Remarks (fragments) / Time in quantum gravity / subsequent discussion / Wormholes and time in quantum gravity

0:00 This is saying, if tomorrow you said to put a Berger alarm in your house in the country, then there is a Berger alarm. So you spend hours there and you put a Berger alarm tomorrow. Will that affect the probability that there was a Berger alarm there before? Oh, I see. You're putting this at the end? This is in the fifth. Oh, but it's at the end. It's the last thing? Yes, after the last thing. The rest of that product is off the world? Oh, that's a good thing. It should sound good. I took some of your videos, but it's not that it doesn't exist. Oh, there was one, huh? Well, maybe we should give the chance to the last speaker, speaking of time and quantum gravity. Well, that's the title of it. Introducing this workshop, which I will start with. Thank you for your attention and see you in the next lecture. The argument of my talk is, what I want to do is try to bring an argument for a negative answer to this archetype, which is, in particular, time is treated in standard quantum mechanics, and then the axiom of quantum mechanics, as described, for instance, in 1930. And the main argument that I want to use is this. And, so let me start from isolated mechanics. Or better, no, let me start from, yeah. In general, mechanics, any mechanics, can be, that's the general term of quantum mechanics.

2:30 We have a system that can be in a series of moving time, with a map, and then we observe both. We have one state, we have a number. Now from this point of view, time is absolutely crucial for the very definition of a theory. I remember my first year in Italy, at college, the European way of mechanics, the study of the evolution of things. This is not the only piece of mechanics, and that is the Schrodinger picture, and obviously the other one of the mechanics, and I like the Eisenberg picture, in which states, the Eisenberg state has to be formed somehow according to the entities, and the observables evolve. So what does evolving observables mean? It means that Schrodinger observable becomes a one-parameter family. What I want to tell us is that the observable at t equal one and the observable at t equal two are... There are two different, so classically they are given by two different function of the phase. Quantum mechanically they are given by different circle joint operators. We have the set of observable and in the set of observable we have all this open plane and so we can do that. Now, this is not at all peculiar to quantum mechanics. There are formulation of class. In some sense, what I've written here, in some sense, in the eyes of the people, mechanics is reducing. Because if you have the room for each one of these... Over each one of these states, you don't have to care about any evolution or anything. Obviously kinematics becomes in the sense that having the definition of all these observable on the states is equivalent to the equation of motion. Now, what is the physical operational meaning of the generalized Heisenberg picture?

5:00 In the Schrodinger picture, you assume to be able to perform two kinds of operations. You are soon to be able to look what the time is in the middle of the clock and a different kind of operation is made. Now, I saw a number that I can take from the system, but however does not give me information on the system. And then I can observe, it's not observable, I observe an operation on the system that gives me a number that I can predict if I know the string, or vice versa, that gives me information on the string. In general, one two-observer moment may be composed by a couple of partial-observables and so on. So here are examples. And I just want to go fast. Let me just rapidly say that this is a parametrized system. I don't know if anyone understands what is written here. Tau, the variable, is nothing. It has no operational meaning. It's not a partial observer. It's not a two-observer. It's just a rubric or something. There's no way to attach an operational meaning to tau. x0, x1, x2 are on the same footing partial observable. A true observable, what is a true observable in a system like that? Well, a true observable is, for instance, this. This is an isomere observable. So if the value of one coordinate at the given fixed value of t0, so this is a number, a real number, that is an expression, is non-trivial, as I said. The definition of observable, of the isomere observable is non-trivial because somehow you have to solve the dynamic to define that. And well, I note that in a parametrized system like this, clubs are elaborately gauge-observed in the sense that they commute the constraints. This function of space-space here commutes the constraints of the relativistic path. I'm arriving close to my first conclusion, which is the following. Let's give a tentative definition of time. From a formal, mathematical point of view, I want to say that time is the presence of that structure on the set of observables that we have on the theory, and from the physical point of view, I want to say that time is the experimental part.

