Quantum Mechanics

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Quantum Mechanics
A Gentle Introduction
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An (almost) self-contained introduction to the basic ideas of quantum mechanics. The theory and important experimental results will be discussed.
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[Music] and so he studied physics and and thinking we just all need a lot better understanding of quantum mechanics because he sees the Styria 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
well thank you for the warm welcome
it will be about quantum mechanics we will see whether the gentle introduction will be lie depending on how good you can follow me so at first there will be
a short introduction a bit me a discussion about physical theories and what is the aim of this talk and then we
will discuss the experiments most of this as high school physics you 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 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 a set and but we will not do it in a 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 a set in German and in science theory and childish we will need mathematics and most of this will be linear algebra so a lot of quantum mechanics is just linear algebra and steroids that means in infinite dimensions and in doing so
we'll try to find a certain post-classical and charlisse kite or livid nurse to understand the theory since there were a lot of math as the allergy advice said there will be crash courses tuned in to explain mathematical effects sorry for the mathematicians that are here they probably suffer because a lie a lot so at first how the scientific theories work to analysts really understand quantum mechanics we must understand the setting and setting Wed 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 X F equals 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 hip hypothesis stamp the experimental tests their attitude theory but what happens if there's a 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 such inconsistent results are found then our old theory has been falsified
this is this term is due to Papa who said that theory is scientific as long as it can be falsified that is as long as we can prove that it's not true and we can never prove the theory true but only prove it wrong and all that we have not yet proven wrong 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 as Occam's razor or one could also say the principle of least surprise from software engineering and then we try
that our theories again consistent with the experimental results and of course the new theory must explain why the hell that for example Newtonian mechanics worked for 200 years if it's absolutely wrong and so the old theory must at some limit contain the new one and now how does it begin with quantum mechanics as already set 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 seeing equation the force equals mass times the acceleration was given forces and to known force laws the immediately the immediate distance action Newtonian gravitation and the Maxwell electrodynamics this funny equation here this final equation here is a way of writing down the Maxwell equations that basically contain all the known electromagnetic effects and finally there was 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 as said could not be explained by classical theories for example the photoelectric effect discovered perhaps on topics in 1887 or the discrete spectral lines of atoms first shown by found over and the spectrum of the Sun and then color and then studied by Bunsen and cut off with the so-called moon antenna you all know it from your chemistry classes and further radioactive rays were really a mystery nobody had understood how can it happen that something just decays at random
intervals it was unclear and then the people looked into the atom rather forth using alpha particles to bombard the gold foil and so they must be positively charged nuclei and they already knew that they were negatively charged what we now call electrons particles in the atom so this and this was really strange
that atoms are stable that 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 pump the air out and close 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 he 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 the plate and front that is positively charged so we accelerate our electrons towards the plate there's a pinhole on the plate and we get a beam of electrons and now we had those evacuated to tubes and those electron guns so we put a electron gun in the evacuated tube perhaps left a bit of gas in because then it glowed when was when the atoms and the gas were hit by the electron 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 microscopically 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 plump having or so with the electrons sitting in there but the Rutherford Gygax Mastan gaya experiment so it was where a default invented the idea and mass 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 this nice thing about gold you can just hammered out two 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 this could not have happened you can calculate you can you can estimate the possible reflections 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 rather foothold it and around the days there's a cloud of electrons or he thought orbiting electrons but orbiting electrons atoms are stable this doesn't really make sense on classical physics because in classical physics all accelerated charges must radiate energy and be slowed by this process and this means atoms that are stable and composed
of some strange electrons and heavy nuclei they're just not possible it's it's no goal so at least at this moment it was completely clear classical physics as then you'd up until then as wrong and a next experiment in this
direction was the photoelectric effect what's shown there is a schematic of a photo tube and a photo tube is again a vacuum tube out of glass and there's a for example cesium laya in in the tube at one side and there's a ring electrode removed from it and if we shine light on this they flow the current but the peculiar thing is that if we use a by a biased 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 photo tube and that was again really weird for a people of the time because the frequency shouldn't shouldn't make any difference for the energy and this was when Einstein derived that our 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 even at the high school level sorts throughout 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 setup of a so-called discharge tube where we have high voltage between the terminals and the 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 the diffraction creating that Salt's light out according to its wavelength and then look on a screen or use some more fancy optical instrument to do precision measurements as Putin 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 mono crystalline surface and such a mono crystalline surface is just like a diffraction creating grating a periodically arranged thing and off periodically arranged things there does happen regular interference pattern creation so they saw an interference pattern with electrons but electrons and that particles how can particle so what
