Augmenting Reality: Axions, Anyons, and Entangled Histories

[Music] so it's my pleasure today to say welcome to Frank we'll check and he's coming to the department of physical of Stockholm University and this is the kind of reception for him to the department we could say so you were installed as professor of the you Slocum University in late September in the city hall and you gave a short talk there maybe this is the longer version of the same thing so it was in early 2015 we got a message that the VR had granted 10 years contract to recruit Frank will check to Stockholm so we got 60 millions to recruit him to build up great activities during the coming 10 years and of course our Dean under Collier then sitting down there was very important in this process so thanks to you for this so this will be kind of introducing you locally here at Alba Nova and I think you will talk about different aspects of what you would like to promote when being here and this professorship was then came about by a calling procedure by the vice-chancellor and he started now the first on may 2016 half year ago so he will then be spending different periods during the year in Stockholm and we are very happy to see the latest newsletter from the Stockholm University because see Frank saying I love Stockholm we like that Alice Castro come that's you speak Swedish I understand so now you have four affiliations if you get in me email from Frank it says Stockholm University it says Herman Feshbach professor MIT chief scientist with check quantum sentry Sejong University of Technology Honshu and its distinguished origin professor Arizona State University you're a busy man I mean you have a very long CV and I will not just spend a lot of time to go through that cuz we would would like to listen to you instead but let me just say a few things connecting to your visits to Stockholm of course the first one was 2004 when you received the Nobel Prize together with the grouse and Pulitzer for the discovery of asymptotic freedom in the theory of strong interaction that was in 2004 and then in 2007 you were here as no DEET a visiting professor spending I think in a couple of months yeah and then you present the Oscar Klein memorial lecture in 2013 we got this climb medal and last spring 2015 you present the Lisa Meitner Distinguished Lecture so you have been a close friend to us here coming frequently so now we are honored and proud to have you here as a colleague with us and we expect a lot of changes for the future for you inspiring us to new areas in research and as we wrote in the advertisement there will be a reception afterwards to celebrate your your coming here so it's time for you to present your talk augmenting reality axioms anions and untangles histories Thank You vice thank you well thank you for that lovely introduction Sven and good evening it's 321 but I looked outside it's a it's a great pleasure to introduce myself here to those of you who may not know and I'm going to be discussing in this lecture of my current interests necessarily the discussion will be superficial that I'll be here and I'll be very happy to talk with you further about the things that may intrigue you there's a lot to cover so without further ado I'm going to just start talking about physics so there will be three subjects accion's and eons and entangled histories first is accion's a few aspects of experience are as striking as the asymmetry between the past and the future if you run a movie of everyday life backwards that's the operation of time reversal it doesn't look like everyday life see the this is something you don't see very often although if you looked at small little bits of that process the laws of physics are obeyed things can spontaneously if they have enough energy that come together and come up to that make the building and then at the end you found that the energy came from an explosion but it doesn't look like everyday life at all things like that don't happen in everyday experience and we're very familiar with the difference between the past in the future we remember one and guess about the other and yet amazingly time reversal symmetry was a notable property of the fundamental laws of physics for several centuries starting with Newtonian mechanics which is based on accelerations so it has two powers of time if you change the sign the law doesn't change and continuing through general relativity and quantum electrodynamics that situation raises two basic questions one question about the foundations of statistical physics and the macroscopic description of the world is how do we get from laws that are symmetric in time to appearances that are so very asymmetric this is the arrow of time problem it's a fascinating problem but it's not the subject of of this lecture the problem that I want to focus on is a kind of why problem why are the fundamental laws symmetric it's not just not necessary in the description of the world this is a natural of everyday experience and yet the laws seem to have this property this is a naturality problem if you are as long as time reversal or T symmetry appeared to be an exact fundamental feature of physical law it was unclear that asking why would be fruitful when you can keep asking why about anything why why why why why eventually you have to hit rock bottom and fact that the laws are the same forwards and backwards of time might have been rock bottom I think that's the attitude that Newton and Maxwell for example had but the issue became richer more structured and the question more unavoidable in 1964 when Cronin and Fitch together with Christensen and Turley discovered a subtle effect in came a Zonda case that slightly violates time reversal symmetry for sticklers it was actually CP symmetry that they said that they found a violation of but CP T is kind of sacred so it's equipped morally equivalent to time reversal violation in 1973 building on the emerging core theories or standard model of strong and electroweak interactions kobayashi and maskawa made a major advance on this why question in the context of the core theories or standard model we discovered that