0:00:00.000,0:00:18.595
*35C3 preroll music*
0:00:18.595,0:00:26.930
Herald Angel: And, so he studied physics[br]and I'm thinking we just all need a lot
0:00:26.930,0:00:33.550
better understanding of quantum mechanics,[br]because he sees this theory being misused
0:00:33.550,0:00:42.329
a lot by some weird esoteric theories,[br]kind of abusing it to just justify
0:00:42.329,0:00:48.250
everything and anything. So he wants to[br]change that and he wants to have people
0:00:48.250,0:00:53.809
with some understanding of this very[br]important theory and so he will start
0:00:53.809,0:00:58.570
today with all of us here and try to[br]explain to us the wonders of quantum
0:00:58.570,0:01:08.724
mechanics. Have a go.[br]*applause*
0:01:08.724,0:01:11.700
Sebastian Riese: Well thank you for a warm[br]welcome. It will be about quantum
0:01:11.700,0:01:18.110
mechanics. We will see whether the gentle[br]introduction will be a lie depending on
0:01:18.110,0:01:23.380
how good you can follow me. So at first[br]there will be a short introduction, a bit
0:01:23.380,0:01:29.560
meta discussion about physical theories[br]and what is the aim of this talk. And then
0:01:29.560,0:01:35.241
we will discuss the experiments. Most of[br]this is high school physics, you've
0:01:35.241,0:01:40.360
probably seen it before. And then it will[br]get ugly because we'll do the theory and
0:01:40.360,0:01:45.080
we'll really do the theory, we'll write[br]down the equations of quantum mechanics
0:01:45.080,0:01:50.450
and try to make them plausible and[br]hopefully understandable to a lot of
0:01:50.450,0:01:56.860
people. And finally some applications will[br]be discussed. So what is the concept of
0:01:56.860,0:02:02.470
this talk. The key experiments will be[br]reviewed as said, and but we will not do
0:02:02.470,0:02:07.110
it in historical fashion. We will look at[br]the experiments as physical facts and
0:02:07.110,0:02:13.450
derive the theory from them. And since[br]quantum mechanics is rather abstract and
0:02:13.450,0:02:19.140
not, as I said in German and in science[br]theory "anschaulich", we will need
0:02:19.140,0:02:23.780
mathematics and most of this will be[br]linear algebra. So a lot of quantum
0:02:23.780,0:02:28.600
mechanics is just linear algebra on[br]steroids, that means in infinite
0:02:28.600,0:02:35.550
dimensions. And in doing so we'll try to[br]find a certain post classical
0:02:35.550,0:02:40.871
"Anschaulichkeit" or lividness to[br]understand the theory. Since there'll be a
0:02:40.871,0:02:48.610
lot of math as the allergy advice said,[br]there will be crash courses driven in to
0:02:48.610,0:02:53.350
explain mathematical facts. Sorry for the[br]mathematicians that are here they probably
0:02:53.350,0:03:03.520
suffer because I lie a lot. So at first:[br]How do scientific theories work? To really
0:03:03.520,0:03:08.500
understand quantum mechanics we must[br]understand the setting and setting where
0:03:08.500,0:03:14.990
it was created and how scientific theories[br]are created in general. A scientific
0:03:14.990,0:03:19.920
theory is a net of interdependent[br]propositions so we have one proposition
0:03:19.920,0:03:27.100
for example "F = M times a" in classical[br]mechanics and we have another proposition
0:03:27.100,0:03:32.010
that the gravitational force equals is[br]proportional to the product of the masses
0:03:32.010,0:03:38.140
divided by the distance between the masses[br]squared, so something like this. And when
0:03:38.140,0:03:44.540
we go around, make experiments, look into[br]nature, develop theories, calculate, we
0:03:44.540,0:03:51.300
test those we test hypotheses, different[br]hypotheses and try to determine which one
0:03:51.300,0:03:57.030
describes our experimental results best.[br]And if the hypothesis stands the
0:03:57.030,0:04:02.790
experimental tests they're added to the[br]theory. But what happens if there's an
0:04:02.790,0:04:07.120
experimental result that totally[br]contradicts what we've seen before? And
0:04:07.120,0:04:12.520
that happened in the late 19th and early[br]20th century. There are new results that
0:04:12.520,0:04:18.690
could not be explained. So if such[br]inconsistent results are found then our
0:04:18.690,0:04:24.940
old theory has been falsified. This term[br]is due to Popper who said that a theory is
0:04:24.940,0:04:28.770
scientific as long as it can be falsified,[br]that is at least as long as we can prove
0:04:28.770,0:04:33.940
that it's not true and we can never prove[br]a theory true but only prove it wrong. And
0:04:33.940,0:04:39.350
all that we have not yet proven wrong are[br]at least some approximation to truth. And
0:04:39.350,0:04:45.460
if this happens we have to amend our old[br]theory and we have to use care there and
0:04:45.460,0:04:51.810
find a minimal amendment. This principle[br]is Occam's Razor. One could also say the
0:04:51.810,0:04:58.660
principle of least surprise from software[br]engineering. And then we try that our
0:04:58.660,0:05:03.940
theory is again consistent with the[br]experimental results. And of course the
0:05:03.940,0:05:09.030
new theory must explain why the hell that,[br]for example Newtonian mechanics work for
0:05:09.030,0:05:14.520
two hundred years if it's absolutely[br]wrong. And so the old theory must in some
0:05:14.520,0:05:20.910
limit contain the new one. And now how[br]does it begin with quantum mechanics. As
0:05:20.910,0:05:25.820
already said the time frame is the late[br]19th and early 20th century. And there
0:05:25.820,0:05:32.100
were three or four fundamental theories of[br]physics known then: Classical mechanics,
0:05:32.100,0:05:36.290
which is just governed by the single[br]equation the force equals mass times the
0:05:36.290,0:05:44.780
acceleration with given forces. And two[br]known force laws: The immediate distance
0:05:44.780,0:05:51.410
action Newtonian gravitation and the[br]Maxwell electro dynamics, this funny
0:05:51.410,0:05:56.320
equation here. This funny equation here is[br]a way of writing down the Maxwell
0:05:56.320,0:06:04.960
equations that basically contain all the[br]known electromagnetic effects. And finally
0:06:04.960,0:06:09.580
there were the beginnings of the Maxwell[br]Boltzmann statistical physics, but
0:06:09.580,0:06:17.250
classical statistical physics is a pain,[br]doesn't really work. So several
0:06:17.250,0:06:22.620
experimental results I said could not be[br]explained by classical theories. For
0:06:22.620,0:06:27.890
example the photoelectric effect[br]discovered by Hertz and Hallwachs in 1887,
0:06:27.890,0:06:32.130
or the discrete spectral lines of atoms[br]first shown by Fraunhofer in the spectrum
0:06:32.130,0:06:38.110
of the sun and then studied by Bunsen and[br]Kirchhoff with the so-called
0:06:38.110,0:06:43.430
"Bunsenbrenner", you all know it from the[br]chemistry classes. And further,
0:06:43.430,0:06:47.900
radioactive rays were really a mystery[br]nobody understood: How can it happen that
0:06:47.900,0:06:54.770
something just decays at random intervals?[br]It was unclear. And then the people looked
0:06:54.770,0:07:00.810
into the atom, Rutherford using alpha[br]particles to bombard a gold foil and saw
0:07:00.810,0:07:05.259
there must be positively charged nucleii[br]and they already knew that they were
0:07:05.259,0:07:13.490
negatively charged, what we now call[br]electrons, particles in the atom. So this
