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Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:18.60,Default,,0000,0000,0000,,{\i1}35C3 preroll music{\i0}
Dialogue: 0,0:00:18.60,0:00:26.93,Default,,0000,0000,0000,,Herald Angel: And, so he studied physics\Nand I'm thinking we just all need a lot
Dialogue: 0,0:00:26.93,0:00:33.55,Default,,0000,0000,0000,,better understanding of quantum mechanics,\Nbecause he sees this theory being misused
Dialogue: 0,0:00:33.55,0:00:42.33,Default,,0000,0000,0000,,a lot by some weird esoteric theories,\Nkind of abusing it to just justify
Dialogue: 0,0:00:42.33,0:00:48.25,Default,,0000,0000,0000,,everything and anything. So he wants to\Nchange that and he wants to have people
Dialogue: 0,0:00:48.25,0:00:53.81,Default,,0000,0000,0000,,with some understanding of this very\Nimportant theory and so he will start
Dialogue: 0,0:00:53.81,0:00:58.57,Default,,0000,0000,0000,,today with all of us here and try to\Nexplain to us the wonders of quantum
Dialogue: 0,0:00:58.57,0:01:08.72,Default,,0000,0000,0000,,mechanics. Have a go.\N{\i1}applause{\i0}
Dialogue: 0,0:01:08.72,0:01:11.70,Default,,0000,0000,0000,,Sebastian Riese: Well thank you for a warm\Nwelcome. It will be about quantum
Dialogue: 0,0:01:11.70,0:01:18.11,Default,,0000,0000,0000,,mechanics. We will see whether the gentle\Nintroduction will be a lie depending on
Dialogue: 0,0:01:18.11,0:01:23.38,Default,,0000,0000,0000,,how good you can follow me. So at first\Nthere will be a short introduction, a bit
Dialogue: 0,0:01:23.38,0:01:29.56,Default,,0000,0000,0000,,meta discussion about physical theories\Nand what is the aim of this talk. And then
Dialogue: 0,0:01:29.56,0:01:35.24,Default,,0000,0000,0000,,we will discuss the experiments. Most of\Nthis is high school physics, you've
Dialogue: 0,0:01:35.24,0:01:40.36,Default,,0000,0000,0000,,probably seen it before. And then it will\Nget ugly because we'll do the theory and
Dialogue: 0,0:01:40.36,0:01:45.08,Default,,0000,0000,0000,,we'll really do the theory, we'll write\Ndown the equations of quantum mechanics
Dialogue: 0,0:01:45.08,0:01:50.45,Default,,0000,0000,0000,,and try to make them plausible and\Nhopefully understandable to a lot of
Dialogue: 0,0:01:50.45,0:01:56.86,Default,,0000,0000,0000,,people. And finally some applications will\Nbe discussed. So what is the concept of
Dialogue: 0,0:01:56.86,0:02:02.47,Default,,0000,0000,0000,,this talk. The key experiments will be\Nreviewed as said, and but we will not do
Dialogue: 0,0:02:02.47,0:02:07.11,Default,,0000,0000,0000,,it in historical fashion. We will look at\Nthe experiments as physical facts and
Dialogue: 0,0:02:07.11,0:02:13.45,Default,,0000,0000,0000,,derive the theory from them. And since\Nquantum mechanics is rather abstract and
Dialogue: 0,0:02:13.45,0:02:19.14,Default,,0000,0000,0000,,not, as I said in German and in science\Ntheory "anschaulich", we will need
Dialogue: 0,0:02:19.14,0:02:23.78,Default,,0000,0000,0000,,mathematics and most of this will be\Nlinear algebra. So a lot of quantum
Dialogue: 0,0:02:23.78,0:02:28.60,Default,,0000,0000,0000,,mechanics is just linear algebra on\Nsteroids, that means in infinite
Dialogue: 0,0:02:28.60,0:02:35.55,Default,,0000,0000,0000,,dimensions. And in doing so we'll try to\Nfind a certain post classical
Dialogue: 0,0:02:35.55,0:02:40.87,Default,,0000,0000,0000,,"Anschaulichkeit" or lividness to\Nunderstand the theory. Since there'll be a
Dialogue: 0,0:02:40.87,0:02:48.61,Default,,0000,0000,0000,,lot of math as the allergy advice said,\Nthere will be crash courses driven in to
Dialogue: 0,0:02:48.61,0:02:53.35,Default,,0000,0000,0000,,explain mathematical facts. Sorry for the\Nmathematicians that are here they probably
Dialogue: 0,0:02:53.35,0:03:03.52,Default,,0000,0000,0000,,suffer because I lie a lot. So at first:\NHow do scientific theories work? To really
Dialogue: 0,0:03:03.52,0:03:08.50,Default,,0000,0000,0000,,understand quantum mechanics we must\Nunderstand the setting and setting where
Dialogue: 0,0:03:08.50,0:03:14.99,Default,,0000,0000,0000,,it was created and how scientific theories\Nare created in general. A scientific
Dialogue: 0,0:03:14.99,0:03:19.92,Default,,0000,0000,0000,,theory is a net of interdependent\Npropositions so we have one proposition
Dialogue: 0,0:03:19.92,0:03:27.10,Default,,0000,0000,0000,,for example "F = M times a" in classical\Nmechanics and we have another proposition
Dialogue: 0,0:03:27.10,0:03:32.01,Default,,0000,0000,0000,,that the gravitational force equals is\Nproportional to the product of the masses
Dialogue: 0,0:03:32.01,0:03:38.14,Default,,0000,0000,0000,,divided by the distance between the masses\Nsquared, so something like this. And when
Dialogue: 0,0:03:38.14,0:03:44.54,Default,,0000,0000,0000,,we go around, make experiments, look into\Nnature, develop theories, calculate, we
Dialogue: 0,0:03:44.54,0:03:51.30,Default,,0000,0000,0000,,test those we test hypotheses, different\Nhypotheses and try to determine which one
Dialogue: 0,0:03:51.30,0:03:57.03,Default,,0000,0000,0000,,describes our experimental results best.\NAnd if the hypothesis stands the
Dialogue: 0,0:03:57.03,0:04:02.79,Default,,0000,0000,0000,,experimental tests they're added to the\Ntheory. But what happens if there's an
Dialogue: 0,0:04:02.79,0:04:07.12,Default,,0000,0000,0000,,experimental result that totally\Ncontradicts what we've seen before? And
Dialogue: 0,0:04:07.12,0:04:12.52,Default,,0000,0000,0000,,that happened in the late 19th and early\N20th century. There are new results that
Dialogue: 0,0:04:12.52,0:04:18.69,Default,,0000,0000,0000,,could not be explained. So if such\Ninconsistent results are found then our
Dialogue: 0,0:04:18.69,0:04:24.94,Default,,0000,0000,0000,,old theory has been falsified. This term\Nis due to Popper who said that a theory is
Dialogue: 0,0:04:24.94,0:04:28.77,Default,,0000,0000,0000,,scientific as long as it can be falsified,\Nthat is at least as long as we can prove
Dialogue: 0,0:04:28.77,0:04:33.94,Default,,0000,0000,0000,,that it's not true and we can never prove\Na theory true but only prove it wrong. And
Dialogue: 0,0:04:33.94,0:04:39.35,Default,,0000,0000,0000,,all that we have not yet proven wrong are\Nat least some approximation to truth. And
Dialogue: 0,0:04:39.35,0:04:45.46,Default,,0000,0000,0000,,if this happens we have to amend our old\Ntheory and we have to use care there and
Dialogue: 0,0:04:45.46,0:04:51.81,Default,,0000,0000,0000,,find a minimal amendment. This principle\Nis Occam's Razor. One could also say the
Dialogue: 0,0:04:51.81,0:04:58.66,Default,,0000,0000,0000,,principle of least surprise from software\Nengineering. And then we try that our
Dialogue: 0,0:04:58.66,0:05:03.94,Default,,0000,0000,0000,,theory is again consistent with the\Nexperimental results. And of course the
Dialogue: 0,0:05:03.94,0:05:09.03,Default,,0000,0000,0000,,new theory must explain why the hell that,\Nfor example Newtonian mechanics work for
Dialogue: 0,0:05:09.03,0:05:14.52,Default,,0000,0000,0000,,two hundred years if it's absolutely\Nwrong. And so the old theory must in some
Dialogue: 0,0:05:14.52,0:05:20.91,Default,,0000,0000,0000,,limit contain the new one. And now how\Ndoes it begin with quantum mechanics. As
Dialogue: 0,0:05:20.91,0:05:25.82,Default,,0000,0000,0000,,already said the time frame is the late\N19th and early 20th century. And there
Dialogue: 0,0:05:25.82,0:05:32.10,Default,,0000,0000,0000,,were three or four fundamental theories of\Nphysics known then: Classical mechanics,
Dialogue: 0,0:05:32.10,0:05:36.29,Default,,0000,0000,0000,,which is just governed by the single\Nequation the force equals mass times the
Dialogue: 0,0:05:36.29,0:05:44.78,Default,,0000,0000,0000,,acceleration with given forces. And two\Nknown force laws: The immediate distance
Dialogue: 0,0:05:44.78,0:05:51.41,Default,,0000,0000,0000,,action Newtonian gravitation and the\NMaxwell electro dynamics, this funny
Dialogue: 0,0:05:51.41,0:05:56.32,Default,,0000,0000,0000,,equation here. This funny equation here is\Na way of writing down the Maxwell
Dialogue: 0,0:05:56.32,0:06:04.96,Default,,0000,0000,0000,,equations that basically contain all the\Nknown electromagnetic effects. And finally
Dialogue: 0,0:06:04.96,0:06:09.58,Default,,0000,0000,0000,,there were the beginnings of the Maxwell\NBoltzmann statistical physics, but
Dialogue: 0,0:06:09.58,0:06:17.25,Default,,0000,0000,0000,,classical statistical physics is a pain,\Ndoesn't really work. So several
Dialogue: 0,0:06:17.25,0:06:22.62,Default,,0000,0000,0000,,experimental results I said could not be\Nexplained by classical theories. For
Dialogue: 0,0:06:22.62,0:06:27.89,Default,,0000,0000,0000,,example the photoelectric effect\Ndiscovered by Hertz and Hallwachs in 1887,
Dialogue: 0,0:06:27.89,0:06:32.13,Default,,0000,0000,0000,,or the discrete spectral lines of atoms\Nfirst shown by Fraunhofer in the spectrum
Dialogue: 0,0:06:32.13,0:06:38.11,Default,,0000,0000,0000,,of the sun and then studied by Bunsen and\NKirchhoff with the so-called
Dialogue: 0,0:06:38.11,0:06:43.43,Default,,0000,0000,0000,,"Bunsenbrenner", you all know it from the\Nchemistry classes. And further,
Dialogue: 0,0:06:43.43,0:06:47.90,Default,,0000,0000,0000,,radioactive rays were really a mystery\Nnobody understood: How can it happen that
Dialogue: 0,0:06:47.90,0:06:54.77,Default,,0000,0000,0000,,something just decays at random intervals?\NIt was unclear. And then the people looked
Dialogue: 0,0:06:54.77,0:07:00.81,Default,,0000,0000,0000,,into the atom, Rutherford using alpha\Nparticles to bombard a gold foil and saw
Dialogue: 0,0:07:00.81,0:07:05.26,Default,,0000,0000,0000,,there must be positively charged nucleii\Nand they already knew that they were
