Frank Wilczek - “Symmetries of Time”

it's my great honor today to be able to host this English scientist prank website and to give her opium today Frank it's Easter where'd you study at MIT and then didn't know Chicago Chicago a student at Kingston and during his thesis work he made a major discovery in physics namely the asymptotic freedom of the strong attraction which eventually earned him the Nobel Prize for Physics in since then he became a professor in Santa Barbara where I first met Frank when I was a postdoc and then it's Princeton you may know this book called Co God Einstein's office Frank was working at CERN Institute for destiny he didn't I just asking he didn't get a chance opposite but he got something better because Einstein stopped recently you may have seen there's a TV series for genius and they film the Einstein the story of my Spanish - knocks that stuff Frankie's to live and now he is simultaneously Professor X for different places and for those who are you students put on the list and professor at Nadia and Stockholm in Sweden professor at Arizona and very recently he became the founding director of the Peabody Institute in Jakarta and frankly is really beside his distinguished by Prize winning work on strong faction he made contribution to almost all branches of physics in astrophysics fundamental particle physics condensed matter physics one of the convention of the concept of any arm which was first realized in Compton effect but there recently the topic he will talk about today from an crystal is realized in am whole experiment Frank later thank you well thank you it's it's really inspiring to be here at Stanford where are so many ideas better extremely significant and provocative and lucrative half originated and have to see so many friends and I've had very interesting conversations in the last couple of days and I look forward to more over the coming week so my topic today is symmetries of time time is a central element of physics we can't live without it and I think it's fair to say that outside of physics people don't think of time as a material they think of it as kind of a sequence of psychological events that has some kind of loose structure but in physics we can talk about time as a thing and we can talk about that thing having properties and it's been very important certainly in my career to think about the symmetries of time and that's what I'd like to talk with you about today so I'll talk about some older work about the symmetries of time some present work ongoing work it's still exciting and I think and the best is yet to come and it's appropriate in a discussion of time to talk about past present and future so the first symmetry of time I want to talk about is time reversal symmetry also called T this is a classic subject that in my self-serving point of view it's the whole point of it is to lead to axioms so 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 it does not look like everyday life the second law of thermodynamics famously captures this idea that entropy increases doesn't decrease and here's an experiment showing that if you run a movie backwards it doesn't look like everyday life of course this one doesn't exactly look like everyday life even if you run forwards but even less does it look like everyday life if you run it backwards yet it'll Bay's the laws of physics to a very very high accuracy if you've looked back at the atoms they're all moving in accordance with micro physical laws do you find a very peculiar initial state with the ground shaking and dust on the ground for no particular reason then it all comes together and makes sense and the energy that it takes to lift all this stuff you've learned came from liberation of chemical energy and a building so macroscopic time reversal is not and in everyday life time reversal symmetry is just not a feature of experience yet somewhat paradoxically and even problematically time reversal symmetry was a notable property of the fundamental laws of physics for several centuries starting with Newtonian mechanics where you meet second derivatives of with respect to time so you can change the sign and continuing through general relativity and quantum electrodynamics they all have time reversal of symmetry why why do you have this gratuitous symmetry that is not necessary to describe experience and yet has featured in the laws of physics as long as T symmetry appeared to be an exact fundamental feature of physical laws it was unclear that asking that question would be fruitful you can always keep asking why any of you who've dealt with a small child know that they'll keep asking why why is the sky blue and you start to talk about scattering of light and atoms and then they ask why of Maxwell's equations and quantum mechanics asy and well you say string theory and then they ask why and they say and at some point you just have to say that's just the way it is that's rock bottom and if t symmetry were an exact feature of the fundamental laws that would have been a sensible answer that's just the way it is okay it's a very elegant principle sort of thing you might like to have in the fundamental laws of danger it just might have been rock bottom however that answer became inadequate in 1964 when James Cronin and Val Fitch discovered a subtle effect in the decay in the decay of K maisons that slightly violates t symmetry now actually for purists they found an effect that violates CP symmetry combining charge conjugation and parity but there are very profound reasons to believe that cpt symmetry is an exact law of nature so this could also be interpreted as violation of T symmetry and in the intervening years there have been experiments that directly show violation of T symmetry so T symmetry is not rock bottom and it's not even quite true just very nearly so in practical circumstances why well