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*35C3 preroll music*
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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.
*applause*
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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. *laughter* 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. *laughter* 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
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this. Those have the little problem that
they are not in the Hilbert space because
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they're not normalizable. The absolute
value of psi is 1 over 2 pi everywhere, so
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that's bad. But we can write the
superposition of any state by Fourier
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transformation those e to the i k dot r
states are just the basis states of a
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Fourier transformation. We can write any
function in terms of this basis. And we
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can conclude that by Fourier
transformation of the state psi of r to
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some state till the psi of k, we describe
the same information because we know we
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can invert the Fourier transformation and
also this implies the uncertainty
225
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relation. And because this is simply
property of Fourier transformations that
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either the function can be very
concentrated in position space or in
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momentum space. And now that
we have states of definite momentum. And
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the other big ingredient in quantum
mechanics are operators, next to the state
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description. And operators are, just like
matrices, linear operators on the state
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space. Just as we can apply a linear
operator in the form of a matrix to a vector,
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we can apply linear operators to L2
functions. And when we measure an
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observable it will be that it's one of the
eigenvalues of this operator that's the
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measurement value, you know. So
eigenvalues are those values: If a matrix
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that just scales a vector by a certain
amount that is an eigenvalue of the matrix
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and in the same sense we can define
eigenvalues and eigenvectors for, L2
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functions. And there are some facts such
as that non-commuting operators have
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eigenstates that are not common. So we
can't have a description of the basis of
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the state space in terms of function that
are both eigenfunctions of both operators
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and some examples of operators are the
momentum operator which is just minus i
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h-bar Nabla which is the derivation
operator in three dimensions. So in the x
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component we have derivation in the
direction of x and in the y component in
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direction of y and so on. And the position
operator which is just the operator that
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multiplies by the position x in the
position space representation of the wave
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function. And as for the non-
communtitivity of operators we can already
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show that those p and x operators that do
not commute but fulfill a certain
246
00:24:54,710 --> 00:25:00,620
commutation relation. And a commutation
relation is just a measure for how much
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two operators do not commute. And the
commutator is AB minus BA for the objects
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00:25:07,250 --> 00:25:15,180
AB, so if they commute, if AB equals BA
the commutator simply vanishes. And
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there's more on operators just to make it
clear: Linear just means that we can split
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00:25:20,870 --> 00:25:26,660
the argument if it is just some linear
combinations of vectors and apply the
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operator to the individual vectors
occuring, we can define multiplication of
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operators and this just exactly follows
the template that is laid down by finite
253
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dimensional linear algebra. There's
nothing new here. And there are inverse
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00:25:44,110 --> 00:25:49,380
operators for some operators, not for all
of them, that give the identity operator
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if it's multiplied with the original
operator. And further there's the so-
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00:25:54,450 --> 00:26:00,400
called adjoint. Our scalar product had
this little asterisk and this means that
257
00:26:00,400 --> 00:26:04,560
it's not linear in the first component. If
I scale the first component by some
258
00:26:04,560 --> 00:26:10,600
complex number alpha the total scalar
product is not scaled by alpha, but by the
259
00:26:10,600 --> 00:26:17,610
complex conjugate of alpha. This kind of
not quite bi-linearity is sometimes called
260
00:26:17,610 --> 00:26:26,980
sesquilinearity, a seldomly used word, and
