WEBVTT

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<i>35C3 preroll music</i>

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Herald Angel: And, so he studied physics
and I'm thinking we just all need a lot

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better understanding of quantum mechanics,
because he sees this theory being misused

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a lot by some weird esoteric theories,
kind of abusing it to just justify

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everything and anything. So he wants to
change that and he wants to have people

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with some understanding of this very
important theory and so he will start

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today with all of us here and try to
explain to us the wonders of quantum

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mechanics. Have a go.
<i>applause</i>

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Sebastian Riese: Well thank you for a warm
welcome. It will be about quantum

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mechanics. We will see whether the gentle
introduction will be a lie depending on

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how good you can follow me. So at first
there will be a short introduction, a bit

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meta discussion about physical theories
and what is the aim of this talk. And then

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we will discuss the experiments. Most of
this is high school physics, you've

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probably seen it before. And then it will
get ugly because we'll do the theory and

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we'll really do the theory, we'll write
down the equations of quantum mechanics

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and try to make them plausible and
hopefully understandable to a lot of

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people. And finally some applications will
be discussed. So what is the concept of

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this talk. The key experiments will be
reviewed as said, and but we will not do

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it in historical fashion. We will look at
the experiments as physical facts and

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derive the theory from them. And since
quantum mechanics is rather abstract and

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not, as I said in German and in science
theory "anschaulich", we will need

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mathematics and most of this will be
linear algebra. So a lot of quantum

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mechanics is just linear algebra on
steroids, that means in infinite

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dimensions. And in doing so we'll try to
find a certain post classical

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"Anschaulichkeit" or lividness to
understand the theory. Since there'll be a

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lot of math as the allergy advice said,
there will be crash courses driven in to

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explain mathematical facts. Sorry for the
mathematicians that are here they probably

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suffer because I lie a lot. So at first:
How do scientific theories work? To really

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understand quantum mechanics we must
understand the setting and setting where

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it was created and how scientific theories
are created in general. A scientific

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theory is a net of interdependent
propositions so we have one proposition

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for example "F = M times a" in classical
mechanics and we have another proposition

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that the gravitational force equals is
proportional to the product of the masses

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divided by the distance between the masses
squared, so something like this. And when

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we go around, make experiments, look into
nature, develop theories, calculate, we

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test those we test hypotheses, different
hypotheses and try to determine which one

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describes our experimental results best.
And if the hypothesis stands the

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experimental tests they're added to the
theory. But what happens if there's an

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experimental result that totally
contradicts what we've seen before? And

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that happened in the late 19th and early
20th century. There are new results that

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could not be explained. So if such
inconsistent results are found then our

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old theory has been falsified. This term
is due to Popper who said that a theory is

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scientific as long as it can be falsified,
that is at least as long as we can prove

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that it's not true and we can never prove
a theory true but only prove it wrong. And

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all that we have not yet proven wrong are
at least some approximation to truth. And

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if this happens we have to amend our old
theory and we have to use care there and

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find a minimal amendment. This principle
is Occam's Razor. One could also say the

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principle of least surprise from software
engineering. And then we try that our

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theory is again consistent with the
experimental results. And of course the

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new theory must explain why the hell that,
for example Newtonian mechanics work for

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two hundred years if it's absolutely
wrong. And so the old theory must in some

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limit contain the new one. And now how
does it begin with quantum mechanics. As

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already said the time frame is the late
19th and early 20th century. And there

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were three or four fundamental theories of
physics known then: Classical mechanics,

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which is just governed by the single
equation the force equals mass times the

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acceleration with given forces. And two
known force laws: The immediate distance

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action Newtonian gravitation and the
Maxwell electro dynamics, this funny

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equation here. This funny equation here is
a way of writing down the Maxwell

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equations that basically contain all the
known electromagnetic effects. And finally

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there were the beginnings of the Maxwell
Boltzmann statistical physics, but

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classical statistical physics is a pain,
doesn't really work. So several

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experimental results I said could not be
explained by classical theories. For

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example the photoelectric effect
discovered by Hertz and Hallwachs in 1887,

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or the discrete spectral lines of atoms
first shown by Fraunhofer in the spectrum

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of the sun and then studied by Bunsen and
Kirchhoff with the so-called

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"Bunsenbrenner", you all know it from the
chemistry classes. And further,

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radioactive rays were really a mystery
nobody understood: How can it happen that

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something just decays at random intervals?
It was unclear. And then the people looked

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into the atom, Rutherford using alpha
particles to bombard a gold foil and saw

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there must be positively charged nucleii
and they already knew that they were

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negatively charged, what we now call
electrons, particles in the atom. So this

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was really strange that atoms are stable
at composed like this and I will explain

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why a bit later. But now to more detail to
the experiments. The really big

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breakthrough in this time, experimentally
speaking, were vacuum tubes, so you took a

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piece of glass and pumped the air out and
closed it off and put all sorts of devices

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in there. And now one thing is this nice
cathode ray experiment. We have here a so-

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called electron gun and this is a heated
electrode, so here flows the current that

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heats it, so that the electrons get energy
and seep out into the vacuum. Then we have

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an electrode that goes around and a plate
in front that is positively charged. So we

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accelerate our electrons towards the
plate. There's a pinhole in the plate and

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we get a beam of electrons. And now we had
those evacuated tubes and those electron

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guns. So we put the electron gun in the
evacuated tube, perhaps left a bit of gas

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in because then it glowed when it when the
atoms in the gas were hit by the electrons

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so we could see the cathode ray, and then
we play around. We take magnetic fields

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and see how does it react to magnetic
fields. We take electric fields. How does

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it react to electric fields and so on. And
what we find out is we somehow must have

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negatively charged particles that flow
nicely around in our almost vacuum. And

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because atoms are neutral which is just
known macroscopically there must be a

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positively charged component in the atom
as well. And this positively charged

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component was first thought to be kind of
a plum pudding or so with the electrons

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sitting in there. But the Rutherford-
Marsden-Geiger experiment, so it was

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Rutherford invented the idea and Marsden
and Geiger actually performed the

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experimental work, showed that if you had
a really thin gold foil, really only a few

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hundred layers of atoms, that's the nice
thing about gold, you can just hammer it

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out to really, really thin sheets, if you
had that and then shot alpha particles

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that is helium nuclei that are created by
the radioactive decay of many heavy

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elements for example, most uranium
isotopes decay by alpha decay, then they

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were deflected strongly. If the charge
would have been spaced throughout the

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atoms then this could not have happened.
You can calculate, you can

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estimate the possible deflections with an
extended charge and with a concentrated

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charge, and you see the only explanation
for this is that there is a massive and

