Information Loss, Determinism & QM / Limits of QM from GR

0:00 Thank you. Thank you. Thank you. Thank you. Thank you.

2:30 Absolutely, but I'm keeping it for you. Basil is coming, by the way, but he's not going to be here until Roger's speaking. He will be here sometime this morning. Those who are here for the CTC seminar, there's a full program of other talks which are available to find reception. There's also today blackboard seminars which are starting from 2.30 to and they'll be here instead of there are also stickers for name tags at the reception if people want to use I'm told we have enough even if tomorrow people change their clothes there's lunch after we'll meet out here after Roger Penrose's talk at 12.30 and people can go to Wilson College people might try at that point. And now I'll introduce you to the Chair Fokini Markopoulou from the Perimeter Institute. Welcome everybody to a great morning session of quantum mechanics. So our first speaker is Gerard Hoth, who is going to talk about information loss, determination and quantum mechanics. All right, now usually this topic makes up all sorts of philosophical discussions. I'll try to minimize that. I just want to give you a technical message, to show how one could think about things and and what calculations one can do, and reserve the philosophical, the deeper issues for data. I have to explain what I'm doing. First of all, it's quite clear that quantum mechanics is such a brilliant and great achievement of science

5:00 that if you fully should try to replace it or to ruin it by doing something awful to quantum mechanics. Quantum commentary, the approach I have in mind is leaving the fundamental mathematics of quantum mechanics untouched. It's great, really, we should keep that. So, in particular, all the physical predictions from quantum mechanics in atomic physics, in nuclear and particle physics, should remain the same. The question only is that when we want to include the gravitational force, we're looking at tremendous problems. And one cause of the problem, of course, is the fact that we attempt to reference our gravity with the conventional viewpoint of quantum mechanics. The difficulty I have with that is that if you try to formulate what the fundamental laws of nature are in string theory or related topics, there always seems to immerse some sort of non-locality. And what I have in mind is an alternative approach where locality can be built in at the expense of some of the sacred viewpoints on quantum mechanics. Let me explain what I dreamed of this more precisely. Now, in conventional quantum mechanics, one of the starting point is that it doesn't matter, if you have a Hilbert space, it doesn't matter what you choose is the basis of Hilbert space. We can talk about particles, we can talk about fields, or whatever, and all these choices, from a conceptual point of view, are totally equivalent. So, when you do an experiment of particle physics or anything else in quantum mechanics, you can have a particle spin in the z direction, or spin with the x direction, or spin in the y direction, of these you are looking at really doesn't matter, it doesn't matter in the formation of theory and as a consequence you might be using non-commuting operators all the time when you do quantum mechanics and that's where all the deeper peculiarities of quantum mechanics come apart. So the only way in which in my approach to understanding nature at a plot scale, I might deviate from that, is I say there's one particular choice of basis, of human space, which is more special, more special than others. So that, of course, is not in contradiction with quantum mechanics.

7:30 One may always say, take a quantum theory and then say that there's one special choice of basis in terms of which I understand nature better than if I would use any other basis. So that's basically the bottom line of what I'm saying, which is not modifying quantum mechanics in any way, except saying that there's one special choice where things behave in a more logically, more understandable way than otherwise. And so the rules for all the computations get essentially unchanged. So in conventional quantum mechanics, locality usually means that, say, or the sub-correct particles, what it means is that if you have operators and you can localize operators in space and time, that as soon as two operators are separated from each other outside the microphone, they must commute. And that's what locality means, technically, in quantum field theory. And that's a perfect definition of locality as far as quantum theory is possible. It means that you cannot possibly influence any measurement by any sort of mechanism that would go faster than the speed of light. And that's enough to realize a virtual locality that is perfectly fine to work with in fact, it's all we need. So that's where I think at the Planck scale the main difference might arise that in the theory I'm proposing, locality means something else. Locality is something that you can only understand in this special basis. So that's the big difference. That, of course, you can imagine, I'm talking about locality at Planck in distance scales. So at the distance scale of the standard model, these theories are identical. They work out to be the same. But at the Planck scale, locality may mean something different. That is, I think, the main proposal here. And then finally I'll say something about classes, in conventional quantum field theories in particular, you have gauge invariants and most importantly, local gauge invariants, which means that you have large sets of states and you try to formulate a theory from first principles, you start using some gauge theory and take to the gauge, you get a large class of states of urban space. They are not the

10:00 physical states. The physical states are equivalence classes of states where you can perform any gauge transformation. Equivalence classes in my theory now are somewhat different, but we think mathematically they are mounting the same thing. That is, that two states are equivalent if an observer at later times cannot see a difference. And then, so presumably or possibly this may have something to do with gauge symmetry equivalences in conventional quantum field theories. So, let me try to explain what I say. In this special basis, I can specify the state universe is in. And since this is a base element, all the base elements represent different states universe that be in. And you might think of the positions of particles and or the momenta of particles you might think of the color of someone's hair or any other way in which you describe this universe but most importantly this is one single basis so in terms of basis you have observables which observe in which way the elements are for that reason i'm just looking at this one basis only in this one basis now and this is what makes special, one might call naming a simple model universe, that explains perhaps things much better than I want to say. In a model universe, you might have a theory of everything, and this model universe is very simple compared to the real universe, only consisting of three states, a three-dimensional global space, which is just a five-dimensional vector space. And in this vector space, that's the theory of everything. The theory of everything says that the universe in state one will evolve into universe number two. If the universe state number three, and then in state number three it will fall back to state number one. And if you have a law like this, you've said everything about this universe, and so you might then use these elements as a basis, and in that basis, the evolution operator is just that unitary operator. Now, you can say this, but from that point on, you can use ordinary quantum mechanics to proceed. So we can consider superpositions in a way familiar with quantum mechanics, and you may decide that the squares of these coefficients are probabilities. So far, this is just a mathematical, you say, an agreement, a semantic agreement about how to talk about things without this meaning anything physically.