quantum mechanics relativity and gauge symmetry the specific gauge symmetry of the fundamental particles combine to greatly constrain the possible interactions of physics the things that are consistent with those general principles are very restricted and kobayashi and maskawa showed that if you have two generations of quarks which was what was known at the time no time no time reversal violation can arise all the allowed interactions by those sacred principles also happen to respect time reversal symmetry while for three generations you can sneak in a little time reversal violation and you get a one-parameter theory of that effect there's an asterisk here which will be all-important but it'll it'll appear a moment they'll explicate it momentarily so the km work was a brilliant success it was certified by the Swedish Academy recently a third generation was subsequently discovered as they required to bring in T violation these were the B and T quarks and also the tau leptons and they're one parameter theory predicted and now successfully describes many reactions and decays that weren't known at the time a host of T violating effects in weak decays of heavy quarks and yet with more profound understanding of quantum field theory people realize that the km explanation of approximate T symmetry has a big loophole indeed there's another possible T violating interaction that they didn't take into account so actually there's a two parameter theory they had just inadvertently set one of the parameters equal to zero the new interaction is a very subtle one it's an interaction among coloured gluons which is profoundly quantum mechanical and does not show up in any order of perturbation theory so we say it's non perturbative if you don't know what that means means it's subtle this is the form of this interaction you can write it down it's an interaction among the coloured gluons which are very similar in mathematical structure to photons except that there are eight of them instead of just one photon and they respond to the color charges of the strong interaction rather than electromagnetic charges but you can still recognize that their electric fields and magnetic fields of these colored gluons and this is the form of the new interaction written in terms of the color glue on electric and magnetic field it's an e dot B interaction and it's parameterised it's coefficient is written as this parameter theta there's also a strong coupling constant there okay and this is the relativistic notation so this is consistent with all general principles and yet violates time reversal symmetry so it undoes or at least exposes a loose end in the kobayashi maskawa work the theta term changes sign under T you could tell that from the epsilon symbol in the relativistic notation which has one time index or you can tell it from the a dot B form because electric fields don't change the time reversal but magnetic fields do so if theta if the coefficient is not zero we have a new source of T symmetry violation and the theta term is especially dangerous to have because it feeds directly into the structure of nucleons nucleons are held together by gluons and if the gluons have this kind of asymmetry in their interactions it infects the structure of nucleons in such a way that it induces an electric dipole moment let me show that in a picture we're all very familiar with magnetic dipole moments associated with spinning objects such as the earth but also neutrons electrons and other elementary particles have little magnetic fields dipole fields associated with their direction of spin one can also imagine why not electric fields that are dipole with respect all general principles of relativity and so forth but not time reversal symmetry fundamental dipole moments both magnetic and electric are among the most accurately measured quantities in physics you can really do a very good job on them experimentally magnetic dipole moments give precision tests of quantum electrodynamics this is one of the one of the places where quantum electrodynamics gets tested - better than parts per billion in its predictions and constrain possible contributions from beyond the standard model on the other hand no non-vanishing fundamental electric dipole moment has ever been detected neither for electrons muons neutrons protons nor for a smorgasbord of sensitive nuclei atoms and molecules the bounds are extraordinarily small let me show you some of the most important ones so the electric dipole moment of the tellurium or is it tantalum one of those 205 nucleus is 9 times 7 - 25 centimeters I'll skip to the neutron it's less than 6 times 10 to the minus 26 centimeters now in case that number doesn't mean anything to you decide the neutron size whether measured by its Compton wavelength or its geometric size its charge radius is about 10 to the minus 14th centimeters so we're talking about limits on the redistribution of electric charge within a neutron in response to its spinning which are at less than the part per billion level much less so in terms of that theta parameter which would directly induce electric dipole moments we're led to conclude that the absolute value of theta is less than 10 to the minus 10th that is a naturally problem if you have no good explanation of why it shouldn't be of order unity and in fact it's 10 to the minus 10th that's quite a coincidence is it a coincidence I think not over the past 40 years there have been several attempts to address this so-called coincidence or parent coincidence or not coincidence but only one has stood the test of time it involves introducing a new fundamental principle a new symmetry into our core theories called patch a quin symmetry after the physicists who first thought about it which is spontaneously broken now an accurate description of what this symmetry is and it's breaking would require a long technical exposition and I'm not going to do that in this colloquium but very roughly speaking what that the outcome of the theory is that one promotes the numerical parameter theta which was just a coupling constant a parameter of fundamental physics in the standard