WEBVTT 00:00:00.000 --> 00:00:08.364 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:08.364 --> 00:00:10.225 align:middle line:90% 00:00:10.225 --> 00:00:11.600 align:middle line:84% DAVID KAISER: With today's class, 00:00:11.600 --> 00:00:14.600 align:middle line:84% we're now transitioning into the last main kind of unit 00:00:14.600 --> 00:00:17.400 align:middle line:90% thematically for the course. 00:00:17.400 --> 00:00:21.590 align:middle line:84% And so the last main section is trying 00:00:21.590 --> 00:00:26.630 align:middle line:84% to follow one set of threads, a very set of ideas 00:00:26.630 --> 00:00:31.790 align:middle line:84% and developments weaving from the end of the Second World War 00:00:31.790 --> 00:00:33.800 align:middle line:90% toward more recent time periods. 00:00:33.800 --> 00:00:36.770 align:middle line:84% And I would joke and say we're going to follow 00:00:36.770 --> 00:00:39.350 align:middle line:84% what our objectively the single most important developments 00:00:39.350 --> 00:00:41.253 align:middle line:90% in the history of human thought. 00:00:41.253 --> 00:00:42.920 align:middle line:84% That might not be how everyone reads it. 00:00:42.920 --> 00:00:44.180 align:middle line:84% There are things that I find actually 00:00:44.180 --> 00:00:46.430 align:middle line:84% really cool and exciting, so that's why I chose them. 00:00:46.430 --> 00:00:48.403 align:middle line:84% I'll just be honest, this is my favorite. 00:00:48.403 --> 00:00:49.820 align:middle line:84% And so this last unit, we're going 00:00:49.820 --> 00:00:53.000 align:middle line:84% to be looking at some examples within-- 00:00:53.000 --> 00:00:57.770 align:middle line:84% trends within postwar physics, looking in particular 00:00:57.770 --> 00:01:03.620 align:middle line:84% at a merger that gets cobbled together 00:01:03.620 --> 00:01:05.900 align:middle line:84% between high-energy physics, nuclear and particle 00:01:05.900 --> 00:01:09.155 align:middle line:84% physics, and certain ideas about astrophysics and cosmology. 00:01:09.155 --> 00:01:11.280 align:middle line:84% So there are many, many other exciting developments 00:01:11.280 --> 00:01:12.007 align:middle line:90% then and now. 00:01:12.007 --> 00:01:13.590 align:middle line:84% Of course, I actually don't mean these 00:01:13.590 --> 00:01:17.310 align:middle line:84% are the only important ones, but these ideas are themselves, 00:01:17.310 --> 00:01:20.070 align:middle line:84% I think, still very exciting, and they also 00:01:20.070 --> 00:01:23.130 align:middle line:84% offer a way to trace through some 00:01:23.130 --> 00:01:27.510 align:middle line:84% of the further embedding of very particular sometimes very 00:01:27.510 --> 00:01:32.320 align:middle line:84% esoteric-sounding ideas in concrete-changing institutions, 00:01:32.320 --> 00:01:35.430 align:middle line:84% social contexts, political features, and all the rest. 00:01:35.430 --> 00:01:37.950 align:middle line:84% So we can read these developments 00:01:37.950 --> 00:01:42.000 align:middle line:84% in high-energy theory and cosmology and astrophysics 00:01:42.000 --> 00:01:45.600 align:middle line:84% as taking place in shifting contexts by real people, 00:01:45.600 --> 00:01:49.020 align:middle line:84% much as we work so hard to do with the first and the earlier 00:01:49.020 --> 00:01:50.410 align:middle line:90% sections of the class as well. 00:01:50.410 --> 00:01:51.930 align:middle line:84% So that's our we're going to launch 00:01:51.930 --> 00:01:55.220 align:middle line:90% in now for our last main unit. 00:01:55.220 --> 00:01:57.220 align:middle line:84% And again, if you have any questions, of course, 00:01:57.220 --> 00:01:59.230 align:middle line:84% please don't hesitate to reach out to me. 00:01:59.230 --> 00:02:02.040 align:middle line:84% So I think I'll go ahead and start sharing screen, 00:02:02.040 --> 00:02:04.560 align:middle line:84% and we'll launch into this last part of our adventure. 00:02:04.560 --> 00:02:07.580 align:middle line:90% 00:02:07.580 --> 00:02:12.080 align:middle line:84% So today, we're going to focus on some developments that 00:02:12.080 --> 00:02:16.790 align:middle line:84% would begin to coalesce very soon after the Second World War 00:02:16.790 --> 00:02:20.393 align:middle line:84% into what came to be called high-energy physics. 00:02:20.393 --> 00:02:22.560 align:middle line:84% That wasn't quite what people called it at the time, 00:02:22.560 --> 00:02:24.740 align:middle line:84% but we recognize it today as heading 00:02:24.740 --> 00:02:26.270 align:middle line:84% toward things like particle physics 00:02:26.270 --> 00:02:28.130 align:middle line:90% or high-energy phenomena. 00:02:28.130 --> 00:02:30.050 align:middle line:84% And we're going to see that this wasn't-- 00:02:30.050 --> 00:02:33.800 align:middle line:84% as you might expect, this work was not unfolding in a vacuum. 00:02:33.800 --> 00:02:38.180 align:middle line:84% In fact, it was tethered in some surprising ways to developments 00:02:38.180 --> 00:02:39.350 align:middle line:90% during the Second World War. 00:02:39.350 --> 00:02:42.470 align:middle line:84% So it really does, we see again, a pivot from that middle unit 00:02:42.470 --> 00:02:44.600 align:middle line:84% of the course as we head toward the last unit. 00:02:44.600 --> 00:02:47.190 align:middle line:90% 00:02:47.190 --> 00:02:49.440 align:middle line:84% So our three main steps for today, we're 00:02:49.440 --> 00:02:51.430 align:middle line:84% going to actually turn the clock back a bit. 00:02:51.430 --> 00:02:54.900 align:middle line:84% We're going to go back to the early days of quantum theory, 00:02:54.900 --> 00:02:56.700 align:middle line:84% even before the Second World War, 00:02:56.700 --> 00:03:00.060 align:middle line:84% and we'll see that there was a lot of work being done 00:03:00.060 --> 00:03:01.980 align:middle line:90% in the 1920s and 30 seconds. 00:03:01.980 --> 00:03:05.460 align:middle line:84% And then for the second and third parts of today's class, 00:03:05.460 --> 00:03:07.650 align:middle line:84% we're going to see how some of those efforts 00:03:07.650 --> 00:03:10.650 align:middle line:84% were spun in new directions, how they 00:03:10.650 --> 00:03:15.840 align:middle line:84% got a kind of unexpected series of inputs or even jolts 00:03:15.840 --> 00:03:18.480 align:middle line:84% from many physicists' experience during the Second World War. 00:03:18.480 --> 00:03:21.130 align:middle line:90% So that's our plan for today. 00:03:21.130 --> 00:03:24.630 align:middle line:84% So if you remember from not too, too long ago in our class, 00:03:24.630 --> 00:03:28.470 align:middle line:84% we were looking at what came together in rapid order 00:03:28.470 --> 00:03:33.420 align:middle line:84% around 1925 and '26 that came to be called quantum mechanics. 00:03:33.420 --> 00:03:36.090 align:middle line:84% We saw Heisenberg's work on what came 00:03:36.090 --> 00:03:39.450 align:middle line:84% to be known as matrix mechanics, and very soon after that, 00:03:39.450 --> 00:03:42.090 align:middle line:84% Erwin Schrodinger began working on wave mechanics. 00:03:42.090 --> 00:03:43.830 align:middle line:84% And before too long, several people 00:03:43.830 --> 00:03:46.420 align:middle line:84% had shown that these two very different-looking 00:03:46.420 --> 00:03:50.350 align:middle line:84% approaches actually were mathematically relatable. 00:03:50.350 --> 00:03:52.900 align:middle line:84% So we had something called quantum mechanics in hand 00:03:52.900 --> 00:03:55.360 align:middle line:90% really by 1926, '27. 00:03:55.360 --> 00:03:58.420 align:middle line:84% Right on the heels of those developments, 00:03:58.420 --> 00:04:01.780 align:middle line:84% many of those same physicists began right away 00:04:01.780 --> 00:04:04.840 align:middle line:84% trying to apply these new ideas and the new formalism 00:04:04.840 --> 00:04:05.890 align:middle line:90% to radiation. 00:04:05.890 --> 00:04:07.930 align:middle line:84% Not just to say the structure of an atom, 00:04:07.930 --> 00:04:12.730 align:middle line:84% like the Bohr atom as it gets rethought en route 00:04:12.730 --> 00:04:14.890 align:middle line:84% to things like Schrodinger's approach to hydrogen, 00:04:14.890 --> 00:04:16.510 align:middle line:84% but actually trying to apply some 00:04:16.510 --> 00:04:19.300 align:middle line:84% of those same conceptual ideas even 00:04:19.300 --> 00:04:23.590 align:middle line:84% to Maxwell's treatment of light, to electromagnetic radiation. 00:04:23.590 --> 00:04:26.290 align:middle line:84% After all, as we did see a number of weeks ago, 00:04:26.290 --> 00:04:29.620 align:middle line:84% Einstein himself had suggested that light might consist 00:04:29.620 --> 00:04:31.720 align:middle line:84% of light quanta that, by this point, 00:04:31.720 --> 00:04:34.240 align:middle line:84% came to be called photons, Einstein 00:04:34.240 --> 00:04:37.930 align:middle line:84% suggested that, as we saw, all the way back in 1905. 00:04:37.930 --> 00:04:43.540 align:middle line:84% By 1927, by early 1927, Paul Dirac, the British physicist, 00:04:43.540 --> 00:04:45.850 align:middle line:84% some of whose work we looked at recently, 00:04:45.850 --> 00:04:50.230 align:middle line:84% he actually proposed a way to try 00:04:50.230 --> 00:04:53.710 align:middle line:84% to reconcile quantum theory with Maxwellian waves, 00:04:53.710 --> 00:04:57.310 align:middle line:84% with electromagnetic fields as early as 1927. 00:04:57.310 --> 00:04:58.810 align:middle line:84% This is where many historians now 00:04:58.810 --> 00:05:03.010 align:middle line:84% date the earliest stirrings of quantum field theory. 00:05:03.010 --> 00:05:07.420 align:middle line:84% In particular, Dirac's work came to be called Quantum 00:05:07.420 --> 00:05:09.430 align:middle line:90% Electrodynamics, or QED. 00:05:09.430 --> 00:05:13.090 align:middle line:84% It was a quantum treatment of Maxwellian electrodynamics. 00:05:13.090 --> 00:05:17.410 align:middle line:84% And you can see the first main article which really launches 00:05:17.410 --> 00:05:22.330 align:middle line:84% this was submitted already in February of 1927, quite early 00:05:22.330 --> 00:05:25.610 align:middle line:84% in the study of quantum theory more generally. 00:05:25.610 --> 00:05:27.350 align:middle line:84% So again, as we've seen many times, 00:05:27.350 --> 00:05:31.520 align:middle line:84% you would have seen this even before well before this course, 00:05:31.520 --> 00:05:35.660 align:middle line:84% physicists, including very mathematically adept ones like 00:05:35.660 --> 00:05:37.890 align:middle line:84% Paul Dirac, they'd known for a long, 00:05:37.890 --> 00:05:41.060 align:middle line:84% long time that when we have a arbitrary, 00:05:41.060 --> 00:05:42.950 align:middle line:90% very complicated-looking curve-- 00:05:42.950 --> 00:05:46.100 align:middle line:84% let's say some function that has some very strange-looking 00:05:46.100 --> 00:05:51.140 align:middle line:84% pattern to it, we can always decompose that arbitrary curve 00:05:51.140 --> 00:05:55.210 align:middle line:84% or that funny-looking curve thanks to Fourier analysis 00:05:55.210 --> 00:05:59.290 align:middle line:84% and treat it as the sum or the superposition 00:05:59.290 --> 00:06:01.750 align:middle line:84% of very regular waves, very purely 00:06:01.750 --> 00:06:06.320 align:middle line:84% periodic waves, of varying wavelength or frequency. 00:06:06.320 --> 00:06:08.170 align:middle line:84% And as long as we get the weights right-- 00:06:08.170 --> 00:06:11.980 align:middle line:84% 2 parts of this, 3 plus 4i parts of that, the weights 00:06:11.980 --> 00:06:13.370 align:middle line:90% could be complex numbers. 00:06:13.370 --> 00:06:16.780 align:middle line:84% But in general, if we weight these kind of basis vectors 00:06:16.780 --> 00:06:20.530 align:middle line:84% or waves of known properties and we tune the weights 00:06:20.530 --> 00:06:22.270 align:middle line:84% very carefully, then we can actually 00:06:22.270 --> 00:06:25.225 align:middle line:84% reproduce virtually any arbitrary-looking curve, 00:06:25.225 --> 00:06:27.100 align:middle line:84% and that's the foundation of Fourier analysis 00:06:27.100 --> 00:06:28.450 align:middle line:90% going back to the 18th century. 00:06:28.450 --> 00:06:29.960 align:middle line:90% That part is not new. 00:06:29.960 --> 00:06:32.710 align:middle line:84% What Dirac wondered was, could something like that 00:06:32.710 --> 00:06:34.960 align:middle line:84% be used, even in this quantum realm, 00:06:34.960 --> 00:06:38.020 align:middle line:84% for a funny-looking wave or a field extended 00:06:38.020 --> 00:06:41.890 align:middle line:84% in space like a Maxwellian electromagnetic field? 00:06:41.890 --> 00:06:45.580 align:middle line:84% Now his first thought, as early as 1927, 00:06:45.580 --> 00:06:50.320 align:middle line:84% was that the approach won't be merely or only Fourier 00:06:50.320 --> 00:06:51.190 align:middle line:90% analysis. 00:06:51.190 --> 00:06:53.390 align:middle line:84% After all, even Heisenberg had found, 00:06:53.390 --> 00:06:56.450 align:middle line:84% much to his initial confusion, that when 00:06:56.450 --> 00:06:59.420 align:middle line:84% trying to deal with these quantum mechanical ideas, 00:06:59.420 --> 00:07:03.020 align:middle line:84% certain quantities no longer obeyed ordinary rules, say, 00:07:03.020 --> 00:07:06.350 align:middle line:84% of multiplication, of these so-called commutators 00:07:06.350 --> 00:07:08.930 align:middle line:84% or commutation relations kept popping up 00:07:08.930 --> 00:07:12.050 align:middle line:84% where the product of two quantities 00:07:12.050 --> 00:07:14.510 align:middle line:84% would depend on the order in which they were multiplied. 00:07:14.510 --> 00:07:17.270 align:middle line:84% An x times p was not the same as p times x. 00:07:17.270 --> 00:07:19.790 align:middle line:84% And in fact, the difference between those two 00:07:19.790 --> 00:07:22.200 align:middle line:84% scaled with Planck's constant was an indication 00:07:22.200 --> 00:07:25.200 align:middle line:84% there was something inherently quantum mechanical going on. 00:07:25.200 --> 00:07:28.160 align:middle line:84% So Dirac realized-- or suggested-- 00:07:28.160 --> 00:07:31.340 align:middle line:84% that something like that must be going on with these quantum 00:07:31.340 --> 00:07:33.090 align:middle line:90% fields as well. 00:07:33.090 --> 00:07:35.630 align:middle line:84% And so it won't just be a Fourier analysis. 00:07:35.630 --> 00:07:39.170 align:middle line:84% You have to get some of this order of operations structure 00:07:39.170 --> 00:07:41.930 align:middle line:84% to come in, but he wanted to keep 00:07:41.930 --> 00:07:45.470 align:middle line:84% as much as possible of this quite familiar Fourier 00:07:45.470 --> 00:07:46.590 align:middle line:90% approach. 00:07:46.590 --> 00:07:51.488 align:middle line:84% And so he began introducing this notion of fields extended 00:07:51.488 --> 00:07:53.780 align:middle line:84% through space and time, and did, going all the way back 00:07:53.780 --> 00:07:55.970 align:middle line:84% to Michael Faraday, which we looked at in some 00:07:55.970 --> 00:07:58.430 align:middle line:84% of the very earliest classes this term, 00:07:58.430 --> 00:08:00.350 align:middle line:90% but having to do a little tweak. 00:08:00.350 --> 00:08:05.420 align:middle line:84% It wouldn't just be a Faraday or a Maxwell field distributed 00:08:05.420 --> 00:08:07.160 align:middle line:84% through space changing over time, 00:08:07.160 --> 00:08:09.590 align:middle line:84% it would have a little structure-- so a little added 00:08:09.590 --> 00:08:12.810 align:middle line:84% structure to take into account this kind of new quantumness, 00:08:12.810 --> 00:08:13.310 align:middle line:90% let's say. 00:08:13.310 --> 00:08:16.070 align:middle line:84% The fact that these quantities would obey sometimes 00:08:16.070 --> 00:08:18.960 align:middle line:84% some funny commutation relations and all that. 00:08:18.960 --> 00:08:23.000 align:middle line:84% So he wanted to get as close as he could to Fourier analysis 00:08:23.000 --> 00:08:25.880 align:middle line:84% while recognizing that some things might need a little bit 00:08:25.880 --> 00:08:27.870 align:middle line:90% extra mathematical structure. 00:08:27.870 --> 00:08:30.590 align:middle line:84% So if we look at this expression, 00:08:30.590 --> 00:08:33.620 align:middle line:84% the new parts that Dirac has added really 00:08:33.620 --> 00:08:36.049 align:middle line:84% can be summarized in this a and this thing that's 00:08:36.049 --> 00:08:37.773 align:middle line:90% called a dagger. 00:08:37.773 --> 00:08:39.440 align:middle line:84% These are clearly related to each other. 00:08:39.440 --> 00:08:42.900 align:middle line:84% They're complex conjugates of each other, 00:08:42.900 --> 00:08:44.400 align:middle line:90% they're very similar to that. 00:08:44.400 --> 00:08:47.240 align:middle line:84% And in Dirac's hands, these things weren't only 00:08:47.240 --> 00:08:51.680 align:middle line:84% numbers that were kind like an ordinary Fourier analysis, 00:08:51.680 --> 00:08:53.630 align:middle line:84% these were actually quantum operators. 00:08:53.630 --> 00:08:57.950 align:middle line:84% They did stuff or represented specific kinds of changes 00:08:57.950 --> 00:08:59.610 align:middle line:90% to the physical system. 00:08:59.610 --> 00:09:02.960 align:middle line:84% So the one over here that is called a dagger, that 00:09:02.960 --> 00:09:05.330 align:middle line:84% could be interpreted, Dirac suggested, 00:09:05.330 --> 00:09:08.420 align:middle line:84% as creating one quantum, one photon 00:09:08.420 --> 00:09:12.410 align:middle line:84% in a very particular state, a state of given energy 00:09:12.410 --> 00:09:13.550 align:middle line:90% and momentum. 00:09:13.550 --> 00:09:17.720 align:middle line:84% And this a with a hat but with no dagger 00:09:17.720 --> 00:09:19.730 align:middle line:84% would be interpreted as taking away, 00:09:19.730 --> 00:09:24.170 align:middle line:84% as annihilating or absorbing one photon in a definite state 00:09:24.170 --> 00:09:25.950 align:middle line:90% of energy and momentum. 00:09:25.950 --> 00:09:29.150 align:middle line:84% And so-- and then you'd have different weights in front 00:09:29.150 --> 00:09:30.600 align:middle line:90% of each of those processes. 00:09:30.600 --> 00:09:32.660 align:middle line:84% So you have standard Fourier modes, just 00:09:32.660 --> 00:09:36.840 align:middle line:84% like in ordinary 18th century mathematics. 00:09:36.840 --> 00:09:38.750 align:middle line:84% These would be ways of representing, 00:09:38.750 --> 00:09:41.750 align:middle line:84% say, a photon in a state of definite momentum. 00:09:41.750 --> 00:09:43.940 align:middle line:84% You would have this kind of accounting to say, 00:09:43.940 --> 00:09:49.490 align:middle line:84% did you add or subtract a specific quantized excitation 00:09:49.490 --> 00:09:50.630 align:middle line:90% of that field? 00:09:50.630 --> 00:09:52.965 align:middle line:84% That's what the a and a dagger show. 00:09:52.965 --> 00:09:54.590 align:middle line:84% And then again, you have something more 00:09:54.590 --> 00:09:55.790 align:middle line:90% like Fourier weights. 00:09:55.790 --> 00:09:59.330 align:middle line:84% How many of those do you add in to get back your arbitrary 00:09:59.330 --> 00:10:01.487 align:middle line:90% field through space and time? 00:10:01.487 --> 00:10:02.945 align:middle line:84% So if we do this kind of accounting 00:10:02.945 --> 00:10:06.890 align:middle line:84% and it's clearly inspired by ordinary Fourier analysis. 