7:30 Why all our observable has a level? First thing, there's nothing a priori that requires that this is true. This is something that we observe in the world that anytime you want to define an observable which is meaningful, which we experimentally understand, we realize that we can do physics, this is done by two partial observables. So it's always a read-a-plot and maybe you can want the meaning. Nothing a priori requires that. This is an experimental fact of nature, and this is coded in the theorem in the presence of this structure in the state of the observer. Now, if this is true, it follows that mechanics, both from a formal and from a rational point of view, is perfectly well-defined also in the absence of time. It's just the universe in which this is not true, or a formal theorem in which there is no this structure. Maybe there is no structure, or there is a more complicated structure, or something other. I don't know. However, what I wanted to stress is the fact that mechanics make sense, and let me come to quantum mechanics in particular, and obviously quantum mechanics in the Eisenberg picture, I have the states, the states represent the state of the system, the Eisenberg state, so the entire story of the system, are observable, and maybe these observable are not arranged along lines in this way, but they are... This does not prevent me from having probability that sum up to one, as is always required, and the entire measurement. Again, X and T has no rational meaning, there is no way to touch it. This is a partial observable, and what is the two observable? Well, the two observable is again any function in phase space that commutes with a constant, so what is observable in general is something which is called the chromatism invariant. And I want to claim that these are the objects that have to be interpreted as the two observable.

10:00 And these are the objects for which we have to find the observables, self-adjoint operator in the canonical theory. And these are the servers that our theory should be able to predict. And now, if we can quantize according to Dirac's method, So if we quantize the unconstrained space-space, and we start by attaching the self-adjoint operator to partial observables, to objects that do not commute with the constraint, and then we look for a solution of the constraint equation, we have two problems. First, we don't know how to define the true observable, the one which commutes with the constraint, and we have all the problems in the definition of the constraint. Second, we don't know how to define the physical scalar product in the space of physical state, but I want to claim that if we had an intrinsic time, this intrinsic time could be used as a hint to give us the physical scalar product. I'm claiming we don't have the intrinsic time, but this doesn't mean that the scalar product doesn't exist. If we don't know how to reach Boston, that means not that Boston doesn't exist. We don't have this hint. And this problem of how to define the physical problem if you go through the Virat procedure is an absolutely general problem that is present in Young-Mills theory in any time one uses the Virat quantization. Now, there are alternatives. Well, one possibility is just to study this problem and try to look for conditions on the physical. Let me not speak about generativity, but a general system with no time, which we don't have these things for the time, and I give you this morning an example in which theoretical quantization can be exactly used in this way, so start from observables, which are true observables, communities and constraints, and quantize them directly. So find a closed algebra of them and look for a representation of this algebra. So I can conclude, I think.

12:30 And I want to summarize the argument. The argument is the following. First, I claim that it's perfectly reasonable to make physics with no time. The problem of defining the physical scalar problem, in principle, may be obtained by other methods, and I'm not an expert, but from that What I want to say is that the conclusion and the main thing that I want to say is the following, and I want to say that this is a perfectly viable thing to do, so I'm very much in the spirit of what Jim said this morning, because the only point in which I don't agree with you is that I don't agree with you. This is when you said that for sure this is not possible to be done in a canonical theory, and what I'm trying to argue here is that canonical theories as in the Hilbert space quantum mechanics, the earth quantum mechanics, have perfectly room for this, the only thing that you have to do is take away the last action of quantum mechanics, the one related to time, and all the rest makes sense. So, well, you will see this. And so where time comes from, I mean, if the theory makes sense by itself also in the absence of time, it's not difficult at this point to believe that the observed time, the one that we see in the usual life, is just approximate or is something that exists only if you're a physical clock or can be there only in an approximate sense or only in some particular states. And in order to do that, I mean, in order to do that, the main message is to find...

15:00 I really regret, Carlo, that in spite of the fact that you gave us the advice, forget time, you didn't forget yours. You have a long time. Bill? I have a constraint, because when a constraint says operator A is an animal, it's equal to operator B. How do you have an equality relation between two animals? I can have equality in functions, but I need to be aware of one and equal to the other. I don't know what, you know, for example, the constraint word of x, I don't know what that means. So how can one implement the Heisenberg picture? Depends what kind of quantization scheme you are using. If you are using Dirac quantization scheme, you implement the constraint as a greater condition of the physical state. That's a condition of the physical state, and then you have to look for the observable that commutes. If you are using other quantization skills, you have other perspectives. In the group theoretical quantization of the constraining system that I was referring to, you have a way to forget completely about the constraints just by starting from observable depth. In what way is that what you described different from the spreading of these? If you don't have time in your theory, or if you don't have time in the general system that you are working in, there is no feeling that you can never write something like, this does not make sense, for a very easy reason. However, always without this, everything can make sense.