Dialogue: 0,0:07:05.26,0:07:13.49,Default,,0000,0000,0000,,negatively charged, what we now call\Nelectrons, particles in the atom. So this
Dialogue: 0,0:07:13.49,0:07:18.15,Default,,0000,0000,0000,,was really strange that atoms are stable\Nat composed like this and I will explain
Dialogue: 0,0:07:18.15,0:07:23.66,Default,,0000,0000,0000,,why a bit later. But now to more detail to\Nthe experiments. The really big
Dialogue: 0,0:07:23.66,0:07:29.86,Default,,0000,0000,0000,,breakthrough in this time, experimentally\Nspeaking, were vacuum tubes, so you took a
Dialogue: 0,0:07:29.86,0:07:37.58,Default,,0000,0000,0000,,piece of glass and pumped the air out and\Nclosed it off and put all sorts of devices
Dialogue: 0,0:07:37.58,0:07:45.23,Default,,0000,0000,0000,,in there. And now one thing is this nice\Ncathode ray experiment. We have here a so-
Dialogue: 0,0:07:45.23,0:07:53.96,Default,,0000,0000,0000,,called electron gun and this is a heated\Nelectrode, so here flows the current that
Dialogue: 0,0:07:53.96,0:08:00.21,Default,,0000,0000,0000,,heats it, so that the electrons get energy\Nand seep out into the vacuum. Then we have
Dialogue: 0,0:08:00.21,0:08:08.24,Default,,0000,0000,0000,,an electrode that goes around and a plate\Nin front that is positively charged. So we
Dialogue: 0,0:08:08.24,0:08:11.96,Default,,0000,0000,0000,,accelerate our electrons towards the\Nplate. There's a pinhole in the plate and
Dialogue: 0,0:08:11.96,0:08:18.85,Default,,0000,0000,0000,,we get a beam of electrons. And now we had\Nthose evacuated tubes and those electron
Dialogue: 0,0:08:18.85,0:08:24.54,Default,,0000,0000,0000,,guns. So we put the electron gun in the\Nevacuated tube, perhaps left a bit of gas
Dialogue: 0,0:08:24.54,0:08:29.05,Default,,0000,0000,0000,,in because then it glowed when it when the\Natoms in the gas were hit by the electrons
Dialogue: 0,0:08:29.05,0:08:33.94,Default,,0000,0000,0000,,so we could see the cathode ray, and then\Nwe play around. We take magnetic fields
Dialogue: 0,0:08:33.94,0:08:38.13,Default,,0000,0000,0000,,and see how does it react to magnetic\Nfields. We take electric fields. How does
Dialogue: 0,0:08:38.13,0:08:42.88,Default,,0000,0000,0000,,it react to electric fields and so on. And\Nwhat we find out is we somehow must have
Dialogue: 0,0:08:42.88,0:08:53.13,Default,,0000,0000,0000,,negatively charged particles that flow\Nnicely around in our almost vacuum. And
Dialogue: 0,0:08:53.13,0:09:00.52,Default,,0000,0000,0000,,because atoms are neutral which is just\Nknown macroscopically there must be a
Dialogue: 0,0:09:00.52,0:09:08.34,Default,,0000,0000,0000,,positively charged component in the atom\Nas well. And this positively charged
Dialogue: 0,0:09:08.34,0:09:14.08,Default,,0000,0000,0000,,component was first thought to be kind of\Na plum pudding or so with the electrons
Dialogue: 0,0:09:14.08,0:09:21.04,Default,,0000,0000,0000,,sitting in there. But the Rutherford-\NMarsden-Geiger experiment, so it was
Dialogue: 0,0:09:21.04,0:09:25.63,Default,,0000,0000,0000,,Rutherford invented the idea and Marsden\Nand Geiger actually performed the
Dialogue: 0,0:09:25.63,0:09:30.82,Default,,0000,0000,0000,,experimental work, showed that if you had\Na really thin gold foil, really only a few
Dialogue: 0,0:09:30.82,0:09:35.14,Default,,0000,0000,0000,,hundred layers of atoms, that's the nice\Nthing about gold, you can just hammer it
Dialogue: 0,0:09:35.14,0:09:41.53,Default,,0000,0000,0000,,out to really, really thin sheets, if you\Nhad that and then shot alpha particles
Dialogue: 0,0:09:41.53,0:09:47.54,Default,,0000,0000,0000,,that is helium nuclei that are created by\Nthe radioactive decay of many heavy
Dialogue: 0,0:09:47.54,0:09:54.90,Default,,0000,0000,0000,,elements for example, most uranium\Nisotopes decay by alpha decay, then they
Dialogue: 0,0:09:54.90,0:10:00.05,Default,,0000,0000,0000,,were deflected strongly. If the charge\Nwould have been spaced throughout the
Dialogue: 0,0:10:00.05,0:10:04.01,Default,,0000,0000,0000,,atoms then this could not have happened.\NYou can calculate, you can
Dialogue: 0,0:10:04.01,0:10:09.65,Default,,0000,0000,0000,,estimate the possible deflections with an\Nextended charge and with a concentrated
Dialogue: 0,0:10:09.65,0:10:14.19,Default,,0000,0000,0000,,charge, and you see the only explanation\Nfor this is that there is a massive and
Dialogue: 0,0:10:14.19,0:10:22.05,Default,,0000,0000,0000,,really, really small positive thing in\Nthose atoms. So atoms are small,
Dialogue: 0,0:10:22.05,0:10:27.55,Default,,0000,0000,0000,,positively charged nucleus as Rutherford\Ncalled it and around it there's a cloud of
Dialogue: 0,0:10:27.55,0:10:33.82,Default,,0000,0000,0000,,electrons or, he thought, orbiting\Nelectrons. But orbiting electrons atoms
Dialogue: 0,0:10:33.82,0:10:37.68,Default,,0000,0000,0000,,are stable, this doesn't really make sense\Nin classical physics, because in classical
Dialogue: 0,0:10:37.68,0:10:43.03,Default,,0000,0000,0000,,physics all accelerator charges must\Nradiate energy and be slowed by this
Dialogue: 0,0:10:43.03,0:10:51.92,Default,,0000,0000,0000,,process. And this means atoms that are\Nstable and composed of some strange
Dialogue: 0,0:10:51.92,0:10:58.75,Default,,0000,0000,0000,,electrons and having nuclei they're just\Nnot possible. It's a no go, so at least at
Dialogue: 0,0:10:58.75,0:11:02.93,Default,,0000,0000,0000,,this moment it was completely clear\Nclassical physics as they knew it up until
Dialogue: 0,0:11:02.93,0:11:09.87,Default,,0000,0000,0000,,then is wrong. And the next experiment in\Nthis direction was the photoelectric
Dialogue: 0,0:11:09.87,0:11:15.35,Default,,0000,0000,0000,,effect. What's shown there is a schematic\Nof a phototube. And a phototube is again a
Dialogue: 0,0:11:15.35,0:11:22.55,Default,,0000,0000,0000,,vacuum tube out of glass and there is a\Nfor example cesium layer in in the tube at
Dialogue: 0,0:11:22.55,0:11:27.40,Default,,0000,0000,0000,,one side and there is a ring electrode\Nremoved from it. And if we shine light on
Dialogue: 0,0:11:27.40,0:11:34.56,Default,,0000,0000,0000,,this there flows a current. But the\Npeculiar thing is that if we do the bias
Dialogue: 0,0:11:34.56,0:11:44.13,Default,,0000,0000,0000,,voltage across the two terminals of this\Ntube to stop the electrons, we see that
Dialogue: 0,0:11:44.13,0:11:49.04,Default,,0000,0000,0000,,the bias voltage that completely stops the\Nflow is not proportional to the intensity
Dialogue: 0,0:11:49.04,0:11:53.69,Default,,0000,0000,0000,,of the light that is incident onto the\Ntube, but it's proportional to the
Dialogue: 0,0:11:53.69,0:11:59.54,Default,,0000,0000,0000,,frequency of the light that's incident on\Nthe phototube. And that was again really
Dialogue: 0,0:11:59.54,0:12:05.18,Default,,0000,0000,0000,,weird for the people of the time because\Nthe frequency shouldn't make any
Dialogue: 0,0:12:05.18,0:12:11.93,Default,,0000,0000,0000,,difference for the energy. And this was\Nwhen Einstein derived that, or thought of
Dialogue: 0,0:12:11.93,0:12:18.15,Default,,0000,0000,0000,,that there must be some kind of energy\Nportions in the electric field, from this
Dialogue: 0,0:12:18.15,0:12:23.48,Default,,0000,0000,0000,,simple experiment, which is often done in\Nphysics classes even at the high school
Dialogue: 0,0:12:23.48,0:12:31.04,Default,,0000,0000,0000,,level. So it's, from today's view it's not\Na complicated experiment. And to go even
Dialogue: 0,0:12:31.04,0:12:37.15,Default,,0000,0000,0000,,further those weird stable atoms had\Ndiscrete, had discrete lines of emission
Dialogue: 0,0:12:37.15,0:12:43.66,Default,,0000,0000,0000,,and absorption of light. And here we have\Nagain a very simplified experimental set
Dialogue: 0,0:12:43.66,0:12:48.01,Default,,0000,0000,0000,,up of a so-called discharge tube, where we\Nhave high voltage between the terminals
Dialogue: 0,0:12:48.01,0:12:53.45,Default,,0000,0000,0000,,and a thin gas and then a current will\Nflow, will excite the atoms. The atoms
Dialogue: 0,0:12:53.45,0:12:58.56,Default,,0000,0000,0000,,will relax and emit light and this light\Nwill have a specific spectrum with sharp
Dialogue: 0,0:12:58.56,0:13:03.67,Default,,0000,0000,0000,,frequencies that are, that have strong\Nemission and we can see this with a
Dialogue: 0,0:13:03.67,0:13:08.84,Default,,0000,0000,0000,,diffraction grating that sorts light out\Naccording to its wavelength and then look
Dialogue: 0,0:13:08.84,0:13:13.87,Default,,0000,0000,0000,,on the screen or view some more fancy\Noptical instrument to do precision
Dialogue: 0,0:13:13.87,0:13:22.86,Default,,0000,0000,0000,,measurements as Bunsen and Kirchhoff did.\NSo what we knew up until now was that
Dialogue: 0,0:13:22.86,0:13:28.73,Default,,0000,0000,0000,,something was really weird and our\Nphysical theories didn't make sense. And
Dialogue: 0,0:13:28.73,0:13:34.15,Default,,0000,0000,0000,,then it got worse. Someone took an\Nelectron gun and pointed it at a
Dialogue: 0,0:13:34.15,0:13:38.43,Default,,0000,0000,0000,,monocrystalline surface. And such a\Nmonocrystalline surface is just like a
Dialogue: 0,0:13:38.43,0:13:45.67,Default,,0000,0000,0000,,diffraction grating: A periodically\Narranged thing. And off periodically
Dialogue: 0,0:13:45.67,0:13:53.02,Default,,0000,0000,0000,,arranged things there does happen regular\Ninterference pattern creation. So they saw
Dialogue: 0,0:13:53.02,0:13:58.10,Default,,0000,0000,0000,,interference pattern with electrons. But\Nelectrons aren't that particles? How can
Dialogue: 0,0:13:58.10,0:14:03.45,Default,,0000,0000,0000,,particles, so what was thought of then,\Nsince the times of Newton as a little hard
Dialogue: 0,0:14:03.45,0:14:08.84,Default,,0000,0000,0000,,ball, how can a little hard ball flowing\Naround create interference patterns? It