was thought of then since the times of mutinous little house 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 nucleus this doesn't make sense in classical physics so it was as well it was really really bad and here I've added some modern facts that we'll need later on namely that that if we measure but if we try to measure the position of a particle and use different position 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 a coherent manner and the coherence 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 we'll begin with a lot of mathematics the first one is simple complex numbers okay who does who doesn't know complex numbers okay sorry I'll have to ignore
you for the sake of getting to the next
points so I'll just say complex numbers are two
components of Rijeka mental objects with real numbers and one of them is multiplied by a imaginary number I and if we I square the number I it gets minus 1 and this makes many things really beautiful for example all algebraic equations have exactly the number of degree solutions and complex numbers and if you count them correctly and if you work with complex factions 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 set you nail them 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's a null vector we can add vectors we can invert vectors and we can multiply vectors by real numbers so we can say 3.5 times this vector and just scale the the arrow and the these operations interact nicely so that we have the those distributive laws and now it gets interesting even more maths L 2
spaces al 2 spaces are in a way a
infinite dimensional or one form of an infinite dimensional extension effective spaces instead of having just three directions X Y that 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 fact 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 and 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 new norm this norm is induced by a scalar product and this little asterisk for the that is there at the F denotes the complex conjugate so flipping I to minus I and all complex values and if you just if you just plug in F and F into the scalar product you will see that it's in the integral over the squared absolute value and this space this L 2 space is a Hilbert space and the hilbert space is a complete spay vector space with a scalar product where complete means that it's mathematical norms and forget so but nice surprises that most things carry over from finite dimensional space what we know from finite dimensional spaces we can always diagonalize matrices with certain properties and this all more or less works it 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 it 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
Davidson Germer experiments there's diffraction of electrons but there's nothing in electrons that corresponds to a positive electric field in some direction or so some other periodicity has so periodicity of electrons during propagation has never been directly observed and the boy said particles have a wavelength that's related to their momentum and he was motivated primarily by the Bohr fear of the atom to do so and he was shown right by the Davidson Germer experiments so his relation for the wavelength of a particles older than the experiments showing this which is impressive I think and now the idea is they have a complex wave function and let these squared absolute value of the wave function describe the probability density of a particle so we make particles extended but probability measured object 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 face and this face can allow still allow interference effects which we need for explaining the interference peaks and the Davidson Germer experiment and now a lot of textbooks say here there's a wave particle you blah blah blah distinct nonsense play the point is it doesn't get you far to think about quantum objects as either
wave or particle they're just quantum neither wife nor particle doesn't help you either but it doesn't confuse you as much as when you try to think about particles as waves or particles about quantum particles waste or particles and
now that we say we have a complex wave function what about simply using a plane wave with constant probability as the states of definite momentum because we somehow have to describe a particle to say that 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 size 1 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 IKr our states are just the basis states of Fourier transformation we can write any function in terms of this basis and we can conclude that by forget transformation of the state sy of our to some state tilde psi of K we will 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 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 operators are just like mattresses linear operators on the state space just as we can apply an Metro 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 rep so eigenvalues are those values where matrix that's just if metrics just scales vector by a certain amount that is an eigenvector of an eigenvalue of the matrix and in the same sense we can define eigenvalues and eigenvectors for two functions and they're some effect such as that non commuting operators have eigenstates that are not common so we can't have a description of the of all stay of the basis of the state space in terms of functions 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 their derivation in the direction of X and the y component direction of Y and so on and the position operator which is just the operator that multiplies by the position X in the in the position space representation of the wave function and as for the non commutativity of
operators we can already show that those P and X are operators that do not commute but fulfill a certain
commutation relation and the commutation relation is just a measure for how much two operators do not commute and the community commutator as a B - be a for the objects a B so if they commute if a B equals be a the commutator simply vanishes and there's more operators just to make it clear linear just means that we can split the argument if it's out of this lastly just some linear combinations of vectors and apply the operator to the individual vectors occurring we can define multiplication of operators and this just exact he follows the template that is laid down by finite dimensional linear algebra Desna there's nothing new here and they're 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 that 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 by linearity is called sometime called sesquilinear sesquilinear Chi a seldom used word and they're commonly defined classes of operators in terms of how the how the adjoint that is defined directs and how some their 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 we don't know what those expectation values are but we can assume as has something to do with the measurement well use 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 metrics and you can diagonalize linear operators you have some equation apes i equals lambda pi where lambda is just a scalar so and if such an equation holds for some vector side then it sank and any linetsky every scale the vector linearly this will again be an eigenvector and what can happen is that to one eigen eigen value there are several eigen vectors not only one ray of eigenvectors but a higher dimensional subspace and important to notice that so-called hermitian operators that is those that equal their joint which again means that the eigenvalues equal the complex conjugate of the eigenvalues have real eigenvalues because of a complex number equals it's complex
conjugate then it's a reason number and
