49.410 --> 01:15:51.040 align:middle line:84% at each other for a long, long time. 01:15:51.040 --> 01:15:54.240 align:middle line:84% And so there was some thought by some people early 01:15:54.240 --> 01:15:55.980 align:middle line:84% on, starting, really, in the 1920s 01:15:55.980 --> 01:15:58.590 align:middle line:84% and '30s, that maybe the uncertainty 01:15:58.590 --> 01:16:02.280 align:middle line:84% principle, by breaking the iron hold of determinism, 01:16:02.280 --> 01:16:05.580 align:middle line:84% leaves a kind of space within our scientific theorizing 01:16:05.580 --> 01:16:08.940 align:middle line:84% for things that seemed, or at least some might have hoped, 01:16:08.940 --> 01:16:11.760 align:middle line:84% were not fully uniquely determined, 01:16:11.760 --> 01:16:13.860 align:middle line:84% whether that's our own sense of individuality 01:16:13.860 --> 01:16:17.290 align:middle line:84% or the course of human events more broadly and so on. 01:16:17.290 --> 01:16:19.560 align:middle line:84% Now that gets a little tricky because, unfortunately, 01:16:19.560 --> 01:16:20.935 align:middle line:84% the uncertainty principle argues, 01:16:20.935 --> 01:16:22.740 align:middle line:84% at least most physicists would say, 01:16:22.740 --> 01:16:24.390 align:middle line:84% the upside of the uncertainty principle 01:16:24.390 --> 01:16:26.040 align:middle line:90% is that everything's random. 01:16:26.040 --> 01:16:29.400 align:middle line:84% And that's not quite how my thoughts feel. 01:16:29.400 --> 01:16:32.160 align:middle line:84% Before COVID 19, my thoughts didn't always feel only random, 01:16:32.160 --> 01:16:33.420 align:middle line:90% now they do. 01:16:33.420 --> 01:16:35.130 align:middle line:84% So appealing to the certain principle 01:16:35.130 --> 01:16:37.470 align:middle line:90% breaks the hold of determinism. 01:16:37.470 --> 01:16:39.120 align:middle line:84% But what it seems to put in its place 01:16:39.120 --> 01:16:43.020 align:middle line:84% is random mush, as opposed to something that otherwise might 01:16:43.020 --> 01:16:45.553 align:middle line:84% answer to the kind of lived experience of phenomena 01:16:45.553 --> 01:16:46.720 align:middle line:90% of something like free will. 01:16:46.720 --> 01:16:49.840 align:middle line:84% So it's not like that's a single answer that that's done. 01:16:49.840 --> 01:16:53.980 align:middle line:84% But that opens a space for kind of theorizing that goes on 01:16:53.980 --> 01:16:57.640 align:middle line:84% to this day, sometimes on the margins of both kind of physics 01:16:57.640 --> 01:17:00.460 align:middle line:84% and also of areas like neuroscience and philosophy. 01:17:00.460 --> 01:17:02.410 align:middle line:84% But at least it opens a different way 01:17:02.410 --> 01:17:04.330 align:middle line:84% of asking legitimate, hard questions 01:17:04.330 --> 01:17:05.980 align:middle line:90% with some new conceptual inputs. 01:17:05.980 --> 01:17:07.223 align:middle line:90% Let me put it that way. 01:17:07.223 --> 01:17:09.640 align:middle line:84% So even though I don't think people have found that answer 01:17:09.640 --> 01:17:12.850 align:middle line:84% yet, it's interesting that opens a space to ask old questions, 01:17:12.850 --> 01:17:14.740 align:middle line:90% maybe in some new ways. 01:17:14.740 --> 01:17:17.048 align:middle line:84% I wrote a book a couple of years ago 01:17:17.048 --> 01:17:18.840 align:middle line:84% called How The Hippies Saved Physics, which 01:17:18.840 --> 01:17:21.048 align:middle line:84% is a very obnoxious title, where people thought maybe 01:17:21.048 --> 01:17:23.410 align:middle line:84% there were other kind of unexplained or unaccounted 01:17:23.410 --> 01:17:26.080 align:middle line:84% for phenomena that quantum theory might be able to account 01:17:26.080 --> 01:17:29.440 align:middle line:84% for, like claims of ESP, or other so-called occult 01:17:29.440 --> 01:17:31.522 align:middle line:84% phenomena, mind reading, for example. 