00:10:06.890 --> 00:10:09.170 align:middle line:84% Then Dirac showed we could represent 00:10:09.170 --> 00:10:10.940 align:middle line:84% the state of this field-- let's say 00:10:10.940 --> 00:10:13.610 align:middle line:84% it's the Maxwellian electromagnetic field, 00:10:13.610 --> 00:10:17.000 align:middle line:84% you can represent it as a collection of these quanta 00:10:17.000 --> 00:10:20.210 align:middle line:90% in various well-defined states. 00:10:20.210 --> 00:10:23.180 align:middle line:84% The field was nothing other than a collection 00:10:23.180 --> 00:10:27.710 align:middle line:84% of quantum particles in states of definite energy momentum. 00:10:27.710 --> 00:10:31.280 align:middle line:84% And then if a field changed over space or over time, 00:10:31.280 --> 00:10:34.460 align:middle line:84% you could interpret that as changing your Fourier weights, 00:10:34.460 --> 00:10:37.730 align:middle line:84% as either emitting or absorbing quanta 00:10:37.730 --> 00:10:38.960 align:middle line:90% in these specific states. 00:10:38.960 --> 00:10:42.170 align:middle line:84% So it's a way of just doing accounting so far. 00:10:42.170 --> 00:10:44.780 align:middle line:84% Not too long after that, though-- 00:10:44.780 --> 00:10:48.620 align:middle line:84% really, just weeks after Dirac submitted this first paper, 00:10:48.620 --> 00:10:51.270 align:middle line:84% Heisenberg introduced his uncertainty principle, 00:10:51.270 --> 00:10:56.050 align:middle line:84% and not long after that, spring/summer of 1927, 00:10:56.050 --> 00:10:58.920 align:middle line:84% a number of people began trying to these ideas together. 00:10:58.920 --> 00:11:03.420 align:middle line:84% Put together Dirac's accounting scheme to represent some field 00:11:03.420 --> 00:11:07.560 align:middle line:84% extended through space and time as a collection of quanta 00:11:07.560 --> 00:11:10.980 align:middle line:84% in particular states, but then to add 00:11:10.980 --> 00:11:15.630 align:middle line:84% in this very critical caveat from quantum physics 00:11:15.630 --> 00:11:17.970 align:middle line:90% of the uncertainty principle. 00:11:17.970 --> 00:11:19.380 align:middle line:84% The uncertainty principle that we 00:11:19.380 --> 00:11:21.690 align:middle line:84% looked at together briefly in class a number of weeks 00:11:21.690 --> 00:11:25.950 align:middle line:84% ago concerned a trade-off between position and momentum 00:11:25.950 --> 00:11:30.810 align:middle line:84% along that direction in space, say delta x and delta p. 00:11:30.810 --> 00:11:32.550 align:middle line:84% It was very quickly shown by people 00:11:32.550 --> 00:11:34.620 align:middle line:84% like Heisenberg right around the same time. 00:11:34.620 --> 00:11:36.450 align:middle line:84% There were other pairs of quantities 00:11:36.450 --> 00:11:40.230 align:middle line:84% that had similar trade-offs that also obeyed an uncertainty 00:11:40.230 --> 00:11:42.780 align:middle line:84% principle relationship, one of the most important 00:11:42.780 --> 00:11:45.150 align:middle line:84% being the energy involved in a given 00:11:45.150 --> 00:11:48.720 align:middle line:84% physical process and the time over which that process 00:11:48.720 --> 00:11:49.890 align:middle line:90% unfolded. 00:11:49.890 --> 00:11:53.680 align:middle line:84% So if these two quantities could not be precisely specified 00:11:53.680 --> 00:11:56.860 align:middle line:84% at the same time to arbitrary precision, 00:11:56.860 --> 00:11:58.900 align:middle line:84% then much like position and momentum, 00:11:58.900 --> 00:12:01.390 align:middle line:84% there would be this inevitable trade-off. 00:12:01.390 --> 00:12:03.640 align:middle line:84% And in the context of Dirac's kind 00:12:03.640 --> 00:12:07.780 align:middle line:84% of Fourier-inspired accounting trick where the field could 00:12:07.780 --> 00:12:11.830 align:middle line:84% be decomposed as collections of quanta in various states, 00:12:11.830 --> 00:12:14.380 align:middle line:84% the way many people began to interpret the uncertainty 00:12:14.380 --> 00:12:17.590 align:middle line:84% principle in the light of Dirac's formalism 00:12:17.590 --> 00:12:23.230 align:middle line:84% was that certain quanta, certain excitations of that field 00:12:23.230 --> 00:12:25.510 align:middle line:84% could temporarily break the rules. 00:12:25.510 --> 00:12:29.230 align:middle line:84% They could temporarily violate the conservation of energy 00:12:29.230 --> 00:12:32.590 align:middle line:84% by borrowing some energy, delta E, as long 00:12:32.590 --> 00:12:35.380 align:middle line:84% as they paid it back sufficiently quickly 00:12:35.380 --> 00:12:38.200 align:middle line:84% so that there was a trade-off between the precision 00:12:38.200 --> 00:12:39.880 align:middle line:84% with which the energy of that state 00:12:39.880 --> 00:12:42.920 align:middle line:84% could be specified at a given moment in time 00:12:42.920 --> 00:12:48.340 align:middle line:84% and the time over which these conservation-violating 00:12:48.340 --> 00:12:50.290 align:middle line:90% processes could unfold. 00:12:50.290 --> 00:12:53.740 align:middle line:84% So again, if you go back to Dirac's accounting scheme, 00:12:53.740 --> 00:12:55.510 align:middle line:84% that suggested to many people, again, 00:12:55.510 --> 00:12:59.860 align:middle line:84% as early as 1927 and 1928, very early in this game, 00:12:59.860 --> 00:13:03.580 align:middle line:84% that the exact state of a quantum field at any given time 00:13:03.580 --> 00:13:06.473 align:middle line:84% could never be stipulated to arbitrary precision. 00:13:06.473 --> 00:13:08.140 align:middle line:84% There would always exist what came to be 00:13:08.140 --> 00:13:10.540 align:middle line:90% called quantum fluctuations. 00:13:10.540 --> 00:13:12.040 align:middle line:84% These were associated with something 00:13:12.040 --> 00:13:14.110 align:middle line:90% called virtual particles. 00:13:14.110 --> 00:13:17.350 align:middle line:84% Particles that were in some state of energy and momentum, 00:13:17.350 --> 00:13:19.480 align:middle line:90% but they had-- they were like-- 00:13:19.480 --> 00:13:22.810 align:middle line:84% they had broken the rules temporarily. 00:13:22.810 --> 00:13:26.350 align:middle line:84% They were virtual particles by exploiting this energy 00:13:26.350 --> 00:13:30.160 align:middle line:84% uncertainty relation to borrow energy 00:13:30.160 --> 00:13:33.370 align:middle line:84% to be in a particular state briefly and then pay it back 00:13:33.370 --> 00:13:35.390 align:middle line:90% correspondingly quickly. 00:13:35.390 --> 00:13:36.960 align:middle line:84% The first time I heard about this, 00:13:36.960 --> 00:13:38.210 align:middle line:90% I was actually in high school. 00:13:38.210 --> 00:13:40.070 align:middle line:84% I was really enamored of these popular books 00:13:40.070 --> 00:13:41.450 align:middle line:90% by the writer Isaac Asimov. 00:13:41.450 --> 00:13:44.180 align:middle line:84% I'm sure of you know Asimov's writings, including 00:13:44.180 --> 00:13:48.170 align:middle line:84% his famous fiction novels, science fiction novels. 00:13:48.170 --> 00:13:50.510 align:middle line:84% He wrote a number, I think, really very nice 00:13:50.510 --> 00:13:53.040 align:middle line:84% popular books-- nonfiction books as well. 00:13:53.040 --> 00:13:56.240 align:middle line:84% And I remember coming across this idea in this book here, 00:13:56.240 --> 00:13:58.430 align:middle line:84% part of his series called Understanding Physics. 00:13:58.430 --> 00:14:01.130 align:middle line:84% And he had, I think, a really lovely metaphor 00:14:01.130 --> 00:14:03.830 align:middle line:84% for this notion of virtual processes 00:14:03.830 --> 00:14:06.622 align:middle line:84% that could temporarily violate the conservation of energy, 00:14:06.622 --> 00:14:08.330 align:middle line:84% and he described them that they're really 00:14:08.330 --> 00:14:10.730 align:middle line:84% kind of like misbehaving schoolchildren. 00:14:10.730 --> 00:14:12.980 align:middle line:84% That when the teacher has her back, his or her 00:14:12.980 --> 00:14:14.680 align:middle line:84% back turned, children might break 00:14:14.680 --> 00:14:16.430 align:middle line:84% the rules of the classroom-- in this case, 00:14:16.430 --> 00:14:18.830 align:middle line:84% passing a note or something more extraordinary 00:14:18.830 --> 00:14:21.230 align:middle line:84% like standing on your desk and dropping your pants 00:14:21.230 --> 00:14:23.370 align:middle line:90% or whatever it might be. 00:14:23.370 --> 00:14:26.150 align:middle line:84% There could be all kinds of rulebreaking before the teacher 00:14:26.150 --> 00:14:27.500 align:middle line:90% turns back around. 00:14:27.500 --> 00:14:31.370 align:middle line:84% And given-- depending on the nature of the violation, 00:14:31.370 --> 00:14:34.830 align:middle line:84% the students would be wise to wrap it up correspondingly 00:14:34.830 --> 00:14:35.370 align:middle line:90% quickly. 00:14:35.370 --> 00:14:38.225 align:middle line:84% If you're only passing a note, that's not such a big deal. 00:14:38.225 --> 00:14:39.600 align:middle line:84% You might take your time with it. 00:14:39.600 --> 00:14:43.165 align:middle line:84% If you're doing something more outrageous 00:14:43.165 --> 00:14:44.790 align:middle line:84% compared to the rules of the classroom, 00:14:44.790 --> 00:14:47.740 align:middle line:84% you better get it done with a correspondingly shorter delta 00:14:47.740 --> 00:14:48.240 align:middle line:90% t. 00:14:48.240 --> 00:14:50.400 align:middle line:84% That always-- I found that actually very helpful. 00:14:50.400 --> 00:14:52.590 align:middle line:84% This notion that elementary particles 00:14:52.590 --> 00:14:54.360 align:middle line:84% might be like elementary school children 00:14:54.360 --> 00:14:56.790 align:middle line:84% temporarily violating what seemed 00:14:56.790 --> 00:14:58.890 align:middle line:90% to be the laws of nature. 00:14:58.890 --> 00:14:59.400 align:middle line:90% OK. 00:14:59.400 --> 00:15:03.750 align:middle line:84% So why would that matter in the context of Dirac's formulation 00:15:03.750 --> 00:15:05.310 align:middle line:90% of quantized fields? 00:15:05.310 --> 00:15:08.160 align:middle line:84% Again, people began putting these pieces together already 00:15:08.160 --> 00:15:10.450 align:middle line:90% by the late 1920s. 00:15:10.450 --> 00:15:13.230 align:middle line:84% So imagine trying to understand the behavior 00:15:13.230 --> 00:15:16.260 align:middle line:84% of a single electron that's traveling 00:15:16.260 --> 00:15:20.730 align:middle line:84% through space over time between locations, say, x1 and x2. 00:15:20.730 --> 00:15:24.580 align:middle line:84% And let's say it has a definite particular value of momentum. 00:15:24.580 --> 00:15:28.210 align:middle line:84% If these virtual processes could be happening all the time-- 00:15:28.210 --> 00:15:30.960 align:middle line:84% in fact, if they can't even be avoid it because they arise 00:15:30.960 --> 00:15:33.360 align:middle line:84% from the uncertainty principle, then there's 00:15:33.360 --> 00:15:37.380 align:middle line:84% some chance that along the way during its journey, 00:15:37.380 --> 00:15:41.850 align:middle line:84% this electron would spit out a virtual photon, 00:15:41.850 --> 00:15:45.660 align:middle line:84% a virtual quantum of light, as long as it reabsorbed it 00:15:45.660 --> 00:15:47.410 align:middle line:90% some short time later. 00:15:47.410 --> 00:15:50.730 align:middle line:84% So it could be-- during its path from x1 to x2, 00:15:50.730 --> 00:15:53.280 align:middle line:84% there could be a so-called virtual process 00:15:53.280 --> 00:15:57.030 align:middle line:84% or a quantum fluctuation such that what we thought originally 00:15:57.030 --> 00:15:59.050 align:middle line:84% was just a single particle moving 00:15:59.050 --> 00:16:04.270 align:middle line:84% by itself might temporarily dissociate into the electron 00:16:04.270 --> 00:16:07.840 align:middle line:84% and some virtual quantum of the Maxwell field, 00:16:07.840 --> 00:16:12.490 align:middle line:84% a virtual photon, that borrows some energy and some momentum k 00:16:12.490 --> 00:16:15.880 align:middle line:84% and pays it back some short time later. 00:16:15.880 --> 00:16:19.450 align:middle line:84% What became so curious to these physicists early on 00:16:19.450 --> 00:16:22.030 align:middle line:84% is that this photon, according to this scheme, 00:16:22.030 --> 00:16:24.100 align:middle line:84% could borrow any amount of energy. 00:16:24.100 --> 00:16:26.290 align:middle line:84% The borrowed energy, the violation 00:16:26.290 --> 00:16:29.560 align:middle line:84% of the conservation of energy as dictated by the uncertainty 00:16:29.560 --> 00:16:33.520 align:middle line:84% principle could be any amount as long as it paid it back 00:16:33.520 --> 00:16:35.410 align:middle line:90% correspondingly quickly. 00:16:35.410 --> 00:16:39.220 align:middle line:84% So there was no-- this seemed to be no upper limit on how much 00:16:39.220 --> 00:16:41.800 align:middle line:84% energy or momentum could be borrowed, 00:16:41.800 --> 00:16:44.860 align:middle line:84% not quite stolen, by this virtual particle. 00:16:44.860 --> 00:16:46.720 align:middle line:84% So then the question became, could you 00:16:46.720 --> 00:16:49.750 align:middle line:84% calculate likely scenarios in the context 00:16:49.750 --> 00:16:54.350 align:middle line:84% of these temporarily rulebreaking virtual particles? 00:16:54.350 --> 00:16:56.050 align:middle line:84% So Dirac and others went on to show, 00:16:56.050 --> 00:17:00.330 align:middle line:84% based on the equations of how these fields seem to evolve, 00:17:00.330 --> 00:17:02.610 align:middle line:84% that the probability amplitude-- something 00:17:02.610 --> 00:17:05.369 align:middle line:84% like-- remember, like the square root of the probability, 00:17:05.369 --> 00:17:08.490 align:middle line:84% roughly speaking-- would go like 1 over k 00:17:08.490 --> 00:17:12.030 align:middle line:84% where k was the momentum to both emit and then reabsorb 00:17:12.030 --> 00:17:13.440 align:middle line:90% one of these virtual photons. 00:17:13.440 --> 00:17:16.619 align:middle line:84% And that makes some at least intuitive sense. 00:17:16.619 --> 00:17:20.430 align:middle line:84% That's like saying, it's less likely for a very, very high 00:17:20.430 --> 00:17:23.250 align:middle line:84% momentum state to be temporarily created and destroyed. 00:17:23.250 --> 00:17:25.710 align:middle line:84% It's more likely to have borrowed 00:17:25.710 --> 00:17:28.020 align:middle line:84% to have broken the rules more softly, let's say. 00:17:28.020 --> 00:17:29.497 align:middle line:90% So that makes some sense. 00:17:29.497 --> 00:17:31.830 align:middle line:84% It was derived of course, much more carefully than that, 00:17:31.830 --> 00:17:33.413 align:middle line:84% but you can make a little bit of sense 00:17:33.413 --> 00:17:35.730 align:middle line:84% of the nature of the relationship. 00:17:35.730 --> 00:17:40.140 align:middle line:84% Less likely for very high-energy virtual processes. 00:17:40.140 --> 00:17:43.710 align:middle line:84% But nonetheless, as long as the virtual photon paid it back 00:17:43.710 --> 00:17:46.870 align:middle line:84% correspondingly quickly, there seemed to be no upper limit. 00:17:46.870 --> 00:17:50.220 align:middle line:84% And so therefore, to calculate the likelihood for the electron 00:17:50.220 --> 00:17:53.370 align:middle line:84% to travel from x1 to x2, you have to sum up 00:17:53.370 --> 00:17:55.710 align:middle line:90% all of these possibilities. 00:17:55.710 --> 00:17:59.280 align:middle line:84% The virtual photon could have borrowed some value k or k 00:17:59.280 --> 00:18:01.150 align:middle line:84% prime or k double prime all the way, 00:18:01.150 --> 00:18:03.920 align:middle line:84% in principle, all the way up to infinity. 00:18:03.920 --> 00:18:06.555 align:middle line:84% So when you start summing up all of these possibilities, 00:18:06.555 --> 00:18:07.930 align:middle line:84% you actually get something called 00:18:07.930 --> 00:18:10.990 align:middle line:84% a logarithmic divergence, which is a fancy way of saying, 00:18:10.990 --> 00:18:12.920 align:middle line:90% the integral blows up. 00:18:12.920 --> 00:18:15.280 align:middle line:84% It goes like the log of k, but you're 00:18:15.280 --> 00:18:16.840 align:middle line:84% supposed to integrate k the way up 00:18:16.840 --> 00:18:19.240 align:middle line:84% to infinity as if this photon had literally borrowed 00:18:19.240 --> 00:18:21.460 align:middle line:84% an infinite amount of energy, everything up-- 00:18:21.460 --> 00:18:24.380 align:middle line:84% every possibility up to infinity. 00:18:24.380 --> 00:18:27.460 align:middle line:84% So it looked like the likelihood for an electron 00:18:27.460 --> 00:18:31.600 align:middle line:84% to travel from point x1 to point x2 became infinite. 00:18:31.600 --> 00:18:33.970 align:middle line:84% That didn't seem to make much sense. 00:18:33.970 --> 00:18:35.950 align:middle line:84% The way people began to describe it, again, 00:18:35.950 --> 00:18:38.470 align:middle line:84% by the late 1920s and early '30s was 00:18:38.470 --> 00:18:41.620 align:middle line:84% to say the electron's self-energy diverges. 00:18:41.620 --> 00:18:43.180 align:middle line:84% The energy due to its interaction 00:18:43.180 --> 00:18:46.420 align:middle line:84% with its own electromagnetic field blew up. 00:18:46.420 --> 00:18:49.810 align:middle line:84% If the self-energy is diverging, that 00:18:49.810 --> 00:18:54.040 align:middle line:84% was similar to saying its own mass was infinite, 00:18:54.040 --> 00:18:56.890 align:middle line:84% because as we saw many, many weeks ago, according 00:18:56.890 --> 00:18:59.200 align:middle line:84% to Einstein's relation, E equals MC squared, 00:18:59.200 --> 00:19:02.410 align:middle line:84% an energy and a mass are essentially interchangeable. 00:19:02.410 --> 00:19:04.270 align:middle line:84% So it was like saying that the quantum 00:19:04.270 --> 00:19:07.840 align:middle line:84% corrections to the mass of an electron became infinite 00:19:07.840 --> 00:19:10.940 align:middle line:84% and that did not make a lot of sense. 00:19:10.940 --> 00:19:13.300 align:middle line:84% So the very first idea, which a number of physicists 00:19:13.300 --> 00:19:15.670 align:middle line:84% began exploring, again, by the early '30s, 00:19:15.670 --> 00:19:17.960 align:middle line:84% was to simply cut off the integrals. 00:19:17.960 --> 00:19:21.040 align:middle line:84% Let's just say that these virtual photons could not 00:19:21.040 --> 00:19:24.220 align:middle line:84% actually borrow literally infinite momentum. 00:19:24.220 --> 00:19:25.870 align:middle line:90% Maybe there's some upper limit. 00:19:25.870 --> 00:19:28.210 align:middle line:84% And there's some upper-- some finite upper limit 00:19:28.210 --> 00:19:32.410 align:middle line:84% to the integral, then you should have a large, perhaps, 00:19:32.410 --> 00:19:33.810 align:middle line:90% but finite answer. 00:19:33.810 --> 00:19:35.560 align:middle line:84% But there are a couple problems with that, 00:19:35.560 --> 00:19:40.580 align:middle line:84% which, again, were identified very early in the 1930s. 00:19:40.580 --> 00:19:45.040 align:middle line:84% If you just put in by hand some upper momentum, 00:19:45.040 --> 00:19:48.010 align:middle line:84% up to which one integrates these expressions, 00:19:48.010 --> 00:19:49.930 align:middle line:84% then these equations would no longer 00:19:49.930 --> 00:19:52.600 align:middle line:84% respect the symmetries of special relativity. 00:19:52.600 --> 00:19:55.630 align:middle line:84% You would be inserting a preferred momentum 00:19:55.630 --> 00:19:58.650 align:middle line:84% that if you just tried to describe the same process 00:19:58.650 --> 00:20:00.780 align:middle line:84% while riding very quickly on a train, 00:20:00.780 --> 00:20:02.730 align:middle line:84% you'd get totally different answers. 