12:30 physically everything is just the third line but mathematically you might be able to now decide to proceed and define probabilities so you want to solve this theory in a probabilistic way of course real universes are quite a bit more complicated and you might want to to use to help any mathematical technique that you might find and one will be statistics so we apply statistical techniques and it means that we're going to consider probabilities. And the last thing about this is, once you allow yourself to talk about all these other elements of global space, you might discover that you can diagonalize an evolution operator. And if you diagonalize you, you'll find the three cube groups of one as the eigenvalues. And I might decide to call that e to the minus i times a Hamiltonian. And that Hamiltonian is of course something that you recognize, is Hamiltonian with three equally spaced levels, something like this. And that happens to be Hamiltonian of a spin-1 particle in a homogeneous magnetic field. So, from now on, when you see a spin-1 atom in a homogeneous magnetic field, you might say, This is an example of a deterministic theory, because I can go back to this previous basis where this atom shows three states which are just continuously evolving one into the other. So, but then you go to the diagonal basis and then figures like this. So, you see that there are examples of very simple quantum systems in nature where actually it is allowed to interpret the thing if you go to this other basis, this so-called preferred basis, where everything happens deterministically. And so this could be the starting point of a deterministic approach to quantum mechanics, which in particular might be something to consider at the Planck scale. And just to explain my wording, I like to call this thing a vehicle. A vehicle is an operator which is the regular in this fundamental, we call it primordial

15:00 basis. And in the original basis then of the echo, for instance, I can say, this is the universe is the state number one, the universe is the state number two, the universe is the state number three. Well, the operator tells you which state the universe is, is at the point I call a vehicle. And if you have things like that, operate like that, they will commute at all times. So, I would also say in this very special basis, we have very special operators which continue to commute forever. Now this is of course an element that you normally don't see in quantum mechanics. We, in ordinary models of particles, we don't have such operators. But as you see here, in some special examples, it may be possible to construct such operators. So it's a far-fetched, speculative idea that perhaps in the real world, eventually such operators exist. And what I'm speculating about is that if such operators might exist, it might be possible to define them at a flat scale, it will become increasingly more difficult to define such operators in minor scales, in particular, in terms of electrons, protons, or other physical factors. All other operators, just to distinguish them, are changeable. In particular, the Hamiltonian and the evolution operator, all these operators which mix things about, are operators which replace a state by another state, and that are changeable. And the operators that we normally you work with in the world of quantum mechanics and atoms and molecules are practically all changeables or you could also say if changeable is really a foundation of the method then there are complicated functions of both variables and changeables so in the real in the ordinary world that we know we don't know how to compute the variables um there's another example of a deterministic evolution and i'll mention right here is if you have a If you have an operator dT of Q is F, that's a deterministic theory, again you can say this is an equation that happens in a special basis, but I can turn that into a quantum mechanical formula. Introducing the operator P, which is h over i, d, d, q, where that's of course a quantum mechanical P operator, nothing stops me even if I have a deterministic theory to define such as P. And then Hamiltonian is just P times F. So P times F is a Hamiltonian system.

17:30 And if you take a Hamiltonian and work out a certain irritation for that Hamiltonian, you find exactly the top line, so you find a completely deterministic evolution. And it would have been fine and it would have been quite reasonable to suspect that our the world is like this, except for one very important observation. If you start a hematomian of that sort, that hematomian is not bounded from below. P times F is the operator's linear or any type, or whatever the structure F is, P times F is not going to be bounded from below. So this expression, the linear method, will not be bounded from below. So a very The very important difference that you see between a theory of this sort and all of a property mechanics is that there's no ground state, no vacuum. That sounds like perhaps a technical detail, but of course it makes all the difference. If you have a property theory and you remove the vacuum state, if there's nonexistence, then you have something totally different for all of a property mechanics, and it doesn't look interesting at all. So what I'm saying is that it's dangerous, it just does not look like a very interesting theory. Well, to try to recapture my interest, let's consider a harmonic oscillator. And here, consider just any purely harmonic problem of the chemical oscillator. I claim that is one example of the deterministic system. So, now, there are lots of oscillators in the universe, so all these oscillators, if they are harmonic, appear to be deterministic. And what I mean with that is the deterministic system associated to a quantum dynamic oscillator is just a purely periodic motion. So, imagine a particle just moving on a circle like this. The only thing about this determinative system is that it's periodic, and of course, exactly how to define the orders of a circle in the theory, so you might just as well say, despite the moves with a constant velocity along the circle, the only thing you need to know to describe this system is that after a certain amount of time, after a certain period, it comes back to the position where it was before. And now, if you consider a state like, a system like this, but suppose that it can just be in two states.

20:00 The pattern can be sitting here, or sitting here. This is what I'm doing now, is I'm discretizing the system. The pattern is moving on a circle continuously. A bit difficult to consider it. Then I would apply the previous slide to this directly. I have a toning, which is not bounded from below. Now I'm trying to read the system more definitely if, instead of a particle moving a circle, I have a particle that can sit here, or it can sit here, and it just jumps about. Then I have Hamiltonian, which is just two states. And if I diagonalize it, then I get just these two are the states of Hamiltonian. Now I can decide to go to the continuum limit, so I add some more states. But you can sit from here and then go and have four dimensions of the space, we get two more states in the Newtonian. So now if I diagonalize the evolution operator and the right is E to the minus IH, I get these four states. But now let's add some more possibilities. I have particle moving hopping, a system which has now eight states and it's periodic. Then in the Newtonian we get eight states. and so on. So now I have 16 states, and eventually I get totally looking like this, and eventually the continuum limit, it will go on forever. So sure, this looks like the harmonic oscillator, you see. The harmonic oscillator in its adiator state has deeply spaced lines like this. And so you see, if you take the continuum limit of a particle hopping over discrete positions, but with smaller and smaller time intervals, you get the spectrum for the antonio that looks more and more like the spectrum of a harmonic oscillator. However, if you say things this way, you're cheating, because if you have particles strictly on the continuum, you always have to deal with these negative energy states, and they are not so easy to leave out. The reason for that is my antonio really is periodic. As soon as time is discrete, there is a periodiscine Antonium with a period, which is two pi divided by its time quantum. And because of that, it's, in practice, well, in principle, if you leave out of these states here, in practice it's very difficult. As soon as you allow these harmonic oscillators to interact some way, to become unharmonic, you are going to have to face these negative energy states.

