WEBVTT 00:00:00.000 --> 00:00:01.980 align:middle line:90% [SQUEAKING] 00:00:01.980 --> 00:00:03.960 align:middle line:90% [RUSTLING] 00:00:03.960 --> 00:00:04.950 align:middle line:90% [CLICKING] 00:00:04.950 --> 00:00:10.245 align:middle line:90% 00:00:10.245 --> 00:00:12.120 align:middle line:84% DAVID KAISER: But if there are no immediately 00:00:12.120 --> 00:00:14.370 align:middle line:84% pressing questions on the assignments, 00:00:14.370 --> 00:00:15.990 align:middle line:90% then I will jump in. 00:00:15.990 --> 00:00:18.870 align:middle line:84% We can start talking some more about quantum weirdness. 00:00:18.870 --> 00:00:21.700 align:middle line:84% We can continue our discussion from yesterday, 00:00:21.700 --> 00:00:27.030 align:middle line:84% which was clearly insufficiently shocking for you. 00:00:27.030 --> 00:00:29.050 align:middle line:84% You were all very quantum complacent yesterday. 00:00:29.050 --> 00:00:30.970 align:middle line:84% Let's see if I can do a little better today. 00:00:30.970 --> 00:00:34.380 align:middle line:84% So we'll talk about a series of developments of-- 00:00:34.380 --> 00:00:36.360 align:middle line:84% that grew out of efforts to make sense 00:00:36.360 --> 00:00:40.650 align:middle line:84% of this new set of equations, this new mathematical formalism 00:00:40.650 --> 00:00:42.330 align:middle line:90% of quantum mechanics. 00:00:42.330 --> 00:00:45.840 align:middle line:84% Some of these developments came pretty quickly in time, 00:00:45.840 --> 00:00:47.520 align:middle line:84% very soon after Schrodinger had worked 00:00:47.520 --> 00:00:49.080 align:middle line:84% out this new form of the equation, 00:00:49.080 --> 00:00:53.770 align:middle line:84% and others, as we'll see, really came together some years later. 00:00:53.770 --> 00:00:56.400 align:middle line:84% So for today, we're going to talk about these three 00:00:56.400 --> 00:00:57.250 align:middle line:90% examples. 00:00:57.250 --> 00:00:59.522 align:middle line:84% This does not exhaust all the things 00:00:59.522 --> 00:01:01.980 align:middle line:84% one can think about under the heading of quantum weirdness, 00:01:01.980 --> 00:01:03.438 align:middle line:84% but these are some of my favorites, 00:01:03.438 --> 00:01:06.750 align:middle line:84% and I think they really show a range of the kinds of questions 00:01:06.750 --> 00:01:08.610 align:middle line:90% that this work began to open up. 00:01:08.610 --> 00:01:11.550 align:middle line:84% So we'll start by talking about superposition 00:01:11.550 --> 00:01:13.560 align:middle line:90% and Schrodinger's cat paradox. 00:01:13.560 --> 00:01:16.320 align:middle line:84% The Schrodinger's cat is likely familiar to you, at least 00:01:16.320 --> 00:01:16.950 align:middle line:90% in outline. 00:01:16.950 --> 00:01:19.860 align:middle line:84% We'll talk a bit about what were the conceptual stakes 00:01:19.860 --> 00:01:22.350 align:middle line:84% and what was the historical moment, what 00:01:22.350 --> 00:01:24.750 align:middle line:84% was the broader context, in which that work was 00:01:24.750 --> 00:01:26.340 align:middle line:90% being developed. 00:01:26.340 --> 00:01:27.960 align:middle line:84% Then for our second part today, we'll 00:01:27.960 --> 00:01:31.870 align:middle line:84% look at a very famous critique of quantum mechanics, 00:01:31.870 --> 00:01:35.310 align:middle line:84% now usually just referred to by the initials EPR. 00:01:35.310 --> 00:01:37.680 align:middle line:84% As we'll see, that stands for the initials 00:01:37.680 --> 00:01:41.100 align:middle line:84% of the three authors of this paper, Einstein, Podolsky, 00:01:41.100 --> 00:01:41.790 align:middle line:90% and Rosen. 00:01:41.790 --> 00:01:43.060 align:middle line:90% So we'll talk about that. 00:01:43.060 --> 00:01:44.730 align:middle line:84% And then for the last section, we'll 00:01:44.730 --> 00:01:48.810 align:middle line:84% talk about work by the physicist John Bell, now 00:01:48.810 --> 00:01:50.432 align:middle line:90% known as Bell's inequality. 00:01:50.432 --> 00:01:52.140 align:middle line:84% And it relates very directly to something 00:01:52.140 --> 00:01:53.490 align:middle line:90% called quantum entanglement. 00:01:53.490 --> 00:01:56.188 align:middle line:84% For this last one in particular, and really 00:01:56.188 --> 00:01:58.230 align:middle line:84% for throughout today's lecture, but in particular 00:01:58.230 --> 00:02:01.410 align:middle line:84% for part three, again, I'll have to skip over 00:02:01.410 --> 00:02:03.287 align:middle line:90% some of the intermediate steps. 00:02:03.287 --> 00:02:05.370 align:middle line:84% I might show a couple of equations that might look 00:02:05.370 --> 00:02:07.470 align:middle line:90% a little difficult to parse. 00:02:07.470 --> 00:02:11.380 align:middle line:84% But there's the optional lecture notes on the Canvas site. 00:02:11.380 --> 00:02:12.880 align:middle line:84% And you can dig into that a bit more 00:02:12.880 --> 00:02:14.050 align:middle line:90% if things are not so clear. 00:02:14.050 --> 00:02:16.660 align:middle line:84% And obviously, of course, please ask questions now 00:02:16.660 --> 00:02:18.243 align:middle line:84% or email or office hours as well. 00:02:18.243 --> 00:02:19.660 align:middle line:84% So that's where we're going today. 00:02:19.660 --> 00:02:20.860 align:middle line:90% OK. 00:02:20.860 --> 00:02:24.430 align:middle line:84% Let's quickly remind ourselves where we've gotten to so far. 00:02:24.430 --> 00:02:26.890 align:middle line:84% As we saw just in yesterday's class session, 00:02:26.890 --> 00:02:31.660 align:middle line:84% in 1926, starting in winter/spring of '26, 00:02:31.660 --> 00:02:35.850 align:middle line:84% Erwin Schrodinger developed a second, independent approach 00:02:35.850 --> 00:02:37.600 align:middle line:84% to what would be called quantum mechanics, 00:02:37.600 --> 00:02:41.200 align:middle line:84% independent from the work by Werner Heisenberg, 00:02:41.200 --> 00:02:43.820 align:middle line:84% which had been published only a few months earlier. 00:02:43.820 --> 00:02:46.167 align:middle line:84% So whereas Heisenberg had emphasized discreteness 00:02:46.167 --> 00:02:48.250 align:middle line:84% and wound up using matrices, though he didn't even 00:02:48.250 --> 00:02:50.680 align:middle line:84% know it at first, Schrodinger was 00:02:50.680 --> 00:02:53.950 align:middle line:84% developing a different approach, building much more 00:02:53.950 --> 00:02:56.440 align:middle line:84% on a continuity assumption rather than 00:02:56.440 --> 00:02:58.190 align:middle line:90% a discreteness assumption. 00:02:58.190 --> 00:03:00.040 align:middle line:84% And in this case, Schrodinger was 00:03:00.040 --> 00:03:03.970 align:middle line:84% building very directly on work by Louis de Broglie 00:03:03.970 --> 00:03:05.230 align:middle line:90% about matter waves. 00:03:05.230 --> 00:03:09.490 align:middle line:84% Somehow, seemingly solid matter like atoms and parts of atoms 00:03:09.490 --> 00:03:12.100 align:middle line:84% have associated with them in some way that 00:03:12.100 --> 00:03:15.380 align:middle line:84% wasn't so clear some kind of inherent waviness, 00:03:15.380 --> 00:03:19.010 align:middle line:84% that that was maybe the real secret to quantum theory. 00:03:19.010 --> 00:03:22.570 align:middle line:84% So Erwin Schrodinger introduced a whole new formalism building 00:03:22.570 --> 00:03:25.510 align:middle line:84% on this continuity notion of matter waves. 00:03:25.510 --> 00:03:27.830 align:middle line:90% And he began to quantify that. 00:03:27.830 --> 00:03:30.340 align:middle line:84% So he introduced this equation, which you see here in red. 00:03:30.340 --> 00:03:33.940 align:middle line:84% Some of you might even have that tattooed or on T-shirts. 00:03:33.940 --> 00:03:36.220 align:middle line:84% It's an excellent candidate for either 00:03:36.220 --> 00:03:38.590 align:middle line:84% of those things, the time-independent Schrodinger 00:03:38.590 --> 00:03:39.250 align:middle line:90% equation. 00:03:39.250 --> 00:03:44.110 align:middle line:84% And this governs the behavior of this new quantity 00:03:44.110 --> 00:03:46.870 align:middle line:84% that Schrodinger introduced that we now call the quantum wave 00:03:46.870 --> 00:03:50.710 align:middle line:84% function, usually given the Greek letter psi. 00:03:50.710 --> 00:03:54.670 align:middle line:84% As we saw, solutions to this equation obeys superposition, 00:03:54.670 --> 00:03:58.910 align:middle line:84% just like most typical solutions to wave equations do. 00:03:58.910 --> 00:04:00.670 align:middle line:84% So what that means is that if you 00:04:00.670 --> 00:04:02.740 align:middle line:84% have two different solutions to the equation, 00:04:02.740 --> 00:04:06.340 align:middle line:84% we could call them psi 1 and some other solutions psi 2, 00:04:06.340 --> 00:04:09.790 align:middle line:84% then in general, it will be the case that a sum of those two 00:04:09.790 --> 00:04:11.900 align:middle line:84% solutions will also be a solution. 00:04:11.900 --> 00:04:13.120 align:middle line:90% In fact, a weighted sum. 00:04:13.120 --> 00:04:15.870 align:middle line:84% We could weight them with different coefficients 00:04:15.870 --> 00:04:16.370 align:middle line:90% in front. 00:04:16.370 --> 00:04:19.700 align:middle line:84% And that would also still be, in general, a solution. 00:04:19.700 --> 00:04:22.750 align:middle line:84% So that's what yields all this juicy, 00:04:22.750 --> 00:04:26.600 align:middle line:84% wave-like behavior, things like interference. 00:04:26.600 --> 00:04:30.370 align:middle line:84% And so to remind you in a simple cartoon version, two waves that 00:04:30.370 --> 00:04:34.570 align:middle line:84% are each separately solutions of a particular wave equation. 00:04:34.570 --> 00:04:38.740 align:middle line:84% In areas where the crests, the peaks, nearly coincide, 00:04:38.740 --> 00:04:42.100 align:middle line:84% they'll add up to make a larger overall peak. 00:04:42.100 --> 00:04:44.752 align:middle line:84% Other places, one crest will nearly line up with a trough, 00:04:44.752 --> 00:04:46.460 align:middle line:84% and they'll almost cancel each other out. 00:04:46.460 --> 00:04:49.420 align:middle line:84% That's the kind of constructive and destructive interference, 00:04:49.420 --> 00:04:51.760 align:middle line:84% very familiar from classical waves. 00:04:51.760 --> 00:04:54.910 align:middle line:84% This was also a feature of these strange quantum wave 00:04:54.910 --> 00:04:58.690 align:middle line:84% functions that were associated with Schrodinger's equation. 00:04:58.690 --> 00:05:01.780 align:middle line:84% That still didn't answer what psi was a wave of. 00:05:01.780 --> 00:05:03.250 align:middle line:90% It was really not so clear. 00:05:03.250 --> 00:05:07.540 align:middle line:84% Schrodinger offered several tentative suggestions 00:05:07.540 --> 00:05:09.550 align:middle line:84% or hypotheses, and even he himself 00:05:09.550 --> 00:05:12.470 align:middle line:84% showed that most of those weren't self consistent. 00:05:12.470 --> 00:05:16.190 align:middle line:84% And it was really about six months later in the summer 00:05:16.190 --> 00:05:20.060 align:middle line:84% of 1926 when Max Born interpreted 00:05:20.060 --> 00:05:22.440 align:middle line:84% Schrodinger's own work, his own equation, and said, 00:05:22.440 --> 00:05:25.200 align:middle line:84% here's what your equation perhaps might mean. 00:05:25.200 --> 00:05:26.510 align:middle line:90% We've seen this many times. 00:05:26.510 --> 00:05:29.090 align:middle line:84% The equation didn't change, but the effort 00:05:29.090 --> 00:05:32.330 align:middle line:84% to make sense of it-- that was really not so settled. 00:05:32.330 --> 00:05:35.540 align:middle line:84% So Born suggests that the wave function is somehow 00:05:35.540 --> 00:05:41.450 align:middle line:84% related to the probability for various outcomes 00:05:41.450 --> 00:05:42.780 align:middle line:90% to be measured. 00:05:42.780 --> 00:05:45.920 align:middle line:84% So it wasn't a feature of a physical object extended 00:05:45.920 --> 00:05:46.520 align:middle line:90% in space. 00:05:46.520 --> 00:05:50.300 align:middle line:84% It wasn't a shape of some smeared-out electron 00:05:50.300 --> 00:05:51.590 align:middle line:90% through space. 00:05:51.590 --> 00:05:54.740 align:middle line:84% It was somehow, in some way it wasn't at all so clear, 00:05:54.740 --> 00:05:58.190 align:middle line:84% related to the likelihood to measure certain properties 00:05:58.190 --> 00:05:59.940 align:middle line:90% of that electron, for example. 00:05:59.940 --> 00:06:02.870 align:middle line:84% So that psi was not even the probability itself, 00:06:02.870 --> 00:06:05.210 align:middle line:90% but the probability amplitude. 00:06:05.210 --> 00:06:08.810 align:middle line:84% And the absolute square of this, in general, complex number, 00:06:08.810 --> 00:06:10.160 align:middle line:90% complex function-- 00:06:10.160 --> 00:06:12.380 align:middle line:84% the absolute square would give you the probability. 00:06:12.380 --> 00:06:15.470 align:middle line:84% And that's what leads to all these really quite delicious 00:06:15.470 --> 00:06:17.360 align:middle line:84% phenomena, like the double slit experiment 00:06:17.360 --> 00:06:19.500 align:middle line:84% that we talked a bunch about yesterday. 00:06:19.500 --> 00:06:22.730 align:middle line:90% So that's just a recap. 00:06:22.730 --> 00:06:26.090 align:middle line:84% So pretty quickly after that, a British physicist 00:06:26.090 --> 00:06:29.630 align:middle line:84% named Paul Dirac, who was almost exactly the same age 00:06:29.630 --> 00:06:32.960 align:middle line:84% as Heisenberg and Pauli, very young, in his early 00:06:32.960 --> 00:06:36.260 align:middle line:84% to mid 20s at this point, and therefore a generation younger 00:06:36.260 --> 00:06:37.760 align:middle line:90% than Schrodinger-- 00:06:37.760 --> 00:06:39.810 align:middle line:90% Dirac learned about this work. 00:06:39.810 --> 00:06:43.460 align:middle line:84% He was very mathematically gifted and well-trained. 00:06:43.460 --> 00:06:46.700 align:middle line:84% By this point, he was at Cambridge for his PhD. 00:06:46.700 --> 00:06:50.790 align:middle line:84% And he really began to formalize this new quantum mechanics. 00:06:50.790 --> 00:06:53.060 align:middle line:84% He was not only one of the first to demonstrate 00:06:53.060 --> 00:06:55.850 align:middle line:84% a mathematical equivalence between these very 00:06:55.850 --> 00:06:57.980 align:middle line:84% different-looking formalisms from Heisenberg 00:06:57.980 --> 00:06:59.900 align:middle line:84% and Schrodinger; he then went further, 00:06:59.900 --> 00:07:03.800 align:middle line:84% not just to show that one could build a map from Heisenberg's 00:07:03.800 --> 00:07:07.010 align:middle line:84% matrices to Schrodinger's wave equation, but in fact 00:07:07.010 --> 00:07:11.420 align:middle line:84% to formalize the entire thing in this general, abstract, 00:07:11.420 --> 00:07:12.840 align:middle line:90% geometrical way. 00:07:12.840 --> 00:07:16.760 align:middle line:84% So it's really from people like Dirac, among the first, 00:07:16.760 --> 00:07:19.310 align:middle line:84% from whom we begin thinking about these quantum 00:07:19.310 --> 00:07:23.750 align:middle line:84% states as vectors, not in the three-dimensional space 00:07:23.750 --> 00:07:27.120 align:middle line:84% in which we move around, not in the space of x, y, and z, 00:07:27.120 --> 00:07:30.200 align:middle line:84% but in some abstract, mathematical space that we 00:07:30.200 --> 00:07:32.960 align:middle line:84% would now call a Hilbert space, so that there's 00:07:32.960 --> 00:07:37.010 align:middle line:84% a state associated with this wave function psi that would 00:07:37.010 --> 00:07:38.660 align:middle line:90% obey Schrodinger's equation. 00:07:38.660 --> 00:07:43.070 align:middle line:84% And that's really just a vector in some abstract space, 00:07:43.070 --> 00:07:48.680 align:middle line:84% and that the vector could represent, for example, the-- 00:07:48.680 --> 00:07:51.080 align:middle line:84% it's related to the likelihood that we 00:07:51.080 --> 00:07:54.150 align:middle line:84% would measure a particular value for a property of a quantum 00:07:54.150 --> 00:07:54.650 align:middle line:90% system. 00:07:54.650 --> 00:07:56.630 align:middle line:84% You see it's already gotten very abstracted 00:07:56.630 --> 00:08:00.020 align:middle line:84% from this physical picture of real matter moving 00:08:00.020 --> 00:08:01.610 align:middle line:90% through space. 00:08:01.610 --> 00:08:04.510 align:middle line:84% It's now the behavior of these abstract pointers 00:08:04.510 --> 00:08:07.260 align:middle line:90% in an abstract vector space. 00:08:07.260 --> 00:08:09.560 align:middle line:84% So the state vector, this vector psi, 00:08:09.560 --> 00:08:12.560 align:middle line:84% could itself be represented as some weighted sum 00:08:12.560 --> 00:08:14.390 align:middle line:90% of eigenstates. 00:08:14.390 --> 00:08:17.510 align:middle line:84% That is, states that correspond to a definite value 00:08:17.510 --> 00:08:18.830 align:middle line:90% for a specific property. 00:08:18.830 --> 00:08:21.480 align:middle line:84% So again, if this is brand new to you, please don't worry. 00:08:21.480 --> 00:08:24.000 align:middle line:84% For some of you, this might be familiar from other classes. 00:08:24.000 --> 00:08:26.250 align:middle line:84% But it's from Dirac that we start writing things 00:08:26.250 --> 00:08:30.120 align:middle line:84% like this, that there's some vector psi, some state, 00:08:30.120 --> 00:08:33.960 align:middle line:84% and that can in general be written as a sum, 00:08:33.960 --> 00:08:39.750 align:middle line:84% as a superposition, a weighted sum, of distinct basis vectors, 00:08:39.750 --> 00:08:42.120 align:middle line:84% in this case, the so-called eigenstates. 00:08:42.120 --> 00:08:44.220 align:middle line:84% Now, the eigenstates are states that 00:08:44.220 --> 00:08:47.190 align:middle line:84% have definite values for particular property. 00:08:47.190 --> 00:08:49.680 align:middle line:84% And I'll talk about an example to make that a little more 00:08:49.680 --> 00:08:51.030 align:middle line:90% concrete in a moment. 00:08:51.030 --> 00:08:52.170 align:middle line:90% But just to pause. 00:08:52.170 --> 00:08:56.910 align:middle line:84% If this expression is unexpected or something 00:08:56.910 --> 00:08:58.590 align:middle line:84% you haven't seen before, this really 00:08:58.590 --> 00:09:01.470 align:middle line:84% is just quantifying that notion of superposition. 00:09:01.470 --> 00:09:04.740 align:middle line:84% It's just saying that if these eigenstates, these basis 00:09:04.740 --> 00:09:08.490 align:middle line:84% vectors phi, are each solutions to Schrodinger's equation, 00:09:08.490 --> 00:09:11.230 align:middle line:84% then so is their sum and so is their weighted sum. 00:09:11.230 --> 00:09:14.550 align:middle line:84% So these coefficients A, in general, 00:09:14.550 --> 00:09:16.770 align:middle line:84% could be complex numbers, but they're just a number. 00:09:16.770 --> 00:09:18.000 align:middle line:90% They're just a weight. 00:09:18.000 --> 00:09:22.470 align:middle line:84% Take five parts of phi 1 and 6 plus 7 i parts of phi 2. 00:09:22.470 --> 00:09:25.680 align:middle line:84% We're just going to add up a sum because if each of these 00:09:25.680 --> 00:09:28.320 align:middle line:84% is a solution, then is so is their weighted sum. 00:09:28.320 --> 00:09:31.830 align:middle line:84% It's just a way of formalizing superposition. 00:09:31.830 --> 00:09:34.530 align:middle line:84% This is the kind of stuff that Dirac loved. 00:09:34.530 --> 00:09:36.150 align:middle line:90% He ate this stuff for breakfast. 00:09:36.150 --> 00:09:38.880 align:middle line:84% And he wrote this very, very influential textbook, 00:09:38.880 --> 00:09:42.060 align:middle line:84% first edition in 1930, very soon after this work was 00:09:42.060 --> 00:09:44.580 align:middle line:84% first published, trying to put this 00:09:44.580 --> 00:09:48.003 align:middle line:84% all together in this new vector space packaging. 00:09:48.003 --> 00:09:49.920 align:middle line:84% Now, that was very abstract, what I mentioned. 00:09:49.920 --> 00:09:54.180 align:middle line:84% Let's consider a relatively simple example, again, 00:09:54.180 --> 00:09:55.900 align:middle line:84% one that might be familiar to you. 00:09:55.900 --> 00:09:58.890 align:middle line:84% Let's consider basis states or eigenstates 00:09:58.890 --> 00:10:03.910 align:middle line:84% that correspond to the property of the spin of an electron 00:10:03.910 --> 00:10:05.850 align:middle line:84% if we choose to measure that spin along 00:10:05.850 --> 00:10:07.740 align:middle line:84% some definite orientation in space. 00:10:07.740 --> 00:10:10.710 align:middle line:84% We line up our magnets along the z-direction in space. 00:10:10.710 --> 00:10:14.383 align:middle line:84% We hold up to some gradient of some magnetic field pointing 00:10:14.383 --> 00:10:15.300 align:middle line:90% along the z-direction. 00:10:15.300 --> 00:10:16.740 align:middle line:90% We could really do that. 00:10:16.740 --> 00:10:18.510 align:middle line:84% It's a real thing we could measure. 