00:20:02.730 --> 00:20:05.550 align:middle line:84% Even though this was a series of equations 00:20:05.550 --> 00:20:07.570 align:middle line:84% that began with Maxwell's equations, 00:20:07.570 --> 00:20:11.490 align:middle line:84% which, of course, almost by definition, Einstein showed us, 00:20:11.490 --> 00:20:15.250 align:middle line:84% must obey the symmetries of special relativity. 00:20:15.250 --> 00:20:18.870 align:middle line:84% So how would you have a self-consistent description 00:20:18.870 --> 00:20:21.180 align:middle line:84% of elementary particles that could also 00:20:21.180 --> 00:20:23.490 align:middle line:84% be consistent with relativity if you just 00:20:23.490 --> 00:20:26.070 align:middle line:84% put in by hand some upper limit to these integrals? 00:20:26.070 --> 00:20:28.650 align:middle line:84% That didn't seem to work just mathematically. 00:20:28.650 --> 00:20:30.630 align:middle line:84% A little more deeply conceptually, 00:20:30.630 --> 00:20:33.540 align:middle line:84% what that suggested was that if you just put in a cut-off 00:20:33.540 --> 00:20:37.140 align:middle line:84% by hand at some highest but finite value of this 00:20:37.140 --> 00:20:39.840 align:middle line:84% of borrowed momentum for these virtual particles, 00:20:39.840 --> 00:20:43.950 align:middle line:84% then any two observers would basically disagree on anything 00:20:43.950 --> 00:20:45.360 align:middle line:90% they tried to calculate. 00:20:45.360 --> 00:20:48.360 align:middle line:84% By losing these symmetries of special relativity, 00:20:48.360 --> 00:20:50.880 align:middle line:84% then there was no reason for any two calculations 00:20:50.880 --> 00:20:52.860 align:middle line:84% ever to agree for any two observers. 00:20:52.860 --> 00:20:56.280 align:middle line:84% That seemed like a pretty big challenge. 00:20:56.280 --> 00:20:58.580 align:middle line:84% Meanwhile, it wasn't only that an electron moving 00:20:58.580 --> 00:21:01.280 align:middle line:84% through space could temporarily emit 00:21:01.280 --> 00:21:03.500 align:middle line:84% and then reabsorb a virtual photon, 00:21:03.500 --> 00:21:05.720 align:middle line:84% the inverse process could happen as well, 00:21:05.720 --> 00:21:09.920 align:middle line:84% all within the scheme of Dirac's accounting system for quantum 00:21:09.920 --> 00:21:11.720 align:middle line:90% electrodynamics, or QED. 00:21:11.720 --> 00:21:14.870 align:middle line:84% So the inverse could happen in which a single photon is 00:21:14.870 --> 00:21:19.220 align:middle line:84% moving through space from, say, location x1 toward location 00:21:19.220 --> 00:21:19.880 align:middle line:90% x2-- 00:21:19.880 --> 00:21:21.460 align:middle line:90% sorry. 00:21:21.460 --> 00:21:24.640 align:middle line:84% But mid-course, it could actually temporarily, 00:21:24.640 --> 00:21:27.490 align:middle line:84% spontaneously emit and then later 00:21:27.490 --> 00:21:30.220 align:middle line:84% reabsorb a pair of virtual particles-- 00:21:30.220 --> 00:21:34.810 align:middle line:84% in this case, a virtual electron and a virtual positron, 00:21:34.810 --> 00:21:37.310 align:middle line:84% the antimatter cousin of the electron. 00:21:37.310 --> 00:21:39.400 align:middle line:84% This would conserve electric charge, 00:21:39.400 --> 00:21:42.550 align:middle line:84% it would violate conservation of energy only 00:21:42.550 --> 00:21:46.010 align:middle line:84% temporarily just like in that virtual photon case. 00:21:46.010 --> 00:21:48.400 align:middle line:84% So if the uncertainty principle combined 00:21:48.400 --> 00:21:52.720 align:middle line:84% with Dirac's accounting scheme was to hold, 00:21:52.720 --> 00:21:54.850 align:middle line:84% then this kind of virtual process 00:21:54.850 --> 00:21:58.250 align:middle line:84% should be happening all the time as well. 00:21:58.250 --> 00:22:01.630 align:middle line:84% So then one could ask about an electrons interaction again 00:22:01.630 --> 00:22:05.050 align:middle line:84% with itself, with its own electromagnetic field. 00:22:05.050 --> 00:22:07.870 align:middle line:84% After all, the electric and magnetic fields 00:22:07.870 --> 00:22:11.680 align:middle line:84% on this quantized view merely consisted 00:22:11.680 --> 00:22:13.030 align:middle line:90% of collections of photons. 00:22:13.030 --> 00:22:15.850 align:middle line:84% That was the whole point of Dirac's accounting scheme. 00:22:15.850 --> 00:22:17.785 align:middle line:84% How many photons in this state, how many 00:22:17.785 --> 00:22:18.910 align:middle line:90% photons in the other state? 00:22:18.910 --> 00:22:23.250 align:middle line:84% That's what the Maxwell field consisted of on this new view. 00:22:23.250 --> 00:22:26.990 align:middle line:84% So if a single photon could spontaneously 00:22:26.990 --> 00:22:29.660 align:middle line:84% emit these electron-positron pairs, 00:22:29.660 --> 00:22:31.820 align:middle line:84% then that must be happening all the time 00:22:31.820 --> 00:22:34.280 align:middle line:84% in the vicinity of any charged particle 00:22:34.280 --> 00:22:35.960 align:middle line:84% because the electromagnetic field, 00:22:35.960 --> 00:22:41.570 align:middle line:84% that electric and magnetic field propagating outward from that 00:22:41.570 --> 00:22:44.630 align:middle line:84% charged particle could always be subject 00:22:44.630 --> 00:22:47.090 align:middle line:84% to these virtual processes, at least in principle. 00:22:47.090 --> 00:22:48.860 align:middle line:90% So the picture that emerges-- 00:22:48.860 --> 00:22:52.220 align:middle line:84% this one looks like a daisy, some sort of flower, 00:22:52.220 --> 00:22:55.250 align:middle line:84% we have the original electron you actually asking about, 00:22:55.250 --> 00:22:58.130 align:middle line:84% and then this spontaneous set of pairs 00:22:58.130 --> 00:23:01.280 align:middle line:84% of positrons and electrons that could 00:23:01.280 --> 00:23:04.220 align:middle line:84% be popping in and out of existence all the time because 00:23:04.220 --> 00:23:05.760 align:middle line:90% of the uncertainty principle. 00:23:05.760 --> 00:23:08.930 align:middle line:84% And this became known as vacuum polarization. 00:23:08.930 --> 00:23:10.770 align:middle line:84% Polarization, as you may remember, 00:23:10.770 --> 00:23:12.530 align:middle line:84% is just a fancy way of saying that there's 00:23:12.530 --> 00:23:14.990 align:middle line:90% a preferred direction in space. 00:23:14.990 --> 00:23:18.140 align:middle line:84% The idea was that all these virtual particles would become 00:23:18.140 --> 00:23:22.580 align:middle line:84% oriented in space because the positively-charged positrons 00:23:22.580 --> 00:23:24.770 align:middle line:84% would be attracted to the original electron, 00:23:24.770 --> 00:23:26.990 align:middle line:84% the negatively-charged virtual electrons 00:23:26.990 --> 00:23:29.180 align:middle line:84% would be repelled by the original electron. 00:23:29.180 --> 00:23:31.670 align:middle line:84% you'd have this kind of real structure 00:23:31.670 --> 00:23:33.770 align:middle line:84% in space, an orientation, or indeed, 00:23:33.770 --> 00:23:35.940 align:middle line:90% a polarization of space. 00:23:35.940 --> 00:23:39.560 align:middle line:84% So what seemed to be empty space itself, the vacuum, 00:23:39.560 --> 00:23:41.180 align:middle line:90% might not be so empty. 00:23:41.180 --> 00:23:41.850 align:middle line:90% After all. 00:23:41.850 --> 00:23:45.020 align:middle line:84% In fact, it might have a space-dependent structure 00:23:45.020 --> 00:23:48.890 align:middle line:84% to it, and that came to be called vacuum polarization. 00:23:48.890 --> 00:23:51.200 align:middle line:84% So one could, again, try to account 00:23:51.200 --> 00:23:53.780 align:middle line:90% for the size of this effect. 00:23:53.780 --> 00:23:55.730 align:middle line:84% What would happen if you tried to measure 00:23:55.730 --> 00:23:57.800 align:middle line:90% the charge of that electron? 00:23:57.800 --> 00:24:00.560 align:middle line:84% Well, you would no longer encounter just the electron, 00:24:00.560 --> 00:24:02.900 align:middle line:84% so this thinking went, but actually, the electron 00:24:02.900 --> 00:24:08.070 align:middle line:84% plus this cloud of these virtual charged particle pairs. 00:24:08.070 --> 00:24:11.150 align:middle line:84% So if you're measuring the electron from over here, 00:24:11.150 --> 00:24:14.360 align:middle line:84% you're really seeing the complete effect of the electron 00:24:14.360 --> 00:24:19.190 align:middle line:84% plus this screen of the virtual pairs around it. 00:24:19.190 --> 00:24:20.600 align:middle line:84% So you could then ask, well, what 00:24:20.600 --> 00:24:25.190 align:middle line:84% was the impact of the screening from those virtual-charged 00:24:25.190 --> 00:24:26.030 align:middle line:90% particles? 00:24:26.030 --> 00:24:27.740 align:middle line:84% You could try to do the same trick 00:24:27.740 --> 00:24:31.460 align:middle line:84% as the self-energy calculation for the electron. 00:24:31.460 --> 00:24:35.840 align:middle line:84% Count up all the ways that these virtual pairs could temporarily 00:24:35.840 --> 00:24:38.600 align:middle line:84% borrow some energy momentum, as long as they paid it back. 00:24:38.600 --> 00:24:42.660 align:middle line:84% They could, in principal, borrow an infinite amount of momentum. 00:24:42.660 --> 00:24:45.380 align:middle line:84% And so once again, the integral diverged. 00:24:45.380 --> 00:24:47.060 align:middle line:84% It diverged again logarithmically, 00:24:47.060 --> 00:24:48.380 align:middle line:90% it was soon clarified. 00:24:48.380 --> 00:24:50.390 align:middle line:84% So it was like saying that the electron had 00:24:50.390 --> 00:24:53.570 align:middle line:84% some charge of seven in appropriate units 00:24:53.570 --> 00:24:58.260 align:middle line:84% plus infinity, just like it had a mass of 5 plus infinity. 00:24:58.260 --> 00:25:00.450 align:middle line:84% It didn't seem to make any sense at all. 00:25:00.450 --> 00:25:02.660 align:middle line:84% And so the effect of these quantum 00:25:02.660 --> 00:25:06.200 align:middle line:84% fluctuations or virtual particles seemed, once again, 00:25:06.200 --> 00:25:10.130 align:middle line:84% to give an infinite change to the simplest 00:25:10.130 --> 00:25:11.930 align:middle line:84% level or approximate equations, and it 00:25:11.930 --> 00:25:14.030 align:middle line:84% didn't seem at all clear how that could 00:25:14.030 --> 00:25:16.600 align:middle line:90% be happening in real life. 00:25:16.600 --> 00:25:19.983 align:middle line:84% So this led to, as you might imagine, a lot of discussion. 00:25:19.983 --> 00:25:21.900 align:middle line:84% This was right on the heels of quantum theory, 00:25:21.900 --> 00:25:25.290 align:middle line:84% this is still in this period when the physicists, especially 00:25:25.290 --> 00:25:27.810 align:middle line:84% in Central Europe, were able to communicate 00:25:27.810 --> 00:25:30.280 align:middle line:84% all the time by letter, by conference, by visiting 00:25:30.280 --> 00:25:30.780 align:middle line:90% each other. 00:25:30.780 --> 00:25:32.322 align:middle line:84% They'd go to Bohr's Institute, they'd 00:25:32.322 --> 00:25:34.000 align:middle line:90% visit in Gottingen and so on. 00:25:34.000 --> 00:25:37.380 align:middle line:84% And so this became like the hot topic, one of the pressing 00:25:37.380 --> 00:25:42.000 align:middle line:84% concerns for this early kind of quantum theory generation. 00:25:42.000 --> 00:25:44.400 align:middle line:84% Many of the leading physicists-- again, 00:25:44.400 --> 00:25:46.470 align:middle line:90% mostly in Europe at this time-- 00:25:46.470 --> 00:25:50.550 align:middle line:84% who were confronting these new challenges of quantum processes 00:25:50.550 --> 00:25:52.470 align:middle line:84% that simply couldn't be calculated, 00:25:52.470 --> 00:25:55.800 align:middle line:84% couldn't yield any finite answers, 00:25:55.800 --> 00:25:58.260 align:middle line:84% they thought this pointed to a really big 00:25:58.260 --> 00:26:00.390 align:middle line:90% next conceptual revolution. 00:26:00.390 --> 00:26:03.120 align:middle line:84% Remember, the revolution, as they 00:26:03.120 --> 00:26:05.550 align:middle line:84% thought of it, a revolution of quantum theory, 00:26:05.550 --> 00:26:07.080 align:middle line:90% was like months old. 00:26:07.080 --> 00:26:10.020 align:middle line:84% They'd just gone through this seemingly huge 00:26:10.020 --> 00:26:12.430 align:middle line:84% head-spinning rupture of the uncertainty principle 00:26:12.430 --> 00:26:15.150 align:middle line:84% and noncommuting matrices and all these things. 00:26:15.150 --> 00:26:18.640 align:middle line:84% In their own memories, some of their own earlier years 00:26:18.640 --> 00:26:21.040 align:middle line:84% as younger physicists, they tried 00:26:21.040 --> 00:26:25.060 align:middle line:84% to work through and incorporate the large conceptual shifts 00:26:25.060 --> 00:26:26.350 align:middle line:90% associated with relativity. 00:26:26.350 --> 00:26:28.540 align:middle line:84% They think, OK, we're due for another one. 00:26:28.540 --> 00:26:33.790 align:middle line:84% And this became a steady drumbeat interpretation 00:26:33.790 --> 00:26:36.880 align:middle line:84% by people like Niels Bohr and Werner Heisenberg. 00:26:36.880 --> 00:26:37.720 align:middle line:90% That that's OK. 00:26:37.720 --> 00:26:39.470 align:middle line:84% We've been stuck like this before. 00:26:39.470 --> 00:26:42.160 align:middle line:84% This shows that we're going to learn something really, really 00:26:42.160 --> 00:26:46.090 align:middle line:84% drastically different about how nature works to finally get 00:26:46.090 --> 00:26:47.960 align:middle line:90% around these virtual processes. 00:26:47.960 --> 00:26:49.720 align:middle line:84% So one example that Heisenberg floated 00:26:49.720 --> 00:26:53.860 align:middle line:84% by the mid-1930s, for example, was that maybe space 00:26:53.860 --> 00:26:55.390 align:middle line:90% is actually not continuous. 00:26:55.390 --> 00:26:57.140 align:middle line:90% That's a pretty big rupture. 00:26:57.140 --> 00:27:00.280 align:middle line:84% Maybe there's some shortest possible length, 00:27:00.280 --> 00:27:03.900 align:middle line:84% some fundamental shortest length in space, 00:27:03.900 --> 00:27:07.550 align:middle line:84% that space is not a continuous fabric 00:27:07.550 --> 00:27:09.740 align:middle line:84% as described by Einstein's relativity, 00:27:09.740 --> 00:27:12.050 align:middle line:84% but in fact, maybe there's a quantumness to space 00:27:12.050 --> 00:27:14.360 align:middle line:90% itself, a discreteness. 00:27:14.360 --> 00:27:15.920 align:middle line:84% If that were true, then there would 00:27:15.920 --> 00:27:19.070 align:middle line:84% have to exist some largest possible momentum that would 00:27:19.070 --> 00:27:21.810 align:middle line:90% go inversely with that length. 00:27:21.810 --> 00:27:24.440 align:middle line:84% And so there'd be a finite largest momentum, 00:27:24.440 --> 00:27:27.020 align:middle line:84% That means all those integrals would not actually 00:27:27.020 --> 00:27:30.740 align:middle line:84% go to infinity, they would go to the physically allowed largest 00:27:30.740 --> 00:27:35.540 align:middle line:84% maximum length, and that would give a mathematical cure 00:27:35.540 --> 00:27:37.850 align:middle line:84% to these poorly-behaved integrals, 00:27:37.850 --> 00:27:40.100 align:middle line:84% but at an enormous conceptual cost. 00:27:40.100 --> 00:27:45.080 align:middle line:84% I mean, yet another pretty significant rethinking 00:27:45.080 --> 00:27:47.870 align:middle line:84% of space and time, the very fabric 00:27:47.870 --> 00:27:51.922 align:middle line:84% of a continuous space-time would no longer hold. 00:27:51.922 --> 00:27:53.630 align:middle line:84% So that seems like a pretty big challenge 00:27:53.630 --> 00:27:56.570 align:middle line:84% to relativity even if it did give a reason why 00:27:56.570 --> 00:27:59.330 align:middle line:90% these integrals might be finite. 00:27:59.330 --> 00:28:01.640 align:middle line:84% Other people said, well, maybe the problem 00:28:01.640 --> 00:28:04.560 align:middle line:84% isn't with the nature of space, maybe the problem 00:28:04.560 --> 00:28:07.110 align:middle line:84% is with our understanding of the Uncertainty Principle. 00:28:07.110 --> 00:28:09.330 align:middle line:84% This whole idea of these virtual particles, 00:28:09.330 --> 00:28:11.910 align:middle line:84% these quantum fluctuations in the state 00:28:11.910 --> 00:28:15.030 align:middle line:84% of an extended quantum field, that really seemed 00:28:15.030 --> 00:28:17.280 align:middle line:84% to come directly from the uncertainty principle, 00:28:17.280 --> 00:28:20.760 align:middle line:84% that delta e delta t being non-zero. 00:28:20.760 --> 00:28:22.530 align:middle line:84% So others said, well, maybe the fault 00:28:22.530 --> 00:28:26.850 align:middle line:84% is with quantum theory itself, and that this seemingly bedrock 00:28:26.850 --> 00:28:29.280 align:middle line:84% feature of quantum mechanics, Heisenberg's Uncertainty 00:28:29.280 --> 00:28:31.020 align:middle line:84% Principle, maybe that isn't quite 00:28:31.020 --> 00:28:34.470 align:middle line:84% right has to be either tossed out or somehow amended. 00:28:34.470 --> 00:28:38.160 align:middle line:84% And so the mathematical challenges of getting 00:28:38.160 --> 00:28:42.210 align:middle line:84% integrals to converge, which is a well-defined, though very 00:28:42.210 --> 00:28:45.630 align:middle line:84% hard challenge, that inspired in many of these folks 00:28:45.630 --> 00:28:48.720 align:middle line:84% by the late '20s and throughout the 1930s, visions 00:28:48.720 --> 00:28:51.930 align:middle line:84% of some sort of grand rupture in how they would 00:28:51.930 --> 00:28:54.750 align:middle line:84% have to understand space, time, and matter at a very 00:28:54.750 --> 00:28:55.660 align:middle line:90% deep level. 00:28:55.660 --> 00:28:57.570 align:middle line:90% So I'm going to pause there. 00:28:57.570 --> 00:28:58.950 align:middle line:90% Some time for questions on that. 00:28:58.950 --> 00:29:00.210 align:middle line:90% I see something in the chat. 00:29:00.210 --> 00:29:02.590 align:middle line:90% 00:29:02.590 --> 00:29:03.090 align:middle line:90% Ah, good. 00:29:03.090 --> 00:29:04.680 align:middle line:84% So Sarah asks what led to the idea 00:29:04.680 --> 00:29:06.252 align:middle line:90% that virtual particles existed? 00:29:06.252 --> 00:29:06.960 align:middle line:90% Thank you, Sarah. 00:29:06.960 --> 00:29:08.040 align:middle line:90% I should have clarified. 00:29:08.040 --> 00:29:09.870 align:middle line:90% This was a hypothesis. 00:29:09.870 --> 00:29:13.620 align:middle line:84% It seemed to be, at least to many of these folks, what 00:29:13.620 --> 00:29:18.750 align:middle line:84% looked like a straightforward corollary of the Uncertainty 00:29:18.750 --> 00:29:20.743 align:middle line:84% Principle, but you're absolutely right. 00:29:20.743 --> 00:29:22.410 align:middle line:84% One of the first questions they had was, 00:29:22.410 --> 00:29:24.540 align:middle line:84% did we misinterpret the Uncertainty Principle? 00:29:24.540 --> 00:29:26.970 align:middle line:84% Or is there some kind of theoretical out 00:29:26.970 --> 00:29:29.370 align:middle line:84% that will enable us to keep the Uncertainty Principle 00:29:29.370 --> 00:29:32.160 align:middle line:84% but not attribute this particular kind of process 00:29:32.160 --> 00:29:33.370 align:middle line:90% to nature? 