01:17:31.522 --> 01:17:33.730 align:middle line:84% And, again, I don't think they explained that at all. 01:17:33.730 --> 01:17:35.590 align:middle line:84% But it was a way of trying to reason 01:17:35.590 --> 01:17:39.467 align:middle line:84% about strange or unexpected human-scaled phenomena using 01:17:39.467 --> 01:17:41.800 align:middle line:84% a new set of tools that really weren't going to go away, 01:17:41.800 --> 01:17:43.330 align:middle line:84% like the uncertainty principle or like things 01:17:43.330 --> 01:17:45.190 align:middle line:84% we'll talk about in tomorrow's class, things 01:17:45.190 --> 01:17:46.460 align:middle line:90% like quantum entanglement. 01:17:46.460 --> 01:17:48.220 align:middle line:84% So I'm not telling you that's the answer. 01:17:48.220 --> 01:17:50.262 align:middle line:84% I'm telling you that opened up a space for people 01:17:50.262 --> 01:17:54.430 align:middle line:84% to ask either familiar questions from unfamiliar perspectives 01:17:54.430 --> 01:17:56.480 align:middle line:84% or sometimes ask new kinds of questions. 01:17:56.480 --> 01:17:58.390 align:middle line:84% So in that sense, what's the ultimate meaning 01:17:58.390 --> 01:17:59.200 align:middle line:90% of the uncertainty principle? 01:17:59.200 --> 01:17:59.650 align:middle line:90% I don't know. 01:17:59.650 --> 01:18:00.880 align:middle line:84% And, frankly, I don't think anyone knows. 01:18:00.880 --> 01:18:03.310 align:middle line:84% Or at least it's still a subject of really robust debate, 01:18:03.310 --> 01:18:06.860 align:middle line:84% like that quantum-to-classical transition. 01:18:06.860 --> 01:18:09.687 align:middle line:84% And I think it's fantastic that we have tools to even pose 01:18:09.687 --> 01:18:10.520 align:middle line:90% those questions now. 01:18:10.520 --> 01:18:12.437 align:middle line:84% So I get excited by the nature of the question 01:18:12.437 --> 01:18:14.230 align:middle line:84% rather than having a favorite answer. 01:18:14.230 --> 01:18:16.450 align:middle line:90% That's just me proselytizing. 01:18:16.450 --> 01:18:19.750 align:middle line:84% So Richard asks, once general relativity was widely accepted, 01:18:19.750 --> 01:18:21.970 align:middle line:84% were people already ringing alarm 01:18:21.970 --> 01:18:24.220 align:middle line:84% bells about the conflicts between general relativity 01:18:24.220 --> 01:18:25.137 align:middle line:90% and quantum mechanics. 01:18:25.137 --> 01:18:27.880 align:middle line:84% Yes, yes, they were, including Albert Einstein himself, 01:18:27.880 --> 01:18:29.800 align:middle line:84% who had a few opinions on the matter. 01:18:29.800 --> 01:18:32.710 align:middle line:84% And so this goes back in large part 01:18:32.710 --> 01:18:35.837 align:middle line:84% to things like the fall of determinism. 01:18:35.837 --> 01:18:38.170 align:middle line:84% And we'll come to, actually, some of these examples even 01:18:38.170 --> 01:18:39.080 align:middle line:90% in tomorrow's class. 01:18:39.080 --> 01:18:41.620 align:middle line:84% So we'll come to some of Einstein's most enduring 01:18:41.620 --> 01:18:44.380 align:middle line:84% critiques of quantum theory in the light of his thinking 01:18:44.380 --> 01:18:46.515 align:middle line:84% about things like relativity tomorrow. 01:18:46.515 --> 01:18:47.890 align:middle line:84% So partly I'll just bracket that. 01:18:47.890 --> 01:18:50.330 align:middle line:84% And I'll just simply say, yes, it's a great question. 01:18:50.330 --> 01:18:51.705 align:middle line:84% We'll see some examples tomorrow. 