00:10:18.510 --> 00:10:21.570 align:middle line:84% And then we can ask, if we send an electron 00:10:21.570 --> 00:10:23.670 align:middle line:84% through that region of space where 00:10:23.670 --> 00:10:27.540 align:middle line:84% that external magnetic field is, will its spin be pointing up, 00:10:27.540 --> 00:10:29.640 align:middle line:84% directly along the direction of the field, 00:10:29.640 --> 00:10:31.830 align:middle line:84% or directly opposite, antiparallel? 00:10:31.830 --> 00:10:33.390 align:middle line:90% Those are the two options. 00:10:33.390 --> 00:10:35.460 align:middle line:84% The spin could either be exactly along 00:10:35.460 --> 00:10:38.880 align:middle line:84% the specified direction of space or exactly opposite to it. 00:10:38.880 --> 00:10:40.740 align:middle line:90% There's two possible outcomes. 00:10:40.740 --> 00:10:43.590 align:middle line:84% That means there's only two of these basis states, these two 00:10:43.590 --> 00:10:44.700 align:middle line:90% eigenstates. 00:10:44.700 --> 00:10:46.710 align:middle line:84% States with a definite property, the spin 00:10:46.710 --> 00:10:49.710 align:middle line:84% is definitely up along that direction of space, or the spin 00:10:49.710 --> 00:10:52.260 align:middle line:84% is definitely down, with definite values. 00:10:52.260 --> 00:10:55.380 align:middle line:84% And again, the actual value of that angular momentum, 00:10:55.380 --> 00:10:58.470 align:middle line:84% as usual, scaled in terms of Planck's constant. 00:10:58.470 --> 00:11:01.020 align:middle line:84% Now, these two states are opposite to each other. 00:11:01.020 --> 00:11:02.340 align:middle line:90% They're literally orthogonal. 00:11:02.340 --> 00:11:04.710 align:middle line:90% It's spin up or spin down. 00:11:04.710 --> 00:11:06.870 align:middle line:84% And the way this gets formalized-- again, 00:11:06.870 --> 00:11:11.910 align:middle line:84% we learned this following Paul Dirac is that these vectors are 00:11:11.910 --> 00:11:13.350 align:middle line:90% orthogonal to each other. 00:11:13.350 --> 00:11:14.532 align:middle line:90% They have vanishing overlap. 00:11:14.532 --> 00:11:15.990 align:middle line:84% Again, there's a little bit of this 00:11:15.990 --> 00:11:18.750 align:middle line:84% in the associated optional lecture notes. 00:11:18.750 --> 00:11:21.320 align:middle line:84% This is just a fancy way of taking the dot product. 00:11:21.320 --> 00:11:23.480 align:middle line:84% So we have two vectors that are perpendicular 00:11:23.480 --> 00:11:26.120 align:middle line:84% in ordinary space, say one vector pointing exactly 00:11:26.120 --> 00:11:29.060 align:middle line:84% along the x-axis, a second vector pointing directly 00:11:29.060 --> 00:11:30.080 align:middle line:90% along the y-axis. 00:11:30.080 --> 00:11:31.790 align:middle line:84% Take the dot product, and it vanishes 00:11:31.790 --> 00:11:33.110 align:middle line:90% because they're perpendicular. 00:11:33.110 --> 00:11:36.620 align:middle line:84% The same kind of properties hold among these more abstract 00:11:36.620 --> 00:11:39.050 align:middle line:84% vectors in this abstract Hilbert space. 00:11:39.050 --> 00:11:41.060 align:middle line:84% And in this case, these opposite properties-- 00:11:41.060 --> 00:11:44.060 align:middle line:84% it's either spin up or its opposite, spin down. 00:11:44.060 --> 00:11:48.320 align:middle line:84% The corresponding vectors have a vanishing overlap, 00:11:48.320 --> 00:11:51.800 align:middle line:84% or if you like, a vanishing dot product. 00:11:51.800 --> 00:11:54.830 align:middle line:84% Nonetheless, even though the states are individually 00:11:54.830 --> 00:11:58.460 align:middle line:84% opposite to each other, we can construct a perfectly valid 00:11:58.460 --> 00:12:01.440 align:middle line:84% quantum state by using superposition. 00:12:01.440 --> 00:12:03.380 align:middle line:84% So we can build up some state psi 00:12:03.380 --> 00:12:06.860 align:middle line:84% with which to characterize this electron or a whole collection 00:12:06.860 --> 00:12:08.030 align:middle line:90% of electrons. 00:12:08.030 --> 00:12:11.810 align:middle line:84% And we could say that an individual electron would 00:12:11.810 --> 00:12:15.980 align:middle line:84% have some likelihood to be found in spin up upon performing 00:12:15.980 --> 00:12:18.410 align:middle line:84% the measurement, some perhaps different likelihood 00:12:18.410 --> 00:12:20.010 align:middle line:90% to be found in spin down. 00:12:20.010 --> 00:12:22.620 align:middle line:84% So even though the outcomes can't both be found, 00:12:22.620 --> 00:12:24.780 align:middle line:84% we'd find either one or the other, 00:12:24.780 --> 00:12:27.810 align:middle line:84% the quantum state could be this superposition, 00:12:27.810 --> 00:12:31.020 align:middle line:84% this mixture of these seemingly opposite sets of properties. 00:12:31.020 --> 00:12:34.620 align:middle line:84% That's the kind of manipulation that people 00:12:34.620 --> 00:12:39.210 align:middle line:84% began to learn how to do once the British physicist 00:12:39.210 --> 00:12:42.600 align:middle line:84% at Cambridge, Paul Dirac, began to formalize Schrodinger's 00:12:42.600 --> 00:12:45.210 align:middle line:84% notion, building very specifically on this notion 00:12:45.210 --> 00:12:46.480 align:middle line:90% of superposition. 00:12:46.480 --> 00:12:50.170 align:middle line:84% So again, let's stick with our little, simple example 00:12:50.170 --> 00:12:51.870 align:middle line:90% for a few more steps. 00:12:51.870 --> 00:12:53.790 align:middle line:84% If we were to perform a measurement 00:12:53.790 --> 00:12:56.810 align:middle line:84% of the spin of that particle along a particular direction 00:12:56.810 --> 00:12:58.560 align:middle line:84% in space, we'd have to orient our magnets, 00:12:58.560 --> 00:13:00.810 align:middle line:84% so we're going to choose a direction in space 00:13:00.810 --> 00:13:03.540 align:middle line:84% along which to measure spin, then 00:13:03.540 --> 00:13:06.058 align:middle line:84% we can calculate in advance the probability 00:13:06.058 --> 00:13:07.350 align:middle line:90% to get either of these answers. 00:13:07.350 --> 00:13:09.930 align:middle line:84% It will either be spin up or spin down. 00:13:09.930 --> 00:13:12.630 align:middle line:84% And we find that the probability, 00:13:12.630 --> 00:13:16.860 align:middle line:84% according to Max Born, by asking about the absolute square 00:13:16.860 --> 00:13:20.220 align:middle line:84% of the overlap between the general quantum state 00:13:20.220 --> 00:13:21.760 align:middle line:90% and that definite outcome. 00:13:21.760 --> 00:13:26.880 align:middle line:84% And as you can see here, using some of these inner product 00:13:26.880 --> 00:13:30.000 align:middle line:84% relations, that the probability to find spin up 00:13:30.000 --> 00:13:32.010 align:middle line:84% will just be the square of this coefficient, 00:13:32.010 --> 00:13:33.390 align:middle line:90% the absolute square. 00:13:33.390 --> 00:13:35.040 align:middle line:84% The probability to find spin down 00:13:35.040 --> 00:13:37.950 align:middle line:84% is just the absolute square of the other coefficient. 00:13:37.950 --> 00:13:40.470 align:middle line:84% So what's important to step back and recognize here 00:13:40.470 --> 00:13:43.140 align:middle line:84% before we get too lost in the mathematics is 00:13:43.140 --> 00:13:44.850 align:middle line:84% that every single time we measure 00:13:44.850 --> 00:13:47.040 align:middle line:84% spin along that same direction z, 00:13:47.040 --> 00:13:48.630 align:middle line:90% we always get a definite answer. 00:13:48.630 --> 00:13:51.660 align:middle line:84% We always find either spin up or spin down. 00:13:51.660 --> 00:13:54.280 align:middle line:84% We don't find spin at 72 degrees. 00:13:54.280 --> 00:13:57.430 align:middle line:84% We don't find some smeared-out answer or some fuzzy result. 00:13:57.430 --> 00:13:59.130 align:middle line:90% We get a definite answer. 00:13:59.130 --> 00:14:01.320 align:middle line:84% What the equations of quantum mechanics 00:14:01.320 --> 00:14:04.710 align:middle line:84% allowed people to do starting right from the 1920s 00:14:04.710 --> 00:14:08.340 align:middle line:84% was calculate the likelihood the probability 00:14:08.340 --> 00:14:12.930 align:middle line:84% to get this definite answer versus that definite answer. 00:14:12.930 --> 00:14:16.950 align:middle line:84% And yet what the equation seems not to allow physicists to do, 00:14:16.950 --> 00:14:20.130 align:middle line:84% and this is something that people like Max Born and Paul 00:14:20.130 --> 00:14:22.950 align:middle line:84% Dirac and Niels Bohr and Werner Heisenberg and the folks 00:14:22.950 --> 00:14:24.210 align:middle line:90% we've been talking about-- 00:14:24.210 --> 00:14:27.480 align:middle line:84% what they began to grapple with and to really 00:14:27.480 --> 00:14:31.320 align:middle line:84% reconcile themselves to, is that quantum mechanics can only 00:14:31.320 --> 00:14:33.810 align:middle line:84% be used to calculate these probabilities, 00:14:33.810 --> 00:14:36.390 align:middle line:84% that we get definite answers each time 00:14:36.390 --> 00:14:38.490 align:middle line:84% the real measurement is performed, 00:14:38.490 --> 00:14:40.440 align:middle line:84% and the equations tell us the probability 00:14:40.440 --> 00:14:42.930 align:middle line:84% to get that definite answer versus the other. 00:14:42.930 --> 00:14:46.530 align:middle line:84% What the equations do not seem to allow the physicist to do, 00:14:46.530 --> 00:14:50.790 align:middle line:84% then or now, is get any knowledge ahead of time 00:14:50.790 --> 00:14:54.030 align:middle line:84% of what the actual value was for that property 00:14:54.030 --> 00:14:56.500 align:middle line:84% before the measurement was performed. 00:14:56.500 --> 00:15:00.735 align:middle line:84% So if we write down a valid quantum state like this, 00:15:00.735 --> 00:15:03.270 align:middle line:84% this tells us that the object has some likelihood 00:15:03.270 --> 00:15:05.453 align:middle line:84% to be measured with one property, some likelihood 00:15:05.453 --> 00:15:07.120 align:middle line:84% to be measured with some other property. 00:15:07.120 --> 00:15:09.240 align:middle line:84% But we don't know until the actual measurement 00:15:09.240 --> 00:15:14.040 align:middle line:84% is performed which property the particle really has on its own. 00:15:14.040 --> 00:15:15.450 align:middle line:90% Bohr went even further. 00:15:15.450 --> 00:15:17.190 align:middle line:84% It's not just that we don't know. 00:15:17.190 --> 00:15:21.390 align:middle line:84% He began to suggest that maybe the particle itself simply 00:15:21.390 --> 00:15:24.780 align:middle line:84% did not have a definite value prior to its measurement. 00:15:24.780 --> 00:15:27.510 align:middle line:84% So the one statement is that we don't know for sure. 00:15:27.510 --> 00:15:29.720 align:middle line:84% And that's a statement of our ignorance, 00:15:29.720 --> 00:15:31.100 align:middle line:90% the state of our knowledge. 00:15:31.100 --> 00:15:33.530 align:middle line:84% And therefore, we average over our ignorance 00:15:33.530 --> 00:15:35.510 align:middle line:90% by calculating probabilities. 00:15:35.510 --> 00:15:38.210 align:middle line:84% Bohr and others following his line of thinking 00:15:38.210 --> 00:15:41.690 align:middle line:84% reasoned maybe the probabilities are even more radical. 00:15:41.690 --> 00:15:44.720 align:middle line:84% Maybe the world itself, so to speak, didn't know. 00:15:44.720 --> 00:15:48.650 align:middle line:84% What if the electron simply had no definite value of spin, 00:15:48.650 --> 00:15:52.560 align:middle line:84% neither spin up nor spin down, prior to its measurement? 00:15:52.560 --> 00:15:55.220 align:middle line:84% And again, to bring that home, I like 00:15:55.220 --> 00:15:56.980 align:middle line:84% to think of human-scale examples. 00:15:56.980 --> 00:15:57.980 align:middle line:90% What would that be like? 00:15:57.980 --> 00:16:01.940 align:middle line:84% That's as if saying a person had no particular weight until she 00:16:01.940 --> 00:16:03.230 align:middle line:90% stepped on a bathroom scale. 00:16:03.230 --> 00:16:05.390 align:middle line:84% Not that she didn't know or she misremembered 00:16:05.390 --> 00:16:08.670 align:middle line:84% or it might have been one of many values. 00:16:08.670 --> 00:16:10.580 align:middle line:84% What if she literally had no weight 00:16:10.580 --> 00:16:12.532 align:middle line:84% at all, no definite weight at all, 00:16:12.532 --> 00:16:14.240 align:middle line:84% until she stepped-- until she measured it 00:16:14.240 --> 00:16:15.198 align:middle line:90% by stepping on a scale? 00:16:15.198 --> 00:16:18.350 align:middle line:84% That's a pretty radical notion, a very strong break 00:16:18.350 --> 00:16:20.970 align:middle line:84% from how we think about physics either with Newton 00:16:20.970 --> 00:16:22.900 align:middle line:90% or with Maxwell. 00:16:22.900 --> 00:16:25.500 align:middle line:84% And not everyone liked that development. 00:16:25.500 --> 00:16:27.250 align:middle line:84% So one of the first people to really begin 00:16:27.250 --> 00:16:31.180 align:middle line:84% to raise some cautions about that approach 00:16:31.180 --> 00:16:32.410 align:middle line:90% is Albert Einstein. 00:16:32.410 --> 00:16:34.867 align:middle line:84% So he was, of course, a major contributor 00:16:34.867 --> 00:16:35.950 align:middle line:90% to some of the early work. 00:16:35.950 --> 00:16:39.190 align:middle line:84% We saw many of his very important contributions 00:16:39.190 --> 00:16:42.257 align:middle line:84% within the so-called old quantum theory epoch, 00:16:42.257 --> 00:16:43.840 align:middle line:84% even more that we didn't have a chance 00:16:43.840 --> 00:16:45.490 align:middle line:90% to talk about in this class. 00:16:45.490 --> 00:16:47.890 align:middle line:84% He was all over this early quantum theory stuff. 00:16:47.890 --> 00:16:50.560 align:middle line:84% And he was following these more recent developments 00:16:50.560 --> 00:16:51.520 align:middle line:90% very closely. 00:16:51.520 --> 00:16:54.460 align:middle line:84% And he became more and more dissatisfied, 00:16:54.460 --> 00:16:57.100 align:middle line:84% kind of uncomfortable, with this direction 00:16:57.100 --> 00:17:00.640 align:middle line:84% that people like Niels Bohr and many of the younger guard 00:17:00.640 --> 00:17:01.910 align:middle line:90% were pursuing. 00:17:01.910 --> 00:17:05.800 align:middle line:84% So he wrote a series of really amazing letters 00:17:05.800 --> 00:17:07.630 align:middle line:84% to his very close friend Max Born, 00:17:07.630 --> 00:17:10.540 align:middle line:84% the same Born we've seen many times, who worked closely 00:17:10.540 --> 00:17:12.849 align:middle line:84% with Heisenberg who introduced this probability 00:17:12.849 --> 00:17:14.861 align:middle line:84% interpretation for Schrodinger's wavefunctions. 00:17:14.861 --> 00:17:16.069 align:middle line:90% They were very close friends. 00:17:16.069 --> 00:17:18.123 align:middle line:84% They were contemporaries, same age. 00:17:18.123 --> 00:17:19.790 align:middle line:84% They'd known each other for a long time. 00:17:19.790 --> 00:17:21.415 align:middle line:84% And when they weren't in the same city, 00:17:21.415 --> 00:17:22.460 align:middle line:90% they would write letters. 00:17:22.460 --> 00:17:24.200 align:middle line:84% And many years later, those letters 00:17:24.200 --> 00:17:26.150 align:middle line:90% were collected and published. 00:17:26.150 --> 00:17:28.130 align:middle line:90% It's a wonderful collection. 00:17:28.130 --> 00:17:30.020 align:middle line:84% So Einstein, we know, grew frustrated 00:17:30.020 --> 00:17:33.440 align:middle line:84% with this restriction to only calculating probabilities. 00:17:33.440 --> 00:17:36.290 align:middle line:84% And he would often vent his frustration to Born 00:17:36.290 --> 00:17:38.810 align:middle line:84% and actually try to convert Born, Born himself, who 00:17:38.810 --> 00:17:41.690 align:middle line:84% had actually argued for this probabilistic interpretation. 00:17:41.690 --> 00:17:43.308 align:middle line:84% Here's one of the most famous excerpts 00:17:43.308 --> 00:17:44.600 align:middle line:90% of quotations from the letters. 00:17:44.600 --> 00:17:47.370 align:middle line:84% There's a whole series of very juicy letters they exchange. 00:17:47.370 --> 00:17:50.150 align:middle line:84% But as you might well have heard this last part, 00:17:50.150 --> 00:17:52.190 align:middle line:84% comes from a private letter that Einstein 00:17:52.190 --> 00:17:55.880 align:middle line:84% had written to Born in December of 1926, 00:17:55.880 --> 00:17:58.700 align:middle line:84% five months after Born introduced the idea that psi 00:17:58.700 --> 00:17:59.828 align:middle line:90% relates to probabilities. 00:17:59.828 --> 00:18:02.120 align:middle line:84% So Einstein writes that "quantum mechanics is certainly 00:18:02.120 --> 00:18:02.840 align:middle line:90% imposing." 00:18:02.840 --> 00:18:05.330 align:middle line:84% I think by that he means impressive. 00:18:05.330 --> 00:18:08.660 align:middle line:84% "But an inner voice tells me it's not yet the real thing. 00:18:08.660 --> 00:18:11.482 align:middle line:84% The theory says a lot, but does not really bring us any closer 00:18:11.482 --> 00:18:13.940 align:middle line:84% to the secret of the 'old one," by which he means something 00:18:13.940 --> 00:18:16.400 align:middle line:84% like God, kind of spiritual notion. 00:18:16.400 --> 00:18:19.787 align:middle line:84% He goes on, "I, at any rate, am not convinced that He--" sorry. 00:18:19.787 --> 00:18:21.620 align:middle line:84% "I, at any rate, am convinced that He is not 00:18:21.620 --> 00:18:22.328 align:middle line:90% playing at dice." 00:18:22.328 --> 00:18:24.140 align:middle line:84% And you've probably heard this paraphrased. 00:18:24.140 --> 00:18:25.490 align:middle line:84% Einstein claimed that God does not 00:18:25.490 --> 00:18:26.480 align:middle line:90% play dice with the universe. 00:18:26.480 --> 00:18:28.130 align:middle line:84% That's where that quotation comes from, 00:18:28.130 --> 00:18:31.460 align:middle line:84% that surely the world has definite properties, whether we 00:18:31.460 --> 00:18:32.720 align:middle line:90% happen to know them or not. 00:18:32.720 --> 00:18:34.880 align:middle line:90% That's really what he's arguing. 00:18:34.880 --> 00:18:37.190 align:middle line:84% It turns out Einstein didn't only raise this question 00:18:37.190 --> 00:18:38.570 align:middle line:90% with Max Born. 00:18:38.570 --> 00:18:41.270 align:middle line:84% He got very-- into very animated discussions 00:18:41.270 --> 00:18:42.620 align:middle line:90% with Erwin Schrodinger. 00:18:42.620 --> 00:18:44.690 align:middle line:84% And he had many opportunities, starting 00:18:44.690 --> 00:18:47.390 align:middle line:84% very soon after Schrodinger published this pathbreaking 00:18:47.390 --> 00:18:48.470 align:middle line:90% work. 00:18:48.470 --> 00:18:51.110 align:middle line:84% Schrodinger published his work while he was still 00:18:51.110 --> 00:18:53.960 align:middle line:84% a professor in Austria, but very quickly, he 00:18:53.960 --> 00:18:57.140 align:middle line:84% was then hired to the fancy professorship in Berlin 00:18:57.140 --> 00:18:58.820 align:middle line:90% starting in 1927. 00:18:58.820 --> 00:19:01.340 align:middle line:84% In fact, he took over the professorship 00:19:01.340 --> 00:19:03.420 align:middle line:90% when Max Planck retired from it. 00:19:03.420 --> 00:19:05.840 align:middle line:84% So now Schrodinger, starting in 1927, 00:19:05.840 --> 00:19:08.660 align:middle line:84% was the senior-- the ordinarius professor 00:19:08.660 --> 00:19:10.310 align:middle line:84% of theoretical physics in Berlin. 00:19:10.310 --> 00:19:12.520 align:middle line:84% And Einstein was in Berlin at the Prussian Academy. 00:19:12.520 --> 00:19:13.520 align:middle line:90% Now they were neighbors. 00:19:13.520 --> 00:19:15.560 align:middle line:90% They became even better friends. 00:19:15.560 --> 00:19:17.190 align:middle line:84% They would hang out all the time. 00:19:17.190 --> 00:19:20.630 align:middle line:84% We know this from their letters and from other documentation. 00:19:20.630 --> 00:19:21.860 align:middle line:90% They would enjoy these-- 00:19:21.860 --> 00:19:24.230 align:middle line:84% I love this, the [GERMAN] evenings. 00:19:24.230 --> 00:19:26.150 align:middle line:84% These are Viennese sausage parties, 00:19:26.150 --> 00:19:27.530 align:middle line:90% which we should bring back. 00:19:27.530 --> 00:19:29.750 align:middle line:84% They would also go sailing on a lake together. 00:19:29.750 --> 00:19:31.650 align:middle line:84% Einstein owned a summer home in Germany, 00:19:31.650 --> 00:19:33.200 align:middle line:84% and he loved sailing on the lake. 00:19:33.200 --> 00:19:35.540 align:middle line:84% They'd go on sailing trips together. 00:19:35.540 --> 00:19:39.140 align:middle line:84% And they would argue and talk about quantum theory 00:19:39.140 --> 00:19:40.580 align:middle line:90% on many of these visits. 00:19:40.580 --> 00:19:43.400 align:middle line:84% And in fact, Schrodinger began to feel very much 00:19:43.400 --> 00:19:44.030 align:middle line:90% like Einstein. 00:19:44.030 --> 00:19:47.930 align:middle line:84% They became-- both became suspicious or skeptical 00:19:47.930 --> 00:19:50.180 align:middle line:84% of the direction that quantum theory was going, 00:19:50.180 --> 00:19:52.790 align:middle line:84% even though they both, Einstein and Schrodinger each, 00:19:52.790 --> 00:19:55.970 align:middle line:84% had done so much to actually build this formalism of quantum 00:19:55.970 --> 00:19:57.300 align:middle line:90% mechanics. 