Quantum Mechanics Time Travel

So it's great to be here. Primitor Institute had me give this lecture to popular popular lecture last night, but of course the reason I'm really here is to find out what's going on here because this is like the epicenter of quantum information processing and quantum computing in the world. And so I am really here to learn about stuff. I also need to apologize to Olaf Dryer last night when I said that the birds are quick or to escape homework. In the wintertime I would like to point out that there are also just as quick to come back in the spring, not really for the good beer. Okay. All right. So I'd like to talk to you about the quantum mechanics of close time like curves. So of course, since it sounds pretty wacky and it is wacky because it is the quantum mechanics of time travel essentially. And so in quantum mechanics we are accustomed to the situation where our intuitions don't work out to be true and when you add in time travel your intuitions doubly don't work out to be true. Now this may sound kind of wacky and science fictiony and in fact if you look at the history of time travel there is a long literature about the history of time travel. Interestingly for most of it in the distance passes most about time travel to the future which actually isn't that hard because we are doing that right now. So in the Mahabharata there is a great scene where this king goes to visit Brahma and his beautiful palace and he is there for a few days partying like mad and when he comes back countless eons of past and his entire civilization has decayed into dust. And there is a beautiful Japanese story called Urashima Taro where a fisherman, Urashima Taro frees a sea turtle from a net and then a few days later a very beautiful turtle princess comes and invites him to the house of the sea king and he takes her invitation and they are married and it is a great time and he lives there and he is a great splendor for three years but he misses his parents and so he begs her to let him go back and so she says okay you can go back and I'm going to give you this box made with covered with beautiful seashells but you must not open the box. You can already see where this is going and so Urashima Taro comes back he lands on the beach of his island everything looks strange he goes through his village his village is no longer there he finally finds this monument to his parents and to himself saying that he died 300 years ago. So in despair he says well gosh maybe if I open the box all I'll I'll be able to see them again so he opens the box and this mist comes out and develops him and he feels himself rapidly turning into a very old man and then he dies. This is another an Irish legend about Finn McCool the famous Irish hero who goes to visit the king of the ferries and stays there for a few days partying like mad which if you've read the legends of Finn McCool you know he could really party like mad and he comes back and when he goes away the king of the ferries gives him a magic horse which he rides back on and he tells him whatever you do don't get off the horse so what does he do? Of course he gets off the horse just like Urashima Taro you get you know it's like whenever they give you some magic talisman and tell you not to do something they always do it so he gets off the horse and as soon as his foot touches the ground then he turns into an old man and dies right there's a we detect a pattern here in these stories so the the first stories about about travel into the past so time travel into the past show up in the 1700s but they don't really they don't really kind of get the notion of time travel and it's not really until there's I mean there's also Mark Twain's famous story a Connecticut Yankee in King Arthur's court and which this Connecticut engineer he's hit on the head on the job site and he ends up in King Arthur's court where he decides to modernize thing and hence wreaks total havoc destroys the civilization etc which is you know kind of a metaphor for modern times too but it's not really until H.E. Wells's famous story the time machine that we actually see the kind of picture of time travel which we're familiar with from movies and books today and that famous story there's a machine which the time traveler enters and it allows him or her to go back or is in time to a specific date and then come back to the future and or back to the present now now once these stories got started about real time travel people really began to think of the contradictions inherent in time travel and there are really actually so you got to be careful I'm thinking about time travel because you know there are a number of paradoxes which I'll describe and I'll describe how our our theory and I should say our experiment as well because with Ephram Steinberg we did an experiment I'll describe to you effectively sending a photon a few billions of a second backwards in time and what do you do if you send a few what's the first thing you would think of trying to do if you have the photon interacting with its past self what would you have a try to do would you have it by its former self a beer which would be the nice thing to do no of course we have it try to kill itself so we have it try to go backwards in time and kill its former self and then we see what happens I'll give you a hint you know those those movies where they say at the end no animals were harmed in the filming of this movie well that would be to say that no photons were harmed in the course of this experiment would be an exaggeration okay so so the notion so in time travel stories there are basically two types there are two fundamental paradoxes about time travel and one is the so-called grandfather paradox where the time travel goes back in time and either inadvertently or on purpose kills your grandfather before he meets her grandmother so she doesn't exist so she can't go backwards in time so what the hell is that about how does that work there are essentially two resolutions of this paradox one is that when she does this she can kill her grandfather and in doing so she enters an alternate world so there's this famous um i think it's is it a ray-bradberry story where uh called the sound of distant thunder where the time probably goes back to like the Jurassic period and uh uh uh the term and not to change anything but he inadvertently steps on a butterfly and because of the famous butterfly effect when he returns to the present everything is weird like it's sort of like it was but you know the politicians are different and like the language is spelled in a different fashion etc so that's one version and what you enter into an alternative universe when you come back to the present and the other is that you can't do anything that's uh uh inconsistent with the past so um if you look at movies about this so for instance of the movie back to the future not to mention the famous movie back to the future not to mention the slightly less famous movie hot tub time machine which i haven't seen but i haven't described to me is of the type where you go back you come back to the future you when you go back in the past you change the past and you enter an alternative future the other type which is exemplified by uh uh uh the movie um Harry went and the book Harry Potter and the prisoner of azkaban through here has seen a scene this movie okay great alright and glad some people have don't you guys ever get out i know it was nowhere little far from town here but come on so and in that movie Harry and his wizarding buddies are trying doing all this stuff and all kinds of weird crap is happening and they can't figure out what the heck is going on but in the end they figure out that what's happening is that they've been interacting with themselves coming backwards in time but everything is self-consistent so things are weird and strange but they're self-consistent so for the grandfather paradox this would correspond to a situation in which the time traveler is unable to kill her grandfather no matter what she does i'm sorry i'm going to use you for this example since you're sitting with front row so she she points the gun at her grandfather and blam pulls the trigger and whoop the last minute a quantum fluctuation whizzx the bullet out of the way so there are two um uh uh uh uh the prevailing theory of uh close-time like curves