00:29:33.370 --> 00:29:35.640 align:middle line:84% Another question was like, if they're virtual, 00:29:35.640 --> 00:29:37.260 align:middle line:84% if they're just stealing this energy 00:29:37.260 --> 00:29:40.080 align:middle line:84% and paying it back so quickly, how would we ever know? 00:29:40.080 --> 00:29:42.000 align:middle line:84% It was the kind of-- if a tree falls 00:29:42.000 --> 00:29:43.583 align:middle line:90% in a forest kind of argument. 00:29:43.583 --> 00:29:45.750 align:middle line:84% So some people said scrap the Uncertainty Principle, 00:29:45.750 --> 00:29:52.510 align:middle line:84% others said this is kind of an unobservable theoretical story. 00:29:52.510 --> 00:29:54.970 align:middle line:84% And so if your equations blow up, then so what? 00:29:54.970 --> 00:29:56.970 align:middle line:84% That doesn't mean nature's doing this after all, 00:29:56.970 --> 00:29:59.220 align:middle line:84% and we'll come to see how that question, 00:29:59.220 --> 00:30:03.000 align:middle line:84% are these virtual particles part of nature or only an artifact 00:30:03.000 --> 00:30:04.950 align:middle line:84% of the equations, that gets picked up again 00:30:04.950 --> 00:30:06.300 align:middle line:90% after the Second World War. 00:30:06.300 --> 00:30:09.870 align:middle line:84% So there were split decisions, split opinions 00:30:09.870 --> 00:30:13.435 align:middle line:84% throughout the 1920s and '30s on that. 00:30:13.435 --> 00:30:14.310 align:middle line:90% It's a good question. 00:30:14.310 --> 00:30:17.250 align:middle line:84% Fisher asks, in the case of a and a dagger used by Dirac, 00:30:17.250 --> 00:30:20.065 align:middle line:84% was that generalized to all systems points 00:30:20.065 --> 00:30:22.440 align:middle line:84% in space or just approximating them as a quantum harmonic 00:30:22.440 --> 00:30:22.940 align:middle line:90% oscillator? 00:30:22.940 --> 00:30:24.180 align:middle line:90% Good, Fisher. 00:30:24.180 --> 00:30:28.710 align:middle line:84% So the idea was indeed modeled on these harmonic oscillators, 00:30:28.710 --> 00:30:32.220 align:middle line:84% but the idea was that these would be, how we describe, 00:30:32.220 --> 00:30:35.040 align:middle line:84% extended objects through space and changing 00:30:35.040 --> 00:30:39.910 align:middle line:84% over time as these collections of these field oscillations, 00:30:39.910 --> 00:30:41.010 align:middle line:90% of these quanta. 00:30:41.010 --> 00:30:42.840 align:middle line:90% And it was actually Heisenberg-- 00:30:42.840 --> 00:30:45.600 align:middle line:84% I think it was Heisenberg who, a few years later, applied 00:30:45.600 --> 00:30:47.250 align:middle line:90% the same thing even to-- 00:30:47.250 --> 00:30:49.870 align:middle line:84% not just to light like the electromagnetic field, 00:30:49.870 --> 00:30:51.930 align:middle line:84% but even to the field of an electron. 00:30:51.930 --> 00:30:54.930 align:middle line:84% So the idea that gets-- that starts coming together 00:30:54.930 --> 00:30:58.200 align:middle line:84% by the early mid-1930s, really building directly 00:30:58.200 --> 00:31:00.420 align:middle line:84% on this early work by Dirac and others, 00:31:00.420 --> 00:31:04.350 align:middle line:84% was that every kind of matter and radiation in nature 00:31:04.350 --> 00:31:05.730 align:middle line:90% was the hypothesis. 00:31:05.730 --> 00:31:06.480 align:middle line:90% Everything. 00:31:06.480 --> 00:31:10.680 align:middle line:84% Electrons, positrons, protons, neutrons, as soon as they 00:31:10.680 --> 00:31:13.890 align:middle line:84% were known about a few years later, 00:31:13.890 --> 00:31:17.340 align:middle line:84% that they are all excitations, localized 00:31:17.340 --> 00:31:21.270 align:middle line:84% excitations of some kind of underlying quantum fields. 00:31:21.270 --> 00:31:23.700 align:middle line:84% And that to characterize the state of the field, 00:31:23.700 --> 00:31:25.650 align:middle line:84% you could equivalently just add up 00:31:25.650 --> 00:31:28.630 align:middle line:84% how many quanta in this state, how many quanta in that state, 00:31:28.630 --> 00:31:29.130 align:middle line:90% how many-- 00:31:29.130 --> 00:31:30.720 align:middle line:90% much like Fourier analysis. 00:31:30.720 --> 00:31:34.680 align:middle line:84% And so you could change the state of the quantum electron 00:31:34.680 --> 00:31:37.530 align:middle line:84% field by emitting or absorbing electrons, 00:31:37.530 --> 00:31:40.350 align:middle line:84% you could change the state of the quantum Maxwell field 00:31:40.350 --> 00:31:42.210 align:middle line:84% by emitting or absorbing photons, 00:31:42.210 --> 00:31:44.640 align:middle line:84% and that would be like just representing 00:31:44.640 --> 00:31:47.610 align:middle line:84% a continuous function in Fourier space 00:31:47.610 --> 00:31:49.810 align:middle line:84% by manipulating the Fourier weights 00:31:49.810 --> 00:31:51.930 align:middle line:84% or dealing with the original function. 00:31:51.930 --> 00:31:56.730 align:middle line:84% That there should be a kind of equivalent accounting scheme. 00:31:56.730 --> 00:31:58.140 align:middle line:90% But that these were-- 00:31:58.140 --> 00:32:00.060 align:middle line:84% that the particles that people began 00:32:00.060 --> 00:32:03.820 align:middle line:84% measuring in cloud chambers, in cosmic rays-- 00:32:03.820 --> 00:32:06.370 align:middle line:84% from cathode rays, that these were really 00:32:06.370 --> 00:32:09.850 align:middle line:84% localized excitations of a raw quantum field 00:32:09.850 --> 00:32:11.410 align:middle line:90% that somehow came first. 00:32:11.410 --> 00:32:15.400 align:middle line:84% The excitations were accidents of the state of the field, 00:32:15.400 --> 00:32:16.460 align:middle line:90% something like that. 00:32:16.460 --> 00:32:19.720 align:middle line:84% And that it was, again, building on Dirac's early approach 00:32:19.720 --> 00:32:22.780 align:middle line:84% to those others, prominently Heisenberg. 00:32:22.780 --> 00:32:23.905 align:middle line:90% Said, this must happen-- 00:32:23.905 --> 00:32:25.780 align:middle line:84% what if this happens for every form of matter 00:32:25.780 --> 00:32:26.822 align:middle line:90% we've ever thought about? 00:32:26.822 --> 00:32:28.340 align:middle line:90% Electrons, positrons, and so on. 00:32:28.340 --> 00:32:32.290 align:middle line:84% So that was becoming more and more their common set 00:32:32.290 --> 00:32:34.030 align:middle line:84% of assumptions, and that's what led 00:32:34.030 --> 00:32:36.730 align:middle line:84% to things like virtual electron positron pairs, 00:32:36.730 --> 00:32:38.560 align:middle line:84% but then the effects seem to blow up. 00:32:38.560 --> 00:32:41.050 align:middle line:84% Virtual photons, but the effects seem to blow up. 00:32:41.050 --> 00:32:44.170 align:middle line:84% So that's what led to this one step 00:32:44.170 --> 00:32:45.950 align:middle line:84% forward, an infinite number of steps back, 00:32:45.950 --> 00:32:47.590 align:middle line:90% which is not very good progress. 00:32:47.590 --> 00:32:50.067 align:middle line:84% Dealing with infinities is not usually very fun. 00:32:50.067 --> 00:32:50.900 align:middle line:90% Excellent questions. 00:32:50.900 --> 00:32:53.290 align:middle line:84% Any other questions on the virtual particles 00:32:53.290 --> 00:32:54.838 align:middle line:84% quantum field idea more generally? 00:32:54.838 --> 00:32:56.380 align:middle line:84% That was, of course, a bit schematic, 00:32:56.380 --> 00:32:58.088 align:middle line:84% but I want to get at least a gist across. 00:32:58.088 --> 00:33:02.730 align:middle line:90% 00:33:02.730 --> 00:33:04.920 align:middle line:84% If not, that's OK, I'll jump back in. 00:33:04.920 --> 00:33:08.310 align:middle line:84% Because we're going to see how some people return to this 00:33:08.310 --> 00:33:12.090 align:middle line:84% question soon after the end of the Second World War. 00:33:12.090 --> 00:33:14.280 align:middle line:84% So the questions that are already being raised 00:33:14.280 --> 00:33:17.080 align:middle line:90% get seen in a new light. 00:33:17.080 --> 00:33:18.660 align:middle line:84% So as a reminder some of the things 00:33:18.660 --> 00:33:22.080 align:middle line:84% we looked at more recently in class, during the Second World 00:33:22.080 --> 00:33:24.150 align:middle line:84% War, researchers all over the world, 00:33:24.150 --> 00:33:27.420 align:middle line:84% and certainly in many labs in the United States, 00:33:27.420 --> 00:33:31.230 align:middle line:84% got involved in all kinds of basically military-oriented 00:33:31.230 --> 00:33:33.618 align:middle line:84% projects, and the United States most famously. 00:33:33.618 --> 00:33:35.910 align:middle line:84% That included the Radar Project, and Manhattan Project, 00:33:35.910 --> 00:33:37.980 align:middle line:84% but also dozens and dozens of other projects. 00:33:37.980 --> 00:33:40.590 align:middle line:84% And likewise, for physicists, chemists, 00:33:40.590 --> 00:33:43.320 align:middle line:84% and many kinds of engineers in many, many other parts 00:33:43.320 --> 00:33:44.650 align:middle line:90% of the world. 00:33:44.650 --> 00:33:48.210 align:middle line:84% So at the MIT-based Rad Lab at the Allied Headquarters 00:33:48.210 --> 00:33:51.990 align:middle line:84% for Radar, we saw that researchers, physicists, 00:33:51.990 --> 00:33:55.920 align:middle line:84% many kinds of engineers together had really pushed the envelope 00:33:55.920 --> 00:34:00.480 align:middle line:84% in both producing and measuring electromagnetic radiation 00:34:00.480 --> 00:34:03.340 align:middle line:90% of a particular wavelength band. 00:34:03.340 --> 00:34:06.780 align:middle line:84% So the area that they made the most progress in, 00:34:06.780 --> 00:34:08.639 align:middle line:84% where they focused most of their efforts 00:34:08.639 --> 00:34:10.710 align:middle line:84% was in the microwave region of the spectrum, 00:34:10.710 --> 00:34:14.228 align:middle line:84% and in particular, a centimeter wavelength, 1 to 3 centimeters 00:34:14.228 --> 00:34:16.020 align:middle line:84% because you need to do things like pick out 00:34:16.020 --> 00:34:18.710 align:middle line:84% a periscope of a German U-boat, that kind of thing. 00:34:18.710 --> 00:34:20.440 align:middle line:84% So going to short wavelength as opposed 00:34:20.440 --> 00:34:23.500 align:middle line:84% to multiple meters' length like in radial band. 00:34:23.500 --> 00:34:27.010 align:middle line:84% The microwave spectrum was really operationally critical. 00:34:27.010 --> 00:34:29.500 align:middle line:84% We saw a bunch of examples of that 00:34:29.500 --> 00:34:31.719 align:middle line:90% during the Second World War. 00:34:31.719 --> 00:34:33.010 align:middle line:90% So after the war-- 00:34:33.010 --> 00:34:34.835 align:middle line:84% I still find this mind-boggling given 00:34:34.835 --> 00:34:37.210 align:middle line:84% how hard it is to do anything with the federal government 00:34:37.210 --> 00:34:39.730 align:middle line:90% these days as a researcher. 00:34:39.730 --> 00:34:43.510 align:middle line:84% After the end of the war, there was all this suddenly surplus 00:34:43.510 --> 00:34:45.880 align:middle line:84% equipment at places like the Rad Lab. 00:34:45.880 --> 00:34:48.909 align:middle line:84% And many, many researchers who had worked photon 00:34:48.909 --> 00:34:51.400 align:middle line:84% at the Rad Lab during the war were basically 00:34:51.400 --> 00:34:54.520 align:middle line:84% invited to bring along their pickup trucks 00:34:54.520 --> 00:34:56.408 align:middle line:84% and load up their trucks and just take away 00:34:56.408 --> 00:34:58.700 align:middle line:84% whatever equipment they wanted, almost that informally. 00:34:58.700 --> 00:35:01.570 align:middle line:84% It was only slightly better controlled than that. 00:35:01.570 --> 00:35:03.790 align:middle line:90% It was almost a free-for-all. 00:35:03.790 --> 00:35:06.160 align:middle line:84% There was an enormous amount of surplus equipment 00:35:06.160 --> 00:35:07.930 align:middle line:90% from places like the Rad Lab. 00:35:07.930 --> 00:35:12.280 align:middle line:84% In this case, extraordinarily sensitive electronics tuned, 00:35:12.280 --> 00:35:17.950 align:middle line:84% finely tuned to be very accurate in both producing and measuring 00:35:17.950 --> 00:35:20.710 align:middle line:84% microwave-band electromagnetic radiation, 00:35:20.710 --> 00:35:23.500 align:middle line:84% things like filling this table in our own Building 00:35:23.500 --> 00:35:25.870 align:middle line:90% 4 back from the Rad Lab days. 00:35:25.870 --> 00:35:28.240 align:middle line:84% So that wasn't only researchers at MIT, 00:35:28.240 --> 00:35:30.490 align:middle line:84% this was researchers who were going back to their home 00:35:30.490 --> 00:35:33.220 align:middle line:84% universities throughout North America, many 00:35:33.220 --> 00:35:35.440 align:middle line:84% of them in the United States, to places 00:35:35.440 --> 00:35:38.500 align:middle line:84% like Columbia University, for example, and many other sites. 00:35:38.500 --> 00:35:41.830 align:middle line:84% So you had this very informal dispersal, 00:35:41.830 --> 00:35:46.780 align:middle line:84% I'd say very generous dispersal of equipment that was once 00:35:46.780 --> 00:35:49.120 align:middle line:84% highly, highly coveted because it was so mission 00:35:49.120 --> 00:35:52.960 align:middle line:84% critical to the Radar Project, and it went to many, many labs 00:35:52.960 --> 00:35:57.580 align:middle line:84% across the country for postwar peacetime research 00:35:57.580 --> 00:35:59.300 align:middle line:90% in the microwave band. 00:35:59.300 --> 00:36:01.180 align:middle line:84% And so that's what helped to jumpstart 00:36:01.180 --> 00:36:04.960 align:middle line:84% two very significant sets of experiments that took place 00:36:04.960 --> 00:36:09.250 align:middle line:84% at Columbia very soon after the end of the war by Rad Lab 00:36:09.250 --> 00:36:13.150 align:middle line:84% alumni, by physicists who indeed had spent the wartime working 00:36:13.150 --> 00:36:14.800 align:middle line:90% intensively on radar. 00:36:14.800 --> 00:36:18.520 align:middle line:84% These two new experiments were called the Lamb shift, 00:36:18.520 --> 00:36:20.350 align:middle line:84% which we'll talk about first, and then 00:36:20.350 --> 00:36:23.347 align:middle line:84% something that became known as the anomalous magnetic moment. 00:36:23.347 --> 00:36:25.180 align:middle line:84% And I just want to underscore, both of these 00:36:25.180 --> 00:36:28.240 align:middle line:84% came from people using specific skills 00:36:28.240 --> 00:36:31.030 align:middle line:84% that they had honed during the wartime Rad Lab, 00:36:31.030 --> 00:36:33.550 align:middle line:84% and in each case, literally using equipment 00:36:33.550 --> 00:36:36.872 align:middle line:84% that was surplus from the wartime projects. 00:36:36.872 --> 00:36:38.080 align:middle line:90% Let's look at the Lamb shift. 00:36:38.080 --> 00:36:41.320 align:middle line:84% First it was named for the principal author, Willis Lamb. 00:36:41.320 --> 00:36:43.720 align:middle line:84% That's why it's called the Lamb shift. 00:36:43.720 --> 00:36:45.670 align:middle line:84% So as you may remember, going back 00:36:45.670 --> 00:36:50.080 align:middle line:84% when we looked at quantum theory a few weeks ago, even according 00:36:50.080 --> 00:36:53.380 align:middle line:84% to the Bohr model of the atom from so-called old quantum 00:36:53.380 --> 00:36:56.410 align:middle line:84% theory, let alone from the fancier and fancier treatments 00:36:56.410 --> 00:37:00.167 align:middle line:84% of the hydrogen atom for Schrodinger's equation by 1926, 00:37:00.167 --> 00:37:02.500 align:middle line:84% and that's something we didn't talk about in this class, 00:37:02.500 --> 00:37:06.130 align:middle line:84% but Paul Dirac's relativistic generalization 00:37:06.130 --> 00:37:10.300 align:middle line:84% of Schrodinger's equation, which he introduced around 1928. 00:37:10.300 --> 00:37:13.990 align:middle line:84% According to each of these very highly quantitative treatments 00:37:13.990 --> 00:37:16.750 align:middle line:84% of the electron in a hydrogen atom, 00:37:16.750 --> 00:37:22.180 align:middle line:84% the energy of an electron in the 2S state and the 2P state 00:37:22.180 --> 00:37:23.268 align:middle line:90% should be identical. 00:37:23.268 --> 00:37:25.810 align:middle line:84% There might be a splitting if you put the atom in an external 00:37:25.810 --> 00:37:27.970 align:middle line:84% magnetic field, but just on its own, 00:37:27.970 --> 00:37:29.980 align:middle line:84% in the absence of an external field, 00:37:29.980 --> 00:37:32.740 align:middle line:84% the energy of the electron depended only on the so-called 00:37:32.740 --> 00:37:34.270 align:middle line:90% principal quantum number-- 00:37:34.270 --> 00:37:37.540 align:middle line:84% in this case, 2, not on the angular momentum 00:37:37.540 --> 00:37:41.440 align:middle line:84% that would determine distinguish an S state from a P state. 00:37:41.440 --> 00:37:44.060 align:middle line:84% So according to every single iteration 00:37:44.060 --> 00:37:48.770 align:middle line:84% to date of quantum mechanics, say up to the 1940s, 00:37:48.770 --> 00:37:51.650 align:middle line:84% there should be literally zero difference 00:37:51.650 --> 00:37:53.930 align:middle line:84% in the energy levels of a 2S state 00:37:53.930 --> 00:37:58.080 align:middle line:84% and a 2P state for that lonesome electron in a hydrogen atom. 00:37:58.080 --> 00:38:01.380 align:middle line:84% And instead, very soon after the war, this first author, 00:38:01.380 --> 00:38:02.940 align:middle line:84% Willis Lamb, who was, by this point, 00:38:02.940 --> 00:38:07.920 align:middle line:84% a mid-career accomplished professor 00:38:07.920 --> 00:38:10.080 align:middle line:84% who had spent the wall working on radar, 00:38:10.080 --> 00:38:13.260 align:middle line:84% and his then-graduate student, Robert Rutherford, 00:38:13.260 --> 00:38:15.810 align:middle line:84% they were able to use some of the surplus equipment, 00:38:15.810 --> 00:38:17.910 align:middle line:84% and indeed, the skills they'd really worked on 00:38:17.910 --> 00:38:20.490 align:middle line:84% throughout the war, to actually measure 00:38:20.490 --> 00:38:25.840 align:middle line:84% a very, very tiny difference in the energy levels of exactly 00:38:25.840 --> 00:38:28.810 align:middle line:84% those two states that should have had no difference at all. 00:38:28.810 --> 00:38:31.050 align:middle line:84% In fact, it was roughly one part in a million. 00:38:31.050 --> 00:38:34.020 align:middle line:84% That would have been literally unthinkable 00:38:34.020 --> 00:38:36.460 align:middle line:84% that such a tiny shift could even, in principle, 00:38:36.460 --> 00:38:39.450 align:middle line:84% be measured before these advances from the Rad Lab 00:38:39.450 --> 00:38:40.980 align:middle line:84% with the new equipment and so on. 00:38:40.980 --> 00:38:44.400 align:middle line:84% If one didn't have this kind of exceptionally sensitive 00:38:44.400 --> 00:38:47.970 align:middle line:84% microwave-band electronics, then even if you thought 00:38:47.970 --> 00:38:50.097 align:middle line:84% there might be an energy difference of that order, 00:38:50.097 --> 00:38:52.180 align:middle line:84% no one would ever dream that it could be measured. 