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really, really small positive thing in
those atoms. So atoms are small,

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positively charged nucleus as Rutherford
called it and around it there's a cloud of

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electrons or, he thought, orbiting
electrons. But orbiting electrons atoms

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are stable, this doesn't really make sense
in classical physics, because in classical

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physics all accelerator charges must
radiate energy and be slowed by this

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process. And this means atoms that are
stable and composed of some strange

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electrons and having nuclei they're just
not possible. It's a no go, so at least at

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this moment it was completely clear
classical physics as they knew it up until

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then is wrong. And the next experiment in
this direction was the photoelectric

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effect. What's shown there is a schematic
of a phototube. And a phototube is again a

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vacuum tube out of glass and there is a
for example cesium layer in in the tube at

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one side and there is a ring electrode
removed from it. And if we shine light on

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this there flows a current. But the
peculiar thing is that if we do the bias

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voltage across the two terminals of this
tube to stop the electrons, we see that

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the bias voltage that completely stops the
flow is not proportional to the intensity

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of the light that is incident onto the
tube, but it's proportional to the

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frequency of the light that's incident on
the phototube. And that was again really

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weird for the people of the time because
the frequency shouldn't make any

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difference for the energy. And this was
when Einstein derived that, or thought of

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that there must be some kind of energy
portions in the electric field, from this

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simple experiment, which is often done in
physics classes even at the high school

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level. So it's, from today's view it's not
a complicated experiment. And to go even

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further those weird stable atoms had
discrete, had discrete lines of emission

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and absorption of light. And here we have
again a very simplified experimental set

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up of a so-called discharge tube, where we
have high voltage between the terminals

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and a thin gas and then a current will
flow, will excite the atoms. The atoms

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will relax and emit light and this light
will have a specific spectrum with sharp

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frequencies that are, that have strong
emission and we can see this with a

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diffraction grating that sorts light out
according to its wavelength and then look

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on the screen or view some more fancy
optical instrument to do precision

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measurements as Bunsen and Kirchhoff did.
So what we knew up until now was that

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something was really weird and our
physical theories didn't make sense. And

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then it got worse. Someone took an
electron gun and pointed it at a

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monocrystalline surface. And such a
monocrystalline surface is just like a

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diffraction grating: A periodically
arranged thing. And off periodically

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arranged things there does happen regular
interference pattern creation. So they saw

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interference pattern with electrons. But
electrons aren't that particles? How can

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particles, so what was thought of then,
since the times of Newton as a little hard

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ball, how can a little hard ball flowing
around create interference patterns? It

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was really weird. And there's even more
and as already mentioned radioactivity

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with the random decay of a nucleus. This
doesn't make sense in classical physics,

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so it was really, really bad. And here
I've added some modern facts that we'll

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need later on. Namely that if we measure,
if we try to measure the position of a

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particle and use different position
sensors to do so, only one of them, so at

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only at one position will the single
particle register, but it will

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nevertheless show an interference pattern
if I do this experiment with many many

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electrons. So there must somehow be a
strange divide between the free space

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propagation of particles and measuring the
particles. And you can do really weird

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stuff and record the information through
which slit the particle went. And if you

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do this, the interference pattern
vanishes. And then you can even destroy

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this information in a coherent manner and
the interference pattern appears again. So

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what we know up until now is that quantum
mechanics is really, really weird and

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really different from classical mechanics.
And now that we've talked about those

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experiments, we'll begin with the theory,
and the theory will begin with a lot of

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mathematics. The first one is simple.
Complex numbers. Who doesn't know complex

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numbers? Okay. Sorry I'll have to ignore
you for the sake of getting to the next

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points. <i>laughter</i> So I'll just say
complex numbers are two components of, two

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componented objects with real numbers. And
one of them is multiplied by an imaginary

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number i. And if we square the number i it
gets -1. And this makes many things really

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beautiful. For example all algebraic
equations have exactly the number of

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degrees solutions in complex numbers, and
if you count them correctly. And if you

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work with complex functions it's really
beautiful. A function that once

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differentiable is infinitely many times
differentiable and it's, it's nice. So now

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we had complex numbers. You've all said
you know them. <i>laughter</i> So we go onto

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vector spaces, which probably also a lot
of you know. Just to revisit it, a vector

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space is a space of objects called
vectors, above some scalars that must be a

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field. And here we only use complex
numbers as the underlying fields. There is

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a null vector, we can add vectors, we can
invert vectors and we can multiply vectors

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by real numbers. So we can say three that
five times this vector and just scale the

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arrow and these operations interact nicely
so that we have those distributive laws.

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And now it gets interesting. Even more
maths: L2 spaces. L2 spaces are in a way

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an infinite dimensional or one form of an
infinite dimensional extension of vector

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spaces. Instead of having just three
directions x, y, z, we have directions at

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each point of a function. So we have an
analogy here. We have vectors which have

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three discrete components given by x index
i on the right side and we have this

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function and each component is the value
of the function at one point along the

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axis x. And then we can just as for
vectors define a norm on those L2

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functions which is just the integral over
the absolute value squared of this

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function f. And the nice thing about this
choice of norm, there are other choices of

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the norm. This norm is induced by a scalar
product and this little asterisk that is

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there at the f denotes the complex
conjugate, so flipping i to minus i in

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all complex values. And if you just plug
in f and f into the scalar product you

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will see that it's the integral over the
squared absolute value. And this space,

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this L2 space is a Hilbert space and the
Hilbert Space is a complete vector space

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with a scalar product where complete means
that - It's mathematical nonsense.

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Forget it. So but the nice surprise is
that most things carry over from finite

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dimensional space. What we know from
finite dimensional space is we can always

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diagonalize matrices with certain
properties and this more or less works.

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And the mathematicians really, really,
really do a lot of work for this but for

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physicists we just know when to be careful
and how and don't care about it otherwise.

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So just works for us and that's nice. And
now that we have those complex numbers we

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can begin to discuss how particles are
modeled in quantum mechanics. And as we

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know from the Davisson-Germer experiments
there's diffraction of electrons but

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there's nothing in electrons that
corresponds to an electric field in some

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direction or so. Some other periodicity
has, so periodicity of electrons during

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propagation has never been directly
observed. And De Broglie said particles

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have a wavelength that's related to their
momentum. And he was motivated primarily

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by the Bohr theory of the atom to do so.
And he was shown right by the Davisson-

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Germer experiments so his relation for the
wavelength of a particle is older than the

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experiments showing this, which is
impressive I think. And now the idea is

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they have a complex wave function and let
the squared absolute value of the wave

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function describe the probability density
of a particle. So we make particles

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extended but probability measured objects
so there isn't no longer the position of

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the particle as long as we don't measure.
But we have just some description of a

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probability where the particle is. And by
making it complex we have a phase and this

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phase can allow, still allow, interference
effects which we need for explaining the

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interference peaks in the Davisson-Germer
experiment. And now a lot of textbooks say

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here there's a wave particle dualism, blah
blah blah. Distinct nonsense, blah.