model as it comes after you supplement things with this extra symmetry the theta parameter becomes a dynamical field something depends on space and time for end has dynamical equations and it turns out that this dynamical field can and if you set things up in a reasonably simple way it wants to relax to zero so dynamics favors close to a zero value for this parameter and that explains the smallness of the observed theta now the most striking consequence of this proposal is the emergence of a new kind of particle this gives us something to chew on to shoot at to take these ideas from virtual reality into augmented reality which I named I named it the acción in homage to a laundry detergent the people doubted this story but I have evidence when I was a teenager that wasn't much more than a teenager when I developed this theory the that matter I'm not that much more of a teenager not than a teen in yeah I had noticed in the supermarket a laundry detergent named accion and I said gee that sounds like a particle and if I ever get the chance I'm going to name a particle after that laundry detergent and a few years later I got the chance and I said well you know it's it's erasing a stain from the standard model why not and I managed to sneak it past the editors of Physical Review Letters and that's that stuck so accion's are basically the quanta of this theta of X and T field so they're very close to the foundation of this solution of the of the of the T problem the effective theory governing the mass and interactions of accion's contains one main parameter which is a mass scale usually called F phenomenologically it's a very large mass scale greater than 10 to the ninth proton masses they're also to be honest a handful of discrete parameters that affect details of the accion's coupling to matter but to a first approximation the key facts about accion's are that they're very very light scalar particles the mass is 100 MeV squared divided by F but F remember was very large 100 MeV comes from QCD scale and if F is a kind of typical value 10 to the twelfth GeV the mass of the acción is 10 to the minus 5 electron volts which is smaller than the mass of any other particle that has nonzero mass except possibly for one of the neutrinos and accion couplings are proportional to 1 divided by F this means since F is very very large by normal particle physics standards accion's interact very feebly with ordinary matter and with each other since the accident the theory is reasonably definite in terms of this one parameter F one can calculate the predicted cosmological genesis and evolution of accion's through the Big Bang and one predicts in this way the presence of an accion background very roughly analogous to the microwave photon background which is also produced in the early universe through other interactions and interact in an equilibrium at high temperature but different in crucial respects first of all it's not a blackbody distribution of photons in fact it's a or at least starts out as a bose condensate very very cold of feebly interacting nonrelativistic particles that's a dramatic way of just of talking about a classical scalar field the gravitational influence of the acción background is stronger and it's non gravitational interactions are much weaker much feebler this means if you put it all together and if you analyze it also more carefully quantitatively that the accion background this relic of the early universe is predicted to have properties consistent with the observed properties of what the astronomers have discovered the so-called Dark Matter so the bottom line when you put together the limits the properties and the constraints is that if accion's exists at all they must contribute significantly to the dark matter and since they have to be a lot of it why not speculate that there all of it especially since nobody's found the other stuff other candidate so in recent years several clever strategies for accion searches have emerged and this I think is very exciting and one of the things I hope we can explore and develop further in coming months I should mention that there's going to be an accion workshop and actually on Dark Matter workshop here in a little over a week so here's what one method accion's in the presence of a magnetic field can convert into photons which then you can see with your eyeball so that's that experiment it's a little more sophisticated the electro I told you that actually at the theta term would induce a an electric dipole moment that means a residual theta field that's changing gives you a changing electric dipole moment very small but a very small changing electric dipole moment and this is something you can try to detect through very clever magnetic resonance techniques I won't describe them in detail here another thing is that accion's time in magnetic fields produce electric currents I'll show you that in equations a little later well momentarily and you can try to detect the magnetic field set up by the acción background this is the so-called Kadabra experiment another thing is that accion's can form they're very very light particles so their Compton wavelength is very very large and if their Compton wavelength is large enough they fit the size of a black hole and they can make black hole atmospheres so as we learn more about black holes through gravitational radiation and other probes astronomically we can see if in fact they have no hair or accion here which would change their properties quite a bit finally there's some of this story that's already born experimental fruit in condensed matter systems one finds emergent accion's of course with very different parameters but the same kind the same equations in fact the surface of a topological insulator can be considered as a gas of emergent accion's that is it obeys the same equations as a gas of emergent accion's in this case it's not the color electromagnetic fields but the just plain old electromagnetic fields that are significant and let me show you how the equations you get from this lagrangian they're very simple and canonical looking equations in the context of condensed