Dialogue: 0,0:14:08.84,0:14:18.37,Default,,0000,0000,0000,,was really weird. And there's even more\Nand as already mentioned radioactivity
Dialogue: 0,0:14:18.37,0:14:24.42,Default,,0000,0000,0000,,with the random decay of a nucleus. This\Ndoesn't make sense in classical physics,
Dialogue: 0,0:14:24.42,0:14:30.04,Default,,0000,0000,0000,,so it was really, really bad. And here\NI've added some modern facts that we'll
Dialogue: 0,0:14:30.04,0:14:38.10,Default,,0000,0000,0000,,need later on. Namely that if we measure,\Nif we try to measure the position of a
Dialogue: 0,0:14:38.10,0:14:44.41,Default,,0000,0000,0000,,particle and use different position\Nsensors to do so, only one of them, so at
Dialogue: 0,0:14:44.41,0:14:48.45,Default,,0000,0000,0000,,only at one position will the single\Nparticle register, but it will
Dialogue: 0,0:14:48.45,0:14:53.50,Default,,0000,0000,0000,,nevertheless show an interference pattern\Nif I do this experiment with many many
Dialogue: 0,0:14:53.50,0:14:59.47,Default,,0000,0000,0000,,electrons. So there must somehow be a\Nstrange divide between the free space
Dialogue: 0,0:14:59.47,0:15:05.82,Default,,0000,0000,0000,,propagation of particles and measuring the\Nparticles. And you can do really weird
Dialogue: 0,0:15:05.82,0:15:11.32,Default,,0000,0000,0000,,stuff and record the information through\Nwhich slit the particle went. And if you
Dialogue: 0,0:15:11.32,0:15:16.45,Default,,0000,0000,0000,,do this, the interference pattern\Nvanishes. And then you can even destroy
Dialogue: 0,0:15:16.45,0:15:24.64,Default,,0000,0000,0000,,this information in a coherent manner and\Nthe interference pattern appears again. So
Dialogue: 0,0:15:24.64,0:15:28.77,Default,,0000,0000,0000,,what we know up until now is that quantum\Nmechanics is really, really weird and
Dialogue: 0,0:15:28.77,0:15:37.54,Default,,0000,0000,0000,,really different from classical mechanics.\NAnd now that we've talked about those
Dialogue: 0,0:15:37.54,0:15:41.48,Default,,0000,0000,0000,,experiments, we'll begin with the theory,\Nand the theory will begin with a lot of
Dialogue: 0,0:15:41.48,0:15:49.44,Default,,0000,0000,0000,,mathematics. The first one is simple.\NComplex numbers. Who doesn't know complex
Dialogue: 0,0:15:49.44,0:15:59.22,Default,,0000,0000,0000,,numbers? Okay. Sorry I'll have to ignore\Nyou for the sake of getting to the next
Dialogue: 0,0:15:59.22,0:16:05.09,Default,,0000,0000,0000,,points. {\i1}laughter{\i0} So I'll just say\Ncomplex numbers are two components of, two
Dialogue: 0,0:16:05.09,0:16:10.24,Default,,0000,0000,0000,,componented objects with real numbers. And\None of them is multiplied by an imaginary
Dialogue: 0,0:16:10.24,0:16:16.07,Default,,0000,0000,0000,,number i. And if we square the number i it\Ngets -1. And this makes many things really
Dialogue: 0,0:16:16.07,0:16:22.15,Default,,0000,0000,0000,,beautiful. For example all algebraic\Nequations have exactly the number of
Dialogue: 0,0:16:22.15,0:16:29.37,Default,,0000,0000,0000,,degrees solutions in complex numbers, and\Nif you count them correctly. And if you
Dialogue: 0,0:16:29.37,0:16:33.99,Default,,0000,0000,0000,,work with complex functions it's really\Nbeautiful. A function that once
Dialogue: 0,0:16:33.99,0:16:39.85,Default,,0000,0000,0000,,differentiable is infinitely many times\Ndifferentiable and it's, it's nice. So now
Dialogue: 0,0:16:39.85,0:16:46.50,Default,,0000,0000,0000,,we had complex numbers. You've all said\Nyou know them. {\i1}laughter{\i0} So we go onto
Dialogue: 0,0:16:46.50,0:16:53.33,Default,,0000,0000,0000,,vector spaces, which probably also a lot\Nof you know. Just to revisit it, a vector
Dialogue: 0,0:16:53.33,0:16:58.43,Default,,0000,0000,0000,,space is a space of objects called\Nvectors, above some scalars that must be a
Dialogue: 0,0:16:58.43,0:17:03.37,Default,,0000,0000,0000,,field. And here we only use complex\Nnumbers as the underlying fields. There is
Dialogue: 0,0:17:03.37,0:17:07.76,Default,,0000,0000,0000,,a null vector, we can add vectors, we can\Ninvert vectors and we can multiply vectors
Dialogue: 0,0:17:07.76,0:17:13.99,Default,,0000,0000,0000,,by real numbers. So we can say three that\Nfive times this vector and just scale the
Dialogue: 0,0:17:13.99,0:17:24.69,Default,,0000,0000,0000,,arrow and these operations interact nicely\Nso that we have those distributive laws.
Dialogue: 0,0:17:24.69,0:17:33.83,Default,,0000,0000,0000,,And now it gets interesting. Even more\Nmaths: L2 spaces. L2 spaces are in a way
Dialogue: 0,0:17:33.83,0:17:40.21,Default,,0000,0000,0000,,an infinite dimensional or one form of an\Ninfinite dimensional extension of vector
Dialogue: 0,0:17:40.21,0:17:47.08,Default,,0000,0000,0000,,spaces. Instead of having just three\Ndirections x, y, z, we have directions at
Dialogue: 0,0:17:47.08,0:17:53.42,Default,,0000,0000,0000,,each point of a function. So we have an\Nanalogy here. We have vectors which have
Dialogue: 0,0:17:53.42,0:18:01.24,Default,,0000,0000,0000,,three discrete components given by x index\Ni on the right side and we have this
Dialogue: 0,0:18:01.24,0:18:06.79,Default,,0000,0000,0000,,function and each component is the value\Nof the function at one point along the
Dialogue: 0,0:18:06.79,0:18:13.75,Default,,0000,0000,0000,,axis x. And then we can just as for\Nvectors define a norm on those L2
Dialogue: 0,0:18:13.75,0:18:18.69,Default,,0000,0000,0000,,functions which is just the integral over\Nthe absolute value squared of this
Dialogue: 0,0:18:18.69,0:18:23.61,Default,,0000,0000,0000,,function f. And the nice thing about this\Nchoice of norm, there are other choices of
Dialogue: 0,0:18:23.61,0:18:33.40,Default,,0000,0000,0000,,the norm. This norm is induced by a scalar\Nproduct and this little asterisk that is
Dialogue: 0,0:18:33.40,0:18:39.16,Default,,0000,0000,0000,,there at the f denotes the complex\Nconjugate, so flipping i to minus i in
Dialogue: 0,0:18:39.16,0:18:46.86,Default,,0000,0000,0000,,all complex values. And if you just plug\Nin f and f into the scalar product you
Dialogue: 0,0:18:46.86,0:18:53.41,Default,,0000,0000,0000,,will see that it's the integral over the\Nsquared absolute value. And this space,
Dialogue: 0,0:18:53.41,0:18:59.18,Default,,0000,0000,0000,,this L2 space is a Hilbert space and the\NHilbert Space is a complete vector space
Dialogue: 0,0:18:59.18,0:19:04.81,Default,,0000,0000,0000,,with a scalar product where complete means\Nthat - It's mathematical nonsense.
Dialogue: 0,0:19:04.81,0:19:10.05,Default,,0000,0000,0000,,Forget it. So but the nice surprise is\Nthat most things carry over from finite
Dialogue: 0,0:19:10.05,0:19:13.43,Default,,0000,0000,0000,,dimensional space. What we know from\Nfinite dimensional space is we can always
Dialogue: 0,0:19:13.43,0:19:19.18,Default,,0000,0000,0000,,diagonalize matrices with certain\Nproperties and this more or less works.
Dialogue: 0,0:19:19.18,0:19:23.62,Default,,0000,0000,0000,,And the mathematicians really, really,\Nreally do a lot of work for this but for
Dialogue: 0,0:19:23.62,0:19:30.50,Default,,0000,0000,0000,,physicists we just know when to be careful\Nand how and don't care about it otherwise.
Dialogue: 0,0:19:30.50,0:19:38.36,Default,,0000,0000,0000,,So just works for us and that's nice. And\Nnow that we have those complex numbers we
Dialogue: 0,0:19:38.36,0:19:44.53,Default,,0000,0000,0000,,can begin to discuss how particles are\Nmodeled in quantum mechanics. And as we
Dialogue: 0,0:19:44.53,0:19:48.56,Default,,0000,0000,0000,,know from the Davisson-Germer experiments\Nthere's diffraction of electrons but
Dialogue: 0,0:19:48.56,0:19:54.13,Default,,0000,0000,0000,,there's nothing in electrons that\Ncorresponds to an electric field in some
Dialogue: 0,0:19:54.13,0:20:00.05,Default,,0000,0000,0000,,direction or so. Some other periodicity\Nhas, so periodicity of electrons during
Dialogue: 0,0:20:00.05,0:20:07.77,Default,,0000,0000,0000,,propagation has never been directly\Nobserved. And De Broglie said particles
Dialogue: 0,0:20:07.77,0:20:12.49,Default,,0000,0000,0000,,have a wavelength that's related to their\Nmomentum. And he was motivated primarily
Dialogue: 0,0:20:12.49,0:20:19.43,Default,,0000,0000,0000,,by the Bohr theory of the atom to do so.\NAnd he was shown right by the Davisson-
Dialogue: 0,0:20:19.43,0:20:24.30,Default,,0000,0000,0000,,Germer experiments so his relation for the\Nwavelength of a particle is older than the
Dialogue: 0,0:20:24.30,0:20:29.65,Default,,0000,0000,0000,,experiments showing this, which is\Nimpressive I think. And now the idea is
Dialogue: 0,0:20:29.65,0:20:33.45,Default,,0000,0000,0000,,they have a complex wave function and let\Nthe squared absolute value of the wave
Dialogue: 0,0:20:33.45,0:20:39.88,Default,,0000,0000,0000,,function describe the probability density\Nof a particle. So we make particles
Dialogue: 0,0:20:39.88,0:20:46.40,Default,,0000,0000,0000,,extended but probability measured objects\Nso there isn't no longer the position of
Dialogue: 0,0:20:46.40,0:20:50.50,Default,,0000,0000,0000,,the particle as long as we don't measure.\NBut we have just some description of a
Dialogue: 0,0:20:50.50,0:20:56.86,Default,,0000,0000,0000,,probability where the particle is. And by\Nmaking it complex we have a phase and this
Dialogue: 0,0:20:56.86,0:21:01.42,Default,,0000,0000,0000,,phase can allow, still allow, interference\Neffects which we need for explaining the
Dialogue: 0,0:21:01.42,0:21:07.13,Default,,0000,0000,0000,,interference peaks in the Davisson-Germer\Nexperiment. And now a lot of textbooks say
Dialogue: 0,0:21:07.13,0:21:13.25,Default,,0000,0000,0000,,here there's a wave particle dualism, blah\Nblah blah. Distinct nonsense, blah.