the nice thing about those diagonalized matrices and all as we can develop any any vector in terms of the eigen basis of the operator again just like in linear algebra where when you diagonalize 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 because this guarantees us that we can choose a orthonormal that is a basis in the vector space where two basis vectors always have vanishing scalar product orthogonal and are normal that is we scale them to length one because we want our probability interpretation and now probability interpretation we need to have normalized vectors so now we have that and now we want to know how does
the strange function side 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're close to software engineering and one requirement is this that if it's a sharp wave packet so if we have a localized state that not smeared around the whole space then that should follow the classical equation of motion because we want that our new theory contains our own 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 particular 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 Alinea and shown nice show a nice interference effects so we want that because then simply sum of solutions is again a solution that's 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 Schrodinger equation because linearity just says that the right-hand side is some linear operator applied to psi and the time first order and time just means that there must be time derivative time derivative in the equation on the left hand side and this is bass just and we just wanted that there no particular reason we could have done this differently but its 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 humor a hermitian operator and there's even more than this global argument there's local conservation of probability that is a particle can 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 from known from classical mechanics as the Hamilton function and which we here upgrade to a Hamilton operator by using the formula for the classical Hamilton and inserting our P and R 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 L 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 ever Everage over the force so the gradient of the potentials the force we averaged 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 waist 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 that we only still have to explain why the centers of mass of massive particles I usually well localized and that's the question we're still having trouble with today but since the sense that otherwise
works don't worry too much about it and now you probably want to know how to solve the Schrodinger equation or you
don't want to know anything more about quantum mechanics and to do this we make a so called separation and that's where we say we have a form stable 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 Schrodinger equation because we already know that the one equation that we get is d is an eigenvalue krei 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 this specific energy have a simple evolution because the form is constant that only their face changes and depends on the energy and now this thing with the measurement and quantum mechanics is bad you probably know Schrodinger's cat and the point is that you don't know whether the cat's dead or live 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 you measure your cat and then it's dead it isn't that before only by measuring it you kill it and that's really not nice to kill cats we like cats so and the important part here is
the TLDR quantum measurement is probabilistic and inherently changes the
system state so I'll skip the multi particle things we can describe multiple multiple particles and just show the axioms of quantum mechanics shortly don't read them to detail well this is just a summary of what we've discussed so far and the 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's a notational convention in quantum mechanics called racket notation and in bracket notation you label states by their eigenvalues and just think about such a ket as an abstract vector such as x with an with vector arrow over door fat set X is an abstract vector and we can either repress represented by its coordinates X 1 X 2 X 3 or we can work with the abstract vector and this cat such an abstract vector for the l2 function Phi of R and then we can also define the adjoint of this which gives us if we multiply the joint at 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
mattresses which is because it's it's nothing else this is just matrix calculus in a and a new and new clothes now for the applications the first one is quite funny oh I did oh there's a slight missing okay the first one is a quantum eraser at home because if you encode the whichway information into a double slit experiment you lose your you lose the interference pattern and we do this by using a vertical and a horizontal polarization filter and you know from classical physics then it won't it won't make a it won't make an interference pattern and if we add that then at the diagonal polarization filter then the interference pattern will appear again so now just so you've seen that the harmonic oscillator can be exactly solved and quantum mechanics if you can solve the harmonic oscillator in any kind of physics then you're good then you'll get through the exomes and the physics of any study physics so the harmonic oscillators is solved by introducing so-called destroyers and creation and destroyer operators and then we can determine the ground state function with the sat in a much simpler manner than we had to solve the Schrodinger equation explicitly for all those cases and we can we can determine the grounds that the ground state finds and so the function of lowest energy this can all be done and then can from it by applying the creation operator create the higher the higher eigenstates of the system and get all of them then there's this effect of tunneling 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 the particle doesn't penetrate at all but just there 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 a 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 tunneling makes particles travel a to travel instantaneously from A to B and even some real physicists believe it but sorry it's not true the particle state is extended anyway and to defining what how fast the particle travels is actually not a well-defined thing and deep quantum regimes and also the
Schrodinger equation is not relativistic so there's nothing nothing really nothing stopping your particle from flying around with 30 times the speed of light it's just not in a theory another important consequence of quantum
mechanics is so-called entanglement and this is a really weird one because it shows that our the universe that we live in is in a way non-local inherently non-local because we can create some state of we can straight a state for some internal degrees of freedom of two atoms and move them apart then measure the one system and the measurement result and the one system will determine the measurement result and the other system no matter how far removed they are from each other and this was first discovered in a paper by Einstein Podolsky 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 as actually known what the result will be this is utterly weird but one can prove this experimentally as those are bail tests there's a bell in equality that's a limit for theories where they are hidden variables and it's by real experiments they violate this inequality and they make sure that there are no hidden variables and there's a myth surrounding entanglement namely that you can transfer information with it between two sides and sent aeneas lee but again there's nothing hindering you in nonrelativistic quantum mechanics to distribute information arbitrarily fast it doesn't have a speed limit but you can also can't 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