22:30 So I am not trying to deceive myself in thinking that I solved a goal, but one can decide somehow to project out these negative energy states. So the more precise way to formulate the theorem is that a particle moving continuously across a circle has a spectrum which is identical to the harmonic oscillator, except there's an extra set of states downstairs which you want to remove to project out. So I do need a kind of projection mechanism. seems to be unnecessary, as long as you look at a harmonic oscillator where all these levels are exactly preserved in time, so you never need to worry about those, but as soon as you try to lose interactions, these are causing nasty problems, so, and in fact, well, there is a way to construct vehicles in a harmonic oscillator by just using these positive states only, and you can do that with any out of any accuracy, because infinite accuracy. And these vehicles indeed show that you have periodic motion. So, the harmonic offset that comes close to the timing system, I want to look at. But you see already the difficulty. The difficulty is the absence, the presence or absence of A ground state, a vacuum state, and this is where most of the problems are. Now, by the way, I don't know if you can see it, but my background comes to position two pets. So, let me say it this way then. We could consider the assignment of theoretical physicists to find the vehicles of this world. Maybe they are there lurking around at the Planck scale, but they are too difficult for us to identify in terms of ordinary operators that we know about in physics. But in some very simple models of nature, I can come very close to identify vehicles, so that you get an interesting prospect of actually being able to make some more deterministic models of nature. So, one example is the atom in a magnetic field, say, if you have an atom stick in a magnetic field, then you know this is a periodic system, and it can be modeled as a universe, where things hop from one state to the next. But there are other examples. An example I like very much, and I'll say more about it, is a mass that's non-interacting neutrino.

25:00 Imagine, well, we want to get the standard model in this picture. Standard model is not here as yet. It will take quite a while to get the vehicles of the standard model. In the meantime, I could find the vehicles if I would have chiral Dirac particles, So neutrinos, at least mainly neutrinos, but they're not interacting. So the physical neutrinos, of course, does interact, but only get weak. So if they're not interacting, I can identify the variables for the system. It's very interesting system, I'll say more about it. Other examples I've no time to discuss. If you have a scalar field theory, again, of three particles. You see, in principle, if you would have three scalar particles, the field theory that consists of just a large amount of harmonic oscillators. So, say, a phonon in a solid, a solid is purely harmonic, phonons in all the magnetic particles, so purely quantum field theory starts off with oscillators. So since I just said that a harmonic oscillator in many aspects is a deterministic system of the particle moving periodically above the circle, therefore anything consisting of is also a deterministic system. So surely I could identify the be-able operators if you just use a field theory full of armored oscillators. It is quite technical and there are quite a bit of footnotes to be placed here, but it's an interesting system. And even more so, if you give these for bosons a vector property. Now, by itself, of course, that also the Maxwell fields, the large interactions, consist of three oscillators, but they're oriented in space. They are vectors. And so one problem I want to set out to do was, can you make a location invariant description of the vehicles of the system, which was a hard job to do, but it worked out fine, provided that the particles will be Maxwell particles. I could do it for massive spin-run particles, but I could do it So it seems that in the standard model, there are at least ingredients of subsets of fields and particles non-directing where individuals can be identified.

27:30 But in the real world, there's quite a lot of things to be done. Let me explain the neutrino business, because it's nice and interesting. Because neutrinos are not harmonious oscillators, they are fermionic particles. And first consider a single neutrino and try to quantize that, well, we know the Hamiltonian for single neutrino is Pauli Hamiltonian because there's no master, it would have been a direct Hamiltonian. Without the master, you only have two components. So, you just use the Pauli matrices, and I forgot the delta function, this is the formula the Pauli matrices for the Hamiltonian, and the B-ables can be identified for the first chord class of humans. To B, P-hat, now P-hat is the orientation of momentum, moduloid sign and moduloid length. So I'm not saying how long, how large momentum is, but only in which direction the momentum is pointing, and I'm not specifying the sign. We would say, choose a sign such that the X component is positive. We would erase the information about the sign of the momentum. Then P hat dot sigma, where sigma is the spin operator, two sigmas. P hat dot sigma is the kind of velocity of the signal. And then P hat dot X is the most interesting quantity. In itself, Xs and momentum do not commute. But these operators together happen to be a commuting set. And that is actually quite simple. the momentum, yes, so what you have to do is look how these things evolve in time, and you find that this is how x of t evolves, and p dot x evolves this way. So if these operators commute at time equals zero, it's very easy to see they will commute with all parts because they sit in each other's place in the equation portion of the system. So these operators, the fact that these operators commute at t equals zero is actually also not so difficult to prove. At t equals zero, the only thing I have to prove is p hat of x commutes with the others because p hat and sigma was obviously commuting, so these two should commute with this one

