Arrows of Time and Generalised Quantum Theory

0:00 I hope you've enjoyed your lunch and also the beautiful weather that Jonathan has arranged. I'd like to say that he is the miracle conference organiser. Although there are other people listed on the organising committee, really we've got absolutely nothing to do with it. Jonathan has done everything. And our first speaker this afternoon is Jim Harcourt, and he'll be talking about arrows of time and generalized quantum theory. Thank you, Ed. It's a little bit daunting to talk about arrows of time when Robert Penrose might be in the audience. I'm pleased to see that he is not true. I remember the story of a famous Penn State football player who was very good at his trade and he died and went to heaven. And when he got to St. Peter, St. Peter asked him what the detail was, and then he asked him what the title of his talk was. And the famous football player said, talk at him? Oh, yes, St. Peter, everybody who gets in here has to give a job talk. We have many sports fans up here, and we're all interested in hearing your talk on the inside story of football at Penn State. And the football player said, oh, I don't want to talk about that. I've given that talk so many times. I want to talk about the Johnstown Flood, the famous Flood in the West, the man I also lived through. And St. Peter said, well, we really would like to hear about the Penn State football, the man insisted, and it went on and on. Finally, St. Peter said, well, all right, but I have to warn you, no, be in the audience. Chris Aichel is certainly one of the people who has entertained the possibility that usual quantum mechanics has to be generalized before we can apply it to quantum cosmology and to quantum gravity. That's because there are two reasons. First, the usual formulations assume that the output of the theory is that the output of these measurements are made by observers, and assume, in one way or another, the usual quasi-classical world of everyday experience.

2:30 But in a theory of the whole thing, there can't be any general division between observer and observer. Measurements can't be fundamental notions in a theory that seeks to describe the early universe where neither existed. And in a general quantum mechanical situation, there's no reason for there to be any set of variables to behave classically in all circumstances. So, for that reason, quantum mechanics has to be generalized. That's the problem of closed systems. But also, quantum mechanics, the usual laws, as they are stated, rely on incorporating motion to fix back long geometry. For example, the Schrodinger equation and the T-bears is a metrical motion which is supplied by a fixed geometry. But in quantum gravity, geometry is a quantum-dynamical variable. It's fluctuating and without a definition. It's not fixed at all. So for these two reasons, quantum mechanics has to be generalized. And the thesis of my talk today is that the generalization of quantum mechanics necessary for quantum cosmology and quantum gravity may shed some light on the arrows of time that are exhibited by our universe. Now, it's a remarkable fact, I think, that we live in a time-asymmetric universe, where they're clearly arrows of time, but governed by time-mutual dynamical laws. I think that's even surprising, you know what, I think if you could ask me, just coming off the screen with other knowledge of physics, they would suggest that a time asymmetric universe is being magically described by time asymmetric dynamical elements. But it interferes not to be the case. And I'll say a little bit more about why this is later on. In the face of time asymmetries of the universe and time symmetrical dynamical laws, The only source of explanation is asymmetries and their boundary conditions. I'd just like to run through a few of the famous time-made symmetries about the time in the universe and explain very briefly how these arise from time-made symmetries between the initial and final boundary conditions.

5:00 These ones I'll consider. First off here are the second law of thermodynamics. the retardation of electromagnetic radiation, and the psychological distinction between past, present, and future. The psychological horror of time, as it's sometimes quoted. First, a thermodynamic era. As Paulson said a long time ago, the second law of thermodynamics can be proved in the time reversible mechanical theory if one assumes that the present state of the universe could fall from an improbable lighting special state. is pendos, and that's the same thing a little bit later. The terminology at all times is usually expressed in terms of increasing entropy. Of course, there are many different entropies. Entropy depends on coarse graining. So the particular entropy we have in mind here is the entropy associated with the coarse graining defined by the quasi-classical realm of everyday experience, forced ratings by ranges of values of approximately conserved, intervals of approximately conserved densities, such as energy, momentum, species, and what were assumed in the chosen bodies. The fact is that we live in a universe, apparently, where if there's no final boundary condition, we want to make a difference, there was an early boundary condition in which that entropy was low, low compared to what it might have been, and therefore it has a tendency to decrease since. boundary condition is what is wise to determine any value of the time. The electromagnetic error similarly can be seen to arise from asymmetric boundary conditions applied to non-symmetric laws, in this case, Maxwell's equations. Any solution to Maxwell's equations with fixed sources, fixed currents, J-U, can be written in either one of two ways, either in terms of targeting responsible sources and free incoming fields, or advanced fields of the force on the point sources, and free ongoing fields. The asymmetric boundary condition that the in field is approximately zero and the outfield is not zero is what gives rise to the retardation, which is then, this is approximately zero, in the entire field, which we see as a rising and retargeting of the given sources.