17:30 We never measure physics. How do you tell when you sense some of these effects? By means of a clock. Because if you knew that, that would be a good thing to observe, and that would be difficult for you to understand. Why do you want to consider only Einstein's equations? Do you want to make everything out of gravity? No, no, no. Einstein's complete set of equations. But do you want not only Einstein's equations, but all the other kind of equations, and all other fields? No, but I still want even more. There will be an argument by the moment that they keep their theory of the flag in the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air, the air. And then that is specified to all to find the Gerber role immediately. We're not just saying, if you want to do this, do this, do this. What I would like to emphasize is that when we're solving a sustained equation on a manifold,

20:00 even in quantum mechanics, and we're not really talking about quantum technology, I get some wave function over the full manifold. Then, to go back and interpret it, I want to look at events. I don't have to worry about time as defined from some evolution equation. I can see the history. If I'm in this region of this manifold, I can start talking about what's going on there. And so I can define clocks relative to behavior in that region. Clocks don't have to have global existence. Clocks don't have to have any particular existence. They just have to be local behaviors. So I don't need to have, for instance, very physical notes in a clock. I just have to have this notion of space-time event in the observable space field. If you have a location on the manifold relative to other locations on the manifold. I think that, you know, it depends what you mean for event. If you want to, as event, you mean the name of a particular point of space-time, which is exactly what you don't have in general relativity. If you put event, you mean that in couple with general relativity, say a particle is a particle, and you say the event is where the particle is in the moment in which the clock is in time to work in a particle. Our psychological thoughts are certainly not perfect because we ended ten minutes after our time, but let us meet a quarter past five to continue. Some of the things in it I'm already reconsidering. The whole thing may eventually be withdrawn, but as it stands, it represents my current thinking on the matter. Wormholes are solutions to the Euclidean field equations, the field equations either of pure gravity or of gravity coupled to some other field. Their importance was stressed last year by Hawking, by a Russian group of which Rubikov is the most prominent member, and by Giddings and Strominger. Giddings and Strominger actually constructed explicit wormhole solutions for a theory of gravity coupled to a massless axion field represented as an anti-symmetric three-form, the relevant technical detail. It is anti-symmetric. Not only irrelevant, but redundant.

22:30 Hawking was able to find them only in the sense of what we would call constrained instantons engaged field theory. The Russian group didn't bother to find solutions, but said, surely configurations of this kind will be important. We see in this drawing the wormholes. What a nice pointer. We see the wormholes. We see the row holes in two of their guises. Here we see a wormhole connecting two asymptotically flat portions of space. They may be part of two disconnected manifolds or part of two distantly separated parts of the same manifold. And also we see why they have this name. They look very much like the wormholes John Wheeler considered some years ago, except that they are four geometries rather than three geometries. Here we see a wormhole that has been cut in half in its middle and attached to another space, and as is explained in these papers, unless I will not have time to go into great detail here, the second groin can be interpreted as the production of a baby universe by quantum tunneling from an initial manifold. The Euclidean drawing, perhaps a better way of saying it, is to say that quantum tunneling induces a transition matrix element between a space which only has one large component and a space which has one large component on the other. Can that be also thought of as a counter-offer? It can indeed! If we wish, we can have a, I suggest that none of the 12 questions be postponed until the discussion is finished. Now, in all the specific models that have been proposed, the wormholes turn out to have a size of the order, the significant wormhole configurations, the Newtonian functional integral, turn out to have a size on the order of the trunk length and an action on the order of one. This makes it difficult to get any concrete idea of what kinds of approximations you are making when you do semi-classical reasoning and the loop gas instanton sums.

25:00 And therefore, for purposes of this talk, I will assume that there is a wormhole size that is somewhat larger than the Franklin, and there is a wormhole action that is some... I have not been able to construct models which have this character, but let me adopt it as a white lie. It will help me keep things straight, and then afterwards you might say, well, maybe the qualitative ideas will work out, even if this quantitative basis is not applicable, an ancient, if not necessarily honorable, QCD tradition. The original proposal was that wormholes would lead to an apparent breakdown of quantum coherence at a macroscopic scale. This has turned out to be completely false. However, as I will attempt to argue for you, If at least one makes some rather optimistic but not totally insane assumptions, wormholes lead to something even more interesting and something which, unlike quantum incoherence, has actually been observed in the real world, to which they lead to a vanishing of the cosmological constant. By the way, please feel free to interrupt me with questions as I go on. As long as they're just questions about you didn't understand what I said, what does that mean, and so on. If you have hostile questions in which to assault me, I would prefer that that be postponed until, well, perhaps indefinitely, but I will tolerate it being postponed until I get through with the formal exposition. Otherwise, we'll go off in odd directions and I won't get to cover you. Five stages. First I will explain how to sum wormholes. Perhaps I could briefly tell you what I mean by that. By summing wormholes I mean we want to start out with some Euclidean manifold that has lots of wormholes perhaps going from the same manifold to another or connecting one otherwise disconnected component with another. And a lot of baby universes, and we want to write the sum of all possible wormhole locations in terms of the manifold script of all wormholes and baby universes.

