*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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