Leonard Susskind - Copenhagen vs Everett, and ER=EPR [2016]

thank you Gary my choice of topic today long usual it's quantum mechanics and it's connection with gravity but not quite not the machinery of quantum mechanics not how do you solve a certain Hamiltonian or have you calculate some entanglement entropy I mean the foundations of quantum mechanics the [Music] interpretation the things that they warn you in graduate school don't get involved in because it's dangerous it'll ruin your mind what will happen to you is what happened to Einstein or something like that and my I always pretty much had that view of it that the fineman's view largely fineman's view was quantum mechanics is so confusing and the problem of the interpretation of quantum mechanics is so hard that it's just hard to tell if there's any problem and the damn thing works so let's just use it I have to say that was always my feeling about it also put it on the side don't worry about it the last two years or so have made me feel a little bit different about it and the reason is one particular thing one particular so-called discovery or a development I was involved in it and it's the ER equals EPR connection that made me think that there are deep things going on at the level of the interpretation of quantum mechanics or the foundations of quantum mechanics that will not be understood until we understand quantum gravity if I can give you any sense that something like that may be true and that it's worth thinking about interpretive questions of quantum mechanics and how they connect with questions of gravity I will have done my job here so let's loosen this up I have no idea what to do with it now volume yeah I login okay thank you we want to get slideshow right current slide anybody got any idea what that is Jonathan why don't you tell me what it is quantum mechanics is non-local in some funny way let me just tell you very quickly in what sense it is non-local of course it doesn't mean you can send in information faster than the speed of light or anything like that quantum mechanics is non-local when you try to think about simulating it on classical machines if you were to for example fill up space with lots of classical machines meaning machines mean computers and try to program them you even allowed to interconnect them locally ones next to each other and he tried to fool somebody the operator of the system into thinking that the system really contained quantum objects and that you were making measurements and performing operations on the quantum system you would find that you would fail unless you allowed non-local connections between the classical computers and one very easy way to see that is that in order to encode entangled information you would have to have some kind of central processor encoding entangled wave functions and those were and that central processor would have to be able to communicate instantly with everywhere in order to be able to actually now that doesn't mean that quantum mechanics is really a non-local it means that attempting to simulate it is non-local why did I are the only reason I pointed that out is to tell you what that picture was plays no role in the rest of the talk all right the title of this talk originally was three short seminars with no conclusions I'll probably lie a little bit and try to make some conclusion at the end and the three short seminars are er equals EPR and the every Copenhagen interpretation the Everett versus Copenhagen interpretation of quantum mechanics or something I call Gaz brains the second little clock is teleportation through the wormhole can you quiet can you teleport things through a wormhole into turns out to be yes and the last one is two slits in a wormhole something about the two slit experiment so doing very elementary things okay quantum mechanics allows a certain kind of non-local connectivity it's called entanglement einstein-podolsky-rosen entanglement this is just a cartoon picture of two very very distant particles there are distinct if you go around in the outer in space I folded the space over just to make these two points close to each other but they're really very far and this is a cartoon representation of two entangled particles and the line here represents nothing more than the fact that they're entangled so quantum mechanics allows that kind of nonlocality that we associate with entanglement general relativity allows another kind of non-local connectivity the existence of classical solutions which are called einstein-rosen bridges Arnstein rows and bridges as I said are classical solutions and again they can connect very very distant regions in both cases incidentally but in particular in the einstein-rosen case so einstein-rosen without the the sorry the einstein-rosen bridge case but also for entire ordinary entangle me observers outside cannot communicate with each other through the wormhole but what they can do is they can send things into the wormhole from either side that can meet in the center so while communication from the outside makes no sense that's the non traverse ability of classical wormholes it is possible under certain circumstances certain circumstances that may have to be engineered and it may even be hard to engineer them but two people can jump in and test whether there was a wormhole there by jumping in and discovering each other Alice and Bob can discover each other they say we know there was a wormhole there it's a cold comfort because I'll soon buy at the singularity but never mind they've done a little experiment that tells them there was a wormhole all right the punchline of the ER equals e PR joke is that ER and EPR may really be in some sense the same thing in what sense are they the same thing well that's the first thing I want to talk about a little bit in what sense may they be the same thing and how far should we expect to be able to push this idea JM stands for one maldacena and LS stands for myself first of all I I assert now I think most of you who studied both black holes particularly in anti-de sitter space recognize this and would probably largely agree with it and tangled black well let's start with this one black holes connected by einstein-rosen bridges are entangled I think probably 95% of the community of people have thought about two sided black holes and things would agree that black holes connected by einstein-rosen bridges must be entangled on the other hand go a little bit further and this is the converse