35C3 - Quantum Mechanics

35C3 preroll music

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

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

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

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

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

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

mechanics. Have a go.
applause

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

understand quantum mechanics we must
understand the setting and setting where

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

action Newtonian gravitation and the
Maxwell electro dynamics, this funny

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Rutherford invented the idea and Marsden
and Geiger actually performed the

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

diffraction grating: A periodically
arranged thing. And off periodically

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

this. Those have the little problem that
they are not in the Hilbert space because

they're not normalizable. The absolute
value of psi is 1 over 2 pi everywhere, so

that's bad. But we can write the
superposition of any state by Fourier

transformation those e to the i k dot r
states are just the basis states of a

Fourier transformation. We can write any
function in terms of this basis. And we

can conclude that by Fourier
transformation of the state psi of r to

some state till the psi of k, we describe
the same information because we know we

can invert the Fourier transformation and
also this implies the uncertainty

relation. And because this is simply
property of Fourier transformations that

either the function can be very
concentrated in position space or in

momentum space. And now that
we have states of definite momentum. And

the other big ingredient in quantum
mechanics are operators, next to the state

description. And operators are, just like
matrices, linear operators on the state

space. Just as we can apply a linear
operator in the form of a matrix to a vector,

we can apply linear operators to L2
functions. And when we measure an

observable it will be that it's one of the
eigenvalues of this operator that's the

measurement value, you know. So
eigenvalues are those values: If a matrix

that just scales a vector by a certain
amount that is an eigenvalue of the matrix

and in the same sense we can define
eigenvalues and eigenvectors for, L2

functions. And there are some facts such
as that non-commuting operators have

eigenstates that are not common. So we
can't have a description of the basis of

the state space in terms of function that
are both eigenfunctions of both operators

and some examples of operators are the
momentum operator which is just minus i

h-bar Nabla which is the derivation
operator in three dimensions. So in the x

component we have derivation in the
direction of x and in the y component in

direction of y and so on. And the position
operator which is just the operator that

multiplies by the position x in the
position space representation of the wave

function. And as for the non-
communtitivity of operators we can already

show that those p and x operators that do
not commute but fulfill a certain

commutation relation. And a commutation
relation is just a measure for how much

two operators do not commute. And the
commutator is AB minus BA for the objects

AB, so if they commute, if AB equals BA
the commutator simply vanishes. And

there's more on operators just to make it
clear: Linear just means that we can split

the argument if it is just some linear
combinations of vectors and apply the

operator to the individual vectors
occuring, we can define multiplication of

operators and this just exactly follows
the template that is laid down by finite

dimensional linear algebra. There's
nothing new here. And there are inverse

operators for some operators, not for all
of them, that give the identity operator

if it's multiplied with the original
operator. And further there's the so-

called adjoint. Our scalar product had
this little asterisk and this means that

it's not linear in the first component. If
I scale the first component by some

complex number alpha the total scalar
product is not scaled by alpha, but by the

complex conjugate of alpha. This kind of
not quite bi-linearity is sometimes called

sesquilinearity, a seldomly used word, and
they're commonly defined classes of

operators in terms of how the adjoint that
is defined there acts and how some other

operators for example where the adjoint is
the inverse which is a generalization from

the fact that for rotation operators in
normal Euclidean space, the transpose is

the inverse. And now that we have
operators we can define expectation values

just by some formula. For now, we don't
know what expectation values are, but we

can assume, it has something to do with
the measurement values of the operator

because: why else would I tell you about
it. And later on we will show that this is

actually the expectation value of the
quantity if we prepare a system always in

the same fashion and then do measurements
on it, we get random results each time,

but the expectation value will be this
combination. And now again: a bit of

mathematics: eigenvalue problems. Well
known: You can diagonalize a matrix and

you can diagonalize linear operators. You
have some equation A psi equals lambda

psi, where lambda is just a scalar. And if
such an equation holds for some vector psi

then it's an eigenvector and if we scale
the vector linearly, this will again be an

eigenvector. And what can happen is that
to one eigenvalue there are several

eigenvectors, not only one ray of
eigenvectors, but a higher dimensional

subspace. And important to know is that
so-called Hermitian operators, that is

those that equal their adjoint, which
again means that the eigenvalues equal the

complex conjugate of the eigenvalues have
a real eigenvalues. Because if a complex

number equals its complex conjugate, then
it's a real number. And the nice thing

about those diagonalized matrices and all
is: we can develop any vector in terms of