0:07:13.490,0:07:18.150
was really strange that atoms are stable[br]at composed like this and I will explain
0:07:18.150,0:07:23.660
why a bit later. But now to more detail to[br]the experiments. The really big
0:07:23.660,0:07:29.860
breakthrough in this time, experimentally[br]speaking, were vacuum tubes, so you took a
0:07:29.860,0:07:37.580
piece of glass and pumped the air out and[br]closed it off and put all sorts of devices
0:07:37.580,0:07:45.229
in there. And now one thing is this nice[br]cathode ray experiment. We have here a so-
0:07:45.229,0:07:53.960
called electron gun and this is a heated[br]electrode, so here flows the current that
0:07:53.960,0:08:00.210
heats it, so that the electrons get energy[br]and seep out into the vacuum. Then we have
0:08:00.210,0:08:08.240
an electrode that goes around and a plate[br]in front that is positively charged. So we
0:08:08.240,0:08:11.961
accelerate our electrons towards the[br]plate. There's a pinhole in the plate and
0:08:11.961,0:08:18.850
we get a beam of electrons. And now we had[br]those evacuated tubes and those electron
0:08:18.850,0:08:24.539
guns. So we put the electron gun in the[br]evacuated tube, perhaps left a bit of gas
0:08:24.539,0:08:29.050
in because then it glowed when it when the[br]atoms in the gas were hit by the electrons
0:08:29.050,0:08:33.940
so we could see the cathode ray, and then[br]we play around. We take magnetic fields
0:08:33.940,0:08:38.130
and see how does it react to magnetic[br]fields. We take electric fields. How does
0:08:38.130,0:08:42.879
it react to electric fields and so on. And[br]what we find out is we somehow must have
0:08:42.879,0:08:53.129
negatively charged particles that flow[br]nicely around in our almost vacuum. And
0:08:53.129,0:09:00.519
because atoms are neutral which is just[br]known macroscopically there must be a
0:09:00.519,0:09:08.339
positively charged component in the atom[br]as well. And this positively charged
0:09:08.339,0:09:14.079
component was first thought to be kind of[br]a plum pudding or so with the electrons
0:09:14.079,0:09:21.040
sitting in there. But the Rutherford-[br]Marsden-Geiger experiment, so it was
0:09:21.040,0:09:25.630
Rutherford invented the idea and Marsden[br]and Geiger actually performed the
0:09:25.630,0:09:30.819
experimental work, showed that if you had[br]a really thin gold foil, really only a few
0:09:30.819,0:09:35.139
hundred layers of atoms, that's the nice[br]thing about gold, you can just hammer it
0:09:35.139,0:09:41.529
out to really, really thin sheets, if you[br]had that and then shot alpha particles
0:09:41.529,0:09:47.540
that is helium nuclei that are created by[br]the radioactive decay of many heavy
0:09:47.540,0:09:54.900
elements for example, most uranium[br]isotopes decay by alpha decay, then they
0:09:54.900,0:10:00.050
were deflected strongly. If the charge[br]would have been spaced throughout the
0:10:00.050,0:10:04.009
atoms then this could not have happened.[br]You can calculate, you can
0:10:04.009,0:10:09.649
estimate the possible deflections with an[br]extended charge and with a concentrated
0:10:09.649,0:10:14.189
charge, and you see the only explanation[br]for this is that there is a massive and
0:10:14.189,0:10:22.050
really, really small positive thing in[br]those atoms. So atoms are small,
0:10:22.050,0:10:27.550
positively charged nucleus as Rutherford[br]called it and around it there's a cloud of
0:10:27.550,0:10:33.820
electrons or, he thought, orbiting[br]electrons. But orbiting electrons atoms
0:10:33.820,0:10:37.679
are stable, this doesn't really make sense[br]in classical physics, because in classical
0:10:37.679,0:10:43.029
physics all accelerator charges must[br]radiate energy and be slowed by this
0:10:43.029,0:10:51.920
process. And this means atoms that are[br]stable and composed of some strange
0:10:51.920,0:10:58.749
electrons and having nuclei they're just[br]not possible. It's a no go, so at least at
0:10:58.749,0:11:02.930
this moment it was completely clear[br]classical physics as they knew it up until
0:11:02.930,0:11:09.869
then is wrong. And the next experiment in[br]this direction was the photoelectric
0:11:09.869,0:11:15.350
effect. What's shown there is a schematic[br]of a phototube. And a phototube is again a
0:11:15.350,0:11:22.550
vacuum tube out of glass and there is a[br]for example cesium layer in in the tube at
0:11:22.550,0:11:27.399
one side and there is a ring electrode[br]removed from it. And if we shine light on
0:11:27.399,0:11:34.559
this there flows a current. But the[br]peculiar thing is that if we do the bias
0:11:34.559,0:11:44.129
voltage across the two terminals of this[br]tube to stop the electrons, we see that
0:11:44.129,0:11:49.040
the bias voltage that completely stops the[br]flow is not proportional to the intensity
0:11:49.040,0:11:53.689
of the light that is incident onto the[br]tube, but it's proportional to the
0:11:53.689,0:11:59.540
frequency of the light that's incident on[br]the phototube. And that was again really
0:11:59.540,0:12:05.179
weird for the people of the time because[br]the frequency shouldn't make any
0:12:05.179,0:12:11.929
difference for the energy. And this was[br]when Einstein derived that, or thought of
0:12:11.929,0:12:18.149
that there must be some kind of energy[br]portions in the electric field, from this
0:12:18.149,0:12:23.480
simple experiment, which is often done in[br]physics classes even at the high school
0:12:23.480,0:12:31.040
level. So it's, from today's view it's not[br]a complicated experiment. And to go even
0:12:31.040,0:12:37.149
further those weird stable atoms had[br]discrete, had discrete lines of emission
0:12:37.149,0:12:43.660
and absorption of light. And here we have[br]again a very simplified experimental set
0:12:43.660,0:12:48.010
up of a so-called discharge tube, where we[br]have high voltage between the terminals
0:12:48.010,0:12:53.449
and a thin gas and then a current will[br]flow, will excite the atoms. The atoms
0:12:53.449,0:12:58.560
will relax and emit light and this light[br]will have a specific spectrum with sharp
0:12:58.560,0:13:03.670
frequencies that are, that have strong[br]emission and we can see this with a
0:13:03.670,0:13:08.839
diffraction grating that sorts light out[br]according to its wavelength and then look
0:13:08.839,0:13:13.869
on the screen or view some more fancy[br]optical instrument to do precision
0:13:13.869,0:13:22.860
measurements as Bunsen and Kirchhoff did.[br]So what we knew up until now was that
0:13:22.860,0:13:28.730
something was really weird and our[br]physical theories didn't make sense. And
0:13:28.730,0:13:34.149
then it got worse. Someone took an[br]electron gun and pointed it at a
0:13:34.149,0:13:38.430
monocrystalline surface. And such a[br]monocrystalline surface is just like a
0:13:38.430,0:13:45.670
diffraction grating: A periodically[br]arranged thing. And off periodically
0:13:45.670,0:13:53.019
arranged things there does happen regular[br]interference pattern creation. So they saw
0:13:53.019,0:13:58.100
interference pattern with electrons. But[br]electrons aren't that particles? How can
0:13:58.100,0:14:03.450
particles, so what was thought of then,[br]since the times of Newton as a little hard
0:14:03.450,0:14:08.839
ball, how can a little hard ball flowing[br]around create interference patterns? It