statement and I will assume it that entangled black holes always have some form of einstein-rosen bridge between them these are converses of each other and I'm going to assume they're both true I don't think it's sensitive to have them entangled but I think what is sensitive is the character of the nature of the geometry inside the but we'll talk about what it means okay what about objects like elementary particles entangled elementary particles is there any sense in which there is a wormhole between them I don't know maybe someday there will be a notion of quantum geometry in which this thing makes sense down to the single qubit level well the single qubit or the entire qubit level but at least until the last part of the lecture I will not assume that I will assume er equals EPR for black holes okay so what is the meaning of it I will take the meaning of it to be that entanglement is a fungible resource now I didn't know what the word fungible was until about a month ago resource I know what that means a useful thing for doing things in this case the useful thing for doing things it's useful human communication such things as quantum teleportation and so forth what is fungible mean fungible here is the key point that it it can be its form can be changed energy is a fungible resource it can go from electrical energy to chemical energy the mechanical energy the potential energy bla bla bla bla bla and you can always go back and forth between them so that's what fungible means in some forms of entanglement oh one other thing is entanglement conserved like energy not in general but if you have two distant systems which are too far away to communicate or interact with each other and all you're allowed to do is local operations on each side then it's and then it's conserved so the entanglement between two distant systems is conserved and in that sense it's conserved as a resource okay so what forms this ground state entanglement everybody in this room is probably calculating ground state entanglement of something or other some quantum field theory or rather there's entangled particles I will add to the list now einstein-rosen bridges are in stein Rosen bridges that's that's the meaning here of the R equals EPR that is one of the kinds of entanglements that can be traded back and forth for each other with each other and the fourth Pradhan lecture not on the third part of the lecture I'll give you one more form of entanglement okay let's start with vacuum entanglement just want to show you can go back and forth between them vacuum entanglement means just simply stated virtual pairs can be produced in the vacuum and the virtual pairs will generally be entangled if you scatter particles off the virtual pair scatter real particles off the virtual pair the entanglement can easily be transformed to the real particles this thing just becomes a final diagram in which two unentangled particles come in interact and go out and tangled but you can also think of it as a transfer of the entanglement here to the to the particles let's suppose that Alice and Bob have made a bunch of entangled particles somehow perhaps from the vacuum so Bob and Alice now have a lot of entangled particles bob has his share Alice has her share and the shares consist each in each case of half of the bell pairs bill pairs imagining bell pairs all right we separate them they go far from each other as far as you like and then Bob takes his particles Alice takes her particles and squeezes them together until they form two black holes maybe gravity squeezes them together they form two black holes then the idea of ER equals EPR is that that creates something which has some form of wormhole between them now how can they test whether the wormhole they can jump in and see if they find each other well generally they won't find each other generally that won't work but there are operations that they can do on the two sides that can convert them back to a configuration where which is still entangled where they can jump in and find each other that's an assumption that's an assumption that there are unitary operations local unitary operations on either side that will convert the entangled two state to some particular form which allows which is smooth enough to allow to allow them to discover each other I hear some work what can they do from there well Bob concealed his black hole in a box prevent it from evaporating Alice can let her evaporate this is just supposed to be a cloud of in a cloud of particles here this cloud of particles or the result of Alice allowing her bike hole to evaporate and then we have entanglement between the black hole and the cloud of particles both clouds of particles both black holes can evaporate and then we have two clouds of particles in fact when that happens when that happens what you get is a big cloud of particles which is so thoroughly scrambled up that no matter which way you slice it or cut it you'll find that it's extremely highly entangled well you can go from this by operations on the two sides local operations on the two sides you can readjust and get back to the Alice Bob sharing bell pairs so these are all forms of entanglement and this is an example of the fungibility of of entanglement and including this guy over here is it useful to think of a single bell pair as a highly quantum mechanical version of an einstein-rosen bridge I don't know and mostly I won't assume it except at the end for fun okay so let's get now to ER equals e PR and its relationship to Everett and Copenhagen first of all what is Copenhagen Copenhagen I mean the Copenhagen interpretation of quantum mechanics and what is that in Copenhagen you imagine there's a single outside observer who is not part of the system very important they not be part of the system has control over the system and can do experiments every time an experiment is done the state of the system irreversibly very important irreversibly collapses the wavefunction that's Copenhagen you won't know where you know no Copenhagen you use it it's a brilliant idea and it's very very useful okay but it makes an assumption unrealistic unfair assumption the unfair assumption is that there's some sort of uber observer who himself is not part of it the quantum mechanical system the experiment is not governed by the rules of quantum mechanics but an extraneous no rule involving collapse Everett's idea and the basic thought that Everett had which is all I really want to take from Everett is we