they're commonly defined classes of
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00:26:26,980 --> 00:26:35,990
operators in terms of how the adjoint that
is defined there acts and how some other
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00:26:35,990 --> 00:26:39,890
operators for example where the adjoint is
the inverse which is a generalization from
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00:26:39,890 --> 00:26:45,520
the fact that for rotation operators in
normal Euclidean space, the transpose is
264
00:26:45,520 --> 00:26:53,950
the inverse. And now that we have
operators we can define expectation values
265
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just by some formula. For now, we don't
know what expectation values are, but we
266
00:26:59,270 --> 00:27:03,690
can assume, it has something to do with
the measurement values of the operator
267
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
268
00:27:09,510 --> 00:27:15,160
actually the expectation value of the
quantity if we prepare a system always in
269
00:27:15,160 --> 00:27:20,780
the same fashion and then do measurements
on it, we get random results each time,
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00:27:20,780 --> 00:27:29,200
but the expectation value will be this
combination. And now again: a bit of
271
00:27:29,200 --> 00:27:34,840
mathematics: eigenvalue problems. Well
known: You can diagonalize a matrix and
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you can diagonalize linear operators. You
have some equation A psi equals lambda
273
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psi, where lambda is just a scalar. And if
such an equation holds for some vector psi
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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
275
00:27:52,770 --> 00:28:01,380
eigenvector. And what can happen is that
to one eigenvalue there are several
276
00:28:01,380 --> 00:28:05,350
eigenvectors, not only one ray of
eigenvectors, but a higher dimensional
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00:28:05,350 --> 00:28:11,940
subspace. And important to know is that
so-called Hermitian operators, that is
278
00:28:11,940 --> 00:28:17,690
those that equal their adjoint, which
again means that the eigenvalues equal the
279
00:28:17,690 --> 00:28:23,980
complex conjugate of the eigenvalues have
a real eigenvalues. Because if a complex
280
00:28:23,980 --> 00:28:33,070
number equals its complex conjugate, then
it's a real number. And the nice thing
281
00:28:33,070 --> 00:28:39,570
about those diagonalized matrices and all
is: we can develop any vector in terms of
282
00:28:39,570 --> 00:28:46,890
the eigenbasis of the operator, again just
like in linear algebra where when you
283
00:28:46,890 --> 00:28:51,420
diagonalize a matrix, you get a new basis
for your vector space and now you can
284
00:28:51,420 --> 00:28:57,640
express all vectors in that new basis. And
if the operator is Hermitian the
285
00:28:57,640 --> 00:29:05,050
eigenvectors have a nice property, namely
they are orthogonal if the eigenvalues are
286
00:29:05,050 --> 00:29:11,380
different. And this is good because this
guarantees us that we can choose an
287
00:29:11,380 --> 00:29:16,610
orthonormal, that is a basis in the vector
space where to basis vectors always have
288
00:29:16,610 --> 00:29:24,090
vanishing scalar product are orthogonal
and are normal, that is: we scale them to
289
00:29:24,090 --> 00:29:29,200
length one, because we want our
probability interpretation, and in our
290
00:29:29,200 --> 00:29:37,220
probability interpretation we need to have
normalized vectors. So now we have that
291
00:29:37,220 --> 00:29:41,890
and now we want to know: How does this
strange function psi, that describes the
292
00:29:41,890 --> 00:29:49,580
state of the system, evolve in time. And
for this we can have several requirements
293
00:29:49,580 --> 00:29:55,640
that it must fulfill. So again we are
close to software engineering and one
294
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
295
00:30:01,400 --> 00:30:06,620
that is not smeared around the whole
space, then it should follow the classical
296
00:30:06,620 --> 00:30:12,580
equation of motion because we want that
our new theory contains our old theory.
297
00:30:12,580 --> 00:30:18,450
And the time evolution must conserve the
total probability of finding the particle
298
00:30:18,450 --> 00:30:21,990
because otherwise we couldn't do
probability interpretation of our wave
299
00:30:21,990 --> 00:30:29,010
function, if the total probability of the
particle wouldn't remain one. Further we
300
00:30:29,010 --> 00:30:35,110
wish the equation to be first order in
time and to be linear because for example
301
00:30:35,110 --> 00:30:41,950
the Maxwell equations are linear and show
nice interference effects, so we want that
302
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
303
00:30:46,370 --> 00:30:51,840
have and if it works that way: Why not?
And the third and the fourth requirement
304
00:30:51,840 --> 00:31:00,600
together already give us more or less the
form of the Schroedinger equation. Because
305
00:31:00,600 --> 00:31:04,830
linearity just says that the right-hand
side of some linear operator applied to
306
00:31:04,830 --> 00:31:12,340
psi and the first order in time just means
that there must be a single time
307
00:31:12,340 --> 00:31:19,840
derivative in the equation on the left-
hand side. And this i-h bar: we just wanted
308
00:31:19,840 --> 00:31:23,550
that there, no particular reason we could
have done this differently, but it's
309
00:31:23,550 --> 00:31:31,710
convention. Now with this equation we can
look: What must happen for the probability
310
00:31:31,710 --> 00:31:42,290
to be conserved and by a simple
calculation we can show that it must be a
311
00:31:42,290 --> 00:31:47,870
Hermitian operator. And there is even more
than this global argument. There's local
312
00:31:47,870 --> 00:31:52,020
conservation of probability, that is, a
particle can't simply vanish here and
313
00:31:52,020 --> 00:31:59,250
appear there, but it must flow from one
point to the other with local operations.