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The point is it doesn't get you far to
think about quantum objects as either wave

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or particle, they're just quantum. Neither
wave nor particle. Doesn't help you either

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but it doesn't confuse you as much as when
you tried to think about particles as

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waves or particles, or about quantum
particles as waves or particles. And now

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that we say we have a complex wave
function what about simply using a plain

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wave with constant probability as the
states of definite momentum because we

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somehow have to describe a particle to say
that has a certain momentum and we do

00:21:55.920 --> 00:22:00.110
this. Those have the little problem that
they are not in the Hilbert space because

00:22:00.110 --> 00:22:07.420 line:1
they're not normalizable. The absolute
value of psi is 1 over 2 pi everywhere, so

00:22:07.420 --> 00:22:13.630
that's bad. But we can write the
superposition of any state by Fourier

00:22:13.630 --> 00:22:19.550
transformation those e to the i k dot r
states are just the basis states of a

00:22:19.550 --> 00:22:25.550
Fourier transformation. We can write any
function in terms of this basis. And we

00:22:25.550 --> 00:22:30.050
can conclude that by Fourier
transformation of the state psi of r to

00:22:30.050 --> 00:22:35.500
some state till the psi of k, we describe
the same information because we know we

00:22:35.500 --> 00:22:39.810
can invert the Fourier transformation and
also this implies the uncertainty

00:22:39.810 --> 00:22:47.720
relation. And because this is simply
property of Fourier transformations that

00:22:47.720 --> 00:22:52.130
either the function can be very
concentrated in position space or in

00:22:52.130 --> 00:22:58.340
momentum space. And now that
we have states of definite momentum. And

00:22:58.340 --> 00:23:04.530
the other big ingredient in quantum
mechanics are operators, next to the state

00:23:04.530 --> 00:23:09.380
description. And operators are, just like
matrices, linear operators on the state

00:23:09.380 --> 00:23:16.090
space. Just as we can apply a linear
operator in the form of a matrix to a vector,

00:23:16.090 --> 00:23:24.710
we can apply linear operators to L2
functions. And when we measure an

00:23:24.710 --> 00:23:30.011
observable it will be that it's one of the
eigenvalues of this operator that's the

00:23:30.011 --> 00:23:36.940
measurement value, you know. So
eigenvalues are those values: If a matrix

00:23:36.940 --> 00:23:44.330
that just scales a vector by a certain
amount that is an eigenvalue of the matrix

00:23:44.330 --> 00:23:49.410
and in the same sense we can define
eigenvalues and eigenvectors for, L2

00:23:49.410 --> 00:23:57.250
functions. And there are some facts such
as that non-commuting operators have

00:23:57.250 --> 00:24:05.830
eigenstates that are not common. So we
can't have a description of the basis of

00:24:05.830 --> 00:24:12.160
the state space in terms of function that
are both eigenfunctions of both operators

00:24:12.160 --> 00:24:16.760
and some examples of operators are the
momentum operator which is just minus i

00:24:16.760 --> 00:24:23.810
h-bar Nabla which is the derivation
operator in three dimensions. So in the x

00:24:23.810 --> 00:24:27.810
component we have derivation in the
direction of x and in the y component in

00:24:27.810 --> 00:24:34.230
direction of y and so on. And the position
operator which is just the operator that

00:24:34.230 --> 00:24:42.560
multiplies by the position x in the
position space representation of the wave

00:24:42.560 --> 00:24:48.250
function. And as for the non-
communtitivity of operators we can already

00:24:48.250 --> 00:24:54.710
show that those p and x operators that do
not commute but fulfill a certain

00:24:54.710 --> 00:25:00.620
commutation relation. And a commutation
relation is just a measure for how much

00:25:00.620 --> 00:25:07.250
two operators do not commute. And the
commutator is AB minus BA for the objects

00:25:07.250 --> 00:25:15.180
AB, so if they commute, if AB equals BA
the commutator simply vanishes. And

00:25:15.180 --> 00:25:20.870
there's more on operators just to make it
clear: Linear just means that we can split

00:25:20.870 --> 00:25:26.660
the argument if it is just some linear
combinations of vectors and apply the

00:25:26.660 --> 00:25:32.340
operator to the individual vectors
occuring, we can define multiplication of

00:25:32.340 --> 00:25:38.240
operators and this just exactly follows
the template that is laid down by finite

00:25:38.240 --> 00:25:44.110
dimensional linear algebra. There's
nothing new here. And there are inverse

00:25:44.110 --> 00:25:49.380
operators for some operators, not for all
of them, that give the identity operator

00:25:49.380 --> 00:25:54.450
if it's multiplied with the original
operator. And further there's the so-

00:25:54.450 --> 00:26:00.400
called adjoint. Our scalar product had
this little asterisk and this means that

00:26:00.400 --> 00:26:04.560
it's not linear in the first component. If
I scale the first component by some

00:26:04.560 --> 00:26:10.600
complex number alpha the total scalar
product is not scaled by alpha, but by the

00:26:10.600 --> 00:26:17.610
complex conjugate of alpha. This kind of
not quite bi-linearity is sometimes called

00:26:17.610 --> 00:26:26.980
sesquilinearity, a seldomly used word, and
they're commonly defined classes of

00:26:26.980 --> 00:26:35.990
operators in terms of how the adjoint that
is defined there acts and how some other

00:26:35.990 --> 00:26:39.890
operators for example where the adjoint is
the inverse which is a generalization from

00:26:39.890 --> 00:26:45.520
the fact that for rotation operators in
normal Euclidean space, the transpose is

00:26:45.520 --> 00:26:53.950
the inverse. And now that we have
operators we can define expectation values

00:26:53.950 --> 00:26:59.270
just by some formula. For now, we don't
know what expectation values are, but we

00:26:59.270 --> 00:27:03.690
can assume, it has something to do with
the measurement values of the operator

00:27:03.690 --> 00:27:09.510
because: why else would I tell you about
it. And later on we will show that this is

00:27:09.510 --> 00:27:15.160
actually the expectation value of the
quantity if we prepare a system always in

00:27:15.160 --> 00:27:20.780
the same fashion and then do measurements
on it, we get random results each time,

00:27:20.780 --> 00:27:29.200
but the expectation value will be this
combination. And now again: a bit of

00:27:29.200 --> 00:27:34.840
mathematics: eigenvalue problems. Well
known: You can diagonalize a matrix and