00:38:52.180 --> 00:38:55.680 align:middle line:84% That's what begins to change very dramatically after the war 00:38:55.680 --> 00:38:58.780 align:middle line:84% when people like Lamb realized they were measuring exquisitely 00:38:58.780 --> 00:39:02.650 align:middle line:84% sensitive shifts in the context of honing their radar 00:39:02.650 --> 00:39:04.400 align:middle line:90% devices all the time. 00:39:04.400 --> 00:39:07.090 align:middle line:84% Moreover, this energy difference would 00:39:07.090 --> 00:39:10.030 align:middle line:84% be right in the sweet spot for which their electronics had 00:39:10.030 --> 00:39:11.980 align:middle line:90% been designed during the war. 00:39:11.980 --> 00:39:14.290 align:middle line:84% And in fact, I highlight this part 00:39:14.290 --> 00:39:17.080 align:middle line:84% from the very first page of this now-famous article, 00:39:17.080 --> 00:39:20.110 align:middle line:84% they go on and say the great wartime advances 00:39:20.110 --> 00:39:23.200 align:middle line:84% in microwave techniques in the vicinity of 3 centimeters 00:39:23.200 --> 00:39:25.720 align:middle line:84% wavelength, by which he means radar, 00:39:25.720 --> 00:39:29.590 align:middle line:84% made possible the use of new physical tools for the study 00:39:29.590 --> 00:39:31.600 align:middle line:84% of the n equals 2, principal quantum number 00:39:31.600 --> 00:39:35.458 align:middle line:84% 2, fine structure states of the hydrogen atom. 00:39:35.458 --> 00:39:37.750 align:middle line:84% He basically tells us, we can do this because of radar, 00:39:37.750 --> 00:39:38.723 align:middle line:90% that was true. 00:39:38.723 --> 00:39:40.390 align:middle line:84% It was just amazing to see him write it. 00:39:40.390 --> 00:39:44.110 align:middle line:84% The energy difference corresponded to be something-- 00:39:44.110 --> 00:39:46.600 align:middle line:84% corresponding to radiation with wavelength 00:39:46.600 --> 00:39:49.090 align:middle line:84% just under 3 centimeters, exactly the sweet spot 00:39:49.090 --> 00:39:52.030 align:middle line:84% they'd been focusing so much effort on during the war. 00:39:52.030 --> 00:39:53.500 align:middle line:84% In particular, what they found when 00:39:53.500 --> 00:39:57.040 align:middle line:84% they did these experiments was the energy of the 2S state, 00:39:57.040 --> 00:39:59.920 align:middle line:84% the spherically symmetric state for the electron, 00:39:59.920 --> 00:40:04.270 align:middle line:84% was just a little bit higher, by about part in a million, 00:40:04.270 --> 00:40:06.610 align:middle line:84% compared to that of the 2P state. 00:40:06.610 --> 00:40:10.060 align:middle line:84% So the 2P energy state was consistent with these earlier 00:40:10.060 --> 00:40:13.660 align:middle line:84% 1920s calculations for the energy and the 2S state 00:40:13.660 --> 00:40:16.600 align:middle line:84% seemed to be elevated just a little bit by roughly one 00:40:16.600 --> 00:40:17.980 align:middle line:90% part in a million. 00:40:17.980 --> 00:40:19.990 align:middle line:84% So just coming back to Sarah's question 00:40:19.990 --> 00:40:25.360 align:middle line:84% from the chat, this so-called Lamb shift, this tiny but now 00:40:25.360 --> 00:40:29.680 align:middle line:84% remarkably measurable difference in the energies between the 2S 00:40:29.680 --> 00:40:33.610 align:middle line:84% and the 2P states, that began to get a bunch of theorists, 00:40:33.610 --> 00:40:36.220 align:middle line:84% after the war, to go back to this question 00:40:36.220 --> 00:40:37.270 align:middle line:90% of virtual particles. 00:40:37.270 --> 00:40:39.850 align:middle line:84% Could this energy shift, this now measured 00:40:39.850 --> 00:40:43.210 align:middle line:84% experimental result, could that be accounted for? 00:40:43.210 --> 00:40:47.140 align:middle line:84% Could that be attributed to the real physical impact 00:40:47.140 --> 00:40:51.070 align:middle line:84% of these previously hypothetical virtual particles? 00:40:51.070 --> 00:40:52.720 align:middle line:84% This was what looked like the first 00:40:52.720 --> 00:40:56.950 align:middle line:84% maybe direct evidence that could lead to a notion 00:40:56.950 --> 00:40:58.930 align:middle line:84% that virtual particles are part of the world 00:40:58.930 --> 00:41:02.960 align:middle line:84% and not only a pencil-and-paper hypothesis. 00:41:02.960 --> 00:41:05.500 align:middle line:84% So Willis Lamb presented these preliminary results 00:41:05.500 --> 00:41:08.050 align:middle line:84% at a meeting I'll talk more about later today, 00:41:08.050 --> 00:41:09.850 align:middle line:84% a meeting on Shelter Island, which 00:41:09.850 --> 00:41:13.185 align:middle line:84% is a tiny little island just off the north fork of Long Island. 00:41:13.185 --> 00:41:15.310 align:middle line:84% Many of you, I'm sure, have heard about Long Island 00:41:15.310 --> 00:41:16.390 align:middle line:90% near New York City. 00:41:16.390 --> 00:41:19.570 align:middle line:84% And there are some very much smaller islands nearby, 00:41:19.570 --> 00:41:21.820 align:middle line:84% one of which is called Shelter Island. 00:41:21.820 --> 00:41:24.430 align:middle line:84% And there was a meeting there, a private meeting 00:41:24.430 --> 00:41:28.780 align:middle line:84% of physicists in June of 1947 right around the time that they 00:41:28.780 --> 00:41:32.060 align:middle line:84% submitted these results and Lamb had been invited to present. 00:41:32.060 --> 00:41:34.480 align:middle line:84% So on the train ride back to Upstate New 00:41:34.480 --> 00:41:37.720 align:middle line:84% York from that meeting, the Cornell physicist, Hans Bethe, 00:41:37.720 --> 00:41:40.600 align:middle line:84% actually worked out a rough calculation 00:41:40.600 --> 00:41:42.880 align:middle line:84% of what came to be called the Lamb shift by trying 00:41:42.880 --> 00:41:44.830 align:middle line:84% to take literally, to take seriously 00:41:44.830 --> 00:41:46.790 align:middle line:84% this notion of virtual particles. 00:41:46.790 --> 00:41:49.840 align:middle line:84% So we'll look at sketch level of what 00:41:49.840 --> 00:41:52.000 align:middle line:90% Bethe's new argument was like. 00:41:52.000 --> 00:41:54.490 align:middle line:84% This was not the end of the story by any means, 00:41:54.490 --> 00:41:57.490 align:middle line:84% but it really helped reorient a number of physicists 00:41:57.490 --> 00:42:01.280 align:middle line:84% to think seriously about virtual particles in a new light. 00:42:01.280 --> 00:42:04.270 align:middle line:84% So his idea was that if these virtual particles exist, 00:42:04.270 --> 00:42:06.460 align:middle line:84% they're constantly popping in and out of existence. 00:42:06.460 --> 00:42:08.830 align:middle line:84% You couldn't not have them because the Uncertainty 00:42:08.830 --> 00:42:09.640 align:middle line:90% Principle. 00:42:09.640 --> 00:42:12.670 align:middle line:84% Then the original electron in that hydrogen atom 00:42:12.670 --> 00:42:13.690 align:middle line:90% would behave-- 00:42:13.690 --> 00:42:15.830 align:middle line:84% would be subject to something like Brownian motion. 00:42:15.830 --> 00:42:19.810 align:middle line:84% It would be constantly jostled by this bombardment 00:42:19.810 --> 00:42:22.630 align:middle line:84% by these virtual particles that are constantly borrowing 00:42:22.630 --> 00:42:24.320 align:middle line:90% and paying back this energy. 00:42:24.320 --> 00:42:26.720 align:middle line:84% It'll be nudged here, nudged there. 00:42:26.720 --> 00:42:28.720 align:middle line:84% So the effect of that on the behavior 00:42:28.720 --> 00:42:31.840 align:middle line:84% of the original electron in the hydrogen atom, 00:42:31.840 --> 00:42:35.320 align:middle line:84% Bethe suggested, would be smearing out 00:42:35.320 --> 00:42:39.040 align:middle line:84% of the position of that electron because it's constantly 00:42:39.040 --> 00:42:40.300 align:middle line:90% being bombarded. 00:42:40.300 --> 00:42:42.430 align:middle line:84% There'd be some quantum fluctuation 00:42:42.430 --> 00:42:44.410 align:middle line:90% in its position delta r. 00:42:44.410 --> 00:42:46.780 align:middle line:84% So if its position is now smeared out 00:42:46.780 --> 00:42:49.270 align:middle line:84% with some within some finite range, 00:42:49.270 --> 00:42:51.700 align:middle line:84% then how would that impact its potential energy? 00:42:51.700 --> 00:42:55.210 align:middle line:84% After all, remember, in the hydrogen atom, 00:42:55.210 --> 00:42:57.630 align:middle line:84% you have a positively-charged proton 00:42:57.630 --> 00:43:01.590 align:middle line:84% exerting a Coulomb attraction, an electromagnetic attraction 00:43:01.590 --> 00:43:04.120 align:middle line:84% on this negatively-charged electron. 00:43:04.120 --> 00:43:06.420 align:middle line:84% So if the position of the electron 00:43:06.420 --> 00:43:08.400 align:middle line:84% is being constantly jostled because 00:43:08.400 --> 00:43:11.820 align:middle line:84% of the real physical impact of virtual particles, 00:43:11.820 --> 00:43:15.115 align:middle line:84% then you'd have to Taylor-expand the potential energy. 00:43:15.115 --> 00:43:16.740 align:middle line:84% It would be what you originally thought 00:43:16.740 --> 00:43:21.630 align:middle line:84% it was, plus some correction due to the jostling, some delta r 00:43:21.630 --> 00:43:22.482 align:middle line:90% displacement. 00:43:22.482 --> 00:43:24.690 align:middle line:84% And just for the ordinary rules for Taylor expansion, 00:43:24.690 --> 00:43:26.940 align:middle line:84% that would then multiply the first derivative 00:43:26.940 --> 00:43:29.550 align:middle line:84% of the potential in the radial direction. 00:43:29.550 --> 00:43:33.235 align:middle line:84% There'd be a second-order correction proportional 00:43:33.235 --> 00:43:35.610 align:middle line:84% to the second derivative of potential, and, in principle, 00:43:35.610 --> 00:43:36.930 align:middle line:90% on from there. 00:43:36.930 --> 00:43:40.560 align:middle line:84% Bethe next argues that this linear term that goes directly 00:43:40.560 --> 00:43:41.850 align:middle line:90% with the-- 00:43:41.850 --> 00:43:44.880 align:middle line:84% directly proportional to this smearing, 00:43:44.880 --> 00:43:46.230 align:middle line:90% that'll probably average out. 00:43:46.230 --> 00:43:48.810 align:middle line:84% That should cancel out, Bethe suggests, 00:43:48.810 --> 00:43:51.660 align:middle line:84% because the electron's as likely to get kicked downward 00:43:51.660 --> 00:43:54.900 align:middle line:84% toward the proton as to get kicked further away. 00:43:54.900 --> 00:43:58.000 align:middle line:84% So on average, that displacement should vanish. 00:43:58.000 --> 00:44:00.700 align:middle line:84% Even though it's non-zero at any given moment, 00:44:00.700 --> 00:44:03.010 align:middle line:84% its average value would likely vanish. 00:44:03.010 --> 00:44:06.520 align:middle line:84% However, as is typical for any fluctuation phenomena, 00:44:06.520 --> 00:44:09.880 align:middle line:84% in classical physics as well as quantum mechanics, 00:44:09.880 --> 00:44:13.090 align:middle line:84% Bethe next argued that the square of that displacement 00:44:13.090 --> 00:44:15.040 align:middle line:90% will not vanish typically. 00:44:15.040 --> 00:44:19.030 align:middle line:84% That there'll be some non-vanishing average value 00:44:19.030 --> 00:44:23.230 align:middle line:84% for the square of that smearing, the delta r squared term. 00:44:23.230 --> 00:44:26.902 align:middle line:84% It might be tiny, but it won't actually average out to 0. 00:44:26.902 --> 00:44:28.360 align:middle line:84% If that's the case, then you really 00:44:28.360 --> 00:44:31.630 align:middle line:84% better look at into this term that it multiplies 00:44:31.630 --> 00:44:34.150 align:middle line:84% in your expansion, how do you incorporate 00:44:34.150 --> 00:44:36.340 align:middle line:84% the second derivative of the potential? 00:44:36.340 --> 00:44:38.350 align:middle line:84% Well again, if you use the particular potential 00:44:38.350 --> 00:44:40.900 align:middle line:84% of interest, the Coulomb potential, 00:44:40.900 --> 00:44:43.180 align:middle line:84% the second derivative will yield-- 00:44:43.180 --> 00:44:46.420 align:middle line:84% will have most impact really right at the origin, right 00:44:46.420 --> 00:44:48.280 align:middle line:90% at r equals 0. 00:44:48.280 --> 00:44:51.920 align:middle line:84% In fact, it's proportional to a delta function. 00:44:51.920 --> 00:44:55.690 align:middle line:84% And so in a picture form, what that suggested to Bethe 00:44:55.690 --> 00:44:58.800 align:middle line:84% was that because of this unavoidable jostling 00:44:58.800 --> 00:45:00.810 align:middle line:84% of the electron due to constantly 00:45:00.810 --> 00:45:04.080 align:middle line:84% being kicked and pushed around by these virtual particles, 00:45:04.080 --> 00:45:08.760 align:middle line:84% there will be a contribution to the effective potential that 00:45:08.760 --> 00:45:10.710 align:middle line:90% is a positive-- 00:45:10.710 --> 00:45:12.810 align:middle line:84% look at the sign here, it's a positive shift, 00:45:12.810 --> 00:45:16.260 align:middle line:84% some small amount but positive addition 00:45:16.260 --> 00:45:18.720 align:middle line:84% to the energy you otherwise would have calculated, 00:45:18.720 --> 00:45:21.790 align:middle line:84% and it'll only really matter very close to the origin. 00:45:21.790 --> 00:45:24.300 align:middle line:84% So whereas this function would, in principle, fall off 00:45:24.300 --> 00:45:26.880 align:middle line:84% all the way to minus infinity as you go toward the origin 00:45:26.880 --> 00:45:29.520 align:middle line:84% when r-- if r literally could become 0, 00:45:29.520 --> 00:45:30.870 align:middle line:90% this thing would diverge. 00:45:30.870 --> 00:45:34.920 align:middle line:84% Instead, you shift the shape of that function 00:45:34.920 --> 00:45:39.780 align:middle line:84% with this positive correction term that really would only 00:45:39.780 --> 00:45:44.610 align:middle line:84% matter very, very close to the origin, to near r equals 0. 00:45:44.610 --> 00:45:46.950 align:middle line:84% So then he goes on further, he's working this out 00:45:46.950 --> 00:45:49.350 align:middle line:84% on the train ride back up to Schenectady 00:45:49.350 --> 00:45:51.000 align:middle line:90% before he gets back to Ithaca. 00:45:51.000 --> 00:45:52.380 align:middle line:90% It's a pretty good train ride. 00:45:52.380 --> 00:45:54.660 align:middle line:84% Next, Bethe says, well, this really 00:45:54.660 --> 00:45:58.540 align:middle line:84% should preferentially affect electrons in the 2S state 00:45:58.540 --> 00:45:59.925 align:middle line:90% rather than the 2P state. 00:45:59.925 --> 00:46:01.300 align:middle line:84% Remember, Lamb had found not just 00:46:01.300 --> 00:46:03.040 align:middle line:84% that there was a difference, but it 00:46:03.040 --> 00:46:06.670 align:middle line:84% was the 2S state whose energy was ever so slightly raised 00:46:06.670 --> 00:46:08.695 align:middle line:84% compared to the quantum mechanical prediction. 00:46:08.695 --> 00:46:10.570 align:middle line:84% He said, oh, well that also might make sense. 00:46:10.570 --> 00:46:13.780 align:middle line:84% If the positive shift in the potential energy 00:46:13.780 --> 00:46:16.450 align:middle line:84% really only matters very near the origin, 00:46:16.450 --> 00:46:18.730 align:middle line:84% it's the electron in the 2S state-- 00:46:18.730 --> 00:46:21.190 align:middle line:84% that's this spherically symmetric shape 00:46:21.190 --> 00:46:24.070 align:middle line:84% that has any non-vanishing chance, 00:46:24.070 --> 00:46:27.200 align:middle line:84% every now and then to find itself near the origin. 00:46:27.200 --> 00:46:29.050 align:middle line:84% That's the fancy way to say that, is 00:46:29.050 --> 00:46:32.080 align:middle line:84% to say that the quantum wave function for the electron 00:46:32.080 --> 00:46:35.560 align:middle line:84% in the 2S state has a non-vanishing value 00:46:35.560 --> 00:46:37.633 align:middle line:84% at the origin, it has some probability 00:46:37.633 --> 00:46:39.800 align:middle line:84% to be found at the origin at least some of the time, 00:46:39.800 --> 00:46:42.730 align:middle line:84% so its energy will be affected by this modified 00:46:42.730 --> 00:46:44.770 align:middle line:90% shape of the potential. 00:46:44.770 --> 00:46:48.940 align:middle line:84% On the other hand, an electron in the 2P state 00:46:48.940 --> 00:46:51.790 align:middle line:84% has basically no chance ever to be at the origin. 00:46:51.790 --> 00:46:55.870 align:middle line:84% Its wave function literally vanishes at r equals 0, 00:46:55.870 --> 00:46:59.350 align:middle line:84% and so its energy is basically unaffected by the change. 00:46:59.350 --> 00:47:01.480 align:middle line:84% If you're only changing the shape of the potential 00:47:01.480 --> 00:47:04.120 align:middle line:84% in a region that this electron never goes near, 00:47:04.120 --> 00:47:06.470 align:middle line:84% then its energy should be unaffected, 00:47:06.470 --> 00:47:10.070 align:middle line:84% and yet there might be a small but positive shift in the S 00:47:10.070 --> 00:47:10.570 align:middle line:90% state. 00:47:10.570 --> 00:47:11.500 align:middle line:90% That's pretty cool. 00:47:11.500 --> 00:47:14.860 align:middle line:84% It was at least trying to say, here's a plausibility story 00:47:14.860 --> 00:47:17.020 align:middle line:84% for why there might be a shift and why 00:47:17.020 --> 00:47:18.880 align:middle line:84% it might be raising the 2S state-- 00:47:18.880 --> 00:47:20.230 align:middle line:90% the energy of the 2S state. 00:47:20.230 --> 00:47:23.230 align:middle line:84% Now keep in mind, Bethe still couldn't calculate this 00:47:23.230 --> 00:47:25.090 align:middle line:84% exactly, he still had all these integrals 00:47:25.090 --> 00:47:27.553 align:middle line:84% blowing up when he tried to really calculate the effect. 00:47:27.553 --> 00:47:29.470 align:middle line:84% In this case, it was like saying how would you 00:47:29.470 --> 00:47:30.400 align:middle line:90% calculate this part? 00:47:30.400 --> 00:47:31.930 align:middle line:84% That's the part that really comes 00:47:31.930 --> 00:47:34.600 align:middle line:84% from summing up all the borrowed energy from this quantum 00:47:34.600 --> 00:47:35.690 align:middle line:90% fluctuations. 00:47:35.690 --> 00:47:37.480 align:middle line:84% So he did something again pretty darn 00:47:37.480 --> 00:47:40.330 align:middle line:84% clever on that fateful train ride. 00:47:40.330 --> 00:47:42.700 align:middle line:84% He said, well, if this integral is blowing up 00:47:42.700 --> 00:47:46.287 align:middle line:84% like the logarithm, let me put in by hand a maximum value. 00:47:46.287 --> 00:47:48.370 align:middle line:84% So it breaks the symmetries of special relativity, 00:47:48.370 --> 00:47:51.760 align:middle line:84% it has all the illnesses that people had identified 00:47:51.760 --> 00:47:54.820 align:middle line:84% in the 1930s, but he said he had a new motivation 00:47:54.820 --> 00:47:56.710 align:middle line:84% to try because it looked like maybe this is 00:47:56.710 --> 00:47:58.490 align:middle line:90% a measurable effect, after all. 00:47:58.490 --> 00:48:03.620 align:middle line:84% So he chooses a perfectly reasonable maximum momentum 00:48:03.620 --> 00:48:05.270 align:middle line:84% that could have been borrowed, and he 00:48:05.270 --> 00:48:08.750 align:middle line:84% gives it equal to-- basically the equivalent to the rest 00:48:08.750 --> 00:48:10.490 align:middle line:90% energy of an electron. 00:48:10.490 --> 00:48:13.730 align:middle line:84% So he's going to integrate not to infinity, but to imagine 00:48:13.730 --> 00:48:16.070 align:middle line:84% that these virtual particles could have borrowed up 00:48:16.070 --> 00:48:19.247 align:middle line:84% to the energy of an actual electron at rest. 00:48:19.247 --> 00:48:21.330 align:middle line:84% And he said, if it's a little different than that, 00:48:21.330 --> 00:48:23.300 align:middle line:84% the answer will only vary logarithmically. 