matter you also predict a quantized value for this kappa parameter and we have many interesting effects it says a magnetic field will induce charge on the surface of such a material this is the effect that I told you the abracadabra experiment is looking for a time-dependent accion field acts as a current that sources other magnetic fields and this is a dramatic transport property of the topological insulators or other materials that have this kind of emergent accion it a an electric field induces a transverse current and I was thrilled to see a few months ago that experiments demonstrate this effect the quantized Faraday and curve rotation so if you shine light through these surfaces there there's a parity and time reversal of a violating effect that the plane of rotation rotates a little bit when it going to goes goes through that's called a Faraday effect when it's reflected that's called the car effect not Kerr it's that's very important this is and here is there an important part of their abstract so it provides evidence for the long-sought accion electrodynamics and topological magneto electric effect and very nicely you can even check the quantization which is a very unusual thing in condensed matter to see quantized properties emerging it's like like in the Josephson effect or the quantum Hall effect there aren't very many examples like that and they this is another one they find that they get a value which is reasonably close to the predicted or the known fine structure constant you could work harder and do better presumably but that's that's I should I say measuring how much little rotations have polarizations have rotated is not as easy as measuring voltages so one shouldn't expect comparable accuracy okay so that's accion's now let me move on to any ons in 2 plus 1 dimensions quantum kinematics allows new possibilities for quantum statistics besides bosons and fermions there are several perspectives on this phenomena that give different kinds of insights into it one is that in two plus one dimensions if you think about the world lines we can think of them as strands in a 3-dimensional space and in two plus one demand in three dimensions strands can get tangled up this is called braiding theory and is the theory behind why people can braid their hair and it doesn't fall apart in higher dimensions braids can always be undone continuously it turns out I'll let you do that thought experiment and so there's no topological distinction that records how much one path as wound around another and a result of that is that the only way to have paths that are to have different ways that to get from the same kind of initial state to a final state that are sensitive to the topology of paths is if you change two identical particles positions if you do permutations and that gives you bosons and fermions but in two dimensions it's much more general you can do all kinds of tangling up and introduce topological interactions so that's the that's one way another way this is the way I first got introduced into this is that if you believe in a spin statistics theorem and realize that in two dimensions the angular momentum algebra is trivial it's just there's no it's abelian there's no non-trivial commutator there's nothing to fix the normalization so angular so you can have a fractional offset in the quantization and you would expect therefore fractional statistics and the most profound way the most useful is the perspective of discrete gauge Theory that's to notice that in two dimensions tubes of flux degenerate into points so they can be a so flux can be associated with particles magnetic flux can be associated with particles which means that you can have our no-foam effects that is effects that occur without any magnetic field but just with potentials that give quantum mechanical phases as one particle goes around another and this construction supports either a billion or not a billion interactions and also doesn't require that the particles be identical you can have funny quantum phases between different kinds of particles so particles that partake of these new possibilities are called any ons i introduced that name to suggest anything goes in two dimensions in both in three dimensions or more it turns out there are bosons and fermions are basically the only consistent possibilities but in condensed matter systems two dimensional system two dimensions are very common you can freeze out motion in the third dimension in fact of course most of micro electronics is based on two-dimensional chips so any ons arise in nature not only as these mathematical possibilities in virtual reality but as in augmented reality in our conception of the world as elementary excitations or quasi particles in highly entangled quantum states of matter they are in fact defects in the pattern of entanglement so you can think of the different spins say in a system having an entangled wavefunction and if you have defects in the pattern of the entanglement if there's a non-trivial n't of pattern in the ground state you can have defects in it and those turn out if you imagine rotating one defect around another things can get even more tangled up and that would give you additional phases or even non-abelian effects so there's a memory of the motion like it's imprinted on the wavefunction and that's the source of any on behavior in the world now typically the effect in truce by an electron is larger than the most basic defect in these states bigger it's more than the quantum of disturbance and therefore electrons can fishin into several of the more basic defects which are any ons logically because they have fractions of the electrons statistics of its effect on the wave on the wave function as as you move them around for the electrons this can be a shattering experience that's a joke sure but here and here's a picture of it the electron is getting pierced by a flux tube but the reoffer result from this process emerge with brilliant new powers now there now they have memories and it may be possible to exploit the memory possibilities of any odds to do useful quantum information processing and