27:30 That's of course just very straightforward to root gas instanton technology, and I will explain the results of that, although I will not explain every step in the derivation. The next step is the construction of expectation values in quantum gravity using the Euclidean functional integral following Hartle and Hawking, but not too far. Then I will put these two things together and do the wormhole summation over the Hartle-Hawking-Euclidean Sorry, I should have said something which I didn't. When we do the wormhole summation, we will discover something remarkable. As a result of the wormhole summation, a large number of parameters will appear in the effective field theory below the wormhole energy scale, and these parameters will not in any way, at least at first glance, be determined by the underlying fundamental physics. They will be somewhat similar to the famous theta angle of gauge field theory. Totally arbitrary parameters that nevertheless affect the physics that occurs at a lower energy scale. And this by itself, even if we didn't get to three, four, and five, would be quite remarkable. That in particular, a fundamental theory of everything, like, take an example of random super string theory, would in fact be telling us much, much less than its proponents believe it to be, of an optimistic... However, as we shall see as this proceeds, this is an illusion because in fact there is new physics that comes into play that fixes the combined effect of the parameters that come from the fundamental theory of everything and the parameters that come from the... In particular, to return to where I was before I backtracked, in particular, in point three, I will use the Euclidean functional integral and the wormhole sum to show that these parameters adjust themselves in such a way that the cosmological constant necessarily vanishes.

30:00 I stress that this is the real, genuine, 100% bottom-line cosmological constant, including all radiative corrections from all sources, from all physicists, through the wormhole energy scale on down. It is not some cosmological constant associated with a metastable inflationary phase, nor is it a cosmological constant associated with a pre-approximation or a mini-superspace approximation. It's the real thing. In the first part of the argument, I will worry about what would happen if we alter the Heidel-Walking boundary conditions. I will show that if we stay within the framework of the Euclidean functional integral, but appropriately change the boundary conditions, it is possible to arrange matters so we obtain a non-vanishing cosmological constant. However, this arrangement is unnatural. Here I'm not using natural in the sense favored by breakfast food manufacturers, but in a technical sense of high energy physics. If we choose boundary conditions that make the cosmological constant non-vanishing, and then make a small change in Planck scale physics, these become boundary conditions in which the cosmological constant once again vanishes. Therefore, a fair way of stating it is to say that before wormhole physics, it required fine-tuning to make the cosmological constant vanish. After wormhole physics, it requires fine-tuning to make the cosmological constant non-vanish. I believe that this is progress. Finally, I will, if I have time, and we may run out of time before I get to that stage, but it's all in the paper. I will explain how an infinite number and possibly all of the ambiguities apparently removed on stage one are in fact removed altogether, but by the same mechanism that fixes the constant, by mechanisms closely related to that which fixes the constant.

32:30 Some warnings about this work. Although, this thing rests on two things. One is the existence of wormhole solutions, and the other is including quantum gravity. Therefore, it is doubly a house built on sand. Wormholes may not exist in some given field theory. If they exist, their effects may in fact be swamped by some more exotic configuration of even more elaborate topological structure. And I don't have any way of telling that. Euclidean formulation of quantum gravity is a terrible mess. Nobody quite knows how to do calculations. It's full of arbitrary and ad hoc assumptions. And some of the most plausible equations you can write down can be shown to be false, which is the back of the envelope calculation. So I hope I have organized my computation in such a way as to be relatively insensitive to these problems, that if there's any way of making sense out of Euclidean quantum gravity, then this thing should run. But it's possible there's no way of making sense out of Euclidean quantum gravity, in which case this thing won't run. The whole reason wormholes can enable a cosmological... Back up again. Sorry, it's the first time I've given a talk on this. I'm not perfectly organized. One of the ways of phrasing the old problem with the cosmological constant is what might be called the problem of rearrangement. The constants of nature, which contribute to the cosmological constants, are presumably fixed at the time when things begin to resemble an ordinary four-dimensional theory, some shortly after the Planck effort, whenever that is. An experimenter then could have measured all the constants of nature. He would have had, of course, a hard time. He'd have to work quickly under conditions of high energy density and with minimal government support. He could have measured all the constants of nature then and he knew that when everything settled down, when all this shit expanded away, the world would have been approximately flat. The cosmological constant would have been zero.