314
00:31:59,250 --> 00:32:05,360
This can be shown when you consider this
in more detail. Now we know how this
315
00:32:05,360 --> 00:32:09,460
equation of motion looks like, but we
don't know what this mysterious object H
316
00:32:09,460 --> 00:32:16,500
might be. And this mysterious object H is
the operator of the energy of the system
317
00:32:16,500 --> 00:32:21,770
which is known from classical mechanics as
the Hamilton function and which we here
318
00:32:21,770 --> 00:32:26,610
upgrade to the Hamilton operator by using
the formula for the classical Hamilton
319
00:32:26,610 --> 00:32:33,480
function and inserting our p into our
operators. And we can also extend this to
320
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
321
00:32:39,710 --> 00:32:45,960
consistent with Newtonian mechanics. We
can show the Ehrenfest theorem, that's the
322
00:32:45,960 --> 00:32:55,160
first equation. And then those equations
are almost Newton's equation of motion for
323
00:32:55,160 --> 00:33:05,690
the centers of mass of the particle
because this is the expectation value of
324
00:33:05,690 --> 00:33:10,670
the momentum, this is the expectation
value of the position of the particle.
325
00:33:10,670 --> 00:33:15,740
This just looks exactly like the classical
equation. The velocity is the momentum
326
00:33:15,740 --> 00:33:23,140
divided by the mass. But this is weird:
Here we average over the force, so the
327
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
328
00:33:29,920 --> 00:33:34,980
force at the center position, so we can't
in general solve this equation. But again
329
00:33:34,980 --> 00:33:38,620
if we have a sharply defined wave packet
we recover the classical equations of
330
00:33:38,620 --> 00:33:44,640
motion, which is nice. So we have shown
our new theory does indeed explain why our
331
00:33:44,640 --> 00:33:51,250
old theory worked. We only still have to
explain why the centers of mass of massive
332
00:33:51,250 --> 00:33:55,520
particles are usually well localized and
that's a question we're still having
333
00:33:55,520 --> 00:34:08,010
trouble with today. But since it otherwise
works: don't worry too much about it. And
334
00:34:08,010 --> 00:34:12,319
now you probably want to know how to solve
the Schroedinger equation. Or you don't
335
00:34:12,319 --> 00:34:18,201
want to know anything more about quantum
mechanics. And to do this we make a so-
336
00:34:18,201 --> 00:34:24,559
called separation ansatz, where we say, we
have a form stable part of our wave
337
00:34:24,559 --> 00:34:30,609
function multiplied by some time dependent
part. And if we do this we can write down
338
00:34:30,609 --> 00:34:35,589
the general solution for the Schroedinger
equation. Because we already know that the
339
00:34:35,589 --> 00:34:41,009
one equation that we get is an eigenvalue
equation or an eigenvector equation for
340
00:34:41,009 --> 00:34:45,849
the energy eigenvalues, that is the
eigenvalues of the Hamilton operator. And
341
00:34:45,849 --> 00:34:50,519
we know that we can develop any function
in terms of those and so the general
342
00:34:50,519 --> 00:34:58,170
solution must be of the form shown here.
And those states of specific energy have a
343
00:34:58,170 --> 00:35:02,220
simple evolution because their form is
constant and only their phase changes and
344
00:35:02,220 --> 00:35:08,960
depends on the energy. And now this thing
with the measurement in quantum mechanics
345
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
346
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
347
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
348
00:35:19,480 --> 00:35:23,930
something. So You measure
your cat and then it's dead. It isn't dead
349
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.
350
00:35:29,089 --> 00:35:36,970
We like cats. The important part here is,
the TL;DR, quantum measurement is
351
00:35:36,970 --> 00:35:42,970
probabilistic and inherently changes the
system state. So I'll skip the multi
352
00:35:42,970 --> 00:35:52,770
particle things. We can't describe
multiple particles. And just show the
353
00:35:52,770 --> 00:35:58,700
axioms of quantum mechanics shortly. Don't
don't read them too detailed, but this is
354
00:35:58,700 --> 00:36:04,009
just a summary of what we've discussed so
far. And the thing about the multiple
355
00:36:04,009 --> 00:36:09,730
particles is the axiom 7 which says that
the sign of the wave function must change
356
00:36:09,730 --> 00:36:15,109
if we exchange the coordinates of
identical fermions. And this makes atom
357
00:36:15,109 --> 00:36:20,739
stable by the way. Without this atoms as
we know them would not exist. And finally
358
00:36:20,739 --> 00:36:26,809
there is a notational convention in
quantum mechanics called Bra-Ket-notation.