ought to be able to do better and we ought to be able to think about systems which have many many subsystems any one of which well first of all any one of which would could be thought of as an observer they observe the rest of the system they observe each other and all of this should be contained within the rules of a single quantum mechanical description all right so I would say when you start no no I would say that when you when you start to talk that way you're talking about Everett so it's it's fungibility of Everett I I would say that when you when you start talking that way then you're talking then you are talking Everett's language but the main point is that these are sort of two useful ways well one of them is useful the other may be deeper and more general okay so now we're gonna yeah we're going right there we're going straight to witness friend okay everybody no weakness friend I mean anybody here never heard of Wigner oh thank god [Laughter] all right there was witness friend witness friend was an imaginary character and witness friend was a part of a cat experiment I think that we're gonna cooked up but it just asks himself something like the question supposing my friend goes in well the cat begins in a cat state half dead half alive but let's go further than that let's just say an enormous superposition of many states witness friend comes in and observes the cat the result of that in Copenhagen quantum mechanics is to collapse the cat the cat wavefunction on the other hand Wigner is waiting outside the room he can look at witness friend he can observe he could also observe the cat but these lines here are not important ones it's the lines connecting the observers Wigner can measure witness friend and he can confirm or find out what a witness friend saw okay but Wigner if he wants to he may think of his friend and the cat as forming a single system and before he comes in how would he describe that system while we know how we describe it we would describe it by saying Wigner witness friend and the cat are entangled then witness friend can come in and so forth and so on I introduced Einstein over here at the I told a joke that originally I had him called Schrodinger but the cat got so scared of Schrodinger that he ran away and I had to call my wife living my stupid joke okay all right so let's start with Copenhagen this is step number one witness friend observes the cat and collapses the wavefunction that's the standard Copenhagen picture same step in Everett's language in every I don't know if this is Everett's language or not this is a language of entanglement that that the to interact and enter into a entangled State this is a typical entangled state summed over the cat's witness friend states or we may also find for example if we wait a little bit and allow them to evolve they'll stay entangled but the entanglement wavefunction here may change to some general unitary matrix so a more general version of the maximally entangled state here would involve a unitary matrix here and that unitary matrix could involve the evolution of the system but now let's use the fungibility of entanglement to relate this to a question about black holes we'll take the cap and squeeze them into a black hole we'll take Witness friend squeeze him into a black hole and what will we have we all have two black holes by virtue of the fact that they were entangled they will have some sort of wormhole presumably by some sort of operations originally I said the cap and Witness friend can now jump into the black holes well the cat is the black hole and weakness renders the cat also the black hole so we need somebody else the cat's friend is Alice we can his friends friend is a Bob Bob can jump into witness friend Alice can jump into the cat and meet in the center that's the that's the idea of going back and forth between basic quantum mechanical ideas and ideas about wormholes in this case another way to describe the entangled state if you like if you like tensor networks is to say that the cat and wing this friend are connected by a tensor network the tensor network is just another way of talking about the wormhole and the one thing that happens is as time goes on the tensor network gets longer and longer as a function as a consequence of the natural evolution of black holes that's not too important in this lecture but ok now step number 2 Wigner is friend has measured the cat now Wigner is going to come to the room and measures friend let's see what happens we start with the entangled state of the cat and witness friend and then Wigner comes in measures and collide this is the Copenhagen description collapses the wavefunction to one of many of the pieces of the entangled state and let's say that witness friend does the experiment in the Z basis the Z basis were thinking a bunch of qubits in some basis makes the measurement what does that look like all right so let's so let's see if we can who can guess what that looks like here's it I will go back to the tension network description but it's not important the cat and witness friend are connected by this large tensor network that represents the wormhole and now somebody comes in measures witness friend projects witness friend onto a simple state a state which is just a product state makes the measurement in the Z basis projects witness friend onto a very definite and simple state and now the two sides are no longer entangled they're not entangled witness friend is in a definite state the cat is in a definite state if you're interested at all in complexity I would tell you if the care of this was a very complex state then it will be the cat which inherits all the complexity but that's ok that's not important right here let's call this snipping this is a new geometric concept snipping the einstein-rosen bridge making the experiment at one end of an einstein-rosen bridge cuts it and snipped it like with a scissor according to Copenhagen the measurement is completely irreversible the complexity on both sides grows but whatever happens as long as the two ends cannot come into contact with each other they remain unentangled and Alice and Bob can no longer meet behind the horizon so that's the that's the Copenhagen picture of what happens in step 2 step two according to Everett the cat witness friend and Wigner all become entangled in a tripartite entangled state remember they're all in a pure state the cook combination of them they're in some pure state first witness friend is