is due to David Dorch quantum mechanics of close-time like curves is due to David Dorch this is a theory of the first kind where you can enter an alternative universe and the one lying to tell you about projective close-time like curves is of the second kind where you uh cannot actually go back and kill your grandfather okay all right so are there any questions at at this point any more time travel stories you want me to hear about i've been collecting time travel movies and then any any good time travel movies you want me to go and watch it's okay yeah how would you know your uh you travel back and time if you can't what no you can interact you can interact but you can't you cannot cause something to happen which you what you know not to be the case right so in obviously there's someone who's not seen prisoner of Oscar Bond so um um what's your problem it's so uh uh uh uh uh yeah so so you can interact with the past and make all kinds of weird things happen and in the future you'll remember that those weird things happen so you can certainly interact with things but you can't go and actually change the past so you know you can't go back and that that horrible blind date that you had when you were like 15 you know you can't go back and undo that i'm sorry so more yes uh primer primer that's the time travel movie ah yeah yeah yeah i've heard that this is a really awesome movie here is seen primer yeah yeah i've heard this is a really awesome this is what this is I'm definitely on my list of things and what's what there's a spawn like eight monkeys or ten monkeys 12 monkeys 12 monkeys 12 monkeys i'm told with one with one the slight mishap is of the second kind where you go back and time the time travel goes back and time tries to change some horrible thing happening and it doesn't happen i've heard a son awesome movie too yeah same time traveler's wife oh the book the time traveler's wife you know i started reading that and maybe because i'm too close to the subject i had to stop after after like 50 pages so what is that which does that which category is that it's like ask man it's very good but it asks uh you know and the grandfather paradox is technical back and time with the brilliant grandfather this asks can you go back and time a lot of my your most intimate relationships right yeah what i thought was very good excellent so that actually sounds like so or that is the is this possible to modify your most indefinitely okay i gotta go see the movie okay alright yeah future armor yeah see the problem is there's so many of these things that i can't see them all but yeah is that so which type does this fall under i'm basically that is again about the he managed to keep his brother he did manage okay there you go awesome he oh okay so this brings up another one yeah i always say that if i went back in the time and met my grandfather i really was very fond of my grandfather i was certainly buying a beer and only if we had too many beers and got an a fight would i accidentally kill him yeah so here's there's there's another famous story about the grandfather paradox in which the time travel goes back in time you know goes to a club gets meet a beautiful woman sleeps with her they do not practice safe sex which i do not recommend and then she gets pregnant and it turns she gives birth to his mother so it's he he is his own grandfather alright that's another grandfather paradox this actually thank you for bringing that up so this is the second major paradox about time travel is let me explain it in in less kind of since i talked about quantum hanky panky last night i'm uncomfortable being seen as the resident quantum pornography uh hey you know you know if you look at technologies one of the main things that drives their introduction is pornography right so if we could come up with quantum pornography that might be good pictures of naked electron whatever mine so uh yeah so the second primer major major paradox is what's called the unproved theorem paradox so in this paradox uh the time traveler reads a cool proof of a theorem in a book and she goes back in time and she shows the proof to a mathematician and the mathematician says wow what a cool proof i'm going to include it in my book and the book of course is the same book in which you obtained the theorem of the proof in the first place and now you have something that's you know this is actually quite disturbing because you have a carefully constructed beautiful proof that came from nowhere it was never produced and actually this other version of the grandfather story is in fact the unproved theorem paradox in disguise because if you go back and become your own grandfather then a quarter of your DNA came from nowhere right it was never subjected to natural selection or anything like that so in fact the problem there is that this unproved theorem paradox these are I mean I've tried to do a lot of research on the kind of like philosophy and things of time travel I haven't been able to find time travel paradoxes which are not variations on these two themes so any theory of time travel in quantum mechanics or elsewhere has got to come up with a resolution of these these paradoxes and so I will tell you what are resolutions of those paradoxes are but first let me give a little bit of history so the fact we probably wouldn't be discussing this as all if Kurt Gerdel in 1948 hadn't you know when he was a famous logician and when he got the Institute of Advanced Study he thought he would Einstein was there and he got Gerdel Einstein were buddies so Gerdel learned general relativity and Gerdel because he was fond of paradoxes he decided that he would say wow you know maybe it's possible to have a space time that has closed time like curves and it so you know it's just as you have this funny space time manifold and it could possibly be possible that you have a path that goes backwards and you end up in the past and the way that this normally looks is a famous coffee cup picture so time goes up here we have like this is in like a one plus one dimensional space time space so it looks down here space is just like some big circle and then here is the handle of the coffee cup and time is flowing here over here but down here if you go around this handle time goes like that and you can end up interacting with yourself in the past okay so actually the Gerdel space times are really weird looking there there are these big clouds of massive clouds of swirling dust it seems important to have rotation in these space times I've closed time like curves but they do indeed have close time like curve this is a this is what's called a time like wormhole so and and unless you think that this is just some weird wacky thing and by the way Google images have some great pictures of of Gerdel space times and I've been told that Gerdel when he told Einstein about this it was sort of like a birthday present for Einstein and Einstein hated it Einstein was not Mr. Paradox guy he didn't like it didn't like quantum mechanics and like paradoxes everything was supposed to be cut and dried but not so good but it's also a fact so that that basically when you any take take any space time and it's rotating sufficiently then and there's a sufficient amount of mass you'll get a close time like curves so the interior of a curve black hole rotating black hole inevitably has close time like curves in it back me up all of for some other gravitational person here I mean this is this is actually a fact and unless you think that's like that's you know who cares about what happens in a sort of curve black hole if our space time itself if our universe is actually overdense and so it's collapsing then it is effectively a black hole and if there's even a tiny bit of net rotation of the whole universe then there would be close time like curves within our universe so you know it's not general relativity allows close time like curves and you could say in some sense circumstances that even encourages them to happen so how do you deal with this well there's a so how in pickle do you deal with things like the second law of thermodynamics going around here what's the quantum structure of these of the quantum states can you even have a quantum Hilbert space picture of what's going on inside this close time like curve the actor to that actually is you can have a quantum Hilbert space