Dialogue: 0,0:21:13.25,0:21:19.76,Default,,0000,0000,0000,,The point is it doesn't get you far to\Nthink about quantum objects as either wave
Dialogue: 0,0:21:19.76,0:21:25.85,Default,,0000,0000,0000,,or particle, they're just quantum. Neither\Nwave nor particle. Doesn't help you either
Dialogue: 0,0:21:25.85,0:21:30.05,Default,,0000,0000,0000,,but it doesn't confuse you as much as when\Nyou tried to think about particles as
Dialogue: 0,0:21:30.05,0:21:37.93,Default,,0000,0000,0000,,waves or particles, or about quantum\Nparticles as waves or particles. And now
Dialogue: 0,0:21:37.93,0:21:43.55,Default,,0000,0000,0000,,that we say we have a complex wave\Nfunction what about simply using a plain
Dialogue: 0,0:21:43.55,0:21:50.57,Default,,0000,0000,0000,,wave with constant probability as the\Nstates of definite momentum because we
Dialogue: 0,0:21:50.57,0:21:55.92,Default,,0000,0000,0000,,somehow have to describe a particle to say\Nthat has a certain momentum and we do
Dialogue: 0,0:21:55.92,0:22:00.11,Default,,0000,0000,0000,,this. Those have the little problem that\Nthey are not in the Hilbert space because
Dialogue: 0,0:22:00.11,0:22:07.42,Default,,0000,0000,0000,,they're not normalizable. The absolute\Nvalue of psi is 1 over 2 pi everywhere, so
Dialogue: 0,0:22:07.42,0:22:13.63,Default,,0000,0000,0000,,that's bad. But we can write the\Nsuperposition of any state by Fourier
Dialogue: 0,0:22:13.63,0:22:19.55,Default,,0000,0000,0000,,transformation those e to the i k dot r\Nstates are just the basis states of a
Dialogue: 0,0:22:19.55,0:22:25.55,Default,,0000,0000,0000,,Fourier transformation. We can write any\Nfunction in terms of this basis. And we
Dialogue: 0,0:22:25.55,0:22:30.05,Default,,0000,0000,0000,,can conclude that by Fourier\Ntransformation of the state psi of r to
Dialogue: 0,0:22:30.05,0:22:35.50,Default,,0000,0000,0000,,some state till the psi of k, we describe\Nthe same information because we know we
Dialogue: 0,0:22:35.50,0:22:39.81,Default,,0000,0000,0000,,can invert the Fourier transformation and\Nalso this implies the uncertainty
Dialogue: 0,0:22:39.81,0:22:47.72,Default,,0000,0000,0000,,relation. And because this is simply\Nproperty of Fourier transformations that
Dialogue: 0,0:22:47.72,0:22:52.13,Default,,0000,0000,0000,,either the function can be very\Nconcentrated in position space or in
Dialogue: 0,0:22:52.13,0:22:58.34,Default,,0000,0000,0000,,momentum space. And now that\Nwe have states of definite momentum. And
Dialogue: 0,0:22:58.34,0:23:04.53,Default,,0000,0000,0000,,the other big ingredient in quantum\Nmechanics are operators, next to the state
Dialogue: 0,0:23:04.53,0:23:09.38,Default,,0000,0000,0000,,description. And operators are, just like\Nmatrices, linear operators on the state
Dialogue: 0,0:23:09.38,0:23:16.09,Default,,0000,0000,0000,,space. Just as we can apply a linear\Noperator in the form of a matrix to a vector,
Dialogue: 0,0:23:16.09,0:23:24.71,Default,,0000,0000,0000,,we can apply linear operators to L2\Nfunctions. And when we measure an
Dialogue: 0,0:23:24.71,0:23:30.01,Default,,0000,0000,0000,,observable it will be that it's one of the\Neigenvalues of this operator that's the
Dialogue: 0,0:23:30.01,0:23:36.94,Default,,0000,0000,0000,,measurement value, you know. So\Neigenvalues are those values: If a matrix
Dialogue: 0,0:23:36.94,0:23:44.33,Default,,0000,0000,0000,,that just scales a vector by a certain\Namount that is an eigenvalue of the matrix
Dialogue: 0,0:23:44.33,0:23:49.41,Default,,0000,0000,0000,,and in the same sense we can define\Neigenvalues and eigenvectors for, L2
Dialogue: 0,0:23:49.41,0:23:57.25,Default,,0000,0000,0000,,functions. And there are some facts such\Nas that non-commuting operators have
Dialogue: 0,0:23:57.25,0:24:05.83,Default,,0000,0000,0000,,eigenstates that are not common. So we\Ncan't have a description of the basis of
Dialogue: 0,0:24:05.83,0:24:12.16,Default,,0000,0000,0000,,the state space in terms of function that\Nare both eigenfunctions of both operators
Dialogue: 0,0:24:12.16,0:24:16.76,Default,,0000,0000,0000,,and some examples of operators are the\Nmomentum operator which is just minus i
Dialogue: 0,0:24:16.76,0:24:23.81,Default,,0000,0000,0000,,h-bar Nabla which is the derivation\Noperator in three dimensions. So in the x
Dialogue: 0,0:24:23.81,0:24:27.81,Default,,0000,0000,0000,,component we have derivation in the\Ndirection of x and in the y component in
Dialogue: 0,0:24:27.81,0:24:34.23,Default,,0000,0000,0000,,direction of y and so on. And the position\Noperator which is just the operator that
Dialogue: 0,0:24:34.23,0:24:42.56,Default,,0000,0000,0000,,multiplies by the position x in the\Nposition space representation of the wave
Dialogue: 0,0:24:42.56,0:24:48.25,Default,,0000,0000,0000,,function. And as for the non-\Ncommuntitivity of operators we can already
Dialogue: 0,0:24:48.25,0:24:54.71,Default,,0000,0000,0000,,show that those p and x operators that do\Nnot commute but fulfill a certain
Dialogue: 0,0:24:54.71,0:25:00.62,Default,,0000,0000,0000,,commutation relation. And a commutation\Nrelation is just a measure for how much
Dialogue: 0,0:25:00.62,0:25:07.25,Default,,0000,0000,0000,,two operators do not commute. And the\Ncommutator is AB minus BA for the objects
Dialogue: 0,0:25:07.25,0:25:15.18,Default,,0000,0000,0000,,AB, so if they commute, if AB equals BA\Nthe commutator simply vanishes. And
Dialogue: 0,0:25:15.18,0:25:20.87,Default,,0000,0000,0000,,there's more on operators just to make it\Nclear: Linear just means that we can split
Dialogue: 0,0:25:20.87,0:25:26.66,Default,,0000,0000,0000,,the argument if it is just some linear\Ncombinations of vectors and apply the
Dialogue: 0,0:25:26.66,0:25:32.34,Default,,0000,0000,0000,,operator to the individual vectors\Noccuring, we can define multiplication of
Dialogue: 0,0:25:32.34,0:25:38.24,Default,,0000,0000,0000,,operators and this just exactly follows\Nthe template that is laid down by finite
Dialogue: 0,0:25:38.24,0:25:44.11,Default,,0000,0000,0000,,dimensional linear algebra. There's\Nnothing new here. And there are inverse
Dialogue: 0,0:25:44.11,0:25:49.38,Default,,0000,0000,0000,,operators for some operators, not for all\Nof them, that give the identity operator
Dialogue: 0,0:25:49.38,0:25:54.45,Default,,0000,0000,0000,,if it's multiplied with the original\Noperator. And further there's the so-
Dialogue: 0,0:25:54.45,0:26:00.40,Default,,0000,0000,0000,,called adjoint. Our scalar product had\Nthis little asterisk and this means that
Dialogue: 0,0:26:00.40,0:26:04.56,Default,,0000,0000,0000,,it's not linear in the first component. If\NI scale the first component by some
Dialogue: 0,0:26:04.56,0:26:10.60,Default,,0000,0000,0000,,complex number alpha the total scalar\Nproduct is not scaled by alpha, but by the
Dialogue: 0,0:26:10.60,0:26:17.61,Default,,0000,0000,0000,,complex conjugate of alpha. This kind of\Nnot quite bi-linearity is sometimes called
Dialogue: 0,0:26:17.61,0:26:26.98,Default,,0000,0000,0000,,sesquilinearity, a seldomly used word, and\Nthey're commonly defined classes of
Dialogue: 0,0:26:26.98,0:26:35.99,Default,,0000,0000,0000,,operators in terms of how the adjoint that\Nis defined there acts and how some other
Dialogue: 0,0:26:35.99,0:26:39.89,Default,,0000,0000,0000,,operators for example where the adjoint is\Nthe inverse which is a generalization from
Dialogue: 0,0:26:39.89,0:26:45.52,Default,,0000,0000,0000,,the fact that for rotation operators in\Nnormal Euclidean space, the transpose is
Dialogue: 0,0:26:45.52,0:26:53.95,Default,,0000,0000,0000,,the inverse. And now that we have\Noperators we can define expectation values
Dialogue: 0,0:26:53.95,0:26:59.27,Default,,0000,0000,0000,,just by some formula. For now, we don't\Nknow what expectation values are, but we
Dialogue: 0,0:26:59.27,0:27:03.69,Default,,0000,0000,0000,,can assume, it has something to do with\Nthe measurement values of the operator
Dialogue: 0,0:27:03.69,0:27:09.51,Default,,0000,0000,0000,,because: why else would I tell you about\Nit. And later on we will show that this is
Dialogue: 0,0:27:09.51,0:27:15.16,Default,,0000,0000,0000,,actually the expectation value of the\Nquantity if we prepare a system always in
Dialogue: 0,0:27:15.16,0:27:20.78,Default,,0000,0000,0000,,the same fashion and then do measurements\Non it, we get random results each time,
Dialogue: 0,0:27:20.78,0:27:29.20,Default,,0000,0000,0000,,but the expectation value will be this\Ncombination. And now again: a bit of
Dialogue: 0,0:27:29.20,0:27:34.84,Default,,0000,0000,0000,,mathematics: eigenvalue problems. Well\Nknown: You can diagonalize a matrix and
Dialogue: 0,0:27:34.84,0:27:39.82,Default,,0000,0000,0000,,you can diagonalize linear operators. You\Nhave some equation A psi equals lambda
Dialogue: 0,0:27:39.82,0:27:47.08,Default,,0000,0000,0000,,psi, where lambda is just a scalar. And if\Nsuch an equation holds for some vector psi
Dialogue: 0,0:27:47.08,0:27:52.77,Default,,0000,0000,0000,,then it's an eigenvector and if we scale\Nthe vector linearly, this will again be an
Dialogue: 0,0:27:52.77,0:28:01.38,Default,,0000,0000,0000,,eigenvector. And what can happen is that\Nto one eigenvalue there are several
Dialogue: 0,0:28:01.38,0:28:05.35,Default,,0000,0000,0000,,eigenvectors, not only one ray of\Neigenvectors, but a higher dimensional
Dialogue: 0,0:28:05.35,0:28:11.94,Default,,0000,0000,0000,,subspace. And important to know is that\Nso-called Hermitian operators, that is
Dialogue: 0,0:28:11.94,0:28:17.69,Default,,0000,0000,0000,,those that equal their adjoint, which\Nagain means that the eigenvalues equal the
Dialogue: 0,0:28:17.69,0:28:23.98,Default,,0000,0000,0000,,complex conjugate of the eigenvalues have\Na real eigenvalues. Because if a complex
Dialogue: 0,0:28:23.98,0:28:33.07,Default,,0000,0000,0000,,number equals its complex conjugate, then\Nit's a real number. And the nice thing
Dialogue: 0,0:28:33.07,0:28:39.57,Default,,0000,0000,0000,,about those diagonalized matrices and all\Nis: we can develop any vector in terms of
Dialogue: 0,0:28:39.57,0:28:46.89,Default,,0000,0000,0000,,the eigenbasis of the operator, again just\Nlike in linear algebra where when you
Dialogue: 0,0:28:46.89,0:28:51.42,Default,,0000,0000,0000,,diagonalize a matrix, you get a new basis\Nfor your vector space and now you can
Dialogue: 0,0:28:51.42,0:28:57.64,Default,,0000,0000,0000,,express all vectors in that new basis. And\Nif the operator is Hermitian the
Dialogue: 0,0:28:57.64,0:29:05.05,Default,,0000,0000,0000,,eigenvectors have a nice property, namely\Nthey are orthogonal if the eigenvalues are
Dialogue: 0,0:29:05.05,0:29:11.38,Default,,0000,0000,0000,,different. And this is good because this\Nguarantees us that we can choose an
Dialogue: 0,0:29:11.38,0:29:16.61,Default,,0000,0000,0000,,orthonormal, that is a basis in the vector\Nspace where to basis vectors always have
Dialogue: 0,0:29:16.61,0:29:24.09,Default,,0000,0000,0000,,vanishing scalar product are orthogonal\Nand are normal, that is: we scale them to
Dialogue: 0,0:29:24.09,0:29:29.20,Default,,0000,0000,0000,,length one, because we want our\Nprobability interpretation, and in our
Dialogue: 0,0:29:29.20,0:29:37.22,Default,,0000,0000,0000,,probability interpretation we need to have\Nnormalized vectors. So now we have that
Dialogue: 0,0:29:37.22,0:29:41.89,Default,,0000,0000,0000,,and now we want to know: How does this\Nstrange function psi, that describes the
Dialogue: 0,0:29:41.89,0:29:49.58,Default,,0000,0000,0000,,state of the system, evolve in time. And\Nfor this we can have several requirements
Dialogue: 0,0:29:49.58,0:29:55.64,Default,,0000,0000,0000,,that it must fulfill. So again we are\Nclose to software engineering and one
Dialogue: 0,0:29:55.64,0:30:01.40,Default,,0000,0000,0000,,requirement is, that if it is a sharp wave\Npacket, so if we have a localized state
Dialogue: 0,0:30:01.40,0:30:06.62,Default,,0000,0000,0000,,that is not smeared around the whole\Nspace, then it should follow the classical
Dialogue: 0,0:30:06.62,0:30:12.58,Default,,0000,0000,0000,,equation of motion because we want that\Nour new theory contains our old theory.