00:27:34.840 --> 00:27:39.820
you can diagonalize linear operators. You
have some equation A psi equals lambda

00:27:39.820 --> 00:27:47.080
psi, where lambda is just a scalar. And if
such an equation holds for some vector psi

00:27:47.080 --> 00:27:52.770
then it's an eigenvector and if we scale
the vector linearly, this will again be an

00:27:52.770 --> 00:28:01.380
eigenvector. And what can happen is that
to one eigenvalue there are several

00:28:01.380 --> 00:28:05.350
eigenvectors, not only one ray of
eigenvectors, but a higher dimensional

00:28:05.350 --> 00:28:11.940
subspace. And important to know is that
so-called Hermitian operators, that is

00:28:11.940 --> 00:28:17.690
those that equal their adjoint, which
again means that the eigenvalues equal the

00:28:17.690 --> 00:28:23.980
complex conjugate of the eigenvalues have
a real eigenvalues. Because if a complex

00:28:23.980 --> 00:28:33.070
number equals its complex conjugate, then
it's a real number. And the nice thing

00:28:33.070 --> 00:28:39.570
about those diagonalized matrices and all
is: we can develop any vector in terms of

00:28:39.570 --> 00:28:46.890
the eigenbasis of the operator, again just
like in linear algebra where when you

00:28:46.890 --> 00:28:51.420
diagonalize a matrix, you get a new basis
for your vector space and now you can

00:28:51.420 --> 00:28:57.640
express all vectors in that new basis. And
if the operator is Hermitian the

00:28:57.640 --> 00:29:05.050
eigenvectors have a nice property, namely
they are orthogonal if the eigenvalues are

00:29:05.050 --> 00:29:11.380
different. And this is good because this
guarantees us that we can choose an

00:29:11.380 --> 00:29:16.610
orthonormal, that is a basis in the vector
space where to basis vectors always have

00:29:16.610 --> 00:29:24.090
vanishing scalar product are orthogonal
and are normal, that is: we scale them to

00:29:24.090 --> 00:29:29.200
length one, because we want our
probability interpretation, and in our

00:29:29.200 --> 00:29:37.220
probability interpretation we need to have
normalized vectors. So now we have that

00:29:37.220 --> 00:29:41.890
and now we want to know: How does this
strange function psi, that describes the

00:29:41.890 --> 00:29:49.580
state of the system, evolve in time. And
for this we can have several requirements

00:29:49.580 --> 00:29:55.640
that it must fulfill. So again we are
close to software engineering and one

00:29:55.640 --> 00:30:01.400
requirement is, that if it is a sharp wave
packet, so if we have a localized state

00:30:01.400 --> 00:30:06.620
that is not smeared around the whole
space, then it should follow the classical

00:30:06.620 --> 00:30:12.580
equation of motion because we want that
our new theory contains our old theory.

00:30:12.580 --> 00:30:18.450
And the time evolution must conserve the
total probability of finding the particle

00:30:18.450 --> 00:30:21.990
because otherwise we couldn't do
probability interpretation of our wave

00:30:21.990 --> 00:30:29.010
function, if the total probability of the
particle wouldn't remain one. Further we

00:30:29.010 --> 00:30:35.110
wish the equation to be first order in
time and to be linear because for example

00:30:35.110 --> 00:30:41.950
the Maxwell equations are linear and show
nice interference effects, so we want that

00:30:41.950 --> 00:30:46.370
because then simply a sum of solutions is
again a solution, it's a good property to

00:30:46.370 --> 00:30:51.840
have and if it works that way: Why not?
And the third and the fourth requirement

00:30:51.840 --> 00:31:00.600
together already give us more or less the
form of the Schroedinger equation. Because

00:31:00.600 --> 00:31:04.830
linearity just says that the right-hand
side of some linear operator applied to

00:31:04.830 --> 00:31:12.340
psi and the first order in time just means
that there must be a single time

00:31:12.340 --> 00:31:19.840 line:1
derivative in the equation on the left-
hand side. And this i-h bar: we just wanted

00:31:19.840 --> 00:31:23.550
that there, no particular reason we could
have done this differently, but it's

00:31:23.550 --> 00:31:31.710
convention. Now with this equation we can
look: What must happen for the probability

00:31:31.710 --> 00:31:42.290
to be conserved and by a simple
calculation we can show that it must be a

00:31:42.290 --> 00:31:47.870
Hermitian operator. And there is even more
than this global argument. There's local

00:31:47.870 --> 00:31:52.020
conservation of probability, that is, a
particle can't simply vanish here and

00:31:52.020 --> 00:31:59.250
appear there, but it must flow from one
point to the other with local operations.

00:31:59.250 --> 00:32:05.360
This can be shown when you consider this
in more detail. Now we know how this

00:32:05.360 --> 00:32:09.460
equation of motion looks like, but we
don't know what this mysterious object H

00:32:09.460 --> 00:32:16.500
might be. And this mysterious object H is
the operator of the energy of the system

00:32:16.500 --> 00:32:21.770
which is known from classical mechanics as
the Hamilton function and which we here

00:32:21.770 --> 00:32:26.610
upgrade to the Hamilton operator by using
the formula for the classical Hamilton

00:32:26.610 --> 00:32:33.480
function and inserting our p into our
operators. And we can also extend this to

00:32:33.480 --> 00:32:39.710
a magnetic field. And by doing so we can
show that our theory is more or less

00:32:39.710 --> 00:32:45.960
consistent with Newtonian mechanics. We
can show the Ehrenfest theorem, that's the

00:32:45.960 --> 00:32:55.160
first equation. And then those equations
are almost Newton's equation of motion for

00:32:55.160 --> 00:33:05.690
the centers of mass of the particle
because this is the expectation value of

00:33:05.690 --> 00:33:10.670
the momentum, this is the expectation
value of the position of the particle.