picture but you cannot assign a quantum state just to give away telegraphs and with a punctures so the next hint of how you might deal with quantum mechanics of close time like curves comes from John Wheeler this is not anything he published it's it's the amusingly this is reported by fine men in his Nobel Prize acceptance speech which is online so you can get it and you go look at it and there's this this place where he he starts off with kind of us dry stuff but then he starts talking about his experience and there's this place where he says I'm going to try to paraphrase it in the Feynman asked kind of way he says well John Wheeler John Wheeler called me up from the institute and he said I know why all electrons have the same mass and Feynman said really and Wheeler then said yes and I also know why they had the same mass as the positron and find us why why and Wheeler said well you know time by the way time is always going to go up in this picture because anything to do with general relativity is time going up okay so get used to it so uh Wheeler says well look electrons and positrons are always created in pairs E plus E minus and they're always destroyed in pairs E minus E plus so we can think that what's going on is that there's just one electron that's going forward and backward in time and that when it's going forward in time and it's electron and when it gets destroyed it turns around and becomes a positron so the reason that they all of the same mass is the only one of them and the reason why they have opposite charge but identical charge is that when you do charge your time reversal you take plus charge to minus charge by a famous theorem of quantum field theory the CBT theorem so in Feynman said then then he says this was totally crazy but I did steal from this the notion that positrons are going backwards in time so in fact at the heart of contemporary quantum field theory with the notion that positrons are electrons going backwards in time there comes there's this crazy idea of Wheeler's that says look there's only one electron and one positron and of course if you went and go look at Feynman diagrams you realize why this isn't really true because of course you can have other Feynman diagrams that are like this and they're connected by photons and so there's probably not only one electron and one in the universe though it is a kind of a nice idea if there's only one electron okay so you can think so what I'm going to tell you right now is then what I'm going to tell you are theory which is with Lorenzo McCone you talk of Chicano roll Garcia Perez Patron and then also we have Ephraim Steinberg's experimental group at universe of Toronto did the experiment what I'm going to tell you you can think of as essentially the mathematical adaptation of this Wheeler notion of positrons being electrons going backwards in time and it's going to rely strictly on entanglement and indeed when you create electrons and positrons and pairs out of the vacuum their spins are in entanglement singlet states and when you destroy them the only place that can be destroyed is in entanglet singlet states and this is going to be key for how the theory of time travel works but let me continue with the theory a little bit because I think it's important to know about I'm you know I have this master's degree in history in philosophy of science from Cambridge so I actually think that theory the history of ideas is actually quite important to understanding what the next idea is going to come from okay so around on 1988 Kipform and or Yurtsiver and then later in the early 1990s Jim Hardell and David Pulitzer looked at path integral approaches so path integral of course you know what you do is you take a bunch of classical trajectories and you assign them an action and you sum E to the IAS over all classical trajectories and what they did is they say we we we we we only take classical trajectories classical paths which are self-consistent right so we just assigned in classical and classical mechanics you don't have as many world stuff that David Deutsch advocated but you we we only going to take these classical paths that are self-consistent so we sum over a self-consistent classical paths and this is actually perfectly reasonable idea and you can formulate it the problem is that path integrals are very hard to evaluate so they never got very far with this approach but you know they were able to look at it and then David Deutsch in 1990 came up with this oh and maybe I should actually start yeah this is this is the right order so in 1990 no no this is not the right order yeah that's the right order okay right David yeah that's not something right so I want to especially mention that that Charlie Bennett and Ben Schumacher Charlie Bennett in particular starting with the the the invention of teleportation which was when was teleportation it was around do you remember Debbie 94 92 yeah so so starting with teleportation Charlie Bennett talked about you know with teleportation you have I'm going to all I'll be kind of graphically suggestive about this you have an entangled singlet and then you make a measurement right here and then you send classical information over here you perform some operation dependent on this classical information this is a bell measurement and then you do something right here and if you have a state psi you end up getting the state psi here and Charlie Bennett always talked about teleportation as if this part where did the information go is if the quantum information went here and this is the quantum information going backwards in time and forth again so and and this by the way this idea is in is at the essence of what I'm going to tell you about so unfortunately so I this is kind of a unfortunately Ben and Schumacher have never published anything on this they've talked about it for years they never really developed so far as I can tell any explicit theory about this so you could also say that what we're doing is really developing a theory out of this really it was a metaphorical description that Charlie Bennett has been using for decades now okay so now let's get down to and this is okay this is this is all history now it's going to be like math and stuff like that so there are any more historical questions or comments or things like that we bored by hearing the history of this maybe you were that's okay okay I'm sorry arbitrage why didn't you send a half billion second after the stopman was up there so that could be so so that's consistent with both with both so this is this is like this is like a many world's version so enter another world let's call this this is enter another world and this is is same self-consistent world so if you send information about you know what the price of the Swiss frank is going to be back in time and then invest in the Swiss frank well as long as the amount of your investment is sufficiently small that the history of the Swiss frank is the same then it's okay but if you try to buy all the Swiss frank then it will it will call things to go haywire so then would fall in this many world's worship so you could you can imagine you know making money off of time travel in either of these worlds and this way you can make a lot more money in this world in the Deutsche version the many world version yeah okay okay so enough of this fun fooling around with with history fooling around with the past which is of course what time travel is about let me now actually tell you how these things work and the first thing I'd like to tell you is about David Deutsche's theory so I'm going to review who here is familiar with Deutsche's theory of close time microbes yeah some people have so let me just tell you how how Deutsche I'll switch colors for for blue for serious stuff so this Deutsche let me describe to you what the storage paper in 1990 does it's it by the way even though we think our theory of time travel is better for reasons I'll tell you this is a beautiful and elegant theory because it's very hard to formulate quantum mechanics in these contexts these these path integral approaches are are good start but it's tough to like to deal with these paradoxes so let me tell you what Deutsche suggested and how he dealt with his paradox here so Deutsche's no I guess I won't do this one I'll throw that one on the ground and we'll use this one okay so the