30:00 to the others, perhaps not so easy, except when you realize that p hat of x commutes with p hat, obviously, because p hat of x, apart from, in fact, it's a varientation operator, the operator which blows up the length of the vector without affecting its orientation. But p hat was defined to be the orientation where the length has been divided out. So p hat, by definition, is invariant of the varientations. And that's why these two operators commute. And that eventually is why all these operators commute. So they commute at time equal zero. They commute at all times. This is a set of vehicles. This is actually a deterministic system. In terms of this basis. So that's what I meant when I said find a single basis where everything commutes. And then I have deterministic theory. And the implementation of that, I already saw it. So this is really what I claim this represents. P hat of x is the coordinate of something in the direction of P hat. That's only one of the three coordinates. So you can say it describes a sheet. And the orientation of the sheet is given by P hat, apart from the sign. P hat of sigma tells you which direction the sheet is moving. So we have a sigma, it's adding the sign which I just had to move before. So what you have is oriented plane sheet, moving the speed of light in one direction. Since it moves to the speed of light, it moves in a deterministic way. There's no such a way to do anything like this because part of this is massless. So from now on, if you consider a theory of masses and generals, you should have to mind that this theory is a deterministic system retinos are just sheets. Now, all this is very nice, but of course, we have two problems. One problem is the fact that the Newtonian game is not bound to be long. Sigma dot p is linear in momentum. This is not about the Newtonian. This thing doesn't have a Gram-State. Well, in this case, fortunately, Paul Dirac told us what to do. He had to second quantize. And so, you have to consider a large number of these metrinons, and then they analyze the Hamiltonian, and say all many energy states are somehow filled, and then if all the positive energy states are kept empty, then you have a state which has less energy than any other state you can construct.

32:30 So, the only thing to do with other states is to take a part to perform the C into the empty region of positive energies, and that should increase the energy of the system. So the act found a way to solve the form of non-definite nanotony by second proposition. All you say is that you don't have one sheet, you have a very large cluster of sheets moving all directions, and then you see that there is a vector state. But, if you want to do this more precisely, because I'm going a bit too fast, You have to do this not precisely, you have to do this by introducing a cutoff, because this only works if this set of levels goes all the way to minus infinity. But if you want to understand better what goes on, you first try to produce a cutoff, so that in any given momentum direction, the sheet can only be in discretized positions, either filled or empty. So now we have a five number of states with the power of the exclusion principle that either is or is not a sheet on all these discrete positions. And that would then be a system where the sheet is hot with integer time steps. Again, if you have time steps delta t which is an integer, the Hamiltonian is again not a continuum. The Hamiltonian is continuous, but it's periodic with two pi over delta t to be the period. In that case, again, I have a difficulty that this sequence of lines comes somewhere. I have an Antonin that was periodic. But then, because she says, not one Fermi level, but two Fermi levels, I put them on the screen to another Fermi level, where Antonin is as low as anything yet. And they decided to switch on the periodic identification of positive energies. So you get another Fermi level where the energies are the other way around. So I haven't really solved the positive energy problem. It's only, you know, you can make yourself believe if you solve it, but if you look at it, you haven't. So that means that this problem is going, I'm going to encounter tremendous difficulties if I try to make it continuous in the act. Or even simpler, if I just try to give them a mass, because so far they are massless. So how do we do all this? It is here to think more powerful schemes than necessary, and a key ingredient is what

35:00 I haven't said so much about yet, is information loss. Why would information loss be necessary here? And now this is one nice thing one can do with this theory, which you cannot do with ordinary quantum mechanics. With ordinary quantum mechanics, if you introduce information loss, you will find it in your And we had a discussion yesterday, we had a discussion all the time, what does a quantum theory mean if the evolution operator is not punitive? Well, it's very hard to make any sense out of such a quantum theory, except if you have a single special basis where it can work in terms of which things are deterministic. Because in that basis, you might decide to introduce information loss. So here's the simplest example of the universe evolving in discrete steps. 2 goes to 3, 3 goes to 1, but there's also a 4th state, and a 4th state at the bottom is if the universe is in this state, it evolves to state number 2. And this is my model universe. And of course, so you see a model universe like this, you say, what a crazy model this Because state number 4 you can't get into, you can only get out of. So if after one step you're sure that you're in this closed cycle, so why did I talk about universe number 4 at all? Well, in this model universe, you'd be quite right with criticizing it this way, and you'd say, all right, the model universe is the same as it had before, so surely it's going to be described by the same unitary evolution operator as well before. So that shows there's no problem with this universe. But why did it introduce state number four? Well, in the real universe, I have a large number of states, much larger than just these four. So many states that I find it extremely difficult to distinguish states of this kind from states of this kind. In fact, you can't. It's too complicated. Actually, the real universe is not known to appear wrong at all. It seems to be evolved forever. So we have never simply reached the Poirier cycle of this universe because it's so big. So the distinction we state before, state number one, is much more subtle and much more difficult to see. So, in practice, we're going to look how to make a distinction and look at something else. In practice, what we do is introduce equivalence classes. Stake number one and state number four are fundamentally equivalent because after a few time steps, you cannot possibly distinguish them. So, I have these equivalence classes. I put the brackets around them.

37:30 So, state number one, state number four are equivalent. this class evolves into the class of statement two, the class of statement two evolves to statement three, and so on. So now I have a unitary evolution, but only among the equivalence classes. And so, what you have to do, if you have information loss in this special basis, is you can still do quantum mechanics, but not in terms of the individual states, but in terms of the equivalence classes. So that's our next step. Do the equivalence classes. And now I can return to the neutrinos, because now this gives you a new twist to the story. A new twist is this, that originally I said neutrinos are moving sheets, but now I say these sheets are not sheets at all in my theory. They represent the equivalent class of neutrinos. So assume now that the neutrino here is a particle. It's a point like object. And the particle has a flag that actually gives you the direction of its momentum, p hat. p hat commutes with the coordinate of this sheet. So there's a p hat, there's a particle, but the velocity in a p hat direction is completely fixed in is C, but there's a random motion along this sheet. So we can't figure out where the particle has been in the past on this sheet. So imagine that the information as to where on the sheet the particle has gotten lost. I can't, I don't know really what the complete location of this particle is, but just let's say it, that it's hopeless to try to figure out where on the sheet the particle was in the past, so all these positional algorithms, And the evolution of the equivalence class appears to be non-local, it's a sheet. And as you might realize that the sheet, of course, appears to find a locality. I don't know where in the universe this material is. Somewhere on the sheet, it could be way out somewhere else. But in fact, if you say the sheet is an equivalence class, and if it moves in this direction, its position in the transfer direction uncontrollable, unknowable because that information gets lost. Then I have a model of neutrino where technically speaking only the sheets are, the glasses above which I have information and so this is why I think in the real world neutrinos look like this, we can't control the transverse movement.