359
00:36:26,809 --> 00:36:35,380
And in Bra-Ket-notation you label states
by their eigenvalues and just think about
360
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
361
00:36:42,470 --> 00:36:48,849
is an abstract vector and we can either
represent it by its coordinates x1 x2 x3,
362
00:36:48,849 --> 00:36:53,059
or we can work with the abstract vector
and this Ket is such an abstract vector
363
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
364
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
365
00:37:07,690 --> 00:37:15,249
really nice and compact notation for many
physics problems. And the last equation
366
00:37:15,249 --> 00:37:20,750
there just looks like component wise, like
working with components of matrices, which
367
00:37:20,750 --> 00:37:31,579
is because it's nothing else. This is just
matrix calculus in new clothes. Now for
368
00:37:31,579 --> 00:37:43,559
the applications. The first one is quite
funny. There's a slide missing. Okay. Uh
369
00:37:43,559 --> 00:37:48,670
the first one is a quantum eraser at home.
Because if you encode the "which way"
370
00:37:48,670 --> 00:37:56,050
information into a double slit experiment
you lose your interference pattern. And we
371
00:37:56,050 --> 00:38:01,220
do this by using a vertical and horizontal
polarisation filter. And you know from
372
00:38:01,220 --> 00:38:16,390
classical physics then it won't make an
interference pattern. And if we then add a
373
00:38:16,390 --> 00:38:25,641
diagonal polarization filter then the
interference pattern will appear again. So
374
00:38:25,641 --> 00:38:31,470
now, just so you've seen it, the harmonic
oscillator can be exactly solved in
375
00:38:31,470 --> 00:38:36,499
quantum mechanics. If you can solve the
harmonic oscillator in any kind of physics
376
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
377
00:38:41,930 --> 00:38:47,771
harmonic oscillator is solved by
introducing so-called creation and
378
00:38:47,771 --> 00:38:53,560
destroyer operators and then we can
determine the ground state function, in a
379
00:38:53,560 --> 00:38:57,720
much simpler manner than if we had to
solve the Schroedinger equation explicitly
380
00:38:57,720 --> 00:39:05,559
for all those cases. And we can determine
the ground state function, so the function
381
00:39:05,559 --> 00:39:11,440
of lowest energy. This can all be done and
then from it by applying the creation
382
00:39:11,440 --> 00:39:18,609
operator create the highest eigenstate of
the system and get all of them. Then
383
00:39:18,609 --> 00:39:22,589
there's this effect of tunnelling that
you've probably heard about and this just
384
00:39:22,589 --> 00:39:27,609
means that in quantum mechanics a
potential barrier that is too high for the
385
00:39:27,609 --> 00:39:32,460
particle to penetrate does not mean that
the particle doesn't penetrate at all but
386
00:39:32,460 --> 00:39:36,749
that the probability of finding the
particle inside the barrier decays
387
00:39:36,749 --> 00:39:42,589
exponentially. And this can for example be
understood in terms of this uncertainty
388
00:39:42,589 --> 00:39:47,569
relation because if we try to compress the
particle to the smaller part of the
389
00:39:47,569 --> 00:39:52,009
boundary layer then its momentum has to be
high so it can reach farther in because
390
00:39:52,009 --> 00:39:58,829
then it has more energy. And there's this
myth that tunnelling makes particles
391
00:39:58,829 --> 00:40:04,530
traveling to travel instantaneously from A
to B and even some real physicists believe
392
00:40:04,530 --> 00:40:12,700
it. But sorry it's not true. The particle
states is extended anyway and to defining
393
00:40:12,700 --> 00:40:17,140
what how fast the particle travels is
actually not a well-defined thing in deep
394
00:40:17,140 --> 00:40:23,079
quantum regimes, and also the Schroedinger
equations is not relativistic. So there is
395
00:40:23,079 --> 00:40:27,630
nothing, really nothing stopping your
particle from flying around with 30 times
396
00:40:27,630 --> 00:40:34,339
the speed of light. It's just not in the
theory. Another important consequence of
397
00:40:34,339 --> 00:40:38,670
quantum mechanics is so-called
entanglement and this is a really weird
398
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,
399
00:40:44,109 --> 00:40:51,859
inherently non-local. Because we can
create some states for some internal
400
00:40:51,859 --> 00:40:57,400
degrees of freedom of two atoms and move
them apart then measure the one system and
401
00:40:57,400 --> 00:41:01,460
the measurement result in the one system
will determine the measurement result in
402
00:41:01,460 --> 00:41:07,790
the other system, no matter how far
removed they are from each other. And this
403
00:41:07,790 --> 00:41:12,099
was first discovered in a paper by
Einstein, Podolski and Rosen and they
404
00:41:12,099 --> 00:41:17,619
thought it was an argument that quantum
mechanics is absurd. This can't be true,