0:14:08.839,0:14:18.369
was really weird. And there's even more[br]and as already mentioned radioactivity
0:14:18.369,0:14:24.420
with the random decay of a nucleus. This[br]doesn't make sense in classical physics,
0:14:24.420,0:14:30.040
so it was really, really bad. And here[br]I've added some modern facts that we'll
0:14:30.040,0:14:38.100
need later on. Namely that if we measure,[br]if we try to measure the position of a
0:14:38.100,0:14:44.410
particle and use different position[br]sensors to do so, only one of them, so at
0:14:44.410,0:14:48.449
only at one position will the single[br]particle register, but it will
0:14:48.449,0:14:53.500
nevertheless show an interference pattern[br]if I do this experiment with many many
0:14:53.500,0:14:59.470
electrons. So there must somehow be a[br]strange divide between the free space
0:14:59.470,0:15:05.819
propagation of particles and measuring the[br]particles. And you can do really weird
0:15:05.819,0:15:11.319
stuff and record the information through[br]which slit the particle went. And if you
0:15:11.319,0:15:16.449
do this, the interference pattern[br]vanishes. And then you can even destroy
0:15:16.449,0:15:24.639
this information in a coherent manner and[br]the interference pattern appears again. So
0:15:24.639,0:15:28.769
what we know up until now is that quantum[br]mechanics is really, really weird and
0:15:28.769,0:15:37.540
really different from classical mechanics.[br]And now that we've talked about those
0:15:37.540,0:15:41.480
experiments, we'll begin with the theory,[br]and the theory will begin with a lot of
0:15:41.480,0:15:49.439
mathematics. The first one is simple.[br]Complex numbers. Who doesn't know complex
0:15:49.439,0:15:59.220
numbers? Okay. Sorry I'll have to ignore[br]you for the sake of getting to the next
0:15:59.220,0:16:05.089
points. *laughter* So I'll just say[br]complex numbers are two components of, two
0:16:05.089,0:16:10.240
componented objects with real numbers. And[br]one of them is multiplied by an imaginary
0:16:10.240,0:16:16.069
number i. And if we square the number i it[br]gets -1. And this makes many things really
0:16:16.069,0:16:22.149
beautiful. For example all algebraic[br]equations have exactly the number of
0:16:22.149,0:16:29.369
degrees solutions in complex numbers, and[br]if you count them correctly. And if you
0:16:29.369,0:16:33.989
work with complex functions it's really[br]beautiful. A function that once
0:16:33.989,0:16:39.850
differentiable is infinitely many times[br]differentiable and it's, it's nice. So now
0:16:39.850,0:16:46.499
we had complex numbers. You've all said[br]you know them. *laughter* So we go onto
0:16:46.499,0:16:53.329
vector spaces, which probably also a lot[br]of you know. Just to revisit it, a vector
0:16:53.329,0:16:58.430
space is a space of objects called[br]vectors, above some scalars that must be a
0:16:58.430,0:17:03.369
field. And here we only use complex[br]numbers as the underlying fields. There is
0:17:03.369,0:17:07.760
a null vector, we can add vectors, we can[br]invert vectors and we can multiply vectors
0:17:07.760,0:17:13.990
by real numbers. So we can say three that[br]five times this vector and just scale the
0:17:13.990,0:17:24.690
arrow and these operations interact nicely[br]so that we have those distributive laws.
0:17:24.690,0:17:33.830
And now it gets interesting. Even more[br]maths: L2 spaces. L2 spaces are in a way
0:17:33.830,0:17:40.210
an infinite dimensional or one form of an[br]infinite dimensional extension of vector
0:17:40.210,0:17:47.080
spaces. Instead of having just three[br]directions x, y, z, we have directions at
0:17:47.080,0:17:53.420
each point of a function. So we have an[br]analogy here. We have vectors which have
0:17:53.420,0:18:01.240
three discrete components given by x index[br]i on the right side and we have this
0:18:01.240,0:18:06.790
function and each component is the value[br]of the function at one point along the
0:18:06.790,0:18:13.750
axis x. And then we can just as for[br]vectors define a norm on those L2
0:18:13.750,0:18:18.690
functions which is just the integral over[br]the absolute value squared of this
0:18:18.690,0:18:23.610
function f. And the nice thing about this[br]choice of norm, there are other choices of
0:18:23.610,0:18:33.400
the norm. This norm is induced by a scalar[br]product and this little asterisk that is
0:18:33.400,0:18:39.160
there at the f denotes the complex[br]conjugate, so flipping i to minus i in
0:18:39.160,0:18:46.860
all complex values. And if you just plug[br]in f and f into the scalar product you
0:18:46.860,0:18:53.410
will see that it's the integral over the[br]squared absolute value. And this space,
0:18:53.410,0:18:59.180
this L2 space is a Hilbert space and the[br]Hilbert Space is a complete vector space
0:18:59.180,0:19:04.810
with a scalar product where complete means[br]that - It's mathematical nonsense.
0:19:04.810,0:19:10.050
Forget it. So but the nice surprise is[br]that most things carry over from finite
0:19:10.050,0:19:13.430
dimensional space. What we know from[br]finite dimensional space is we can always
0:19:13.430,0:19:19.180
diagonalize matrices with certain[br]properties and this more or less works.
0:19:19.180,0:19:23.620
And the mathematicians really, really,[br]really do a lot of work for this but for
0:19:23.620,0:19:30.500
physicists we just know when to be careful[br]and how and don't care about it otherwise.
0:19:30.500,0:19:38.360
So just works for us and that's nice. And[br]now that we have those complex numbers we
0:19:38.360,0:19:44.530
can begin to discuss how particles are[br]modeled in quantum mechanics. And as we
0:19:44.530,0:19:48.560
know from the Davisson-Germer experiments[br]there's diffraction of electrons but
0:19:48.560,0:19:54.130
there's nothing in electrons that[br]corresponds to an electric field in some
0:19:54.130,0:20:00.050
direction or so. Some other periodicity[br]has, so periodicity of electrons during
0:20:00.050,0:20:07.770
propagation has never been directly[br]observed. And De Broglie said particles
0:20:07.770,0:20:12.490
have a wavelength that's related to their[br]momentum. And he was motivated primarily
0:20:12.490,0:20:19.430
by the Bohr theory of the atom to do so.[br]And he was shown right by the Davisson-
0:20:19.430,0:20:24.300
Germer experiments so his relation for the[br]wavelength of a particle is older than the
0:20:24.300,0:20:29.650
experiments showing this, which is[br]impressive I think. And now the idea is
0:20:29.650,0:20:33.450
they have a complex wave function and let[br]the squared absolute value of the wave
0:20:33.450,0:20:39.880
function describe the probability density[br]of a particle. So we make particles
0:20:39.880,0:20:46.400
extended but probability measured objects[br]so there isn't no longer the position of
0:20:46.400,0:20:50.500
the particle as long as we don't measure.[br]But we have just some description of a
0:20:50.500,0:20:56.860
probability where the particle is. And by[br]making it complex we have a phase and this
0:20:56.860,0:21:01.420
phase can allow, still allow, interference[br]effects which we need for explaining the
0:21:01.420,0:21:07.130
interference peaks in the Davisson-Germer[br]experiment. And now a lot of textbooks say
0:21:07.130,0:21:13.250
here there's a wave particle dualism, blah[br]blah blah. Distinct nonsense, blah.
