How entangled black holes create Einstein-Rosen bridges | ER=EPR | Leonard Susskind

I once gave a seminar at Harvard long time ago and after about 10 or 15 minutes Sydney Coleman jumped up and he said Oh what you're doing is beautiful I love it I've never seen it before but let me try to finish the seminar for you sit down well I did and he finished the seminar beautifully so if you're as good as Sydney Coleman I invite you to to finish my seminar for me but otherwise please just let me finish this is true story well it's just yours or any of my stories with okay um a thing which I've learned through experience is that when you keep seeing thinking the same thoughts over and over and over again and in the process refine them and refine them and refine them using the same logic over and over and over you often just get deeper and deeper and deeper into your confusion and the more precise you try to make those arguments the more you get confused the reason is you don't want to take wrong arguments and be too precise with them just just a mistake better question your assumptions best question your assumptions even the most the ones you think are most solid when you get into these really really paradoxical situations and assume that you're making some mistake we're talking about the abs eternal black hole and Warren has studied over the years consists of two quantum field theories one on the left one on the right that's the that's the holographic dual of the system to two quantum field theories and if you're interested in the thermal field idealized double state which I think we know although I think still could be argued I think but but I but most of us agree that this state has no firewalls so let's analyze it and see what's going on all right the thermal field double just to remind you I think most of you know it I'm gonna feel double state it's just some over the energy levels of either side e to the minus beta over 2 e and tangled State highly entangled state a lefty right and that's the set up and it's a symmetry symmetry on the time translation invariance or a time translation invariance means this funny kind of time translation invariance where you push up on one side push down on the other side but that's sufficient to say that if there's no firewall at time T equals zero then there will never be a firewall because by symmetry you can get up into the corner here and discover that there would be no firewall for Bob jumping and over here by applying the symmetry operation which lowers you here and raises you on the right hand side okay the thermal field double state can be thought of in at least three ways the first way as a trick for calculating correlation functions in the thermodynamic system non equal time correlation functions I'm not interested in that sense the second the second way you can think of it is as a pair of black holes infinitely distant from each other or you can say aren't two completely separate non interacting sheets two separate black holes and two completely non interacting worlds where the two black holes are maximally entangled maximally entangled I take to be in this kind of state here all right so if you have two black holes in otherwise non-interacting world in fact not otherwise and of completely non-interacting world but you entangle them in this form here the statement is that they form a einstein-rosen bridge between them formal no that's the right word they have an einstein-rosen bridge between them and if so at least under some in certain circumstances you come to the very interesting fact that these two non-interacting worlds nevertheless can communicate not communicate outside the outside while somebody falling in here can meet somebody here and that's a rather curious fact that that even though they are completely disconnected worlds if you manage to make a pair of black holes that have this kind of entanglement it seems that two people could jump into the same black one into the left black hole one into the right black hole and meet at the center if they jump in early enough curious the third interpretation is two black holes in the same space-time but very far from each other so a black hole over here and another black hole over here but again with horizons identified corresponding again to the same kind of maximum entanglement same kind of maximal entanglement nobody has ever proved that that such correlated black holes have n Stein bridges between them but I'll take it as a given and we'll talk about a little bit we'll talk about what it means okay first question that should occur to you is how do you how the devil do you make such things how do you create such things which have this kind of entanglement for very very distant black holes like this what's the formation mechanism okay so let me begin with one example which is known this is an example I can't remember who the authors were I know Andy and were you involved a young Garfinkel right studying pale creation of near extremal black holes in an electric field what they found was that pair creation can happen number one number two the coefficient in front of it the density of states coefficient was consistent with saying that they were maximally entangled in other words there was a factor of e to the entropy of one of the black holes which corresponds to exactly this kind of situation over here maximal entanglement between the two of them and finally their geometry there instant-on indeed did contain a an einstein-rosen bridge between the black holes they were accelerating outward accelerating away from each other so indeed you can separate them and the bridge just grows rapidly so it is possible to to create to create this kind of situation so let's talk about the various ways of creating two distant and tangled black holes or even just taking two black holes which don't have bridges between them and create a bridge between them the simplest way would be to make a whole bunch of there's my picture for two little black holes created nearby perhaps by the swing of creation mechanism is one and it's intact well it is entangled with this one over here but for the moment it just has a bridge you create sets of pairs like this and then you just let them fly out and take care for them put them into this black hole they care for them and put them into this black hole these bridges will sort of grow together though was it coalesce is the right word they'll coalesce and form some kind of bridge between here and here I think under appropriate some circumstances you can make that bridge be a classical pretty classical geometry okay the other thing that you can do to create entanglement between the two black holes is create entangled Bell pairs I always draw a bell pair by putting a line between the two particles okay so what I will mean by two particles or two qubits with a line between them is a bell pair Bell pair means a maximally entangled and that doesn't even have to be maximally entangled you're using your entangled systems as a resource stretch them apart the same way drop them into the black holes and you'll create entanglement between them it is a conjecture there's no theorem because I don't even think there's a basis for for being enough to even formulate the theorem but the conjecture is that if you create enough entanglement this way you will create an einstein-rosen bridge between the two black holes okay so the hypothesis the conjecture is this conjecture which we write through the which Juan wrote though the clever acronym ER equals EPR when I saw that I just do it had to be right how can a few wrong how can we waste such a such a thing that's the way I used to ride it when I would write in the one messages I would say using P equals 14 okay now clearly clearly this does not mean that any kind of maximal entanglement between some qubits I don't have to separate them doesn't matter where they are in space that any kind of entanglement between qubits forms classical geometry for example just having things in form of bell pairs this bell pair on a tack I'll entangled with this Bell pair on entangled with this bell pair if we want to think of this as a very highly quantum mechanical bridge which I don't think means very much the whole thing does not form any kind of classical geometry it just forms a whole bunch of these super quantum mechanical things all right now supposing we come along let's call this the left hand side let's call it alice's share the right hand side bob share and now come along with a unitary scrambling operator that only scrambles that scrambles the right hand side a random unitary that scrambles that axon I guess it's Alice's share a ket remember which was which which acts on alice's share and that creates an entangled state where everybody is entangled with everybody else everybody is entangled with everybody else store very very high entanglement entropy maximum entanglement entropy very close and it's pretty clear that that has to make some kind of for the extent that this hypothesis is true it creates something which is connected in a way which we can't separate off any subsystem of them so I would tend to draw this again this is in the in the spirit of free flying for a while until we get some ideas and get just let's think of this then as some kind of structure this is the wormhole the real space let me draw it this way here space that's it yeah look oh yes you're right so there are qubits out here and somewhere is in the einstein-rosen bridge associated with them is more connected it must be more connected and to the extent that it does form a geometry you might expect that the area of that geometry is proportional the area when you cut through it in any particular way measures the entanglement entropy of the set that you've cut in pairs the way you've cut it into halves

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Keywords: Albert Einstein, Leonard Susskind, Leonard, physics, quantum, quantum mechanics, quantum entanglement, theoretical, stanford university, university, california, sidney coleman, lecture, professor, black hole, er=epr, schwinder, pair creation, science

Id: pY5D7ZgWuXc

Length: 12min 39sec (759 seconds)

Published: Sun Apr 15 2018