40:00 A little catch here, something to be aware of, this vibrates Lerner's invariance, because the velocity will be bigger than the velocity of light. If the material would move like this, it would have to move faster than light, because it already goes to the speed of light in the longitudinal direction. So I've got the very Lerner's invariance with this proposal. That's not so pleasant, but that's the way things might be. Indeed, there is a reason And I'd like to continue and show that if you look at things this way, you might generate a world which looks very much like the quantum world we actually live in. For instance, take two degrees of freedom, a Q1 and a Q2. And now, assuming that I have a deterministic system where Q1 and Q2 are evolving, but that information is not preserved. Suppose now there's an evolution law that tells you that the Jacobian of the motion is not conserved. So that at every point of the Q1, Q2 plane, I have an arrow saying in which direction this point is moving. But these arrows form a flow, like a liquid flow, where density is not conserved. So, for instance, there are lines to which these arrows are being connected. So, if you let this thing evolve, suppose it's periodic, the drop-off line at A will be emerged there. So, it's periodic instead of equations. Then, you can easily find out that if it's periodic, that if the system comes closer to this line, it comes closer and closer and closer, eventually these red lines or the green lines are the stable orbits. So if you have information loss of this sort of deterministic system, you might well develop And these orbits, they show how the equivalence classes are moving. The regions in between are essentially, after a while, they get lost. That information disappears from the system. If you look carefully, it's not so easily visible in this game. There are white lines here in between, which are the opposite. It's the lines to which you'll move if you go backwards in time. So this system showing two continuous coordinates actually shows something remarkable.

42:30 even though there's information loss, there still may be time reversal symmetry. If you go backwards in time, your white orbits in between are the stable orbits rather than the red and the green orbit. So actually because of periodicity, the red orbit is one solution, green orbit is the other. There are two solutions in positive time, and there are two similar solutions if you go backwards in time, but they're simply similar to someone else. So it's part of information loss, such as theory might easily retain But the most important thing I want to ask your attention for is that you see them getting discrete orbits. So discrete states in the system like you sit. And of course, this reminds one of the situation in proper defense that discrete systems to emerge in a natural way. Discrete states linked to orbits of the planet in hydrogen atom, which are also discrete. It seems to be the origin of that would ultimately lie on information possible in the class integration portion. Well, there's a positive that Antonia has been bugging me for so much that it's trying to look for other ways of trying to get rid of that. The belief is that ultimately we introduce information as well on that, but also maybe at the later stage introducing gravitational interactions, which are very, very difficult You might find a deeper reason as to why, in this world of renor, there seems to be a natural way to say that there's a bound in Hamiltonian. There's a lower bound called vector state. And that vector state is indeed a very complicated statistical solution equation, not something simple. That's vector fluctuations in all this. And so one approach was to consider, for instance, the true classical harmonic oscillator. A de-permistic harmonic oscillator, x dot is y, y dot is minus x, x dot is y, y dot is minus x, a classic harmonic oscillator. Now I can introduce the quantum operators px and py, and then this Hamiltonian, y, since x dot is y, I take px, multiply y, that's Hamiltonian, which generates the x equation. equation, this part generator generates the y equation. So the generator is y of px minus x of py. This would be the deterministic generator for this system. Again, I have not introduced

45:00 information loss at this point. This is just a harmonic ostomator. Now, let me now do all the tricks I have in my books about public mechanics. I'll rewrite generator this way. by writing this as sums or differences of squares. So px plus y squared, the cross-product of that sits here. So if I subtract these two squares, I get y of px. If I subtract these two squares, I get that. And then you see that the Hamiltonian can be written as a square minus another square. And that square contains two operators, p1 and q1, where p1 and Q1 are these combinations. X minus PY. Oh, that's this one, this is a Q, and this is a PX plus Y is a P1, and that's a Q2 and a P2, which sit here. And now the nice thing about this is that the P1 and the Q1 do not commute, but the one operator is commuting the two operators. And so, this Hamiltonian can be written as a difference. It's in two Hamiltonians, which commute among each other. So, H1 commutes with H2. And H1 and H2 are both positive. The only thing now is the minus sign in between. So, I have a system where I have H1 minus H2. That's actually also an operator by which is a density matrix in I have these density matrices in kind all the time that maybe a classical system generates not the evolution of a wave function rather than the density matrix. But H1 tells you how the gets are evolving, H2 tells you how the bras are evolving. And H1 and H2 are then mutually commutated. Well, I could also continue by saying that I have two independent quantum oscillators, but somehow one oscillator not talking to the other. So maybe there's a parallel world, world parallel to ours, but Hamiltonian is minus our Hamiltonian, but we are not communicating with that universe, the two Hamiltonians commute. In that case, we also generate quite naturally a bound, a Hamiltonian which is naturally bounded, even from a deterministic system. So this could be a way to proceed. then a more daring step would be H2 not only is invisible, but H2 might be unstable. We could introduce some non-Newtonian motion there where H2 somehow is constrained to be