0:21:13.250,0:21:19.760
The point is it doesn't get you far to[br]think about quantum objects as either wave
0:21:19.760,0:21:25.850
or particle, they're just quantum. Neither[br]wave nor particle. Doesn't help you either
0:21:25.850,0:21:30.050
but it doesn't confuse you as much as when[br]you tried to think about particles as
0:21:30.050,0:21:37.930
waves or particles, or about quantum[br]particles as waves or particles. And now
0:21:37.930,0:21:43.550
that we say we have a complex wave[br]function what about simply using a plain
0:21:43.550,0:21:50.570
wave with constant probability as the[br]states of definite momentum because we
0:21:50.570,0:21:55.920
somehow have to describe a particle to say[br]that has a certain momentum and we do
0:21:55.920,0:22:00.110
this. Those have the little problem that[br]they are not in the Hilbert space because
0:22:00.110,0:22:07.420
they're not normalizable. The absolute[br]value of psi is 1 over 2 pi everywhere, so
0:22:07.420,0:22:13.630
that's bad. But we can write the[br]superposition of any state by Fourier
0:22:13.630,0:22:19.550
transformation those e to the i k dot r[br]states are just the basis states of a
0:22:19.550,0:22:25.550
Fourier transformation. We can write any[br]function in terms of this basis. And we
0:22:25.550,0:22:30.050
can conclude that by Fourier[br]transformation of the state psi of r to
0:22:30.050,0:22:35.500
some state till the psi of k, we describe[br]the same information because we know we
0:22:35.500,0:22:39.810
can invert the Fourier transformation and[br]also this implies the uncertainty
0:22:39.810,0:22:47.720
relation. And because this is simply[br]property of Fourier transformations that
0:22:47.720,0:22:52.130
either the function can be very[br]concentrated in position space or in
0:22:52.130,0:22:58.340
momentum space. And now that[br]we have states of definite momentum. And
0:22:58.340,0:23:04.530
the other big ingredient in quantum[br]mechanics are operators, next to the state
0:23:04.530,0:23:09.380
description. And operators are, just like[br]matrices, linear operators on the state
0:23:09.380,0:23:16.090
space. Just as we can apply a linear[br]operator in the form of a matrix to a vector,
0:23:16.090,0:23:24.710
we can apply linear operators to L2[br]functions. And when we measure an
0:23:24.710,0:23:30.011
observable it will be that it's one of the[br]eigenvalues of this operator that's the
0:23:30.011,0:23:36.940
measurement value, you know. So[br]eigenvalues are those values: If a matrix
0:23:36.940,0:23:44.330
that just scales a vector by a certain[br]amount that is an eigenvalue of the matrix
0:23:44.330,0:23:49.410
and in the same sense we can define[br]eigenvalues and eigenvectors for, L2
0:23:49.410,0:23:57.250
functions. And there are some facts such[br]as that non-commuting operators have
0:23:57.250,0:24:05.830
eigenstates that are not common. So we[br]can't have a description of the basis of
0:24:05.830,0:24:12.160
the state space in terms of function that[br]are both eigenfunctions of both operators
0:24:12.160,0:24:16.760
and some examples of operators are the[br]momentum operator which is just minus i
0:24:16.760,0:24:23.810
h-bar Nabla which is the derivation[br]operator in three dimensions. So in the x
0:24:23.810,0:24:27.810
component we have derivation in the[br]direction of x and in the y component in
0:24:27.810,0:24:34.230
direction of y and so on. And the position[br]operator which is just the operator that
0:24:34.230,0:24:42.560
multiplies by the position x in the[br]position space representation of the wave
0:24:42.560,0:24:48.250
function. And as for the non-[br]communtitivity of operators we can already
0:24:48.250,0:24:54.710
show that those p and x operators that do[br]not commute but fulfill a certain
0:24:54.710,0:25:00.620
commutation relation. And a commutation[br]relation is just a measure for how much
0:25:00.620,0:25:07.250
two operators do not commute. And the[br]commutator is AB minus BA for the objects
0:25:07.250,0:25:15.180
AB, so if they commute, if AB equals BA[br]the commutator simply vanishes. And
0:25:15.180,0:25:20.870
there's more on operators just to make it[br]clear: Linear just means that we can split
0:25:20.870,0:25:26.660
the argument if it is just some linear[br]combinations of vectors and apply the
0:25:26.660,0:25:32.340
operator to the individual vectors[br]occuring, we can define multiplication of
0:25:32.340,0:25:38.240
operators and this just exactly follows[br]the template that is laid down by finite
0:25:38.240,0:25:44.110
dimensional linear algebra. There's[br]nothing new here. And there are inverse
0:25:44.110,0:25:49.380
operators for some operators, not for all[br]of them, that give the identity operator
0:25:49.380,0:25:54.450
if it's multiplied with the original[br]operator. And further there's the so-
0:25:54.450,0:26:00.400
called adjoint. Our scalar product had[br]this little asterisk and this means that
0:26:00.400,0:26:04.560
it's not linear in the first component. If[br]I scale the first component by some
0:26:04.560,0:26:10.600
complex number alpha the total scalar[br]product is not scaled by alpha, but by the
0:26:10.600,0:26:17.610
complex conjugate of alpha. This kind of[br]not quite bi-linearity is sometimes called
0:26:17.610,0:26:26.980
sesquilinearity, a seldomly used word, and[br]they're commonly defined classes of
0:26:26.980,0:26:35.990
operators in terms of how the adjoint that[br]is defined there acts and how some other
0:26:35.990,0:26:39.890
operators for example where the adjoint is[br]the inverse which is a generalization from
0:26:39.890,0:26:45.520
the fact that for rotation operators in[br]normal Euclidean space, the transpose is
0:26:45.520,0:26:53.950
the inverse. And now that we have[br]operators we can define expectation values
0:26:53.950,0:26:59.270
just by some formula. For now, we don't[br]know what expectation values are, but we
0:26:59.270,0:27:03.690
can assume, it has something to do with[br]the measurement values of the operator
0:27:03.690,0:27:09.510
because: why else would I tell you about[br]it. And later on we will show that this is
0:27:09.510,0:27:15.160
actually the expectation value of the[br]quantity if we prepare a system always in
0:27:15.160,0:27:20.780
the same fashion and then do measurements[br]on it, we get random results each time,
0:27:20.780,0:27:29.200
but the expectation value will be this[br]combination. And now again: a bit of
0:27:29.200,0:27:34.840
mathematics: eigenvalue problems. Well[br]known: You can diagonalize a matrix and
0:27:34.840,0:27:39.820
you can diagonalize linear operators. You[br]have some equation A psi equals lambda
0:27:39.820,0:27:47.080
psi, where lambda is just a scalar. And if[br]such an equation holds for some vector psi
0:27:47.080,0:27:52.770
then it's an eigenvector and if we scale[br]the vector linearly, this will again be an
0:27:52.770,0:28:01.380
eigenvector. And what can happen is that[br]to one eigenvalue there are several
0:28:01.380,0:28:05.350
eigenvectors, not only one ray of[br]eigenvectors, but a higher dimensional
0:28:05.350,0:28:11.940
subspace. And important to know is that[br]so-called Hermitian operators, that is
0:28:11.940,0:28:17.690
those that equal their adjoint, which[br]again means that the eigenvalues equal the
0:28:17.690,0:28:23.980
complex conjugate of the eigenvalues have[br]a real eigenvalues. Because if a complex
0:28:23.980,0:28:33.070
number equals its complex conjugate, then[br]it's a real number. And the nice thing
0:28:33.070,0:28:39.570
about those diagonalized matrices and all[br]is: we can develop any vector in terms of
0:28:39.570,0:28:46.890
the eigenbasis of the operator, again just[br]like in linear algebra where when you
0:28:46.890,0:28:51.420
diagonalize a matrix, you get a new basis[br]for your vector space and now you can
0:28:51.420,0:28:57.640
express all vectors in that new basis. And[br]if the operator is Hermitian the
0:28:57.640,0:29:05.050
eigenvectors have a nice property, namely[br]they are orthogonal if the eigenvalues are
0:29:05.050,0:29:11.380
different. And this is good because this[br]guarantees us that we can choose an
0:29:11.380,0:29:16.610
orthonormal, that is a basis in the vector[br]space where to basis vectors always have
0:29:16.610,0:29:24.090
vanishing scalar product are orthogonal[br]and are normal, that is: we scale them to
0:29:24.090,0:29:29.200
length one, because we want our[br]probability interpretation, and in our
0:29:29.200,0:29:37.220
probability interpretation we need to have[br]normalized vectors. So now we have that
0:29:37.220,0:29:41.890
and now we want to know: How does this[br]strange function psi, that describes the
0:29:41.890,0:29:49.580
state of the system, evolve in time. And[br]for this we can have several requirements
0:29:49.580,0:29:55.640
that it must fulfill. So again we are[br]close to software engineering and one
0:29:55.640,0:30:01.400
requirement is, that if it is a sharp wave[br]packet, so if we have a localized state
0:30:01.400,0:30:06.620
that is not smeared around the whole[br]space, then it should follow the classical
0:30:06.620,0:30:12.580
equation of motion because we want that[br]our new theory contains our old theory.