the eigenbasis of the operator, again just
like in linear algebra where when you

diagonalize a matrix, you get a new basis
for your vector space and now you can

express all vectors in that new basis. And
if the operator is Hermitian the

eigenvectors have a nice property, namely
they are orthogonal if the eigenvalues are

different. And this is good because this
guarantees us that we can choose an

orthonormal, that is a basis in the vector
space where to basis vectors always have

vanishing scalar product are orthogonal
and are normal, that is: we scale them to

length one, because we want our
probability interpretation, and in our

probability interpretation we need to have
normalized vectors. So now we have that

and now we want to know: How does this
strange function psi, that describes the

state of the system, evolve in time. And
for this we can have several requirements

that it must fulfill. So again we are
close to software engineering and one

requirement is, that if it is a sharp wave
packet, so if we have a localized state

that is not smeared around the whole
space, then it should follow the classical

equation of motion because we want that
our new theory contains our old theory.

And the time evolution must conserve the
total probability of finding the particle

because otherwise we couldn't do
probability interpretation of our wave

function, if the total probability of the
particle wouldn't remain one. Further we

wish the equation to be first order in
time and to be linear because for example

the Maxwell equations are linear and show
nice interference effects, so we want that

because then simply a sum of solutions is
again a solution, it's a good property to

have and if it works that way: Why not?
And the third and the fourth requirement

together already give us more or less the
form of the Schroedinger equation. Because

linearity just says that the right-hand
side of some linear operator applied to

psi and the first order in time just means
that there must be a single time

derivative in the equation on the left-
hand side. And this i-h bar: we just wanted

that there, no particular reason we could
have done this differently, but it's

convention. Now with this equation we can
look: What must happen for the probability

to be conserved and by a simple
calculation we can show that it must be a

Hermitian operator. And there is even more
than this global argument. There's local

conservation of probability, that is, a
particle can't simply vanish here and

appear there, but it must flow from one
point to the other with local operations.

This can be shown when you consider this
in more detail. Now we know how this

equation of motion looks like, but we
don't know what this mysterious object H

might be. And this mysterious object H is
the operator of the energy of the system

which is known from classical mechanics as
the Hamilton function and which we here

upgrade to the Hamilton operator by using
the formula for the classical Hamilton

function and inserting our p into our
operators. And we can also extend this to

a magnetic field. And by doing so we can
show that our theory is more or less

consistent with Newtonian mechanics. We
can show the Ehrenfest theorem, that's the

first equation. And then those equations
are almost Newton's equation of motion for

the centers of mass of the particle
because this is the expectation value of

the momentum, this is the expectation
value of the position of the particle.

This just looks exactly like the classical
equation. The velocity is the momentum

divided by the mass. But this is weird:
Here we average over the force, so the

gradient of the potential is the force, we
average over the force and do not take the

force at the center position, so we can't
in general solve this equation. But again

if we have a sharply defined wave packet
we recover the classical equations of

motion, which is nice. So we have shown
our new theory does indeed explain why our

old theory worked. We only still have to
explain why the centers of mass of massive

particles are usually well localized and
that's a question we're still having

trouble with today. But since it otherwise
works: don't worry too much about it. And

now you probably want to know how to solve
the Schroedinger equation. Or you don't

want to know anything more about quantum
mechanics. And to do this we make a so-

called separation ansatz, where we say, we
have a form stable part of our wave

function multiplied by some time dependent
part. And if we do this we can write down

the general solution for the Schroedinger
equation. Because we already know that the

one equation that we get is an eigenvalue
equation or an eigenvector equation for

the energy eigenvalues, that is the
eigenvalues of the Hamilton operator. And

we know that we can develop any function
in terms of those and so the general

solution must be of the form shown here.
And those states of specific energy have a

simple evolution because their form is
constant and only their phase changes and

depends on the energy. And now this thing
with the measurement in quantum mechanics

is bad. You probably know Schroedinger's
cat and the point is: there you don't know

whether the cat is dead or alive while you
don't look inside the box. While you don't

look inside the box as long as you don't
measure it's in a superposition or

something. So You measure
your cat and then it's dead. It isn't dead

before only by measuring it you kill it.
And that's really not nice to kill cats.

We like cats. The important part here is,
the TL;DR, quantum measurement is

probabilistic and inherently changes the
system state. So I'll skip the multi

particle things. We can't describe
multiple particles. And just show the

axioms of quantum mechanics shortly. Don't
don't read them too detailed, but this is

just a summary of what we've discussed so
far. And the thing about the multiple

particles is the axiom 7 which says that
the sign of the wave function must change

if we exchange the coordinates of
identical fermions. And this makes atom

stable by the way. Without this atoms as
we know them would not exist. And finally

there is a notational convention in
quantum mechanics called Bra-Ket-notation.