interacted with the cat made a wormhole and now Wigner comes and interacts with the assemblage both of them and the whole thing enters into some kind of tripartite entangled state tripartite entangled state means well it says three entangled subsystems in some way and if ER be really is true if VR equals the RB is really true this tripartite entangled state ought to correspond to some kind of wormhole or some kind of einstein-rosen bridge and if so a meeting in the interior should somehow be possible well now we have a little bit of a contradiction the Copenhagen way of saying things suggested that when they when you snip it's no longer possible for the two sides to commute to meet in the center on the other hand the Everett way seems to suggest some sort of tripartite and tangled State which would involve some kind of einstein-rosen bridge and you should be able to meet in the center now you could stop right in you could say oK you've demonstrated the contradiction aren't I don't think so it means you make a measurement at one end you measure one black hole you make a complete set of measurements on one black hole of course because they become become unentangled if you have an entangled state and you measure one end you destroy the entanglement right and the space-time will change right that's the that's the Copenhagen view of it the every way also says the space-time changes but in way that corresponds to three subsystems being entangled presumably if we now take Wigner and collapse him into a black hole then we would have some sort of tripartite wormhole I don't think that that's correct all right so I think there's a contradiction the one one version of thinking about it you can't send any kind of message through the wormhole the other way of thinking about it well you have some sort of tripartite wormhole it ought to be possible to send something not something through it but something from both sides which meets at the center is there a contradiction it says no but we need to know a little bit more about tripartite entanglement okay so here's here's the initial of the notes reduce it down to us a cubit problem the cat witness friend Wagner they're all single qubits the cat and witness friend after witness friend measures the cat they find themselves in an entangled State Wigner hasn't come into the room yet Wigner comes into the room makes a measurement here's the way the measurement happens if he he starts in the down state the zero state if Wigner finds his friend in the zero state he stays in the zero state if we can define system salt it finds his friend in the one state he flips to the one state that comes to tutor measurement a measurement with the apparatus and the observer and everything else is just one qubit and that takes you to a state 0 0 0 + 1 1 1 it is an entangled state and has a name that's call GHz state G stands for green burger horn and Zeilinger this is a sort of generalization of a bell pair to three qubits and it is entangled but it's entangled in a rather interesting way if any party like for example Wigner is traced over the other two let's suppose we trace over Wigner this will be the resulting density matrix of the cat and witness friend this is called a separable density matrix it has the property that it is just the sum of two unentangled density matrices and it this kind of density matrix has no entanglement at all between the cat and witness friend this destruction of the entanglement is a representation of the Copenhagen collapse of the wavefunction and that's kind of the end of the story okay but although no two parties in this GHG State are entangled with each other each is entangled with the union of the other two the H is entangled with the union of the other two and this allows possibilities that Copenhagen would have no way of expressing not without that without enlarging the system and using the using what you said right which I call over it okay all right let's let's just come back to cats which are made out of lots of qubits here's a cat which is made out of lots of qubits when his friend is made out of lots of qubits after step one the cat and witness friend incidentally when I speak of Linda's friend I'm speaking about a register that has a memory when you do a measurement you have to be able to register the result of the measurement or the experiment no experiment has ever done unless it's been registered in quantum mechanics so what I speak a witness friend I mean a system which has a memory which is rigid rich enough to encode the result of the measurement of all the qubits of the cat alright when that happens the becomes entangled witness friend perhaps in the form of a product of Bell pairs Wigner is still over here on the outside he hasn't done anything yet but then when Wigner makes his measurement what happens is the system becomes a product Gog states let me go back a step I forgot to tell you what this is this is a little pencil network that just represents the ghz state of this three legs comes together at the center and it's a tensor which simply says that the three letter it's nonzero if all three legs are the same otherwise it otherwise it's zero so this is an attempt to try to draw some pictures representing the ghz state after the measurement by Wigner of witness friend well we just get is a product a tensor network consisting of a product of these ghz triplets each degree of freedom of the calf has now been measured and is now encoded in one of the qubits of Wigner's register so that's what tension network might look like for Wigner measuring his friend now once this happens and assuming that we now collapse the three participants into black holes we can now follow them and these tensile Networks begin to grow they begin to grow just because wormholes have this growth property they tend to grow and in fact they tend to grow very quickly that's the increase of their complexity in another language but I don't want to talk about complexity so we'll just say they grow and they do so after a while after having done the measurement and collapsed the three participants you will have some kind of tripartite wormhole but it will have some obstruction in it and that obstruction is very interesting it represents the GHz character of the measurement or the state that's produced by a measurement but on the other hand it now becomes an object it's an object down deep in the wormhole of a tripartite wormhole system we can think of it as a physical structure