0:30:12.580,0:30:18.450
And the time evolution must conserve the[br]total probability of finding the particle
0:30:18.450,0:30:21.990
because otherwise we couldn't do[br]probability interpretation of our wave
0:30:21.990,0:30:29.010
function, if the total probability of the[br]particle wouldn't remain one. Further we
0:30:29.010,0:30:35.110
wish the equation to be first order in[br]time and to be linear because for example
0:30:35.110,0:30:41.950
the Maxwell equations are linear and show[br]nice interference effects, so we want that
0:30:41.950,0:30:46.370
because then simply a sum of solutions is[br]again a solution, it's a good property to
0:30:46.370,0:30:51.840
have and if it works that way: Why not?[br]And the third and the fourth requirement
0:30:51.840,0:31:00.600
together already give us more or less the[br]form of the Schroedinger equation. Because
0:31:00.600,0:31:04.830
linearity just says that the right-hand[br]side of some linear operator applied to
0:31:04.830,0:31:12.340
psi and the first order in time just means[br]that there must be a single time
0:31:12.340,0:31:19.840
derivative in the equation on the left-[br]hand side. And this i-h bar: we just wanted
0:31:19.840,0:31:23.550
that there, no particular reason we could[br]have done this differently, but it's
0:31:23.550,0:31:31.710
convention. Now with this equation we can[br]look: What must happen for the probability
0:31:31.710,0:31:42.290
to be conserved and by a simple[br]calculation we can show that it must be a
0:31:42.290,0:31:47.870
Hermitian operator. And there is even more[br]than this global argument. There's local
0:31:47.870,0:31:52.020
conservation of probability, that is, a[br]particle can't simply vanish here and
0:31:52.020,0:31:59.250
appear there, but it must flow from one[br]point to the other with local operations.
0:31:59.250,0:32:05.360
This can be shown when you consider this[br]in more detail. Now we know how this
0:32:05.360,0:32:09.460
equation of motion looks like, but we[br]don't know what this mysterious object H
0:32:09.460,0:32:16.500
might be. And this mysterious object H is[br]the operator of the energy of the system
0:32:16.500,0:32:21.770
which is known from classical mechanics as[br]the Hamilton function and which we here
0:32:21.770,0:32:26.610
upgrade to the Hamilton operator by using[br]the formula for the classical Hamilton
0:32:26.610,0:32:33.480
function and inserting our p into our[br]operators. And we can also extend this to
0:32:33.480,0:32:39.710
a magnetic field. And by doing so we can[br]show that our theory is more or less
0:32:39.710,0:32:45.960
consistent with Newtonian mechanics. We[br]can show the Ehrenfest theorem, that's the
0:32:45.960,0:32:55.160
first equation. And then those equations[br]are almost Newton's equation of motion for
0:32:55.160,0:33:05.690
the centers of mass of the particle[br]because this is the expectation value of
0:33:05.690,0:33:10.670
the momentum, this is the expectation[br]value of the position of the particle.
0:33:10.670,0:33:15.740
This just looks exactly like the classical[br]equation. The velocity is the momentum
0:33:15.740,0:33:23.140
divided by the mass. But this is weird:[br]Here we average over the force, so the
0:33:23.140,0:33:29.920
gradient of the potential is the force, we[br]average over the force and do not take the
0:33:29.920,0:33:34.980
force at the center position, so we can't[br]in general solve this equation. But again
0:33:34.980,0:33:38.620
if we have a sharply defined wave packet[br]we recover the classical equations of
0:33:38.620,0:33:44.640
motion, which is nice. So we have shown[br]our new theory does indeed explain why our
0:33:44.640,0:33:51.250
old theory worked. We only still have to[br]explain why the centers of mass of massive
0:33:51.250,0:33:55.520
particles are usually well localized and[br]that's a question we're still having
0:33:55.520,0:34:08.010
trouble with today. But since it otherwise[br]works: don't worry too much about it. And
0:34:08.010,0:34:12.319
now you probably want to know how to solve[br]the Schroedinger equation. Or you don't
0:34:12.319,0:34:18.201
want to know anything more about quantum[br]mechanics. And to do this we make a so-
0:34:18.201,0:34:24.559
called separation ansatz, where we say, we[br]have a form stable part of our wave
0:34:24.559,0:34:30.609
function multiplied by some time dependent[br]part. And if we do this we can write down
0:34:30.609,0:34:35.589
the general solution for the Schroedinger[br]equation. Because we already know that the
0:34:35.589,0:34:41.009
one equation that we get is an eigenvalue[br]equation or an eigenvector equation for
0:34:41.009,0:34:45.849
the energy eigenvalues, that is the[br]eigenvalues of the Hamilton operator. And
0:34:45.849,0:34:50.519
we know that we can develop any function[br]in terms of those and so the general
0:34:50.519,0:34:58.170
solution must be of the form shown here.[br]And those states of specific energy have a
0:34:58.170,0:35:02.220
simple evolution because their form is[br]constant and only their phase changes and
0:35:02.220,0:35:08.960
depends on the energy. And now this thing[br]with the measurement in quantum mechanics
0:35:08.960,0:35:13.200
is bad. You probably know Schroedinger's[br]cat and the point is: there you don't know
0:35:13.200,0:35:16.033
whether the cat is dead or alive while you[br]don't look inside the box. While you don't
0:35:16.033,0:35:19.480
look inside the box as long as you don't[br]measure it's in a superposition or
0:35:19.480,0:35:23.930
something. So You measure[br]your cat and then it's dead. It isn't dead
0:35:23.930,0:35:29.089
before only by measuring it you kill it.[br]And that's really not nice to kill cats.
0:35:29.089,0:35:36.970
We like cats. The important part here is,[br]the TL;DR, quantum measurement is
0:35:36.970,0:35:42.970
probabilistic and inherently changes the[br]system state. So I'll skip the multi
0:35:42.970,0:35:52.770
particle things. We can't describe[br]multiple particles. And just show the
0:35:52.770,0:35:58.700
axioms of quantum mechanics shortly. Don't[br]don't read them too detailed, but this is
0:35:58.700,0:36:04.009
just a summary of what we've discussed so[br]far. And the thing about the multiple
0:36:04.009,0:36:09.730
particles is the axiom 7 which says that[br]the sign of the wave function must change
0:36:09.730,0:36:15.109
if we exchange the coordinates of[br]identical fermions. And this makes atom
0:36:15.109,0:36:20.739
stable by the way. Without this atoms as[br]we know them would not exist. And finally
0:36:20.739,0:36:26.809
there is a notational convention in[br]quantum mechanics called Bra-Ket-notation.