00:48:23.300 --> 00:48:26.030 align:middle line:84% So that's a pretty good order of magnitude, physically 00:48:26.030 --> 00:48:29.090 align:middle line:84% reasonable scale to try even though mathematically, it's 00:48:29.090 --> 00:48:29.993 align:middle line:90% totally illegitimate. 00:48:29.993 --> 00:48:31.910 align:middle line:84% It breaks all the symmetries and all the rest. 00:48:31.910 --> 00:48:35.420 align:middle line:84% When he put in that value, he found very close agreement 00:48:35.420 --> 00:48:37.580 align:middle line:84% to Lamb's measured result. Not only 00:48:37.580 --> 00:48:40.400 align:middle line:84% was there a positive shift for the 2S state, 00:48:40.400 --> 00:48:43.340 align:middle line:84% he could now estimate semi-plausibly 00:48:43.340 --> 00:48:45.740 align:middle line:84% how big that shift should be and compare it 00:48:45.740 --> 00:48:48.230 align:middle line:84% to these highly-sensitive new results 00:48:48.230 --> 00:48:50.620 align:middle line:90% that Lamb had just presented. 00:48:50.620 --> 00:48:52.720 align:middle line:84% So that starts getting people to think 00:48:52.720 --> 00:48:56.200 align:middle line:84% pretty seriously that virtual particles maybe are actually 00:48:56.200 --> 00:49:00.820 align:middle line:84% part of the world and not just a kind of clever trick on paper. 00:49:00.820 --> 00:49:03.430 align:middle line:84% The other big result right around the same time 00:49:03.430 --> 00:49:06.580 align:middle line:84% that really cemented that new approach turned out 00:49:06.580 --> 00:49:09.550 align:middle line:84% came from the same kinds of historical processes 00:49:09.550 --> 00:49:10.960 align:middle line:90% just down the hall. 00:49:10.960 --> 00:49:14.980 align:middle line:84% So literally down the hall from where Willis Lamb and Robert 00:49:14.980 --> 00:49:16.930 align:middle line:84% Rutherford were working at Columbia, 00:49:16.930 --> 00:49:20.050 align:middle line:84% another group of physicists was working at Columbia, also 00:49:20.050 --> 00:49:23.860 align:middle line:84% Rad Lab veterans, also using surplus equipment 00:49:23.860 --> 00:49:25.570 align:middle line:90% for microwave electronics. 00:49:25.570 --> 00:49:29.710 align:middle line:84% This was a group led by Isidor Rabi, who 00:49:29.710 --> 00:49:32.110 align:middle line:84% I think had either just one or was about to win the Nobel 00:49:32.110 --> 00:49:34.720 align:middle line:84% Prize, and then two of his younger colleagues, Nafe 00:49:34.720 --> 00:49:35.800 align:middle line:90% and Nelson. 00:49:35.800 --> 00:49:38.500 align:middle line:84% So they were also trying to perform these very, very 00:49:38.500 --> 00:49:41.350 align:middle line:84% sensitive experimental measurements on the behavior 00:49:41.350 --> 00:49:44.230 align:middle line:84% of hydrogen atoms, very similar to what Willis Lamb was doing, 00:49:44.230 --> 00:49:47.770 align:middle line:84% because like Lamb, they now had this incredible experimental 00:49:47.770 --> 00:49:51.750 align:middle line:84% control and experience in the microwave band. 00:49:51.750 --> 00:49:55.490 align:middle line:84% So only a few weeks before Lamb and Rutherford wrote up 00:49:55.490 --> 00:50:01.340 align:middle line:84% their results, this group, starting in mid-May of '47, 00:50:01.340 --> 00:50:03.980 align:middle line:84% had likewise performed very sensitive measurements 00:50:03.980 --> 00:50:07.190 align:middle line:84% on properties of an electron in a hydrogen atom, 00:50:07.190 --> 00:50:11.150 align:middle line:84% and again, they found a very tiny but now measurable 00:50:11.150 --> 00:50:14.180 align:middle line:84% deviation from their theoretical expectations. 00:50:14.180 --> 00:50:16.700 align:middle line:84% This time, it involved quantities related 00:50:16.700 --> 00:50:18.650 align:middle line:90% to the spin of the electron. 00:50:18.650 --> 00:50:20.780 align:middle line:84% Remember a couple-- again, a couple classes 00:50:20.780 --> 00:50:24.740 align:middle line:84% back when we were talking about the last vestiges 00:50:24.740 --> 00:50:26.750 align:middle line:84% of the old quantum theory, people 00:50:26.750 --> 00:50:30.530 align:middle line:84% like Samuel Goudsmit and George Uhlenbeck and soon others 00:50:30.530 --> 00:50:33.860 align:middle line:84% introduced this hypothesis of quantum mechanical spin. 00:50:33.860 --> 00:50:37.340 align:middle line:84% Maybe the electron spins like on its own axis 00:50:37.340 --> 00:50:39.590 align:middle line:84% like the Earth spins to turn day to night, 00:50:39.590 --> 00:50:42.800 align:middle line:84% and not only has an orbital spin around the proton, 00:50:42.800 --> 00:50:46.460 align:middle line:84% say, an analogy to the Earth moving around the sun. 00:50:46.460 --> 00:50:49.820 align:middle line:84% That intrinsic spin or angular momentum 00:50:49.820 --> 00:50:52.040 align:middle line:90% would yield a magnetic moment. 00:50:52.040 --> 00:50:54.410 align:middle line:84% The behavior of such a spinning charged 00:50:54.410 --> 00:50:56.780 align:middle line:84% object in an external magnetic field 00:50:56.780 --> 00:50:59.630 align:middle line:84% would depend on this quantity called the magnetic moment. 00:50:59.630 --> 00:51:02.690 align:middle line:84% In fact, by this time, this had been named the Bohr magneton, 00:51:02.690 --> 00:51:06.260 align:middle line:84% the actual value of the magnetic moment associated 00:51:06.260 --> 00:51:08.420 align:middle line:90% with the spin of an electron. 00:51:08.420 --> 00:51:10.370 align:middle line:84% It has an electric charge, it has 00:51:10.370 --> 00:51:14.300 align:middle line:84% some unit of angular momentum, h bar over 2. 00:51:14.300 --> 00:51:16.100 align:middle line:84% And so there would be an expectation 00:51:16.100 --> 00:51:22.160 align:middle line:84% for a magnitude, how large would the magnetic moment be 00:51:22.160 --> 00:51:23.120 align:middle line:90% for an electron. 00:51:23.120 --> 00:51:25.460 align:middle line:84% And what Rabi and his colleagues found 00:51:25.460 --> 00:51:27.770 align:middle line:84% was that if you really measure this extremely 00:51:27.770 --> 00:51:31.850 align:middle line:84% sensitively in a way they only could now just begin to do, 00:51:31.850 --> 00:51:36.770 align:middle line:84% the value they kept measuring of the magnetic moment of electron 00:51:36.770 --> 00:51:38.900 align:middle line:84% was actually a little bit larger-- 00:51:38.900 --> 00:51:41.485 align:middle line:84% in this case, about one part in a thousand 00:51:41.485 --> 00:51:42.860 align:middle line:84% instead of one part in a million. 00:51:42.860 --> 00:51:45.500 align:middle line:84% But still, something that would have been barely measurable, 00:51:45.500 --> 00:51:48.110 align:middle line:84% if at all, before the Second World War 00:51:48.110 --> 00:51:50.150 align:middle line:90% now is within their toolkit. 00:51:50.150 --> 00:51:53.450 align:middle line:84% Now they can actually measure slight differences 00:51:53.450 --> 00:51:55.820 align:middle line:90% of a few parts in 10 to the 3. 00:51:55.820 --> 00:51:57.280 align:middle line:84% And again, it seemed to be shifted 00:51:57.280 --> 00:52:00.230 align:middle line:84% to the larger value than what the quantum theoretical 00:52:00.230 --> 00:52:02.510 align:middle line:90% prediction suggested. 00:52:02.510 --> 00:52:05.960 align:middle line:84% So again, like Willis Lamb, Rabi presented 00:52:05.960 --> 00:52:09.230 align:middle line:84% this experimental result at that same Shelter Island conference, 00:52:09.230 --> 00:52:12.500 align:middle line:84% which I'll say more about in a moment, in June of '47. 00:52:12.500 --> 00:52:15.320 align:middle line:84% So these mostly theoretical physicists who were attending 00:52:15.320 --> 00:52:18.710 align:middle line:84% the meeting at Shelter Island, they heard from a small number 00:52:18.710 --> 00:52:22.670 align:middle line:84% of experimentalists, including Willis Lamb and Isidor Rabi, 00:52:22.670 --> 00:52:24.790 align:middle line:84% and these were, again, like hot-off-the-presses, 00:52:24.790 --> 00:52:27.290 align:middle line:84% totally cutting-edge results, some of which hadn't even been 00:52:27.290 --> 00:52:31.340 align:middle line:84% published yet, these folks at the meeting had a sneak preview 00:52:31.340 --> 00:52:35.990 align:middle line:84% of these very high-precision new wartime-enabled new 00:52:35.990 --> 00:52:37.610 align:middle line:90% experiments. 00:52:37.610 --> 00:52:40.100 align:middle line:84% So once again, theorists, hearing this kind 00:52:40.100 --> 00:52:42.380 align:middle line:84% of unexpected result from Isidor Rabi, 00:52:42.380 --> 00:52:44.540 align:middle line:84% wondered if this could also be a kind 00:52:44.540 --> 00:52:49.580 align:middle line:84% of measurable empirical effect of genuine virtual particles 00:52:49.580 --> 00:52:51.500 align:middle line:84% changing the behavior of that electron. 00:52:51.500 --> 00:52:55.040 align:middle line:84% To go back to this kind of flower petal or daisy picture 00:52:55.040 --> 00:52:58.220 align:middle line:84% of the polarized vacuum, you have the original electron 00:52:58.220 --> 00:53:01.190 align:middle line:84% and the virtual electron positron 00:53:01.190 --> 00:53:04.220 align:middle line:84% pairs springing up all around it due to the uncertainty 00:53:04.220 --> 00:53:05.150 align:middle line:90% principle. 00:53:05.150 --> 00:53:08.960 align:middle line:84% Well, each of those are also objects 00:53:08.960 --> 00:53:11.850 align:middle line:84% with some electric charge and with some intrinsic spin. 00:53:11.850 --> 00:53:14.180 align:middle line:84% So maybe the system, the electron 00:53:14.180 --> 00:53:17.840 align:middle line:84% plus its cloud of virtual particles, 00:53:17.840 --> 00:53:19.850 align:middle line:84% maybe that whole system was contributing 00:53:19.850 --> 00:53:22.130 align:middle line:84% to the effective magnetic moment. 00:53:22.130 --> 00:53:25.190 align:middle line:84% That would be like having a bunch of compass needles 00:53:25.190 --> 00:53:28.980 align:middle line:84% all aligning in the Earth's external magnetic field. 00:53:28.980 --> 00:53:31.610 align:middle line:84% And so the total effect would be-- 00:53:31.610 --> 00:53:33.380 align:middle line:84% you'd have to add up the effect from all 00:53:33.380 --> 00:53:35.300 align:middle line:84% of those spinning compass needles, 00:53:35.300 --> 00:53:37.430 align:middle line:90% not just the one you began with. 00:53:37.430 --> 00:53:40.760 align:middle line:84% And maybe that would be enough to just slightly nudge 00:53:40.760 --> 00:53:43.070 align:middle line:84% the measured value of that magnetic moment 00:53:43.070 --> 00:53:46.862 align:middle line:84% to be a little bit higher, this contribution from the cloud 00:53:46.862 --> 00:53:48.320 align:middle line:84% might indeed be a little bit higher 00:53:48.320 --> 00:53:52.010 align:middle line:84% than if you only consider the electron it's its own. 00:53:52.010 --> 00:53:54.180 align:middle line:90% So I'll pause there. 00:53:54.180 --> 00:53:57.000 align:middle line:90% Any questions there? 00:53:57.000 --> 00:53:59.420 align:middle line:84% So Alex says, the greatest reuse pile ever. 00:53:59.420 --> 00:54:00.650 align:middle line:90% That is basically true. 00:54:00.650 --> 00:54:05.750 align:middle line:84% I just can't believe, again, how generous and relaxed 00:54:05.750 --> 00:54:07.130 align:middle line:90% the federal government was. 00:54:07.130 --> 00:54:08.960 align:middle line:84% The federal government might not often 00:54:08.960 --> 00:54:10.730 align:middle line:84% merit those two adjectives these days. 00:54:10.730 --> 00:54:13.490 align:middle line:84% It was generous and relaxed in letting people 00:54:13.490 --> 00:54:17.180 align:middle line:84% like literally just truck back to their home labs 00:54:17.180 --> 00:54:20.780 align:middle line:84% tons and tons of surplus equipment. 00:54:20.780 --> 00:54:22.400 align:middle line:90% And Tiffany writes only to me-- 00:54:22.400 --> 00:54:23.900 align:middle line:84% I don't if you mentioned it to everyone, Tiffany, 00:54:23.900 --> 00:54:25.480 align:middle line:84% but you say, [INAUDIBLE] benefit from this as well. 00:54:25.480 --> 00:54:26.855 align:middle line:84% Do you want to say more, Tiffany? 00:54:26.855 --> 00:54:31.790 align:middle line:90% 00:54:31.790 --> 00:54:33.200 align:middle line:90% Very directly, yeah. 00:54:33.200 --> 00:54:35.408 align:middle line:84% In fact again, much like with the Columbia groups-- 00:54:35.408 --> 00:54:36.200 align:middle line:90% thank you, Tiffany. 00:54:36.200 --> 00:54:38.300 align:middle line:84% It wasn't just the equipment, it was young people 00:54:38.300 --> 00:54:39.770 align:middle line:84% like Ray Weiss, who, at the time, 00:54:39.770 --> 00:54:41.660 align:middle line:90% was quite young, as you know. 00:54:41.660 --> 00:54:45.350 align:middle line:84% So Ray-- our very own Ray Weiss, I will go on record 00:54:45.350 --> 00:54:47.990 align:middle line:84% and say our beloved Ray Weiss, I adore him, 00:54:47.990 --> 00:54:50.810 align:middle line:84% and also our Nobel Laureate, he got his start 00:54:50.810 --> 00:54:52.700 align:middle line:84% at MIT as an undergraduate working 00:54:52.700 --> 00:54:55.490 align:middle line:84% in the then-brand new Research Lab for Electronics, 00:54:55.490 --> 00:54:59.270 align:middle line:84% which exactly, as Tiffany says, was an intentional carryover 00:54:59.270 --> 00:55:04.160 align:middle line:84% of the wartime Rad Lab to a postwar footing. 00:55:04.160 --> 00:55:07.670 align:middle line:84% And Ray is basically the equivalent of a UROP student 00:55:07.670 --> 00:55:09.770 align:middle line:84% from very early on, began working literally 00:55:09.770 --> 00:55:11.780 align:middle line:84% with surplus equipment and learning how to use-- 00:55:11.780 --> 00:55:15.310 align:middle line:84% how to conduct very precise microwave-band 00:55:15.310 --> 00:55:16.310 align:middle line:90% electronic measurements. 00:55:16.310 --> 00:55:17.360 align:middle line:90% That's a great example, Tiffany. 00:55:17.360 --> 00:55:18.050 align:middle line:90% Yeah, good. 00:55:18.050 --> 00:55:22.110 align:middle line:90% 00:55:22.110 --> 00:55:23.085 align:middle line:90% So thank goodness. 00:55:23.085 --> 00:55:24.960 align:middle line:84% Thank goodness the black holes still collided 00:55:24.960 --> 00:55:28.560 align:middle line:84% and we had government surplus stuff to measure it 00:55:28.560 --> 00:55:29.820 align:middle line:90% a little while later. 00:55:29.820 --> 00:55:30.760 align:middle line:90% Yeah. 00:55:30.760 --> 00:55:31.260 align:middle line:90% Good. 00:55:31.260 --> 00:55:33.090 align:middle line:84% Any other questions on the Lamb shift, 00:55:33.090 --> 00:55:36.780 align:middle line:84% the anomalous magnetic moment, the impact 00:55:36.780 --> 00:55:40.777 align:middle line:84% of the Rad Lab on tools and skills and personnel? 00:55:40.777 --> 00:55:41.610 align:middle line:90% I find that really-- 00:55:41.610 --> 00:55:42.690 align:middle line:90% I just love that-- 00:55:42.690 --> 00:55:45.330 align:middle line:90% that unexpected continuity. 00:55:45.330 --> 00:55:48.750 align:middle line:84% And we'll see another example of that in the last part of class 00:55:48.750 --> 00:55:50.240 align:middle line:90% today. 00:55:50.240 --> 00:55:52.580 align:middle line:84% If there are no other questions, again, I'll charge on, 00:55:52.580 --> 00:55:55.860 align:middle line:84% but please don't be shy about asking. 00:55:55.860 --> 00:55:57.270 align:middle line:84% Let's see, Fisher has a question. 00:55:57.270 --> 00:55:58.850 align:middle line:90% How did Lamb to look for this? 00:55:58.850 --> 00:56:00.330 align:middle line:90% Good. 00:56:00.330 --> 00:56:00.910 align:middle line:90% Very good. 00:56:00.910 --> 00:56:03.420 align:middle line:84% I don't think that Lamb was intentionally 00:56:03.420 --> 00:56:06.180 align:middle line:84% trying to ask about virtual particles, per se. 00:56:06.180 --> 00:56:10.050 align:middle line:84% I think what Lamb realized was that there were all these-- 00:56:10.050 --> 00:56:11.850 align:middle line:84% it was actually called the fine structure, 00:56:11.850 --> 00:56:15.510 align:middle line:84% all these very minute shifts in the energy states of electrons 00:56:15.510 --> 00:56:16.450 align:middle line:90% and hydrogen atoms. 00:56:16.450 --> 00:56:18.075 align:middle line:84% Remember, that had been recognized even 00:56:18.075 --> 00:56:21.210 align:middle line:84% in the 1890s, although obviously not nearly the same level 00:56:21.210 --> 00:56:22.440 align:middle line:90% of precision, of course. 00:56:22.440 --> 00:56:25.950 align:middle line:84% But that's what gave rise to things like the Zeeman effect, 00:56:25.950 --> 00:56:27.690 align:middle line:90% the anomalous Zeeman splitting. 00:56:27.690 --> 00:56:30.390 align:middle line:84% If you put a gas of hydrogen atoms 00:56:30.390 --> 00:56:33.810 align:middle line:84% in an external electric field or an external magnetic field, 00:56:33.810 --> 00:56:37.500 align:middle line:84% the spectral lines that come out can show these very minute 00:56:37.500 --> 00:56:39.870 align:middle line:84% shifts, and that was read back as saying 00:56:39.870 --> 00:56:42.220 align:middle line:84% there's a shift in the energy states of the electrons. 00:56:42.220 --> 00:56:45.990 align:middle line:84% And so part of what was of interest for people like Willis 00:56:45.990 --> 00:56:49.680 align:middle line:84% Lamb was to ask, could there be measurable effects from, say, 00:56:49.680 --> 00:56:51.900 align:middle line:90% the spin of the nucleus? 00:56:51.900 --> 00:56:53.850 align:middle line:84% Could the could the fact that the nucleus has 00:56:53.850 --> 00:56:56.490 align:middle line:84% some moving parts affect the measured energy 00:56:56.490 --> 00:56:59.432 align:middle line:84% states of, say, the electrons from the spectrum and so on? 00:56:59.432 --> 00:57:01.390 align:middle line:84% So those were things that were just never going 00:57:01.390 --> 00:57:03.430 align:middle line:84% to be measurable using the techniques 00:57:03.430 --> 00:57:06.917 align:middle line:84% from the 19-teens or '20s, but he thought, again, 00:57:06.917 --> 00:57:08.500 align:middle line:84% the article-- the title of the article 00:57:08.500 --> 00:57:10.330 align:middle line:84% itself was about the fine structure. 00:57:10.330 --> 00:57:13.630 align:middle line:84% He was interested in, what's the best, most quantitatively 00:57:13.630 --> 00:57:16.900 align:middle line:84% precise way with which we can characterize the energy states 00:57:16.900 --> 00:57:18.910 align:middle line:90% of electrons in hydrogen? 00:57:18.910 --> 00:57:21.190 align:middle line:84% And so he didn't go in asking about virtual particles, 00:57:21.190 --> 00:57:24.880 align:middle line:84% per se, but he said, I have a pretty cool new set of tools 00:57:24.880 --> 00:57:29.380 align:middle line:84% to measure in that energy band, and he and his student, 00:57:29.380 --> 00:57:31.480 align:middle line:84% Rutherford, then relatively quickly 00:57:31.480 --> 00:57:34.250 align:middle line:84% were able to find this, indeed, unexpected energy shift. 