405
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
406
00:41:23,359 --> 00:41:32,970
there that is such an entangled state of
two particles. But important to remark is
407
00:41:32,970 --> 00:41:37,029
that there are no hidden variables, that
means the measurement result is not
408
00:41:37,029 --> 00:41:42,250
determined beforehand. It is only when we
measure that is actually known what the
409
00:41:42,250 --> 00:41:47,741
result will be. This is utterly weird but
one can prove this experimentally. Those
410
00:41:47,741 --> 00:41:52,239
are Bell tests. There's a Bell-inequality
that's the limit for theories where they
411
00:41:52,239 --> 00:41:57,410
are hidden variables and it's by real
experiments they violate the inequality
412
00:41:57,410 --> 00:42:02,819
and thereby show that there are no hidden
variables. And there's a myth surrounding
413
00:42:02,819 --> 00:42:07,250
entanglement, namely that you can transfer
information with it between two sides
414
00:42:07,250 --> 00:42:12,910
instantaneously. But again there's nothing
hindering you in non relativistic quantum
415
00:42:12,910 --> 00:42:18,309
mechanics to distribute information
arbitrarily fast. It doesn't have a speed
416
00:42:18,309 --> 00:42:24,440
limit but you can't also count communicate
with those entangled pairs of particles.
417
00:42:24,440 --> 00:42:28,319
You can just create correlated noise at
two ends which is what quantum
418
00:42:28,319 --> 00:42:36,109
cryptography is using. So now because this
is the hackers congress, some short
419
00:42:36,109 --> 00:42:41,549
remarks and probably unintelligible due to
their strong compression about quantum
420
00:42:41,549 --> 00:42:47,190
information. A qubit, the fundamental unit
of quantum information, is a system with
421
00:42:47,190 --> 00:42:53,852
two states zero and one. So just like a
bit. But now we allow arbitrary super
422
00:42:53,852 --> 00:42:58,309
positions of those states because that is
what quantum mechanics allows. We can
423
00:42:58,309 --> 00:43:03,000
always superimpose states and quantum
computers are really bad for most
424
00:43:03,000 --> 00:43:08,940
computing tasks because they have to,
even if they build quantum computers they
425
00:43:08,940 --> 00:43:14,171
will never be as capable as the state-of-
the-art silicon electrical computer. So
426
00:43:14,171 --> 00:43:18,359
don't fear for your jobs because of
quantum computers. But the problem is they
427
00:43:18,359 --> 00:43:23,599
can compute some things faster. For
example factoring primes and working with
428
00:43:23,599 --> 00:43:29,599
some elliptic curve algorithms and so on
and determining discrete logarithm so our
429
00:43:29,599 --> 00:43:35,339
public key crypto would be destroyed by
them. And this all works by using the
430
00:43:35,339 --> 00:43:41,220
superposition to construct some kind of
weird parallelism. So it's actually I
431
00:43:41,220 --> 00:43:47,359
think nobody really can imagine how it
works but we can compute it which is often
432
00:43:47,359 --> 00:43:51,670
the case in quantum mechanics. And then
there's quantum cryptography and that
433
00:43:51,670 --> 00:43:56,279
fundamentally solves the same problem as a
Diffie-Hellman key exchange. We can
434
00:43:56,279 --> 00:44:01,150
generate the shared key and we can check
by the statistics of our measured values
435
00:44:01,150 --> 00:44:07,349
that there is no eavesdropper, which is
cool actually. But it's also quite useless
436
00:44:07,349 --> 00:44:10,201
because we can't detect a man in the
middle. How should the quantum particle
437
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
438
00:44:14,630 --> 00:44:18,839
some shared secret or public key
infrastructure whatever. So it doesn't
439
00:44:18,839 --> 00:44:27,210
solve the problem that we don't have
solved. And then the fun fact about this
440
00:44:27,210 --> 00:44:30,970
is that all the commercial implementations
of quantum cryptography were susceptible
441
00:44:30,970 --> 00:44:35,150
to side channel text, for example you
could just shine the light with a fiber
442
00:44:35,150 --> 00:44:40,920
that was used, read out the polarization
filter state that they used and then you
443
00:44:40,920 --> 00:44:50,609
could mimic the other side. So that's not
good either. So finally some references
444
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
445
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
446
00:45:00,650 --> 00:45:04,579
are also available in translation but the
second one has a really really nice and
447
00:45:04,579 --> 00:45:09,650
accessible introduction in the last few
pages so it's just 20 pages and it's
448
00:45:09,650 --> 00:45:14,660
really good and understandable. So if you
can get your hands on the books and are
449
00:45:14,660 --> 00:45:22,079
really interested, read it. So thank you
for the attention and I'll be answering
450
00:45:22,079 --> 00:45:24,259
your questions next.