0:36:26.809,0:36:35.380
And in Bra-Ket-notation you label states[br]by their eigenvalues and just think about
0:36:35.380,0:36:42.470
such a Ket as an abstract vector such as x[br]with a vector arrow over it or a fat set x
0:36:42.470,0:36:48.849
is an abstract vector and we can either[br]represent it by its coordinates x1 x2 x3,
0:36:48.849,0:36:53.059
or we can work with the abstract vector[br]and this Ket is such an abstract vector
0:36:53.059,0:37:02.089
for the L2 function psi of r. And then we[br]can also define the adjoint of this which
0:37:02.089,0:37:07.690
gives us, if we multiply the adjoint and a[br]function, the scalar product. So this is a
0:37:07.690,0:37:15.249
really nice and compact notation for many[br]physics problems. And the last equation
0:37:15.249,0:37:20.750
there just looks like component wise, like[br]working with components of matrices, which
0:37:20.750,0:37:31.579
is because it's nothing else. This is just[br]matrix calculus in new clothes. Now for
0:37:31.579,0:37:43.559
the applications. The first one is quite[br]funny. There's a slide missing. Okay. Uh
0:37:43.559,0:37:48.670
the first one is a quantum eraser at home.[br]Because if you encode the "which way"
0:37:48.670,0:37:56.050
information into a double slit experiment[br]you lose your interference pattern. And we
0:37:56.050,0:38:01.220
do this by using a vertical and horizontal[br]polarisation filter. And you know from
0:38:01.220,0:38:16.390
classical physics then it won't make an[br]interference pattern. And if we then add a
0:38:16.390,0:38:25.641
diagonal polarization filter then the[br]interference pattern will appear again. So
0:38:25.641,0:38:31.470
now, just so you've seen it, the harmonic[br]oscillator can be exactly solved in
0:38:31.470,0:38:36.499
quantum mechanics. If you can solve the[br]harmonic oscillator in any kind of physics
0:38:36.499,0:38:41.930
then you're good, then you'll get through[br]the axioms when you study physics. So the
0:38:41.930,0:38:47.771
harmonic oscillator is solved by[br]introducing so-called creation and
0:38:47.771,0:38:53.560
destroyer operators and then we can[br]determine the ground state function, in a
0:38:53.560,0:38:57.720
much simpler manner than if we had to[br]solve the Schroedinger equation explicitly
0:38:57.720,0:39:05.559
for all those cases. And we can determine[br]the ground state function, so the function
0:39:05.559,0:39:11.440
of lowest energy. This can all be done and[br]then from it by applying the creation
0:39:11.440,0:39:18.609
operator create the highest eigenstate of[br]the system and get all of them. Then
0:39:18.609,0:39:22.589
there's this effect of tunnelling that[br]you've probably heard about and this just
0:39:22.589,0:39:27.609
means that in quantum mechanics a[br]potential barrier that is too high for the
0:39:27.609,0:39:32.460
particle to penetrate does not mean that[br]the particle doesn't penetrate at all but
0:39:32.460,0:39:36.749
that the probability of finding the[br]particle inside the barrier decays
0:39:36.749,0:39:42.589
exponentially. And this can for example be[br]understood in terms of this uncertainty
0:39:42.589,0:39:47.569
relation because if we try to compress the[br]particle to the smaller part of the
0:39:47.569,0:39:52.009
boundary layer then its momentum has to be[br]high so it can reach farther in because
0:39:52.009,0:39:58.829
then it has more energy. And there's this[br]myth that tunnelling makes particles
0:39:58.829,0:40:04.530
traveling to travel instantaneously from A[br]to B and even some real physicists believe
0:40:04.530,0:40:12.700
it. But sorry it's not true. The particle[br]states is extended anyway and to defining
0:40:12.700,0:40:17.140
what how fast the particle travels is[br]actually not a well-defined thing in deep
0:40:17.140,0:40:23.079
quantum regimes, and also the Schroedinger[br]equations is not relativistic. So there is
0:40:23.079,0:40:27.630
nothing, really nothing stopping your[br]particle from flying around with 30 times
0:40:27.630,0:40:34.339
the speed of light. It's just not in the[br]theory. Another important consequence of
0:40:34.339,0:40:38.670
quantum mechanics is so-called[br]entanglement and this is a really weird
0:40:38.670,0:40:44.109
one, because it shows that the universe[br]that we live in is in a way non-local,
0:40:44.109,0:40:51.859
inherently non-local. Because we can[br]create some states for some internal
0:40:51.859,0:40:57.400
degrees of freedom of two atoms and move[br]them apart then measure the one system and
0:40:57.400,0:41:01.460
the measurement result in the one system[br]will determine the measurement result in
0:41:01.460,0:41:07.790
the other system, no matter how far[br]removed they are from each other. And this
0:41:07.790,0:41:12.099
was first discovered in a paper by[br]Einstein, Podolski and Rosen and they
0:41:12.099,0:41:17.619
thought it was an argument that quantum[br]mechanics is absurd. This can't be true,
0:41:17.619,0:41:23.359
but sorry it is true. So this works and[br]this kind of state that we've written
0:41:23.359,0:41:32.970
there that is such an entangled state of[br]two particles. But important to remark is
0:41:32.970,0:41:37.029
that there are no hidden variables, that[br]means the measurement result is not
0:41:37.029,0:41:42.250
determined beforehand. It is only when we[br]measure that is actually known what the
0:41:42.250,0:41:47.741
result will be. This is utterly weird but[br]one can prove this experimentally. Those
0:41:47.741,0:41:52.239
are Bell tests. There's a Bell-inequality[br]that's the limit for theories where they
0:41:52.239,0:41:57.410
are hidden variables and it's by real[br]experiments they violate the inequality
0:41:57.410,0:42:02.819
and thereby show that there are no hidden[br]variables. And there's a myth surrounding
0:42:02.819,0:42:07.250
entanglement, namely that you can transfer[br]information with it between two sides
0:42:07.250,0:42:12.910
instantaneously. But again there's nothing[br]hindering you in non relativistic quantum
0:42:12.910,0:42:18.309
mechanics to distribute information[br]arbitrarily fast. It doesn't have a speed
0:42:18.309,0:42:24.440
limit but you can't also count communicate[br]with those entangled pairs of particles.