00:19:57.300 --> 00:19:59.420 align:middle line:84% So one of their surviving letters-- 00:19:59.420 --> 00:20:02.253 align:middle line:84% Einstein asks Schrodinger to imagine a particular situation. 00:20:02.253 --> 00:20:03.920 align:middle line:84% He wanted to drive home why we shouldn't 00:20:03.920 --> 00:20:07.650 align:middle line:84% be content to stop only with calculating probabilities. 00:20:07.650 --> 00:20:09.620 align:middle line:84% So imagine that someone had hidden a ball, 00:20:09.620 --> 00:20:14.150 align:middle line:84% let's say a red ball, into one of two identical closed boxes. 00:20:14.150 --> 00:20:15.170 align:middle line:90% And we can't peek. 00:20:15.170 --> 00:20:17.510 align:middle line:84% We don't know where the assistant placed the ball. 00:20:17.510 --> 00:20:21.410 align:middle line:84% Prior to opening either box, we could calculate a probability 00:20:21.410 --> 00:20:25.040 align:middle line:84% that we would find the ball in either box one or box two. 00:20:25.040 --> 00:20:27.800 align:middle line:84% So before we check, before we perform the measurement 00:20:27.800 --> 00:20:30.770 align:middle line:84% by measuring where the ball actually is, 00:20:30.770 --> 00:20:32.720 align:middle line:84% our probability would say the likelihood 00:20:32.720 --> 00:20:35.510 align:middle line:84% to find the ball in box one is 50% 00:20:35.510 --> 00:20:38.223 align:middle line:84% and the likelihood in box two is also 50%. 00:20:38.223 --> 00:20:39.890 align:middle line:84% Einstein writes to Schrodinger, "Is this 00:20:39.890 --> 00:20:41.180 align:middle line:90% a complete description? 00:20:41.180 --> 00:20:41.750 align:middle line:90% NO." 00:20:41.750 --> 00:20:42.530 align:middle line:90% All capitals. 00:20:42.530 --> 00:20:43.490 align:middle line:90% "NO. 00:20:43.490 --> 00:20:45.440 align:middle line:84% A complete statement is, the ball 00:20:45.440 --> 00:20:47.600 align:middle line:90% is or is not in the first box." 00:20:47.600 --> 00:20:49.640 align:middle line:84% There should be a value to the property 00:20:49.640 --> 00:20:52.940 align:middle line:84% of the ball's location, whether or not we know what it is. 00:20:52.940 --> 00:20:55.910 align:middle line:84% We can calculate probabilities based on our ignorance, 00:20:55.910 --> 00:20:57.890 align:middle line:90% not based on how the world is. 00:20:57.890 --> 00:21:00.530 align:middle line:84% And Einstein thought people had been too quick to conflate one 00:21:00.530 --> 00:21:02.310 align:middle line:90% with the other. 00:21:02.310 --> 00:21:04.640 align:middle line:84% Now, these discussions, which are often very spirited 00:21:04.640 --> 00:21:05.390 align:middle line:90% and very friendly. 00:21:05.390 --> 00:21:08.360 align:middle line:84% They really came to each other very much. 00:21:08.360 --> 00:21:10.730 align:middle line:84% Those direct face-to-face interactions 00:21:10.730 --> 00:21:14.557 align:middle line:84% were pretty soon disrupted with the rise of the Nazis. 00:21:14.557 --> 00:21:16.640 align:middle line:84% And we'll talk more about the rise of Nazis again, 00:21:16.640 --> 00:21:18.780 align:middle line:84% actually, starting in the next class session. 00:21:18.780 --> 00:21:21.230 align:middle line:84% But as I'm sure you know, Hitler was 00:21:21.230 --> 00:21:24.230 align:middle line:84% elected in an open election as chancellor of Germany 00:21:24.230 --> 00:21:26.150 align:middle line:90% in January of 1933. 00:21:26.150 --> 00:21:27.980 align:middle line:84% And very quickly, the Nazi party then 00:21:27.980 --> 00:21:29.720 align:middle line:84% took over more and more elements of 00:21:29.720 --> 00:21:33.050 align:middle line:84% the German federal government and local governments. 00:21:33.050 --> 00:21:35.990 align:middle line:84% And so by that spring, within just months 00:21:35.990 --> 00:21:39.530 align:middle line:84% of Hitler's first election, both Einstein and Schrodinger 00:21:39.530 --> 00:21:41.870 align:middle line:90% independently left Germany. 00:21:41.870 --> 00:21:44.690 align:middle line:84% Einstein-- we'll talk more about their reasons for leaving. 00:21:44.690 --> 00:21:47.660 align:middle line:84% The point is, they were now no longer in Berlin. 00:21:47.660 --> 00:21:50.030 align:middle line:84% In fact, they were no longer on the same continent. 00:21:50.030 --> 00:21:52.310 align:middle line:84% Einstein resettled to the United States. 00:21:52.310 --> 00:21:54.050 align:middle line:84% He moved to Princeton, New Jersey. 00:21:54.050 --> 00:21:57.950 align:middle line:84% Schrodinger moved at first to Oxford in England. 00:21:57.950 --> 00:22:01.070 align:middle line:84% He later settled for the wall years in Dublin, in Ireland, 00:22:01.070 --> 00:22:04.030 align:middle line:84% but he got out of Germany, out of the continent. 00:22:04.030 --> 00:22:05.850 align:middle line:90% So now they were an ocean apart. 00:22:05.850 --> 00:22:08.910 align:middle line:84% And that was personally very disruptive. 00:22:08.910 --> 00:22:11.427 align:middle line:84% But for us historians, it was very lucky 00:22:11.427 --> 00:22:14.010 align:middle line:84% because now they could only talk to each other through letter. 00:22:14.010 --> 00:22:17.710 align:middle line:84% And most of these letters were saved and have survived. 00:22:17.710 --> 00:22:20.340 align:middle line:84% So we can see how their conversation continued, 00:22:20.340 --> 00:22:22.093 align:middle line:84% but now we have more of their conversation 00:22:22.093 --> 00:22:24.510 align:middle line:84% because we all had to be written down because they weren't 00:22:24.510 --> 00:22:27.210 align:middle line:84% sitting up all night eating their Vienna sausages 00:22:27.210 --> 00:22:28.560 align:middle line:90% or sailing on the lake. 00:22:28.560 --> 00:22:29.670 align:middle line:90% So here's one example. 00:22:29.670 --> 00:22:31.587 align:middle line:84% Again, I write about this in one of the essays 00:22:31.587 --> 00:22:33.930 align:middle line:84% in the reader for today, one of the readings. 00:22:33.930 --> 00:22:36.390 align:middle line:84% Here's a letter that Einstein wrote to Schrodinger now 00:22:36.390 --> 00:22:40.560 align:middle line:84% about two years or so after they had both fled Germany. 00:22:40.560 --> 00:22:45.060 align:middle line:84% He says, "Imagine a charge of gunpowder, of weaponry, that's 00:22:45.060 --> 00:22:48.510 align:middle line:84% intrinsically unstable, that has even odds, even 00:22:48.510 --> 00:22:51.940 align:middle line:84% likelihood, to explode over the course of one year." 00:22:51.940 --> 00:22:54.000 align:middle line:84% So now he's no longer talking about a kind 00:22:54.000 --> 00:22:57.000 align:middle line:84% of emotionally neutral situation, 00:22:57.000 --> 00:22:59.040 align:middle line:84% like a red ball and a blue box right. 00:22:59.040 --> 00:23:01.860 align:middle line:84% Suddenly, he's thinking about-- the world is racing toward war, 00:23:01.860 --> 00:23:03.300 align:middle line:90% at least certainly Europe is. 00:23:03.300 --> 00:23:07.140 align:middle line:84% Let's talk about worldly things like caches of weapons 00:23:07.140 --> 00:23:11.520 align:middle line:84% and what's going to happen with that stockpile over time. 00:23:11.520 --> 00:23:14.800 align:middle line:84% The nature of the discussion changes quite dramatically. 00:23:14.800 --> 00:23:17.100 align:middle line:84% So in Einstein's letter, his private letter, he says, 00:23:17.100 --> 00:23:19.338 align:middle line:84% "In principle, the situation can easily 00:23:19.338 --> 00:23:20.880 align:middle line:84% be represented quantum mechanically." 00:23:20.880 --> 00:23:23.820 align:middle line:84% It would be a superposition of these two opposite properties, 00:23:23.820 --> 00:23:27.450 align:middle line:84% but a sum of the two, just like with any superposition. 00:23:27.450 --> 00:23:30.870 align:middle line:84% After the course of a year, this is no longer the case. 00:23:30.870 --> 00:23:33.060 align:middle line:84% This might make sense as the state 00:23:33.060 --> 00:23:35.010 align:middle line:84% of the system at the start of one 00:23:35.010 --> 00:23:37.470 align:middle line:84% year, is what Einstein is suggesting, but after a year, 00:23:37.470 --> 00:23:39.390 align:middle line:84% this can no longer be an accurate description, 00:23:39.390 --> 00:23:41.040 align:middle line:90% at least argues Einstein. 00:23:41.040 --> 00:23:45.480 align:middle line:84% Rather, the wave function describes a blend of not yet 00:23:45.480 --> 00:23:47.410 align:middle line:90% and of already exploded systems. 00:23:47.410 --> 00:23:49.020 align:middle line:90% But how could that be, right? 00:23:49.020 --> 00:23:52.860 align:middle line:84% In reality, there's just no intermediary between exploded 00:23:52.860 --> 00:23:54.300 align:middle line:90% and not exploded. 00:23:54.300 --> 00:23:55.890 align:middle line:84% Think about the nature of his examples 00:23:55.890 --> 00:23:58.057 align:middle line:84% now, even though he's still talking about statistics 00:23:58.057 --> 00:23:59.250 align:middle line:90% and probability. 00:23:59.250 --> 00:24:01.950 align:middle line:84% Schrodinger writes back a few weeks later, 00:24:01.950 --> 00:24:03.300 align:middle line:90% and now there's a twist. 00:24:03.300 --> 00:24:06.990 align:middle line:84% This is where the so-called Schrodinger cat is first 00:24:06.990 --> 00:24:08.700 align:middle line:90% introduced, first written down. 00:24:08.700 --> 00:24:11.130 align:middle line:84% It's actually first a private letter 00:24:11.130 --> 00:24:14.250 align:middle line:84% from Schrodinger to Einstein responding to this exploding 00:24:14.250 --> 00:24:16.195 align:middle line:90% cache of gunpowder. 00:24:16.195 --> 00:24:17.320 align:middle line:90% Schrodinger sits with that. 00:24:17.320 --> 00:24:19.410 align:middle line:84% And he writes back this example, now. 00:24:19.410 --> 00:24:22.620 align:middle line:84% This is from his private letter in response. 00:24:22.620 --> 00:24:24.600 align:middle line:84% He says, "Confined in a steel chamber 00:24:24.600 --> 00:24:27.540 align:middle line:84% is a Geiger counter prepared with a tiny amount 00:24:27.540 --> 00:24:28.650 align:middle line:90% of radioactive uranium." 00:24:28.650 --> 00:24:32.010 align:middle line:84% That's over here in our cartoon, courtesy of Wikimedia. 00:24:32.010 --> 00:24:35.520 align:middle line:84% "So that so small, such a small amount of radioactivity, 00:24:35.520 --> 00:24:38.040 align:middle line:84% that in the next hour it is just as probable 00:24:38.040 --> 00:24:41.230 align:middle line:84% as not to expect one atomic decay." 00:24:41.230 --> 00:24:43.740 align:middle line:84% So it has a 50/50 chance to decay in one hour. 00:24:43.740 --> 00:24:45.900 align:middle line:84% Its half life, let's say, is one hour. 00:24:45.900 --> 00:24:48.100 align:middle line:84% There's an amplified relay system, 00:24:48.100 --> 00:24:51.420 align:middle line:84% so if any radioactive decay is detected here, 00:24:51.420 --> 00:24:55.500 align:middle line:84% it will trigger this thing to drop a hammer 00:24:55.500 --> 00:24:57.780 align:middle line:90% to shatter a bottle. 00:24:57.780 --> 00:24:59.220 align:middle line:84% And the bottle contains what they 00:24:59.220 --> 00:25:04.430 align:middle line:84% called prussic acid, which is a certain kind of cyanide poison. 00:25:04.430 --> 00:25:07.880 align:middle line:84% And cruelly, a cat is also trapped in the steel chamber. 00:25:07.880 --> 00:25:09.230 align:middle line:90% So it is a windowless box. 00:25:09.230 --> 00:25:12.440 align:middle line:84% You put a cat inside, which is not very friendly to the cat, 00:25:12.440 --> 00:25:14.720 align:middle line:84% radioactive source with a sensitive detector 00:25:14.720 --> 00:25:16.220 align:middle line:90% with a particular half life. 00:25:16.220 --> 00:25:19.730 align:middle line:84% It's only 50/50 odds to detect even a single decay 00:25:19.730 --> 00:25:20.900 align:middle line:90% after one hour. 00:25:20.900 --> 00:25:23.450 align:middle line:84% If even one decay happens, it will trigger the thing 00:25:23.450 --> 00:25:26.150 align:middle line:84% and break the vial and kill the cat. 00:25:26.150 --> 00:25:28.700 align:middle line:84% If no decays happen to happen in that hour, 00:25:28.700 --> 00:25:30.710 align:middle line:90% the vial will not break-- 00:25:30.710 --> 00:25:33.725 align:middle line:84% be broken, and the cat will live. 00:25:33.725 --> 00:25:35.350 align:middle line:84% After one hour, the living and dead cat 00:25:35.350 --> 00:25:38.890 align:middle line:84% are smeared out in equal measure according to quantum mechanics. 00:25:38.890 --> 00:25:42.010 align:middle line:84% Again, we can write this Schrodinger-like superposition 00:25:42.010 --> 00:25:44.080 align:middle line:90% of totally opposite properties. 00:25:44.080 --> 00:25:46.270 align:middle line:84% And yet quantum mechanics, they both argue, 00:25:46.270 --> 00:25:48.100 align:middle line:84% has no way to tell the difference 00:25:48.100 --> 00:25:50.140 align:middle line:84% or to tell us what the real state of the world 00:25:50.140 --> 00:25:52.445 align:middle line:90% is, only the likelihood. 00:25:52.445 --> 00:25:53.320 align:middle line:90% Einstein writes back. 00:25:53.320 --> 00:25:56.200 align:middle line:84% He can say, "Your cat shows that we are in complete agreement." 00:25:56.200 --> 00:25:57.867 align:middle line:84% Now they're talking about life and death 00:25:57.867 --> 00:26:01.368 align:middle line:84% with poison and gunpowder, not about balls and urns. 00:26:01.368 --> 00:26:03.910 align:middle line:84% A wave function "that contains the living as well as the dead 00:26:03.910 --> 00:26:07.330 align:middle line:84% cat just cannot be taken as a description of the real state 00:26:07.330 --> 00:26:08.950 align:middle line:90% of affairs." 00:26:08.950 --> 00:26:11.770 align:middle line:84% And by the way, this is the version, almost word for word, 00:26:11.770 --> 00:26:14.680 align:middle line:84% that then Schrodinger publishes in this very famous article 00:26:14.680 --> 00:26:15.580 align:middle line:90% later that autumn. 00:26:15.580 --> 00:26:18.250 align:middle line:84% It comes out in November of 1935. 00:26:18.250 --> 00:26:20.227 align:middle line:84% And that's the first published version 00:26:20.227 --> 00:26:22.060 align:middle line:84% that comes to be known as Schrodinger's cat. 00:26:22.060 --> 00:26:24.017 align:middle line:84% It's almost exactly word for word 00:26:24.017 --> 00:26:26.350 align:middle line:84% what Schrodinger had first written in his private letter 00:26:26.350 --> 00:26:27.280 align:middle line:90% to Einstein. 00:26:27.280 --> 00:26:28.810 align:middle line:84% And there's an irony in all this, 00:26:28.810 --> 00:26:34.160 align:middle line:84% a kind of historical irony, that by the mid-1930s, by 1935, 00:26:34.160 --> 00:26:36.470 align:middle line:84% Schrodinger had become quite skeptical, actually 00:26:36.470 --> 00:26:39.440 align:middle line:84% quite critical, of some of his own contributions 00:26:39.440 --> 00:26:40.580 align:middle line:90% to quantum mechanics. 00:26:40.580 --> 00:26:42.830 align:middle line:84% It was Schrodinger who wrote down the Schrodinger wave 00:26:42.830 --> 00:26:43.550 align:middle line:90% equation. 00:26:43.550 --> 00:26:45.560 align:middle line:84% Schrodinger said, isn't this great? 00:26:45.560 --> 00:26:47.600 align:middle line:84% We know how waves behave mathematically. 00:26:47.600 --> 00:26:49.730 align:middle line:84% They obey things like superposition. 00:26:49.730 --> 00:26:54.320 align:middle line:84% And yet 10 years later, between 1926 and 1935, 00:26:54.320 --> 00:26:57.170 align:middle line:84% on the order of 10 years, Schrodinger, like Einstein, 00:26:57.170 --> 00:27:02.090 align:middle line:84% had become quite uncomfortable with the conceptual direction 00:27:02.090 --> 00:27:05.430 align:middle line:84% with which people were trying to make sense of his own equation. 00:27:05.430 --> 00:27:07.740 align:middle line:84% So he became actually an outspoken critic. 00:27:07.740 --> 00:27:10.550 align:middle line:84% And so the irony, at least, I think, for us today, 00:27:10.550 --> 00:27:15.050 align:middle line:84% is that he invented this now totally famous cat paradox. 00:27:15.050 --> 00:27:16.820 align:middle line:84% There are internet memes up and down, 00:27:16.820 --> 00:27:19.790 align:middle line:84% not to help teach people about his equations, 00:27:19.790 --> 00:27:21.440 align:middle line:90% but actually as a critique. 00:27:21.440 --> 00:27:24.020 align:middle line:84% He invented the paradox to say there's 00:27:24.020 --> 00:27:26.850 align:middle line:84% something rotten and wrong with quantum mechanics, 00:27:26.850 --> 00:27:29.750 align:middle line:84% not as a fun way to teach the theory. 00:27:29.750 --> 00:27:30.980 align:middle line:90% So I'll pause there. 00:27:30.980 --> 00:27:32.980 align:middle line:84% We can have a little discussion, some questions. 00:27:32.980 --> 00:27:37.220 align:middle line:90% 00:27:37.220 --> 00:27:40.730 align:middle line:84% So Gary asks, is it possible that even after measuring 00:27:40.730 --> 00:27:44.690 align:middle line:84% a definitive measure, like the weight on the scale, 00:27:44.690 --> 00:27:46.370 align:middle line:84% the electron or the person does not 00:27:46.370 --> 00:27:49.625 align:middle line:84% have at all definite values, but its elemental state 00:27:49.625 --> 00:27:50.250 align:middle line:90% probabilistic-- 00:27:50.250 --> 00:27:51.958 align:middle line:84% I'm not-- Gary, this is a little garbled. 00:27:51.958 --> 00:27:54.170 align:middle line:90% Let's see. 00:27:54.170 --> 00:27:57.860 align:middle line:84% I think the idea is that it would be one thing to say that 00:27:57.860 --> 00:28:01.220 align:middle line:84% the answer's-- the definite answer we'll get anytime we 00:28:01.220 --> 00:28:03.860 align:middle line:84% perform a measurement is an answer drawn from some 00:28:03.860 --> 00:28:06.865 align:middle line:84% distribution with some weighted probabilities. 00:28:06.865 --> 00:28:08.240 align:middle line:84% But it's a different thing to say 00:28:08.240 --> 00:28:11.300 align:middle line:84% there was actually no value of that property whatsoever. 00:28:11.300 --> 00:28:13.380 align:middle line:84% If we had never performed a measurement, 00:28:13.380 --> 00:28:17.423 align:middle line:84% the person would never have had any weight, not that we 00:28:17.423 --> 00:28:19.340 align:middle line:84% wouldn't know which weight it had from within, 00:28:19.340 --> 00:28:22.130 align:middle line:84% say, a Gaussian distribution or a bimodal. 00:28:22.130 --> 00:28:24.410 align:middle line:84% It's that-- the more radical interpretation 00:28:24.410 --> 00:28:28.610 align:middle line:84% that at least people like Niels Bohr began to articulate 00:28:28.610 --> 00:28:33.281 align:middle line:84% was that there was no definite value at all for that property. 00:28:33.281 --> 00:28:35.660 align:middle line:84% And that could be a property as basic 00:28:35.660 --> 00:28:36.998 align:middle line:90% as is the cat alive or dead. 00:28:36.998 --> 00:28:38.790 align:middle line:84% That's what Schrodinger was thinking about. 00:28:38.790 --> 00:28:42.360 align:middle line:84% Not just what's the value of its portfolio 00:28:42.360 --> 00:28:44.445 align:middle line:84% if the stock market closed in New York 00:28:44.445 --> 00:28:45.570 align:middle line:90% but is still open in Tokyo. 00:28:45.570 --> 00:28:47.820 align:middle line:84% There could be reasons why certain values might 00:28:47.820 --> 00:28:49.330 align:middle line:90% be subject to uncertainty. 00:28:49.330 --> 00:28:51.300 align:middle line:84% But this was like, let's take one value. 00:28:51.300 --> 00:28:52.800 align:middle line:84% Every time we perform a measurement, 00:28:52.800 --> 00:28:54.220 align:middle line:90% we get a definite answer. 00:28:54.220 --> 00:28:57.160 align:middle line:84% It's not that the question is poorly posed. 00:28:57.160 --> 00:29:00.280 align:middle line:84% It's that there was no answer before we asked the question. 00:29:00.280 --> 00:29:02.880 align:middle line:84% I think that's what got people like Einstein and Schrodinger 00:29:02.880 --> 00:29:05.370 align:middle line:90% even more riled up. 00:29:05.370 --> 00:29:06.180 align:middle line:90% [LAUGHS] 00:29:06.180 --> 00:29:08.820 align:middle line:84% Alex suggests that Schrodinger better hope the cat is dead, 00:29:08.820 --> 00:29:09.970 align:middle line:84% or else the cat's going to come for him. 00:29:09.970 --> 00:29:10.470 align:middle line:90% It's true. 00:29:10.470 --> 00:29:12.570 align:middle line:84% The prussic acid is a pretty cruel-- 00:29:12.570 --> 00:29:15.750 align:middle line:90% that's not so nice. 00:29:15.750 --> 00:29:19.200 align:middle line:84% And so coming back to Gary's point, that the idea was that 00:29:19.200 --> 00:29:23.060 align:middle line:84% what if nature simply doesn't have definite properties 00:29:23.060 --> 00:29:24.950 align:middle line:90% until we ask questions of it? 00:29:24.950 --> 00:29:27.985 align:middle line:84% And that might be perfectly comfortable for us today. 