00:33:10.670 --> 00:33:15.740
This just looks exactly like the classical
equation. The velocity is the momentum

00:33:15.740 --> 00:33:23.140
divided by the mass. But this is weird:
Here we average over the force, so the

00:33:23.140 --> 00:33:29.920
gradient of the potential is the force, we
average over the force and do not take the

00:33:29.920 --> 00:33:34.980
force at the center position, so we can't
in general solve this equation. But again

00:33:34.980 --> 00:33:38.620
if we have a sharply defined wave packet
we recover the classical equations of

00:33:38.620 --> 00:33:44.640
motion, which is nice. So we have shown
our new theory does indeed explain why our

00:33:44.640 --> 00:33:51.250
old theory worked. We only still have to
explain why the centers of mass of massive

00:33:51.250 --> 00:33:55.520
particles are usually well localized and
that's a question we're still having

00:33:55.520 --> 00:34:08.010
trouble with today. But since it otherwise
works: don't worry too much about it. And

00:34:08.010 --> 00:34:12.319
now you probably want to know how to solve
the Schroedinger equation. Or you don't

00:34:12.319 --> 00:34:18.201
want to know anything more about quantum
mechanics. And to do this we make a so-

00:34:18.201 --> 00:34:24.559
called separation ansatz, where we say, we
have a form stable part of our wave

00:34:24.559 --> 00:34:30.609
function multiplied by some time dependent
part. And if we do this we can write down

00:34:30.609 --> 00:34:35.589
the general solution for the Schroedinger
equation. Because we already know that the

00:34:35.589 --> 00:34:41.009
one equation that we get is an eigenvalue
equation or an eigenvector equation for

00:34:41.009 --> 00:34:45.849
the energy eigenvalues, that is the
eigenvalues of the Hamilton operator. And

00:34:45.849 --> 00:34:50.519
we know that we can develop any function
in terms of those and so the general

00:34:50.519 --> 00:34:58.170
solution must be of the form shown here.
And those states of specific energy have a

00:34:58.170 --> 00:35:02.220
simple evolution because their form is
constant and only their phase changes and

00:35:02.220 --> 00:35:08.960
depends on the energy. And now this thing
with the measurement in quantum mechanics

00:35:08.960 --> 00:35:13.200
is bad. You probably know Schroedinger's
cat and the point is: there you don't know

00:35:13.200 --> 00:35:16.033
whether the cat is dead or alive while you
don't look inside the box. While you don't

00:35:16.033 --> 00:35:19.480
look inside the box as long as you don't
measure it's in a superposition or

00:35:19.480 --> 00:35:23.930
something. So You measure
your cat and then it's dead. It isn't dead

00:35:23.930 --> 00:35:29.089
before only by measuring it you kill it.
And that's really not nice to kill cats.

00:35:29.089 --> 00:35:36.970
We like cats. The important part here is,
the TL;DR, quantum measurement is

00:35:36.970 --> 00:35:42.970
probabilistic and inherently changes the
system state. So I'll skip the multi

00:35:42.970 --> 00:35:52.770
particle things. We can't describe
multiple particles. And just show the

00:35:52.770 --> 00:35:58.700
axioms of quantum mechanics shortly. Don't
don't read them too detailed, but this is

00:35:58.700 --> 00:36:04.009
just a summary of what we've discussed so
far. And the thing about the multiple

00:36:04.009 --> 00:36:09.730
particles is the axiom 7 which says that
the sign of the wave function must change

00:36:09.730 --> 00:36:15.109
if we exchange the coordinates of
identical fermions. And this makes atom

00:36:15.109 --> 00:36:20.739
stable by the way. Without this atoms as
we know them would not exist. And finally

00:36:20.739 --> 00:36:26.809
there is a notational convention in
quantum mechanics called Bra-Ket-notation.

00:36:26.809 --> 00:36:35.380
And in Bra-Ket-notation you label states
by their eigenvalues and just think about

00:36:35.380 --> 00:36:42.470
such a Ket as an abstract vector such as x
with a vector arrow over it or a fat set x

00:36:42.470 --> 00:36:48.849
is an abstract vector and we can either
represent it by its coordinates x1 x2 x3,

00:36:48.849 --> 00:36:53.059
or we can work with the abstract vector
and this Ket is such an abstract vector

00:36:53.059 --> 00:37:02.089
for the L2 function psi of r. And then we
can also define the adjoint of this which

00:37:02.089 --> 00:37:07.690
gives us, if we multiply the adjoint and a
function, the scalar product. So this is a

00:37:07.690 --> 00:37:15.249
really nice and compact notation for many
physics problems. And the last equation

00:37:15.249 --> 00:37:20.750
there just looks like component wise, like
working with components of matrices, which

00:37:20.750 --> 00:37:31.579
is because it's nothing else. This is just
matrix calculus in new clothes. Now for

00:37:31.579 --> 00:37:43.559
the applications. The first one is quite
funny. There's a slide missing. Okay. Uh

00:37:43.559 --> 00:37:48.670
the first one is a quantum eraser at home.
Because if you encode the "which way"

00:37:48.670 --> 00:37:56.050
information into a double slit experiment
you lose your interference pattern. And we

00:37:56.050 --> 00:38:01.220
do this by using a vertical and horizontal
polarisation filter. And you know from

00:38:01.220 --> 00:38:16.390
classical physics then it won't make an
interference pattern. And if we then add a

00:38:16.390 --> 00:38:25.641
diagonal polarization filter then the
interference pattern will appear again. So

00:38:25.641 --> 00:38:31.470
now, just so you've seen it, the harmonic
oscillator can be exactly solved in

00:38:31.470 --> 00:38:36.499
quantum mechanics. If you can solve the
harmonic oscillator in any kind of physics

00:38:36.499 --> 00:38:41.930
then you're good, then you'll get through
the axioms when you study physics. So the

00:38:41.930 --> 00:38:47.771
harmonic oscillator is solved by
introducing so-called creation and

00:38:47.771 --> 00:38:53.560
destroyer operators and then we can
determine the ground state function, in a

00:38:53.560 --> 00:38:57.720
much simpler manner than if we had to
solve the Schroedinger equation explicitly

00:38:57.720 --> 00:39:05.559
for all those cases. And we can determine
the ground state function, so the function

00:39:05.559 --> 00:39:11.440
of lowest energy. This can all be done and
then from it by applying the creation

00:39:11.440 --> 00:39:18.609
operator create the highest eigenstate of
the system and get all of them. Then

00:39:18.609 --> 00:39:22.589
there's this effect of tunnelling that
you've probably heard about and this just

00:39:22.589 --> 00:39:27.609
means that in quantum mechanics a
potential barrier that is too high for the

00:39:27.609 --> 00:39:32.460
particle to penetrate does not mean that
the particle doesn't penetrate at all but

00:39:32.460 --> 00:39:36.749
that the probability of finding the
particle inside the barrier decays

00:39:36.749 --> 00:39:42.589
exponentially. And this can for example be
understood in terms of this uncertainty

00:39:42.589 --> 00:39:47.569
relation because if we try to compress the
particle to the smaller part of the

00:39:47.569 --> 00:39:52.009
boundary layer then its momentum has to be
high so it can reach farther in because

00:39:52.009 --> 00:39:58.829
then it has more energy. And there's this
myth that tunnelling makes particles

00:39:58.829 --> 00:40:04.530
traveling to travel instantaneously from A
to B and even some real physicists believe