this was a profound question and the satisfying answer is that we've almost nailed it I should say the almost satisfying answer is that we've almost nailed it the basic sacred principles of modern physics relativity plus quantum mechanics and sorry Lenny local symmetry are very powerful and when you combine all of them you find very powerful constraints very strong constraints on the laws of nature and what kobayashi and maskawa taught us in the context of the standard model which is our instantiation of these principles is that when you have the particles we actually have with the the color and flavor and weak and electromagnetic charges they have there are exactly two possible sources of T violation there are exactly two interactions which could give you T symmetry violation one of them which is the one that kobayashi and maskawa actually identified arises when you have three families of quarks and it beautifully explains what Cronin and Fitch observed and by now a lot more starting with the prediction that there are three families but going on now that the the study of heavy maisons and quarks has it advanced to describe quantitatively a raft of experimental results it's been extraordinarily fruitful and kobayashi and maskawa deservedly won a Nobel Prize for their very profound but simple suggestion but they didn't realize that there was another possible T violating interaction this is much more subtle it's not visible in perturbation theory and it doesn't happen to very good approximation it would represent a interaction between gluons in the in in QCD which is like an e dot B interaction is the analog of e dot d you don't see e dot B very much in discussions of Maxwell's equations because it doesn't contribute to the classical equations of motion and so you don't have to worry about it for most purposes but in QCD it's very different when you quantize the theory you find that this a dot B interaction does play a role and it is directly violating parity and time reversal symmetry because E is natural and B is unnatural under time reversal so Y is still open we have a question why it is that interaction so small allowed by the sacred principles we explained everything else in terms of them why not why is that still a loophole over the past 40 plus years since this became evident there have been several attempts to explain it but only one has stood the test of time little joke there and the idea is can be explained non mathematically quite simply it's basically due to Roberto Pesci and Helen Quinn the idea is to promote the unwanted term which appears as a number in the standard model as it comes into a dynamical entity so you have a coupling constant G which is supposed to be outside of time a universal eternal feature of the world and say no that's an illusion it's really G of X and T it's something that can variant it's a field like other entities within the standard model the new kind of field and if it's a field and the dynamics is right you could hope that the dynamics drives it to zero and then you'd have a theory of evolution that tells you why that interaction is not present now what Steven Weinberg and I added to this is to realize that this fix comes with a price or it comes with an experimental bonus if you like a kind of phenomenologically testable consequence this new field like all quantum fields is made out of a new kind of particle it's a particle I named the acción in homage to a laundry detergent it was a little story there I'll tell I mean when I was a teenager I went shopping one time with my mother to get groceries and there on the shelves with his accion laundry did and already at that time I was thinking to the you know I was gonna maybe be a physicist and if I ever got a chain that sounded like a part of it's really it's it's Greek it's soft it's short it's got the that the hard sound and everything else perfect for a particle and I vowed that if I ever got a chance I would name a particle back see on and I got the chance because this is a particle that cleans up that was appropriate because it's a particle that cleans up a problem with an axial current and it turns out and I could I told the editors of Physical Review Letters who were very conservative about naming things that it was because it has to do an axial current I didn't didn't tell them about the detergent but there's here's the application it's a true story and there's the evidence okay so do these accion's exist we still don't know for sure but what's happened in recent years is that the stakes have risen dramatically we can calculate that accion's to do their job have to have very specific properties and that they would get produced in the Big Bang and survive to this day they're very very weakly interacting very light particles that you can calculate how they could produce you can calculate how they interact with matter very weakly and they survive to this day the relic accion gas has properties that are consistent with the observed properties that the astronomers Dark Matter astronomy and cosmology I'm sure you've heard at many colloquia has this nagging problem that gravity as as reflected in the motion of bodies we can see is too large to be accounted for by the gravity of bodies that we do see and so astronomers and cosmologists have been led to postulate that there's a new kind of matter some kind of dark matter it's not dark it's just transparent and over the years they've discovered various properties of this matter but basically its properties are that it doesn't interact significantly with ordinary matter and it's produced as a cold particle in the early universe and then just follow that II and then you get the right kind of phenomenology and I should add that phenomenology that shows that assuming a new kind of particle that's produced cold and the big bang has recently been shown to give