00:29:27.985 --> 00:29:29.360 align:middle line:84% It's not very comfortable for me. 00:29:29.360 --> 00:29:31.700 align:middle line:84% But that's the sharpened question 00:29:31.700 --> 00:29:34.460 align:middle line:84% that led people like Einstein and Schrodinger 00:29:34.460 --> 00:29:37.970 align:middle line:84% to begin to really question even their own work or the direction 00:29:37.970 --> 00:29:39.620 align:middle line:84% in which their work was being taken. 00:29:39.620 --> 00:29:42.470 align:middle line:90% 00:29:42.470 --> 00:29:44.570 align:middle line:84% And again, it's for properties that otherwise 00:29:44.570 --> 00:29:46.123 align:middle line:90% could be trivially measured. 00:29:46.123 --> 00:29:48.290 align:middle line:84% So it's not like it's a hard measurement to perform. 00:29:48.290 --> 00:29:50.360 align:middle line:84% Oh, I don't know what the answer is. 00:29:50.360 --> 00:29:52.297 align:middle line:84% There's a lot of statistical uncertainty. 00:29:52.297 --> 00:29:53.630 align:middle line:90% It might have been this or that. 00:29:53.630 --> 00:29:56.270 align:middle line:84% It's like, nope, the answer was this versus that. 00:29:56.270 --> 00:29:57.840 align:middle line:90% I can tell them clearly apart. 00:29:57.840 --> 00:29:59.810 align:middle line:84% And yet until I actually do the measurement, 00:29:59.810 --> 00:30:02.730 align:middle line:84% I have no definite way of knowing which it will be. 00:30:02.730 --> 00:30:04.400 align:middle line:84% And maybe neither does the electron. 00:30:04.400 --> 00:30:07.010 align:middle line:84% That was the weirder part, that last step. 00:30:07.010 --> 00:30:10.080 align:middle line:84% Maybe it's not about our lack of knowledge about this system. 00:30:10.080 --> 00:30:13.190 align:middle line:84% What if the world itself simply had no particular value 00:30:13.190 --> 00:30:15.300 align:middle line:90% for objects in the world? 00:30:15.300 --> 00:30:19.678 align:middle line:90% 00:30:19.678 --> 00:30:20.470 align:middle line:90% Stephen, thank you. 00:30:20.470 --> 00:30:23.760 align:middle line:84% That's a fantastic question, and a really hard one. 00:30:23.760 --> 00:30:25.145 align:middle line:90% So it's unfair to ask me. 00:30:25.145 --> 00:30:26.020 align:middle line:90% It's a good question. 00:30:26.020 --> 00:30:26.950 align:middle line:90% It's a great question. 00:30:26.950 --> 00:30:28.830 align:middle line:84% That's still a subject of research. 00:30:28.830 --> 00:30:30.420 align:middle line:84% That's still something actively worked 00:30:30.420 --> 00:30:33.010 align:middle line:90% on by experts in the field. 00:30:33.010 --> 00:30:35.490 align:middle line:84% So Bohr himself had an answer for that. 00:30:35.490 --> 00:30:37.650 align:middle line:84% It's not an answer that everyone accepts anymore. 00:30:37.650 --> 00:30:42.150 align:middle line:84% Bohr's answer was that there should be some irreversibly 00:30:42.150 --> 00:30:44.520 align:middle line:90% amplified detection event. 00:30:44.520 --> 00:30:46.710 align:middle line:84% So maybe-- and that's a mouthful. 00:30:46.710 --> 00:30:48.210 align:middle line:84% Everything Bohr said was a mouthful. 00:30:48.210 --> 00:30:50.127 align:middle line:90% He spoke very verbose. 00:30:50.127 --> 00:30:51.210 align:middle line:90% It wasn't clear in Danish. 00:30:51.210 --> 00:30:52.293 align:middle line:90% It wasn't clear in German. 00:30:52.293 --> 00:30:53.778 align:middle line:90% It wasn't clear in English. 00:30:53.778 --> 00:30:54.570 align:middle line:90% That's [INAUDIBLE]. 00:30:54.570 --> 00:30:58.800 align:middle line:84% But his idea was that maybe the electron-- some little electron 00:30:58.800 --> 00:31:01.320 align:middle line:84% interacts with some little equally microscopic thing. 00:31:01.320 --> 00:31:03.630 align:middle line:90% How would we know? 00:31:03.630 --> 00:31:06.300 align:middle line:84% To Bohr, the measurement was completed 00:31:06.300 --> 00:31:12.410 align:middle line:84% when some irreversible signal of that event, 00:31:12.410 --> 00:31:14.390 align:middle line:84% of that interaction, was amplified 00:31:14.390 --> 00:31:16.430 align:middle line:84% to macroscopic scales, irreversible 00:31:16.430 --> 00:31:17.600 align:middle line:90% being the key point. 00:31:17.600 --> 00:31:23.540 align:middle line:84% So that could be, like, there was-- 00:31:23.540 --> 00:31:25.580 align:middle line:84% the photographic film was developed 00:31:25.580 --> 00:31:29.360 align:middle line:84% and there was really a spot here, not a spot there. 00:31:29.360 --> 00:31:31.700 align:middle line:84% There was something that we can't-- that can't be washed 00:31:31.700 --> 00:31:32.240 align:middle line:90% away. 00:31:32.240 --> 00:31:34.700 align:middle line:84% Now, let me be clear, that's not at all the 00:31:34.700 --> 00:31:38.330 align:middle line:84% taken for granted answer today, and a real question remains. 00:31:38.330 --> 00:31:39.920 align:middle line:84% The so-called measurement problem 00:31:39.920 --> 00:31:44.070 align:middle line:84% has its own name, which is, what counts as a measurement? 00:31:44.070 --> 00:31:47.060 align:middle line:84% And if the whole world is ultimately 00:31:47.060 --> 00:31:50.630 align:middle line:84% made of atoms and atoms obey quantum theory, 00:31:50.630 --> 00:31:52.880 align:middle line:84% then aren't the measuring apparatuses also subject 00:31:52.880 --> 00:31:54.960 align:middle line:84% to all these same quantum effects? 00:31:54.960 --> 00:31:56.990 align:middle line:84% So the question has to do with, as you 00:31:56.990 --> 00:32:00.560 align:middle line:84% say, what's the scale at which the quantum mechanical effects 00:32:00.560 --> 00:32:03.840 align:middle line:90% are no longer dominant? 00:32:03.840 --> 00:32:05.910 align:middle line:84% And that's, I think, what Bohr was gesturing 00:32:05.910 --> 00:32:10.020 align:middle line:84% toward in this notion of an irreversibly amplified 00:32:10.020 --> 00:32:12.850 align:middle line:90% classical signal. 00:32:12.850 --> 00:32:16.500 align:middle line:84% And as you can see from the rate at which I'm waving my hands, 00:32:16.500 --> 00:32:18.210 align:middle line:84% clearly I'm hand waving, because it 00:32:18.210 --> 00:32:21.780 align:middle line:84% is genuinely still actively debated, even 00:32:21.780 --> 00:32:22.905 align:middle line:90% among the experts today. 00:32:22.905 --> 00:32:29.075 align:middle line:90% 00:32:29.075 --> 00:32:29.950 align:middle line:90% That's exactly right. 00:32:29.950 --> 00:32:31.480 align:middle line:84% And it does go right back to what 00:32:31.480 --> 00:32:33.688 align:middle line:84% we called what we spoke very briefly about yesterday, 00:32:33.688 --> 00:32:35.800 align:middle line:84% the so-called quantum to classical transition. 00:32:35.800 --> 00:32:39.040 align:middle line:84% We can get buckyballs to do two double-sided interference. 00:32:39.040 --> 00:32:40.750 align:middle line:84% We can't get you or me to do that. 00:32:40.750 --> 00:32:42.460 align:middle line:84% So it's very directly related to that. 00:32:42.460 --> 00:32:45.820 align:middle line:84% So one line-- let me just go off hook a little bit, 00:32:45.820 --> 00:32:47.380 align:middle line:90% jump ahead a few decades. 00:32:47.380 --> 00:32:49.390 align:middle line:84% One line of reasoning, and Amanda 00:32:49.390 --> 00:32:52.390 align:middle line:84% hints at this already in the chat as well. 00:32:52.390 --> 00:32:55.000 align:middle line:84% One line of reasoning is that this does apply even to you 00:32:55.000 --> 00:32:57.640 align:middle line:84% and me into macroscopic things, to you and me on bicycles, 00:32:57.640 --> 00:32:58.690 align:middle line:90% to viruses. 00:32:58.690 --> 00:33:03.790 align:middle line:84% You might know where I'm going, and that both answers are real. 00:33:03.790 --> 00:33:07.000 align:middle line:84% They're just real in causally disjointed regions 00:33:07.000 --> 00:33:08.750 align:middle line:90% of the universe. 00:33:08.750 --> 00:33:11.440 align:middle line:84% This is what's now often called the many worlds interpretation, 00:33:11.440 --> 00:33:13.390 align:middle line:90% very eye raising-- 00:33:13.390 --> 00:33:15.880 align:middle line:90% eyebrow raising title. 00:33:15.880 --> 00:33:18.310 align:middle line:84% The original title is the relative state formulation. 00:33:18.310 --> 00:33:21.100 align:middle line:84% What if it really is quantum mechanics all the way down, 00:33:21.100 --> 00:33:24.560 align:middle line:84% and we just have consistent-- self-consistent branches? 00:33:24.560 --> 00:33:27.760 align:middle line:84% So the cat is both alive and dead, 00:33:27.760 --> 00:33:29.900 align:middle line:84% but any observer who sees it as alive, 00:33:29.900 --> 00:33:32.630 align:middle line:84% that version of that observer is now 00:33:32.630 --> 00:33:37.460 align:middle line:84% following one track in a kind of forked path coming, 00:33:37.460 --> 00:33:41.390 align:middle line:84% to a fork in the road, and that anything else that observer's 00:33:41.390 --> 00:33:43.640 align:middle line:84% path will witness will be consistent with having found 00:33:43.640 --> 00:33:45.313 align:middle line:90% the cat either alive or dead. 00:33:45.313 --> 00:33:46.230 align:middle line:90% I forgot which I said. 00:33:46.230 --> 00:33:48.980 align:middle line:84% So one example is this is all quantum mechanics, period. 00:33:48.980 --> 00:33:50.550 align:middle line:90% And just deal with it. 00:33:50.550 --> 00:33:53.000 align:middle line:84% And that is very much like what Amanda suggested to Gary. 00:33:53.000 --> 00:33:56.660 align:middle line:84% A different, or a distinct approach, 00:33:56.660 --> 00:33:58.058 align:middle line:90% sometimes they get combined. 00:33:58.058 --> 00:33:59.600 align:middle line:84% A distinct approach is to say there's 00:33:59.600 --> 00:34:02.330 align:middle line:84% something that happens from the so-called environment, 00:34:02.330 --> 00:34:03.980 align:middle line:84% from having lots and lots of quantum 00:34:03.980 --> 00:34:06.890 align:middle line:84% mechanical stuff together and interacting together, 00:34:06.890 --> 00:34:10.250 align:middle line:84% that the essential quantumness can be smeared out. 00:34:10.250 --> 00:34:13.699 align:middle line:84% It can decohere, is the technical term, 00:34:13.699 --> 00:34:15.199 align:middle line:84% that the effect of the environment 00:34:15.199 --> 00:34:19.639 align:middle line:84% is in some sense to reduce the range of quantum possibilities 00:34:19.639 --> 00:34:21.469 align:middle line:84% to one definite outcome because there 00:34:21.469 --> 00:34:23.867 align:middle line:84% are additional physical interactions that we haven't 00:34:23.867 --> 00:34:24.659 align:middle line:90% taken into account. 00:34:24.659 --> 00:34:26.449 align:middle line:84% And that's more like how much stuff 00:34:26.449 --> 00:34:28.760 align:middle line:84% do you need before quantum behaves like classical. 00:34:28.760 --> 00:34:30.949 align:middle line:84% That's like a big box is different than a very, very 00:34:30.949 --> 00:34:31.940 align:middle line:90% tiny electron. 00:34:31.940 --> 00:34:33.980 align:middle line:84% So it's more like, do you have enough stuff, 00:34:33.980 --> 00:34:36.050 align:middle line:84% enough environment, that it's going 00:34:36.050 --> 00:34:39.290 align:middle line:84% to somehow smear out the range of possibilities 00:34:39.290 --> 00:34:41.420 align:middle line:90% and leave only one left? 00:34:41.420 --> 00:34:43.820 align:middle line:84% And sometimes people combine the two. 00:34:43.820 --> 00:34:45.909 align:middle line:84% Maybe it's actually the decoherence plus 00:34:45.909 --> 00:34:48.000 align:middle line:90% the many worlds is the answer. 00:34:48.000 --> 00:34:50.090 align:middle line:84% So that's-- when we go to the cutting edge, 00:34:50.090 --> 00:34:53.760 align:middle line:84% the cognoscenti today, we'll worry about the measurement 00:34:53.760 --> 00:34:54.260 align:middle line:90% problem. 00:34:54.260 --> 00:34:56.449 align:middle line:84% These are the kinds of questions they ask. 00:34:56.449 --> 00:34:59.120 align:middle line:84% They're only able to ask them because of the conceptual work 00:34:59.120 --> 00:35:00.830 align:middle line:90% being done back in 1935. 00:35:00.830 --> 00:35:02.137 align:middle line:90% The inverse is not true, right? 00:35:02.137 --> 00:35:04.220 align:middle line:84% Schrodinger and Einstein didn't have these options 00:35:04.220 --> 00:35:05.660 align:middle line:90% to think about at the time. 00:35:05.660 --> 00:35:07.100 align:middle line:84% So these are all coming downstream 00:35:07.100 --> 00:35:09.423 align:middle line:84% from worrying about exactly this question about-- 00:35:09.423 --> 00:35:11.090 align:middle line:84% the electron could have been either way. 00:35:11.090 --> 00:35:12.027 align:middle line:90% Didn't have an answer. 00:35:12.027 --> 00:35:13.610 align:middle line:84% The cat doesn't make sense, so that it 00:35:13.610 --> 00:35:14.150 align:middle line:90% could've have been either. 00:35:14.150 --> 00:35:15.380 align:middle line:90% Maybe it could, right? 00:35:15.380 --> 00:35:19.860 align:middle line:84% So that's why that's still going on today. 00:35:19.860 --> 00:35:20.840 align:middle line:90% So let's see. 00:35:20.840 --> 00:35:24.200 align:middle line:84% Aiden asks, is it theoretically possible to accurately predict 00:35:24.200 --> 00:35:27.050 align:middle line:84% if the uranium will decay or not in short scenario, 00:35:27.050 --> 00:35:29.240 align:middle line:84% but we as humans with the technology available 00:35:29.240 --> 00:35:30.310 align:middle line:90% just don't know enough? 00:35:30.310 --> 00:35:30.920 align:middle line:90% Very good. 00:35:30.920 --> 00:35:32.590 align:middle line:84% So Aiden, that's the kind of thing-- 00:35:32.590 --> 00:35:34.960 align:middle line:84% we'll actually come to that very soon in the next part. 00:35:34.960 --> 00:35:37.210 align:middle line:84% That's the kind of thing that Schrodinger and Einstein 00:35:37.210 --> 00:35:38.410 align:middle line:90% said should be possible. 00:35:38.410 --> 00:35:41.200 align:middle line:84% They didn't have the final answer in hand. 00:35:41.200 --> 00:35:43.090 align:middle line:84% But that's what they wondered-- that's what 00:35:43.090 --> 00:35:46.690 align:middle line:84% they thought any reliable theory of physics 00:35:46.690 --> 00:35:48.340 align:middle line:90% should enable one to do. 00:35:48.340 --> 00:35:51.010 align:middle line:84% So they never said quantum mechanics is wrong in the sense 00:35:51.010 --> 00:35:53.560 align:middle line:90% that it violates measurements. 00:35:53.560 --> 00:35:55.360 align:middle line:84% It yields the correct probabilities 00:35:55.360 --> 00:35:57.220 align:middle line:84% for definite experimental outcomes. 00:35:57.220 --> 00:35:59.260 align:middle line:90% It's accurate as far as it goes. 00:35:59.260 --> 00:36:01.250 align:middle line:84% But they said it doesn't go far enough. 00:36:01.250 --> 00:36:04.210 align:middle line:84% So some ultimate physical theory, they argued, 00:36:04.210 --> 00:36:06.340 align:middle line:84% should enable you to say in advance 00:36:06.340 --> 00:36:10.652 align:middle line:84% the uranium nucleus really will or will not decay, 00:36:10.652 --> 00:36:11.860 align:middle line:90% not just it has a likelihood. 00:36:11.860 --> 00:36:14.710 align:middle line:84% It has a definite state in advance. 00:36:14.710 --> 00:36:16.450 align:middle line:84% So the electron spin really will spin up, 00:36:16.450 --> 00:36:18.158 align:middle line:84% even though we didn't know it in advance. 00:36:18.158 --> 00:36:20.380 align:middle line:84% And so that's more what Einstein and Schrodinger 00:36:20.380 --> 00:36:21.955 align:middle line:90% said should be possible. 00:36:21.955 --> 00:36:23.080 align:middle line:90% Let's keep aiming for that. 00:36:23.080 --> 00:36:24.220 align:middle line:90% Let's not stop short. 00:36:24.220 --> 00:36:25.810 align:middle line:84% They didn't have a worked out model 00:36:25.810 --> 00:36:27.185 align:middle line:84% that would allow them to do that. 00:36:27.185 --> 00:36:28.580 align:middle line:90% That was their aspiration. 00:36:28.580 --> 00:36:35.480 align:middle line:90% 00:36:35.480 --> 00:36:36.830 align:middle line:90% It's a great point, Yangwei. 00:36:36.830 --> 00:36:38.630 align:middle line:84% It's tricky because on the one hand, 00:36:38.630 --> 00:36:42.110 align:middle line:84% Schrodinger and Einstein both were being kind of wildly 00:36:42.110 --> 00:36:44.420 align:middle line:90% creative and original. 00:36:44.420 --> 00:36:46.400 align:middle line:84% I mean, Schrodinger gave us this wave function 00:36:46.400 --> 00:36:47.817 align:middle line:84% we didn't have-- we, collectively, 00:36:47.817 --> 00:36:48.650 align:middle line:90% didn't have before. 00:36:48.650 --> 00:36:51.620 align:middle line:84% And yet you're quite right that his approach was, in some sense 00:36:51.620 --> 00:36:54.920 align:middle line:84% to retain as much as possible of that look and feel. 00:36:54.920 --> 00:36:58.040 align:middle line:84% So it's not like it's just a boring repetition 00:36:58.040 --> 00:36:59.570 align:middle line:90% of what had come before. 00:36:59.570 --> 00:37:03.020 align:middle line:84% It's not-- there's real original work being done. 00:37:03.020 --> 00:37:06.680 align:middle line:84% But the character of it, some other kind of way of describing 00:37:06.680 --> 00:37:08.010 align:middle line:90% it-- it does feel different. 00:37:08.010 --> 00:37:09.890 align:middle line:84% And I think it felt different at the time 00:37:09.890 --> 00:37:16.460 align:middle line:84% to practitioners than the kind of frankly brash, young, very-- 00:37:16.460 --> 00:37:17.120 align:middle line:90% what can I say? 00:37:17.120 --> 00:37:20.540 align:middle line:84% Kind of alpha male aggressive work, 00:37:20.540 --> 00:37:24.170 align:middle line:84% at least in portrayal, by people like Heisenberg and Pauli. 00:37:24.170 --> 00:37:26.400 align:middle line:84% Pauli loved telling everyone else they were wrong. 00:37:26.400 --> 00:37:29.210 align:middle line:84% In fact, his favorite expression was not-- 00:37:29.210 --> 00:37:32.540 align:middle line:90% he would say, that's not right. 00:37:32.540 --> 00:37:33.725 align:middle line:90% That's not even wrong. 00:37:33.725 --> 00:37:35.100 align:middle line:84% It's not even-- that's so stupid, 00:37:35.100 --> 00:37:37.080 align:middle line:84% it's not even a candidate for being right or wrong. 00:37:37.080 --> 00:37:38.640 align:middle line:84% That's not a nice thing to say to people, right? 00:37:38.640 --> 00:37:40.500 align:middle line:84% Pauli was pretty-- he had an acid tongue, 00:37:40.500 --> 00:37:44.290 align:middle line:84% even as a 20-year-old, let alone as a 50-year-old. 00:37:44.290 --> 00:37:45.820 align:middle line:84% He was just mean, aggressive, mean, 00:37:45.820 --> 00:37:47.070 align:middle line:90% "I'm smarter than all of you." 00:37:47.070 --> 00:37:49.560 align:middle line:84% There was that kind of thing going on, to be sure. 00:37:49.560 --> 00:37:52.080 align:middle line:90% And so Schrodinger was-- 00:37:52.080 --> 00:37:55.770 align:middle line:84% and Einstein both were doing creative, original, new stuff 00:37:55.770 --> 00:37:57.570 align:middle line:90% well into their 40s and 50s. 00:37:57.570 --> 00:38:00.680 align:middle line:90% It gives me hope, frankly. 00:38:00.680 --> 00:38:02.430 align:middle line:84% But it did have a different kind of style, 00:38:02.430 --> 00:38:04.513 align:middle line:84% and in some sense, a different character than some 00:38:04.513 --> 00:38:06.690 align:middle line:90% of these folks in their mid-20s. 00:38:06.690 --> 00:38:10.015 align:middle line:84% Let me press on before we all debate the Hugh Everett 00:38:10.015 --> 00:38:12.390 align:middle line:84% many worlds interpretation because then we'll never leave 00:38:12.390 --> 00:38:13.640 align:middle line:90% that branch of the multiverse. 00:38:13.640 --> 00:38:17.460 align:middle line:84% But let me go on now to talk about the second big critique 00:38:17.460 --> 00:38:19.980 align:middle line:84% of quantum theory by Einstein and his younger 00:38:19.980 --> 00:38:23.200 align:middle line:84% colleagues, the so-called EPR thought experiment. 00:38:23.200 --> 00:38:25.200 align:middle line:84% So this was published in the very same year 00:38:25.200 --> 00:38:26.550 align:middle line:90% as Schrodinger's cat. 00:38:26.550 --> 00:38:28.380 align:middle line:84% It actually came out a bit earlier. 00:38:28.380 --> 00:38:30.838 align:middle line:84% And this is one of the things that Einstein and Schrodinger 00:38:30.838 --> 00:38:33.220 align:middle line:84% were writing about across the ocean. 00:38:33.220 --> 00:38:36.000 align:middle line:84% So soon after Einstein got settled at the Institute 00:38:36.000 --> 00:38:37.590 align:middle line:84% for Advanced Study in Princeton-- 00:38:37.590 --> 00:38:40.080 align:middle line:84% it's in the same town as Princeton University, 00:38:40.080 --> 00:38:42.510 align:middle line:84% though it is formally a separate institution. 00:38:42.510 --> 00:38:44.970 align:middle line:84% He began working with these two younger colleagues, Boris 00:38:44.970 --> 00:38:46.770 align:middle line:90% Podolsky and Nathan Rosen. 00:38:46.770 --> 00:38:49.710 align:middle line:84% And they developed an even more elaborate and really very 00:38:49.710 --> 00:38:53.430 align:middle line:84% compelling, very, very tricky critique, 00:38:53.430 --> 00:38:56.070 align:middle line:84% of quantum theory, as what we now call the EPR, 00:38:56.070 --> 00:38:57.855 align:middle line:90% for their initials. 