01:18:51.705 --> 01:18:54.392 align:middle line:90% We could talk more 01:18:54.392 --> 01:18:56.350 align:middle line:84% Lulu asks, how's my mental and emotional state? 01:18:56.350 --> 01:18:59.642 align:middle line:84% I think you can see, I'm still agitated I love this stuff. 01:18:59.642 --> 01:19:01.600 align:middle line:84% And tomorrow I won't be able to contain myself. 01:19:01.600 --> 01:19:03.558 align:middle line:84% I'll talk about some of my own group's research 01:19:03.558 --> 01:19:06.590 align:middle line:84% in the foundations of quantum mechanics. 01:19:06.590 --> 01:19:08.870 align:middle line:84% So good, I mean, not that the research is so good. 01:19:08.870 --> 01:19:09.870 align:middle line:90% The question is so good. 01:19:09.870 --> 01:19:11.860 align:middle line:84% OK, Aiden says, does Heisenberg's principle 01:19:11.860 --> 01:19:14.140 align:middle line:84% mean there's neither freewill nor determinism? 01:19:14.140 --> 01:19:16.630 align:middle line:84% So what we can do is recognize that now, 01:19:16.630 --> 01:19:18.873 align:middle line:84% as a question with which we, as a community, 01:19:18.873 --> 01:19:21.040 align:middle line:84% now have new tools to try to puzzle through answers. 01:19:21.040 --> 01:19:23.027 align:middle line:90% I'll put it that way. 01:19:23.027 --> 01:19:24.610 align:middle line:84% I mean, one of the things that happens 01:19:24.610 --> 01:19:28.300 align:middle line:84% is people try to explain certain esoteric features 01:19:28.300 --> 01:19:30.160 align:middle line:84% of consciousness using quantum theory. 01:19:30.160 --> 01:19:35.140 align:middle line:84% But then it turns out that human brains are dense, hot, and wet. 01:19:35.140 --> 01:19:36.640 align:middle line:84% And a lot of these quantum effects 01:19:36.640 --> 01:19:40.090 align:middle line:84% work really well when we're near vacuum at low temperatures 01:19:40.090 --> 01:19:41.830 align:middle line:90% and super dry. 01:19:41.830 --> 01:19:44.080 align:middle line:84% So even though some things could happen, in principle, 01:19:44.080 --> 01:19:46.630 align:middle line:84% among quantum objects, having to maintain 01:19:46.630 --> 01:19:48.910 align:middle line:84% a kind of inherent quantumness is 01:19:48.910 --> 01:19:51.050 align:middle line:84% really hard in an environment like the human brain. 01:19:51.050 --> 01:19:52.630 align:middle line:84% So, again, that launches new kinds 01:19:52.630 --> 01:19:55.790 align:middle line:84% of questions and investigations, rather than saying, 01:19:55.790 --> 01:19:57.250 align:middle line:90% oh, we've solved it. 01:19:57.250 --> 01:19:59.110 align:middle line:84% So those things become really interesting 01:19:59.110 --> 01:20:01.510 align:middle line:84% and lots of smart people ask a hard question about them 01:20:01.510 --> 01:20:04.540 align:middle line:84% around the world because we have this new injection 01:20:04.540 --> 01:20:07.968 align:middle line:84% of new conceptual things to really wonder about. 01:20:07.968 --> 01:20:08.760 align:middle line:90% Let me pause there. 01:20:08.760 --> 01:20:10.260 align:middle line:90% I don't want to run too long. 01:20:10.260 --> 01:20:13.760 align:middle line:84% Remember we have class tomorrow, twice in a row this week. 01:20:13.760 --> 01:20:15.380 align:middle line:84% We're back in our ordinary Zoom link. 01:20:15.380 --> 01:20:16.790 align:middle line:90% You can find it through Canvas. 01:20:16.790 --> 01:20:18.373 align:middle line:84% And so tomorrow we'll sit a little bit 01:20:18.373 --> 01:20:22.040 align:middle line:84% longer with some of these weird and wacky quantum phenomena. 01:20:22.040 --> 01:20:23.990 align:middle line:90% So stay well, see you tomorrow. 01:20:23.990 --> 01:20:25.900 align:middle line:90% Talk to you soon. 01:20:25.900 --> 01:20:36.000 align:middle line:90%