whose properties in fact reflect the duality between Copenhagen and Everett I'll come back to what I meant by that in a moment all right let's earth there are wormholes or einstein-rosen bridges on Mars and his colleagues have studied them a great length which are smooth they are the analog of the thermal field double einstein-rosen bridge for two particles for two black holes they're smooth they have smooth geometries and one would expect that if somebody jumped in over here and somebody jumped in over here they might meet you might even expect that three people could meet in the center okay the GHz brain whatever it is is different than this it's fundamentally different in that no two observers can ever detect each other when they fall in this this and here's what's known incidentally just from an information theory point of view or it's not known it's suspected by these authors and these authors here that if you try to distill different kinds of entanglements out of these smooth wormholes they have very very little if any ghz entanglement they don't contain any of these ghz entangled triplets on the other hand this ghz brain that we constructed by making a measurement in this way it's full of G of GHz States lots of them and we could distill them this distinction is invariant under local operations on operations that take place at the two ends of the 3 ends locally just distinction so this is a different kind of beast than this whatever it is it's a different kind of thing but it is a thing what do we know about it well from the Copenhagen side we know that no two of them can send messages which we'll meet in the centre that we've established on the basis of the Copenhagen interpretation once the there's made it snips the it snips the the einstein-rosen bridge and there's no possibility anymore of meeting at the center that's presumably true of love yes that should be true on the other hand from the Everett point of view what you create is a three-sided einstein-rosen bridge and each side is entangled with the union of the other two this presumably means that a message can be sent if Wigner and his friend cooperate in some way if they can cooperate in some way then a message can be sent into the interior this would be the expectation and if that message was sent in from the other side they should be able to meet in the center we do have entanglement between the side and the side we simply just don't have entanglement between any pair the suggestion would be that a message can be sent messages from the two sides can be sent that would meet at the center but only if wiggins friend and Wigner can cooperate in some way more than cooperate they basically have to reverse the measurement process how do you do that so I'll give you one algorithm protocol for doing that Einstein is going to help them Einstein is gonna observe Wigner number Wigner and the Witness friend observed the cat we're gonna observe this friend and now Einstein is going to come and observe a Wigner now if Einstein observes Wigner in the same Z basis that Wigner did his experiment all he does is confirm all he does is confirm and get the same answer that wouldn't it out what happens is you get a bigger cat state you get a state one one one one plus zero zero zero zero okay it's boring it's not very interesting what's very interesting was what happens if Einstein does a little trick he measures way but in the ex basis in a a conjugate basis here's what the X basis was your own one mean the Z basis Sigma Z left and right mean the X base is Sigma X here's the relation between the Z basis and the X basis with Sigma over square root of 2 set equal to 1 okay so let's see what happens we start in the ghz state and then stein is going to come along and see what happens we start in the GI in the ghz state an Einstein is going to make a measurement of the last qubit here this is now our qubit description we're going to measure the last qubit but in the X basis so what we'd like to do is we would like to express this state in the X basis of the last qubit that's easy to do 0 is left + right 1 is left - right if we combine them together what we find is left left iced Einstein having measured left its correlated to 0 0 + 1 1 this is an entangled State so by virtue of having measured in the X basis and having detected left Einstein has pushed this back to the original and tangled state between the cat and and witness friend on the other hand if he measures right he still projects this back to an entangled State but it's the entangled state 0 0 minus 1 1 so off hand Einstein may know which of these two is correct but nobody else as far as everybody else is concerned we don't know where there's this one or this one we don't know which entangled state it is can Einstein do anything to make sure that you get back to the particular initial an entangled state that the cat and witness friend began in namely this one yes Einstein can't do something here's what he does if he detects left he does nothing why because he's got the right state on the other half of the system if he detects the right he simply acts with Z with Sigma Z on witness friend that means he flips the sign of this piece here he flips the sign of the wavefunction of witness friend and returns the state the 0 0 + 1 1 in other words by doing by taking the classical information that he has after he does the experiment and using it to decide what operation to do nothing or operating with Z he inevitably returns Wigner sorry the cat and witness friend to the original entangled State and that's interesting somehow what is Einstein done he's reversed the measurement that the Wigner did he's reversed the measurement and basically got back the original entangled State what does that mean in terms of wormholes and so forth well if we have lots and lots and lots of qubits and we apply exactly the same logic after Einstein measures Wigner Wigner and the cat and Witness friend will be in one of many many states Einstein will know which one but being one of many many states for example Einstein might have measured left left left left left 20-point measured Wigner in which case the cap and witness friend are projected back to the original entangled state that they started in which we'll assume had a nice wormhole on the other hand he may find Wigner in some other state then there will be entanglement between the two sides but the entanglement will presumably be of some other kind not consistent with a smooth