7:30 Of course, in cosmology, it's not true that the free fields, at least at the start, say, at the time that we have them, are approximately zero. There is all the energy in electromagnetic radiation and the cosmic background radiation, which indeed, even today, at three degrees T, supplies the dominant source of electromagnetic energy in the universe. That radiation has shifted to very little temperatures and very long wavelengths. Therefore, if you think of the electromagnetic radiation, if radiation, for example, is visible today, then that will be approximately retarded because it's essentially . The psychological error of time can be similarly understood. Here is information gathering and utilizing systems. Here is a little bottle of wine. This is a model of a robot that operates on a discrete set of time steps. every timestamp it ships the contents which is recorded in these registers to the right here and erases the final one and it records a new piece of information from the external world on the first one and thus at any one time it has a coarse-grained time discrete with what it sees where this is the most recent information and these are successfully put away in the past It uses this information to compute from a process of unconscious computation, to compute a schema of the model of the universe, which we all do, I think, contain such things as the rules for success, get food, yes, be food, no, vanilla ice cream tastes good, and that's of information, right, from the schema and the process of computation and to its behavior. Well, the important point is that there are two hours of time that you contribute to this. The idea supports information, confuses reactions, and exhibits behavior. Information that it gets, invisible wavelengths, for example, is from the past because electromagnetic radiation is retarded. So that's one of the reasons why it was in the past.

10:00 Importantly, the recording of information is typically irreversible, not necessarily irreversible according to Mandauer, but the erasure of information in the spinal set is necessarily irreversible. Therefore, the cycle of punctual parallel time is operated most simply if it is congruent with the radiation arrow of time, which is where it in the thermodynamic arrow of time which governs the universal processes. So that's an example of three arrows of time, the universal rising from asymmetric boundary conditions. There are other arrows. You have to be a little bit careful in this game to distinguish between arrows of time that are exhibited by the fundamental laws and apparent arrows of time. So an example of apparent time-based symmetry, here are two of them. One is, or could be, the time-based symmetry and the weak interactions. So even if the states and dynamics and so forth, for example, super-screen theory are kind of rehearsed with very effective theories that are applicable in limited circumstances and you tie an asymmetric. And at least it's a possibility that the, for example, it's believed, well, it's incredibly difficult to get a straight answer out of the same theorists, right, and the best I can get is that the theory is believed to be time-reversed and invariant, and therefore one possibility, for example, is the asymmetries and weak interactions arise in, or symmetry-breaking, and therefore the universe could exhibit on very large scales the time-reversed and invariant of hours of time pointing one way or the other in a routine of action, but overall time symmetric. Another example is the expansion of the universe. We see the universe as expanding, of course, but in Stevens, no boundary lay function of the universe is real, and hence it's time symmetric. Therefore, the ensemble of semi-classical trajectories is also time symmetric. So, with each trajectory expanding or contracting, but there are just as many trajectories, just as radius of the universe versus time, that expand as there are contracting them on the other side. However, because of the psychological error of time, and the error of time associated with thermodynamics, the obvious, any information gathered utilizing system, whatever one is operating on, will see the direction for the big thing as the past.