47:30 in the ground state. That's a more daring approach. You know, I've been trying to say maybe there's a way of introducing information loss in the system such as H2 is somehow constrained to be in the ground state, which means that the operator is in H2 effectively zero, which means Y is nearly equal to X. X is nearly minus Y. In that case, the Q2 and P2 effectively zero. Q1 is this and P1 is that. And then you get simply this Antonio B, X comes to Y squared, or Q squared or P squared, the conventional harmonic oscillator without, and the other one is then somehow disappearing from the system. That could be. So, we then have a system that the classical harmonic oscillator really coincides with the harmonic, so that could be this approach. Actually, one can work a bit further in that, I'll go very briefly because I think my time is out of it. So, a procedure would be that, if you look at it, it's H1 and H2, you can find that they're related to two preserved properties. One is the dilaton operator, this is general dilatations, the classical harmonic oscillator is invariant on the scale constellations. The other thing conserved in the classical operators of x-scrap is a y-scrap, I call rho-scrap. So the hematonic difference with d, the hematonic difference with rho. And so H1 and H2, which I had in the previous slide, could actually be written by saying a different, original hematonic, and I manipulate it as I please using rho and d since rho and d commutes with it. So, and you all need to commute with each other, but that doesn't matter. So, I take the H1 and H2, I just this, and then you find that the origin of the tonics is H1 minus H2. And you find that in this case, if you say that H2, for some reason, goes to the RG brain information loss, on the intubation of 2 is invisible, then the Hamiltonian will approach basically X-W wire strength. Actually, you can do this. The nice thing of descending from this plane

50:00 is that you discover you don't even need the on the D at all. You can just replicate only the first part of it and do that for any oscillator, whether it's harmonic or not. You see, the The anamonic oscillator was invariant on the dilletations but the anamonic oscillator may be not invariant on the dilletations. Actually you discover that you don't need the dilletor operator, you will do the same thing there. Or this is a little intermezzo, remember for the black hole you have universe 1 and universe 2 connected by the horizon here. If you look at the Hamiltonian on the black hole you get also H1 minus H2. You get the H1 here, you get the negative anatomic, your style runs backwards in the sense, in this part of the universe. So, having H1 minus H2 happens very often in many branches of quantum mechanics. It's operated for a density matrix, but also happens to be operated for a black hole. So having these differences, somehow the information H2 is irrelevant. What happens behind the horizon of a black hole is something that we cannot see. So you have to remove H2 out of your system and say the true hematonic system is only H1, which is positive. So in the platform you have a similar situation that finding hematonic is invisible because of the information loss. This is one of the reasons why I thought that H2 would somehow be hematonic and more longer the thing. So in the case of an analog oscillator, in the slide, but in, so this is a Again, picture that there is a Hamiltonian and there is some quantity U, which is just an observable quantity in the original basis. And it may seem that the Hamiltonian somehow links onto U. This is the idea that the Hamiltonian of this system in the special basis is somehow linked onto a plastic-legged quantity U. And this happens if you have a system which has stable and unstable orbits.

52:30 You have information loss saying that there's no such thing as conserved energy in a classical system. It has conserved hematonia. The hematonia generates an evolution. But the energy used is not exactly conserved. It's only conserved on stable attractors, stable orbits in the orbit system. So that would naturally force things to go in discrete orbits. It could be a different reason why the hydrogen atoms on the screen, or the screen in between, are unstable not only because they're in the focus, but also because the information in between the regions gets dissipated away. So that could also be the reason why the electronic atoms on the screen. This is a procedure which can also be overcome more. So, if the Hamiltonian is somehow a tie-in if you consider a quantity, then you know that the Hamiltonian for an oscillate is a periodic, so U must be an integer multiple of omega, and so the Hamiltonian is naturally, the system is periodic, the Hamiltonian is this key. but now we see only discrete orbits are surviving. So, this is, yes, in metaphysics, it's, if you have two oscillators, one oscillator takes the same period, this is the other oscillator, that's called a lock-in system. So, here they have two conserved quantities, H and U. When U is nearly conserved, H is exactly conserved. But if U is nearly conserved, it could be that U locks in to become equal to H, just like harmonic oscillators. It's the same thing as what Christian Huygens observed long ago, that you have two clocks of the same band hanging against the wall, They, after a while, they seem to be going in harmony with each other, they seem to show exactly the same time and across the same time, because they're going to one lock-in mode of oscillation, and that could be happening here, too, in that age, and you become identical. In that case, it ages from ties, you lose those from ties also, and then you get authentically discrete orbits. You can extend this picture to any non-harmonic oscillator as well.

55:00 In an harmonic oscillator, the hematomium is periodic, but the period t might actually be dependent on which orbit you are in. So you get orbit-dependent periodistopies, and in that case, if information loss sets then again, hematonia might be linked to some preserved quantity, and then you get this picture of the unamomal oscillate, but also unamomal oscillate are going to discrete states, where the orbits in between are the unstable orbits, and these are the mechanical orbits in which the oscillate is nice to sit. So you see that with information loss, it's quite natural to get a phenomenal proposition in a very simple classical picture. So, So this is, well, intuitive perhaps, but this is the reason why it could be that the quantum mechanical nature of our world is due to information loss, but not information loss at the atomic scale, but information loss at the Planck scale. And, well, yes, I wanted to say a few more things about information loss. If the universe is going to a planetary cycle, now, our own universe is not known for going to cycles, it's much too big. So the only relevant discussion about Planck-Quantare cycles is if you look at a very small section of the universe, suppose it would isolate a very tiny bit of it, and have a simplified model for that, that might go into a cycle. And in general, this is a picture that there are many ions to the cycle. The universe could start anywhere here and then it evolved and and go into a cycle, not only the cycle stays there, but it could start from outside the cycle. So this would be the spaceable cycle. You might enter this cycle, you might enter this one, or that one, depending on how you start it. And these cycles will be the ultimate quantum states. These lines add to it, how you get started. In most parts of the universe, these sidelines will be much, much longer than the actual cycles. So the importance process are just those cycles. Oh, yes, I guess the other important thing on the same black holes. This is, again, a motivation for why we think information must be necessary.