extraordinarily accurate results for the structure of the universe there were various advertised problems about cusps and satellite galaxies there are no problems so here's the kind of evidence for dark matter that got the stories that story started the rotation curves of visible objects at the outskirts of galaxies if the matter just tracked the visible light would fall off as you receded from where Maher whilst most of the visible matter is but in fact it doesn't and you can account for the observations if you have distributed around the galaxy a large halo of this non-interacting but still gravitating stuff I said you can find this around the galaxy but it would be more accurate to say that the galaxy is an impurity in the dark matter because the dark matter weighs about six times as much here's a beautiful well there's evidence for this dark matter on many different scales if you say that you have a theory of of this phenomenon you there's a lot to account for and this hypothesis of a new particle accounts for at all another kind of evidence is gravitational lensing or again you find the bending of light that you observe is too large to be accounted for by the gravity of the of the visible matter you observe okay so the bottom line after a lengthy analysis of what happens in the early universe and how accion's get produced is that if they exist at all they must contribute significantly to the dark matter and plausibly they dominate it because it's not so easy to become like to have good guesses or what the dark matter is this is something we need and it's a bonus several clever strategies for accion detection have emerged it's not easy part of being the dark matter is that it has to interact very very weakly with ordinary matter and that's what the theory predicts and it won't be easy but many determined people are at work here is a photo from the Center for accion and precision physics in South Korea which is of one of several very well-funded very determined groups doing accion searches this is the basic strategy for their experiment with an artist rendition or my rendition this is my closest approach to heart so you have accion's floating all around in the universe once in a while very rarely if you have a magnetic field there's a basic vertex a basic Kleinman graph if you like where in accion couples to two photons if you have a magnetic field the present the acción can convert to a photon and you know how to observe photons these are actually microwave photons but okay mm-hmm here's another very ingenious proposal this is called abracadabra and I used it I use it basically cuz it's a pretty picture that's another proposal to set up a magnetic field you suck you this time on a much larger scale when you have time dependent accion's they produce effective current interacting in the electric field they also produce a magnetic field they also produce effective fields which will generate AC magnetic fields which you can detect with very sensitively with squids so they're very ingenious proposals I won't try to do them justice here suddenly several of them have come out of Stanford in fact another one is that accion's can form atmospheres around black holes you may have read the propaganda that black holes have no hair but there are certain kinds of things that accion that black holes can have is hair and accion's are one of them if the acción Compton wavelength is comparable to the size of the black hole then due to quantum mechanical effects that doesn't get sucked in can gets produced if the black hole is spinning gets produced spontaneously and forms an atmosphere and this can modify the properties of black holes modify the gravitational radiation when black holes collide or just when they're moving around and now that the era of gravitational wave astronomy is well launched we can look forward to tests of whether these atmospheres in fact exist so a Spectre is haunting physics the specter of accion's they're out there the truth is out there and you shouldn't think of it as scary though because they are restoring the balance between the past and the future and it would be a beautiful end or beautiful climax to this story of T violation that has had this been fascinating very fruitful history if it totally unexpectedly led us to an explanation of what the dark matter is ok so now I'd like to turn to the other main symmetry of time which is time translation symmetry call it tau and here the road that is not to accion's but to time crystals that's where one road leads so time translation symmetry may be the most fundamental symmetry of all it says that the basic laws of nature don't change as a function of time it's without that we wouldn't have science in a recognizable form we need to be able to do experiments and get the same results if the next day also in the neighboring lab and so those those time translation and translation symmetries are extremely profound and basic to the success of the scientific method strangely enough it doesn't seem to have a less than seven syllable name time translation symmetry so I'm giving it one towel I ran out of laundry detergents so tau is the principle which instructs us we can discover eternal laws and it's connected through neuro serum through I mean earthers theorems to the conservation of energy so pretty basic now there's a now modern physicists when they hear about a symmetry you want to also hear about its breaking and it's spontaneous breaking spontaneous breaking of spatial symmetry spatial translation symmetry is commonplace and in fact really was the first non-trivial instance of symmetry and it's breaking to be studied powerfully in physics and mathematics indeed most common materials like to form crystals at low temperatures and spontaneously will go into the crystalline state at low temperatures where the symmetry of spatial translations