35:00 So you have the problem of rearrangement. How could they have arranged things back then so it would come out to be zero now? Now wormholes answer this problem because they enable otherwise disconnected manifolds to be in communication through the wormhole. So even when speaking in non-Euclidean and Tuscan language, even when our universe was small and high, At the other end of a wormhole, there could have been a universe that was large and cold. Therefore, through the wormhole, we see the ultimate value of the cosmological concept. Prearrangement, speaking very roughly, is replaced by precognition. Now, this idea derives from a model Andre Linde promulgated last fall, and I should give him credit, in which he found he constructed a classical theory involving two universes which have this essential feature, the replacement of prearrangements by precognition. One of the two universes locally sees a global average over the other since they're governed by the same physics. It therefore sees the ultimate value of the cosmological concept and adjusts itself so it will come out to be zero. Secondly, the idea of determining the cosmological constant by looking for bumps in the probability distribution of the wavefront in the universe goes back, like so much else in this field, to Stephen Hawking. He floated a proposal at the time of Shelter Island 2 that appeared in Physics Letters earlier in 1984. We try to do exactly the same thing if I have time, and in fact many of the mechanisms I will find here are somewhat souped up versions of those that occur in Hawking's seminal work. If I have time, and if I doubt, I will discourse at greater length of a comparison between our works. And finally, Tom Banks has tried to do something very similar using a Minkowskian rather than Euclidean formulation. His theory is sufficiently different from mine that I'm not capable of making point-to-point comparisons. I know they are not exactly the same, because while I get a total extinction of the cosmological constant, he gets merely a suppression by a very large factor associated with an inflationary phase. Now that I've made sure everyone who deserves credit has got credit, I can now go faster through the less interesting part, that is to say, the physics.

37:30 The first thing is the summing wormholes. We start out with some background manifolds and we can decorate in an arbitrary number of ways with wormholes which may even connect otherwise disconnected parts of the universe, connect part of one universe with another part of the same universe, or go off and terminate on baby universes. Wormholes and baby universes may exist in many types. There might be many instanton solutions to the instanton-like solutions to Euclidean field equations. I will assume initially I have Ni baby universe of type I, and finally I have Ni prime. If you ask me what I mean by initial and final, I mean the top of the paper and the bottom of the paper, anti respectively. Okay, at this stage, I'm not going to interpret what these diagrams are good for. I'm just going to sum them up. To do the summing, the task is to write the sum of everything in terms of this. Well, more properly, the task is to start out with a manifold like this where all of the fields, including the metric, are slowly varying on the wormhole scale and therefore on the even shorter Planck distance scale a fortiori. And integrate overall fluctuations up to the Planck scale, of which we assume wormholes are the only ones that have a significant amount of things, and get an effective field theory on the lower scale. It's convenient to introduce creation and annihilation operators for baby universes. That's not describing something, saying there's something in the dynamics that creates and annihilates them, that's just a bookkeeping device. I'll assume they're labeled by a discrete index. The generalization of the continuous index. I also will assume there is each wormhole type i has an action, s sub i, and that there is an amplitude for inserting a wormhole n in a slowly varying manifold that is of the form k i square root of g, t 4 x. k i in general depends on all of the fields on the slowly varying, all of the fields on the script manifold over here. And, in general, will be the usual sum of things with forms determined by dimensional analysis characteristic Lenz scales.