451
00:45:24,259 --> 00:45:33,159
*Applause*
452
00:45:33,159 --> 00:45:41,240
Herald: Thank you Sebastian. Do we have
questions? And don't be afraid to sound
453
00:45:41,240 --> 00:45:45,380
naive or anything. I'm sure if you didn't
understand something many other people
454
00:45:45,380 --> 00:45:49,099
would thank you for a good question.
Sebastian: As to understanding things in
455
00:45:49,099 --> 00:45:53,180
quantum mechanics, Fineman said "You can't
understand quantum mechanics, you can just
456
00:45:53,180 --> 00:45:57,269
accept that there there's nothing to
understand. That's just too weird."
457
00:45:57,269 --> 00:46:01,590
Herald: Ok,we've found some questions. So
microphone one please.
458
00:46:01,590 --> 00:46:09,349
M1: Can you explain that, if you measure a
system, it looks like you changed the
459
00:46:09,349 --> 00:46:15,130
state of the system. How is it defined
where the system starts? No. How is it
460
00:46:15,130 --> 00:46:20,200
defined when the system ends and the
measurement system begins. Or in other
461
00:46:20,200 --> 00:46:24,410
words why does the universe have a
state? Is there somewhere out there who
462
00:46:24,410 --> 00:46:29,450
measures the universe?
S: No. There's at least the beginning of a
463
00:46:29,450 --> 00:46:34,880
solution by now which is called
"decoherence" which says that this
464
00:46:34,880 --> 00:46:39,970
measurement structure that we observe is
not inherent in quantum mechanics but
465
00:46:39,970 --> 00:46:43,920
comes from the interaction with the
environment. And we don't care for the
466
00:46:43,920 --> 00:46:48,460
states of the environment. And if we do
this, the technical term is traced out the
467
00:46:48,460 --> 00:46:52,529
states of the environment. Then the
remaining state of the measurement
468
00:46:52,529 --> 00:46:59,789
apparatus and the system we're interested
in will be just classically a randomized
469
00:46:59,789 --> 00:47:05,700
states. So it's rather a consequence
of the complex dynamics of a system state
470
00:47:05,700 --> 00:47:10,739
and environment in quantum mechanics. But
this is really the burning question. We
471
00:47:10,739 --> 00:47:15,690
don't really know. We have this we know
decoherence make some makes it nice and
472
00:47:15,690 --> 00:47:20,749
looks good. But it also doesn't answer the
question finally. And this is what all
473
00:47:20,749 --> 00:47:25,430
those discussions about interpretations of
quantum mechanics are about. How shall we
474
00:47:25,430 --> 00:47:28,940
make sense of this weird measurement
process.
475
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
476
00:47:37,150 --> 00:47:44,220
theory section. I don't understand what
you were trying to do. Did you want to
477
00:47:44,220 --> 00:47:49,369
show that you cannot understand really
quantum mechanics without the mathematics
478
00:47:49,369 --> 00:47:51,990
or?
S: Well, yes you can't understand quantum
479
00:47:51,990 --> 00:47:56,010
mechanics without the mathematics and my
point to show was that mathematics, or at
480
00:47:56,010 --> 00:48:02,380
least my hope to show was that mathematics
is halfways accessible. Probably not
481
00:48:02,380 --> 00:48:07,799
understandable after just exposure of a
short talk but just to give an
482
00:48:07,799 --> 00:48:12,849
introduction where to look
M4: OK. So you are trying to combat the
483
00:48:12,849 --> 00:48:18,050
esoterics and say they don't really
understand the theory because they don't
484
00:48:18,050 --> 00:48:29,380
understand the mathematics. I understand
the mathematics. I'm just interested. What
485
00:48:29,380 --> 00:48:33,809
were you trying to say?
S: I was just trying to present the
486
00:48:33,809 --> 00:48:39,339
theory. That was my aim.
M4: Okay. Thank you.
487
00:48:39,339 --> 00:48:45,759
Herald: Okay, microphone 2 please.
M2: I know the answer to this question is
488
00:48:45,759 --> 00:48:48,569
that ...