0:42:24.440,0:42:28.319
You can just create correlated noise at[br]two ends which is what quantum
0:42:28.319,0:42:36.109
cryptography is using. So now because this[br]is the hackers congress, some short
0:42:36.109,0:42:41.549
remarks and probably unintelligible due to[br]their strong compression about quantum
0:42:41.549,0:42:47.190
information. A qubit, the fundamental unit[br]of quantum information, is a system with
0:42:47.190,0:42:53.852
two states zero and one. So just like a[br]bit. But now we allow arbitrary super
0:42:53.852,0:42:58.309
positions of those states because that is[br]what quantum mechanics allows. We can
0:42:58.309,0:43:03.000
always superimpose states and quantum[br]computers are really bad for most
0:43:03.000,0:43:08.940
computing tasks because they have to,[br]even if they build quantum computers they
0:43:08.940,0:43:14.171
will never be as capable as the state-of-[br]the-art silicon electrical computer. So
0:43:14.171,0:43:18.359
don't fear for your jobs because of[br]quantum computers. But the problem is they
0:43:18.359,0:43:23.599
can compute some things faster. For[br]example factoring primes and working with
0:43:23.599,0:43:29.599
some elliptic curve algorithms and so on[br]and determining discrete logarithm so our
0:43:29.599,0:43:35.339
public key crypto would be destroyed by[br]them. And this all works by using the
0:43:35.339,0:43:41.220
superposition to construct some kind of[br]weird parallelism. So it's actually I
0:43:41.220,0:43:47.359
think nobody really can imagine how it[br]works but we can compute it which is often
0:43:47.359,0:43:51.670
the case in quantum mechanics. And then[br]there's quantum cryptography and that
0:43:51.670,0:43:56.279
fundamentally solves the same problem as a[br]Diffie-Hellman key exchange. We can
0:43:56.279,0:44:01.150
generate the shared key and we can check[br]by the statistics of our measured values
0:44:01.150,0:44:07.349
that there is no eavesdropper, which is[br]cool actually. But it's also quite useless
0:44:07.349,0:44:10.201
because we can't detect a man in the[br]middle. How should the quantum particle
0:44:10.201,0:44:14.630
knows of the other side is the one with[br]that we want to talk to. We still need
0:44:14.630,0:44:18.839
some shared secret or public key[br]infrastructure whatever. So it doesn't
0:44:18.839,0:44:27.210
solve the problem that we don't have[br]solved. And then the fun fact about this
0:44:27.210,0:44:30.970
is that all the commercial implementations[br]of quantum cryptography were susceptible
0:44:30.970,0:44:35.150
to side channel text, for example you[br]could just shine the light with a fiber
0:44:35.150,0:44:40.920
that was used, read out the polarization[br]filter state that they used and then you
0:44:40.920,0:44:50.609
could mimic the other side. So that's not[br]good either. So finally some references
0:44:50.609,0:44:55.150
for further study. The first one is really[br]difficult. Only try this if you've read the
0:44:55.150,0:45:00.650
other two but the second one. Sorry that[br]they're in German. The first and the last
0:45:00.650,0:45:04.579
are also available in translation but the[br]second one has a really really nice and
0:45:04.579,0:45:09.650
accessible introduction in the last few[br]pages so it's just 20 pages and it's
0:45:09.650,0:45:14.660
really good and understandable. So if you[br]can get your hands on the books and are
0:45:14.660,0:45:22.079
really interested, read it. So thank you[br]for the attention and I'll be answering
0:45:22.079,0:45:24.259
your questions next.
0:45:24.259,0:45:33.159
*Applause*
0:45:33.159,0:45:41.240
Herald: Thank you Sebastian. Do we have[br]questions? And don't be afraid to sound
0:45:41.240,0:45:45.380
naive or anything. I'm sure if you didn't[br]understand something many other people
0:45:45.380,0:45:49.099
would thank you for a good question.[br]Sebastian: As to understanding things in
0:45:49.099,0:45:53.180
quantum mechanics, Fineman said "You can't[br]understand quantum mechanics, you can just
0:45:53.180,0:45:57.269
accept that there there's nothing to[br]understand. That's just too weird."
0:45:57.269,0:46:01.590
Herald: Ok,we've found some questions. So[br]microphone one please.
0:46:01.590,0:46:09.349
M1: Can you explain that, if you measure a[br]system, it looks like you changed the
0:46:09.349,0:46:15.130
state of the system. How is it defined[br]where the system starts? No. How is it
0:46:15.130,0:46:20.200
defined when the system ends and the[br]measurement system begins. Or in other
0:46:20.200,0:46:24.410
words why does the universe have a[br]state? Is there somewhere out there who
0:46:24.410,0:46:29.450
measures the universe?[br]S: No. There's at least the beginning of a
0:46:29.450,0:46:34.880
solution by now which is called[br]"decoherence" which says that this
0:46:34.880,0:46:39.970
measurement structure that we observe is[br]not inherent in quantum mechanics but
0:46:39.970,0:46:43.920
comes from the interaction with the[br]environment. And we don't care for the
0:46:43.920,0:46:48.460
states of the environment. And if we do[br]this, the technical term is traced out the
0:46:48.460,0:46:52.529
states of the environment. Then the[br]remaining state of the measurement
0:46:52.529,0:46:59.789
apparatus and the system we're interested[br]in will be just classically a randomized
0:46:59.789,0:47:05.700
states. So it's rather a consequence[br]of the complex dynamics of a system state
0:47:05.700,0:47:10.739
and environment in quantum mechanics. But[br]this is really the burning question. We
0:47:10.739,0:47:15.690
don't really know. We have this we know[br]decoherence make some makes it nice and
0:47:15.690,0:47:20.749
looks good. But it also doesn't answer the[br]question finally. And this is what all
0:47:20.749,0:47:25.430
those discussions about interpretations of[br]quantum mechanics are about. How shall we
0:47:25.430,0:47:28.940
make sense of this weird measurement[br]process.
0:47:28.940,0:47:37.150
Herald: Okay. Microphone 4 in the back please.[br]M4: Could you comment on your point in the
0:47:37.150,0:47:44.220
theory section. I don't understand what[br]you were trying to do. Did you want to
0:47:44.220,0:47:49.369
show that you cannot understand really[br]quantum mechanics without the mathematics
0:47:49.369,0:47:51.990
or?[br]S: Well, yes you can't understand quantum
0:47:51.990,0:47:56.010
mechanics without the mathematics and my[br]point to show was that mathematics, or at
0:47:56.010,0:48:02.380
least my hope to show was that mathematics[br]is halfways accessible. Probably not
0:48:02.380,0:48:07.799
understandable after just exposure of a[br]short talk but just to give an
0:48:07.799,0:48:12.849
introduction where to look[br]M4: OK. So you are trying to combat the
0:48:12.849,0:48:18.050
esoterics and say they don't really[br]understand the theory because they don't
0:48:18.050,0:48:29.380
understand the mathematics. I understand[br]the mathematics. I'm just interested. What
0:48:29.380,0:48:33.809
were you trying to say?[br]S: I was just trying to present the
0:48:33.809,0:48:39.339
theory. That was my aim.[br]M4: Okay. Thank you.
0:48:39.339,0:48:45.759
Herald: Okay, microphone 2 please.[br]M2: I know the answer to this question is
0:48:45.759,0:48:48.569
that ...[br]Herald: Can you go a little bit closer to
0:48:48.569,0:48:52.660
the microphone maybe move it up please.[br]M2: So I know the answer to this question
0:48:52.660,0:48:59.510
is that atoms behave randomly but could[br]you provide an argument why they behave
0:48:59.510,0:49:07.369
randomly and it is not the case that we[br]don't have a model that's. So, are atoms
0:49:07.369,0:49:12.019
behaving randomly? Or is it the case that[br]we don't have a model accurate enough to
0:49:12.019,0:49:17.890
predict the way they behave?[br]S: Radioactive decay is just as random as
0:49:17.890,0:49:24.089
quantum measurement and since if we[br]were to look at the whole story and look
0:49:24.089,0:49:28.219
at the coherent evolution of the whole[br]system we would have to include the
0:49:28.219,0:49:33.809
environment and the problem is that the[br]state space that we have to consider grows
0:49:33.809,0:49:37.809
exponentially. That's the point of quantum[br]mechanics. If I have two particles I have
0:49:37.809,0:49:42.900
a two dimensional space. I have 10[br]particles I have a 1024 dimensional space
0:49:42.900,0:49:47.269
and that's only talking about non[br]interacting particles. So things explode
0:49:47.269,0:49:51.950
in quantum mechanics and large systems.[br]And therefore I would go so far as to say
0:49:51.950,0:49:57.140
that it's objectively impossible to[br]determine a radioactive decay although
0:49:57.140,0:50:03.670
there are things, there is I think one[br]experimentally confirmed method of letting
0:50:03.670,0:50:11.279
an atom decay on purpose. This involves[br]meta stable states of nuclei and then you
0:50:11.279,0:50:15.690
can do something like spontaneous emission[br]in a laser. You shine a strong gamma
0:50:15.690,0:50:21.710
source by it and this shortens the[br]lifespan of the nucleus. But other than
0:50:21.710,0:50:25.410
that.[br]M4: So in a completely hypothetical case. If you
0:50:25.410,0:50:29.839
know all the starting conditions and what[br]happens afterwards,wouldn't it be able,
0:50:29.839,0:50:37.220
we could say it's deterministic? I[br]mean I'm playing with heavy words here.