is reduced to a discrete subgroup if you move the crystal a little bit it doesn't look quite the same until you've displaced each atom to its nearest neighbor so physicists are accustomed to making analogies and connections between space and time and so it seems very natural to ask whether there are states of matter that correspond to time crystals what would that mean it would mean this is a spatial crystal you have orderly arrangements of atoms in space a time crystal would be an orderly arrangement of events in time that some material would spontaneously fall into a beating heart is a sort of time crystal it's the beat is a event that's periodic in time but it's not very precise that requires feeding and maintenance and it's complicated for physics if we want something that deserves the name spontaneous symmetry breaking there are more technical requirements that address these kinds of questions and a time crystal in the sense of physics should be precise should not require feeding and maintenance and ideally should be simple so we can characterize it completely so that it gives us the question can tile be broken spontaneously this turns out to be quite a subtle question when I first proposed it I got a lot of flack about it it's a subtle question so I'll give them that much but it's recently borne fruit the answer is yes and if you don't believe me this is the announcement in science alert a little over a year ago the credibility somewhat undermined because this picture has absolutely nothing to do with the discovery a nicer I mean a more dignified although still extremely fanciful announcement was made on the cover of nature and less than a year ago where this in this in this issue which I have framed right next to the axiom they were two experiments that announce the existence of time crystals plus a news feature plus a news and views plus a cover it was quite an issue of nature and inside they have a description of how to create a time crystal which is at an appropriate level for a colloquium so I shamelessly stealing it so basically they're different there are several different variants now this is the simplest with just two states I should say that these time crystals are not breaking of Spawn taint of continuous time translation symmetry they are systems that are subject to a periodic disturbance but the physical behavior doesn't reflect that periodicity it reflects a longer period isset II and in the written some of the original experiments was a factor of two and others it's three by now many other numbers have been realized so basically the phenomenon is as follows if you have a non interacting set of spins and flip their spins with the flipped them with the appropriate pulses you can get them to go up and down and up and down and if they start off with if if they're if you apply the wrong frequency or if they're not perfectly aligned then that order will go away after a while and you'll have normal equilibration so however what's observed in the time crystals is as a result of interactions this pattern of up and down which would be ideal would happen for the ideal frequency and alignment actually doesn't go away completely even when you have the wrong frequency and an or random state to begin with so and this this kind of rigidity against frequency and this long-range order is for physicists the hallmark of spontaneous symmetry breaking to do this you have to have both interactions between the spins so that they want to behave all together so ferromagnetic or anti ferromagnetic will also work and you have to have disorder so that they can synchronize you have to have diverge a range of possible frequencies they can all agree on the disorder allows them to do that and with those two basic ingredients you can you can get time crystals and one of the experiments this was done by carefully arranged arrays of small numbers of atoms with carefully timed pulses of lasers in the other it was much more naturalistic it was in what's called nitrogen vacancies in in diamond and yet you still get this kind of behavior in a much more natural setting so the implication of this is that there's a structured equilibrium that you disturb this system but if the disturbance doesn't result just in heating it up or in a unique equilibrium that the equilibrium is structured and can oscillate between two different possibilities and to me this is the really beautiful thing for a phaser physicist when you talk about new phases of matter you want to know what's the phase diagram and here as a function of detuning and interaction you see that they're sharp phase transitions between the time crystal behavior and not drawing crystal behavior so the big picture is that the study of tau breaking is revealing shortcomings in the hitherto conventional view of equilibrium nodal e notably including the emergence of robust self-organized quantum structures and noisy randomized systems and if you haven't had colloquia devoted to the details of these experiments you really should because they're very beautiful and there's much more to it than I've tried to convey here usually technological developments take a long time to come to market but in the case the time crystals it's been remarkably fast in fact a causal you can buy time crystals on the internet and they're used by Doctor Who to travel backwards and forwards in time okay so that's a very interesting branch of many body physics and I've just shown you the tip of the iceberg and it's a growing subject there have been dozens of papers since those original ones last year many of them experimental but I'd like to put a take things in a slightly different direction here and talk about a different kind of time crystal if you like but something I find quite fascinating this is ongoing work mechanical time crystals these are simply dynamical systems that want to