40:00 The wormhole scale starts out at constant, then there are terms with a couple of derivatives, and a wormhole over the wormhole Lenz scale squared, et cetera. Or I should say wormhole Lenz scale. That's the setup. It's a straightforward one. Now here is the answer. We do the sum over fluctuations and wormholes with n i and n i prime fixed of e to the minus s. This can be written in terms of a certain operator, e to the minus s effective, which I will describe immediately. In fact, you can read and describe below. Evaluated between this initial state and this final state. S effective is the integral of an effective action. It contains two parts. L naught, the result of just doing the normal integral over fluctuations from the Planck scale to the Wormrow scale. And this operator part, constructed out of the entities defined above. I do not have time to derive this formula here, but at least I can make it plausible. As you can imagine, if I were to normal order S-effective, The terms involving annihilation operators would take care of the baby universes in the past. The term involving creation operators would take care of the baby universes in the future. And the normal ordering terms would take care of the wormholes that begin and end on M. They just determine the boundary conditions on this manifold. Yes, I'll make a numerical value in a moment. It's a perfectly legitimate formula. At this stage, this is just a fancy, operated way of summing up the bookkeeping. Yes, Ki is, of course, a function of x, and it depends on all the fields. No, the index i indicates the type of wormhole. As the wormhole carries zero value of the conserved charge, Ki will be some number, but possibly easy to use by squared or by some scalar field on the nanopole.

42:30 Brian wants to know how you use the wormhole. Oh, by the values of the antinode field. This is put on some metric that has some fields on it that are slowly varying on the wormhole scale, including the gravitational field. K-I is some function of those fields, which is usually the derivative of this fancy. So this will look, this looks like a normal local logarithm density on whatever fields live on here. The long wavelength part. The long wavelength, where long and short are separated to one whole scale, part of the gravitational fields. It's not a function at all. No, it's a local function. So finally we go over that, I guess. Yeah, it's a local function of that. Yeah, but he wants to know whether there's any difference between the anguish and the insinuation. No, the warm-up, the baby universe is no, the baby universe is a closed universe. It carries out zero momentum and zero energy. The amputees who created the baby universe have no exit at that time. There's a creation operator for a baby universe that has charge one, a baby universe that's in some internal excitation state, a baby universe that's twisted up like a pretzel. I tells you all of those things. What it doesn't tell you is where the baby universe is in M because the baby universe ain't nowhere in M. It's like Melitius' god that is not in time but in eternity. Except they're covariant. Not only is it nowhere in time, it's nowhere in space. These quantities are independent of space and time. This is a long story. I can lecture quickly. I may end up lecturing quickly, but you won't let me. The amazing thing about this expression... And if this were three months ago, I would be giving another talk about why these things didn't lead to quantum incoherence, and I would talk much more about this, is that this expression, although it involves operators, involves operators that all commute with each other. Not commute with each other as space-like separations, just plain commute with each other. If we think of AI and the adjoint...

45:00 As being raising and lowering operators for a harmonic oscillator, this is like the position operator for a harmonic oscillator, and the position operator for a bunch of independent harmonic oscillators to use with each other. Therefore, we can go to a basis in which this combination is simultaneously diagonalized, what I will call an alpha basis with eigenvalues alpha i. Of course, to express the n eigenstates in terms of the alpha eigenstates is trivial, that's just harmonic oscillator technology, it's just the nth eigenstate of the harmonic oscillator, aside from the square root of 2, which is in there, because I didn't bother to put it. In terms of an alpha basis, this effective action, or this either-minus effective action, is completely diagonal. Since everything is an operator in which the alpha states are eigenstates, and indeed we can introduce an object called S effective of alpha, in which the operators A plus A adjoint, which have just levitated themselves off the top of the screen, let me bring them down again, in which the operators A plus A adjoint are replaced by these alphas, which are just a bunch of numbers. So this is the objects I referred to earlier that play the role of the theta angle rather than like the theta angle in QCD. In this formulation, it looks like the alphas are just arbitrary parameters. The Hilbert space of this theory seems to have neatly foliated itself into a bunch of subspaces determined by the values of the alphas. What we had originally in L0 is practically of no interest to us, since most or all of it could be absorbed depending on how many baby universes there are, kinds of baby universes, most or all of it can be reabsorbed in an additive redefinition of the alphas. The fundamental theory of everything turns out to end up telling us nothing, because all its predictive power has gone down the wormhole. And there we are. This is the position I was in at the end of my first paper on this subject, which you might have seen, called Black Holes as Red Herrings, and it's also the position Hawking came to in his paper with Islam, that came out around the same time. Yes?

47:30 So supposing you didn't have one hole, but you had some kind of configuration, and this sometimes is something like that, that just happened to live on a scale much smaller than you could just do in studying. Could you go through this?