12:30 So the whole ensemble is symmetric, but apparent asymmetries arise from symmetry breaking. Now, what's the reason that we have time-symmetrical dynamical laws that are governed by time-symmetric boundary conditions? Well, I don't, of course, exactly the reason why the underlying dynamical laws are time-symmetric, but it's true that contemporary fundamental dynamical theories are built on symmetry principles. One time, one other. And it's sort of vernacular that they incorporate symmetries that are related to time. A simple example is the CPP theorem on Q theory, where in Ransinger's plus locality, I mean, on a field theory in CPP, you might object that CPP is not the same as T, but it's the host in some sense. So in the face of these dynamical models, there are now two possibilities for the observed asymmetries. And the first question we have to ask is whether all the asymmetries could be apparent. That is, the basic overall picture of the universe could be timesymmetric, and the asymmetries that we see arise from just the special symmetry breaking in special circumstances, so that our little piece of the universe appears to be asymmetrical. The classic example of this is the idea where we have an expanding and protracted universe in which it is time-symmetric in the sense that it has time-symmetrically related boundary conditions here and here and the entropy increases on one side and then decreases moving this way, it's decreasing moving that way. So it would be perfect time symmetry, but of course, the idea is we would look here on a regime where it's increasing and then over here you can see the pass in the sense that it's increasing in that direction. However, it appears that this idea, while it's kind of a firm conclusion, I think, is not looking too good. But the key observation, I think, which was made by Davis and Tronger, is you would think that if you made this time longer and longer, it would be harder and harder to distinguish this or longer eventually to distinguish.

15:00 But you can, in the same sense, see the final singularity, because the optical depth, with realistic cross-sections, from the point here to the corresponding point here, remains finite no matter how long this time becomes. And that's because, it's true that time is getting longer, but the universe is expanding more, so the matter is getting more dilute. Therefore, the contribution, the integrated contribution of the optical depth remains finite. So, I don't want to go into it in detail, but there is a certain amount of evidence that, because we can see the time symmetry, time symmetry, we don't have it. David Cray says that there are orders of magnitude showing from the brightness of the night sky that we wouldn't have a time-symmetric universe. Raymond Buffon says that if the universe were time-symmetry, it would necessarily be irregular at both ends of the Big Bang, and that they crunch, and that's of course something which we don't see because we see highly irregular in a big band. Highly irregular. So we seem to be forced, if these ideas are true, to the idea that the time-symmetrical So, analytical laws give rise to the timing symmetries that we see by asymmetries between the initial and final division. What is one obstacle to this point of view? What is the arrow of time in quantum mechanics? One of the mechanics has built into it a narrower time, at least this is usually formulated. The Schrodinger equation, for example, is unimpressive in the sense that you can write to afford it back in time, where the time of operation can be applied to an equivalent solution. But the second law of evolution, right, the idea that on a measurement, the wave function is reduced by the application of a projection operator of the trisons of the outland dimension, and then be normalized, which is equally essential to describing predicting probabilities of histories of sequences of things, It's not unversible in the frame. You can't run it back to the same time.

17:30 Pay off the projections somehow. You don't even know where the projections might have been put in because the projections operate when the system was measured in the given time of the present. You generally don't know when it was measured in the past. Now that's usually thought not to be such a bad thing because it's thought that measurement is an irreversible and therefore the second level of evolution should operate in the same direction as the thermodynamic error. But that's a little bit problematic because it's, after all, shouldn't be possible to intelligent aliens who are in the future might get into their heads to reverse the thermodynamic error of time of space, so it runs the other way, the prevailing quantum mechanical time, which you consider what they can do. And then, for observers in such a large volume, what power of quantum mechanical time do you apply to it? Do you run it forward like this, or do you run it backwards because the quantum mechanical time is running backwards? Of course, if the existing quantum mechanical laws are merely effective to you, that is, you should incorporate particular Then that won't be a problem because the effective theories put in one part of the universe by one way or in another part of the universe by the other. And that will be my basic thesis here. So, we know, as we argued in the beginning, that quantum mechanics need to be generalized for quantum mechanics and quantum gravity, so that it doesn't incorporate an idea of measurement, and it doesn't incorporate an idea of fixed space time. Can it be also generalized so that it's time neutral, so that there's no quantum quantum mechanical parallel of time, and the parallel of quantum mechanical time that we observed arises from the asymmetries and the boundary conditions in a completely time-mutual framework, how you argue that it can. To do that, I need to describe to you a little bit about decoherent history's quantum mechanics