Dialogue: 0,0:30:12.58,0:30:18.45,Default,,0000,0000,0000,,And the time evolution must conserve the\Ntotal probability of finding the particle
Dialogue: 0,0:30:18.45,0:30:21.99,Default,,0000,0000,0000,,because otherwise we couldn't do\Nprobability interpretation of our wave
Dialogue: 0,0:30:21.99,0:30:29.01,Default,,0000,0000,0000,,function, if the total probability of the\Nparticle wouldn't remain one. Further we
Dialogue: 0,0:30:29.01,0:30:35.11,Default,,0000,0000,0000,,wish the equation to be first order in\Ntime and to be linear because for example
Dialogue: 0,0:30:35.11,0:30:41.95,Default,,0000,0000,0000,,the Maxwell equations are linear and show\Nnice interference effects, so we want that
Dialogue: 0,0:30:41.95,0:30:46.37,Default,,0000,0000,0000,,because then simply a sum of solutions is\Nagain a solution, it's a good property to
Dialogue: 0,0:30:46.37,0:30:51.84,Default,,0000,0000,0000,,have and if it works that way: Why not?\NAnd the third and the fourth requirement
Dialogue: 0,0:30:51.84,0:31:00.60,Default,,0000,0000,0000,,together already give us more or less the\Nform of the Schroedinger equation. Because
Dialogue: 0,0:31:00.60,0:31:04.83,Default,,0000,0000,0000,,linearity just says that the right-hand\Nside of some linear operator applied to
Dialogue: 0,0:31:04.83,0:31:12.34,Default,,0000,0000,0000,,psi and the first order in time just means\Nthat there must be a single time
Dialogue: 0,0:31:12.34,0:31:19.84,Default,,0000,0000,0000,,derivative in the equation on the left-\Nhand side. And this i-h bar: we just wanted
Dialogue: 0,0:31:19.84,0:31:23.55,Default,,0000,0000,0000,,that there, no particular reason we could\Nhave done this differently, but it's
Dialogue: 0,0:31:23.55,0:31:31.71,Default,,0000,0000,0000,,convention. Now with this equation we can\Nlook: What must happen for the probability
Dialogue: 0,0:31:31.71,0:31:42.29,Default,,0000,0000,0000,,to be conserved and by a simple\Ncalculation we can show that it must be a
Dialogue: 0,0:31:42.29,0:31:47.87,Default,,0000,0000,0000,,Hermitian operator. And there is even more\Nthan this global argument. There's local
Dialogue: 0,0:31:47.87,0:31:52.02,Default,,0000,0000,0000,,conservation of probability, that is, a\Nparticle can't simply vanish here and
Dialogue: 0,0:31:52.02,0:31:59.25,Default,,0000,0000,0000,,appear there, but it must flow from one\Npoint to the other with local operations.
Dialogue: 0,0:31:59.25,0:32:05.36,Default,,0000,0000,0000,,This can be shown when you consider this\Nin more detail. Now we know how this
Dialogue: 0,0:32:05.36,0:32:09.46,Default,,0000,0000,0000,,equation of motion looks like, but we\Ndon't know what this mysterious object H
Dialogue: 0,0:32:09.46,0:32:16.50,Default,,0000,0000,0000,,might be. And this mysterious object H is\Nthe operator of the energy of the system
Dialogue: 0,0:32:16.50,0:32:21.77,Default,,0000,0000,0000,,which is known from classical mechanics as\Nthe Hamilton function and which we here
Dialogue: 0,0:32:21.77,0:32:26.61,Default,,0000,0000,0000,,upgrade to the Hamilton operator by using\Nthe formula for the classical Hamilton
Dialogue: 0,0:32:26.61,0:32:33.48,Default,,0000,0000,0000,,function and inserting our p into our\Noperators. And we can also extend this to
Dialogue: 0,0:32:33.48,0:32:39.71,Default,,0000,0000,0000,,a magnetic field. And by doing so we can\Nshow that our theory is more or less
Dialogue: 0,0:32:39.71,0:32:45.96,Default,,0000,0000,0000,,consistent with Newtonian mechanics. We\Ncan show the Ehrenfest theorem, that's the
Dialogue: 0,0:32:45.96,0:32:55.16,Default,,0000,0000,0000,,first equation. And then those equations\Nare almost Newton's equation of motion for
Dialogue: 0,0:32:55.16,0:33:05.69,Default,,0000,0000,0000,,the centers of mass of the particle\Nbecause this is the expectation value of
Dialogue: 0,0:33:05.69,0:33:10.67,Default,,0000,0000,0000,,the momentum, this is the expectation\Nvalue of the position of the particle.
Dialogue: 0,0:33:10.67,0:33:15.74,Default,,0000,0000,0000,,This just looks exactly like the classical\Nequation. The velocity is the momentum
Dialogue: 0,0:33:15.74,0:33:23.14,Default,,0000,0000,0000,,divided by the mass. But this is weird:\NHere we average over the force, so the
Dialogue: 0,0:33:23.14,0:33:29.92,Default,,0000,0000,0000,,gradient of the potential is the force, we\Naverage over the force and do not take the
Dialogue: 0,0:33:29.92,0:33:34.98,Default,,0000,0000,0000,,force at the center position, so we can't\Nin general solve this equation. But again
Dialogue: 0,0:33:34.98,0:33:38.62,Default,,0000,0000,0000,,if we have a sharply defined wave packet\Nwe recover the classical equations of
Dialogue: 0,0:33:38.62,0:33:44.64,Default,,0000,0000,0000,,motion, which is nice. So we have shown\Nour new theory does indeed explain why our
Dialogue: 0,0:33:44.64,0:33:51.25,Default,,0000,0000,0000,,old theory worked. We only still have to\Nexplain why the centers of mass of massive
Dialogue: 0,0:33:51.25,0:33:55.52,Default,,0000,0000,0000,,particles are usually well localized and\Nthat's a question we're still having
Dialogue: 0,0:33:55.52,0:34:08.01,Default,,0000,0000,0000,,trouble with today. But since it otherwise\Nworks: don't worry too much about it. And
Dialogue: 0,0:34:08.01,0:34:12.32,Default,,0000,0000,0000,,now you probably want to know how to solve\Nthe Schroedinger equation. Or you don't
Dialogue: 0,0:34:12.32,0:34:18.20,Default,,0000,0000,0000,,want to know anything more about quantum\Nmechanics. And to do this we make a so-
Dialogue: 0,0:34:18.20,0:34:24.56,Default,,0000,0000,0000,,called separation ansatz, where we say, we\Nhave a form stable part of our wave
Dialogue: 0,0:34:24.56,0:34:30.61,Default,,0000,0000,0000,,function multiplied by some time dependent\Npart. And if we do this we can write down
Dialogue: 0,0:34:30.61,0:34:35.59,Default,,0000,0000,0000,,the general solution for the Schroedinger\Nequation. Because we already know that the
Dialogue: 0,0:34:35.59,0:34:41.01,Default,,0000,0000,0000,,one equation that we get is an eigenvalue\Nequation or an eigenvector equation for
Dialogue: 0,0:34:41.01,0:34:45.85,Default,,0000,0000,0000,,the energy eigenvalues, that is the\Neigenvalues of the Hamilton operator. And
Dialogue: 0,0:34:45.85,0:34:50.52,Default,,0000,0000,0000,,we know that we can develop any function\Nin terms of those and so the general
Dialogue: 0,0:34:50.52,0:34:58.17,Default,,0000,0000,0000,,solution must be of the form shown here.\NAnd those states of specific energy have a
Dialogue: 0,0:34:58.17,0:35:02.22,Default,,0000,0000,0000,,simple evolution because their form is\Nconstant and only their phase changes and
Dialogue: 0,0:35:02.22,0:35:08.96,Default,,0000,0000,0000,,depends on the energy. And now this thing\Nwith the measurement in quantum mechanics
Dialogue: 0,0:35:08.96,0:35:13.20,Default,,0000,0000,0000,,is bad. You probably know Schroedinger's\Ncat and the point is: there you don't know
Dialogue: 0,0:35:13.20,0:35:16.03,Default,,0000,0000,0000,,whether the cat is dead or alive while you\Ndon't look inside the box. While you don't
Dialogue: 0,0:35:16.03,0:35:19.48,Default,,0000,0000,0000,,look inside the box as long as you don't\Nmeasure it's in a superposition or
Dialogue: 0,0:35:19.48,0:35:23.93,Default,,0000,0000,0000,,something. So You measure\Nyour cat and then it's dead. It isn't dead
Dialogue: 0,0:35:23.93,0:35:29.09,Default,,0000,0000,0000,,before only by measuring it you kill it.\NAnd that's really not nice to kill cats.
Dialogue: 0,0:35:29.09,0:35:36.97,Default,,0000,0000,0000,,We like cats. The important part here is,\Nthe TL;DR, quantum measurement is
Dialogue: 0,0:35:36.97,0:35:42.97,Default,,0000,0000,0000,,probabilistic and inherently changes the\Nsystem state. So I'll skip the multi
Dialogue: 0,0:35:42.97,0:35:52.77,Default,,0000,0000,0000,,particle things. We can't describe\Nmultiple particles. And just show the
Dialogue: 0,0:35:52.77,0:35:58.70,Default,,0000,0000,0000,,axioms of quantum mechanics shortly. Don't\Ndon't read them too detailed, but this is
Dialogue: 0,0:35:58.70,0:36:04.01,Default,,0000,0000,0000,,just a summary of what we've discussed so\Nfar. And the thing about the multiple
Dialogue: 0,0:36:04.01,0:36:09.73,Default,,0000,0000,0000,,particles is the axiom 7 which says that\Nthe sign of the wave function must change
Dialogue: 0,0:36:09.73,0:36:15.11,Default,,0000,0000,0000,,if we exchange the coordinates of\Nidentical fermions. And this makes atom
Dialogue: 0,0:36:15.11,0:36:20.74,Default,,0000,0000,0000,,stable by the way. Without this atoms as\Nwe know them would not exist. And finally
Dialogue: 0,0:36:20.74,0:36:26.81,Default,,0000,0000,0000,,there is a notational convention in\Nquantum mechanics called Bra-Ket-notation.