00:40:04.530 --> 00:40:12.700
it. But sorry it's not true. The particle
states is extended anyway and to defining

00:40:12.700 --> 00:40:17.140
what how fast the particle travels is
actually not a well-defined thing in deep

00:40:17.140 --> 00:40:23.079
quantum regimes, and also the Schroedinger
equations is not relativistic. So there is

00:40:23.079 --> 00:40:27.630
nothing, really nothing stopping your
particle from flying around with 30 times

00:40:27.630 --> 00:40:34.339
the speed of light. It's just not in the
theory. Another important consequence of

00:40:34.339 --> 00:40:38.670
quantum mechanics is so-called
entanglement and this is a really weird

00:40:38.670 --> 00:40:44.109
one, because it shows that the universe
that we live in is in a way non-local,

00:40:44.109 --> 00:40:51.859
inherently non-local. Because we can
create some states for some internal

00:40:51.859 --> 00:40:57.400
degrees of freedom of two atoms and move
them apart then measure the one system and

00:40:57.400 --> 00:41:01.460
the measurement result in the one system
will determine the measurement result in

00:41:01.460 --> 00:41:07.790
the other system, no matter how far
removed they are from each other. And this

00:41:07.790 --> 00:41:12.099
was first discovered in a paper by
Einstein, Podolski and Rosen and they

00:41:12.099 --> 00:41:17.619
thought it was an argument that quantum
mechanics is absurd. This can't be true,

00:41:17.619 --> 00:41:23.359
but sorry it is true. So this works and
this kind of state that we've written

00:41:23.359 --> 00:41:32.970
there that is such an entangled state of
two particles. But important to remark is

00:41:32.970 --> 00:41:37.029
that there are no hidden variables, that
means the measurement result is not

00:41:37.029 --> 00:41:42.250
determined beforehand. It is only when we
measure that is actually known what the

00:41:42.250 --> 00:41:47.741
result will be. This is utterly weird but
one can prove this experimentally. Those

00:41:47.741 --> 00:41:52.239
are Bell tests. There's a Bell-inequality
that's the limit for theories where they

00:41:52.239 --> 00:41:57.410
are hidden variables and it's by real
experiments they violate the inequality

00:41:57.410 --> 00:42:02.819
and thereby show that there are no hidden
variables. And there's a myth surrounding

00:42:02.819 --> 00:42:07.250
entanglement, namely that you can transfer
information with it between two sides

00:42:07.250 --> 00:42:12.910
instantaneously. But again there's nothing
hindering you in non relativistic quantum

00:42:12.910 --> 00:42:18.309
mechanics to distribute information
arbitrarily fast. It doesn't have a speed

00:42:18.309 --> 00:42:24.440
limit but you can't also count communicate
with those entangled pairs of particles.

00:42:24.440 --> 00:42:28.319
You can just create correlated noise at
two ends which is what quantum

00:42:28.319 --> 00:42:36.109
cryptography is using. So now because this
is the hackers congress, some short

00:42:36.109 --> 00:42:41.549
remarks and probably unintelligible due to
their strong compression about quantum

00:42:41.549 --> 00:42:47.190
information. A qubit, the fundamental unit
of quantum information, is a system with

00:42:47.190 --> 00:42:53.852
two states zero and one. So just like a
bit. But now we allow arbitrary super

00:42:53.852 --> 00:42:58.309
positions of those states because that is
what quantum mechanics allows. We can

00:42:58.309 --> 00:43:03.000
always superimpose states and quantum
computers are really bad for most

00:43:03.000 --> 00:43:08.940
computing tasks because they have to,
even if they build quantum computers they

00:43:08.940 --> 00:43:14.171
will never be as capable as the state-of-
the-art silicon electrical computer. So

00:43:14.171 --> 00:43:18.359
don't fear for your jobs because of
quantum computers. But the problem is they

00:43:18.359 --> 00:43:23.599
can compute some things faster. For
example factoring primes and working with

00:43:23.599 --> 00:43:29.599
some elliptic curve algorithms and so on
and determining discrete logarithm so our

00:43:29.599 --> 00:43:35.339
public key crypto would be destroyed by
them. And this all works by using the

00:43:35.339 --> 00:43:41.220
superposition to construct some kind of
weird parallelism. So it's actually I

00:43:41.220 --> 00:43:47.359
think nobody really can imagine how it
works but we can compute it which is often

00:43:47.359 --> 00:43:51.670
the case in quantum mechanics. And then
there's quantum cryptography and that

00:43:51.670 --> 00:43:56.279
fundamentally solves the same problem as a
Diffie-Hellman key exchange. We can

00:43:56.279 --> 00:44:01.150
generate the shared key and we can check
by the statistics of our measured values

00:44:01.150 --> 00:44:07.349
that there is no eavesdropper, which is
cool actually. But it's also quite useless

00:44:07.349 --> 00:44:10.201
because we can't detect a man in the
middle. How should the quantum particle

00:44:10.201 --> 00:44:14.630
knows of the other side is the one with
that we want to talk to. We still need

00:44:14.630 --> 00:44:18.839
some shared secret or public key
infrastructure whatever. So it doesn't

00:44:18.839 --> 00:44:27.210
solve the problem that we don't have
solved. And then the fun fact about this

00:44:27.210 --> 00:44:30.970
is that all the commercial implementations
of quantum cryptography were susceptible

00:44:30.970 --> 00:44:35.150
to side channel text, for example you
could just shine the light with a fiber

00:44:35.150 --> 00:44:40.920
that was used, read out the polarization
filter state that they used and then you

00:44:40.920 --> 00:44:50.609
could mimic the other side. So that's not
good either. So finally some references

00:44:50.609 --> 00:44:55.150
for further study. The first one is really
difficult. Only try this if you've read the

00:44:55.150 --> 00:45:00.650
other two but the second one. Sorry that
they're in German. The first and the last

00:45:00.650 --> 00:45:04.579
are also available in translation but the
second one has a really really nice and

00:45:04.579 --> 00:45:09.650
accessible introduction in the last few
pages so it's just 20 pages and it's

00:45:09.650 --> 00:45:14.660
really good and understandable. So if you
can get your hands on the books and are

00:45:14.660 --> 00:45:22.079
really interested, read it. So thank you
for the attention and I'll be answering

00:45:22.079 --> 00:45:24.259
your questions next.