57:30 We won't eventually improve reality, the gravitation collapse at some point, and there will be black holes, as you know, the gravitation location gives something like black holes, there of course, there's an enormous amount of information loss. The difference class of black holes are actually very large. They take two different objects thrown into a black hole, and after a while, this thing looks equal. So, this is the proper type of information loss, and the theory then about the black holes is that the only way to subject to the rules of quantum mechanics is to say that if two black holes are different, and after a while they become the same, then they are in the same equivalence class. So the only way to apply quantum mechanics to that is to find a basis of building space where this equivalence class is from a single element of building space. Doing this adds a fundamental sense of non-locality, and this is why in relation to this way of the conventional one, has a non-local element to it. So the non-locality is not in the physics, it's in our description. You have to remember that, in our attempt to write a quantity of gravity, of course, it is also non-locality, not non-locality in physics, but non-locality in our description. So, as you know, in the black hole, if you assume that the entropy due to distinct the black holes can be in, countable, like here, there's one bit or byte per unit of surface area in the Black Hole, and we have these tremendous puzzles in nature, how can this puzzle be reconciled to eternity? Well, the idea is that these are also equivalence classes of states. These are not the complete set of states that Black Hole can be in. These are the equivalence classes of states that Black Hole can be in. If we look at the ontological states, all the other states that Black Hole they will probably draw with the bulk of the universe. So the entropy law and the holographic law of the counting number of states in our theories of black holes, they refer to be people's glasses. If you have the total number of states you risk them in, it's much, much much more, that that information cannot be resolved after a certain amount of time.

1:00:00 So this is a picture of the human light in half, here's another prototype of such a model called the cellular automaton. I forgot what kind of rule I put in here, it doesn't really matter much. The rule is, every square in here gets updated after one step of the computer, and the rule The rule is that, whatever the rule is, the way a square is being updated only depends on what its immediate neighbors are doing. So it doesn't matter what happens far away, if you ask what's the next value of the actual spot, it only depends on its immediate neighbors. And you can write many programs of this sort and you always get something interesting which evolves. The most interesting cellular automata, however, are those where lots of information gets lost. You say in most cases the squares are zeros, every now and then there will be ones. But it's impossible to retrieve the past from the future because the information simply disappears. So these cellular automata cannot at all be in two to the n states where n is a number of squares in the bulk. But maybe, after a long while, the total number of different states can be in, going 2 to the power of the number of squares at the circumference. So that the empathy of the thing is much lower than it seems to be, it's actually only going to brush with the area, with the boundary, rather than the bottom. And this is what we see happening in black holes without really having an understanding of it. And I think this would be the physical reason for this. So the assumption is that somehow there are all these factors and variables of degrees of freedom at the black standard. do not resemble the ordinary particles of foods that we are used to, but the things we call particles and fields are actually very very complicated functions of that. So in such a model, at day-life distances you expect statistical features which could very well resemble the very popular chemical world of human beings. So that is sort of bottom line what I want to say. The real question is not so much what Einstein said, which is actually the belief that God gambles, but the belief that God gambles. Our only problem is how does he gamble?

1:02:30 And here we have some discussion. It suggested that by introducing equivalence classes, you could have a situation where the information lost would be effectively unobservable, and hence you should be talking about equivalence classes, because there's no way of distinguishing them. However, then you consider the example of throwing in a turtle and a donkey into a black hole and saying that because you can't tell the difference, but that presumably is going to be an example of that. However, I could keep a record of whether I threw a donkey or a turtle in it, so I would know the difference. And that means that representing in terms of equivalence class could work, because I can actually say which one, which class, which number of class I was in. Now, when you keep a record, of course you keep the record in a safe place, far from the black hole, right? That's non-locality. So, this means, as soon as you keep a record, these classes are not equivalent. These states are not equivalent, right? Oh, they're only equivalent if there's no record anywhere in your memory, and you look at the system, by hell. What was invented? What was the document? I don't remember. It has been forgotten. But in a very fundamental way, no way to retrieve information. Then the problem with equivalence class. But you're quite right. Of course, someone could seek to keep a record somewhere. As soon as that's the case, this takes a lot of equipment. So it means that the notion of equipment class is extremely non-local. And to my mind, this explains the apparent non-locality that people need to understand the details of the mechanics. So our language, our description of the system, is extremely non-local because of this. So, you're quite right, if you have a record, then it's no longer equivalent. But only if you, for some reason, you have to not check the record. Now, of course, in the case of Duncan Turner, it's easy to keep the record of this, just one bit of information, essentially. But in reality, of course, the idea is that the amount of information lost in the universe is so gigantic, so enormous, that it's hopeless to try to keep the record.

1:05:00 That's the whole point of it. It's impossible to keep tackling this. And as soon as that's the case, then you have two information losses. Then you have to consider those equivalence losses. In non-locality theories, we're often asked to consider counterfactual measurements. You know, I measured the particle this way, but I could have measured it that way. Somehow the particle must be prepared for any possible measurement of the anatomy. How does your deterministic ideas deal with these types of questions? Yes, so the very important thing is to sort of adapt to the state. That adapt to the state, as I said already, are difficult to define adapt to the state in the first place. So I can only answer the question properly. If this problem of the positivity that I'm going to really answer, So, because it's hard to say exactly how it works, the idea is that the vector state is not all you need, and it's all the most complicated states at all of today's time. So, when you consider different possible experiments, different possible techniques, As soon as you decide to measure the X component of the particle, then it's that thing which is equivalent by states, the y-component is simply a superposition of the states, which you cannot measure. But the relation between the concept of a field on a Pythagol, or the spin of a Pythagol, the momentum of a Pythagol, and the degrees of freedom at the Planck scale will be an an extremely complicated one, full of suppositions. And we have gotten used to a language, saying there's a pattern of spin. But that language is very difficult in us. The general assumption is that that language came about because we discovered the mathematics of suppositions,