that's that's a very lively interesting subject but I hope I've intrigued you with Bert Halperin recently in his Lisa Meisner lecture here talked quite a bit about this quasi particles in many fractional quantum Hall effect states are firmly predicted to be any ons there's also good numerical evidence for it and many experimental confirmations of the underlying theory so there's no doubt among theorists that quasiparticles in many many fractional quantum Hall states are any odds of different kinds but direct experimental tests have proved difficult because the anions are usually electrically charged they are all kinds of practical problems which I'll just flash it may be possible to overcome them they're practical not fundamental and people are working hard to try to overcome them and there are other ways of accessing some of the same behavior but here I want to discuss a new radically different possibility that has got me excited recently so this is a lot more to say about any ons but I have to be selective and but I just want to whet your appetite so to speak ok so it is widely expected based on solvable models and numerical work that several two-dimensional insulators should exhibit what are called spin liquid phases spin liquid is not a well-defined concept presently different different people mean different things by it the basic idea is that if you have a system that has electrons that don't move but they could still have spin degrees of freedom so these spins spins can move around if the spins are frozen like in a ferromagnet or an anti ferromagnetic that's a solid then they don't move if you're at high temperatures and they move freely that's a spin gas and in between if there are other phases that you don't know how to talk about that spin work words that's the rough definition the percent the precise definition is a little less vague but as I said not universally agreed upon but the qualitative features include formation of a gap in the energy spectrum although some people also talk about gapless spin liquids high degrees of entanglement and absence of a local order parameter so phases that structure that's quantum mechanical therefore not visible as in ferromagnets or antiferromagnets but you can tell something is going on because there are phase transitions and maybe some other subtle signals several candidates spin liquids support any onic excitations this is known from numerical work in theory that feature provides in principle and exotically beautiful signature of the phase you just look at the material and work and see if it has any ons but how do you do that that's been very problematic in the quantum Hall effect as I mentioned but in spin liquids we have a big advantage that the any ons are electrically neutral so all those problems I mentioned don't really come up and I think there's a quite specific beautiful thing that one can isolate that that that that will nail this the orbital angular momentum associated with a new channel if you start to produce new kinds of any on anti any on pairs or to has a direct quantitative or other pairs of excitations with any ionic properties has a direct quantitative effect on the near threshold behavior this is simple basic quantum mechanics going back to Eugene Victor and nuclear physics if you open up a new channel so you barely have enough energy to produce these new kinds of particles in a collision centrifugal barriers can thin out the wavefunction you have very very little momentum the wave functions very spread out and centrifugal barriers really spread it out so they introduce a suppression near the origin and that shows up directly in the behavior of the cross-section near your threshold so I'll just give you a qualitative idea if you have fermions there's a suppression because the minimum angular momentum you can have for two identical fermions is is one for bosons there's no such depression so the cross-section sets right in you have symmetric wave functions no suppression zero angular momentum is allowed if there's a hardcore repulsion you get a suppression right at zero momentum but it shoots back up if you have particles that have half the statistics of an electron so called semi ins so when you move one around the other you get all the way you get a minus sign not just half way then then the allowed angular momentum is half integer and you get in between behavior and experimentalists I think should be able to tell the difference among these things and that will be a very direct signature that one can aspire to see these effects in neutron scattering and also in point contact tunneling I expect that the threshold spectroscopy of quantum statistics that this this indicates will evolve rapidly from a demonstration of the existence of any ons to a tool for figuring out the behavior of these spin liquids and distinguishing one from another okay so much for any ons now I'd like to talk about entangled histories I experimental physicists are achieving new levels of control over the production and manipulation of entanglement much of this effort is inspired by the vision of quantum computing but quantum computing is very difficult it's going to be a long time probably before we have general-purpose useful quantum computers however a lot of work a lot of money is going into this new capabilities are being discovered along the way and it could be fruitful to consider what other benefits we can get from these new abilities to manipulate quantum variables very delicately so in that spirit I'd like to revisit some very basic aspects of quantum theory and measurement it this will turn out to lead us to an enriched concept of what history means in quantum theory so from the perspective of quantum theory interference arises from the possibility of getting to the same final state through several distinct paths if you if that's possible then according to the rules of quantum mechanics you're supposed to add the amplitudes and then Square as opposed to just adding the separate probabilities which are the squares of the amplitude so I'll insult your sophistication by actually showing the equation so the total