Herald: Can you go a little bit closer to
489
00:48:48,569 --> 00:48:52,660
the microphone maybe move it up please.
M2: So I know the answer to this question
490
00:48:52,660 --> 00:48:59,510
is that atoms behave randomly but could
you provide an argument why they behave
491
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
492
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
493
00:49:12,019 --> 00:49:17,890
predict the way they behave?
S: Radioactive decay is just as random as
494
00:49:17,890 --> 00:49:24,089
quantum measurement and since if we
were to look at the whole story and look
495
00:49:24,089 --> 00:49:28,219
at the coherent evolution of the whole
system we would have to include the
496
00:49:28,219 --> 00:49:33,809
environment and the problem is that the
state space that we have to consider grows
497
00:49:33,809 --> 00:49:37,809
exponentially. That's the point of quantum
mechanics. If I have two particles I have
498
00:49:37,809 --> 00:49:42,900
a two dimensional space. I have 10
particles I have a 1024 dimensional space
499
00:49:42,900 --> 00:49:47,269
and that's only talking about non
interacting particles. So things explode
500
00:49:47,269 --> 00:49:51,950
in quantum mechanics and large systems.
And therefore I would go so far as to say
501
00:49:51,950 --> 00:49:57,140
that it's objectively impossible to
determine a radioactive decay although
502
00:49:57,140 --> 00:50:03,670
there are things, there is I think one
experimentally confirmed method of letting
503
00:50:03,670 --> 00:50:11,279
an atom decay on purpose. This involves
meta stable states of nuclei and then you
504
00:50:11,279 --> 00:50:15,690
can do something like spontaneous emission
in a laser. You shine a strong gamma
505
00:50:15,690 --> 00:50:21,710
source by it and this shortens the
lifespan of the nucleus. But other than
506
00:50:21,710 --> 00:50:25,410
that.
M4: So in a completely hypothetical case. If you
507
00:50:25,410 --> 00:50:29,839
know all the starting conditions and what
happens afterwards,wouldn't it be able,
508
00:50:29,839 --> 00:50:37,220
we could say it's deterministic? I
mean I'm playing with heavy words here.
509
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?
510
00:50:43,619 --> 00:50:48,470
That's what I'm understanding.
Herald: Maybe think about that question
511
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.
512
00:50:53,099 --> 00:50:57,690
Signal Angel do we have questions on the
Internet?
513
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
514
00:51:04,940 --> 00:51:12,150
been just calculated using a quantum
eigensolver. So is there still some use of
515
00:51:12,150 --> 00:51:16,849
quantum computing in quantum mechanics?
S: Yes definitely. One of the main
516
00:51:16,849 --> 00:51:22,309
motivations for inventing quantum
computers was quantum simulators.
517
00:51:22,309 --> 00:51:26,700
Feynman invented this kind of
quantum computing and he showed that with
518
00:51:26,700 --> 00:51:32,009
digital quantum computer you can
efficiently simulate quantum systems. While
519
00:51:32,009 --> 00:51:36,489
you can't simulate quantum systems with a
classical computer because of this problem
520
00:51:36,489 --> 00:51:41,790
of the exploding dimensions of the Hilbert
space that you have to consider. And for
521
00:51:41,790 --> 00:51:46,280
this quantum computers are really really
useful and will be used once they work,
522
00:51:46,280 --> 00:51:52,760
which is the question when it will be.
Perhaps never. Beyond two or three qubits
523
00:51:52,760 --> 00:51:59,180
or 20 or 100 qubits but you need scalability
for a real quantum computer. But quantum
524
00:51:59,180 --> 00:52:03,349
simulation is a real thing and it's a good
thing and we need it.
525
00:52:03,349 --> 00:52:07,960
Herald: Okay. Then we have microphone 1
again.
526
00:52:07,960 --> 00:52:13,779
M1: So very beginning, you said that the
theory is a set of interdependent
527
00:52:13,779 --> 00:52:21,539
propositions. Right? And then if a new
hypothesis is made it can be confirmed by
528
00:52:21,539 --> 00:52:28,219
an experiment.
S: That can't be confirmed but, well it's
529
00:52:28,219 --> 00:52:33,559
a philosophical question about the common
stance, it can be made probable but not
530
00:52:33,559 --> 00:52:37,210
be confirmed because we can never
absolutely be sure that there won't be
531
00:52:37,210 --> 00:52:40,599
some new experiment that shows that the
hypothesis is wrong.