20:00 and about Chris's generalized quantum mechanics, which is the framework in which this will be discussed. So to begin, for a little review, the quantum mechanics of closed systems, which is what answers the problem that first need for generalization of independent dimensional measurements, we need to consider a little model of the universe that we have seen in this audience of neglected quantum gravity, which is a pretty good approximation anytime after the first 10 to the minus 43 seconds in the universe. And in thinking of the whole universe being a large number of particles and molecules in the box, perhaps 10 to 20,000 mc parsecs on the side, maybe expanding, then the usual apparatus of Hilbert's base states, short-hand operation, and so forth, can be applied, which will simplify our discussion. What's assumed for any closed system, and is given by theory, is the Hamiltonian, or whatever, the dynamics, quantum mechanical theory, and the initial condition, say the neural quantum theory of a function of the universe. The most general objective of any quantum mechanical theory of a closed system is the prediction of the probabilities of force-pringable What are the mysteries of that system? Thus, for example, we might be interested in the orbit of the Earth around the sun. Part of the quantum mechanics, the Earth would take any possible orbit around the sun. Let's say we're closer to the sun. It's only a question of probabilities which orbit it takes. We hope, of course, that the situation that the Earth will take that we have today, The probability is high that the Earth moves along the classical capillary orbit. The orbits are typically coarse-grained. For example, if we're describing the Earth as a capillary orbit, it's coarse-grained because we're only interested in the center of mass of the Earth, and not in any physical degrees of freedom of the Earth. It's coarse-grained because we don't consider the center of mass position and the earth of arbitrary accuracy, but rather we consider it due to some generous range of accuracy for what we could possibly do. And it's coarse-grained also because people don't specify the center of mass at all possible

22:30 times, but at a sweet series of times corresponding to classical observations. So in that sense, we're dealing most generally with coarse-grained alternative histories of the system and trying to predict probabilities. But not every set of alternative histories that can be described can be assigned probabilities. No worries that we're clearly illustrated in the famous two-slit experiment. Here we have a source of electrons, which are passing through a screen with two holes, to be detected at some point Y with another screen over here. In a simple model, there are two possible first-game histories, one in which the electron went to the outer slit and arrived at Y, and one in which the electron went to the lower slit and arrived at Y. But it's not possible in the usual story to assign probabilities to those two alternatives. That's because the probability of Y at point Y will not be given by the sum of the probability to go to the other slither and arrive at Y, and the probability that goes to the lower slither and arrive at Y. That's because the quantum mechanics probabilities are squares analogues, and the square of the sum is not equivalent to the sum of the squares because of quantum So some rule is needed to determine which sets of histories can be assigned probabilities and which cannot. I emphasize it's not a matter that we don't know which list the electrons went through. That would be the case when the probabilities are 50-50. We can't assign any of the probabilities at all. The usual rule is that you can assign probabilities to the histories that have been measured. the electron went through, then the interference is destroyed, the sum will lose a bay, and everything is consistent. But that's exactly the kind of rule which you cannot have in cosmology, at least if you want to apply it to the Earth-Universe, because there is no motion of measure of splitting the system in the two parts of one which measures the other. So the generalization, which is due to refus on this Gil-Mann and all, is just this. The post-system has a Hamiltonian, it has a state, and probabilities can be assigned to exactly those sets of alternative histories