probability is not the sum of the probabilities if the processes can both contribute with the same initial and final States but for interference to occur the final state of the whole universe including measuring devices and the external world must be consistent with either of the two contributing processes having occurred and this I think for a long time has blocked people thinking about measuring histories and quantum mechanics because if you want to measure interference it's crucial to maintain or create ambiguity among different paths I call the strategic in ignorant and to get to histories to interfere we need to make sure the final state of the world including the final state of the measuring apparatus does not allow us to distinguish which happened but if we hope to measure observables that basic requirement that the different possibilities can't be distinguishable runs into tension with the idea that measurement disturbs or collapses the wavefunction of the system being observed if it collapses the wavefunction when you make a measurement then that definitely affects subsequent measurements and you don't get histories you just get the state at one so to get around this difficulty we can correlate auxiliary bits with the system sequence of states without disturbing its evolution uncontrollably in this way we can monitor but not measure the system's behavior and then later if we want to actually make a measurement we can operate on the auxiliary built spits with great flexibility let me let me show you an example that these words are very abstract so let's look at the classic two slit experiment and we imagine monitor bits the one behind each of the two slits which are going to monitor but not measure where the photon went in the following way they're set to down initially and then if a photon comes through that slit they flip to up now that's not a measurement that can be a unitary operation it's the kind of thing that people in quantum computing call call a see not operation and is a very simple gate compared to what you need to do full-scale quantum computing so here's the kind of monitoring if you start with down and the photon goes through it switches to up if you start with down the photon doesn't go through it stays down this can be an extended to a unitary operator if you have also these things and that makes what's called a control not okay you flip the spin if and only if the control bit is yes and here's a picture of it now so we have I'm sorry go back to the picture just for definition purposes so we have a monitor bit m1 up here and m2 down here so if we measure the Z spin of m1 after this process we learn which slit the particle went through and there's no interference we get D 1 squared or D 2 squared depending on whether the spin was up or down however if we measure the total spin of M 1 at plus M 2 it's quite different when spin 1 appears as the total spin that means we're in the symmetric state and we get interference with D 1 plus D 2 squared if spin 0 appears we're in the anti-symmetric state and D 1 minus D 2 squared appears we can also consider more involved measurements of course we can shift the relative phase and so we don't have to measure either Z spin or total spin we can measure all kinds of things we can also do things in the opposite order we can measure the position where the photon lands before investigating those monitor bits and make predictions about what the monitor bits are likely to do we can compute their density matrix I'll leave it as an exercise for you in Bayesian statistics to figure out the density matrix given that gives those results there it is okay so to me this gives a very nice perspective and explication of the foundational strangeness of quantum mechanics that you can change the course change in a certain sense the behavior of what the electrons are doing based on what you do to the spins later or vice versa now we can apply the same procedure conceptually to monitor aspects of assistants behavior at different times that is its history if the top slit was one time in the bottom so that was another time turn it on its side that's that's the that's the idea so if we consider for instance something as simple as a spin 1/2 particle we can monitor but not measure chosen components of its spin at several times and later make measurements on the monitor bit to get information about what happened let's see how this works concretely I will in view of the time I will forego the definitions such as they are and go right to an example so suppose we want to measure two formal objects at this point it would be hubris to call them observables because I want to don't haven't told you how to observe them but I will and they are of the form you measure some opera you have an operator at some time t2 and an operator at some time t1 and you want to apply that to the system so these are historical or temporal observables because they depend on the properties at two different times and those operators commute even though at the separate times the things don't commute the Sigma is anti commute Sigma 2 and Sigma 1 at time t2 anti commute as do Sigma 1 and Sigma 3 at time t1 but the product of both of them commute so you can measure them jointly if they really are applied as coherent objects and you can figure out what their eigen history is what it is if you measure if you measure say that the expectation the result of measuring both of these is one that's the eigenvalue you get and if you do that you find that the history that corresponds to measuring plus for both these variables they can obviously be either plus or minus because they square to 1 if you measure plus for both of them that corresponds to this history so it says either at time t1 you had spin up and then it stayed up or you had spin up and it's been down with equal weight or with weight all you have these kinds of flipping this is an entangled history it tells us what we know about the state of the world or what happened I should say after we measure plus plus on those auxiliary bits on those monitor bits and it's a remarkable object despite its simplicity you