And in Bra-Ket-notation you label states
by their eigenvalues and just think about

such a Ket as an abstract vector such as x
with a vector arrow over it or a fat set x

is an abstract vector and we can either
represent it by its coordinates x1 x2 x3,

or we can work with the abstract vector
and this Ket is such an abstract vector

for the L2 function psi of r. And then we
can also define the adjoint of this which

gives us, if we multiply the adjoint and a
function, the scalar product. So this is a

really nice and compact notation for many
physics problems. And the last equation

there just looks like component wise, like
working with components of matrices, which

is because it's nothing else. This is just
matrix calculus in new clothes. Now for

the applications. The first one is quite
funny. There's a slide missing. Okay. Uh

the first one is a quantum eraser at home.
Because if you encode the "which way"

information into a double slit experiment
you lose your interference pattern. And we

do this by using a vertical and horizontal
polarisation filter. And you know from

classical physics then it won't make an
interference pattern. And if we then add a

diagonal polarization filter then the
interference pattern will appear again. So

now, just so you've seen it, the harmonic
oscillator can be exactly solved in

quantum mechanics. If you can solve the
harmonic oscillator in any kind of physics

then you're good, then you'll get through
the axioms when you study physics. So the

harmonic oscillator is solved by
introducing so-called creation and

destroyer operators and then we can
determine the ground state function, in a

much simpler manner than if we had to
solve the Schroedinger equation explicitly

for all those cases. And we can determine
the ground state function, so the function

of lowest energy. This can all be done and
then from it by applying the creation

operator create the highest eigenstate of
the system and get all of them. Then

there's this effect of tunnelling that
you've probably heard about and this just

means that in quantum mechanics a
potential barrier that is too high for the

particle to penetrate does not mean that
the particle doesn't penetrate at all but

that the probability of finding the
particle inside the barrier decays

exponentially. And this can for example be
understood in terms of this uncertainty

relation because if we try to compress the
particle to the smaller part of the

boundary layer then its momentum has to be
high so it can reach farther in because

then it has more energy. And there's this
myth that tunnelling makes particles

traveling to travel instantaneously from A
to B and even some real physicists believe

it. But sorry it's not true. The particle
states is extended anyway and to defining

what how fast the particle travels is
actually not a well-defined thing in deep

quantum regimes, and also the Schroedinger
equations is not relativistic. So there is

nothing, really nothing stopping your
particle from flying around with 30 times

the speed of light. It's just not in the
theory. Another important consequence of

quantum mechanics is so-called
entanglement and this is a really weird

one, because it shows that the universe
that we live in is in a way non-local,

inherently non-local. Because we can
create some states for some internal

degrees of freedom of two atoms and move
them apart then measure the one system and

the measurement result in the one system
will determine the measurement result in

the other system, no matter how far
removed they are from each other. And this

was first discovered in a paper by
Einstein, Podolski and Rosen and they

thought it was an argument that quantum
mechanics is absurd. This can't be true,

but sorry it is true. So this works and
this kind of state that we've written

there that is such an entangled state of
two particles. But important to remark is

that there are no hidden variables, that
means the measurement result is not

determined beforehand. It is only when we
measure that is actually known what the

result will be. This is utterly weird but
one can prove this experimentally. Those

are Bell tests. There's a Bell-inequality
that's the limit for theories where they

are hidden variables and it's by real
experiments they violate the inequality

and thereby show that there are no hidden
variables. And there's a myth surrounding

entanglement, namely that you can transfer
information with it between two sides

instantaneously. But again there's nothing
hindering you in non relativistic quantum

mechanics to distribute information
arbitrarily fast. It doesn't have a speed

limit but you can't also count communicate
with those entangled pairs of particles.