25:00 Of course, the difference between the two individual histories is negligible as a consequence of that state and the Hamiltonian. Right now, I want to show you that I'm formulated this precisely, fairly precisely. That should be described in such a frame about the quantum mechanics, but they don't play a fundamental role. So, for quantum mechanics and closed systems, we need three ingredients. Now, the fine-grained histories, which are the most refined possible description in the system. The notion of coarse-graining is actually easy to record. So, addition to the fine-grained histories and the classes, and the better interference between the coarse-grained histories so that we can tell in which situation it vanishes. So, here's the story of one language, the language of operators, to find, of course, great histories, and just to establish the patient, alternatives in one moment at a time can be reduced to yes-no alternatives. Is the particle in this range, yes or no? Those yes-no are represented by projection operators and will the patient all use K corresponds to the particular set. Thus, when you're moving around the sun, you might divide the space up in a lot of little boxes here, and you can ask for the center of mass in this box, or not in that box, or in this box, or in this box. The set K, the principal is with a whole set of boxes, or we could test about alternatives in the momentum, in case we were in a different set, and alpha labels the particular box, here's the derivative there, and T is the time, and this Heisenberg picture representation. A history is a sequence of alternatives in a series of times. So, if you go over to the Earth, it might be described by this box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box, that box. This box. They're all over many different parts of the history. So, it's a sequence of elephants, and a series of times, and it's represented by the corresponding chain of protection operators, like it's multiplied by the other. So that's how plant-and-history is said to be fine-grained if all the protection operators are one-dimensional. And coarse-graining, if they're not a little one dimension, of course, we looking at the universe deal with enormously coarse-graining alternatives, right? It's specified in very few variables. So coarse-graining is really the general case.

27:30 If you don't like that sort of awkward picture, you can look at it in terms of sums of paths, where the fine-graining paths are just the fine-graining paths. The coarse-grained consists of bundling these paths into little groups. So, for example, if you're considering the set of alternatives, Karastani and the motion of the Earth, you might specify a range of positions, say three different kinds. And of course, grain histories consist of all the fine grain paths of the center of mass that actually pass through those regions of that time. Then for each such history, each such class of paths, you can define a finite sum of paths that are acting in the initial state, that gives you an operator C acting on the side, which turns out to be exactly the same as the chain of projections which I looked on before, and this defines, well, that's how it works in some of the history structures. So we have, how do we get the coherence of probabilities? We have a set of districts which corresponds to the class operator to change the projection. We can define branch state vectors for each S3 in the set by applying the output of the initial state. We can define the decoherence function by, which is a function, a complex value function on the pairs of this group, despite the overlap, and that's the measure of the difference between S3. The set of histories decohered, if the decoherence function was negligible for all alpha prime values of alpha, and the probabilities of histories are then the diagonal elements of the decoherence functional, equivalent to just the operator of C, like psi squared. And those, as a consequence of the equivalence, those probabilities are consistent. That is, the most general form probability symbols, which you remember from the two-slip experiment was the obstacle to assigning probabilities to history. That is, if you have a horse-braining set of histories, that is, you take a given set and you group them into bigger sets,

30:00 as a horse-braining, so that the operators are sums of the horse-braining set, which is the most general of the same. Well, that's a very skeevy introduction here. It's just the history of quantum mechanics. But the main point for this talk is this formulation of quantum mechanics still has a narrow of time. It still has a narrow of time because of the formula for the probabilities. In fact, it's much worse, right, than the unusual formulation of bi-mechanics, because the psi on one end, in terms of third probability, there's nothing on the other, so there's a definite arrow here in the direction. It's much worse because the p's are no longer necessarily associated with measurements, therefore there's no question about being associated with any sort of So this error of time would have to be fundamental. It is helpful to have this error of time because it allows the definition of states at a moment of time. States which are sufficient for future predictions but not for the past ones. Let's suppose you have, for example, a probability of a set of histories, and ultimately that can be given by a point of view here. And you'd like to calculate the conditional probability, though a certain number of events have already happened. Say you were at the horse races, and so many horses have already come in, you want to calculate the probabilities for the next races. Well, that's the conditional probability for these events that have happened already, and these are seeking to predict, constructed in the usual way. In fact, it's easy to see, but that probability can be calculated by applying the chain of projections that have not yet happened to a wave function, which is the function of the time, which is just given by the chain of projections that have already happened, and then one of these. That's the usual story. In the Heisenberg picture, the states are constant in between the action of these projections, and then add an alternative to the reduce by the action of the projection.