can compute with it but I'm not going to belabor that in view of the time let me well actually I will just I'll do it just won't spend a lot of time on it but I want to say that if you so you can calculate given an initial spin that you don't disturb it with that could be in any direction and you don't disturb its dynamics but just monitor it and later measure what its possible histories are you can measure the probabilities that different historical patterns occurred so it's not it's it's not just talk it's not just baloney it's not just you know interpretation of quantum mechanics this is something you can actually concretely calculate with and and test if you can measure these kinds of observables so how would you go about measuring observables like a and B the key is to set up a pro it's very much like the two-slit experiment turned on its side as I anticipated that's why I told you about it the key is to set up appropriate monitor bits and measure them judiciously so to measure a we set up a monitor bit for spin in the X direction at time t1 it's a sigma x and they monitor bit in the y direction at time t2 and then we measure neither one of those but only the joint product which in computer YZ is a not X or ok if both of them are up it's it's one or both them down it's one but if one is up and one is down it's zero minus one actually and similarly to measure B do a similar kind of thing with the appropriate changes of direction so that's how you measure those things they are very concrete procedures they do rely on being able to construct these sophisticated quantum gates but if you have that ability it's simple and straightforward so in general the eigenstates of temporal observables are entangled histories as we saw already in that simple example and therefore when we measure the value of such observables we often discover facts about the past of our system that can't be summarized can't be captured by saying that it had a specific temporal sequence of properties or States it has to have these kinds of entangled histories where different things might have happened at intermediate times that can't be just a product of States rather what we infer is that it had a parallel evolution through several distinct sequences of properties or to put it more dramatically several distinct histories or worlds diverged but later came together so entangled histories as far as I'm concerned are a precise tangible mathematical reflection of the intuitive many-worlds interpretation of quantum theory but they have math behind them in experiments and protocols so to make temporal entanglement observable as a practical matter we should focus on very small worlds that haven't diverged very much and then make them interfere so that you can show that they both existed simultaneously we can do that using small numbers of monitor bits as I sketched above or the way I'd like to put it is we can nurture strutting your kitten's short of Schrodinger Katz and shorten your kittens are much cuter then we're fun and more manageable and you can actually get them to do what you want okay so let me make a conclusion I hope I've intrigued you with some of these ideas and conclusion I certainly feel justified in drawing is that creative physics allows us to get beyond everyday reality we get to consider very very interesting ideas about fundamentals about the whole universe it's really fun to entertain such thoughts to entertain virtual realities that go beyond everyday reality but to me it takes on a different level and I see much of my mission in life as going from virtual reality to augmented reality to take those ideas into things that you actually can and do observe so thank you very much and hi Oh okay we have time for questions would like to start then I warm up okay ah well they were originally well they originally introduced on their own but they were there was thought to be a possible application to the cooperate superconductors when very little was known about the cooperate superconductors and I think we can say with complete confidence that the cooperate superconductors are not described by the theory called any on superconductivity but I don't think that's the end of the story just a few weeks ago I learned that experimentalists in cold atom physics are trying to set up the Hamiltonians that were used in the theory of any on superconductors as and realize them in cold item systems and if they do that they will in fact observe any on superconductivity so so we'll see it wasn't entirely wasted effort I hope yes [Music] well it's the mature version of this is not yet in print so not really there are some there are there is a an experiment that does a version of entangled histories using using optics that's kind of clumsy but as used to illustrate the the principles so there is an experiment but not quite an ideal illustration of this dynamics but it'll I don't think these experiments are terribly difficult once you know what you're doing and would be great fun I think even the two-slit experiment would take that very familiar phenomenon in into very into interesting directions you know make it much more dramatic the different possibilities because you can you can choose whether to make them interfere or not later and and see that what you measure for the spins much later affects what happened to the electron very cool the problems that the successful experiments or the kind of history well they're not experimental problems there I mean a lot a philosophical problem their philosophical insight that's the way the world works and let me make a general comment ok I just can't just leave it at that I guess the people talk about many-worlds interpretation and and things like that very loosely ok they talk about reality the reality of these of these many worlds but you know some things are more real than others I guess some things that are very remote from any observational consequence those are virtual reality and that's fine virtual reality is great fun but it's not the same as augmented reality where you actually get to sense it and observe it and interact with it and to me augmented