00:38:57.855 --> 00:38:58.980 align:middle line:90% And this was in the reader. 00:38:58.980 --> 00:39:00.100 align:middle line:90% So again, it's very short. 00:39:00.100 --> 00:39:01.390 align:middle line:90% It's deceptively short. 00:39:01.390 --> 00:39:03.788 align:middle line:84% It's only four pages, but it's pretty tricky 00:39:03.788 --> 00:39:05.580 align:middle line:84% so I'm going to take a little while to walk 00:39:05.580 --> 00:39:07.538 align:middle line:84% through the argument, which might not have been 00:39:07.538 --> 00:39:08.970 align:middle line:90% so easy upon a first reading. 00:39:08.970 --> 00:39:09.780 align:middle line:90% And that's OK. 00:39:09.780 --> 00:39:11.670 align:middle line:90% It's a very tricky paper. 00:39:11.670 --> 00:39:13.980 align:middle line:84% So they're imagining a thought experiment like this, 00:39:13.980 --> 00:39:15.720 align:middle line:90% in a kind of cartoon form. 00:39:15.720 --> 00:39:18.960 align:middle line:84% There's some source, that's the capital S here, 00:39:18.960 --> 00:39:20.700 align:middle line:84% that will shoot out pairs of particles 00:39:20.700 --> 00:39:21.840 align:middle line:90% in opposite directions. 00:39:21.840 --> 00:39:23.850 align:middle line:84% We can call them particles A and B. 00:39:23.850 --> 00:39:27.008 align:middle line:84% And each particle will be measured some distance apart. 00:39:27.008 --> 00:39:29.550 align:middle line:84% There's some detector here that will perform some measurement 00:39:29.550 --> 00:39:33.390 align:middle line:84% on particle A, some separate detector some distance away 00:39:33.390 --> 00:39:36.120 align:middle line:84% that will eventually measure some property of particle B. 00:39:36.120 --> 00:39:37.830 align:middle line:84% And the physicist here can choose 00:39:37.830 --> 00:39:40.110 align:middle line:84% to perform one of two types of measurements. 00:39:40.110 --> 00:39:43.050 align:middle line:84% In the original EPR paper, the authors 00:39:43.050 --> 00:39:45.870 align:middle line:84% considered either measuring the position along the x-axis. 00:39:45.870 --> 00:39:47.910 align:middle line:84% They can form a measurement of x. 00:39:47.910 --> 00:39:50.520 align:middle line:84% Or they could choose to perform a measurement of the momentum 00:39:50.520 --> 00:39:53.200 align:middle line:90% in that direction, p sub x. 00:39:53.200 --> 00:39:55.960 align:middle line:84% Now, according to quantum mechanics, prior 00:39:55.960 --> 00:39:58.720 align:middle line:84% to either measurement, the system, the system particles 00:39:58.720 --> 00:40:03.070 align:middle line:84% A and B, would be in some superposition, not just 00:40:03.070 --> 00:40:04.930 align:middle line:84% a single cat that's either alive or dead, 00:40:04.930 --> 00:40:07.602 align:middle line:84% but basically, it's like two cats, either of which 00:40:07.602 --> 00:40:08.560 align:middle line:90% could be alive or dead. 00:40:08.560 --> 00:40:09.880 align:middle line:90% But here's the twist. 00:40:09.880 --> 00:40:12.790 align:middle line:84% The properties we will eventually measure of one 00:40:12.790 --> 00:40:17.140 align:middle line:84% are tangled up or entangled with the properties 00:40:17.140 --> 00:40:19.510 align:middle line:84% we will eventually measure of particle two. 00:40:19.510 --> 00:40:23.350 align:middle line:84% So each particle is in some as-yet indefinite state, 00:40:23.350 --> 00:40:25.510 align:middle line:84% and yet their two states are somehow 00:40:25.510 --> 00:40:26.920 align:middle line:90% connected to each other. 00:40:26.920 --> 00:40:28.660 align:middle line:84% And that's written quantitatively 00:40:28.660 --> 00:40:31.030 align:middle line:84% as this special kind of superposition. 00:40:31.030 --> 00:40:34.150 align:middle line:84% There's two different two-particle states that 00:40:34.150 --> 00:40:35.920 align:middle line:90% are then put in superposition. 00:40:35.920 --> 00:40:37.990 align:middle line:84% Either particle A will have one property 00:40:37.990 --> 00:40:39.790 align:middle line:84% and particle B will have some other, 00:40:39.790 --> 00:40:42.142 align:middle line:84% or particle A will have that second property 00:40:42.142 --> 00:40:43.600 align:middle line:84% and particle B will have the first. 00:40:43.600 --> 00:40:46.400 align:middle line:84% That's two-- that's a superposition of two particle 00:40:46.400 --> 00:40:46.900 align:middle line:90% states. 00:40:46.900 --> 00:40:49.990 align:middle line:84% So it's even more elaborate than a single cat. 00:40:49.990 --> 00:40:53.180 align:middle line:84% And what got them so exercised, what got them so upset 00:40:53.180 --> 00:40:55.580 align:middle line:84% about this, Einstein, Podolsky, and Rosen, 00:40:55.580 --> 00:40:58.610 align:middle line:84% is that this quantum state, this version of psi, 00:40:58.610 --> 00:41:00.080 align:middle line:90% does not factorize. 00:41:00.080 --> 00:41:03.380 align:middle line:84% We can't write it, at least according to quantum mechanics, 00:41:03.380 --> 00:41:06.980 align:middle line:84% as some mathematical description of the behavior of particle 00:41:06.980 --> 00:41:10.940 align:middle line:84% A over here and then separately in some factorizable way, 00:41:10.940 --> 00:41:15.770 align:middle line:84% some way of describing the behavior of particle B, that as 00:41:15.770 --> 00:41:18.410 align:middle line:84% soon as we say anything about the likely behavior of particle 00:41:18.410 --> 00:41:20.630 align:middle line:84% A, in the same breath, we have to say something 00:41:20.630 --> 00:41:22.970 align:middle line:84% about the behavior of particle B and vice versa. 00:41:22.970 --> 00:41:24.140 align:middle line:90% OK. 00:41:24.140 --> 00:41:26.580 align:middle line:84% Why was that so concerning for them? 00:41:26.580 --> 00:41:29.150 align:middle line:84% Well, let's suppose that physicists one over here 00:41:29.150 --> 00:41:33.290 align:middle line:84% at this detector happens to select a position measurement 00:41:33.290 --> 00:41:36.810 align:middle line:84% for particle A. And then from the conservation of momentum, 00:41:36.810 --> 00:41:39.380 align:middle line:84% she could immediately infer the position of particle B 00:41:39.380 --> 00:41:41.570 align:middle line:84% once she completes her measurement. 00:41:41.570 --> 00:41:44.730 align:middle line:84% On the other hand-- sorry, again, on the other hand, 00:41:44.730 --> 00:41:47.540 align:middle line:84% she could have chosen to perform the other kind of measurement. 00:41:47.540 --> 00:41:49.280 align:middle line:84% She could have chosen just as well 00:41:49.280 --> 00:41:51.960 align:middle line:84% to have measured the momentum along the x-direction 00:41:51.960 --> 00:41:54.230 align:middle line:84% and then immediately inferred the momentum 00:41:54.230 --> 00:41:56.750 align:middle line:84% some other property of particle B. 00:41:56.750 --> 00:42:00.170 align:middle line:84% What if she waited until the very last possible moment 00:42:00.170 --> 00:42:03.230 align:middle line:84% to decide which measurement to perform? 00:42:03.230 --> 00:42:07.130 align:middle line:84% So now there's no time for even a light signal traveling 00:42:07.130 --> 00:42:10.040 align:middle line:84% at the very fast speed of light to get from here 00:42:10.040 --> 00:42:13.130 align:middle line:84% and catch up with the particle B in time 00:42:13.130 --> 00:42:15.170 align:middle line:84% to give it a kind of status update. 00:42:15.170 --> 00:42:17.990 align:middle line:84% Oh, when you get measured, make sure your properties agree 00:42:17.990 --> 00:42:20.450 align:middle line:84% with what are consistent with what was just measured 00:42:20.450 --> 00:42:22.170 align:middle line:90% of particle A over here. 00:42:22.170 --> 00:42:25.730 align:middle line:84% So if even a single light beam couldn't have updated particle 00:42:25.730 --> 00:42:29.900 align:middle line:84% B in time, then particle B must have had all its own relevant 00:42:29.900 --> 00:42:33.020 align:middle line:84% properties on its own prior, to its measurement. 00:42:33.020 --> 00:42:35.880 align:middle line:84% It wouldn't have time to wait for an update. 00:42:35.880 --> 00:42:38.630 align:middle line:84% So the only thing that made sense to Einstein, Podolsky, 00:42:38.630 --> 00:42:40.970 align:middle line:84% and Rosen was that particle B already 00:42:40.970 --> 00:42:42.380 align:middle line:90% had its answers at the ready. 00:42:42.380 --> 00:42:45.050 align:middle line:84% It already had definite values for those properties. 00:42:45.050 --> 00:42:47.450 align:middle line:84% It was not, like Bohr would have insisted, 00:42:47.450 --> 00:42:50.540 align:middle line:84% a person who has not yet stepped on a bathroom scale. 00:42:50.540 --> 00:42:52.430 align:middle line:84% Particle B would have had definite values, 00:42:52.430 --> 00:42:54.117 align:middle line:84% both for position and for momentum. 00:42:54.117 --> 00:42:55.700 align:middle line:84% And we didn't know what they were yet, 00:42:55.700 --> 00:42:57.730 align:middle line:90% but the particle had them. 00:42:57.730 --> 00:43:00.640 align:middle line:84% The problem with that, according to EPR, 00:43:00.640 --> 00:43:05.140 align:middle line:84% is that quantum mechanics has no way to describe quantitatively 00:43:05.140 --> 00:43:07.515 align:middle line:84% particle B's properties on its own, 00:43:07.515 --> 00:43:09.640 align:middle line:84% separate from what's going to happen to particle A. 00:43:09.640 --> 00:43:11.800 align:middle line:84% So they conclude in this famous paper 00:43:11.800 --> 00:43:14.970 align:middle line:84% that quantum mechanics must be incomplete. 00:43:14.970 --> 00:43:17.610 align:middle line:84% And so this assumption, the supposed 00:43:17.610 --> 00:43:20.490 align:middle line:84% incompleteness of quantum theory, that-- 00:43:20.490 --> 00:43:23.140 align:middle line:84% sorry, that conclusion rests on two assumptions. 00:43:23.140 --> 00:43:25.710 align:middle line:84% The first of them, they tell us right on the opening page. 00:43:25.710 --> 00:43:27.880 align:middle line:84% It became known as the reality criterion. 00:43:27.880 --> 00:43:29.910 align:middle line:84% This is on the first page of their paper. 00:43:29.910 --> 00:43:33.600 align:middle line:84% And quoting their own text, "If, without in any way disturbing 00:43:33.600 --> 00:43:36.450 align:middle line:84% a system, we can predict with certainty, 00:43:36.450 --> 00:43:38.790 align:middle line:84% that is, with probability equal to unity, 00:43:38.790 --> 00:43:40.800 align:middle line:84% the value of a physical quantity, 00:43:40.800 --> 00:43:43.290 align:middle line:84% then there exists an element of reality, 00:43:43.290 --> 00:43:45.330 align:middle line:84% something about the world, not just 00:43:45.330 --> 00:43:47.640 align:middle line:84% about our knowledge of the world, corresponding 00:43:47.640 --> 00:43:49.095 align:middle line:90% to that physical quantity." 00:43:49.095 --> 00:43:50.970 align:middle line:84% So that's an assumption, that quantum objects 00:43:50.970 --> 00:43:52.830 align:middle line:84% possess their own properties on their own. 00:43:52.830 --> 00:43:55.470 align:middle line:84% They carry them around as they move through space, 00:43:55.470 --> 00:43:58.410 align:middle line:84% independent of and prior to our efforts to measure them. 00:43:58.410 --> 00:44:00.740 align:middle line:84% The person has a value of her weight, 00:44:00.740 --> 00:44:02.490 align:middle line:84% and it can be revealed upon a measurement. 00:44:02.490 --> 00:44:05.040 align:middle line:84% The measurement doesn't create her value of the weight. 00:44:05.040 --> 00:44:07.650 align:middle line:84% That's what they're responding to Niels Bohr. 00:44:07.650 --> 00:44:09.120 align:middle line:84% A little later in the paper, they 00:44:09.120 --> 00:44:13.080 align:middle line:84% make explicit their second, equally critical assumption, 00:44:13.080 --> 00:44:15.510 align:middle line:84% that would later be called locality. 00:44:15.510 --> 00:44:19.200 align:middle line:84% It's now on page 779 of their short article. 00:44:19.200 --> 00:44:20.700 align:middle line:90% Here's their wording for that. 00:44:20.700 --> 00:44:22.320 align:middle line:84% "Since at the time of measurement 00:44:22.320 --> 00:44:26.070 align:middle line:84% of the two systems, particles A and B, they no longer interact, 00:44:26.070 --> 00:44:30.650 align:middle line:84% no real change can take place in the second system, particle B, 00:44:30.650 --> 00:44:32.400 align:middle line:84% in consequence of anything that might have 00:44:32.400 --> 00:44:34.120 align:middle line:90% been done to the first system." 00:44:34.120 --> 00:44:36.510 align:middle line:84% That's what we think as of localism, 00:44:36.510 --> 00:44:40.020 align:middle line:84% that local causes yield only local effects, 00:44:40.020 --> 00:44:42.870 align:middle line:84% or if we think about Einstein's work on relativity, 00:44:42.870 --> 00:44:46.800 align:middle line:84% that no force or information or influence of any kind 00:44:46.800 --> 00:44:49.890 align:middle line:84% can travel across space arbitrarily quickly. 00:44:49.890 --> 00:44:52.470 align:middle line:84% Things could travel maybe as fast as light, 00:44:52.470 --> 00:44:54.210 align:middle line:90% but not infinitely fast. 00:44:54.210 --> 00:44:58.170 align:middle line:84% And that's the updating paradox that they had for particle B. 00:44:58.170 --> 00:45:00.060 align:middle line:84% So even a dozen years later, this 00:45:00.060 --> 00:45:02.760 align:middle line:84% was still upsetting Einstein, that quantum mechanics seemed 00:45:02.760 --> 00:45:04.710 align:middle line:90% to fail this test. 00:45:04.710 --> 00:45:08.160 align:middle line:84% And he wrote, again, in a very famous letter again to Max Born 00:45:08.160 --> 00:45:12.540 align:middle line:84% in the late 1940s, "I cannot seriously believe in quantum 00:45:12.540 --> 00:45:15.670 align:middle line:84% mechanics because a theory cannot be reconciled with 00:45:15.670 --> 00:45:19.210 align:middle line:84% the idea that physics should represent a reality in time 00:45:19.210 --> 00:45:22.630 align:middle line:84% and space free from spooky actions at a distance," 00:45:22.630 --> 00:45:26.470 align:middle line:84% a phrase that has followed this field since 1947, or I guess, 00:45:26.470 --> 00:45:29.410 align:middle line:84% since the letters were published in the early '70s, that he 00:45:29.410 --> 00:45:31.850 align:middle line:84% thought anything-- any physical theory, 00:45:31.850 --> 00:45:34.480 align:middle line:84% including quantum mechanics, that says that these two 00:45:34.480 --> 00:45:37.990 align:middle line:84% particles could remain coordinated across arbitrary 00:45:37.990 --> 00:45:40.060 align:middle line:90% distance-- that's a ghost story. 00:45:40.060 --> 00:45:41.890 align:middle line:84% That's spooky action at a distance. 00:45:41.890 --> 00:45:45.340 align:middle line:84% That's not a proper physical theory in which local causes 00:45:45.340 --> 00:45:47.120 align:middle line:90% yield local effects. 00:45:47.120 --> 00:45:48.490 align:middle line:90% So let me pause there. 00:45:48.490 --> 00:45:51.580 align:middle line:84% Again, it's a complicated article, the EPR paper. 00:45:51.580 --> 00:45:54.340 align:middle line:84% It's a classic, but it's very dense. 00:45:54.340 --> 00:45:56.620 align:middle line:84% So what I hope we would get out of it upon reading 00:45:56.620 --> 00:45:59.290 align:middle line:84% it was at least that-- those important highlights, 00:45:59.290 --> 00:46:02.890 align:middle line:84% that they draw a conclusion about the nature of explanation 00:46:02.890 --> 00:46:06.820 align:middle line:84% in quantum theory and that their conclusion rests squarely 00:46:06.820 --> 00:46:10.540 align:middle line:84% on those two separate, but equally important, assumptions. 00:46:10.540 --> 00:46:12.640 align:middle line:84% Objects have their own properties, like it or not. 00:46:12.640 --> 00:46:13.540 align:middle line:90% The cat's just dead. 00:46:13.540 --> 00:46:14.355 align:middle line:90% Get over it, right? 00:46:14.355 --> 00:46:16.480 align:middle line:84% Even though we didn't look yet, that kind of thing. 00:46:16.480 --> 00:46:18.100 align:middle line:90% That's the elements of reality. 00:46:18.100 --> 00:46:21.790 align:middle line:84% And stuff can't travel arbitrarily fast. 00:46:21.790 --> 00:46:23.407 align:middle line:84% And Tiffany says-- she's quite right. 00:46:23.407 --> 00:46:25.240 align:middle line:84% Tiffany, thank you so much for sharing that. 00:46:25.240 --> 00:46:27.053 align:middle line:84% There's a really lovely, lovely book. 00:46:27.053 --> 00:46:29.470 align:middle line:84% It's actually a kind of graphic novel I think you'd enjoy, 00:46:29.470 --> 00:46:34.780 align:middle line:84% very creative, by a pair of authors, Jeffrey and Tanya Bub. 00:46:34.780 --> 00:46:36.280 align:middle line:90% Those are father and daughter. 00:46:36.280 --> 00:46:38.230 align:middle line:90% It's a lovely pairing. 00:46:38.230 --> 00:46:40.750 align:middle line:84% Jeffrey Bub is a very accomplished physicist 00:46:40.750 --> 00:46:43.510 align:middle line:84% and philosopher of science, now very senior, 00:46:43.510 --> 00:46:45.850 align:middle line:84% and his daughter Tanya is a really terrific and very 00:46:45.850 --> 00:46:47.590 align:middle line:90% accomplished graphic artist. 00:46:47.590 --> 00:46:50.500 align:middle line:84% And they teamed up to write this very fun and quirky 00:46:50.500 --> 00:46:53.110 align:middle line:84% and creative graphic novel all about this notion 00:46:53.110 --> 00:46:55.270 align:middle line:84% of Einstein's critique and more recent thoughts. 00:46:55.270 --> 00:46:57.310 align:middle line:84% It's called Totally Random is what it's called, 00:46:57.310 --> 00:46:57.935 align:middle line:90% Totally Random. 00:46:57.935 --> 00:46:59.833 align:middle line:90% It's a great, great book. 00:46:59.833 --> 00:47:01.750 align:middle line:84% And what would Einstein say about current work 00:47:01.750 --> 00:47:03.908 align:middle line:90% on entanglement? 00:47:03.908 --> 00:47:04.700 align:middle line:90% I don't know, Gary. 00:47:04.700 --> 00:47:06.470 align:middle line:84% I can make predictions for what he'd say. 00:47:06.470 --> 00:47:07.940 align:middle line:90% I don't know what he'd say. 00:47:07.940 --> 00:47:09.898 align:middle line:84% But I think about that a lot, for reasons we'll 00:47:09.898 --> 00:47:11.870 align:middle line:84% talk about in the last part of today's class. 00:47:11.870 --> 00:47:12.840 align:middle line:90% It's a fair question. 00:47:12.840 --> 00:47:14.510 align:middle line:84% But there's a lot that's been done 00:47:14.510 --> 00:47:18.170 align:middle line:84% since his time with which we've been able to sharpen 00:47:18.170 --> 00:47:18.990 align:middle line:90% these questions. 00:47:18.990 --> 00:47:20.900 align:middle line:84% And so the questions that he set in motion 00:47:20.900 --> 00:47:23.870 align:middle line:84% have really energized generations of work ever since. 00:47:23.870 --> 00:47:26.750 align:middle line:90% That's pretty amazing. 00:47:26.750 --> 00:47:30.080 align:middle line:84% Isn't it more accurate to say spooky at a distance 00:47:30.080 --> 00:47:32.228 align:middle line:84% because no physical action happens? 00:47:32.228 --> 00:47:32.770 align:middle line:90% That's right. 00:47:32.770 --> 00:47:35.000 align:middle line:84% So Alex, what Einstein was worried about 00:47:35.000 --> 00:47:37.280 align:middle line:90% was it sounded like telepathy. 00:47:37.280 --> 00:47:39.620 align:middle line:84% It sounded like some occult connection, 00:47:39.620 --> 00:47:42.140 align:middle line:84% where somehow these two things at arbitrary 00:47:42.140 --> 00:47:44.990 align:middle line:84% distance-- it might not just be between Princeton, New Jersey 00:47:44.990 --> 00:47:47.540 align:middle line:84% and Dublin, where his friend Schrodinger was. 00:47:47.540 --> 00:47:50.300 align:middle line:84% It could be between Princeton, New Jersey and the Andromeda 00:47:50.300 --> 00:47:51.200 align:middle line:90% galaxy. 00:47:51.200 --> 00:47:53.960 align:middle line:84% And somehow instantaneously, at least 00:47:53.960 --> 00:47:56.180 align:middle line:84% according to quantum mechanics, instantaneously, 00:47:56.180 --> 00:48:01.590 align:middle line:84% these objects will behave in a rigidly coordinated way, 00:48:01.590 --> 00:48:04.310 align:middle line:84% even though there was no time to let one know 00:48:04.310 --> 00:48:06.110 align:middle line:90% what the other was going to do. 00:48:06.110 --> 00:48:09.290 align:middle line:84% So it really is this-- no physical mechanism. 00:48:09.290 --> 00:48:12.080 align:middle line:84% Nothing could have traveled through the intervening space 00:48:12.080 --> 00:48:14.397 align:middle line:90% to connect them. 00:48:14.397 --> 00:48:15.980 align:middle line:84% And that's what he thought was spooky. 00:48:15.980 --> 00:48:18.140 align:middle line:84% And spooky was not meant to be like, oh, cool, it's spooky. 00:48:18.140 --> 00:48:18.740 align:middle line:90% I'm intrigued. 00:48:18.740 --> 00:48:20.660 align:middle line:90% Like, that's garbage, right? 00:48:20.660 --> 00:48:24.380 align:middle line:84% Think back to what we saw in the previous class, Schrodinger 00:48:24.380 --> 00:48:26.100 align:middle line:84% and Heisenberg calling each other's work 00:48:26.100 --> 00:48:28.380 align:middle line:84% disgusting and repulsive and trash. 