32:30 So it's a ball to reduce, ball to reduce, ball to reduce, but if you're taking the reduction, it's constant. That's okay for future predictions, but if you try and turn the thing around and calculate the conditional probabilities, given what we know now, what happened in the past, you can't do it using only a notion of state at the present moment. You build the present information in initial conditions. Well, what I want to discuss now is generalizations of quantum mechanics that are time neutral. They don't have a hard time. They introduce to this one. So that I introduced to a little bit of the notion of generalized quantum theory, which is due to and so forth. well, here we can only put on two transparencies. It's the same three that we've already seen in the usual formulation You need a notion of which are the most possible of the system which, for example, as in the case of particles, or in the field configurations, in the case of fields, we'll see geometries, we need a notion of coarse radium, which are the partitions of these fine-grained distances in the classes, and the measure of interference, which is the deep-oherence function. The new ingredient here is that the deep-oherence function is going to be characterized axiomatically, This is, in fact, this is by now a rather antique notation, compared to the one Tristan used, but I can stick to it anyway. So if these coherence functions is any complex-layered function that has the value of property. It's remission, in the sense of the conditions we see in fact in this function. It's positive in the diagonal element. It's normalized. And most importantly, it evades the principle of superposition, expressed in this bilingual form. And if you have a coarse-grained of a set, then the deep-reherence function for the coarse-grained set is the double sum over the deep-reherence functions in the fine-grained set.

35:00 If you have open information such a function, then you re-calculate the fine decoherence. You use the off-diagonal elements vanishing, you can define the probabilities for histories, which are the diagonal elements, and these probabilities are numbers between 0 and 1, the constant of the vaccines, and they have the most traveled probably in time. So the key point is that the usual plan mechanics, as I've described it before, is one way of satisfying those axioms. But it's not the only way. Therein lies the possibility of endemic timing. And here it is. It's really just a souped up version of the work of Mark Horonov, Ervin, and Nikovits many years ago, right? You just have a plot right down of the squared function which has both initial and final conditions in it. There's a density matrix for the initial condition and a density matrix for the final condition. And this is time neutral because you can see from the second property of the trace, So the plane-brain histories are the same as before, but the measure of interference incorporates not only an initial condition, an initial state, but a final initial condition as well. And that theory is time-mutual. There is no quantum mechanical level of time. In such a time-mutual situation, the observed asymmetries of time are explained by differences between the initial and final conditions. So, for example, the initial condition might be a low boundary waveform issue, and the final condition might be a condition of complete image. And that seems to work pretty well for our universe, but in this theory it becomes a quantitative question. A question for prediction, a question of why, as I discussed the time-symmetric universe before, what is the best final condition to put in here, or how well we know it is. But there's a price to be paid for this. As I illustrated, the notion of state in the quantum mechanical system is itself an inherently kind of asymmetric notion. And therefore, in general, we won't be able to have a notion of state evolving through space-like surfaces

37:30 because since the original version of state was put only for future prediction, now the theory is time-neutral, it can't do either prediction through the future or the past. Now we turn to quantum gravity, or at least this cartoon version of quantum gravity, we talk about quantum space time. Quantum space time is already an issue about defining the number of time, because there's no definite notion of time. After all, it's quantum gravity. There's no fixed time to be talking about whether it's symmetric or not symmetric. Well, that's true, right? But there are histories, and histories are technically histories of boundaries and matter, which have different boundary conditions on the different ends of the histories. So, for example, here's a cartoon version of the expanding universe, this is supposed to be the whole universe. And in fact, with that we can have the no boundary proposal in the beginning of the universe in the condition of ignorance on the end. That is not exactly tiny symmetry, it's history symmetry, but it will give rise to these different boundary conditions, in the classical limit in which we get classical spacetime. Let me just illustrate that. Well, here's a further cartoon versions of general x-con mechanics for geometry. We might take the idea that the high-grade histories are four-dimensional geometries with matter fields on them. That's the method of generalization. The coarse-brain histories are partitions of those in the classes, if you work with them in the very classes, as Carol would do. So, for example, if you're interested in the question of whether the universe expanded with a big volume or not, you might take a volume and then partition all of the histories in between by whether the geometries had a space-like surface that had a volume bigger than some crucial volume, or whether they did not. And you can calculate whether those will turn them to equal here, and calculate the probabilities, and you get the probabilities. You can find the group events measured just before in the usual quantum mechanics by summing over histories, in principle, and by taking the overlap through the overlap, which is a wave-option sort of form.