0:50:37.220,0:50:43.619
But is it just that we say it's randomised[br]because it's very very complex right?
0:50:43.619,0:50:48.470
That's what I'm understanding.[br]Herald: Maybe think about that question
0:50:48.470,0:50:53.099
one more time and we have the signal angel[br]in between and then you can come back.
0:50:53.099,0:50:57.690
Signal Angel do we have questions on the[br]Internet?
0:50:57.690,0:51:04.940
Angel: There's one question from the Internet[br]which is the ground state of a BEH-2 has
0:51:04.940,0:51:12.150
been just calculated using a quantum[br]eigensolver. So is there still some use of
0:51:12.150,0:51:16.849
quantum computing in quantum mechanics?[br]S: Yes definitely. One of the main
0:51:16.849,0:51:22.309
motivations for inventing quantum[br]computers was quantum simulators.
0:51:22.309,0:51:26.700
Feynman invented this kind of[br]quantum computing and he showed that with
0:51:26.700,0:51:32.009
digital quantum computer you can[br]efficiently simulate quantum systems. While
0:51:32.009,0:51:36.489
you can't simulate quantum systems with a[br]classical computer because of this problem
0:51:36.489,0:51:41.790
of the exploding dimensions of the Hilbert[br]space that you have to consider. And for
0:51:41.790,0:51:46.280
this quantum computers are really really[br]useful and will be used once they work,
0:51:46.280,0:51:52.760
which is the question when it will be.[br]Perhaps never. Beyond two or three qubits
0:51:52.760,0:51:59.180
or 20 or 100 qubits but you need scalability[br]for a real quantum computer. But quantum
0:51:59.180,0:52:03.349
simulation is a real thing and it's a good[br]thing and we need it.
0:52:03.349,0:52:07.960
Herald: Okay. Then we have microphone 1[br]again.
0:52:07.960,0:52:13.779
M1: So very beginning, you said that the[br]theory is a set of interdependent
0:52:13.779,0:52:21.539
propositions. Right? And then if a new[br]hypothesis is made it can be confirmed by
0:52:21.539,0:52:28.219
an experiment.[br]S: That can't be confirmed but, well it's
0:52:28.219,0:52:33.559
a philosophical question about the common[br]stance, it can be made probable but not
0:52:33.559,0:52:37.210
be confirmed because we can never[br]absolutely be sure that there won't be
0:52:37.210,0:52:40.599
some new experiment that shows that the[br]hypothesis is wrong.
0:52:40.599,0:52:44.920
M1: Yeah. Because the slide said that[br]the experiment confirms...
0:52:44.920,0:52:51.150
S: Yeah, confirm in the sense that it[br]doesn't disconfirm it. So it makes
0:52:51.150,0:52:57.040
probable that it's a good explanation of[br]the reality and that's the point. Physics
0:52:57.040,0:53:01.710
is just models. We do get[br]nothing about the ontology that is about
0:53:01.710,0:53:06.349
the actual being of the world out of[br]physics. We just get models to describe
0:53:06.349,0:53:11.539
the world but all what I say about this[br]wave function and what we say about
0:53:11.539,0:53:18.150
elementary particles. We can't say they[br]are in the sense that you and I are here
0:53:18.150,0:53:22.749
and exist because we can't see them we[br]can't access them directly. We can only
0:53:22.749,0:53:28.960
use them as description tools. But this is[br]my personal position on philosophy of
0:53:28.960,0:53:33.380
science. So there are people who disagree.[br]M1: Ok, thanks.
0:53:33.380,0:53:39.960
Herald: Microphone 2 please.[br]M2: Or maybe superposition. By the way, so
0:53:39.960,0:53:47.550
on the matter of the collapsing of the[br]wave function, so this was already treated
0:53:47.550,0:53:52.589
on the interpretation of Copenhagen and[br]then as you mentioned it was expanded by
0:53:52.589,0:53:59.331
the concept of decoherence. And is this, so[br]the decoherence is including also the
0:53:59.331,0:54:03.319
Ghirardi–Rimini–Weber interpretation or[br]not?
0:54:03.319,0:54:06.880
S: Could decoherence be used in[br]computation or?
0:54:06.880,0:54:13.019
M2: No so for the Ghirardi–Rimini–Weber[br]interpretation of the collapsing of the
0:54:13.019,0:54:15.700
wave function.[br]S:That's one that I don't know.
0:54:15.700,0:54:24.269
I'm not so much into interpretations.[br]I actually think that there's interesting
0:54:24.269,0:54:29.630
work done there but I think they're a bit[br]irrelevant because in the end what I just
0:54:29.630,0:54:33.690
said I don't think you can derive[br]ontological value from our physical
0:54:33.690,0:54:40.519
theories and in this belief, I think that[br]the interpretations are in a sense void,
0:54:40.519,0:54:44.890
they just help us to rationalize what[br]we're doing but they don't really add
0:54:44.890,0:54:49.339
something to the theory as long as they[br]don't change what can be measured.
0:54:49.339,0:54:58.180
M2: Oh okay. Thanks.[br]S: Sorry for being an extremist.
0:54:58.180,0:55:03.580
M2: Totally fine.[br]Herald: Someone just left from microphone 1
0:55:03.580,0:55:07.810
I don't know if they want to come[br]back. I don't see any more questions as to
0:55:07.810,0:55:13.680
signal angel have anything else. There is[br]some more. Signal angel, do you have
0:55:13.680,0:55:16.519
something?[br]Signal Angel: No.
0:55:16.519,0:55:19.609
Herald: Okay. Then we have[br]microphone 4.
0:55:19.609,0:55:27.809
M4: I want to ask a maybe a noob question.[br]I want to know, are the probabilities of
0:55:27.809,0:55:32.770
quantum mechanics inherent part of nature[br]or maybe in some future we'll have a
0:55:32.770,0:55:37.490
science that will determine all these[br]values exactly?
0:55:37.490,0:55:44.799
S: Well if decoherency theory is true,[br]then quantum mechanics is absolutely
0:55:44.799,0:55:53.779
deterministic. But so let's say, Everett[br]says that all those possible measurement
0:55:53.779,0:55:58.869
outcomes do happen and the whole state of[br]the system is in a superposition and by
0:55:58.869,0:56:03.839
looking at our measurement device and[br]seeing some value we in a way select one
0:56:03.839,0:56:10.219
strand of those superpositions and live in[br]this of the many worlds and in this sense
0:56:10.219,0:56:21.349
everything happens deterministically, but[br]we just can't access any other values. So
0:56:21.349,0:56:27.999
I think it's for now rather a[br]of philosophy than of science.
0:56:27.999,0:56:32.900
M4: I see. Thanks.
0:56:32.900,0:56:38.559
Herald: Anything else? I don't see any[br]people lined up at microphones. So last
0:56:38.559,0:56:46.709
chance to round up now, I think. Well then[br]I think we're closing this and have a nice
0:56:46.709,0:56:59.510
applause again for Sebastian.[br]*applause*
0:56:59.510,0:57:02.654
Sebastian: Thank you. And I hope I didn't[br]create more fear of
0:57:02.654,0:57:05.080
quantum mechanics than[br]I dispersed.
0:57:05.080,0:57:30.000
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