00:48:28.380 --> 00:48:30.810 align:middle line:84% It's in that spirit that Einstein 00:48:30.810 --> 00:48:33.180 align:middle line:84% is writing to his very dear friend Max Born, 00:48:33.180 --> 00:48:35.683 align:middle line:84% still trying to convince him in 1947, 00:48:35.683 --> 00:48:38.100 align:middle line:84% still trying to convince him in 1955, right up to the time 00:48:38.100 --> 00:48:38.700 align:middle line:90% that he died. 00:48:38.700 --> 00:48:40.380 align:middle line:90% He just couldn't let this go. 00:48:40.380 --> 00:48:44.947 align:middle line:84% Any other questions on the EPR thought experiment or the role 00:48:44.947 --> 00:48:46.530 align:middle line:84% of those two assumptions and all that? 00:48:46.530 --> 00:48:51.970 align:middle line:90% 00:48:51.970 --> 00:48:52.780 align:middle line:90% Yeah. 00:48:52.780 --> 00:48:53.380 align:middle line:90% Thank you, Stephen, so much. 00:48:53.380 --> 00:48:54.440 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:48:54.440 --> 00:48:55.300 align:middle line:84% DAVID KAISER: So on the one hand, 00:48:55.300 --> 00:48:57.800 align:middle line:84% that's a great preview for the last part of today's lecture. 00:48:57.800 --> 00:48:59.090 align:middle line:90% So on the one hand, hang on. 00:48:59.090 --> 00:49:00.490 align:middle line:84% There's also a lot of optional stuff. 00:49:00.490 --> 00:49:01.657 align:middle line:90% I know it's, like, midterms. 00:49:01.657 --> 00:49:03.190 align:middle line:84% It's a busy, busy time of the term. 00:49:03.190 --> 00:49:04.420 align:middle line:84% You're all working on paper, too. 00:49:04.420 --> 00:49:04.990 align:middle line:90% Hint, hint. 00:49:04.990 --> 00:49:05.710 align:middle line:90% So you're busy. 00:49:05.710 --> 00:49:07.720 align:middle line:84% But there's optional stuff on the Canvas site 00:49:07.720 --> 00:49:10.150 align:middle line:84% for today's class session as well just for whenever 00:49:10.150 --> 00:49:11.470 align:middle line:90% you have time and curiosity. 00:49:11.470 --> 00:49:12.470 align:middle line:90% And there's plenty more. 00:49:12.470 --> 00:49:14.320 align:middle line:84% I'd be delighted to talk more about this 00:49:14.320 --> 00:49:15.770 align:middle line:90% individually as well. 00:49:15.770 --> 00:49:19.150 align:middle line:84% But one of the optional things for-- on today's group 00:49:19.150 --> 00:49:21.640 align:middle line:84% of readings, totally optional, is 00:49:21.640 --> 00:49:24.880 align:middle line:84% a chapter I wrote over the summer, still a draft, 00:49:24.880 --> 00:49:28.840 align:middle line:84% on the current status of experimental tests of quantum 00:49:28.840 --> 00:49:32.980 align:middle line:84% entanglement and ways to try to really check, 00:49:32.980 --> 00:49:36.430 align:middle line:84% have we closed down every possible objection, even 00:49:36.430 --> 00:49:38.890 align:middle line:84% far-flung but logically consistent objection, 00:49:38.890 --> 00:49:41.650 align:middle line:84% that someone like Einstein, or let's say, an Einsteinian, 00:49:41.650 --> 00:49:44.140 align:middle line:84% might raise to the existing battery of tests, 00:49:44.140 --> 00:49:47.740 align:middle line:84% and what would it take to close down every possible alternative 00:49:47.740 --> 00:49:49.480 align:middle line:90% explanation? 00:49:49.480 --> 00:49:50.998 align:middle line:84% And so there's a lot of work that's 00:49:50.998 --> 00:49:52.790 align:middle line:84% going on around the world to this day, some 00:49:52.790 --> 00:49:54.380 align:middle line:84% of it with my own group and, of course, many groups 00:49:54.380 --> 00:49:55.110 align:middle line:90% around the world. 00:49:55.110 --> 00:49:57.340 align:middle line:90% So that's on there. 00:49:57.340 --> 00:49:59.090 align:middle line:84% Not that I'm asking you to read another 40 00:49:59.090 --> 00:50:01.430 align:middle line:84% pages during a busy time, but there's some resources. 00:50:01.430 --> 00:50:04.020 align:middle line:84% And I'd be glad to chat with Stephen, and really, frankly, 00:50:04.020 --> 00:50:04.520 align:middle line:90% anyone. 00:50:04.520 --> 00:50:05.810 align:middle line:90% I love this stuff. 00:50:05.810 --> 00:50:07.710 align:middle line:90% About these bigger questions. 00:50:07.710 --> 00:50:11.480 align:middle line:84% So let me give you the bumper sticker version. 00:50:11.480 --> 00:50:14.480 align:middle line:84% I think every-- well, I don't know if I'd say every. 00:50:14.480 --> 00:50:18.080 align:middle line:84% The vast majority of working physicists today 00:50:18.080 --> 00:50:20.900 align:middle line:84% agree that quantum entanglement is a fact of the world 00:50:20.900 --> 00:50:24.770 align:middle line:84% that particles seem to betray this very strong correlation 00:50:24.770 --> 00:50:25.880 align:middle line:90% across arbitrary distance. 00:50:25.880 --> 00:50:28.130 align:middle line:84% And I'll talk more about some experiments lately 00:50:28.130 --> 00:50:30.380 align:middle line:84% that have shown that more clearly. 00:50:30.380 --> 00:50:32.780 align:middle line:84% Is there a physical mechanism for that? 00:50:32.780 --> 00:50:35.450 align:middle line:84% Maybe there's some more exotic structure of space time. 00:50:35.450 --> 00:50:37.970 align:middle line:84% Maybe there's a wormhole that would give an Einstein 00:50:37.970 --> 00:50:41.210 align:middle line:84% description for a local physics that just was traveling 00:50:41.210 --> 00:50:43.280 align:middle line:84% a more complicated path through space and time 00:50:43.280 --> 00:50:44.678 align:middle line:90% than our naive picture. 00:50:44.678 --> 00:50:46.220 align:middle line:84% I don't think that's the best answer, 00:50:46.220 --> 00:50:48.233 align:middle line:90% but that's a legitimate answer. 00:50:48.233 --> 00:50:49.400 align:middle line:90% Maybe it's some other thing. 00:50:49.400 --> 00:50:52.460 align:middle line:84% So people are still trying to get a physical mechanism that 00:50:52.460 --> 00:50:54.560 align:middle line:90% might fill in the dots. 00:50:54.560 --> 00:50:57.080 align:middle line:84% But there seems to be little room for doubt 00:50:57.080 --> 00:51:00.410 align:middle line:84% anymore that the phenomenon of entanglement is robust 00:51:00.410 --> 00:51:02.780 align:middle line:90% and can be reproduced at will. 00:51:02.780 --> 00:51:05.300 align:middle line:90% The idea that maybe-- 00:51:05.300 --> 00:51:07.820 align:middle line:84% a separate possibility is the one 00:51:07.820 --> 00:51:10.100 align:middle line:84% that I think is not the leading-- 00:51:10.100 --> 00:51:15.020 align:middle line:84% not the best way to go, would be to say that everything comes 00:51:15.020 --> 00:51:17.990 align:middle line:84% down to initial conditions, that the Big Bang, everything 00:51:17.990 --> 00:51:18.770 align:middle line:90% was preordained. 00:51:18.770 --> 00:51:21.440 align:middle line:84% It's not just that everything's determined, that A leads to B, 00:51:21.440 --> 00:51:23.870 align:middle line:84% but everything was so-called super determined, 00:51:23.870 --> 00:51:25.755 align:middle line:84% that even my choice to teach this lecture-- 00:51:25.755 --> 00:51:27.380 align:middle line:84% I didn't have that much choice, but you 00:51:27.380 --> 00:51:29.983 align:middle line:84% know, my choice of what to do on my slides, the choice 00:51:29.983 --> 00:51:31.400 align:middle line:84% of the National Science Foundation 00:51:31.400 --> 00:51:33.560 align:middle line:84% to give my group our grant, the choice-- 00:51:33.560 --> 00:51:36.080 align:middle line:84% the fact that all these cascading, 00:51:36.080 --> 00:51:38.840 align:middle line:84% seemingly random decisions since the Big Bang itself, 00:51:38.840 --> 00:51:40.490 align:middle line:90% have all been preordained. 00:51:40.490 --> 00:51:45.260 align:middle line:84% That's a-- I think a not very compelling and yet 00:51:45.260 --> 00:51:46.910 align:middle line:84% logically self-consistent explanation 00:51:46.910 --> 00:51:47.930 align:middle line:90% for all these phenomena. 00:51:47.930 --> 00:51:49.910 align:middle line:84% But what's amazing to me in the light 00:51:49.910 --> 00:51:52.340 align:middle line:84% of experiments like my own, but many others, 00:51:52.340 --> 00:51:54.230 align:middle line:90% is that's what's left. 00:51:54.230 --> 00:51:56.360 align:middle line:84% You get to say, it's quantum mechanics. 00:51:56.360 --> 00:51:58.700 align:middle line:84% Like, just, it's quantum mechanics, right? 00:51:58.700 --> 00:51:59.660 align:middle line:90% Sorry, Einstein. 00:51:59.660 --> 00:52:01.380 align:middle line:84% Or it's something that sounds, frankly, 00:52:01.380 --> 00:52:02.900 align:middle line:84% even more bizarre and potentially 00:52:02.900 --> 00:52:07.150 align:middle line:84% not even really subject to experimental tests, right? 00:52:07.150 --> 00:52:09.650 align:middle line:84% So what we've been trying to do in the years since Einstein, 00:52:09.650 --> 00:52:12.500 align:middle line:84% Podolsky, and Rosen, and really since John Bell, whom I'll 00:52:12.500 --> 00:52:15.410 align:middle line:84% talk about in a moment, is to clear out all-- 00:52:15.410 --> 00:52:19.640 align:middle line:84% as many intervening, logical possibilities that 00:52:19.640 --> 00:52:20.838 align:middle line:90% could have been left. 00:52:20.838 --> 00:52:22.380 align:middle line:84% Oh, it could have been this, or this, 00:52:22.380 --> 00:52:23.420 align:middle line:90% or this, or this, or this. 00:52:23.420 --> 00:52:25.170 align:middle line:84% OK, well, let's design updated experiments 00:52:25.170 --> 00:52:28.490 align:middle line:84% to clear out as many of those other possibilities as we can 00:52:28.490 --> 00:52:29.850 align:middle line:90% and see what's left. 00:52:29.850 --> 00:52:34.490 align:middle line:84% And Stephen, the short answer today is what's left, 00:52:34.490 --> 00:52:36.030 align:middle line:90% is quantum mechanics. 00:52:36.030 --> 00:52:39.750 align:middle line:84% There's some nonmechanical connection 00:52:39.750 --> 00:52:42.060 align:middle line:84% that leads to correlations that are measured reliably 00:52:42.060 --> 00:52:44.310 align:middle line:84% all around the world all the time. 00:52:44.310 --> 00:52:46.860 align:middle line:84% That's not because it's like two tin cans connected 00:52:46.860 --> 00:52:48.125 align:middle line:90% by a piece of twine. 00:52:48.125 --> 00:52:49.500 align:middle line:84% It's not a mechanical connection. 00:52:49.500 --> 00:52:51.330 align:middle line:84% We've ruled out all those kinds of models, 00:52:51.330 --> 00:52:52.530 align:middle line:90% or many, many of them. 00:52:52.530 --> 00:52:55.200 align:middle line:84% It's either that, or some, really, 00:52:55.200 --> 00:52:58.200 align:middle line:84% more even strange-sounding possibilities. 00:52:58.200 --> 00:53:01.230 align:middle line:84% Strangeness is, of course, a surjective judgment. 00:53:01.230 --> 00:53:03.495 align:middle line:84% But not-- they're no more appealing to what 00:53:03.495 --> 00:53:05.370 align:middle line:84% Einstein would have been arguing for, either. 00:53:05.370 --> 00:53:06.990 align:middle line:84% The Einstein-like options we've really 00:53:06.990 --> 00:53:10.613 align:middle line:84% been able to pretty well put in a box and subject them to test. 00:53:10.613 --> 00:53:12.780 align:middle line:84% That's really what I'll talk about in this next part 00:53:12.780 --> 00:53:13.322 align:middle line:90% of the class. 00:53:13.322 --> 00:53:15.030 align:middle line:90% But it's a big, juicy question. 00:53:15.030 --> 00:53:16.920 align:middle line:84% I'd be delighted to talk more about it, now 00:53:16.920 --> 00:53:19.770 align:middle line:84% or whenever any of you has a chance to catch your breath, 00:53:19.770 --> 00:53:21.430 align:middle line:84% maybe after midterms and all that. 00:53:21.430 --> 00:53:23.250 align:middle line:84% Let me press on, then, to the last part. 00:53:23.250 --> 00:53:26.970 align:middle line:84% Because this now comes to some of the more recent developments 00:53:26.970 --> 00:53:29.310 align:middle line:84% in exactly this kind of discussion. 00:53:29.310 --> 00:53:35.580 align:middle line:84% So almost exactly 30 years after that EPR paper, late in 1964, 00:53:35.580 --> 00:53:39.400 align:middle line:84% the Irish physicist John Bell went back to that question. 00:53:39.400 --> 00:53:41.080 align:middle line:84% He really scrutinized the EPR paper. 00:53:41.080 --> 00:53:43.330 align:middle line:84% You can see he even titled his own paper 00:53:43.330 --> 00:53:46.240 align:middle line:84% "On the Einstein-Podolsky-Rosen Paradox." 00:53:46.240 --> 00:53:48.670 align:middle line:84% And he went back to those two critical assumptions 00:53:48.670 --> 00:53:49.780 align:middle line:90% that the authors had made. 00:53:49.780 --> 00:53:52.062 align:middle line:84% And just to remind you, the first one 00:53:52.062 --> 00:53:53.520 align:middle line:84% is what they had called the reality 00:53:53.520 --> 00:53:56.220 align:middle line:84% criterion, these elements of reality, 00:53:56.220 --> 00:53:57.720 align:middle line:84% the assumption is that each particle 00:53:57.720 --> 00:53:59.910 align:middle line:84% has definite properties on its own, 00:53:59.910 --> 00:54:01.950 align:middle line:84% prior to an independent measurement. 00:54:01.950 --> 00:54:03.630 align:middle line:84% And to my mind, that's like saying 00:54:03.630 --> 00:54:06.540 align:middle line:84% that each particle carries with it a kind of logbook 00:54:06.540 --> 00:54:09.602 align:middle line:84% or an instruction manual that anywhere it goes through space, 00:54:09.602 --> 00:54:12.060 align:middle line:84% it has an answer to the question that might be asked of it. 00:54:12.060 --> 00:54:14.170 align:middle line:84% It has a definite value for its weight. 00:54:14.170 --> 00:54:16.815 align:middle line:84% It has a definite value for its spin along the z-direction. 00:54:16.815 --> 00:54:20.670 align:middle line:84% We might not have measured it yet, but it had a real value. 00:54:20.670 --> 00:54:22.110 align:middle line:90% That was their assumption one. 00:54:22.110 --> 00:54:24.480 align:middle line:84% And assumption two, remember, is this locality, 00:54:24.480 --> 00:54:27.180 align:middle line:84% that no force or information or influence 00:54:27.180 --> 00:54:30.180 align:middle line:84% can travel across space arbitrarily quickly. 00:54:30.180 --> 00:54:33.180 align:middle line:84% What Bell argued is that these are actually assumptions. 00:54:33.180 --> 00:54:35.790 align:middle line:84% Any conclusion is only as good as the assumptions 00:54:35.790 --> 00:54:37.740 align:middle line:90% that went into its derivation. 00:54:37.740 --> 00:54:41.970 align:middle line:84% And this pair of assumptions became called local realism. 00:54:41.970 --> 00:54:45.450 align:middle line:84% The local part is this notion consistent with relativity. 00:54:45.450 --> 00:54:48.420 align:middle line:84% There's a speed limit before A could affect B. 00:54:48.420 --> 00:54:50.370 align:middle line:84% And the realism part refers to the object 00:54:50.370 --> 00:54:52.920 align:middle line:84% having real or definite properties on its own, 00:54:52.920 --> 00:54:55.710 align:middle line:90% independent of us and measuring. 00:54:55.710 --> 00:54:59.020 align:middle line:84% What Bell suggested in this paper late in 1964 00:54:59.020 --> 00:55:00.310 align:middle line:90% is that these are assumptions. 00:55:00.310 --> 00:55:02.685 align:middle line:84% Maybe we should try to test them instead of just conclude 00:55:02.685 --> 00:55:04.970 align:middle line:84% that quantum mechanics is or is not correct. 00:55:04.970 --> 00:55:07.340 align:middle line:84% So we introduced what we now call Bell tests. 00:55:07.340 --> 00:55:09.820 align:middle line:84% And you see these are very closely modeled 00:55:09.820 --> 00:55:11.950 align:middle line:90% on that original EPR framework. 00:55:11.950 --> 00:55:13.660 align:middle line:84% So we have some source of particles 00:55:13.660 --> 00:55:16.660 align:middle line:84% that are prepared in a special way, some source that 00:55:16.660 --> 00:55:19.350 align:middle line:84% shoots out pairs of particles A and B, 00:55:19.350 --> 00:55:22.270 align:middle line:84% two identical measuring devices at-- 00:55:22.270 --> 00:55:25.630 align:middle line:90% apart from each other in space. 00:55:25.630 --> 00:55:28.390 align:middle line:84% And these have-- these boxes are now kind of generalized. 00:55:28.390 --> 00:55:31.120 align:middle line:84% There's some choice of what measurement to perform we 00:55:31.120 --> 00:55:32.650 align:middle line:90% call that the detector setting. 00:55:32.650 --> 00:55:34.825 align:middle line:84% I'll use lowercase letters, little a and b. 00:55:34.825 --> 00:55:36.700 align:middle line:84% That's like saying we could choose to measure 00:55:36.700 --> 00:55:38.650 align:middle line:90% the spin along the x-direction. 00:55:38.650 --> 00:55:39.850 align:middle line:90% We set the dial. 00:55:39.850 --> 00:55:41.380 align:middle line:84% That's how we orient our magnets. 00:55:41.380 --> 00:55:44.360 align:middle line:84% We could choose to measure the spin along the y-direction. 00:55:44.360 --> 00:55:46.210 align:middle line:84% We change the dial, rotate the magnets, 00:55:46.210 --> 00:55:48.010 align:middle line:84% choose to measure some intervening angle. 00:55:48.010 --> 00:55:49.563 align:middle line:84% So we choose the question to ask. 00:55:49.563 --> 00:55:51.730 align:middle line:84% We choose the measurement, the specific measurement, 00:55:51.730 --> 00:55:52.648 align:middle line:90% to be performed. 00:55:52.648 --> 00:55:54.940 align:middle line:84% And that's encoded in these detector settings, little a 00:55:54.940 --> 00:55:56.230 align:middle line:90% and b. 00:55:56.230 --> 00:55:57.640 align:middle line:90% We set the question. 00:55:57.640 --> 00:55:59.240 align:middle line:84% The particle encounters the device. 00:55:59.240 --> 00:56:00.490 align:middle line:90% The device gives us an answer. 00:56:00.490 --> 00:56:01.870 align:middle line:90% That's the measurement outcome. 00:56:01.870 --> 00:56:03.850 align:middle line:90% We'll call that capital A and B. 00:56:03.850 --> 00:56:06.010 align:middle line:84% Now, to be a little more quantitative, 00:56:06.010 --> 00:56:07.540 align:middle line:84% one of the things that Bell did was 00:56:07.540 --> 00:56:10.780 align:middle line:84% to consider certain kinds of properties, certain questions 00:56:10.780 --> 00:56:13.390 align:middle line:84% we could ask, for which the answer is always 00:56:13.390 --> 00:56:16.540 align:middle line:84% of the form either plus 1 or minus 1. 00:56:16.540 --> 00:56:18.250 align:middle line:84% If we measure position, the answer 00:56:18.250 --> 00:56:21.790 align:middle line:84% could be 1.07 meter, 1.0732 meters. 00:56:21.790 --> 00:56:23.860 align:middle line:84% It could be anywhere along a continuum. 00:56:23.860 --> 00:56:25.810 align:middle line:90% Likewise for momentum. 00:56:25.810 --> 00:56:28.600 align:middle line:84% So Bell clarified, let's stick with measurements 00:56:28.600 --> 00:56:31.450 align:middle line:84% for which the answer is discrete and one of two 00:56:31.450 --> 00:56:34.720 align:middle line:84% possible discrete outcomes, like spin or like 00:56:34.720 --> 00:56:36.850 align:middle line:84% polarization of a photon of light. 00:56:36.850 --> 00:56:39.100 align:middle line:84% It's either polarized exactly parallel 00:56:39.100 --> 00:56:43.010 align:middle line:84% to the polarizing filter or perpendicular, not in between. 00:56:43.010 --> 00:56:45.190 align:middle line:84% So the answers we can always be put 00:56:45.190 --> 00:56:47.320 align:middle line:84% in the form of a kind of yes/no question, 00:56:47.320 --> 00:56:50.790 align:middle line:84% spin up, spin down, heads or tails, that kind of thing. 00:56:50.790 --> 00:56:53.210 align:middle line:84% And then we're going to introduce these correlation 00:56:53.210 --> 00:56:53.910 align:middle line:90% functions. 00:56:53.910 --> 00:56:55.327 align:middle line:84% This is a fancy way of just saying 00:56:55.327 --> 00:56:57.890 align:middle line:84% what's the product of those two outcomes. 00:56:57.890 --> 00:57:00.110 align:middle line:84% No matter what question we ask, no matter 00:57:00.110 --> 00:57:02.870 align:middle line:84% how we set the detector setting, little a and little b, 00:57:02.870 --> 00:57:06.920 align:middle line:84% the outcome, capital A, was either a plus 1 or a minus 1, 00:57:06.920 --> 00:57:08.480 align:middle line:84% no matter what question we asked. 00:57:08.480 --> 00:57:10.757 align:middle line:84% Spin along this direction, spin along this direction, 00:57:10.757 --> 00:57:11.840 align:middle line:90% spin along this direction. 00:57:11.840 --> 00:57:13.580 align:middle line:84% The answer for any of those questions 00:57:13.580 --> 00:57:18.410 align:middle line:84% will either be spin up, plus 1, or spin down, minus 1. 00:57:18.410 --> 00:57:20.690 align:middle line:84% So we can compare the answers, even 00:57:20.690 --> 00:57:22.370 align:middle line:90% as we ask different questions. 