40:00 That's a fully four-initial atomic annex of space value. In general, you don't get classical predictions, but it can happen. The sum over the action of four geometries could be dominated, for example, by one specific four geometries. and that's, for example, the stationary phase-top approximation. That's a classical geometry. And therefore, this big interval over geometry here is not a place, but I just evaluate this kind of possible geometry in a subsequent interval over fields. But that's field theory and current space-top. So that's the usual familiar story. The theory then is that that's approximately equivalent to the field theory of the plates for geometry, for causal structure, time, and, as a consequence of the structure of the distribution of its function, time asymmetries and asymmetries between the two from the boundary conditions. So it seems that we can do it in a sketchy way, that the observed time asymmetries of the universe, of our planet universe, can be seen as an urgent phenomenon classical approximation of your classical space-time that arise from boundary conditions in a time-neutral theory of dynamics, as well as a time-neutral formulation of quantum mechanics with no built-in arrows of time. In case you missed it, that was my conclusion. But you can hardly fail to observe that in this discussion I didn't end up with the imperial standards of rigor. I am here in the imperial college. So I'll just... Thank you Chris.

42:30 What is gained by the core screening? As you pointed out, it's essentially what ABL did, and you had to go to the Bernabeu was on the same screen. So what he gained by the core screening? Core screening is a fact of life. As I look at you, right, and think, first of all, what do I need to describe you? There are all sorts of positions of every single molecule in the size of you, and the the two densities, and then also I've ignored all the other variables of the entire 10-degree particles and 80th particles of the universe. So coarse graining is the way we deal with it. If we did not coarse graine, in general, then there would be no decoherence, because physically, the decoherence is the disappearance of phases between histories, which as the founders of quantum mechanics said, comes about because they move from some degrees of freedom into objects. So that's expressed precisely by the notion of this one. So of course painting is both what we do and it's essential to the story. So you can eliminate the preparation and the registration? Well, I'm talking about cosmology here. So the preparation and the registration would be in the projection library. I don't happen to believe that you have to do cosmology to the one who graduated. Well, it would be the same thing, I think, right? I mean, you'd have then some initial statement and then some final statement. I wouldn't have stakes. I would just have a preparation and a registration and I could use an ensemble between our Bernabalda ABL. Well, I think if you deal with any realistic system, what I'm talking about is the aerotons that are exhibited by the universe. I think the answer is yes, but let's discuss this afterwards. Just a clarification, when you talk about history in this context, one of your alphas, you introduce them as sequences of properties. In your generalized way of things, they don't They don't need to be such, is that correct? So they don't need to be... To be sequences of... I might have been a little swift in here.

45:00 I mean, for most of the talk I discussed the quantum mechanics of the system in a box. With a well-defined time in a particular length frame if you want. Yeah, I'm asking what happened with it. Actually, go to the general picture that you described at the end. Oh, in the gravitational case. Yes, so in the gravitational case there isn't any time. So a given alpha can be something which is not possible to divide it in a sequence of properties that are different. No, you have to be sort of, you have to deal with it in a four dimensional sense. So for example, you might ask about the probability that the universe has three space-like surfaces with given alpha. But, in a general quantum mechanical theory, you'll get histories, so classically, maybe the volumes would be ordered in time, with bigger volumes like, if there were some expanding divisions. But, quantum mechanically, the analog is defining paths, where there will be no such ordering. Therefore, the ordering would be an emerging property only in the classical limit. But, in general, there would be no one. something that's always slightly bothered me about this formulations you have a density matrix at the beginning of time but why should I have one every moment of time in between logically that seems quite reasonable you can, that's equally a generalized one yeah but isn't that a bit too much can you repeat the question? well, Chris noted that And I had an emission of final density matrix, and I could have had another decoherence functional satisfying as axioms if I put a few more density matrices in various other times. And that's perfectly true. It does satisfy the axiom. Well, what can I tell you? We need a theory that's a very weak structure of generalized quantum mechanics. Those would be, for example, if we have divine interventions or something like that, those would be represented by such density matrices. I'm trying to get the minimum theory that's consistent with the present that exhibits time and time. If you didn't deal with the universe, just the finite system would have to be deviant. Yeah. Baez? Do you think it would have any influence to the issue of aerosol time if space-time was as free as some approaches to quantum gravity?