You can just create correlated noise at
two ends which is what quantum

cryptography is using. So now because this
is the hackers congress, some short

remarks and probably unintelligible due to
their strong compression about quantum

information. A qubit, the fundamental unit
of quantum information, is a system with

two states zero and one. So just like a
bit. But now we allow arbitrary super

positions of those states because that is
what quantum mechanics allows. We can

always superimpose states and quantum
computers are really bad for most

computing tasks because they have to,
even if they build quantum computers they

will never be as capable as the state-of-
the-art silicon electrical computer. So

don't fear for your jobs because of
quantum computers. But the problem is they

can compute some things faster. For
example factoring primes and working with

some elliptic curve algorithms and so on
and determining discrete logarithm so our

public key crypto would be destroyed by
them. And this all works by using the

superposition to construct some kind of
weird parallelism. So it's actually I

think nobody really can imagine how it
works but we can compute it which is often

the case in quantum mechanics. And then
there's quantum cryptography and that

fundamentally solves the same problem as a
Diffie-Hellman key exchange. We can

generate the shared key and we can check
by the statistics of our measured values

that there is no eavesdropper, which is
cool actually. But it's also quite useless

because we can't detect a man in the
middle. How should the quantum particle

knows of the other side is the one with
that we want to talk to. We still need

some shared secret or public key
infrastructure whatever. So it doesn't

solve the problem that we don't have
solved. And then the fun fact about this

is that all the commercial implementations
of quantum cryptography were susceptible

to side channel text, for example you
could just shine the light with a fiber

that was used, read out the polarization
filter state that they used and then you

could mimic the other side. So that's not
good either. So finally some references

for further study. The first one is really
difficult. Only try this if you've read the

other two but the second one. Sorry that
they're in German. The first and the last

are also available in translation but the
second one has a really really nice and

accessible introduction in the last few
pages so it's just 20 pages and it's

really good and understandable. So if you
can get your hands on the books and are

really interested, read it. So thank you
for the attention and I'll be answering

your questions next.

Applause

Herald: Thank you Sebastian. Do we have
questions? And don't be afraid to sound

naive or anything. I'm sure if you didn't
understand something many other people

would thank you for a good question.
Sebastian: As to understanding things in

quantum mechanics, Fineman said "You can't
understand quantum mechanics, you can just

accept that there there's nothing to
understand. That's just too weird."

Herald: Ok,we've found some questions. So
microphone one please.

M1: Can you explain that, if you measure a
system, it looks like you changed the

state of the system. How is it defined
where the system starts? No. How is it

defined when the system ends and the
measurement system begins. Or in other

words why does the universe have a
state? Is there somewhere out there who

measures the universe?
S: No. There's at least the beginning of a

solution by now which is called
"decoherence" which says that this

measurement structure that we observe is
not inherent in quantum mechanics but

comes from the interaction with the
environment. And we don't care for the

states of the environment. And if we do
this, the technical term is traced out the

states of the environment. Then the
remaining state of the measurement

apparatus and the system we're interested
in will be just classically a randomized

states. So it's rather a consequence
of the complex dynamics of a system state

and environment in quantum mechanics. But
this is really the burning question. We

don't really know. We have this we know
decoherence make some makes it nice and

looks good. But it also doesn't answer the
question finally. And this is what all

those discussions about interpretations of
quantum mechanics are about. How shall we

make sense of this weird measurement
process.

Herald: Okay. Microphone 4 in the back please.
M4: Could you comment on your point in the

theory section. I don't understand what
you were trying to do. Did you want to

show that you cannot understand really
quantum mechanics without the mathematics

or?
S: Well, yes you can't understand quantum

mechanics without the mathematics and my
point to show was that mathematics, or at

least my hope to show was that mathematics
is halfways accessible. Probably not

understandable after just exposure of a
short talk but just to give an

introduction where to look
M4: OK. So you are trying to combat the

esoterics and say they don't really
understand the theory because they don't

understand the mathematics. I understand
the mathematics. I'm just interested. What

were you trying to say?
S: I was just trying to present the

theory. That was my aim.
M4: Okay. Thank you.

Herald: Okay, microphone 2 please.
M2: I know the answer to this question is

that ...
Herald: Can you go a little bit closer to

the microphone maybe move it up please.
M2: So I know the answer to this question

is that atoms behave randomly but could
you provide an argument why they behave

randomly and it is not the case that we
don't have a model that's. So, are atoms

behaving randomly? Or is it the case that
we don't have a model accurate enough to

predict the way they behave?
S: Radioactive decay is just as random as

quantum measurement and since if we
were to look at the whole story and look

at the coherent evolution of the whole
system we would have to include the

environment and the problem is that the
state space that we have to consider grows

exponentially. That's the point of quantum
mechanics. If I have two particles I have

a two dimensional space. I have 10
particles I have a 1024 dimensional space

and that's only talking about non
interacting particles. So things explode

in quantum mechanics and large systems.
And therefore I would go so far as to say

that it's objectively impossible to
determine a radioactive decay although

there are things, there is I think one
experimentally confirmed method of letting

an atom decay on purpose. This involves
meta stable states of nuclei and then you

can do something like spontaneous emission
in a laser. You shine a strong gamma

source by it and this shortens the
lifespan of the nucleus. But other than

that.
M4: So in a completely hypothetical case. If you

know all the starting conditions and what
happens afterwards,wouldn't it be able,

we could say it's deterministic? I
mean I'm playing with heavy words here.