move either in their ground state or in any state depending and in different examples so the kind of systems are very simple their ring molecules or let me let me not say ring molecules at the huh their collections of spins and of them and we assume that they close up to make zero now this I want to get into technicalities this can be imposed either as a constraint or as just a selection principle on solutions and you get different pictures depending on which you do but let me just fudge those questions so as a spin system you can take it as it stands however if you interpret these unit vectors as positions in space this can be an interesting very unconventional model of ring molecules why is it unconventional it's unconventional because usually when you do the mechanics of ring molecules you would introduce for every rod not only its position but also its velocity but for spins you don't do that it's just a spin so this is more minimal you use only the position coordinates to describe the dynamics and the result of the analysis is that generically under very general circumstances if you have the coefficients here unless there varies very specially tuned you'll get motion in the ground state this is a kind of emergent precession the different spins make effective fields and they can make an effective and they'll all process around the emergent effective field as well as wobbling so here at the equation these are the only equations I have I think in this let's talk the crucial thing is that plus own bracket is not the conventional Poisson bracket these are not P's and Q's they're spins or if you like one component of spin becomes the canonical conjugate of another so it's minimal when people talk about effective theories they usually don't go this far in pruning degrees of freedom but is certainly a logical possibility and leads to very interesting consequences the equations of motion therefore simply like this and then I'll just go to movies these are different arrays this is a triangle with the couplings one one minus one around this is a ring with those so this is meant to be like benzene with single and double bonds schematically that have various strain and you see it doesn't rotate but it's jiggling you can see if you look very closely jiggles this is a different thing where I we've included a defect if you like and it rotates other interesting things when we happen when we add volume interactions of this kind which are also rotationally invariant a uniform volume interaction gives that and if you have a volume interaction at the end you look well fancifully something that looks like a flagellum or just crazy dancing molecule okay so it's as a rep model of spin systems I think it's it can't be criticized it's a model of spin systems and those kinds of interactions as a model of molecules it's very speculative it introduces noncommutative geometry we have different components of the positions not commuting with each other it's a logical possibility whether it's realized in nature is not clear yeah this is all classical at this point yeah well we'll do the quantum mechanics eventually but this is all no of course if it's big enough the classical system and if the spin is big enough it should be a pretty good approximation yeah let me just say one thing in defense of this is that this kind of motion where the commotion in one direction becomes the canonical conjugate of motion in the other direction is the kind of thing you get in a strong magnetic field it's very sort of thing you get in an emergen form in various forms of the quantum Hall effect so if you right have the right kind of electron wave function and write down the effective theory of nuclei in the presence of that wave function it's not inconceivable that you would get something like this although I must say it's probably pretty far-fetched okay so now I'd like to this is another word I was always hoping to introduce into the English language temmie its virtue is that if you do cyclic permutations it's always a word and as far as I can tell this is the only Explorer letter example in the English language and but to make it work we have to have Tammy so this motivates me to try to think of something that I could call Tammy and just kidding so I'm gonna mix up the past in the future that means there are other motivations so this is this is trying to care take the symmetries of time to another level if you like by thinking about symmetries also of time treatment of time in in boundary conditions usually in physics we apply past boundary conditions so if the past state is alpha beta and the future state is Gamma Delta we determined gamma and Delta in terms of alpha and beta now why I wrote it in this block diagonal formula see in a moment you could also if the unit if the evolution is unitary or reversible in general you could you can also determine the past in terms of the future in principle what about treating them on a more equal footing how about taking some of the past and some of the future and treated them more symmetrically so for instance suppose I give you alpha and Delta can I determine theta and gamma so do I get a unique specification of the universe or of my dynamic 'el system by this kind of mixed boundary condition well it's a very simple and pleasant exercise to to do this and this is the answer so if D is invertible then you can indeed take half not half it doesn't have to be half it could be one feature of the future that you build in and but you can you can invert it and have the future as well as the past boundary conditions influencing the present as I said this is unique as long as the determinant of D is not equal to zero but the determinant of D not equal to zero is two conditions it's a complex number not vanishing and so generically it's not zero similar to the argument of non level crossing that's