47:30 Where's Raphael's work? He would say yes, I would say yes. So some formulations, for example, he has a natural growth. But there are lots of discrete formulations, for example, I don't think there's any inherent error, for example, in dynamical triangulations for the regi-calculus, those are the discrete term regression. Yeah, when you talked about the corresponding entropy, you talked about the hydrodynamic variables. But of course, you mentioned it in connection with Roger's point, which was heavily relying on the entropy of black holes. So, which part of training do you regard as appropriate when it comes to entropy as I thought? The thermodynamic one doesn't seem to be the right one there. No, I agree with you. You have to augment it a little bit. I'm not sure exactly how to do that. But, certainly, the everyday entropy you read about in physics and chemistry books is the entropy that I describe. It's a hybrid dynamic variable. Otherwise, there would be no particular reason for it to be associated with it. For example, in Avery-Stokes equations, an equation for the entropy, that deals with these hydrodynamic curves and the dissipations associated with that increase in entropy. Ah, Noah! You missed the joke, I told you. I missed the joke. Luckily, it's about you. I heard one of them now I was going to ask if this is aimed at a quantum gravity theory as I presume it's a quantum mechanics which would cope with quantum gravity what would your view be on the singularity issue which has always been one of the big problems in quantum gravity which after all is related to what you feed in at the beginning and the end so if you have an asymmetry just sort of plugged in there you expect to find that based some quantum gravity theory at some stage, or how do you view that? Well, I'm a hard-carrying dual boundary person. We don't have any singularities at the beginning of this. But it's certainly consistent with the general point of view that there is the case that fluctuations are very small in the beginning of the matter degrees of freedom and grow.

50:00 So we would expect in your picture in the classical domain we start from a regular initial condition which is supposed to be singular and evolved to time asymmetric. Could you just plug that in? I mean, you're not expecting out of your quantum gravity theory to come something which tells you what you're supposed to plug in. All of these, everything that I've said presumes that we specify as a part of the theory, the asymmetric initial and final condition. So you're not expecting it. I'm not expecting you to deduce those. Well, I mean, in I suppose I could deduce them, but nothing I've said allows me to deduce them. Because you could have time-neutral theories, as I indicated, with time-symmetric initial and final conditions. You could have time-neutral theories with time-symmetric initial and final conditions. It's just that the evidence of the observations seems to be infinitesimally against those. Well, I'll describe that for a little bit. You described your final condition on the intuitive state with the words post-ignorance. Who's ignorant? Oh, I take it back. Indifference. Who's indifferent? Now you say, who's indifferent? Totally mixed. Maximal missing information. What, like it says? Well, information is sort of like that. Well, that's nice. Let's not go there. Any more questions? This is a comment that you made that you can turn into a question by disagreeing with me. I don't know if the comment is appropriate to address it yourself. This is like the Prime Minister's question. It frames everything in terms of the questions. But I thought, I'm not a rhetorical question. I thought that there was a subtle difference, maybe important, between the way you express the asymmetry and boundary conditions in the quantum case and the box close to the dimensional box in the gravitational case, which was that in the quantum case, the initial condition is really on the way from it, so some asymmetric attribution of amplitudes to the histories, whereas in the gravitational case, where you don't have an external time, the condition was on the history.

52:30 There should be some difference between what they look at one end, what they're like at one end, and what they're like at the other end. Right. That's correct. That's what he said. You were going to disagree with that or something? No, no. I think it's... I like the observation. Maybe showing one thing that's finding gravity as such as it has to our understanding. Thank you. Thank you for your questions next time.