00:57:22.370 --> 00:57:24.140 align:middle line:84% And we'll average that, the brackets here, 00:57:24.140 --> 00:57:26.780 align:middle line:84% and we will take an average over many, many trials 00:57:26.780 --> 00:57:29.330 align:middle line:84% in which we ask a certain pair of questions, 00:57:29.330 --> 00:57:32.540 align:middle line:84% spin along this direction here, spin along some other direction 00:57:32.540 --> 00:57:35.000 align:middle line:84% here, and see how often the answers were 00:57:35.000 --> 00:57:37.580 align:middle line:90% exactly the same or opposite. 00:57:37.580 --> 00:57:38.270 align:middle line:90% OK. 00:57:38.270 --> 00:57:41.060 align:middle line:84% And then Bell derived this really innocuous-looking 00:57:41.060 --> 00:57:41.990 align:middle line:90% expression. 00:57:41.990 --> 00:57:45.360 align:middle line:84% This is a comparison of the correlations. 00:57:45.360 --> 00:57:47.600 align:middle line:84% So how do those outcomes of measurements 00:57:47.600 --> 00:57:51.283 align:middle line:84% behave as we vary the pairs of questions being asked? 00:57:51.283 --> 00:57:52.200 align:middle line:90% That's all this means. 00:57:52.200 --> 00:57:54.242 align:middle line:84% And again, I'm going to go a little quickly here. 00:57:54.242 --> 00:57:56.880 align:middle line:84% There's the optional lecture notes 00:57:56.880 --> 00:58:00.600 align:middle line:84% that focus just on Bell's work in particular 00:58:00.600 --> 00:58:02.250 align:middle line:84% on the course on the Canvas side. 00:58:02.250 --> 00:58:04.170 align:middle line:84% So this quantity S is really just 00:58:04.170 --> 00:58:06.300 align:middle line:84% saying, as we do each of these comparisons 00:58:06.300 --> 00:58:09.990 align:middle line:84% with question a and b, question a prime and b, 00:58:09.990 --> 00:58:12.540 align:middle line:84% question a with b prime-- you get the idea. 00:58:12.540 --> 00:58:15.240 align:middle line:90% How do these answers line up? 00:58:15.240 --> 00:58:18.360 align:middle line:84% Are they giving the same answer, plus 1 with plus 1, minus 1 00:58:18.360 --> 00:58:21.810 align:middle line:84% with minus 1, or are they giving opposite answers? 00:58:21.810 --> 00:58:24.690 align:middle line:84% Now, Bell goes on-- and again, a deceptively simple 00:58:24.690 --> 00:58:25.560 align:middle line:90% or a short paper. 00:58:25.560 --> 00:58:28.050 align:middle line:84% It's only six journal pages, very brief. 00:58:28.050 --> 00:58:30.210 align:middle line:90% And yet again, it's very dense. 00:58:30.210 --> 00:58:33.990 align:middle line:84% He goes on to show that any theory that would obey this 00:58:33.990 --> 00:58:37.080 align:middle line:84% local realism of the Einstein-Podolsky-Rosen 00:58:37.080 --> 00:58:40.230 align:middle line:84% framework, no matter what the specific model is, 00:58:40.230 --> 00:58:41.040 align:middle line:90% it should be put-- 00:58:41.040 --> 00:58:43.410 align:middle line:84% one should be able to put it in this general form. 00:58:43.410 --> 00:58:45.990 align:middle line:84% Bell argues there must be some properties 00:58:45.990 --> 00:58:48.330 align:middle line:84% of those particles that come from how they're prepared. 00:58:48.330 --> 00:58:51.660 align:middle line:84% So the lambda is some of shared properties because of some way 00:58:51.660 --> 00:58:53.880 align:middle line:84% of preparing particles A and B together. 00:58:53.880 --> 00:58:56.280 align:middle line:84% There's some likelihood to get this set of properties 00:58:56.280 --> 00:58:59.080 align:middle line:84% versus another, so we're to average over all those. 00:58:59.080 --> 00:59:01.590 align:middle line:84% But then there's some probability 00:59:01.590 --> 00:59:04.560 align:middle line:84% to get a definite answer here when we subject 00:59:04.560 --> 00:59:05.970 align:middle line:90% particle A to a measurement. 00:59:05.970 --> 00:59:08.490 align:middle line:84% We choose to perform a particular measurement, 00:59:08.490 --> 00:59:11.460 align:middle line:84% and the outcome we get should depend on the question we asked 00:59:11.460 --> 00:59:13.530 align:middle line:84% and the shared properties of the particles. 00:59:13.530 --> 00:59:16.500 align:middle line:84% That's what this is encoding very abstractly. 00:59:16.500 --> 00:59:18.780 align:middle line:84% Likewise, we should be able to predict what answer 00:59:18.780 --> 00:59:20.280 align:middle line:90% we'll get at the other device. 00:59:20.280 --> 00:59:22.620 align:middle line:84% The answer capital B should depend 00:59:22.620 --> 00:59:24.570 align:middle line:84% on the question we ask there, our detector 00:59:24.570 --> 00:59:26.850 align:middle line:84% setting, the orientation of our magnets, say, 00:59:26.850 --> 00:59:29.250 align:middle line:84% and of these shared properties lambda. 00:59:29.250 --> 00:59:32.340 align:middle line:84% And then Bell shows that any framework like this, 00:59:32.340 --> 00:59:35.340 align:middle line:84% any model that is consistent with local realism, 00:59:35.340 --> 00:59:37.170 align:middle line:90% will have an upper limit. 00:59:37.170 --> 00:59:40.020 align:middle line:84% There'll be a limit to how correlated 00:59:40.020 --> 00:59:41.520 align:middle line:90% these measurements can be. 00:59:41.520 --> 00:59:43.660 align:middle line:84% So they can line up a bunch of the time. 00:59:43.660 --> 00:59:45.990 align:middle line:84% They can't line up arbitrarily often. 00:59:45.990 --> 00:59:48.540 align:middle line:84% This becomes known as Bell's inequality. 00:59:48.540 --> 00:59:51.540 align:middle line:84% This combination of comparisons, combination 00:59:51.540 --> 00:59:55.290 align:middle line:84% of correlation functions, should be bounded for any theory, 00:59:55.290 --> 00:59:57.840 align:middle line:84% he argues, any possible theory, that 00:59:57.840 --> 01:00:01.800 align:middle line:84% is consistent with the local realism assumptions of EPR. 01:00:01.800 --> 01:00:03.540 align:middle line:84% And let me just dig in here a little bit. 01:00:03.540 --> 01:00:06.330 align:middle line:84% And again, there's some more in the lecture notes. 01:00:06.330 --> 01:00:07.380 align:middle line:90% Why does it say that? 01:00:07.380 --> 01:00:11.250 align:middle line:84% Look at the form that he's chosen to write. 01:00:11.250 --> 01:00:14.910 align:middle line:84% He's encoded this locality, that the measurement outcome 01:00:14.910 --> 01:00:17.520 align:middle line:84% here, whether we get spin up or spin down, 01:00:17.520 --> 01:00:20.310 align:middle line:84% depends on the question we ask locally 01:00:20.310 --> 01:00:22.320 align:middle line:84% and on the shared properties that the particle 01:00:22.320 --> 01:00:23.490 align:middle line:90% could have carried with it. 01:00:23.490 --> 01:00:26.130 align:middle line:84% It cannot depend in this framework on either 01:00:26.130 --> 01:00:29.100 align:middle line:84% the question that's asked very far away or on the answer 01:00:29.100 --> 01:00:30.420 align:middle line:90% that's found very far away. 01:00:30.420 --> 01:00:31.890 align:middle line:90% That's this local realism. 01:00:31.890 --> 01:00:34.110 align:middle line:84% The particle must have had its own properties 01:00:34.110 --> 01:00:36.240 align:middle line:84% to answer, so to speak, its own question. 01:00:36.240 --> 01:00:38.550 align:middle line:84% And that's like saying the answer we 01:00:38.550 --> 01:00:42.340 align:middle line:84% get here can depend on local things local to the box, things 01:00:42.340 --> 01:00:44.340 align:middle line:84% that-- properties that particle brought with it, 01:00:44.340 --> 01:00:46.605 align:middle line:84% the particular question we chose to ask. 01:00:46.605 --> 01:00:48.480 align:middle line:84% The answer here shouldn't depend on something 01:00:48.480 --> 01:00:52.170 align:middle line:84% that could be done arbitrarily late in the process arbitrarily 01:00:52.170 --> 01:00:53.640 align:middle line:90% far away, OK? 01:00:53.640 --> 01:00:56.320 align:middle line:84% And yet, again, the calculation is pretty short. 01:00:56.320 --> 01:00:59.640 align:middle line:84% I go through it with all the intervening steps 01:00:59.640 --> 01:01:02.910 align:middle line:84% just to make it very explicit in those lecture notes. 01:01:02.910 --> 01:01:06.690 align:middle line:84% Quantum mechanics predicts really unambiguously 01:01:06.690 --> 01:01:08.640 align:middle line:84% that for certain kinds of systems, 01:01:08.640 --> 01:01:11.700 align:middle line:84% certain pairs of particles we might prepare in certain ways-- 01:01:11.700 --> 01:01:15.150 align:middle line:84% these measurements should be more strongly correlated 01:01:15.150 --> 01:01:17.790 align:middle line:84% than Bell's limit would allow, that the answers 01:01:17.790 --> 01:01:19.860 align:middle line:84% at these distant devices should line up 01:01:19.860 --> 01:01:22.380 align:middle line:84% even more often than any local realist 01:01:22.380 --> 01:01:25.020 align:middle line:84% theory could accommodate or could account for. 01:01:25.020 --> 01:01:27.960 align:middle line:84% And not by a little bit, by as much as 40%, 01:01:27.960 --> 01:01:31.110 align:middle line:84% that when you do this comparison of the correlations, 01:01:31.110 --> 01:01:34.095 align:middle line:84% this single number S could be as large as 2 01:01:34.095 --> 01:01:35.220 align:middle line:90% times the square root of 2. 01:01:35.220 --> 01:01:38.980 align:middle line:84% That's like roughly 2.8, 2.81, 2.82, something like that, 01:01:38.980 --> 01:01:41.460 align:middle line:84% which is considerably larger than this upper limit 01:01:41.460 --> 01:01:44.060 align:middle line:90% from Bell's inequality of 2. 01:01:44.060 --> 01:01:45.890 align:middle line:84% So that still sounds pretty abstract. 01:01:45.890 --> 01:01:48.307 align:middle line:84% And Stephen, this might be the talk you were referring to. 01:01:48.307 --> 01:01:50.930 align:middle line:84% You might have heard this last spring. 01:01:50.930 --> 01:01:53.310 align:middle line:84% But for others who might not have heard it. 01:01:53.310 --> 01:01:55.250 align:middle line:84% I like to think of this entanglement, 01:01:55.250 --> 01:01:59.690 align:middle line:84% the conceptual stakes, in terms of the following parable. 01:01:59.690 --> 01:02:02.840 align:middle line:84% Again, I find it helpful to bring this up to human scale. 01:02:02.840 --> 01:02:06.170 align:middle line:84% So I imagine a pair of twins, Alice and Bob, 01:02:06.170 --> 01:02:07.118 align:middle line:90% who work very hard. 01:02:07.118 --> 01:02:09.410 align:middle line:84% They're both very bright and diligent and hard working. 01:02:09.410 --> 01:02:12.260 align:middle line:84% And when it comes time to go to college, Alice, who is frankly, 01:02:12.260 --> 01:02:15.830 align:middle line:84% just more diligent and more smart, she gets an MIT, 01:02:15.830 --> 01:02:17.900 align:middle line:84% and so she comes to Cambridge, Massachusetts. 01:02:17.900 --> 01:02:20.990 align:middle line:84% And her very affable but somewhat duller brother Bob 01:02:20.990 --> 01:02:23.032 align:middle line:90% goes to Cambridge, England. 01:02:23.032 --> 01:02:25.490 align:middle line:84% Alice-- this is the part that's now hard for us to imagine. 01:02:25.490 --> 01:02:27.117 align:middle line:84% Alice physically comes to campus. 01:02:27.117 --> 01:02:28.700 align:middle line:84% That's hard for some of us to imagine. 01:02:28.700 --> 01:02:30.140 align:middle line:90% She then goes to restaurants. 01:02:30.140 --> 01:02:31.650 align:middle line:90% What is this crazy story? 01:02:31.650 --> 01:02:34.530 align:middle line:84% So imagine prepandemic, Alice comes to MIT. 01:02:34.530 --> 01:02:37.160 align:middle line:84% She goes to her favorite local restaurant near campus. 01:02:37.160 --> 01:02:39.320 align:middle line:84% And after dinner, the waiter asks, what would you 01:02:39.320 --> 01:02:40.293 align:middle line:90% like for dessert? 01:02:40.293 --> 01:02:41.960 align:middle line:84% So he's going to pose a question to her, 01:02:41.960 --> 01:02:43.790 align:middle line:90% and she'll give an answer. 01:02:43.790 --> 01:02:46.940 align:middle line:84% He's posing a question to her about baked goods. 01:02:46.940 --> 01:02:49.010 align:middle line:84% He says, tonight, your choice is you can have 01:02:49.010 --> 01:02:51.050 align:middle line:90% either a brownie or a cookie. 01:02:51.050 --> 01:02:53.210 align:middle line:84% She has one of two possible choices. 01:02:53.210 --> 01:02:56.360 align:middle line:84% That's like the spin either being spin up or spin down. 01:02:56.360 --> 01:02:58.280 align:middle line:84% The waiter has specified the question. 01:02:58.280 --> 01:02:59.450 align:middle line:90% That's the little a. 01:02:59.450 --> 01:03:01.520 align:middle line:84% I'll measure spin along this direction. 01:03:01.520 --> 01:03:04.220 align:middle line:84% I'll ask about baked goods preferences. 01:03:04.220 --> 01:03:06.350 align:middle line:84% He's setting the question, and Alice 01:03:06.350 --> 01:03:10.010 align:middle line:84% can give one of two possible outcomes, brownie or cookie, 01:03:10.010 --> 01:03:11.952 align:middle line:90% plus 1 or minus 1. 01:03:11.952 --> 01:03:13.910 align:middle line:84% Some other nights-- she likes this place a lot. 01:03:13.910 --> 01:03:16.340 align:middle line:84% She goes back there very often for dinner. 01:03:16.340 --> 01:03:18.860 align:middle line:84% On other nights, the waiter asks her a different question. 01:03:18.860 --> 01:03:22.520 align:middle line:84% He now asks a different kind of question by rotating that dial. 01:03:22.520 --> 01:03:25.700 align:middle line:84% And he measures in some different measurement basis, 01:03:25.700 --> 01:03:28.160 align:middle line:84% like he's rotating the magnets for spin. 01:03:28.160 --> 01:03:31.220 align:middle line:84% This new question is actually about frozen dessert. 01:03:31.220 --> 01:03:34.310 align:middle line:84% She can either have on that night an ice cream sundae 01:03:34.310 --> 01:03:35.660 align:middle line:90% or frozen yogurt. 01:03:35.660 --> 01:03:37.460 align:middle line:90% Again, he poses the question. 01:03:37.460 --> 01:03:39.560 align:middle line:84% She has one of two possible answers that she can 01:03:39.560 --> 01:03:41.960 align:middle line:90% give, a plus 1 or a minus 1. 01:03:41.960 --> 01:03:44.190 align:middle line:84% The waiter selects which question 01:03:44.190 --> 01:03:46.050 align:middle line:90% to ask by some local process. 01:03:46.050 --> 01:03:49.080 align:middle line:84% Maybe he flips a coin back in the kitchen. 01:03:49.080 --> 01:03:50.830 align:middle line:90% Alice has no clear preference. 01:03:50.830 --> 01:03:52.200 align:middle line:90% She likes all these options. 01:03:52.200 --> 01:03:53.700 align:middle line:84% And we know that because if you look 01:03:53.700 --> 01:03:56.160 align:middle line:84% at the tally of all her dessert orders after she 01:03:56.160 --> 01:03:58.590 align:middle line:84% keeps going for more and more fatty desserts. 01:03:58.590 --> 01:04:01.230 align:middle line:84% I don't recommend this experiment too often. 01:04:01.230 --> 01:04:04.440 align:middle line:84% But she winds up choosing each option on average 01:04:04.440 --> 01:04:05.820 align:middle line:90% equally often. 01:04:05.820 --> 01:04:09.060 align:middle line:84% So when she's offered question one about baked goods, 01:04:09.060 --> 01:04:11.598 align:middle line:84% on average, half the time, she orders a brownie. 01:04:11.598 --> 01:04:13.140 align:middle line:84% Half the time, she orders the cookie, 01:04:13.140 --> 01:04:14.910 align:middle line:84% in an order that looks totally random. 01:04:14.910 --> 01:04:16.500 align:middle line:84% It's not clear which night she'll 01:04:16.500 --> 01:04:19.500 align:middle line:84% order a cookie or brownie, but averaged over the whole set, 01:04:19.500 --> 01:04:21.510 align:middle line:84% she has equal numbers of those choices, 01:04:21.510 --> 01:04:23.580 align:middle line:84% and likewise for the frozen desserts. 01:04:23.580 --> 01:04:26.940 align:middle line:84% Unbeknownst to Alice, an ocean apart, her brother Bob 01:04:26.940 --> 01:04:28.710 align:middle line:84% is now going to a pub in Cambridge 01:04:28.710 --> 01:04:33.690 align:middle line:84% and being posed the same questions at the same time. 01:04:33.690 --> 01:04:35.830 align:middle line:84% The question's drawn from the same pair. 01:04:35.830 --> 01:04:39.760 align:middle line:84% So in some visits, Bob's waiter will ask him about baked goods, 01:04:39.760 --> 01:04:41.460 align:middle line:84% and he has one of two possible choices, 01:04:41.460 --> 01:04:43.170 align:middle line:84% either the brownie or the cookie. 01:04:43.170 --> 01:04:46.980 align:middle line:84% On other evenings, the waiter asks Bob about frozen goods. 01:04:46.980 --> 01:04:48.720 align:middle line:84% He can choose one of two options. 01:04:48.720 --> 01:04:51.000 align:middle line:84% Again, the waiter chooses by some random process. 01:04:51.000 --> 01:04:52.710 align:middle line:90% Bob has no clear preference. 01:04:52.710 --> 01:04:57.060 align:middle line:84% He, again, is choosing each option in equal frequency, 01:04:57.060 --> 01:04:59.730 align:middle line:84% but in what looks like a random order. 01:04:59.730 --> 01:05:02.280 align:middle line:84% They come back for Thanksgiving, and the first thing 01:05:02.280 --> 01:05:04.710 align:middle line:84% they want to do after being away for the first semester 01:05:04.710 --> 01:05:07.522 align:middle line:84% of college is compare their 10,000 dessert orders. 01:05:07.522 --> 01:05:09.480 align:middle line:84% That's what I would talk about with my sibling. 01:05:09.480 --> 01:05:13.230 align:middle line:84% So they realize there are some pretty surprising correlations 01:05:13.230 --> 01:05:16.980 align:middle line:84% that get found when they compare these sets of answers. 01:05:16.980 --> 01:05:18.780 align:middle line:84% When they both happen to have been 01:05:18.780 --> 01:05:21.540 align:middle line:84% asked the first question about baked goods, 01:05:21.540 --> 01:05:23.200 align:middle line:90% they both gave the same answer. 01:05:23.200 --> 01:05:26.040 align:middle line:84% They both gave either the brownie answer or the cookie 01:05:26.040 --> 01:05:28.320 align:middle line:84% answer at the same time, even though they 01:05:28.320 --> 01:05:31.540 align:middle line:84% might have ordered the opposite choice the next time. 01:05:31.540 --> 01:05:33.703 align:middle line:84% So when they were both asked the same question, 01:05:33.703 --> 01:05:35.370 align:middle line:84% their answers lined up, even though they 01:05:35.370 --> 01:05:37.502 align:middle line:84% seem to be answering them independently. 01:05:37.502 --> 01:05:39.210 align:middle line:84% When they were asked different questions, 01:05:39.210 --> 01:05:41.670 align:middle line:84% there, again, was a correlation, that when 01:05:41.670 --> 01:05:43.390 align:middle line:84% Alice was asked about baked goods, 01:05:43.390 --> 01:05:45.840 align:middle line:84% she took the brownie at the time when 01:05:45.840 --> 01:05:48.430 align:middle line:84% Bob took the frozen yogurt, but not the ice cream when 01:05:48.430 --> 01:05:50.430 align:middle line:84% he was asked about frozen goods, and vice versa. 01:05:50.430 --> 01:05:54.610 align:middle line:84% There was a correlation in the cross question answers as well. 01:05:54.610 --> 01:05:59.070 align:middle line:84% And then when they're both asked question B about frozen goods, 01:05:59.070 --> 01:06:01.150 align:middle line:90% their answers once again align. 01:06:01.150 --> 01:06:03.700 align:middle line:84% When they both happen to be asked about frozen goods, 01:06:03.700 --> 01:06:06.830 align:middle line:84% they both ordered either the ice cream sundae or the fro-yo 01:06:06.830 --> 01:06:07.870 align:middle line:90% at the same time. 01:06:07.870 --> 01:06:10.090 align:middle line:90% Why should this be surprising? 01:06:10.090 --> 01:06:12.130 align:middle line:84% If we just look at how Bob is answering 01:06:12.130 --> 01:06:15.400 align:middle line:84% all alone in this British pub, his answer 01:06:15.400 --> 01:06:19.180 align:middle line:84% to the same question about frozen goods seems to change 01:06:19.180 --> 01:06:21.400 align:middle line:84% and seems to in some sense depend, or at least 01:06:21.400 --> 01:06:23.235 align:middle line:84% be correlated, with something that's 01:06:23.235 --> 01:06:25.360 align:middle line:84% happening an ocean away for which he's not supposed 01:06:25.360 --> 01:06:26.980 align:middle line:90% to have any information. 01:06:26.980 --> 01:06:29.020 align:middle line:84% That's what Einstein said shouldn't happen, 01:06:29.020 --> 01:06:31.750 align:middle line:84% that the world shouldn't have that kind of telepathy, 01:06:31.750 --> 01:06:33.590 align:middle line:90% that kind of spooky connection. 01:06:33.590 --> 01:06:37.180 align:middle line:84% And in particular, if Bob is answering his questions out 01:06:37.180 --> 01:06:40.743 align:middle line:84% of some kind of local logbook or instruction manual, how-- 01:06:40.743 --> 01:06:42.160 align:middle line:84% he doesn't have enough information 01:06:42.160 --> 01:06:44.800 align:middle line:84% at his location, at his British pub, 01:06:44.800 --> 01:06:47.830 align:middle line:84% to know how to get his answers to line up 01:06:47.830 --> 01:06:50.170 align:middle line:84% with those that Alice will give at the same moment 01:06:50.170 --> 01:06:52.280 align:middle line:90% thousands of miles away. 01:06:52.280 --> 01:06:55.690 align:middle line:84% So how could we subject that kind of human parable 01:06:55.690 --> 01:06:57.040 align:middle line:90% to experimental test? 01:06:57.040 --> 01:06:58.640 align:middle line:84% And there's many, many ways to do it. 01:06:58.640 --> 01:07:00.015 align:middle line:84% I'm going to talk about an effort 01:07:00.015 --> 01:07:03.070 align:middle line:84% that my own group did just about two years ago 01:07:03.070 --> 01:07:05.290 align:middle line:84% with this absolutely gorgeous mountaintop 01:07:05.290 --> 01:07:07.090 align:middle line:84% observatory in the Canary Islands 01:07:07.090 --> 01:07:10.120 align:middle line:84% just off the coast of Morocco at the Roque de Los Muchachos 01:07:10.120 --> 01:07:11.230 align:middle line:90% Observatory. 