familiar in quantum mechanics and in fact since there are two even if you have a D as a function of time they determinate usually will almost never vanish solo this line of thought can lead us through interesting adventures we can think about a time symmetric form of Big Bang cosmology where you have a big bang in the past from one kind of matter a big bang in the future for another kind of matter say that interacts with it very very weakly maybe it's accion so and they won't come into equilibrium but you can emit you can imagine that each bill as we no matter in our universe does organizes into conscious beings who experience the flow of time and have a second law of thermodynamics and so forth but the arrows would be different well if they come to equilibrium yeah so the gravitational interaction has very very weak so but so I think it's I think if I think not in not generically alone you have warring thermodynamic arrows and this leads to the paradoxes of ok I'm moving forwards in time this other guy is moving backwards in time we're both sentient beings I tell I give him a message to kill my grandmother horse let's make something kinder tell him to ask George Lucas not to make the third installment of Star Wars anyway that would give them a better plot alright anyway that you can give him so so this is at the macroscopic level there really is such a paradox but it mustn't the framework is consistent it must have a resolution now I don't know how to model conscious observers and things that can do this but I think the resolution the only resolution I can see is that when you do this kind of message passing you wind up on a different branch of the evolution of the universe so this conceptually leads you into the idea that there are different branches and if you do this kind of procedure it just takes me to a different branch of the wavefunction anyway this is all very speculative at the end it's it's the first piece of science I've done whose main application is probably to science fiction but it's interesting and you can set up experimental situations where this formulation is relevant and I'm hoping that in the future or maybe in the past some clarity will emerge on these questions and we'll have yet another brilliant installment in the history of the symmetry of time thank you it in your 2012 overview letter ground state yes right that can be anything well it's like humpty-dumpty the word means what I say it means well know that definitions can evolve with time and the fruitful the most fruitful definition of a time crystal is still being refined I think and you know for instance there are mechanical time crystals and many-body time crystals that are different things I just so I think what is emerging though is that it's important to think about spontaneous breaking a time reversal time translation symmetry it's fruitful to do so and it should not be regarded as a taboo subject that you can break any other symmetry but not time translation symmetry so that's that's my breaking of taboos which some people get very offended by well it is a time crystal in the sense of well the ground state of harmonic gossip what the graph state doesn't do anything accountant correlation functions would well let's let's to make it clear let's not take the ground so let's take an excited coherent state a coherent state that's actually doing something yeah and I think you know by the loose definition the loosest definition it would be but it doesn't have a kind of robustness rigidity that you associate with phase transitions there's no sharp kind of there's no specific no latent heat or anything of the kind associated no let me say what I think is a clearer example that's related to that is the AC Josephson effect okay if you put a constant voltage across a superconductor you will find an AC circuit a AC current arising and I think that is a legitimate example of a time crystal now as usually as it's usually set up there's dissipation but you can make the dissipation very very small there's also radiation you can get rid of the radiation by various tricks including making it a superfluid instead of a superconductor and so so I don't so I think in essence the Josephson Junction is a good example yes which is a homogeneous but it's but it's not a one degree of freedom I mean it's it's a many-body thing it has a kind of rigidity to it so so that maybe that's an answer oh hi Mike yes informations yes if a system is chaotic well there's this I guess I don't understand the question there's a different distinction between the symmetries of the underlying equations and the symmetries of their solutions so some chaos some chaotic systems are time reversals are were we talking about time translation symmetry or time reversal reversal okay so many most chaotic systems in the literature are dissipative systems so they're intrinsically not time-reversal symmetric I think they're they can also have reversible examples just like the shift register as a discrete example that's and you can run it either way and it's chaotic in the sense that you reveal digits that you didn't know before all the times you can't predict them I don't see that there's a problem I think it gets more chaotic in either direction from from the same initial condition yeah it's it's this I think it's very much related to the question about the second law of thermodynamics arising from reversible laws entropy increases in both directions typically because the situation's we start with are usually high in unusually high entropy states low entropy I'm sorry well husbands if not the same thing again so

Channel: Stanford Physics

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Keywords: stanford, physics, colloquium, time, frank wilczek

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Length: 52min 7sec (3127 seconds)

Published: Wed Jan 17 2018