Dialogue: 0,0:36:26.81,0:36:35.38,Default,,0000,0000,0000,,And in Bra-Ket-notation you label states\Nby their eigenvalues and just think about
Dialogue: 0,0:36:35.38,0:36:42.47,Default,,0000,0000,0000,,such a Ket as an abstract vector such as x\Nwith a vector arrow over it or a fat set x
Dialogue: 0,0:36:42.47,0:36:48.85,Default,,0000,0000,0000,,is an abstract vector and we can either\Nrepresent it by its coordinates x1 x2 x3,
Dialogue: 0,0:36:48.85,0:36:53.06,Default,,0000,0000,0000,,or we can work with the abstract vector\Nand this Ket is such an abstract vector
Dialogue: 0,0:36:53.06,0:37:02.09,Default,,0000,0000,0000,,for the L2 function psi of r. And then we\Ncan also define the adjoint of this which
Dialogue: 0,0:37:02.09,0:37:07.69,Default,,0000,0000,0000,,gives us, if we multiply the adjoint and a\Nfunction, the scalar product. So this is a
Dialogue: 0,0:37:07.69,0:37:15.25,Default,,0000,0000,0000,,really nice and compact notation for many\Nphysics problems. And the last equation
Dialogue: 0,0:37:15.25,0:37:20.75,Default,,0000,0000,0000,,there just looks like component wise, like\Nworking with components of matrices, which
Dialogue: 0,0:37:20.75,0:37:31.58,Default,,0000,0000,0000,,is because it's nothing else. This is just\Nmatrix calculus in new clothes. Now for
Dialogue: 0,0:37:31.58,0:37:43.56,Default,,0000,0000,0000,,the applications. The first one is quite\Nfunny. There's a slide missing. Okay. Uh
Dialogue: 0,0:37:43.56,0:37:48.67,Default,,0000,0000,0000,,the first one is a quantum eraser at home.\NBecause if you encode the "which way"
Dialogue: 0,0:37:48.67,0:37:56.05,Default,,0000,0000,0000,,information into a double slit experiment\Nyou lose your interference pattern. And we
Dialogue: 0,0:37:56.05,0:38:01.22,Default,,0000,0000,0000,,do this by using a vertical and horizontal\Npolarisation filter. And you know from
Dialogue: 0,0:38:01.22,0:38:16.39,Default,,0000,0000,0000,,classical physics then it won't make an\Ninterference pattern. And if we then add a
Dialogue: 0,0:38:16.39,0:38:25.64,Default,,0000,0000,0000,,diagonal polarization filter then the\Ninterference pattern will appear again. So
Dialogue: 0,0:38:25.64,0:38:31.47,Default,,0000,0000,0000,,now, just so you've seen it, the harmonic\Noscillator can be exactly solved in
Dialogue: 0,0:38:31.47,0:38:36.50,Default,,0000,0000,0000,,quantum mechanics. If you can solve the\Nharmonic oscillator in any kind of physics
Dialogue: 0,0:38:36.50,0:38:41.93,Default,,0000,0000,0000,,then you're good, then you'll get through\Nthe axioms when you study physics. So the
Dialogue: 0,0:38:41.93,0:38:47.77,Default,,0000,0000,0000,,harmonic oscillator is solved by\Nintroducing so-called creation and
Dialogue: 0,0:38:47.77,0:38:53.56,Default,,0000,0000,0000,,destroyer operators and then we can\Ndetermine the ground state function, in a
Dialogue: 0,0:38:53.56,0:38:57.72,Default,,0000,0000,0000,,much simpler manner than if we had to\Nsolve the Schroedinger equation explicitly
Dialogue: 0,0:38:57.72,0:39:05.56,Default,,0000,0000,0000,,for all those cases. And we can determine\Nthe ground state function, so the function
Dialogue: 0,0:39:05.56,0:39:11.44,Default,,0000,0000,0000,,of lowest energy. This can all be done and\Nthen from it by applying the creation
Dialogue: 0,0:39:11.44,0:39:18.61,Default,,0000,0000,0000,,operator create the highest eigenstate of\Nthe system and get all of them. Then
Dialogue: 0,0:39:18.61,0:39:22.59,Default,,0000,0000,0000,,there's this effect of tunnelling that\Nyou've probably heard about and this just
Dialogue: 0,0:39:22.59,0:39:27.61,Default,,0000,0000,0000,,means that in quantum mechanics a\Npotential barrier that is too high for the
Dialogue: 0,0:39:27.61,0:39:32.46,Default,,0000,0000,0000,,particle to penetrate does not mean that\Nthe particle doesn't penetrate at all but
Dialogue: 0,0:39:32.46,0:39:36.75,Default,,0000,0000,0000,,that the probability of finding the\Nparticle inside the barrier decays
Dialogue: 0,0:39:36.75,0:39:42.59,Default,,0000,0000,0000,,exponentially. And this can for example be\Nunderstood in terms of this uncertainty
Dialogue: 0,0:39:42.59,0:39:47.57,Default,,0000,0000,0000,,relation because if we try to compress the\Nparticle to the smaller part of the
Dialogue: 0,0:39:47.57,0:39:52.01,Default,,0000,0000,0000,,boundary layer then its momentum has to be\Nhigh so it can reach farther in because
Dialogue: 0,0:39:52.01,0:39:58.83,Default,,0000,0000,0000,,then it has more energy. And there's this\Nmyth that tunnelling makes particles
Dialogue: 0,0:39:58.83,0:40:04.53,Default,,0000,0000,0000,,traveling to travel instantaneously from A\Nto B and even some real physicists believe
Dialogue: 0,0:40:04.53,0:40:12.70,Default,,0000,0000,0000,,it. But sorry it's not true. The particle\Nstates is extended anyway and to defining
Dialogue: 0,0:40:12.70,0:40:17.14,Default,,0000,0000,0000,,what how fast the particle travels is\Nactually not a well-defined thing in deep
Dialogue: 0,0:40:17.14,0:40:23.08,Default,,0000,0000,0000,,quantum regimes, and also the Schroedinger\Nequations is not relativistic. So there is
Dialogue: 0,0:40:23.08,0:40:27.63,Default,,0000,0000,0000,,nothing, really nothing stopping your\Nparticle from flying around with 30 times
Dialogue: 0,0:40:27.63,0:40:34.34,Default,,0000,0000,0000,,the speed of light. It's just not in the\Ntheory. Another important consequence of
Dialogue: 0,0:40:34.34,0:40:38.67,Default,,0000,0000,0000,,quantum mechanics is so-called\Nentanglement and this is a really weird
Dialogue: 0,0:40:38.67,0:40:44.11,Default,,0000,0000,0000,,one, because it shows that the universe\Nthat we live in is in a way non-local,
Dialogue: 0,0:40:44.11,0:40:51.86,Default,,0000,0000,0000,,inherently non-local. Because we can\Ncreate some states for some internal
Dialogue: 0,0:40:51.86,0:40:57.40,Default,,0000,0000,0000,,degrees of freedom of two atoms and move\Nthem apart then measure the one system and
Dialogue: 0,0:40:57.40,0:41:01.46,Default,,0000,0000,0000,,the measurement result in the one system\Nwill determine the measurement result in
Dialogue: 0,0:41:01.46,0:41:07.79,Default,,0000,0000,0000,,the other system, no matter how far\Nremoved they are from each other. And this
Dialogue: 0,0:41:07.79,0:41:12.10,Default,,0000,0000,0000,,was first discovered in a paper by\NEinstein, Podolski and Rosen and they
Dialogue: 0,0:41:12.10,0:41:17.62,Default,,0000,0000,0000,,thought it was an argument that quantum\Nmechanics is absurd. This can't be true,
Dialogue: 0,0:41:17.62,0:41:23.36,Default,,0000,0000,0000,,but sorry it is true. So this works and\Nthis kind of state that we've written
Dialogue: 0,0:41:23.36,0:41:32.97,Default,,0000,0000,0000,,there that is such an entangled state of\Ntwo particles. But important to remark is
Dialogue: 0,0:41:32.97,0:41:37.03,Default,,0000,0000,0000,,that there are no hidden variables, that\Nmeans the measurement result is not
Dialogue: 0,0:41:37.03,0:41:42.25,Default,,0000,0000,0000,,determined beforehand. It is only when we\Nmeasure that is actually known what the
Dialogue: 0,0:41:42.25,0:41:47.74,Default,,0000,0000,0000,,result will be. This is utterly weird but\None can prove this experimentally. Those
Dialogue: 0,0:41:47.74,0:41:52.24,Default,,0000,0000,0000,,are Bell tests. There's a Bell-inequality\Nthat's the limit for theories where they
Dialogue: 0,0:41:52.24,0:41:57.41,Default,,0000,0000,0000,,are hidden variables and it's by real\Nexperiments they violate the inequality
Dialogue: 0,0:41:57.41,0:42:02.82,Default,,0000,0000,0000,,and thereby show that there are no hidden\Nvariables. And there's a myth surrounding
Dialogue: 0,0:42:02.82,0:42:07.25,Default,,0000,0000,0000,,entanglement, namely that you can transfer\Ninformation with it between two sides
Dialogue: 0,0:42:07.25,0:42:12.91,Default,,0000,0000,0000,,instantaneously. But again there's nothing\Nhindering you in non relativistic quantum
Dialogue: 0,0:42:12.91,0:42:18.31,Default,,0000,0000,0000,,mechanics to distribute information\Narbitrarily fast. It doesn't have a speed
Dialogue: 0,0:42:18.31,0:42:24.44,Default,,0000,0000,0000,,limit but you can't also count communicate\Nwith those entangled pairs of particles.