00:57:34.250 --> 00:57:34.750 align:middle line:90% Good. 00:57:34.750 --> 00:57:35.290 align:middle line:90% OK. 00:57:35.290 --> 00:57:37.738 align:middle line:84% I'm going to go on to the last part for today, 00:57:37.738 --> 00:57:40.030 align:middle line:84% but again, of course, please keep the questions coming, 00:57:40.030 --> 00:57:41.770 align:middle line:90% I'd be delighted to talk more. 00:57:41.770 --> 00:57:44.680 align:middle line:84% OK, so that middle part for today's class 00:57:44.680 --> 00:57:50.510 align:middle line:84% was all about some kind of experimental continuities, 00:57:50.510 --> 00:57:52.370 align:middle line:84% the fact that it mattered that people 00:57:52.370 --> 00:57:55.620 align:middle line:84% were asking these questions after the Second World War 00:57:55.620 --> 00:57:56.970 align:middle line:90% probably rather than before. 00:57:56.970 --> 00:57:57.470 align:middle line:90% And 00:57:57.470 --> 00:57:58.845 align:middle line:84% So for the last part today, we're 00:57:58.845 --> 00:58:01.010 align:middle line:84% going to ask a similar question, but now 00:58:01.010 --> 00:58:04.400 align:middle line:84% about some theoretical responses, which, again, will-- 00:58:04.400 --> 00:58:07.790 align:middle line:84% I think it's quite amazing-- will find also 00:58:07.790 --> 00:58:10.250 align:middle line:84% seem to depend in a pretty critical way 00:58:10.250 --> 00:58:13.700 align:middle line:84% on the intervening experience of the Second World War. 00:58:13.700 --> 00:58:16.928 align:middle line:84% So I mentioned a few times that Shelter Island meeting, 00:58:16.928 --> 00:58:19.220 align:middle line:84% and I'll just say a bit more about that meeting itself. 00:58:19.220 --> 00:58:21.470 align:middle line:84% It was actually none other than Robert Oppenheimer 00:58:21.470 --> 00:58:22.353 align:middle line:90% who organized it. 00:58:22.353 --> 00:58:24.020 align:middle line:84% In fact, as we'll see in the next class, 00:58:24.020 --> 00:58:26.810 align:middle line:84% he organized three in a row, three annual meetings 00:58:26.810 --> 00:58:28.300 align:middle line:90% of which this was the first. 00:58:28.300 --> 00:58:31.820 align:middle line:84% The June 1947 meeting about one week in duration 00:58:31.820 --> 00:58:35.570 align:middle line:84% was the first of a planned series of three. 00:58:35.570 --> 00:58:37.340 align:middle line:84% And Oppenheimer was very explicit. 00:58:37.340 --> 00:58:40.880 align:middle line:84% He really thought it was time to get the physicists of thinking 00:58:40.880 --> 00:58:44.390 align:middle line:84% again about open questions at the cutting 00:58:44.390 --> 00:58:47.060 align:middle line:84% edge of theoretical physics, including these open questions 00:58:47.060 --> 00:58:50.190 align:middle line:84% in quantum field theory which had really ground 00:58:50.190 --> 00:58:53.010 align:middle line:84% to a halt at the time that he himself 00:58:53.010 --> 00:58:54.840 align:middle line:84% was a student and a postdoc going back 00:58:54.840 --> 00:58:56.580 align:middle line:90% to the '20s and '30s. 00:58:56.580 --> 00:58:59.640 align:middle line:84% He thought, now that the wartime efforts were behind them, 00:58:59.640 --> 00:59:02.340 align:middle line:84% it was time to literally jumpstart the work. 00:59:02.340 --> 00:59:05.310 align:middle line:84% He also had very, let's say, patriotic-- we might say 00:59:05.310 --> 00:59:07.560 align:middle line:90% nationalistic-- goals in mind. 00:59:07.560 --> 00:59:11.460 align:middle line:84% That he wanted to really help further the US-based community 00:59:11.460 --> 00:59:12.420 align:middle line:90% in theoretical physics. 00:59:12.420 --> 00:59:14.460 align:middle line:84% So he invited several leading Europeans 00:59:14.460 --> 00:59:16.200 align:middle line:84% over for the meeting, some of whom 00:59:16.200 --> 00:59:17.610 align:middle line:90% were already in North America. 00:59:17.610 --> 00:59:20.880 align:middle line:84% But his real goal was to get the younger generation 00:59:20.880 --> 00:59:25.150 align:middle line:84% of US-based theorists in a room together-- in fact, 00:59:25.150 --> 00:59:28.380 align:middle line:84% in a lovely bed and breakfast called the Ram's Head Inn. 00:59:28.380 --> 00:59:31.380 align:middle line:84% They literally lived together for a week and did nothing 00:59:31.380 --> 00:59:34.170 align:middle line:84% but talk about quantum physics for a week 00:59:34.170 --> 00:59:36.613 align:middle line:84% being paid for by the National Academy of Sciences. 00:59:36.613 --> 00:59:38.280 align:middle line:84% So here's one of the famous photographs. 00:59:38.280 --> 00:59:40.275 align:middle line:84% This is actually Willis Lamb standing here. 00:59:40.275 --> 00:59:42.150 align:middle line:84% Lamb had actually been trained as a theorist, 00:59:42.150 --> 00:59:44.647 align:middle line:84% but had converted over to an experimentalist. 00:59:44.647 --> 00:59:45.480 align:middle line:90% Here's John Wheeler. 00:59:45.480 --> 00:59:47.100 align:middle line:84% I love this, he's like reading the funny pages, 00:59:47.100 --> 00:59:48.183 align:middle line:90% not even paying attention. 00:59:48.183 --> 00:59:48.960 align:middle line:90% I love that photo. 00:59:48.960 --> 00:59:51.360 align:middle line:84% Here is Abraham Pais who had actually 00:59:51.360 --> 00:59:57.630 align:middle line:84% fled the Nazis as a young person and relocated in Princeton. 00:59:57.630 --> 01:00:03.187 align:middle line:84% Here's Richard Feynman, MIT class of 1935 or so, 1934. 01:00:03.187 --> 01:00:05.520 align:middle line:84% Here's Herman Feshbach, who then made his career at MIT, 01:00:05.520 --> 01:00:06.895 align:middle line:84% and then here's Julian Schwinger. 01:00:06.895 --> 01:00:09.210 align:middle line:84% So here's a photo from the bed-and-breakfast 01:00:09.210 --> 01:00:12.980 align:middle line:84% on Shelter Island literally during that June '47 meeting. 01:00:12.980 --> 01:00:14.850 align:middle line:84% So nearly all the participants actually 01:00:14.850 --> 01:00:16.850 align:middle line:84% already knew each other even though some of them 01:00:16.850 --> 01:00:17.900 align:middle line:90% were still quite young. 01:00:17.900 --> 01:00:19.820 align:middle line:84% Feynman was 29 years old at the time, 01:00:19.820 --> 01:00:21.620 align:middle line:84% Schwinger was also about the same age. 01:00:21.620 --> 01:00:24.980 align:middle line:84% So it wasn't that these were very senior figures who'd 01:00:24.980 --> 01:00:27.000 align:middle line:84% been around each other for decades, 01:00:27.000 --> 01:00:29.540 align:middle line:84% they had been around each other on the wartime projects. 01:00:29.540 --> 01:00:32.210 align:middle line:84% They knew each other because of some of these very intense 01:00:32.210 --> 01:00:34.328 align:middle line:84% experiences from very recent times 01:00:34.328 --> 01:00:36.620 align:middle line:84% even though there were still-- many of them quite young 01:00:36.620 --> 01:00:38.780 align:middle line:90% in their careers. 01:00:38.780 --> 01:00:41.240 align:middle line:84% And as we'll see-- and this is work that I really owe 01:00:41.240 --> 01:00:44.810 align:middle line:84% to my own mentor, Sam Schweber, who wrote this amazing book 01:00:44.810 --> 01:00:45.560 align:middle line:90% on-- 01:00:45.560 --> 01:00:48.530 align:middle line:84% a little piece of which I'll describe now, 01:00:48.530 --> 01:00:50.390 align:middle line:84% that the reaction from some of these folks 01:00:50.390 --> 01:00:54.620 align:middle line:84% soon after the war to these very stubborn problems of infinities 01:00:54.620 --> 01:00:57.620 align:middle line:84% in quantum electrodynamics, their response 01:00:57.620 --> 01:00:59.660 align:middle line:84% was really quite different than what 01:00:59.660 --> 01:01:03.020 align:middle line:84% we saw from people like Niels Bohr and Werner Heisenberg. 01:01:03.020 --> 01:01:05.600 align:middle line:84% Very few of these physicists who came back 01:01:05.600 --> 01:01:07.460 align:middle line:84% to the question of virtual particles 01:01:07.460 --> 01:01:09.800 align:middle line:84% and infinities and all that after their wartime 01:01:09.800 --> 01:01:11.960 align:middle line:84% experiences, very few of them talked 01:01:11.960 --> 01:01:14.863 align:middle line:84% about a grand, sweeping conceptual revolution. 01:01:14.863 --> 01:01:16.280 align:middle line:84% Very few of them said, we're going 01:01:16.280 --> 01:01:18.822 align:middle line:84% to sweep away everything we know about relativity and quantum 01:01:18.822 --> 01:01:19.500 align:middle line:90% theory. 01:01:19.500 --> 01:01:21.740 align:middle line:84% We'll have even grander conceptual leaps. 01:01:21.740 --> 01:01:25.190 align:middle line:84% Instead, as Sam has shown really quite 01:01:25.190 --> 01:01:27.740 align:middle line:84% powerfully in this landmark study, 01:01:27.740 --> 01:01:31.280 align:middle line:84% most of these wartime project veterans 01:01:31.280 --> 01:01:33.550 align:middle line:84% said, well, we have a bunch of equations, 01:01:33.550 --> 01:01:37.310 align:middle line:84% we now have some measurements from people like Lamb and Rabi 01:01:37.310 --> 01:01:40.430 align:middle line:84% and soon others, what can we do to get the numbers out? 01:01:40.430 --> 01:01:42.050 align:middle line:84% That's the phrase that Sam associates 01:01:42.050 --> 01:01:43.560 align:middle line:90% with this generation. 01:01:43.560 --> 01:01:47.390 align:middle line:84% How do you find some clever workaround 01:01:47.390 --> 01:01:49.110 align:middle line:84% to get some numbers out to compare 01:01:49.110 --> 01:01:51.880 align:middle line:84% with real empirical measurements? 01:01:51.880 --> 01:01:55.140 align:middle line:84% So rather than getting stuck with fancy-sounding conceptual 01:01:55.140 --> 01:01:57.727 align:middle line:84% first principles, you have some equations, 01:01:57.727 --> 01:02:00.060 align:middle line:84% you have some reason for confidence in them, get to work 01:02:00.060 --> 01:02:02.010 align:middle line:84% and get some numbers out and compare with what 01:02:02.010 --> 01:02:04.320 align:middle line:90% the other groups are measuring. 01:02:04.320 --> 01:02:06.320 align:middle line:84% And really, I think an amazing example 01:02:06.320 --> 01:02:08.100 align:middle line:84% of that comes in from Julian Schwinger. 01:02:08.100 --> 01:02:10.720 align:middle line:84% Schwinger actually had spent the war at MIT. 01:02:10.720 --> 01:02:12.450 align:middle line:90% He was at the MIT Rad Lab. 01:02:12.450 --> 01:02:16.270 align:middle line:84% He then went all the way back to Harvard after the war was over. 01:02:16.270 --> 01:02:19.110 align:middle line:84% He was actually, for many years, the youngest tenured professor 01:02:19.110 --> 01:02:21.490 align:middle line:90% in any field at Harvard. 01:02:21.490 --> 01:02:25.080 align:middle line:84% He was tenured at age 29 and had spent the war, 01:02:25.080 --> 01:02:27.450 align:middle line:90% as I say, at the Rad Lab. 01:02:27.450 --> 01:02:30.180 align:middle line:84% He was one of these invited participants at Shelter Island. 01:02:30.180 --> 01:02:34.260 align:middle line:84% And as we saw some weeks ago, he had 01:02:34.260 --> 01:02:37.500 align:middle line:84% been immersed in these kinds of engineering effective styles 01:02:37.500 --> 01:02:40.470 align:middle line:84% of calculation during his work at the Rad Lab. 01:02:40.470 --> 01:02:42.720 align:middle line:84% And he himself years later credited the engineers 01:02:42.720 --> 01:02:44.820 align:middle line:84% with really changing his own thinking 01:02:44.820 --> 01:02:47.770 align:middle line:84% about some complicated physical systems. 01:02:47.770 --> 01:02:51.210 align:middle line:84% So as we saw, if you're working with these kinds of waveguides, 01:02:51.210 --> 01:02:53.880 align:middle line:84% rather than spheres and perfect cylinders, 01:02:53.880 --> 01:02:56.970 align:middle line:84% then the usual symmetry arguments that physicists 01:02:56.970 --> 01:02:59.310 align:middle line:84% love and that are often so powerful for us, 01:02:59.310 --> 01:03:01.180 align:middle line:84% those are simply not going to cut it. 01:03:01.180 --> 01:03:02.820 align:middle line:84% So rather than trying to calculate 01:03:02.820 --> 01:03:04.680 align:middle line:84% from first principles, if you're looking 01:03:04.680 --> 01:03:08.850 align:middle line:84% at some really, frankly, ugly piece of real-world equipment 01:03:08.850 --> 01:03:11.670 align:middle line:84% or some complicated, highly non-symmetric piece 01:03:11.670 --> 01:03:13.770 align:middle line:84% of real-world equipment, don't sit down 01:03:13.770 --> 01:03:15.480 align:middle line:84% and start using spherical symmetry 01:03:15.480 --> 01:03:16.950 align:middle line:90% or cylindrical symmetry. 01:03:16.950 --> 01:03:21.780 align:middle line:84% Learn from the engineers to work in terms of effective circuits, 01:03:21.780 --> 01:03:23.980 align:middle line:84% or really more generally, input-output. 01:03:23.980 --> 01:03:25.860 align:middle line:84% So as we saw last time, instead of worrying 01:03:25.860 --> 01:03:28.350 align:middle line:84% about the rules for how to resistors add 01:03:28.350 --> 01:03:30.750 align:middle line:84% if they're in parallel or series and all that, just, say, 01:03:30.750 --> 01:03:32.970 align:middle line:84% stick a lead on here, stick a lead on here, there's 01:03:32.970 --> 01:03:35.178 align:middle line:84% some effective resistance, and get on with your life. 01:03:35.178 --> 01:03:36.840 align:middle line:84% As they say, there's a war on, buddy. 01:03:36.840 --> 01:03:40.600 align:middle line:84% So don't get stuck on this first principles calculation. 01:03:40.600 --> 01:03:44.070 align:middle line:84% So when he then came to Shelter Island, really just two 01:03:44.070 --> 01:03:46.950 align:middle line:84% years after the end of the war-- not even two whole years-- 01:03:46.950 --> 01:03:49.770 align:middle line:84% after the end of the war, and he heard directly 01:03:49.770 --> 01:03:52.380 align:middle line:84% from people like Willis Lamb and Isidor Rabi 01:03:52.380 --> 01:03:55.180 align:middle line:84% about these new microwave-band measurements, 01:03:55.180 --> 01:03:58.140 align:middle line:84% he began thinking about virtual particles. 01:03:58.140 --> 01:04:03.540 align:middle line:84% By his own admission, he began trying 01:04:03.540 --> 01:04:08.190 align:middle line:84% to apply this Rad Lab engineering-style input-output 01:04:08.190 --> 01:04:09.990 align:middle line:84% calculation to what had previously 01:04:09.990 --> 01:04:13.470 align:middle line:90% seemed really incalculable. 01:04:13.470 --> 01:04:15.420 align:middle line:84% So let's take, for example, that question 01:04:15.420 --> 01:04:18.210 align:middle line:84% of the anomalous magnetic moment where 01:04:18.210 --> 01:04:21.570 align:middle line:84% this collection of the electron plus its cloud 01:04:21.570 --> 01:04:23.520 align:middle line:84% of virtual particles seem to have 01:04:23.520 --> 01:04:28.530 align:middle line:84% a different value of its ratio of charge and spin to its mass 01:04:28.530 --> 01:04:30.930 align:middle line:84% compared to what one would expect 01:04:30.930 --> 01:04:33.220 align:middle line:84% in the absence of those virtual particles. 01:04:33.220 --> 01:04:35.760 align:middle line:84% So Schwinger realized, we could never turn off 01:04:35.760 --> 01:04:37.260 align:middle line:90% the uncertainty principle. 01:04:37.260 --> 01:04:41.880 align:middle line:84% So you would never actually have just the electron its own. 01:04:41.880 --> 01:04:44.430 align:middle line:84% So why would you ever set up your equations 01:04:44.430 --> 01:04:47.790 align:middle line:84% as if you have a pristine, pure single electron 01:04:47.790 --> 01:04:50.430 align:middle line:84% and then try to fold in all the messiness of the world? 01:04:50.430 --> 01:04:52.015 align:middle line:84% That's not how we handle waveguides. 01:04:52.015 --> 01:04:53.640 align:middle line:84% You don't start with spherical symmetry 01:04:53.640 --> 01:04:57.750 align:middle line:84% and then cut back to add in more realism. 01:04:57.750 --> 01:05:00.570 align:middle line:84% Just never separate them in the first place. 01:05:00.570 --> 01:05:03.570 align:middle line:84% Treat it more like an input-output relationship. 01:05:03.570 --> 01:05:05.940 align:middle line:84% So his main idea was to never try 01:05:05.940 --> 01:05:08.070 align:middle line:84% to calculate the effect of this electron 01:05:08.070 --> 01:05:10.110 align:middle line:84% and then separately add in the effects of all 01:05:10.110 --> 01:05:11.280 align:middle line:90% these virtual ones. 01:05:11.280 --> 01:05:14.410 align:middle line:84% Just manipulate your equations from the start 01:05:14.410 --> 01:05:17.910 align:middle line:84% so it's always a combination that you're dealing with. 01:05:17.910 --> 01:05:20.280 align:middle line:84% Again, that would be like the effective resistance 01:05:20.280 --> 01:05:21.520 align:middle line:90% on that circuit. 01:05:21.520 --> 01:05:24.120 align:middle line:84% So you can rewrite your equations before you sit down 01:05:24.120 --> 01:05:26.620 align:middle line:84% and try to calculate particular things, 01:05:26.620 --> 01:05:28.980 align:middle line:84% so you're always dealing with the sum 01:05:28.980 --> 01:05:32.760 align:middle line:84% of the so-called bare mass or bare electric charge 01:05:32.760 --> 01:05:37.170 align:middle line:84% plus the corrections or the impact of those virtual quantum 01:05:37.170 --> 01:05:38.110 align:middle line:90% processes. 01:05:38.110 --> 01:05:40.170 align:middle line:84% So instead of trying to write this down and then 01:05:40.170 --> 01:05:43.170 align:middle line:84% calculate this from scratch, rewrite your equations, 01:05:43.170 --> 01:05:45.250 align:middle line:84% you always have the input-output, 01:05:45.250 --> 01:05:49.940 align:middle line:84% the actual quantity that would ever be subject to measurement. 01:05:49.940 --> 01:05:52.330 align:middle line:84% So if you do that, Schwinger then goes on to show, 01:05:52.330 --> 01:05:54.640 align:middle line:84% quite astonishingly, then you never 01:05:54.640 --> 01:05:56.530 align:middle line:84% need to calculate these things on their own 01:05:56.530 --> 01:05:58.270 align:middle line:84% because they never appear on their own. 01:05:58.270 --> 01:06:00.190 align:middle line:84% They always appear in combination 01:06:00.190 --> 01:06:03.790 align:middle line:84% with these other constants, the so-called bare mass 01:06:03.790 --> 01:06:05.380 align:middle line:90% or the bare charge. 01:06:05.380 --> 01:06:06.940 align:middle line:90% And as we'll see, I want to-- 01:06:06.940 --> 01:06:10.960 align:middle line:84% I just want to remind us or give a foreshadowing, it turns out, 01:06:10.960 --> 01:06:14.980 align:middle line:84% it wasn't only Julian Schwinger who pieced this all together, 01:06:14.980 --> 01:06:18.190 align:middle line:84% it just boggles my mind, but totally independently, 01:06:18.190 --> 01:06:21.250 align:middle line:84% and in fact, four years earlier, really, 01:06:21.250 --> 01:06:24.550 align:middle line:84% in the middle of this very horrible, bloody war, 01:06:24.550 --> 01:06:28.660 align:middle line:84% Sin-itiro Tomonaga, a very young Japanese theoretical physicist 01:06:28.660 --> 01:06:31.700 align:middle line:84% working in Tokyo, had come up with the exact same series 01:06:31.700 --> 01:06:32.200 align:middle line:90% of steps. 01:06:32.200 --> 01:06:36.230 align:middle line:84% And he also, it turned out, was immersed in the Japanese radar 01:06:36.230 --> 01:06:36.730 align:middle line:90% project. 01:06:36.730 --> 01:06:40.210 align:middle line:84% And he also, after the war, credited his switch 01:06:40.210 --> 01:06:44.860 align:middle line:84% in thinking to this input-output effective quantities approach 01:06:44.860 --> 01:06:47.270 align:middle line:90% to his work on radar. 