01:07:11.230 --> 01:07:13.750 align:middle line:84% We were using some of the largest optical telescopes 01:07:13.750 --> 01:07:14.470 align:middle line:90% on the planet. 01:07:14.470 --> 01:07:16.240 align:middle line:90% It was fantastic. 01:07:16.240 --> 01:07:16.810 align:middle line:90% OK. 01:07:16.810 --> 01:07:19.442 align:middle line:84% So here's-- we had three main parts to our experiment. 01:07:19.442 --> 01:07:20.650 align:middle line:90% I'll go through very quickly. 01:07:20.650 --> 01:07:22.180 align:middle line:90% We're almost at time. 01:07:22.180 --> 01:07:23.680 align:middle line:84% I'd be glad to chat more about it. 01:07:23.680 --> 01:07:26.763 align:middle line:84% We set up a temporary laboratory here 01:07:26.763 --> 01:07:28.180 align:middle line:84% that was actually a shipping crate 01:07:28.180 --> 01:07:31.090 align:middle line:84% that my colleagues from Vienna shipped over. 01:07:31.090 --> 01:07:32.815 align:middle line:84% And so that was our transmitter station. 01:07:32.815 --> 01:07:34.690 align:middle line:84% That's our source of the entangled particles. 01:07:34.690 --> 01:07:38.830 align:middle line:84% That's where particles A and B are created and then emitted. 01:07:38.830 --> 01:07:42.190 align:middle line:84% And then quite a distance away, about half a kilometer 01:07:42.190 --> 01:07:44.890 align:middle line:84% in each direction, we had our receiving stations, 01:07:44.890 --> 01:07:45.913 align:middle line:90% our detectors. 01:07:45.913 --> 01:07:48.580 align:middle line:84% So let's talk about what's going on in this transmitter station. 01:07:48.580 --> 01:07:50.570 align:middle line:84% What we're doing there is we have a pump laser, 01:07:50.570 --> 01:07:52.150 align:middle line:90% which is just awesome. 01:07:52.150 --> 01:07:54.910 align:middle line:84% It's a laser that's actually tuned to emit light 01:07:54.910 --> 01:07:55.870 align:middle line:90% in the visible range. 01:07:55.870 --> 01:07:58.780 align:middle line:84% It actually looks very much like this color of purple. 01:07:58.780 --> 01:08:00.853 align:middle line:84% You could see it with your own eyes. 01:08:00.853 --> 01:08:02.020 align:middle line:90% It's in the visible portion. 01:08:02.020 --> 01:08:05.440 align:middle line:84% It's in the purple region of the visible spectrum. 01:08:05.440 --> 01:08:08.722 align:middle line:84% We shine that laser light into a very special crystal. 01:08:08.722 --> 01:08:10.180 align:middle line:84% It's only about a square inch long. 01:08:10.180 --> 01:08:11.750 align:middle line:90% It's not very big. 01:08:11.750 --> 01:08:14.230 align:middle line:84% It's what's called a nonlinear crystal. 01:08:14.230 --> 01:08:17.800 align:middle line:84% It has the fantastic property of absorbing 01:08:17.800 --> 01:08:20.590 align:middle line:84% light of a very specific frequency that comes in. 01:08:20.590 --> 01:08:23.140 align:middle line:84% And when that particular frequency combs in, 01:08:23.140 --> 01:08:26.319 align:middle line:84% it absorbs that one photon of light and emits pairs 01:08:26.319 --> 01:08:28.220 align:middle line:90% of particles, pairs of photons. 01:08:28.220 --> 01:08:29.859 align:middle line:90% So they conserve momentum. 01:08:29.859 --> 01:08:31.240 align:middle line:90% They conserve energy. 01:08:31.240 --> 01:08:33.220 align:middle line:84% Each of these particles has less energy 01:08:33.220 --> 01:08:34.689 align:middle line:90% than the incoming particle. 01:08:34.689 --> 01:08:37.100 align:middle line:84% They conserve all the things they should. 01:08:37.100 --> 01:08:38.529 align:middle line:90% But basically, one comes in. 01:08:38.529 --> 01:08:39.123 align:middle line:90% Two come out. 01:08:39.123 --> 01:08:40.540 align:middle line:84% And that's a property the crystal. 01:08:40.540 --> 01:08:43.960 align:middle line:84% Not any old time you shine any light on it, light in; 01:08:43.960 --> 01:08:46.160 align:middle line:84% only light of a very specific frequency. 01:08:46.160 --> 01:08:47.920 align:middle line:84% So we tuned our laser very carefully 01:08:47.920 --> 01:08:49.880 align:middle line:90% in conjunction with our crystal. 01:08:49.880 --> 01:08:52.029 align:middle line:84% So that's like creating our twin. 01:08:52.029 --> 01:08:54.649 align:middle line:84% That's how we create our twins, Alice and Bob, 01:08:54.649 --> 01:08:57.590 align:middle line:84% and then we beam them half a mile in each direction 01:08:57.590 --> 01:08:58.340 align:middle line:90% across the island. 01:08:58.340 --> 01:08:59.899 align:middle line:84% You can see now the guide lasers here 01:08:59.899 --> 01:09:02.890 align:middle line:84% to line up our optics across the island. 01:09:02.890 --> 01:09:05.710 align:middle line:84% So once the particles travel at the speed 01:09:05.710 --> 01:09:08.487 align:middle line:84% of light, half a kilometer in opposite directions, 01:09:08.487 --> 01:09:10.029 align:middle line:84% then we subject them to measurements. 01:09:10.029 --> 01:09:11.689 align:middle line:90% And that's like these dessert-- 01:09:11.689 --> 01:09:14.240 align:middle line:84% these waiters about to take their dessert orders. 01:09:14.240 --> 01:09:16.899 align:middle line:84% We're going to measure properties of those particles 01:09:16.899 --> 01:09:18.640 align:middle line:84% after they've been created together 01:09:18.640 --> 01:09:20.950 align:middle line:84% they have some common history and common properties 01:09:20.950 --> 01:09:24.069 align:middle line:84% but then shoot them off and ask random questions of them 01:09:24.069 --> 01:09:27.069 align:middle line:84% and see how often the answers line up. 01:09:27.069 --> 01:09:29.350 align:middle line:84% So one thing we able to do is close down 01:09:29.350 --> 01:09:31.600 align:middle line:90% that locality explanation. 01:09:31.600 --> 01:09:33.760 align:middle line:84% As we'll see, the answers line up a lot, 01:09:33.760 --> 01:09:35.720 align:middle line:84% just like quantum mechanics says they do. 01:09:35.720 --> 01:09:37.240 align:middle line:84% And we wanted to be sure it couldn't 01:09:37.240 --> 01:09:41.319 align:middle line:84% be because they were somehow sharing information en route. 01:09:41.319 --> 01:09:44.319 align:middle line:84% And we ensured that by the space time 01:09:44.319 --> 01:09:46.060 align:middle line:90% arrangement of the experiment. 01:09:46.060 --> 01:09:50.290 align:middle line:84% The time it took to create the particles, 01:09:50.290 --> 01:09:53.038 align:middle line:84% beam them across the island, and complete a measurement, 01:09:53.038 --> 01:09:54.580 align:middle line:84% not just have it arrive, but actually 01:09:54.580 --> 01:09:57.730 align:middle line:84% complete a measurement in this case of its polarization, 01:09:57.730 --> 01:10:01.960 align:middle line:84% took just over 2 microseconds, 2 millionths of a second, for-- 01:10:01.960 --> 01:10:03.380 align:middle line:90% in each direction. 01:10:03.380 --> 01:10:06.050 align:middle line:84% And yet the light travel time between the detectors 01:10:06.050 --> 01:10:08.450 align:middle line:84% was nearly 3 and 1/2 microseconds. 01:10:08.450 --> 01:10:12.350 align:middle line:84% So there was no time to get an update from, say, Alice's side 01:10:12.350 --> 01:10:16.460 align:middle line:84% to Bob's, either to have said my waiter just asked me 01:10:16.460 --> 01:10:20.090 align:middle line:84% about baked goods or to say I just ordered a brownie, right? 01:10:20.090 --> 01:10:23.250 align:middle line:84% Both the questions that were asked at that particular moment 01:10:23.250 --> 01:10:25.550 align:middle line:84% and the actual measurement outcomes, the answers given, 01:10:25.550 --> 01:10:28.230 align:middle line:84% were space-like separated from each other. 01:10:28.230 --> 01:10:30.800 align:middle line:84% There was no way that information traveling even as 01:10:30.800 --> 01:10:33.500 align:middle line:84% fast as light could have updated one side about what's 01:10:33.500 --> 01:10:35.300 align:middle line:90% happening on the other side. 01:10:35.300 --> 01:10:37.590 align:middle line:84% What else is happening at these receiver stations? 01:10:37.590 --> 01:10:39.200 align:middle line:84% Here's where these amazing instruments 01:10:39.200 --> 01:10:40.220 align:middle line:90% become so important. 01:10:40.220 --> 01:10:41.810 align:middle line:84% I can't believe they let us play with these. 01:10:41.810 --> 01:10:42.590 align:middle line:90% I didn't get to touch them. 01:10:42.590 --> 01:10:43.730 align:middle line:90% They knew better than me. 01:10:43.730 --> 01:10:46.070 align:middle line:84% These are each 4-meter telescopes, 01:10:46.070 --> 01:10:49.250 align:middle line:84% some of the largest anywhere, the Galileo National 01:10:49.250 --> 01:10:51.860 align:middle line:84% Telescope on one side and the William Herschel Telescope 01:10:51.860 --> 01:10:52.830 align:middle line:90% on the other. 01:10:52.830 --> 01:10:56.840 align:middle line:84% So these telescopes were so big, 13-foot polished mirrors, 01:10:56.840 --> 01:10:59.900 align:middle line:84% polished really to perfection, that they could gather light 01:10:59.900 --> 01:11:02.720 align:middle line:84% in a fraction of a second, less than a microsecond, 01:11:02.720 --> 01:11:05.510 align:middle line:84% even from very, very dim very distant objects, 01:11:05.510 --> 01:11:08.720 align:middle line:84% like very distant extragalactic objects like quasars, some 01:11:08.720 --> 01:11:12.020 align:middle line:84% of the most distant galaxies in the universe, distant from us. 01:11:12.020 --> 01:11:14.300 align:middle line:84% So what we were doing is performing real-time 01:11:14.300 --> 01:11:17.840 align:middle line:84% measurements of the color of the light from those quasars, 01:11:17.840 --> 01:11:20.480 align:middle line:84% one telescope pointing in one direction of sky, 01:11:20.480 --> 01:11:22.700 align:middle line:84% the other pointing in the opposite direction of sky, 01:11:22.700 --> 01:11:25.760 align:middle line:84% and taking new measurements of that light every-- 01:11:25.760 --> 01:11:27.500 align:middle line:84% roughly every microsecond, every fraction 01:11:27.500 --> 01:11:30.950 align:middle line:84% of a second, while the entangled particles were in flight. 01:11:30.950 --> 01:11:32.935 align:middle line:90% So you emit the particles first. 01:11:32.935 --> 01:11:35.060 align:middle line:84% They don't know what questions to be asked of them. 01:11:35.060 --> 01:11:36.650 align:middle line:84% They don't know, in a sense, what properties are 01:11:36.650 --> 01:11:38.070 align:middle line:90% about to be measured of them. 01:11:38.070 --> 01:11:40.850 align:middle line:84% And while they're traveling, we perform a real-time measurement 01:11:40.850 --> 01:11:43.280 align:middle line:84% of some of the oldest light in the universe. 01:11:43.280 --> 01:11:45.740 align:middle line:84% Sometimes in that very narrow window, 01:11:45.740 --> 01:11:48.470 align:middle line:84% the light will be more blue than average, sometimes more red 01:11:48.470 --> 01:11:50.330 align:middle line:90% than average. 01:11:50.330 --> 01:11:52.370 align:middle line:84% And so on the times when it's more blue, 01:11:52.370 --> 01:11:55.520 align:middle line:84% that activates local electronics to perform 01:11:55.520 --> 01:11:58.730 align:middle line:84% measurement of the earthbound entangled particle in one 01:11:58.730 --> 01:11:59.640 align:middle line:90% basis. 01:11:59.640 --> 01:12:02.250 align:middle line:84% We measure the polarization in one orientation in space. 01:12:02.250 --> 01:12:05.750 align:middle line:84% That's like the waiter choosing to ask about baked goods. 01:12:05.750 --> 01:12:08.450 align:middle line:84% On those microsecond windows when the light happened-- 01:12:08.450 --> 01:12:11.210 align:middle line:84% the astronomical light happened to be more red than average, 01:12:11.210 --> 01:12:12.740 align:middle line:90% we perform the other measure. 01:12:12.740 --> 01:12:14.720 align:middle line:84% Let's say we ask the other question. 01:12:14.720 --> 01:12:17.120 align:middle line:84% We did this now across the island. 01:12:17.120 --> 01:12:20.630 align:middle line:84% We did this with 20,000 pairs of particles. 01:12:20.630 --> 01:12:23.510 align:middle line:84% And we found that the measurements line up 01:12:23.510 --> 01:12:25.820 align:middle line:84% exactly as quantum mechanics says they would. 01:12:25.820 --> 01:12:28.040 align:middle line:84% We get almost exactly the maximum value 01:12:28.040 --> 01:12:31.280 align:middle line:84% of the correlation that quantum mechanics predicts. 01:12:31.280 --> 01:12:34.010 align:middle line:84% We violate Bell's inequality by more than nine 01:12:34.010 --> 01:12:35.360 align:middle line:90% standard deviations. 01:12:35.360 --> 01:12:38.060 align:middle line:84% The statistical likelihood that was due to a fluke 01:12:38.060 --> 01:12:40.590 align:middle line:90% is 1 part in 10 to the 20. 01:12:40.590 --> 01:12:41.810 align:middle line:90% Take that, Gary Gensler. 01:12:41.810 --> 01:12:45.140 align:middle line:84% I'd like to see you guys do that with your finance stuff. 01:12:45.140 --> 01:12:47.210 align:middle line:84% Anyway, huge statistical significance, 01:12:47.210 --> 01:12:50.010 align:middle line:84% even though the decision of what question to be asked 01:12:50.010 --> 01:12:52.710 align:middle line:84% came from events on opposite sides of the universe 01:12:52.710 --> 01:12:54.387 align:middle line:90% 8 and 12 billion years ago. 01:12:54.387 --> 01:12:56.220 align:middle line:84% So on the basis of experiments like this one 01:12:56.220 --> 01:12:58.770 align:middle line:84% and many others that I described in that optional reading, 01:12:58.770 --> 01:13:01.110 align:middle line:84% many, many kinds of experiments now, 01:13:01.110 --> 01:13:03.150 align:middle line:84% the world really does seem to be as spooky 01:13:03.150 --> 01:13:06.360 align:middle line:84% as Einstein feared or suspected, even 01:13:06.360 --> 01:13:09.810 align:middle line:84% when we close down the kinds of Einstein-like local realist 01:13:09.810 --> 01:13:12.420 align:middle line:84% explanations that otherwise might have been able to account 01:13:12.420 --> 01:13:13.900 align:middle line:90% for those correlations. 01:13:13.900 --> 01:13:15.580 align:middle line:84% So let me very, very rapidly sum up. 01:13:15.580 --> 01:13:17.160 align:middle line:84% I know we're basically at time, just 01:13:17.160 --> 01:13:20.810 align:middle line:90% to summarize today's material. 01:13:20.810 --> 01:13:26.300 align:middle line:84% Schrodinger's equation brings up this property of superposition. 01:13:26.300 --> 01:13:28.790 align:middle line:84% It is a wave equation, and therefore, solutions 01:13:28.790 --> 01:13:31.670 align:middle line:84% obey the wavelike property of superposition 01:13:31.670 --> 01:13:35.030 align:middle line:84% that the sum of any two solutions is itself a solution. 01:13:35.030 --> 01:13:36.920 align:middle line:84% But that-- unlike with water waves, 01:13:36.920 --> 01:13:41.030 align:middle line:84% that led to some pretty jarring or unexpected questions 01:13:41.030 --> 01:13:43.970 align:middle line:84% when we apply that to the outcomes of events. 01:13:43.970 --> 01:13:47.420 align:middle line:84% If the wave functions can obey superposition 01:13:47.420 --> 01:13:50.090 align:middle line:84% and the wave functions are about likelihoods of events 01:13:50.090 --> 01:13:51.920 align:middle line:84% to happen, then what does that do 01:13:51.920 --> 01:13:53.990 align:middle line:90% to the nature of explanation? 01:13:53.990 --> 01:13:56.990 align:middle line:84% And then finally, what happens if multiple things are 01:13:56.990 --> 01:13:59.670 align:middle line:84% in superposition in this entangled way? 01:13:59.670 --> 01:14:02.487 align:middle line:84% So the outcome over here is not only a heads or tails 01:14:02.487 --> 01:14:04.070 align:middle line:84% that we don't know yet, but is somehow 01:14:04.070 --> 01:14:06.740 align:middle line:84% bound up with something that might happen arbitrarily 01:14:06.740 --> 01:14:08.000 align:middle line:90% far apart. 01:14:08.000 --> 01:14:09.530 align:middle line:90% So let me stop sharing. 01:14:09.530 --> 01:14:12.200 align:middle line:84% My apologies for running a little bit long today. 01:14:12.200 --> 01:14:14.448 align:middle line:84% But we do have time for a few more questions now, 01:14:14.448 --> 01:14:15.990 align:middle line:84% or, of course, if you have questions, 01:14:15.990 --> 01:14:18.990 align:middle line:84% please feel free to email, come to office hours. 01:14:18.990 --> 01:14:20.940 align:middle line:84% There's lots more stuff I'm glad to send 01:14:20.940 --> 01:14:22.500 align:middle line:90% your way if you're curious. 01:14:22.500 --> 01:14:25.420 align:middle line:84% Gary is an identical twin, he tells us, 01:14:25.420 --> 01:14:28.470 align:middle line:84% and so even though he answers questions at a distance, 01:14:28.470 --> 01:14:30.150 align:middle line:84% you thought you had some free will. 01:14:30.150 --> 01:14:30.930 align:middle line:90% Exactly. 01:14:30.930 --> 01:14:33.160 align:middle line:84% So with the twins, it's not just that you would share 01:14:33.160 --> 01:14:35.160 align:middle line:90% a DNA and a similar upbringing. 01:14:35.160 --> 01:14:39.995 align:middle line:84% It really is like, would you answer randomly posed questions 01:14:39.995 --> 01:14:41.370 align:middle line:84% when you don't know what question 01:14:41.370 --> 01:14:42.840 align:middle line:90% you'll be asked in advance? 01:14:42.840 --> 01:14:44.817 align:middle line:84% And even when you're asked different questions, 01:14:44.817 --> 01:14:45.900 align:middle line:90% have your answers line up? 01:14:45.900 --> 01:14:48.120 align:middle line:84% That's what-- people often say, oh, they're twins, 01:14:48.120 --> 01:14:49.230 align:middle line:90% they share so much. 01:14:49.230 --> 01:14:50.940 align:middle line:84% Of course they give the same answers. 01:14:50.940 --> 01:14:53.970 align:middle line:84% And that's what these Bell tests really force us to say. 01:14:53.970 --> 01:14:56.850 align:middle line:84% It's not just that they have similar proclivities, 01:14:56.850 --> 01:15:00.630 align:middle line:84% but really that answering questions they couldn't know 01:15:00.630 --> 01:15:03.810 align:middle line:84% in, advance even different questions, in ways 01:15:03.810 --> 01:15:05.280 align:middle line:84% that their answers still line up, 01:15:05.280 --> 01:15:08.610 align:middle line:84% even if one is in Cambridge, Massachusetts and the other 01:15:08.610 --> 01:15:12.450 align:middle line:84% is in Cambridge, England, or on Alpha Centauri. 01:15:12.450 --> 01:15:15.300 align:middle line:84% If that doesn't raise the hair on the top of one's 01:15:15.300 --> 01:15:17.400 align:middle line:84% head, for those of us who-- for those of you who 01:15:17.400 --> 01:15:18.400 align:middle line:90% have hair on your heads. 01:15:18.400 --> 01:15:19.800 align:middle line:90% That discounts both Gary and me. 01:15:19.800 --> 01:15:22.170 align:middle line:84% If that doesn't make you really stay up late at night, 01:15:22.170 --> 01:15:24.080 align:middle line:90% then I don't know. 01:15:24.080 --> 01:15:25.040 align:middle line:90% Then I'm done. 01:15:25.040 --> 01:15:26.195 align:middle line:90% I got nothing else, right? 01:15:26.195 --> 01:15:28.070 align:middle line:84% You guys weren't upset about the double slit. 01:15:28.070 --> 01:15:29.090 align:middle line:90% I did my best. 01:15:29.090 --> 01:15:33.940 align:middle line:84% Entanglement should just-- kind of ups the ante a little bit. 01:15:33.940 --> 01:15:34.910 align:middle line:90% Any questions on that? 01:15:34.910 --> 01:15:39.380 align:middle line:90% 01:15:39.380 --> 01:15:39.880 align:middle line:90% OK. 01:15:39.880 --> 01:15:41.050 align:middle line:90% I've stunned you into silence. 01:15:41.050 --> 01:15:42.467 align:middle line:84% It's also a busy time of the term, 01:15:42.467 --> 01:15:43.610 align:middle line:90% so don't worry about that. 01:15:43.610 --> 01:15:46.030 align:middle line:84% We'll meet again at our regular time on Monday. 01:15:46.030 --> 01:15:47.740 align:middle line:84% In the meantime, I encourage you, please, 01:15:47.740 --> 01:15:49.690 align:middle line:84% please do start thinking about paper 2. 01:15:49.690 --> 01:15:51.227 align:middle line:90% It's a chunkier assignment. 01:15:51.227 --> 01:15:52.810 align:middle line:84% You don't want to leave it to the end. 01:15:52.810 --> 01:15:54.393 align:middle line:84% And of course, as always, please don't 01:15:54.393 --> 01:15:56.050 align:middle line:84% hesitate to contact me or the teaching 01:15:56.050 --> 01:15:59.250 align:middle line:84% assistants for any questions in the meantime. 01:15:59.250 --> 01:16:11.000 align:middle line:90%