reality is special so if you like many worlds as a virtual reality concept and like to spring them that's that's that's that can enrich your experience of existence that's fine but it's a separate thing from pointing out concrete experiments and measurements that are illuminated by this concept of entangled histories which to me is the mathematically precise thing that many world is trying to capture would you go back and say to Maxwell and Newtonian as a resume of you talked about T reversibility that they would understand well you could point okay you could point to the equations F equals MA and as long as F obeys very general conditions that Newton had in his law of gravity and many other things that he thought about that they depend only on positions for instance then then the equation is time reversal invariant if you change T 2 minus T you get exactly the same equation so if you take a configuration and we and run it or reverse all the velocities and run it that and then reverse the velocities run it backwards you get what you started with so that's a very remarkable property that was in the laws and similarly the laws of electromagnetics are like that it's more subtle which makes it more interesting because in Maxwell's equations if you want if you want to display the time reversal symmetry you well there are two things but let me comment on the first first at the level of the cleaned-up Maxwell equations with just ease and B's and no ages or conductivity and so forth then you have to change the sign of the current and not change the sign of the charge and change the sign of the magnetic field but not the electric field but if you do those things and change the sign of time the content of the equations doesn't change so that's a very non-trivial property the Maxwell equations when you do put in [Music] phenomenological effects like finite conductivity it's not time reversal symmetry and any anymore and I don't know I haven't seen it explicitly in Maxwell's writings but clearly he was very aware of the fact that conductivity is associated with dissipative processes associated with things there maybe not so fundamental so it was an instinctive at least understanding of time reversal symmetry although I don't think he I don't know that he brought it out explicitly I would love to be corrected on that or but I somewhat of a student of Maxwell I've never seen it okay and of course general relativity also allows T goes to minus T quantum electrodynamics so it wasn't and there there were consequences derived in atomic physics especially by Eugene Wigner Jean Viktor was a real hero of understanding symmetry in quantum mechanics that were verified absence of electric dipole moments in nuclei he pointed out I believe was a consequence but I'm not sure where I'm going with this but yeah it's an interesting subject it's been very fruitful as of course in a previous incarnation the study of parity symmetry spacial parity as opposed to time parity and it's breaking proved to be a major wedge into getting fundamental understanding of the weak interactions and in fact of all interactions so studying these symmetries and their breaking is is quite has been quite fruitful and I I think will continue to be at least one more big episode contraction was rather small this kind of tabletop experiment bonus or not uh well if you have a big enough table no they'll be here and describing it but I think it's like ten meet no it's big it's ten meters well the bigger the better I guess and so there you have to balance practicality versus sensitivity so it's also matter of you know what they can get people to pay for yes the ratio yes yes there's a much worse in the sense of - ah not many are worse than 10 the Vitis 10 I don't the cosmological constant is yes that's right but that's the only one well we take care about 10 to the minus 10 because it's much less than one you don't have to care okay this is uh I can't force you to care but it's an opportunity okay and yeah I would love to understand why the electron mass is so unnaturally small I mean in this precise sense that it's connected in the standard model with the okawa coupling that's about one in a million ten minus six and if I had a good idea about that I'd be happy to tell you about it but I don't and as far as I know nobody does have a good idea about this so you pursue these clues and some of them turn out to be fruitful and some of them don't you know and but an example of one that turned out to be very fruitful was the equivalence principle people found this unnatural match between gravitational and inertial mass another was parity violation really if you think about it people found that parity violation was only in the weak interactions I was kind of unnatural but unraveling that but to a very rich an insightful story so maybe you should say something about this accion workshop coming up which you mentioned well Sebastian here is the Sebastian bound is the hero of this baby could use to say a few words about what what's happening behind it and also the experiments that are currently running and build that look for accion's and specifically accents if they make up more effective matter so the workshop will be in roughly ten days we'll start a summer trip and run until December 8 of course Frank is one of the organizers so one of the angels worship is also to get people from here excited nak sealants and to facilitate that on the first day you will have some of more introductory talks the Monday December 5th that are supposed to be accessible for all audience or physicists and also the OVC colloquium will be on that we will be on Monday in fact instead of Tuesday and will be a talk by PS fev1 of D heroes of accion's - about how to find dark matter exits Thank You Stella final question some seem to be the case then you're all invited to reception outside the restaurant to celebrate the Franks [Applause]

Channel: Fysikum Stockholm University

Views: 24,282

Rating: 4.9127274 out of 5

Keywords: Frank Wilczek, axions, anyons, entanglement

Id: Fq58uv6UxCk

Length: 70min 26sec (4226 seconds)

Published: Fri Dec 02 2016