wormhole that would be the expectation that you have a mess in here a mess in here if you unitarily rotate a state with a nice wormhole unitarily rotated on one side you get a mess that's known so there's lots of terms here most of them involve states which are bad on the inside they are not nice wormholes but Einstein has some classical information and he can take that classical information and use it to perform a unitary operation on weakness friend again exactly the same kind of logic will bring the cap and Witness friend back to the smooth wormhole state with Wigner being either this this this is or that and einstein knowing it in fact Einstein will be entangled with lidner so Einstein can use the trick of making the measurement in the X basis to reverse the measurement and to bring the cat and witness friend back to the state where in fact somebody can jump in and meet in the center that's how they would test that this that this protocol actually worked that's it for lecture one what's the result the result is experiments can be reversed although this important point here the yeah let's go back to step one important point everything that Einstein did involved Wigner and his friend and not the cat so this was a case where by manipulating witness friend and the cat he made it possible sorry with the trend and Wigner he made it possible for the cat and women and the other side to communicate something into the interior it's consistent with the GHC property yeah no it's not no question the amount of entanglement it's a question of the way of the the pattern of entanglement yeah so when I say you can jump in and meet I mean you have to do possibly some very very complex operation on the two ends before you jump in and meet but whatever it is the the operation is local at the quarry maybe maybe I don't know I never understood the singularity yeah very likely but um but in general in order for Alice and Bob to meet in the center they have to do something difficult it's not an easy operation and they have to arrange the state just right and otherwise they'll hit there or before her that's right which is a complicated thing yeah that's right okay but okay let's come to the second part teleportation through a wormhole just a fun little idea can you teleport information through a wormhole yes yes but let's saw one do we have three systems Alice has a black hole Bob has a black hole and Charlie over here who is special for some reason or another Charlie has some third system the third system I'm going to assume has about as much information as either of these two black holes and it could be a black hole doesn't really matter and what Alice and Bob want to arrange is for Alice to be able to set the Charlie is next to Alice Alice wants to send Charlie to Bob she wants to send the information the quantum information of Charlie to Bob okay but the goal is to send Charlie to Bob without sending any information about Charlie through the exterior route the exterior route means not using the wormhole now those who know about quantum information recognize this problem and saying oh we know exactly what it's going to do next then you probably do but the answer is that if Alice and Bob's black holes are not entangled no wormhole between them this is not possible you can't do this the only way to send Charlie from Alice to Bob is to send Charlie from Alice to Bob and somebody halfway through could intercept it and get the quantum information that was intended for Bob okay but if Alice and Bob are highly in power are entangled in a wormhole or and highly entangled if they share entanglement and two over two black holes share entanglement then in fact you can send information through the all and particularly you can send Charlie through the horn through the wormhole in a way that I'll show you what what the protocol is I'm not going to prove that this works if you want to see the proof of it that's in a paper I wrote but that's but it's more or less obvious that it works all right the first thing you do is you take Alice's and Charlie you take Alice and Charlie and merge them think of them as black holes you can merge them if Charlie is not a black hole that just means you throw Charlie into the black hole and you make a bigger black hole basically with twice the information that I always had in her black hole to begin with then you wait and the waiting is important you wait a scrambling time a scrambling time is the time for the information to get all mixed up in here so that when you look at any subsystem you can't tell what you really have any small subsystem you can't tell what you really have you wait a scrambling time and that's important to the sod and then Alice makes a complete set of measurements on her black hole which is now has twice as big as it was or twice as much information she makes a complete set of measurements on it and she gets a random output in particular the random output is random relative to the state of Charlie why because she waited a scrambling time the scrambling time mixes stuff up badly enough that the clatter that the classical information that Alice gets by doing this experiment is completely uncorrelated to the state of Charlie where is Charlie Charlie is somehow trapped oh one of point is that by making this experiment she snips the wormhole she snips the wormhole the wormholes are now disconnected they're not untangled anymore where is Charlie Charlie some was in the bag here somewhere is in that bag of information there now that doesn't mean Bob can get Charlie out you would expect Bob can't get Charlie out Alice has put all of her information the result of her experiment she's put it into her notebook it's classical information in her notebook and she sends her notebook to Bob okay that takes time we're not going to beat the speed of light constraint here that's not the purpose but anybody who intercepts the the the notebook finds out nothing about Charlie no information about Charlie so the information about charlie is not in that notebook somewhere charlie is somewhere in here or if he's anywheres okay so now bob has all of the information in alice's notebook what does he do with it he reads the notebook he looks at the series of bits and depending on the series of bits he does a unitary transformation on this end over here the particular unitary transformation for each possible outcome of the experiment on the left side here algorithm for what unitary transformation to do on Bob's wormhole