01:06:47.270 --> 01:06:50.180 align:middle line:84% So these two independent approaches 01:06:50.180 --> 01:06:53.630 align:middle line:84% to a longstanding challenge, and it turns out, 01:06:53.630 --> 01:06:55.550 align:middle line:84% Tomonaga really actually got there first 01:06:55.550 --> 01:06:57.380 align:middle line:84% for many of these steps, so that was not 01:06:57.380 --> 01:06:59.182 align:middle line:84% known at the time in the United States 01:06:59.182 --> 01:07:00.890 align:middle line:84% because the nations were at war and there 01:07:00.890 --> 01:07:03.357 align:middle line:84% wasn't regular mail service to deliver 01:07:03.357 --> 01:07:04.440 align:middle line:90% journals and all the rest. 01:07:04.440 --> 01:07:06.650 align:middle line:84% So I'll come back to some of Tomonaga's work 01:07:06.650 --> 01:07:08.990 align:middle line:84% in the next class, but I do want to mention it. 01:07:08.990 --> 01:07:12.980 align:middle line:84% This was jaw-droppingly original when Schwinger did it 01:07:12.980 --> 01:07:16.040 align:middle line:84% in the late '40s to his US-based colleagues, 01:07:16.040 --> 01:07:18.230 align:middle line:84% and only later did they learn that it 01:07:18.230 --> 01:07:20.450 align:middle line:84% had been done actually even earlier under much more 01:07:20.450 --> 01:07:21.690 align:middle line:90% difficult conditions. 01:07:21.690 --> 01:07:22.190 align:middle line:90% OK. 01:07:22.190 --> 01:07:24.315 align:middle line:84% So what was the rest of Schwinger's argument, then? 01:07:24.315 --> 01:07:26.630 align:middle line:84% If you never separate the kind of corrections, 01:07:26.630 --> 01:07:28.730 align:middle line:84% so-called corrections from quantum theory 01:07:28.730 --> 01:07:32.750 align:middle line:84% from those bare quantities, then you can, all of a sudden, 01:07:32.750 --> 01:07:36.050 align:middle line:84% find finite sensible answers after all. 01:07:36.050 --> 01:07:38.930 align:middle line:84% So he goes on to show, that just as the experts had found 01:07:38.930 --> 01:07:43.430 align:middle line:84% in the 1920s and '30s, if you actually try to just calculate 01:07:43.430 --> 01:07:46.620 align:middle line:84% the effect of all these virtual particles on their own, 01:07:46.620 --> 01:07:49.520 align:middle line:84% you really do find these logarithmic divergent 01:07:49.520 --> 01:07:50.390 align:middle line:90% integrals. 01:07:50.390 --> 01:07:53.450 align:middle line:84% And this is-- you have a little more information 01:07:53.450 --> 01:07:56.510 align:middle line:84% about this in the reading for today by physicist 01:07:56.510 --> 01:07:58.760 align:middle line:84% Robert Mills, that so-called tutorial 01:07:58.760 --> 01:08:00.037 align:middle line:90% on the infinities in QED. 01:08:00.037 --> 01:08:02.120 align:middle line:84% This is the kind of thing that Mills writes about. 01:08:02.120 --> 01:08:05.305 align:middle line:84% So Schwinger confirmed that, yes, indeed, 01:08:05.305 --> 01:08:06.680 align:middle line:84% the form of the equations, we can 01:08:06.680 --> 01:08:10.410 align:middle line:84% write them kind of abstractly across many, many applications, 01:08:10.410 --> 01:08:14.125 align:middle line:84% whether it's the corrections due to the bare mass 01:08:14.125 --> 01:08:15.500 align:middle line:84% or the corrections to the charge, 01:08:15.500 --> 01:08:18.399 align:middle line:90% they take this form in general. 01:08:18.399 --> 01:08:20.979 align:middle line:84% And they are generally logarithmically divergent 01:08:20.979 --> 01:08:25.060 align:middle line:84% where y here is basically like the borrowed energy or momentum 01:08:25.060 --> 01:08:26.300 align:middle line:90% of those virtual processes. 01:08:26.300 --> 01:08:28.359 align:middle line:84% So yes, you get log of infinity, which 01:08:28.359 --> 01:08:30.490 align:middle line:90% is still infinity-- sorry. 01:08:30.490 --> 01:08:33.229 align:middle line:84% But instead, if you don't just calculate that on its own, 01:08:33.229 --> 01:08:35.510 align:middle line:84% you always do this grouping first. 01:08:35.510 --> 01:08:38.500 align:middle line:84% So you always deal with the effective quantities, then, 01:08:38.500 --> 01:08:41.450 align:middle line:84% in fact, some remarkable cancellations can occur. 01:08:41.450 --> 01:08:43.990 align:middle line:84% So this is what he began working on in the weeks and months 01:08:43.990 --> 01:08:47.920 align:middle line:84% after hearing from Lamb and Rabi at Shelter Island. 01:08:47.920 --> 01:08:50.665 align:middle line:84% So Schwinger first rewrites all his equations in terms of these 01:08:50.665 --> 01:08:52.540 align:middle line:84% effective quantities-- and this could, again, 01:08:52.540 --> 01:08:54.410 align:middle line:90% be charge or mass, it works-- 01:08:54.410 --> 01:08:55.930 align:middle line:90% you have to do it for both. 01:08:55.930 --> 01:08:58.160 align:middle line:84% Let's say it's charge in this instance, 01:08:58.160 --> 01:09:00.783 align:middle line:84% you have some bare charge which is never 01:09:00.783 --> 01:09:02.950 align:middle line:84% separated from the screening, you can never turn off 01:09:02.950 --> 01:09:04.033 align:middle line:90% the Uncertainty Principle. 01:09:04.033 --> 01:09:06.118 align:middle line:84% In this case, the screening would be a minus sign 01:09:06.118 --> 01:09:07.660 align:middle line:84% because you're actually screening off 01:09:07.660 --> 01:09:10.510 align:middle line:84% part of the original charge that comes in an opposite sign. 01:09:10.510 --> 01:09:12.162 align:middle line:84% The effective charge is a little weaker 01:09:12.162 --> 01:09:14.620 align:middle line:84% than the bare charge would have been because of this cloud, 01:09:14.620 --> 01:09:16.460 align:middle line:90% he reasons. 01:09:16.460 --> 01:09:19.430 align:middle line:84% So now, instead of calculating this part on its own 01:09:19.430 --> 01:09:23.090 align:middle line:84% due to the virtual particles, calculate the combination 01:09:23.090 --> 01:09:25.189 align:middle line:84% together because they never appear separated 01:09:25.189 --> 01:09:26.100 align:middle line:90% from each other. 01:09:26.100 --> 01:09:28.880 align:middle line:84% So all of a sudden, now, you have this as your integral 01:09:28.880 --> 01:09:31.529 align:middle line:84% to evaluate rather than this on its own. 01:09:31.529 --> 01:09:33.470 align:middle line:84% And now, it's just a few more steps 01:09:33.470 --> 01:09:36.529 align:middle line:84% of algebra, which even the youngest tenured professor 01:09:36.529 --> 01:09:38.029 align:middle line:90% at Harvard was able to do. 01:09:38.029 --> 01:09:40.649 align:middle line:84% So now you can just combine the denominators, 01:09:40.649 --> 01:09:44.330 align:middle line:84% now you have a new numerator, just a little more algebra. 01:09:44.330 --> 01:09:45.740 align:middle line:84% All of a sudden, what's happened, 01:09:45.740 --> 01:09:49.850 align:middle line:84% what matters is you've increased the power of momentum 01:09:49.850 --> 01:09:51.950 align:middle line:90% in the denominator. 01:09:51.950 --> 01:09:54.620 align:middle line:84% Instead of integrating over one power of momentum-- that's 01:09:54.620 --> 01:09:57.620 align:middle line:84% what gives you that logarithm, now you're 01:09:57.620 --> 01:10:00.350 align:middle line:84% integrating over two powers, and that's 01:10:00.350 --> 01:10:02.780 align:middle line:84% going to be a convergent integral. 01:10:02.780 --> 01:10:05.060 align:middle line:84% And in fact, you can do that integral, 01:10:05.060 --> 01:10:09.240 align:middle line:84% it becomes a logarithm of a perfectly finite answer. 01:10:09.240 --> 01:10:11.780 align:middle line:84% So this became known as renormalization. 01:10:11.780 --> 01:10:13.550 align:middle line:84% That's the fancy word that was applied 01:10:13.550 --> 01:10:16.310 align:middle line:84% to this based on this early demonstration 01:10:16.310 --> 01:10:18.470 align:middle line:90% by people like Julian Schwinger. 01:10:18.470 --> 01:10:22.370 align:middle line:84% You first arrange, always have the so-called bare 01:10:22.370 --> 01:10:27.020 align:middle line:84% and quantum corrections together because when you evaluate them 01:10:27.020 --> 01:10:30.380 align:middle line:84% together as one joined quantity, you 01:10:30.380 --> 01:10:32.990 align:middle line:90% get these exact cancelations. 01:10:32.990 --> 01:10:35.510 align:middle line:84% It turns out, the bare charge of the electron 01:10:35.510 --> 01:10:37.800 align:middle line:84% really is infinite in this scheme. 01:10:37.800 --> 01:10:39.380 align:middle line:84% It's just that you can never interact 01:10:39.380 --> 01:10:41.070 align:middle line:90% with an electron on its own. 01:10:41.070 --> 01:10:44.810 align:middle line:84% So that infinite initial charge is 01:10:44.810 --> 01:10:47.630 align:middle line:84% partly screened by the infinite effect 01:10:47.630 --> 01:10:50.900 align:middle line:84% of those virtual particles and not arbitrary infinities-- 01:10:50.900 --> 01:10:53.510 align:middle line:84% in fact, particular forms of infinity 01:10:53.510 --> 01:10:55.400 align:middle line:84% that you can show exactly cancel. 01:10:55.400 --> 01:10:58.280 align:middle line:84% As long as we can write them in this grouped form, 01:10:58.280 --> 01:11:02.120 align:middle line:84% the infinity here is exactly canceled by the infinity here, 01:11:02.120 --> 01:11:06.720 align:middle line:84% and it leaves a perfectly unambiguous finite result. 01:11:06.720 --> 01:11:09.620 align:middle line:84% So this avoids that problem of cutting off the integrals 01:11:09.620 --> 01:11:11.160 align:middle line:90% at some arbitrary level. 01:11:11.160 --> 01:11:14.540 align:middle line:84% This can now be made, as Schwinger show very elegantly, 01:11:14.540 --> 01:11:17.090 align:middle line:84% this approach can be made to respect all the symmetries 01:11:17.090 --> 01:11:18.230 align:middle line:90% of special relativity. 01:11:18.230 --> 01:11:20.780 align:middle line:84% Different observers, now in principle, should agree. 01:11:20.780 --> 01:11:23.030 align:middle line:90% You extract finite results. 01:11:23.030 --> 01:11:26.270 align:middle line:84% Basically the trick is by never trying to calculate this apart 01:11:26.270 --> 01:11:26.780 align:middle line:90% from that. 01:11:26.780 --> 01:11:29.330 align:middle line:84% That's really the upshot of that maneuver 01:11:29.330 --> 01:11:31.070 align:middle line:90% that Schwinger introduces. 01:11:31.070 --> 01:11:35.240 align:middle line:84% Then it goes on in the next six months 01:11:35.240 --> 01:11:38.060 align:middle line:84% to show not only is this feasible in principle, 01:11:38.060 --> 01:11:40.100 align:middle line:84% that this type of logarithmically 01:11:40.100 --> 01:11:43.490 align:middle line:84% divergent integral could be cured if you never treat it 01:11:43.490 --> 01:11:45.620 align:middle line:84% on its own, but he then applies it 01:11:45.620 --> 01:11:49.430 align:middle line:84% to the very specific measurement that Rabi and Nafe and Nelson 01:11:49.430 --> 01:11:51.140 align:middle line:84% had reported on at Shelter Island, 01:11:51.140 --> 01:11:53.330 align:middle line:90% that anomalous magnetic moment. 01:11:53.330 --> 01:11:56.960 align:middle line:84% And for the first time in the history of the universe-- 01:11:56.960 --> 01:12:00.380 align:middle line:84% he got here even quicker than Tomonaga, this part, 01:12:00.380 --> 01:12:02.930 align:middle line:84% Schwinger is able not just to find a finite answer, 01:12:02.930 --> 01:12:07.250 align:middle line:84% but to find an answer that agrees to remarkable accuracy 01:12:07.250 --> 01:12:10.820 align:middle line:84% with that hot-off-the-presses experimental measurement that 01:12:10.820 --> 01:12:13.610 align:middle line:84% the Columbia group had just reported. 01:12:13.610 --> 01:12:17.180 align:middle line:84% So not only does he get an answer that the correction from 01:12:17.180 --> 01:12:19.775 align:middle line:84% incorporating the virtual particles goes by actually 01:12:19.775 --> 01:12:22.610 align:middle line:84% a fairly simple-looking expression involving just 01:12:22.610 --> 01:12:24.050 align:middle line:90% constants of nature-- 01:12:24.050 --> 01:12:27.500 align:middle line:84% it's the charge electron squared divided by h bar and c 01:12:27.500 --> 01:12:29.900 align:middle line:84% with this critical factor of 2 pi, 01:12:29.900 --> 01:12:33.320 align:middle line:84% evaluate that numerically, the shift by which 01:12:33.320 --> 01:12:36.590 align:middle line:84% the effective magnetic moment should have risen compared 01:12:36.590 --> 01:12:39.230 align:middle line:84% to the original quantum mechanical prediction 01:12:39.230 --> 01:12:41.660 align:middle line:84% is about one part in 10 to the 3. 01:12:41.660 --> 01:12:45.080 align:middle line:84% In fact, he could calculate out to multiple significant digits 01:12:45.080 --> 01:12:47.090 align:middle line:84% and compare that, and it's unbelievably 01:12:47.090 --> 01:12:50.840 align:middle line:84% spot-on within the experimental error of that early measurement 01:12:50.840 --> 01:12:52.040 align:middle line:90% from the Columbia group. 01:12:52.040 --> 01:12:56.360 align:middle line:84% That finally convinces people, by December of 1947, 01:12:56.360 --> 01:12:58.160 align:middle line:84% that these virtual particles might really 01:12:58.160 --> 01:13:01.640 align:middle line:84% be part of the world after all and that maybe not all hope 01:13:01.640 --> 01:13:02.570 align:middle line:90% is lost. 01:13:02.570 --> 01:13:06.320 align:middle line:84% If you focus, as a very pragmatic wartime researcher 01:13:06.320 --> 01:13:09.920 align:middle line:84% had had to do, if you focus on getting the numbers out 01:13:09.920 --> 01:13:12.800 align:middle line:84% and focus on what relationships should appear on their own 01:13:12.800 --> 01:13:16.430 align:middle line:84% or only in combination, Schwinger shows-- 01:13:16.430 --> 01:13:19.682 align:middle line:84% and others were quickly able to generalize, 01:13:19.682 --> 01:13:21.640 align:middle line:84% that you might be able to calculate the effects 01:13:21.640 --> 01:13:23.350 align:middle line:90% of virtual particles after all. 01:13:23.350 --> 01:13:27.200 align:middle line:84% So let me summarize, I'll have time for some more questions. 01:13:27.200 --> 01:13:30.010 align:middle line:84% So beginning right after the introduction 01:13:30.010 --> 01:13:32.290 align:middle line:84% of quantum mechanics, several physicists, 01:13:32.290 --> 01:13:33.850 align:middle line:84% including the names we already know, 01:13:33.850 --> 01:13:36.610 align:middle line:84% Dirac and Heisenberg and Jordan and Pauli and others, 01:13:36.610 --> 01:13:39.480 align:middle line:84% began developing a quantum field theory trying 01:13:39.480 --> 01:13:42.640 align:middle line:84% to treat extended objects through space and time 01:13:42.640 --> 01:13:45.670 align:middle line:84% as collections of field excitations 01:13:45.670 --> 01:13:49.700 align:middle line:84% obeying these special quantum mechanical rules. 01:13:49.700 --> 01:13:51.460 align:middle line:84% And so you could represent any field 01:13:51.460 --> 01:13:55.030 align:middle line:84% as a collection of quanta in particular states with the very 01:13:55.030 --> 01:13:57.850 align:middle line:84% important caveat that the uncertainty principle at least 01:13:57.850 --> 01:14:01.360 align:middle line:84% suggested that these virtual processes could temporarily 01:14:01.360 --> 01:14:04.060 align:middle line:84% break the rules as long as they paid the energy back 01:14:04.060 --> 01:14:07.450 align:middle line:90% correspondingly quickly. 01:14:07.450 --> 01:14:11.560 align:middle line:84% However, that was a compelling cartoon story. 01:14:11.560 --> 01:14:15.220 align:middle line:84% It led to a total lack of ability 01:14:15.220 --> 01:14:19.820 align:middle line:84% to quantify those behaviors throughout the 1930, 01:14:19.820 --> 01:14:21.340 align:middle line:84% and that led some people to claim 01:14:21.340 --> 01:14:23.620 align:middle line:84% we need another sweeping conceptual evolution 01:14:23.620 --> 01:14:25.240 align:middle line:84% that the whole edifice will change 01:14:25.240 --> 01:14:29.990 align:middle line:84% yet again because these quantum virtual processes yield 01:14:29.990 --> 01:14:31.740 align:middle line:90% infinite results. 01:14:31.740 --> 01:14:33.650 align:middle line:84% And yet after the Second World War, 01:14:33.650 --> 01:14:37.220 align:middle line:84% a new generation of both experimentalists and theorists 01:14:37.220 --> 01:14:40.160 align:middle line:84% returned to this now decades-long challenge, 01:14:40.160 --> 01:14:42.080 align:middle line:84% and they came at it with different skills, 01:14:42.080 --> 01:14:44.010 align:middle line:84% sometimes literally different equipment, 01:14:44.010 --> 01:14:45.710 align:middle line:84% different theoretical approaches, 01:14:45.710 --> 01:14:48.870 align:middle line:84% and a different kind of mindset for many of them, 01:14:48.870 --> 01:14:51.980 align:middle line:84% and were able to find a way to actually yield 01:14:51.980 --> 01:14:54.320 align:middle line:84% finite and, in fact, quite sensible 01:14:54.320 --> 01:14:57.770 align:middle line:84% numerical values from these very abstract-sounding 01:14:57.770 --> 01:14:59.520 align:middle line:90% quantum virtual processes. 01:14:59.520 --> 01:15:00.780 align:middle line:90% So I'll stop there. 01:15:00.780 --> 01:15:03.780 align:middle line:84% I'm happy to say if people have questions for that. 01:15:03.780 --> 01:15:05.720 align:middle line:84% Any questions or comments or concerns? 01:15:05.720 --> 01:15:10.260 align:middle line:90% 01:15:10.260 --> 01:15:12.810 align:middle line:84% I should also say, that Robert Mills piece 01:15:12.810 --> 01:15:15.670 align:middle line:84% is a little more complicated than I would have liked. 01:15:15.670 --> 01:15:17.970 align:middle line:84% It's a pretty handy reading, but it still 01:15:17.970 --> 01:15:19.530 align:middle line:90% assumes a lot of formalism. 01:15:19.530 --> 01:15:22.410 align:middle line:84% So if it was a hard reading, don't worry about it. 01:15:22.410 --> 01:15:24.570 align:middle line:84% What I wanted you to get out of it is at the level 01:15:24.570 --> 01:15:26.548 align:middle line:84% that we talked about at in class today. 01:15:26.548 --> 01:15:28.090 align:middle line:84% I'd be glad if people have questions, 01:15:28.090 --> 01:15:30.300 align:middle line:84% I'd be delighted to talk more about more details, 01:15:30.300 --> 01:15:34.750 align:middle line:84% but if that article was a little off-putting or seemed too hard, 01:15:34.750 --> 01:15:35.250 align:middle line:90% don't worry. 01:15:35.250 --> 01:15:38.400 align:middle line:84% If you've got this basic lesson, that that's what 01:15:38.400 --> 01:15:40.230 align:middle line:84% we want to get out of the Mills piece, 01:15:40.230 --> 01:15:41.550 align:middle line:90% at least that much for now. 01:15:41.550 --> 01:15:45.780 align:middle line:90% 01:15:45.780 --> 01:15:46.415 align:middle line:90% OK. 01:15:46.415 --> 01:15:48.540 align:middle line:84% If there's no questions, I won't force you to stay, 01:15:48.540 --> 01:15:50.248 align:middle line:84% but I invite you to come to office hours, 01:15:50.248 --> 01:15:51.420 align:middle line:90% drop me an email anytime. 01:15:51.420 --> 01:15:53.820 align:middle line:84% And we'll pick up this story on Wednesday 01:15:53.820 --> 01:15:55.860 align:middle line:84% when we look at other folks who returned 01:15:55.860 --> 01:15:58.140 align:middle line:84% to the question of virtual particles and quantum 01:15:58.140 --> 01:15:58.960 align:middle line:90% fluctuations. 01:15:58.960 --> 01:16:00.010 align:middle line:90% So see you Wednesday. 01:16:00.010 --> 01:16:01.640 align:middle line:90% Stay well. 01:16:01.640 --> 01:16:11.000 align:middle line:90%