way that Deutsche's theory works like this you have you have kind of normal what he called chronology respecting degrees of freedom and let's call this this is in the state row A and then you have the close time like curve and this could be many degrees of freedom I'm just going to do this if it's too cubits but it could be many different degrees of freedom and let's call this call this this is row row R B and you have some interaction between these things and then the question is how do you make sense of what what what happens up here now interestingly Deutsche does not tell you what happens over here he does not assign this a degree of freedom this thing going backwards in time this is sort of funny if you think of this coffee cup picture because there's you know something happening in that in the the handle of the coffee cup but Deutsche does not give you a state for this which is already I think that something is a little fishy so Deutsche's self-consistency condition basically says that here we have row prime of A and here we have row prime sorry I should put it right here so at this point right here you have row of AB now let's actually yes so and this is so when the thing comes out look what grow prime of AB when it when it goes in it's in the state row A tensor of R O B and then what he asks is that the state that reduced density matrix for the system that comes out of this close time like curve is the state row B right you can see why this gives you a self-consistency condition because it says that the thing that enters the close time what the state that enters the close time like curve in the future is the same as the state that emerges from the close time like curve in the past so this condition is the trace over A row A U row A tensor row B U dagger is equal to row B okay this is Deutsche's Deutsche's self-consistency self-consistency condition all right so so you see you see how this I mean this this makes sense right he wants this to be the state to be self-consistent and he wants this state to be the same as the state there moreover this is because this is a super operator this is the same as saying if I have some super operator which is this interact with row A VAU and then just look at B this is really a super you're asking that the state row B the an eigenstate with eigenvalue one of this corresponding super operator this process and because super operators always have an eigenstate of an eigenstate with eigenvalue one this the state such states always exist okay so it's a nice self-consistency condition it looks good okay now so let's look at actually what happens then if we do something where let's let's let's let me just leave it at that let me just mention some things that are a little disturbing about this before I go on and tell you I'll tell you our theory and then I will I will compare the two of them there is something a little disturbing here okay so Deutsch is assuming if you look at it he's actually assuming that when the time traveler exits from the curve and there's another you know the rest of their universe is out there that they are in this tensor product state which means that the time traveler when she exits from the curve is completely uncorrelated with the stuff outside of the curve that is she emerges in a universe where none of her memories are any good they don't correspond to the universe she sees that's a little disturbing already because that's certainly not you know that's not this or does she metaro kind of time travel or hgwells kind of time travel it's like you end up in this weird place that has nothing what's over to do with what you remember and the reason for this of course is that so I would describe this in quantum information terms as it I personally would prefer a close-time like curve to behave like a quantum channel and quantum channels preserve correlations with the surroundings but by demanding only that the reduced density matrix be the same as it enters the curve in the future and emerges in the past in this case you're actually erasing all memories about sides so this is not behaving like a quantum channel so this is a bit disturbing I should say that after we wrote a paper and we we corresponded with dork about this and he said that he found aspects of his theory unsatisfactory and I believe that this might be one of those aspects that he found unsatisfactory yes sure this is like so if you know any super operator can be written as an unitary interaction with an environment when you start off in the tensor products state so it's just you know this is of who's he what's his theorem I don't know who's who's theorem it is so so so this any this the the transformation that be undergoes when I take you it interacts with a and I take the trace over a this is certainly a legitimate quantum mechanical transformation it corresponds to a super operator it is linear okay and then so this is a super operator and all super operators have a eigenstate with eigenvalue 1 there is a non-linearity in dork's theory so this transformation is linear there is a non-linearity because what dork is saying is that the only row that we can allow are things that satisfy this so you can't put anything in here you can only put rows that satisfy this so it's not not anything can go go through this close time like curve so there's a non-linear in the sense that you're selecting out of the set of possible states just these rows to be from what you can happen there may be multiple rows to be for which this is a case that that is the eigenvalue may be degenerate and in that case for reasons that I'll describe in just a second Deutsch says take the one with maximum entropy actually I'll describe it in a second so the reason for that is that if you don't take the rows to be that has maximum entropy then you immediately run into this unproof theorem paradox because the unproof theorem paradox you're going to perfectly self-consistice is perfectly self-consistent you can have the unproof theorem go through this everything is fine and I mean if you just think of this kind of some classical transformation and then that's bad Deutsch really doesn't like that if you read his paper which is really excellent and interesting paper he spends a lot of time talking about this unproof theorem paradox and how much he's upset by it and now he so he says okay you take the maximum entropy one all right so let me now contrast this with any more questions about this I'm going to stop talking about this doorchasing right now there's more disturbing things as we'll see in just a second about this actually I'll mention one more disturbing things which is that that Scott Aaronson John Watris and Todd Glenn and a bunch of other people have shown that this is absurdly computationally powerful so there's not linearity of selecting out the particular states allows you to solve anything and you can so Deutsch CTCs allow you to solve anything in piece space in a so plus computation both classical and quantum computation it says that pilot piece base is equal to polynomial time so you can solve any problem in polynomial space in polynomial time and for your computational complexity people out there and I know you're there because I see you you know that this anything that is this case is really bad and if you say that you can do this then computer scientists will immediately disbelieve that this is possible all physical evidence aside so that's actually kind of a bad thing for this and I should say that the way I got involved in this is there is a paper from IBM in which this last summer before this last one where they objected to this Aaronson result and is anybody co-author of the paper here in this room right now I don't well I just want to because I want you to step up and defend it if you if you are anyway this is because of big argument and this was a goddess we we found this argument to be annoying so we decided to work on these close to unlike curves ourselves and when Charlie Bennett came I'm sorry what an oisby about the argument yeah because I don't believe it that's why I don't believe it so so the the the the Aaronson paper is correct I've went through it very carefully the IBM argument says that in the presence of close time like curves you cannot prepare your computer in a particular problem state in order to solve that problem now I don't know if