in intelligible due to their strong compression about quantum information a qubit the fundamental unit of quantum
information is a system with two states 0 and 1 so just like a bit but now we allow arbitrary superposition so arbitrary superposition 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 they have to have it even if they built quantum computers they'll 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 logarithms 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's fundamentally solve 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 was no eavesdropper which is cool actually but
it's also quite useless because we can't detect the 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 a 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 texts for example it could just shine with the light and the fiber that was used read out the polarization filter state that they used and then you could 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 a few furet 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 and the first in the last few pages so it's just 20 pages and it's really good and understandable so if you can you get your hand you can get your hands on the books and are really interested read it so thank you for your attention and I'll be answering your questions next
thank you service yeah um 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 as to understanding things in quantum mechanics Fineman said you can't understand quantum mechanics you can just accept that there's nothing to understand there it's just too weird
Shawn some questions so microphone one please it looks like you change the
state of the system how its defined where the system starts I don't know what how is it defined by the system ends and the measurement system begins or in other words why does the universe interstate is there somewhere out there who measures the universe now there's at least the beginning of a solution by now which is called decoherence and which says that 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 trace out the states of the environment then the remaining state of the measurement apparatus and the system we are interested in will be just classically randomized states so it's it's rather a consequence of the complex dynamics of a system state and environment in quantum mechanics but this this is really the burning question we 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
ok microphone four in the back please could you comment on your point in the
theory section I'm I don't understand what you were trying to to do did you want to show that you cannot understand really quantum mechanics without the mathematics or well yes you can't understand quantum mechanics with other mathematics and my point to show was that they make measurement or at least my hope to show was that in mathematics is half ways accepted but accessible sort of probably not understandable after just exposure of a short talk but just to give an introduction where to look okay so you were trying to combat esoteric stew and and say they they don't really understand the theory because they don't understand the mathematics I'm just interested what you were trying to say I was just trying to present the theory that was my aim thank
you okay microphone two please I know the answer to this question is that and
you so I know the answer to this
question is that atoms behave randomly but could you provide an argument why they behaved for enemy and it's not the case that we don't have a model that's so our atoms behaving randomly or is it the case that we don't have a model accurate enough to predict the way they behave radioactive decay is just as random as quantum measurement and since it since if 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 if I have ten particles I have 1,024 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 radioactive decay although there are things they is I think one experimentally confirmed method of letting an atom decay on purpose that this involves my meat has 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 if you know all the the starting conditions and what happens afterwards you would be able we could say it's deterministic I mean I know I'm playing with with every words here but is it is just that we say it's random is because it's very very complex right maybe think about that question
one more time and we have this signal angel in between and then you can come back from the internet there's one
question from the internet which is the ground state of a b e:h - has been just calculated using a quantum eigen eigen solver so is there still some use of quantum computing in quantum mechanics yes definitely one of the main motivations for inventing quantum computers was quantum simulators Fineman apartment and then invented this kind of quantum computing and he showed that with digital quantum computer you can efficiently simulate quantum system well 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 cubits or 20 or 100 cubits but you need scalability for a real quantum computer but some quantum simulation is a real thing and it's a good thing and we need it okay then we have microphone 1 again
very beginning you say 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 that can't be confirmed but it it well it's a it's a it's a philosophical question about the common stance that 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 because this lied said that the experiment yeah confirm in the sense that it doesn't disconfirm it so it makes probable that it's a good explanation of reality and that's the point physics is just models we don't we do get nothing about the ontology that is about the app actual being of the world out of physics we just get models to describe the world but or 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 microphone to please or me or maybe
superposition by the way so on the matter of the
collapsing of the wavefunction 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 Girardi Remini Weber interpretation or not Cote coherence be used in computation or no no if so for the Girardi Remini Weber interpretation of the collapsing of the wavefunction that's that's one that I don't know okay I'm not so much into interpretation I actually think that this interesting work done there but I think they're a bit irrelevant because in the end what I just said I don't think we can derive ontological value from our physical theories and in this belief I think that the interpretations are in a sense void just 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 sorry for being an extra
missed not only fine someone just left
from microphone one I don't know if they want to come back I don't see any more questions as the signal angel have anything else ah there's some more single angel do you have something no
okay then we have microphone for I wanted to ask a maybe an OOP question a lot to know are there probabilities of quantum mechanics and in earth part of nature or maybe in some future we'll have a science that will determine all these values exactly well if the coherent theory is true then quantum mechanics is absolutely deterministic but so as far as let's say if the Everitt interpretation so ever it 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 it's I think it's rather matter of for now rather matter of philosophy then of science I see things anything else I don't see
any people lined up at microphone so last chance to run up now well then I think we're closing this and have a nice applause again first Weston thank you
and I hope I didn't make create more fear of quantum mechanics than I dispersed [Music] [Music]