Dialogue: 0,0:42:24.44,0:42:28.32,Default,,0000,0000,0000,,You can just create correlated noise at\Ntwo ends which is what quantum
Dialogue: 0,0:42:28.32,0:42:36.11,Default,,0000,0000,0000,,cryptography is using. So now because this\Nis the hackers congress, some short
Dialogue: 0,0:42:36.11,0:42:41.55,Default,,0000,0000,0000,,remarks and probably unintelligible due to\Ntheir strong compression about quantum
Dialogue: 0,0:42:41.55,0:42:47.19,Default,,0000,0000,0000,,information. A qubit, the fundamental unit\Nof quantum information, is a system with
Dialogue: 0,0:42:47.19,0:42:53.85,Default,,0000,0000,0000,,two states zero and one. So just like a\Nbit. But now we allow arbitrary super
Dialogue: 0,0:42:53.85,0:42:58.31,Default,,0000,0000,0000,,positions of those states because that is\Nwhat quantum mechanics allows. We can
Dialogue: 0,0:42:58.31,0:43:03.00,Default,,0000,0000,0000,,always superimpose states and quantum\Ncomputers are really bad for most
Dialogue: 0,0:43:03.00,0:43:08.94,Default,,0000,0000,0000,,computing tasks because they have to,\Neven if they build quantum computers they
Dialogue: 0,0:43:08.94,0:43:14.17,Default,,0000,0000,0000,,will never be as capable as the state-of-\Nthe-art silicon electrical computer. So
Dialogue: 0,0:43:14.17,0:43:18.36,Default,,0000,0000,0000,,don't fear for your jobs because of\Nquantum computers. But the problem is they
Dialogue: 0,0:43:18.36,0:43:23.60,Default,,0000,0000,0000,,can compute some things faster. For\Nexample factoring primes and working with
Dialogue: 0,0:43:23.60,0:43:29.60,Default,,0000,0000,0000,,some elliptic curve algorithms and so on\Nand determining discrete logarithm so our
Dialogue: 0,0:43:29.60,0:43:35.34,Default,,0000,0000,0000,,public key crypto would be destroyed by\Nthem. And this all works by using the
Dialogue: 0,0:43:35.34,0:43:41.22,Default,,0000,0000,0000,,superposition to construct some kind of\Nweird parallelism. So it's actually I
Dialogue: 0,0:43:41.22,0:43:47.36,Default,,0000,0000,0000,,think nobody really can imagine how it\Nworks but we can compute it which is often
Dialogue: 0,0:43:47.36,0:43:51.67,Default,,0000,0000,0000,,the case in quantum mechanics. And then\Nthere's quantum cryptography and that
Dialogue: 0,0:43:51.67,0:43:56.28,Default,,0000,0000,0000,,fundamentally solves the same problem as a\NDiffie-Hellman key exchange. We can
Dialogue: 0,0:43:56.28,0:44:01.15,Default,,0000,0000,0000,,generate the shared key and we can check\Nby the statistics of our measured values
Dialogue: 0,0:44:01.15,0:44:07.35,Default,,0000,0000,0000,,that there is no eavesdropper, which is\Ncool actually. But it's also quite useless
Dialogue: 0,0:44:07.35,0:44:10.20,Default,,0000,0000,0000,,because we can't detect a man in the\Nmiddle. How should the quantum particle
Dialogue: 0,0:44:10.20,0:44:14.63,Default,,0000,0000,0000,,knows of the other side is the one with\Nthat we want to talk to. We still need
Dialogue: 0,0:44:14.63,0:44:18.84,Default,,0000,0000,0000,,some shared secret or public key\Ninfrastructure whatever. So it doesn't
Dialogue: 0,0:44:18.84,0:44:27.21,Default,,0000,0000,0000,,solve the problem that we don't have\Nsolved. And then the fun fact about this
Dialogue: 0,0:44:27.21,0:44:30.97,Default,,0000,0000,0000,,is that all the commercial implementations\Nof quantum cryptography were susceptible
Dialogue: 0,0:44:30.97,0:44:35.15,Default,,0000,0000,0000,,to side channel text, for example you\Ncould just shine the light with a fiber
Dialogue: 0,0:44:35.15,0:44:40.92,Default,,0000,0000,0000,,that was used, read out the polarization\Nfilter state that they used and then you
Dialogue: 0,0:44:40.92,0:44:50.61,Default,,0000,0000,0000,,could mimic the other side. So that's not\Ngood either. So finally some references
Dialogue: 0,0:44:50.61,0:44:55.15,Default,,0000,0000,0000,,for further study. The first one is really\Ndifficult. Only try this if you've read the
Dialogue: 0,0:44:55.15,0:45:00.65,Default,,0000,0000,0000,,other two but the second one. Sorry that\Nthey're in German. The first and the last
Dialogue: 0,0:45:00.65,0:45:04.58,Default,,0000,0000,0000,,are also available in translation but the\Nsecond one has a really really nice and
Dialogue: 0,0:45:04.58,0:45:09.65,Default,,0000,0000,0000,,accessible introduction in the last few\Npages so it's just 20 pages and it's
Dialogue: 0,0:45:09.65,0:45:14.66,Default,,0000,0000,0000,,really good and understandable. So if you\Ncan get your hands on the books and are
Dialogue: 0,0:45:14.66,0:45:22.08,Default,,0000,0000,0000,,really interested, read it. So thank you\Nfor the attention and I'll be answering
Dialogue: 0,0:45:22.08,0:45:24.26,Default,,0000,0000,0000,,your questions next.
Dialogue: 0,0:45:24.26,0:45:33.16,Default,,0000,0000,0000,,{\i1}Applause{\i0}
Dialogue: 0,0:45:33.16,0:45:41.24,Default,,0000,0000,0000,,Herald: Thank you Sebastian. Do we have\Nquestions? And don't be afraid to sound
Dialogue: 0,0:45:41.24,0:45:45.38,Default,,0000,0000,0000,,naive or anything. I'm sure if you didn't\Nunderstand something many other people
Dialogue: 0,0:45:45.38,0:45:49.10,Default,,0000,0000,0000,,would thank you for a good question.\NSebastian: As to understanding things in
Dialogue: 0,0:45:49.10,0:45:53.18,Default,,0000,0000,0000,,quantum mechanics, Fineman said "You can't\Nunderstand quantum mechanics, you can just
Dialogue: 0,0:45:53.18,0:45:57.27,Default,,0000,0000,0000,,accept that there there's nothing to\Nunderstand. That's just too weird."
Dialogue: 0,0:45:57.27,0:46:01.59,Default,,0000,0000,0000,,Herald: Ok,we've found some questions. So\Nmicrophone one please.
Dialogue: 0,0:46:01.59,0:46:09.35,Default,,0000,0000,0000,,M1: Can you explain that, if you measure a\Nsystem, it looks like you changed the
Dialogue: 0,0:46:09.35,0:46:15.13,Default,,0000,0000,0000,,state of the system. How is it defined\Nwhere the system starts? No. How is it
Dialogue: 0,0:46:15.13,0:46:20.20,Default,,0000,0000,0000,,defined when the system ends and the\Nmeasurement system begins. Or in other
Dialogue: 0,0:46:20.20,0:46:24.41,Default,,0000,0000,0000,,words why does the universe have a\Nstate? Is there somewhere out there who
Dialogue: 0,0:46:24.41,0:46:29.45,Default,,0000,0000,0000,,measures the universe?\NS: No. There's at least the beginning of a
Dialogue: 0,0:46:29.45,0:46:34.88,Default,,0000,0000,0000,,solution by now which is called\N"decoherence" which says that this
Dialogue: 0,0:46:34.88,0:46:39.97,Default,,0000,0000,0000,,measurement structure that we observe is\Nnot inherent in quantum mechanics but
Dialogue: 0,0:46:39.97,0:46:43.92,Default,,0000,0000,0000,,comes from the interaction with the\Nenvironment. And we don't care for the
Dialogue: 0,0:46:43.92,0:46:48.46,Default,,0000,0000,0000,,states of the environment. And if we do\Nthis, the technical term is traced out the
Dialogue: 0,0:46:48.46,0:46:52.53,Default,,0000,0000,0000,,states of the environment. Then the\Nremaining state of the measurement
Dialogue: 0,0:46:52.53,0:46:59.79,Default,,0000,0000,0000,,apparatus and the system we're interested\Nin will be just classically a randomized
Dialogue: 0,0:46:59.79,0:47:05.70,Default,,0000,0000,0000,,states. So it's rather a consequence\Nof the complex dynamics of a system state
Dialogue: 0,0:47:05.70,0:47:10.74,Default,,0000,0000,0000,,and environment in quantum mechanics. But\Nthis is really the burning question. We
Dialogue: 0,0:47:10.74,0:47:15.69,Default,,0000,0000,0000,,don't really know. We have this we know\Ndecoherence make some makes it nice and
Dialogue: 0,0:47:15.69,0:47:20.75,Default,,0000,0000,0000,,looks good. But it also doesn't answer the\Nquestion finally. And this is what all
Dialogue: 0,0:47:20.75,0:47:25.43,Default,,0000,0000,0000,,those discussions about interpretations of\Nquantum mechanics are about. How shall we
Dialogue: 0,0:47:25.43,0:47:28.94,Default,,0000,0000,0000,,make sense of this weird measurement\Nprocess.
Dialogue: 0,0:47:28.94,0:47:37.15,Default,,0000,0000,0000,,Herald: Okay. Microphone 4 in the back please.\NM4: Could you comment on your point in the
Dialogue: 0,0:47:37.15,0:47:44.22,Default,,0000,0000,0000,,theory section. I don't understand what\Nyou were trying to do. Did you want to
Dialogue: 0,0:47:44.22,0:47:49.37,Default,,0000,0000,0000,,show that you cannot understand really\Nquantum mechanics without the mathematics
Dialogue: 0,0:47:49.37,0:47:51.99,Default,,0000,0000,0000,,or?\NS: Well, yes you can't understand quantum
Dialogue: 0,0:47:51.99,0:47:56.01,Default,,0000,0000,0000,,mechanics without the mathematics and my\Npoint to show was that mathematics, or at
Dialogue: 0,0:47:56.01,0:48:02.38,Default,,0000,0000,0000,,least my hope to show was that mathematics\Nis halfways accessible. Probably not
Dialogue: 0,0:48:02.38,0:48:07.80,Default,,0000,0000,0000,,understandable after just exposure of a\Nshort talk but just to give an
Dialogue: 0,0:48:07.80,0:48:12.85,Default,,0000,0000,0000,,introduction where to look\NM4: OK. So you are trying to combat the
Dialogue: 0,0:48:12.85,0:48:18.05,Default,,0000,0000,0000,,esoterics and say they don't really\Nunderstand the theory because they don't
Dialogue: 0,0:48:18.05,0:48:29.38,Default,,0000,0000,0000,,understand the mathematics. I understand\Nthe mathematics. I'm just interested. What
Dialogue: 0,0:48:29.38,0:48:33.81,Default,,0000,0000,0000,,were you trying to say?\NS: I was just trying to present the
Dialogue: 0,0:48:33.81,0:48:39.34,Default,,0000,0000,0000,,theory. That was my aim.\NM4: Okay. Thank you.
Dialogue: 0,0:48:39.34,0:48:45.76,Default,,0000,0000,0000,,Herald: Okay, microphone 2 please.\NM2: I know the answer to this question is
Dialogue: 0,0:48:45.76,0:48:48.57,Default,,0000,0000,0000,,that ...\NHerald: Can you go a little bit closer to
Dialogue: 0,0:48:48.57,0:48:52.66,Default,,0000,0000,0000,,the microphone maybe move it up please.\NM2: So I know the answer to this question
Dialogue: 0,0:48:52.66,0:48:59.51,Default,,0000,0000,0000,,is that atoms behave randomly but could\Nyou provide an argument why they behave
Dialogue: 0,0:48:59.51,0:49:07.37,Default,,0000,0000,0000,,randomly and it is not the case that we\Ndon't have a model that's. So, are atoms
Dialogue: 0,0:49:07.37,0:49:12.02,Default,,0000,0000,0000,,behaving randomly? Or is it the case that\Nwe don't have a model accurate enough to
Dialogue: 0,0:49:12.02,0:49:17.89,Default,,0000,0000,0000,,predict the way they behave?\NS: Radioactive decay is just as random as
Dialogue: 0,0:49:17.89,0:49:24.09,Default,,0000,0000,0000,,quantum measurement and since if we\Nwere to look at the whole story and look
Dialogue: 0,0:49:24.09,0:49:28.22,Default,,0000,0000,0000,,at the coherent evolution of the whole\Nsystem we would have to include the
Dialogue: 0,0:49:28.22,0:49:33.81,Default,,0000,0000,0000,,environment and the problem is that the\Nstate space that we have to consider grows
Dialogue: 0,0:49:33.81,0:49:37.81,Default,,0000,0000,0000,,exponentially. That's the point of quantum\Nmechanics. If I have two particles I have
Dialogue: 0,0:49:37.81,0:49:42.90,Default,,0000,0000,0000,,a two dimensional space. I have 10\Nparticles I have a 1024 dimensional space
Dialogue: 0,0:49:42.90,0:49:47.27,Default,,0000,0000,0000,,and that's only talking about non\Ninteracting particles. So things explode
Dialogue: 0,0:49:47.27,0:49:51.95,Default,,0000,0000,0000,,in quantum mechanics and large systems.\NAnd therefore I would go so far as to say
Dialogue: 0,0:49:51.95,0:49:57.14,Default,,0000,0000,0000,,that it's objectively impossible to\Ndetermine a radioactive decay although
Dialogue: 0,0:49:57.14,0:50:03.67,Default,,0000,0000,0000,,there are things, there is I think one\Nexperimentally confirmed method of letting
Dialogue: 0,0:50:03.67,0:50:11.28,Default,,0000,0000,0000,,an atom decay on purpose. This involves\Nmeta stable states of nuclei and then you
Dialogue: 0,0:50:11.28,0:50:15.69,Default,,0000,0000,0000,,can do something like spontaneous emission\Nin a laser. You shine a strong gamma
Dialogue: 0,0:50:15.69,0:50:21.71,Default,,0000,0000,0000,,source by it and this shortens the\Nlifespan of the nucleus. But other than
Dialogue: 0,0:50:21.71,0:50:25.41,Default,,0000,0000,0000,,that.\NM4: So in a completely hypothetical case. If you
Dialogue: 0,0:50:25.41,0:50:29.84,Default,,0000,0000,0000,,know all the starting conditions and what\Nhappens afterwards,wouldn't it be able,
Dialogue: 0,0:50:29.84,0:50:37.22,Default,,0000,0000,0000,,we could say it's deterministic? I\Nmean I'm playing with heavy words here.