this argument is correct or not but the two paper start from different assumptions and I actually quite distrust the argument from the IBM paper anyway we brought Charlie Bennett to MIT and we put him and Scott Aaronson and the steel cage and we have them duke it out and it was inconclusive in the end I actually don't I would prefer not to discuss this paper because I I don't think it's very illuminating sorry shouldn't have brought it up okay all right so so actually when we looked at this I said to myself you know I actually know of another way of doing close time like curves because about you know eight or nine years ago I worked on this problem of how information escapes from black holes this by the way this talk has every wacky possible thing you can imagine it's got close time like curves we're going to have teleportation that's like the least wacky of things and we're going to have how information escapes from black holes so let me review how this model works and so I said you know there's something very funny about this because there's another uh uh Aaronson paper which says that quantum computing plus post selection is equivalent to uh solving the the class of uh computational class polynomial probabilistic polynomial time actually known as PP which when I told my my children that there was a computational complexity to class known as PP they thought that was really hysterical so I because of my work because my working on um on black hole that's escaping from black holes I happened to know that you could make a theory of uh of close time like curves based on quantum mechanical post elections which will now present to you which is um which I thought all along was equivalent to doaches theory I should note that you know Charlie Bennett and men's shoe marker while they're talking they've been talking about this you know going backwards in time and a method that's very short that's very close to what I'm going to describe and they were also not aware that their theory was different from doaches now if you look these two things together so if you can get with post selection and quantum computing you can get post time like curves which I'll show you in just a second then you've proved that PP equals piece space which would be really news to lots of people you would have collapsed part of the polynomial hierarchy which would be pretty amazing so the first the way we start on this is as we said hey look we can prove that PP equals piece space well if you ever worked on these things you know that after a weekend of working on it you realized that you were wrong but it was fun for about a weekend okay and the the resolution was we realized that in fact the close time like curves via post selection are not equivalent to doaches close time like curves so let me tell you how this works so let's look at first at black hole escape from a black hole how does escape from a black hole work okay so here again is time going up here is space here is my picture of a black hole this is the horizon the event horizon of the black hole this is the singularity where everything gets smushed into nothingness okay note that the singularity of a black hole is space like it's not actually point like it's space like which is kind of interesting note also the horizon is light like light goes at 45 degree angles here you can actually you can see why the horizon is light like because if you're right at the horizon of a black hole and you know you send off a beam of light that's just trying to escape from it say it in angle then it's beam of light was just rotating around the black hole so if you want to take a path that hugs the horizon it's a light like path so the horizon is a light like surface so here is the picture of what happens we have this this this poor innocuous state falls into the black hole can be your favorite evil professor or something falling into the black hole and it's going to get smushed at the horizon but wait wait there's more to this picture because outside of the horizon Hawking radiation is being created and the way that Hawking radiation works is that let's do like this you have singlet pairs of particles are created from the vacuum they're created in singlet states because the only thing you can create something out of nothing if it's it's in a singlet because all conserved quantum numbers have to be zero all right they're created as singlets part of the of this vacuum fluctuation has negative energy and it falls into the black hole thereby reducing its mass and the other part is positive energy and it escapes to infinity thereby carrying part of the the mass of the black hole off to infinity and that's our black holes evaporate okay now there's a lot of debate about what happens about information black holes but there's one mechanism proposed by Gary Horowitz and one Meldesina to heavyweight string theorist types and the mechanism the following and I'm going to describe it in the way that makes it sound most plausible the most plausible even though there's nobody knows if that's mechanism takes place or not but let's just let's just let me just just go with me for a second so maybe it's the case that the only way just in the same way it's only way only possible to create something from nothing is for it to be in a singlet state maybe the only way you can have it go away to nothing like at the singularity is for it to be destroyed as a singlet state so suppose that every every state that falls in the black hole gets destroyed as a singlet or projected onto a singlet not let me be more explicit suppose that the the singularity projects incoming stuff onto a singlet together with half of a of a pocket radiation pair all right I mean who knows right the great thing about being a theorist is that that you know we have no idea what happens at the singularity so let's just say it's whatever we want it to be right this is like experimentalists are not allowed this kind of this kind of a leeway all right so now you can say well what is a state out here aha we recognize that this is just like teleportation okay here's a singlet state right here here's this tape side but here we measure and get the singlet which I will actually now and so we measuring get the singlet and what that means if you are familiar with teleportation which I know lots of people are in the singlet state is a one where Alice sends to Bob the information whoa don't do anything you already have the state psi and so I'll draw this like this because now we have projection this is creation of a singlet this is projection onto a singlet and so here is this nice picture which this is the kind of thing that Charlie Bennett was fond of drawing you know that all of the information goes back here and then up here and out here right here all right so is everybody okay with this so so in this case if you project onto a singlet which is a non linear operation right it's like saying we make a bell state measurement and we toss out the all three quarters of it and we renormalize the problem get this so the renormalization of the probability to one is nonlinear and so this is nonlinear quantum mechanics which is dangerous that's how you can solve these hard problems using it but at any rate the state escapes from the black hole okay are people happy with this yeah right so in ordinary teleportation you need you know ordinary teleportation everybody can do that you know people doing this for decades you know it's like anybody can do that and you make a measurement bell state measurement actually making the bell state measurement all the bell state measurement is not so it's hard but make the bell state measurement you get two bits of information Alice sends those two bits to Bob and then Bob does something as a function of those bits so the idea here is that a nonlinear process takes place where instead of having an ordinary quantum measurement it for whatever reason like you're at the singlet already of a black hole it projects you onto the singlet part so it only gives you the singlet part all the other stuff gets tossed away and has now has probability zero so right so only the ones make it out with this is projection of the singlet this is totally illegal in ordinary quantum mechanics so that that's a very good question don't this is not you know it's illegal so this is something nonlinear and bad and then you can