532
00:52:40,599 --> 00:52:44,920
M1: Yeah. Because the slide said that
the experiment confirms...
533
00:52:44,920 --> 00:52:51,150
S: Yeah, confirm in the sense that it
doesn't disconfirm it. So it makes
534
00:52:51,150 --> 00:52:57,040
probable that it's a good explanation of
the reality and that's the point. Physics
535
00:52:57,040 --> 00:53:01,710
is just models. We do get
nothing about the ontology that is about
536
00:53:01,710 --> 00:53:06,349
the actual being of the world out of
physics. We just get models to describe
537
00:53:06,349 --> 00:53:11,539
the world but all what I say about this
wave function and what we say about
538
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
539
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
540
00:53:22,749 --> 00:53:28,960
use them as description tools. But this is
my personal position on philosophy of
541
00:53:28,960 --> 00:53:33,380
science. So there are people who disagree.
M1: Ok, thanks.
542
00:53:33,380 --> 00:53:39,960
Herald: Microphone 2 please.
M2: Or maybe superposition. By the way, so
543
00:53:39,960 --> 00:53:47,550
on the matter of the collapsing of the
wave function, so this was already treated
544
00:53:47,550 --> 00:53:52,589
on the interpretation of Copenhagen and
then as you mentioned it was expanded by
545
00:53:52,589 --> 00:53:59,331
the concept of decoherence. And is this, so
the decoherence is including also the
546
00:53:59,331 --> 00:54:03,319
Ghirardi–Rimini–Weber interpretation or
not?
547
00:54:03,319 --> 00:54:06,880
S: Could decoherence be used in
computation or?
548
00:54:06,880 --> 00:54:13,019
M2: No so for the Ghirardi–Rimini–Weber
interpretation of the collapsing of the
549
00:54:13,019 --> 00:54:15,700
wave function.
S:That's one that I don't know.
550
00:54:15,700 --> 00:54:24,269
I'm not so much into interpretations.
I actually think that there's interesting
551
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
552
00:54:29,630 --> 00:54:33,690
said I don't think you can derive
ontological value from our physical
553
00:54:33,690 --> 00:54:40,519
theories and in this belief, I think that
the interpretations are in a sense void,
554
00:54:40,519 --> 00:54:44,890
they just help us to rationalize what
we're doing but they don't really add
555
00:54:44,890 --> 00:54:49,339
something to the theory as long as they
don't change what can be measured.
556
00:54:49,339 --> 00:54:58,180
M2: Oh okay. Thanks.
S: Sorry for being an extremist.
557
00:54:58,180 --> 00:55:03,580
M2: Totally fine.
Herald: Someone just left from microphone 1
558
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
559
00:55:07,810 --> 00:55:13,680
signal angel have anything else. There is
some more. Signal angel, do you have
560
00:55:13,680 --> 00:55:16,519
something?
Signal Angel: No.
561
00:55:16,519 --> 00:55:19,609
Herald: Okay. Then we have
microphone 4.
562
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
563
00:55:27,809 --> 00:55:32,770
quantum mechanics inherent part of nature
or maybe in some future we'll have a
564
00:55:32,770 --> 00:55:37,490
science that will determine all these
values exactly?
565
00:55:37,490 --> 00:55:44,799
S: Well if decoherency theory is true,
then quantum mechanics is absolutely
566
00:55:44,799 --> 00:55:53,779
deterministic. But so let's say, Everett
says that all those possible measurement
567
00:55:53,779 --> 00:55:58,869
outcomes do happen and the whole state of
the system is in a superposition and by
568
00:55:58,869 --> 00:56:03,839
looking at our measurement device and
seeing some value we in a way select one
569
00:56:03,839 --> 00:56:10,219
strand of those superpositions and live in
this of the many worlds and in this sense
570
00:56:10,219 --> 00:56:21,349
everything happens deterministically, but
we just can't access any other values. So
571
00:56:21,349 --> 00:56:27,999
I think it's for now rather a
of philosophy than of science.
572
00:56:27,999 --> 00:56:32,900
M4: I see. Thanks.
573
00:56:32,900 --> 00:56:38,559
Herald: Anything else? I don't see any
people lined up at microphones. So last
574
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
575
00:56:46,709 --> 00:56:59,510
applause again for Sebastian.
*applause*
576
00:56:59,510 --> 00:57:02,654
Sebastian: Thank you. And I hope I didn't
create more fear of
577
00:57:02,654 --> 00:57:05,080
quantum mechanics than
I dispersed.
578
00:57:05,080 --> 00:57:30,000
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