But is it just that we say it's randomised
because it's very very complex right?

That's what I'm understanding.
Herald: Maybe think about that question

one more time and we have the signal angel
in between and then you can come back.

Signal Angel do we have questions on the
Internet?

Angel: There's one question from the Internet
which is the ground state of a BEH-2 has

been just calculated using a quantum
eigensolver. So is there still some use of

quantum computing in quantum mechanics?
S: Yes definitely. One of the main

motivations for inventing quantum
computers was quantum simulators.

Feynman invented this kind of
quantum computing and he showed that with

digital quantum computer you can
efficiently simulate quantum systems. While

you can't simulate quantum systems with a
classical computer because of this problem

of the exploding dimensions of the Hilbert
space that you have to consider. And for

this quantum computers are really really
useful and will be used once they work,

which is the question when it will be.
Perhaps never. Beyond two or three qubits

or 20 or 100 qubits but you need scalability
for a real quantum computer. But quantum

simulation is a real thing and it's a good
thing and we need it.

Herald: Okay. Then we have microphone 1
again.

M1: So very beginning, you said that the
theory is a set of interdependent

propositions. Right? And then if a new
hypothesis is made it can be confirmed by

an experiment.
S: That can't be confirmed but, well it's

a philosophical question about the common
stance, it can be made probable but not

be confirmed because we can never
absolutely be sure that there won't be

some new experiment that shows that the
hypothesis is wrong.

M1: Yeah. Because the slide said that
the experiment confirms...

S: Yeah, confirm in the sense that it
doesn't disconfirm it. So it makes

probable that it's a good explanation of
the reality and that's the point. Physics

is just models. We do get
nothing about the ontology that is about

the actual being of the world out of
physics. We just get models to describe

the world but all what I say about this
wave function and what we say about

elementary particles. We can't say they
are in the sense that you and I are here

and exist because we can't see them we
can't access them directly. We can only

use them as description tools. But this is
my personal position on philosophy of

science. So there are people who disagree.
M1: Ok, thanks.

Herald: Microphone 2 please.
M2: Or maybe superposition. By the way, so

on the matter of the collapsing of the
wave function, so this was already treated

on the interpretation of Copenhagen and
then as you mentioned it was expanded by

the concept of decoherence. And is this, so
the decoherence is including also the

Ghirardi–Rimini–Weber interpretation or
not?

S: Could decoherence be used in
computation or?

M2: No so for the Ghirardi–Rimini–Weber
interpretation of the collapsing of the

wave function.
S:That's one that I don't know.

I'm not so much into interpretations.
I actually think that there's interesting

work done there but I think they're a bit
irrelevant because in the end what I just

said I don't think you can derive
ontological value from our physical

theories and in this belief, I think that
the interpretations are in a sense void,

they just help us to rationalize what
we're doing but they don't really add

something to the theory as long as they
don't change what can be measured.

M2: Oh okay. Thanks.
S: Sorry for being an extremist.

M2: Totally fine.
Herald: Someone just left from microphone 1

I don't know if they want to come
back. I don't see any more questions as to

signal angel have anything else. There is
some more. Signal angel, do you have

something?
Signal Angel: No.

Herald: Okay. Then we have
microphone 4.

M4: I want to ask a maybe a noob question.
I want to know, are the probabilities of

quantum mechanics inherent part of nature
or maybe in some future we'll have a

science that will determine all these
values exactly?

S: Well if decoherency theory is true,
then quantum mechanics is absolutely

deterministic. But so let's say, Everett
says that all those possible measurement

outcomes do happen and the whole state of
the system is in a superposition and by

looking at our measurement device and
seeing some value we in a way select one

strand of those superpositions and live in
this of the many worlds and in this sense

everything happens deterministically, but
we just can't access any other values. So

I think it's for now rather a
of philosophy than of science.

M4: I see. Thanks.

Herald: Anything else? I don't see any
people lined up at microphones. So last

chance to round up now, I think. Well then
I think we're closing this and have a nice

applause again for Sebastian.
applause

Sebastian: Thank you. And I hope I didn't
create more fear of

quantum mechanics than
I dispersed.

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