see it's bad because already you have things that are propagating fast in the speed of light you clearly have violated the no-cloning theorem because of course this could be down back down here right so you're definitely doing bad things yeah well you hardly address my question but what's on answer here is what determines the physics of when it goes back into the future from the outside so that of course that interestingly the back into the future part is of the back to the future part like and I note that note that the one of the main actors in that is named Christopher Lloyd no relation I believe only distant relation so interestingly that part this part down here is really the kind of uncontroversal part that's just entangled meant it's just an entangled singlet state the controversial part of course is this projection part well sure but I mean it could go at anyone of those times including earlier yeah yeah well of course right because so let me so let me segue of course because I want to actually I realize that that in indulging myself and telling you about history and talking about time travel movies and stuff like that I'm I'm gonna go on short on time so as everybody knows and by the way I've noticed this I try this out just people I meet on the street who have nothing to do with physics and they know this so as everybody knows if you can go faster than the speed of light you can go backwards and time right this everybody knows this I didn't just like you know that's the way it is so so here is is the model for for post-selected or projective close time like curves so we create a singlet down here we project so this is this is create singlet we project onto a singlet up here and we normalize probabilities right we normalize probes to one that's that this is perfectly this is all really easy to do and calculate right because it's just as if you were taking a measurement a bell state measurement and you say what's the conditional probability of everything else given like out of singlet so all probabilities in this this theory are calculated using the conditional probabilities that you got a singlet here all right and then you know so here's this here's this other thing and then you have some transformation and then something else comes out at the end okay so probabilities probabilities of events equals conditional probabilities so it's a very well-defined theory the one thing that you have to say is well what if the probability of this is zero and the answer then is well nothing you know that can't happen so because conditional probabilities are not defined if the probability of the outcome is zero so this just doesn't happen which is good because now you can see already that we are going to always have things that are self-consistent because in this this picture of close time like curves what happens is a valid conditional probability for a sequence of events in quantum mechanics it might be hugely improbable if you don't do the projectional singlet but it's still possible so you can't get things that are exactly impossible like for instance killing your grandfather okay so now this is so once you have this and I I I I want again give Charlie Bennett and Benchuma for credit even though I've actually had rather annoying time dealing with them over this because they have talked about things like this for a long time I know that Clemont told me I didn't know about this paper that that that you guys didn't experiment here with with an MR to look at this notion of like oh look things are going back with time let's look what happens with this and I want to give them credit for for talking about this for years but I'm not going to give them credit for I wish to express my annoyance of them for not writing this up as a paper so that we can actually see what they mean because they never wrote it up it's only exists in the form of like four transparencies on a talk of Charlie Bennett so they have a theory which is like this but it's not clear what they they meant by it in fact when we talk to them they actually use a quite a different language and I'm not sure if we agree on stuff but anyway Charlie told me that they were unaware that their theory was different from doaches and this theory is definitely different from doaches as I'll now show you and I'll show you by coming by giving you a picture of quantum circuit for our grandfather paradox experiment and I'll show you that doaches theory and our theory give different results for what happens so like I can so this over here so let's do a grandfather paradox the simplest version of a grandfather paradox is something like this here's our close-time like curve okay so zero equals dead one equals alive and we're just going to switch this over to having our photon killing itself right so if you do a sigma x you flip this around the x axis right here then what happens is zero equals dead one is equal to a live and you see if you're alive here you're dead here you get turned into dead if you're dead here you get turned into a live here so this is the grandfather paradox the very simplest thing that you can imagine about it and moreover in we're going to actually in our experiment we're going to ask this cube it to declare whether it's dead or alive so here we're going to measure up here so here we measure it we we we we we couple it to two other cubits via controlled not and then we're going to get us to declare if it's dead or alive by the way I think if you look at the grandfather paradox in Charlie Bennett's notes again trying to like decipher what they meant by this it's a different paradox and this might be why they didn't figure out that there there result was different from Dorchus I should we also ask Charlie Bennett to be a co-author on our paper after we've done the experiment discovered that they've been doing this before and after this delay the publication of the paper the submission of the paper by four months while he decided in the end that he hadn't contributed enough to it so sorry I shouldn't express that that shouldn't this is like all like I'm going to hit around here it's like I might as well express like this is the kind of thing that happens in science what the hey you know you got to negotiate with people people get upset if you don't give them credit etc so I'm trying very hard to express what we're going to like to give them credit and express my annoyance okay okay so what happens here all right well in Deutsch this is totally okay right remember Deutsch always works it always gets you something so what is the state that will work here what is the state where if I pop it in here comes around here and it's still the same state I'm sorry right that's right that will work that will work yeah however Deutsch asks us to take the maximum entropy state right so should I hear so the Deutsch basically it'll call us rho b again rho b rho b is equal to 1 half 0 0 plus 1 1 actually you see right now since since this this was very alert also you know we could also just have a state a sigma x state that would also be fine because it's an eigenstate of sigma x right this shows you why Deutsch has to has to say give you the maximum entropy state right here because there's there's several states sigma the the minus one would also work okay there's several states that have this criteria and and this state right here is like the unproved the non never created proof of the theorem right it's a special state sigma x up it went around everything is totally fine itself consistent but at some special state nobody ever picked out why it should be sigma x what was we spin x up so Deutsch says okay we got to use this state into you make it fully mix so that we don't run into this unproved theorem paradox so but now you see something truly strange and alarming here which is it even though the density matrix for the state the time problem or as she enters into the future the close time like curve in the future is the same as the density matrix in the past somehow during the transition around this curve the actual state has been mixed up so zeros become one and one has become zero so this is a bad close like to close time like curve to enter alive because you're dead when you exit of course it's a good one if you're dead because you exit alive right I mean so so we could have both both destruction of life and we could have