here and if he does those transformations correctly out pops Charlie from here yeah of course of course it is of course it is so the next part of the story is well okay then Alice and Bob will stand in the air and it is a big deal I know about this this is called quantum teleportation we've been doing this for years except it's in a fancy plate in a situation with it's just want teleportation and Bob says no yes yes it is just quite easy agrees this is just quantum teleportation but now let's check whether there really was a wormhole there we'll jump in and we'll see if there was a wormhole there and the answer is that if there's a wormhole if Charlie successfully got to the other side there must have been a wormhole there and they will discover a wormhole there if there was no wormhole there and they have to unentangled black holes to begin with they will not meet in the center so the interesting new thing is this correlation would be let's call it the experiment of Alice and Bob jumping in and discovering whether they can meet in the center no meeting no teleportation if there's teleportation it means they can meet that's what that's what the new one correlation is so I find that interesting okay here's another way to picture the same thing same kind of drawing I had in the beginning here's Alice here's Bob there's Charlie Charlie jumps into Alice's black hole Alice makes a measurement and sends classical information around the long way that classical information if it's intercepted says nothing whatever about Charlie if it's not intercepted Bob uses it and produces Charlie okay so that's the that's the teleportation now how much time do we have ten minutes yeah okay two slits in a wormhole now I'm going to tell you another kind of entanglement which usually is not thought of as entanglement but it is entanglement and I was surprised when I thought about this that the the familiar experiment that I never thought had anything to do with entanglement does have to do with entanglement but first let's talk about just interference of wave packets we have a single particle not enough to make any entanglement we have one particle and only one particle but let's put it in some superposition of states wave packet over here or wave packet over here single particle is in a wave function which looks like this we can allow the wavefunction to evolve and if it evolves perhaps these two come together it may be that there will be a node in the wavefunction or there may be nodes in the wavefunction at different places here's what you can be guaranteed if you look for the particle it will not appear where there are nodes for certainty if you had only one of these functions it would appear where those nodes would have been if you have two of them the particle simply won't arrive where the nodes are what does this have to do with entanglement has nothing to do with entanglement this is a problem involving one particle not two particles I'll think about another way here's what I'm going to think about instead of concentrating on the particles I want to concentrate on the degrees of freedom contained within a box a box that happens to contain this wave packet and another box that happens to contain this wave packet this same wave function that I described before can be rewritten in another way it can be rewritten as a wave function saying there is one particle on the side no particles on this side - just because I have a minus sign in the wave function no particles on this side one particle on this side if I concentrate on the field you know the creation and annihilation operators within these boxes all of a sudden I discover my state is a bell state it's an entangled state of two boxes now I'm going to make a crazy assumption I'm going to assume that there is a microscopic version of some sort of er equals EPR if that's true that tells us there is some sort of primitive one qubits worth of a einstein-rosen bridge connecting the two boxes ok now that may be too crazy for you it may well be too crazy for you but let's pursue it anyway let's see what it says let's see where it goes let's take that still slit experiment one way of making a superposition of states would be to send a particle a beam of particles through two slits and they come out in a superposition of States incidentally what this means over here particularly on this side is it doesn't mean a particle over here in a part of over here it means a particle over here or a particle over here in other words I'm imagining one particle goes through and either goes through this slit or it goes through that slit it comes out over here it's either here or it's here it comes out here it's either here or it's here in other words it's in a superposition of states of these two places if instead of concentrating on a particle I concentrate on boxes which surround these two regions what I would say is we end up with a state with an entanglement between a box over here and a box over here if I then go further perhaps too far and say that means that some sort of primitive einstein-rosen bridge between them then after the beam has passed through the two slits there's an einstein-rosen bridge that follows this thing until it hits the screen the einstein-rosen bridge so to speak reminds of particles that both bridges were open that both holes were open what happens if you close one hole in the same picture if you close one hole this is the possibility of the particle going through is destroyed the particle if it goes this way gets stuck over here it doesn't go up past here on the other hand if it goes through the upper hole it goes through that means that the einstein-rosen bridge that forms because of the entanglement between a box over here in a box over here is always connected to here and it's quite simply the point is it's simply different than it was when you open both boxes so the einstein-rosen bridge is the thing which knows whether both boxes were open or not or whether both slits were open or not that may be a little bit too crazy it's beginning to sound too much for my taste like hidden variable theory but nevertheless if we believe that er equals EPR can be pushed to the level of single qubits and this is the kind of picture that might represent a Einstein Rosen bridge picture of the two-slit experiment okay but now can we test can we test whether there is some notion of connectivity spatial connectivity between here and here here's the experiment that I suggest we send