00:45:24.259 --> 00:45:33.159
<i>Applause</i>

00:45:33.159 --> 00:45:41.240
Herald: Thank you Sebastian. Do we have
questions? And don't be afraid to sound

00:45:41.240 --> 00:45:45.380
naive or anything. I'm sure if you didn't
understand something many other people

00:45:45.380 --> 00:45:49.099
would thank you for a good question.
Sebastian: As to understanding things in

00:45:49.099 --> 00:45:53.180
quantum mechanics, Fineman said "You can't
understand quantum mechanics, you can just

00:45:53.180 --> 00:45:57.269
accept that there there's nothing to
understand. That's just too weird."

00:45:57.269 --> 00:46:01.590
Herald: Ok,we've found some questions. So
microphone one please.

00:46:01.590 --> 00:46:09.349
M1: Can you explain that, if you measure a
system, it looks like you changed the

00:46:09.349 --> 00:46:15.130
state of the system. How is it defined
where the system starts? No. How is it

00:46:15.130 --> 00:46:20.200
defined when the system ends and the
measurement system begins. Or in other

00:46:20.200 --> 00:46:24.410
words why does the universe have a
state? Is there somewhere out there who

00:46:24.410 --> 00:46:29.450
measures the universe?
S: No. There's at least the beginning of a

00:46:29.450 --> 00:46:34.880
solution by now which is called
"decoherence" which says that this

00:46:34.880 --> 00:46:39.970
measurement structure that we observe is
not inherent in quantum mechanics but

00:46:39.970 --> 00:46:43.920
comes from the interaction with the
environment. And we don't care for the

00:46:43.920 --> 00:46:48.460
states of the environment. And if we do
this, the technical term is traced out the

00:46:48.460 --> 00:46:52.529
states of the environment. Then the
remaining state of the measurement

00:46:52.529 --> 00:46:59.789
apparatus and the system we're interested
in will be just classically a randomized

00:46:59.789 --> 00:47:05.700
states. So it's rather a consequence
of the complex dynamics of a system state

00:47:05.700 --> 00:47:10.739
and environment in quantum mechanics. But
this is really the burning question. We

00:47:10.739 --> 00:47:15.690
don't really know. We have this we know
decoherence make some makes it nice and

00:47:15.690 --> 00:47:20.749
looks good. But it also doesn't answer the
question finally. And this is what all

00:47:20.749 --> 00:47:25.430
those discussions about interpretations of
quantum mechanics are about. How shall we

00:47:25.430 --> 00:47:28.940
make sense of this weird measurement
process.

00:47:28.940 --> 00:47:37.150
Herald: Okay. Microphone 4 in the back please.
M4: Could you comment on your point in the

00:47:37.150 --> 00:47:44.220
theory section. I don't understand what
you were trying to do. Did you want to

00:47:44.220 --> 00:47:49.369
show that you cannot understand really
quantum mechanics without the mathematics

00:47:49.369 --> 00:47:51.990
or?
S: Well, yes you can't understand quantum

00:47:51.990 --> 00:47:56.010
mechanics without the mathematics and my
point to show was that mathematics, or at

00:47:56.010 --> 00:48:02.380
least my hope to show was that mathematics
is halfways accessible. Probably not

00:48:02.380 --> 00:48:07.799
understandable after just exposure of a
short talk but just to give an

00:48:07.799 --> 00:48:12.849
introduction where to look
M4: OK. So you are trying to combat the

00:48:12.849 --> 00:48:18.050
esoterics and say they don't really
understand the theory because they don't

00:48:18.050 --> 00:48:29.380
understand the mathematics. I understand
the mathematics. I'm just interested. What

00:48:29.380 --> 00:48:33.809
were you trying to say?
S: I was just trying to present the

00:48:33.809 --> 00:48:39.339
theory. That was my aim.
M4: Okay. Thank you.

00:48:39.339 --> 00:48:45.759
Herald: Okay, microphone 2 please.
M2: I know the answer to this question is

00:48:45.759 --> 00:48:48.569
that ...
Herald: Can you go a little bit closer to

00:48:48.569 --> 00:48:52.660
the microphone maybe move it up please.
M2: So I know the answer to this question

00:48:52.660 --> 00:48:59.510
is that atoms behave randomly but could
you provide an argument why they behave

00:48:59.510 --> 00:49:07.369
randomly and it is not the case that we
don't have a model that's. So, are atoms

00:49:07.369 --> 00:49:12.019
behaving randomly? Or is it the case that
we don't have a model accurate enough to

00:49:12.019 --> 00:49:17.890
predict the way they behave?
S: Radioactive decay is just as random as

00:49:17.890 --> 00:49:24.089
quantum measurement and since if we
were to look at the whole story and look

00:49:24.089 --> 00:49:28.219
at the coherent evolution of the whole
system we would have to include the

00:49:28.219 --> 00:49:33.809
environment and the problem is that the
state space that we have to consider grows

00:49:33.809 --> 00:49:37.809
exponentially. That's the point of quantum
mechanics. If I have two particles I have

00:49:37.809 --> 00:49:42.900
a two dimensional space. I have 10
particles I have a 1024 dimensional space

00:49:42.900 --> 00:49:47.269
and that's only talking about non
interacting particles. So things explode

00:49:47.269 --> 00:49:51.950
in quantum mechanics and large systems.
And therefore I would go so far as to say

00:49:51.950 --> 00:49:57.140
that it's objectively impossible to
determine a radioactive decay although

00:49:57.140 --> 00:50:03.670
there are things, there is I think one
experimentally confirmed method of letting

00:50:03.670 --> 00:50:11.279
an atom decay on purpose. This involves
meta stable states of nuclei and then you

00:50:11.279 --> 00:50:15.690
can do something like spontaneous emission
in a laser. You shine a strong gamma

00:50:15.690 --> 00:50:21.710
source by it and this shortens the
lifespan of the nucleus. But other than

00:50:21.710 --> 00:50:25.410
that.
M4: So in a completely hypothetical case. If you

00:50:25.410 --> 00:50:29.839
know all the starting conditions and what
happens afterwards,wouldn't it be able,

00:50:29.839 --> 00:50:37.220
we could say it's deterministic? I
mean I'm playing with heavy words here.

00:50:37.220 --> 00:50:43.619
But is it just that we say it's randomised
because it's very very complex right?

00:50:43.619 --> 00:50:48.470
That's what I'm understanding.
Herald: Maybe think about that question

00:50:48.470 --> 00:50:53.099
one more time and we have the signal angel
in between and then you can come back.

00:50:53.099 --> 00:50:57.690
Signal Angel do we have questions on the
Internet?

00:50:57.690 --> 00:51:04.940
Angel: There's one question from the Internet
which is the ground state of a BEH-2 has

00:51:04.940 --> 00:51:12.150
been just calculated using a quantum
eigensolver. So is there still some use of

00:51:12.150 --> 00:51:16.849
quantum computing in quantum mechanics?
S: Yes definitely. One of the main

00:51:16.849 --> 00:51:22.309
motivations for inventing quantum
computers was quantum simulators.