creation of life from nothing from this so that's pretty weird so Deutsch is criterion which looks perfectly fine to begin with is that is actually now you see when you apply to this grandfather paradox you say hey hold it now I thought you said the state was the same and the answer is the density matrix is the same but you know you're a particular part of the density matrix may have gotten completely screwed up which is bad if you were alive when you entered the curve okay yeah right so of course this also you know as you can tell when you have this kind of system all your intuitions about quantum mechanics and what you've been taught you've got to be careful about yeah so if you think of it as a lack of knowledge from safe woman outside observer the outside observer like the person out here monitoring the situation over here we'll say well I don't know what it was let hold let me go look over here and they'll get statistics up here and what they'll find is basically in Deutsch's case you get if this one is zero the next one is one if this one is one the next one is zero so what it says well I didn't know if it was alive or dead when she was alive or dead when she went in but by gum whatever she was if she was alive she turned out dead and she was dead she turned out alive so I think it's still consistent okay with that so I think yeah let's you know you didn't know beforehand and then you found out yeah yeah yeah I said to use the in which recipe for this problem you should see not as a part of your human yeah this yeah I didn't I didn't derive to you that this was the maximum entropy state from this but I will actually in fact if you note if you look at this include it with the c-naughts take the trace over the c-naught gates you'll find that this state the fully mixed state satisfies dorset itself consistency criterion and because it's pretty clearly the maximum entropy state must want to disagree with that too then then then this is the this is the dorset prediction oh so so if you have the c-naughts yeah sorry about that so if I have if I have like if I have this then then it's okay you're right I'm sorry you're right you're right I'm sorry I didn't mean I was unfairly scoffing at you you're exactly right if you put this in here then this will state doesn't work if you're actually doing these measurement interactions completely correct okay so what happened with with PCTCs well what happens here is that this can never happen if I think of it without the c-naught so let's like to make your life easy you see what happens is the triplet right here sorry the singlet right here gets changed to a triplet which is zero overlap with the singlet so the the projection onto the singlet is zero okay so in in in in in in the in the just the raw grandfather paradox it's an example where it doesn't happen on the other hand what happens let's suppose that you actually have something which is just either minus high theta sigma x so you're performing a partial rotation around the x axis and e to the minus high theta e to minus high theta sigma x is equal to cosine theta times the identity minus i sine theta sigma x and what happens then is that this projection triplet marks out this so in fact the cubit never gets flipped only behaves like the identity you just take the identity part no matter how small it is amplify it back up to one and so what PCTC says that you get zero zero one one if the time flavor entered the curve alive she exits the curve alive if she enter the curve dead she exits the curve dead and that's because these projective closed-time like curves behave like idealized quantum channels they preserve not merely the state of the system when an other is a closed-time like curve they also preserve any legitimate correlations with variables out here so if you remember being alive when you enter the curve or if somebody maybe if you're mother remembers it you were alive when they enter the curve she will see you emerge alive in the past okay so this all already shows you that this um Doris is closed-time like curves are different from these projective closed-time like curves and the main difference is this this quantum channel version I'll also tell you I'm out of time and but I will let me just tell you what happens with with the uh the second grandfather paradox the unproved theorem paradox so let me see if I can get this right this is always a it's always tricky here's the close-time like curve okay so what happens is the uh this person the the time traveler reads the theorem in the uh future okay this is a cubit right here here's the theorem okay and then uh uh in the past she writes the theorem onto this cubit right so she tells the mathematician what the theorem is and then she goes your mirror away so this is this uh this is the unproved theorem paradox and so let's we she needs to be able to read the cubit in the future and then write it back in the past and I claim this is the quantum version of this unproved theorem paradox sorry I'm rushing through it a little bit but so read theorem and this is tell theorem to read the theorem she has to be in the state zero so she knows what the theorem is and then she tells it to the mathematician this is mathematician this is the time traveler so now you can ask what happens here what does the state write here now remember when doich does this does this circuit what happens is he identifies this right here with this right here but now any theorem will do could be zero that's fine one will do as well so he has to take the maximum entropy state in order to get rid of this paradox so basically doich says oh okay look it's got to be the maximum entropy state up here so you get a mixture of zero zero zero with zero zero and one one with one one and you see that doich by introducing this extra entropy in the problem by having this maximum entropy state he has randomized the theorem so that's you know so it's not it's not some special proof or anything like that however you also see another problem or feature let's say it's not a bug it's a feature of doich's theory which is that you're introducing entropy you're taking pure states to mixed states whereas as a moment thought about this process we'll tell you that if this state is a pure state then if you project out in this state is a pure state and you project out part of a pure state then by gum the state is a pure state so PCTC is take pure state to pure states doich just takes pure states to mixture this is doich and what about PCTC's well actually are people who have been doing quantum information for more than six or seven years might recognize this as an entanglement swapping circuit we create entanglement over here and we swap the entanglement over here so what we get right here is the pure state which is zero zero plus one one and so now you see a neat feature which is that we never even worried about this this unproof theorem paradox until we formally the theory and then we looked at how the unproof theorem paradox plays out once you do the theory and you find look the theorem is in a complete mixture how do that happen it's because entanglement stepped in to save the day and we've prevented it says well look you know we have this pure state nothing here ever told the theorem be one thing or another we know that's a pure state so it's got to be an entangled pure state with equal amplitudes for zero and one so the theorem is just a pile of garbage okay so let me just close by saying I I should I I need to thank Efram Steinberg in it and his colleagues so so we have a paper with it describes this with the experiment we did the experiment right so because you can do the experiment because this is just like teleportation where you toss out three quarters of the results so anybody can do it tell but not anybody but but lots of people can do teleportation experiments so we can actually make this happen we can't deterministically send information back in the past and mess with it but we can do an experiment which in a post-selected fashion is completely equivalent now now it's the here's a place where I differ with Charlie and Ben they call this a simulation of time travel I would say point out that this is in some sense a bit more in fact we're being very honest by saying you know if you think of the initial teleportation experiments they were all post-selected too and