not one particle through but many particles through each particle that goes through with either goes through the upper hole on the lower hole and makes an entangled pair of boxes a box over here a box over here by the time it gets to the box over here this the box becomes entangled just from a single particle it becomes an entangled pair of boxes particle here no particle here no particle here a particle here and we do this many times we send many many particles through and we connect we collect them we collect them in the boxes one possibility is that all the particles went through the upper hole another possibility is they go into the lower hole but mostly we will find about equal number of particles here and here and we will find these two sub systems in a highly entangled state highly entangled because each one that went through and tangled the two boxes next we collapse them into black holes we have now created by this interference experiment we've created two entangled black holes Alice and Bob perfectly free to try to jump in and discover whether there's a wormhole between them and I maintain that they will find the wormhole between them which can be thought of as the collective effect of a large number of microscopic wormholes if you like that's just a thing that I find suggestive I think that's the end of lecture three what I would like to say about it is that I think there's evidence that the the non localities of quantum mechanics and non localities of gravity which means einstein-rosen bridges may in a sense be the same thing present that only applies to black holes but entanglement is fungible so you can change it from one form to another changing it back and forth from one form to another and doing experiments on it the game I think that's all I wanted to say one more thing many many other quantum questions that can be translated back and forth meaning bow and his friends have studied the meaning in the language of ER equals EPR of things like the no-cloning theorem other things of that nature and there are many many correspondences of this form that do suggest a much to my mind a much much deeper connection between gravity and quantum mechanics than just saying we should quantize gravity but I'm getting old so I have crazy ideas okay so you can make a lot of progress if you work in the limit what's your view trying to make progress and understand dangerous yeah I don't know that's why I tend to hang my hat on this idea of fungibility and going back and forth you know you wanna you want to ask what's the what's the character of a bell pair a simple bellperre what kind of does it have some sort of primitive notion well about the best I can do is say let's take a lot of them and let's combine a lot of those primitive wormholes and if the whole idea makes sense then we should call a we should create a big wormhole that's the best we know how to do with President perhaps there's some notion of quantum geometry which would allow you to think as I was trying to think in the last part of the lecture here but I that's a yeah yeah that right there's an object there to study yeah no no the expectation is that whatever GHz brain is it is now it is not smooth right it's a it's almost certainly not a smooth classical geometry it's some sort of obstruction which is localized somewheres in the wormhole but I don't think it has a classical geometric description and what we do know is that when you go from three to four then I think there's almost a theorem I think that that there's no GHz for particle GHC in the end the smaller wormholes and right then answer the question yes okay good what's that oh it's complexity from that I don't think so but I didn't think so you caught me by surprise I never thought about that it's complexity fungible I don't know we mail you no no no no no I I think I think all predictions from outside the black holes will be absolutely identical to what you would expect from entanglement yeah I don't think you're gonna I I would be very perturbed if somebody found an experiment you know I think anything's Perriman to from outside the black hole should be consistent and should give the same answer it's just saying they're entangled yeah it's only the only new thing is if you allow your experimenters to jump in and ask whether they find each other or not then there are correlations between whether the black holes are untangled and whether they can find each other or not that's the new kind of thing that would say what's that as they evaporate particles go off they're entangled with the black hole and so einstein-rosen bridges formed between between the evaporating black hole and the entangled particles that go out at the end of the day all you have is particles but the particles are entangled the first half of the particles are highly entangled with the second half of the particles and I believe you should imagine there's an einstein-rosen bridge with the particles just being the mouths of the the many mouths of the of the einstein-rosen bridge so you can't detect things oh yes you can well no no you can't if you stay outside but what you can do again it always comes back to the same thing you've got to commit suicide but but but what you can do is you can collect those entangled particles collapse them back into black holes and then jump in and see whether you can find each other so it's always the same game you use this fungibility to turn things into black holes and then do the experiment of seeing whether you can find each other inside laughter I think not something not easy for somebody to make causal patches entangled within a causal patch doesn't open up into a black hole I think you better get standard answers okay but in that case you do I think we do expect that they can find each other because the inflation stopped so we expect me discover each other a hair yeah yeah yeah but I don't think this is an honest example of the same thing I think this is just an example of the classical end of end of inflation something nasty in between oh yeah you expect something nasty in between yes right right right right but yes I think the sort of space is the case of this right and you can you can jump into the region in between from both sides [Applause] you

Channel: Graduate Mathematics

Views: 71,134

Rating: 4.8950553 out of 5

Keywords: Leonard Susskind, Copenhagen, ER=EPR, quantum mechanics, kitp, ucsb

Id: LndrOIXG3i8

Length: 68min 32sec (4112 seconds)

Published: Fri Nov 03 2017