00:51:22.309 --> 00:51:26.700
Feynman invented this kind of
quantum computing and he showed that with

00:51:26.700 --> 00:51:32.009
digital quantum computer you can
efficiently simulate quantum systems. While

00:51:32.009 --> 00:51:36.489
you can't simulate quantum systems with a
classical computer because of this problem

00:51:36.489 --> 00:51:41.790
of the exploding dimensions of the Hilbert
space that you have to consider. And for

00:51:41.790 --> 00:51:46.280
this quantum computers are really really
useful and will be used once they work,

00:51:46.280 --> 00:51:52.760
which is the question when it will be.
Perhaps never. Beyond two or three qubits

00:51:52.760 --> 00:51:59.180
or 20 or 100 qubits but you need scalability
for a real quantum computer. But quantum

00:51:59.180 --> 00:52:03.349
simulation is a real thing and it's a good
thing and we need it.

00:52:03.349 --> 00:52:07.960
Herald: Okay. Then we have microphone 1
again.

00:52:07.960 --> 00:52:13.779
M1: So very beginning, you said that the
theory is a set of interdependent

00:52:13.779 --> 00:52:21.539
propositions. Right? And then if a new
hypothesis is made it can be confirmed by

00:52:21.539 --> 00:52:28.219
an experiment.
S: That can't be confirmed but, well it's

00:52:28.219 --> 00:52:33.559
a philosophical question about the common
stance, it can be made probable but not

00:52:33.559 --> 00:52:37.210
be confirmed because we can never
absolutely be sure that there won't be

00:52:37.210 --> 00:52:40.599
some new experiment that shows that the
hypothesis is wrong.

00:52:40.599 --> 00:52:44.920
M1: Yeah. Because the slide said that
the experiment confirms...

00:52:44.920 --> 00:52:51.150
S: Yeah, confirm in the sense that it
doesn't disconfirm it. So it makes

00:52:51.150 --> 00:52:57.040
probable that it's a good explanation of
the reality and that's the point. Physics

00:52:57.040 --> 00:53:01.710
is just models. We do get
nothing about the ontology that is about

00:53:01.710 --> 00:53:06.349
the actual being of the world out of
physics. We just get models to describe

00:53:06.349 --> 00:53:11.539
the world but all what I say about this
wave function and what we say about

00:53:11.539 --> 00:53:18.150
elementary particles. We can't say they
are in the sense that you and I are here

00:53:18.150 --> 00:53:22.749
and exist because we can't see them we
can't access them directly. We can only

00:53:22.749 --> 00:53:28.960
use them as description tools. But this is
my personal position on philosophy of

00:53:28.960 --> 00:53:33.380
science. So there are people who disagree.
M1: Ok, thanks.

00:53:33.380 --> 00:53:39.960
Herald: Microphone 2 please.
M2: Or maybe superposition. By the way, so

00:53:39.960 --> 00:53:47.550
on the matter of the collapsing of the
wave function, so this was already treated

00:53:47.550 --> 00:53:52.589
on the interpretation of Copenhagen and
then as you mentioned it was expanded by

00:53:52.589 --> 00:53:59.331
the concept of decoherence. And is this, so
the decoherence is including also the

00:53:59.331 --> 00:54:03.319
Ghirardi–Rimini–Weber interpretation or
not?

00:54:03.319 --> 00:54:06.880
S: Could decoherence be used in
computation or?

00:54:06.880 --> 00:54:13.019
M2: No so for the Ghirardi–Rimini–Weber
interpretation of the collapsing of the

00:54:13.019 --> 00:54:15.700
wave function.
S:That's one that I don't know.

00:54:15.700 --> 00:54:24.269
I'm not so much into interpretations.
I actually think that there's interesting

00:54:24.269 --> 00:54:29.630
work done there but I think they're a bit
irrelevant because in the end what I just

00:54:29.630 --> 00:54:33.690
said I don't think you can derive
ontological value from our physical

00:54:33.690 --> 00:54:40.519
theories and in this belief, I think that
the interpretations are in a sense void,

00:54:40.519 --> 00:54:44.890
they just help us to rationalize what
we're doing but they don't really add

00:54:44.890 --> 00:54:49.339
something to the theory as long as they
don't change what can be measured.

00:54:49.339 --> 00:54:58.180
M2: Oh okay. Thanks.
S: Sorry for being an extremist.

00:54:58.180 --> 00:55:03.580
M2: Totally fine.
Herald: Someone just left from microphone 1

00:55:03.580 --> 00:55:07.810
I don't know if they want to come
back. I don't see any more questions as to

00:55:07.810 --> 00:55:13.680
signal angel have anything else. There is
some more. Signal angel, do you have

00:55:13.680 --> 00:55:16.519
something?
Signal Angel: No.

00:55:16.519 --> 00:55:19.609
Herald: Okay. Then we have
microphone 4.

00:55:19.609 --> 00:55:27.809
M4: I want to ask a maybe a noob question.
I want to know, are the probabilities of

00:55:27.809 --> 00:55:32.770
quantum mechanics inherent part of nature
or maybe in some future we'll have a

00:55:32.770 --> 00:55:37.490
science that will determine all these
values exactly?

00:55:37.490 --> 00:55:44.799
S: Well if decoherency theory is true,
then quantum mechanics is absolutely

00:55:44.799 --> 00:55:53.779
deterministic. But so let's say, Everett
says that all those possible measurement

00:55:53.779 --> 00:55:58.869
outcomes do happen and the whole state of
the system is in a superposition and by

00:55:58.869 --> 00:56:03.839
looking at our measurement device and
seeing some value we in a way select one

00:56:03.839 --> 00:56:10.219
strand of those superpositions and live in
this of the many worlds and in this sense

00:56:10.219 --> 00:56:21.349
everything happens deterministically, but
we just can't access any other values. So

00:56:21.349 --> 00:56:27.999
I think it's for now rather a
of philosophy than of science.

00:56:27.999 --> 00:56:32.900
M4: I see. Thanks.

00:56:32.900 --> 00:56:38.559
Herald: Anything else? I don't see any
people lined up at microphones. So last

00:56:38.559 --> 00:56:46.709
chance to round up now, I think. Well then
I think we're closing this and have a nice

00:56:46.709 --> 00:56:59.510
applause again for Sebastian.
<i>applause</i>

00:56:59.510 --> 00:57:02.654
Sebastian: Thank you. And I hope I didn't
create more fear of

00:57:02.654 --> 00:57:05.080
quantum mechanics than
I dispersed.

00:57:05.080 --> 00:57:30.000
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