if you actually calculate the fidelity of those experiments without post-selection the fidelity is zero point one one one or something like that so when you know people like Zylinger and D martini reported fidelity is of 80% point eight in their teleportation experiments they were they're not that doesn't mean that you could give them a cubit and have them teleport that cubit with fidelity point eight it means that in a post-selected fashion when they post-select for the experiment succeeding then they would teleport your cubit with fidelity of point eight so here I'm telling you right now we're going to post-select it in a post-selected fashion this is completely equivalent to sending things back in time how does this work you could you create the singlet you create this other state you create this this this time evolution we actually have four cubits in this experiment and then here it's as if the it's this measurement is like the photon entering the time throughout the time machine right photon enters the time machine if the red light goes on which means you got a singlet state then everything in the experiment including all the measurements you did in the past yield exactly the same results as if the photon had gone back in time and tried to mess with itself okay so in a post-selected sense this is time travel it's course not real time travel in the same sense the teleportation is not real teleportation that's okay I give them credit for them it's okay I mean here we should be more careful about talking about post-selection so what were the results of the experiment well it's actually very nice so we find indeed that we never the photon never manages to kill itself in the past the the the tool they use are quantum dot source for single photon quantum dot source in entangled per source this is called a photon gun that's its technical name which is useful for us because you can like and describe the the following way so what this means is that like when you take the photon gun and you point it off in that direction let's do it off in that direction in case there's a mirror there then the this the red light goes on a quarter of the time and you never manage to kill yourself in the past now you take the photon gun and you start pointing it closer and closer let's say I the photon take the photon gun I don't want to like like take advantage of you any longer if we managed to save you the last time around I take the photon gun and point it closer and closer to my head and it's tempted photon self-suicide it's more like I don't know what killing yourself in the past it is like we attempt to kill myself in the past and what happens is I still fail when the red light goes on I still fail but now the red light this is the probability of a successful post-selection the probability of the red light going on gets lower and lower until finally so let's call it this angle this is the angle phi we start off at pi pi over two and we end up at zero and finally when you get down to zero the probability of successful post-selection goes to zero because if with 100% probability I'm going to kill myself when going to the past that's not okay it violates logic and so it doesn't happen all right so let me let me summarize oh sorry my mind is a lucky I got mine is sharper I just picked this up it's like you know look Ramana as I told you tomorrow I was going to go over so let me let me summarize close time like curves are a perfectly legitimate part of general activity therefore it's important to figure out what happens and them quantum mechanically now they may not be allowed in our universe or not we don't know Steven Hawking says no he is this chronology protection postulate which is as you can't have close time like curves on the other hand since he doesn't give any reason for why this is so it's like many of his other statements it's like it's just so and by God I believe it to be true okay so we don't know if this is possible certainly possible in the ordinary laws of physics we it's good then to figure out how quantum mechanics would work on this. Deutsch proposes theory we propose a separate theory and we believe that Ben Schumacher and Charlie Bennett had they actually managed to write the paper and work out the theory would have arrived at the same theory okay and it is different from Deutsch's theory it has a nice feature that it can still be described in Hilbert space but of course because you have post-selection you cannot uniquely assign a state to the system as it's moving along right here we were also able to show that this was too really tough because if if you go read these politics or in hardle paper is there about path integrals over grass money and variables and it was been a long time since I did a path integral over grass money and variables but you can show that they are equivalent to policy or path integral method at least for a policy only does it for a single cube it going backward in time but they're equivalent for that in that case so we think that they're actually equivalent generically to these path integral methods and we perform an experiment and by God we're going to probably do this experiment soon as well and if you guys would like to do this experiment will be happy to collaborate with you to figure out the right way to do it so thank you very much you're home on does a group meeting right now so maybe you should you're maybe you should go to your group in yeah I hope that answer questions now and also later yes so just to come back on the paper the dodge order against what eras and then watches so the IBM paper yeah yes I mean she say it with the produce through here yeah I think the difference here is just that we object to the model as trying to compete on a fixed input and we think the computation in L with and should work on an arbitrary input that is decide on this one right so so in the paper where you recall the paper yeah so in that paper I actually say I'm still confused about the paper so so my understanding of it now correct me if I'm wrong so our incident watches just said hey suppose we have an input and we can put an input into this we have access to these close-time like curves and we are allowed to put in any input we want over here and then we say okay what kind of problems we can solve and the answers they can solve problems in piece space and you're guys paper now is your chance to correct me if I'm wrong says well hold it you have to look at how you prepare this input and that if you have these nonlinear systems you're no longer allowed to think of things a mixture as necessarily you know when you apply something to a mixture it's no longer the same as applying it to the individual components of the mixture and then seeing what happens to the individual components so you say well you have to say how do you prepare this input and if it's entangled with some other state or something then you can't necessarily prepare that input yeah I agree with that but having witnessed the Scott Arons and Charlie Bennett's steel cage fight I have to say that the my impression was as I said it was kind of a draw so the I don't think the so the different assumptions are Scott says we can prepare this input and then we want this part of that we have this part of the system and we want to look at what happens whereas you guys say we look at the whole universe and we ask what it means to prepare an input then and then if you just have a mixture of inputs coming in here then you have to redo the calculation again but that I and I agree with that because I mean you know the calculations in your paper are correct about that but what I don't agree with and I don't agree with this okay so I will now I'll now come clean and say I actually don't agree with it rather than saying I don't know whether it's right I don't agree that that's the correct way to talk about whether you can prepare an input or not I don't think that Scott's way is wrong I don't think that your way is wrong either they're both different ways and each is equally self-consistent so I in in the so I in fact don't think that your paper really refutes Scott's result it's simply you choose to have a different definition of what it means to choose an input I got I got the pointy hockey stick here man you know yeah we can do it in the clean room oh no that's not about that that's about next