Dialogue: 0,0:50:37.22,0:50:43.62,Default,,0000,0000,0000,,But is it just that we say it's randomised\Nbecause it's very very complex right?
Dialogue: 0,0:50:43.62,0:50:48.47,Default,,0000,0000,0000,,That's what I'm understanding.\NHerald: Maybe think about that question
Dialogue: 0,0:50:48.47,0:50:53.10,Default,,0000,0000,0000,,one more time and we have the signal angel\Nin between and then you can come back.
Dialogue: 0,0:50:53.10,0:50:57.69,Default,,0000,0000,0000,,Signal Angel do we have questions on the\NInternet?
Dialogue: 0,0:50:57.69,0:51:04.94,Default,,0000,0000,0000,,Angel: There's one question from the Internet\Nwhich is the ground state of a BEH-2 has
Dialogue: 0,0:51:04.94,0:51:12.15,Default,,0000,0000,0000,,been just calculated using a quantum\Neigensolver. So is there still some use of
Dialogue: 0,0:51:12.15,0:51:16.85,Default,,0000,0000,0000,,quantum computing in quantum mechanics?\NS: Yes definitely. One of the main
Dialogue: 0,0:51:16.85,0:51:22.31,Default,,0000,0000,0000,,motivations for inventing quantum\Ncomputers was quantum simulators.
Dialogue: 0,0:51:22.31,0:51:26.70,Default,,0000,0000,0000,,Feynman invented this kind of\Nquantum computing and he showed that with
Dialogue: 0,0:51:26.70,0:51:32.01,Default,,0000,0000,0000,,digital quantum computer you can\Nefficiently simulate quantum systems. While
Dialogue: 0,0:51:32.01,0:51:36.49,Default,,0000,0000,0000,,you can't simulate quantum systems with a\Nclassical computer because of this problem
Dialogue: 0,0:51:36.49,0:51:41.79,Default,,0000,0000,0000,,of the exploding dimensions of the Hilbert\Nspace that you have to consider. And for
Dialogue: 0,0:51:41.79,0:51:46.28,Default,,0000,0000,0000,,this quantum computers are really really\Nuseful and will be used once they work,
Dialogue: 0,0:51:46.28,0:51:52.76,Default,,0000,0000,0000,,which is the question when it will be.\NPerhaps never. Beyond two or three qubits
Dialogue: 0,0:51:52.76,0:51:59.18,Default,,0000,0000,0000,,or 20 or 100 qubits but you need scalability\Nfor a real quantum computer. But quantum
Dialogue: 0,0:51:59.18,0:52:03.35,Default,,0000,0000,0000,,simulation is a real thing and it's a good\Nthing and we need it.
Dialogue: 0,0:52:03.35,0:52:07.96,Default,,0000,0000,0000,,Herald: Okay. Then we have microphone 1\Nagain.
Dialogue: 0,0:52:07.96,0:52:13.78,Default,,0000,0000,0000,,M1: So very beginning, you said that the\Ntheory is a set of interdependent
Dialogue: 0,0:52:13.78,0:52:21.54,Default,,0000,0000,0000,,propositions. Right? And then if a new\Nhypothesis is made it can be confirmed by
Dialogue: 0,0:52:21.54,0:52:28.22,Default,,0000,0000,0000,,an experiment.\NS: That can't be confirmed but, well it's
Dialogue: 0,0:52:28.22,0:52:33.56,Default,,0000,0000,0000,,a philosophical question about the common\Nstance, it can be made probable but not
Dialogue: 0,0:52:33.56,0:52:37.21,Default,,0000,0000,0000,,be confirmed because we can never\Nabsolutely be sure that there won't be
Dialogue: 0,0:52:37.21,0:52:40.60,Default,,0000,0000,0000,,some new experiment that shows that the\Nhypothesis is wrong.
Dialogue: 0,0:52:40.60,0:52:44.92,Default,,0000,0000,0000,,M1: Yeah. Because the slide said that\Nthe experiment confirms...
Dialogue: 0,0:52:44.92,0:52:51.15,Default,,0000,0000,0000,,S: Yeah, confirm in the sense that it\Ndoesn't disconfirm it. So it makes
Dialogue: 0,0:52:51.15,0:52:57.04,Default,,0000,0000,0000,,probable that it's a good explanation of\Nthe reality and that's the point. Physics
Dialogue: 0,0:52:57.04,0:53:01.71,Default,,0000,0000,0000,,is just models. We do get\Nnothing about the ontology that is about
Dialogue: 0,0:53:01.71,0:53:06.35,Default,,0000,0000,0000,,the actual being of the world out of\Nphysics. We just get models to describe
Dialogue: 0,0:53:06.35,0:53:11.54,Default,,0000,0000,0000,,the world but all what I say about this\Nwave function and what we say about
Dialogue: 0,0:53:11.54,0:53:18.15,Default,,0000,0000,0000,,elementary particles. We can't say they\Nare in the sense that you and I are here
Dialogue: 0,0:53:18.15,0:53:22.75,Default,,0000,0000,0000,,and exist because we can't see them we\Ncan't access them directly. We can only
Dialogue: 0,0:53:22.75,0:53:28.96,Default,,0000,0000,0000,,use them as description tools. But this is\Nmy personal position on philosophy of
Dialogue: 0,0:53:28.96,0:53:33.38,Default,,0000,0000,0000,,science. So there are people who disagree.\NM1: Ok, thanks.
Dialogue: 0,0:53:33.38,0:53:39.96,Default,,0000,0000,0000,,Herald: Microphone 2 please.\NM2: Or maybe superposition. By the way, so
Dialogue: 0,0:53:39.96,0:53:47.55,Default,,0000,0000,0000,,on the matter of the collapsing of the\Nwave function, so this was already treated
Dialogue: 0,0:53:47.55,0:53:52.59,Default,,0000,0000,0000,,on the interpretation of Copenhagen and\Nthen as you mentioned it was expanded by
Dialogue: 0,0:53:52.59,0:53:59.33,Default,,0000,0000,0000,,the concept of decoherence. And is this, so\Nthe decoherence is including also the
Dialogue: 0,0:53:59.33,0:54:03.32,Default,,0000,0000,0000,,Ghirardi–Rimini–Weber interpretation or\Nnot?
Dialogue: 0,0:54:03.32,0:54:06.88,Default,,0000,0000,0000,,S: Could decoherence be used in\Ncomputation or?
Dialogue: 0,0:54:06.88,0:54:13.02,Default,,0000,0000,0000,,M2: No so for the Ghirardi–Rimini–Weber\Ninterpretation of the collapsing of the
Dialogue: 0,0:54:13.02,0:54:15.70,Default,,0000,0000,0000,,wave function.\NS:That's one that I don't know.
Dialogue: 0,0:54:15.70,0:54:24.27,Default,,0000,0000,0000,,I'm not so much into interpretations.\NI actually think that there's interesting
Dialogue: 0,0:54:24.27,0:54:29.63,Default,,0000,0000,0000,,work done there but I think they're a bit\Nirrelevant because in the end what I just
Dialogue: 0,0:54:29.63,0:54:33.69,Default,,0000,0000,0000,,said I don't think you can derive\Nontological value from our physical
Dialogue: 0,0:54:33.69,0:54:40.52,Default,,0000,0000,0000,,theories and in this belief, I think that\Nthe interpretations are in a sense void,
Dialogue: 0,0:54:40.52,0:54:44.89,Default,,0000,0000,0000,,they just help us to rationalize what\Nwe're doing but they don't really add
Dialogue: 0,0:54:44.89,0:54:49.34,Default,,0000,0000,0000,,something to the theory as long as they\Ndon't change what can be measured.
Dialogue: 0,0:54:49.34,0:54:58.18,Default,,0000,0000,0000,,M2: Oh okay. Thanks.\NS: Sorry for being an extremist.
Dialogue: 0,0:54:58.18,0:55:03.58,Default,,0000,0000,0000,,M2: Totally fine.\NHerald: Someone just left from microphone 1
Dialogue: 0,0:55:03.58,0:55:07.81,Default,,0000,0000,0000,,I don't know if they want to come\Nback. I don't see any more questions as to
Dialogue: 0,0:55:07.81,0:55:13.68,Default,,0000,0000,0000,,signal angel have anything else. There is\Nsome more. Signal angel, do you have
Dialogue: 0,0:55:13.68,0:55:16.52,Default,,0000,0000,0000,,something?\NSignal Angel: No.
Dialogue: 0,0:55:16.52,0:55:19.61,Default,,0000,0000,0000,,Herald: Okay. Then we have\Nmicrophone 4.
Dialogue: 0,0:55:19.61,0:55:27.81,Default,,0000,0000,0000,,M4: I want to ask a maybe a noob question.\NI want to know, are the probabilities of
Dialogue: 0,0:55:27.81,0:55:32.77,Default,,0000,0000,0000,,quantum mechanics inherent part of nature\Nor maybe in some future we'll have a
Dialogue: 0,0:55:32.77,0:55:37.49,Default,,0000,0000,0000,,science that will determine all these\Nvalues exactly?
Dialogue: 0,0:55:37.49,0:55:44.80,Default,,0000,0000,0000,,S: Well if decoherency theory is true,\Nthen quantum mechanics is absolutely
Dialogue: 0,0:55:44.80,0:55:53.78,Default,,0000,0000,0000,,deterministic. But so let's say, Everett\Nsays that all those possible measurement
Dialogue: 0,0:55:53.78,0:55:58.87,Default,,0000,0000,0000,,outcomes do happen and the whole state of\Nthe system is in a superposition and by
Dialogue: 0,0:55:58.87,0:56:03.84,Default,,0000,0000,0000,,looking at our measurement device and\Nseeing some value we in a way select one
Dialogue: 0,0:56:03.84,0:56:10.22,Default,,0000,0000,0000,,strand of those superpositions and live in\Nthis of the many worlds and in this sense
Dialogue: 0,0:56:10.22,0:56:21.35,Default,,0000,0000,0000,,everything happens deterministically, but\Nwe just can't access any other values. So
Dialogue: 0,0:56:21.35,0:56:27.100,Default,,0000,0000,0000,,I think it's for now rather a\Nof philosophy than of science.
Dialogue: 0,0:56:27.100,0:56:32.90,Default,,0000,0000,0000,,M4: I see. Thanks.
Dialogue: 0,0:56:32.90,0:56:38.56,Default,,0000,0000,0000,,Herald: Anything else? I don't see any\Npeople lined up at microphones. So last
Dialogue: 0,0:56:38.56,0:56:46.71,Default,,0000,0000,0000,,chance to round up now, I think. Well then\NI think we're closing this and have a nice
Dialogue: 0,0:56:46.71,0:56:59.51,Default,,0000,0000,0000,,applause again for Sebastian.\N{\i1}applause{\i0}
Dialogue: 0,0:56:59.51,0:57:02.65,Default,,0000,0000,0000,,Sebastian: Thank you. And I hope I didn't\Ncreate more fear of
Dialogue: 0,0:57:02.65,0:57:05.08,Default,,0000,0000,0000,,quantum mechanics than\NI dispersed.
Dialogue: 0,0:57:05.08,0:57:30.00,Default,,0000,0000,0000,,subtitles created by c3subtitles.de\Nin the year 2020. Join, and help us!