1:07:30 quantum mechanics. Without that, you couldn't even talk about spin X or spin Y. But it's very important to say that these different states in pattern coming in are not describing reality. So for instance, quantum mechanics, that's also a way of saying it, the quantum mechanics is not the theory that describes what the meaning comes on. So our language can have today, or a particle is not really describing properly what's going on. It's not true there's an act in here, there's a screen in a particular direction which you can measure. Our three atoms are these billions and billions of populations of particles. And our description is because particle is basically in Cambridgeshire, which is essentially all population. And because of this, we are using a language and trying to measure what a particle is doing. We are doing things only in that dimension to some effect. So that, the... I don't know how to answer the question better. I think one thing that will need to be taken into account is the biological aspect. In what aspect? The biological aspect of that concept may be a lack of a scale. For example, biological considerations can explain why information and matter should become essentially separate under some conditions. As you know, establishment physics tries to move without sense of such ideas. Well, I said that you don't understand the question. Thank you. You're linking physics to biology? Well, all I mean is that biology has certain arguments which you don't find in physics. And one argument which is only allowed in the physics section of the archive, not quantum physics, is the fact that in a biological, in a context where you have biological evolution, you can evolve to the kinds of information processing which are independent of the material support, which you've certainly explained to me that Bennett was talking about. Okay, well, that will become a long discussion

1:10:00 and I don't think it's unlikely to reach any agreement here because to my mind, a biological system is not different from any other living or lifeless, like a planet or a star in the universe, it's also a complex system which has lots of information in it. So planets keep the information of their past histories in forms of craters, it's a very complicated object with lots of information built in from the past, transmitted to the future. Biological systems in no way are different from that. Well, I agree, but the different phenomenology is that phenomenology I think needs to be Well, to my experience, the phenomena in biology can be reduced to phenomena in chemistry and can be reduced to physics. It's the reduction of change. You're putting that argument in discussion. Personally, I don't see a good reason why. I think we should not begin a real discussion here. I just give you my standpoint. My standpoint is that I do believe in the reduction of change, that biological phenomena can be reduced to chemical, mechanical, and physical phenomena in the world. They can be reduced to the standard model. Standard model, in turn, can be reduced to what happens at the Planck scale. So it's this chain of arguments that I think I have a good reason to believe that that in principle can work even if we do not understand all the details so without understanding details you can still believe that there is an actual chain of logical um explanations are in more complex systems such as biological systems to more basic systems which at the other end of the scale are using eventually all the way to the plank scale i don't see a reason why one should question this dependence of complicated systems onto simpler subsystems. But you do seem to put extra question marks there. You won't do that, but that will become a rather difficult discussion because none of us understands these details where I'm happy to be able to say exactly how things work. Except we might express certain personal beliefs as how things might work.

1:12:30 Could you describe an experiment where you distinguish between the internalistic quantum mechanics and all the quantum mechanics? Because in a lot of what you said, it's in the fluid equivalent, and then you've had some matrimonial equivalents. How do you physically determine what you see at the experiment? The idea is that the theory of proposing should not be distinguishable from quantum mechanics in any experiment. The fundamental distinction comes in building a theory. So the reason for taking these steps is not because I'm going to give you a prediction about the experiment which is different from anybody else's prediction, but it is in order to be able to make a theory, which is different to anybody else's theory, about what happens at the Planck scale. So the ultimate test for these materials will not directly come from the experiment. It will come from building a superior theory of physics at the Planck scale. So we all hope to reach such a theory. And I realize that the string approach is far ahead of me in this respect. So they're also trying to make a theory that works at the Planck scale. But none of us has really seen the theory that works all the way. So the question is, what kind of ingredients should come in such a theory? Where should we be heading? And I find this approach to be a part where what we're trying to do is find a logical, simple formulation of laws of physics at Planck's scale. Something, for instance, like a cellular automaton. Now the ultimate test of this will come if someone succeeds in making a theory. If Faithless succeeds, or if Bill or Umu succeeds in making a theory that works along his lines of thought, fine, then that will be the test. But maybe the ultimate theory can be constructed along these lines. And if these theories are then successful in explaining what we've already been observed as peculiar to the standard model, and if a theory would allow us to predict more things, like what dark matter is, or what the next decimal place to find such a concept is, things like this, then that would be successful. We haven't even come close to any such situations, but this is where the test of the theory should lie.

1:15:00 It will work to make a model that is successful and very important. But the non-commuting operators... But I'm using as many non-commuting operators as anybody else. I would never get a finite scale coming out anyway. I could always take Newton operators and never see a finite problem. Yes, so at Planck's scale they're only computing operators. However, the physical equations, equation motion at Planck's scale are so computated that we can't use these equations to resolve these equations, to elaborate them and to see how they work out in daily life. So the only way to do that is by, by employing the, the complete quantum mechanics machinery with all the non-community operators. Usually a randomization goes through to the hands-on and so forth. Then you're back at where you were in applying non-community operators to describe the world of what you're living today. But you do have Lawrence violation. It's not obvious whether that Lawrence violation will be, or it could be, but it's not obvious could be visible in your ordinary, in other experiments, where you only have some equivalence classes to play with. The equivalence classes are noise and variance, but it is something to be aware of, but noise and variance might not be absolute to that, of course, well, it's not possible, but there's a trivial way to say noise and variance is appropriate, because the initial conditions of the universe obviously breaks Lorentz and Vance. So there's a sense in which Lorentz and Vance is obviously broken, or Titian and Vance is obviously broken. The universe is not Lorentz and Vance, not Titian and Vance. How come? Well, because of symmetry breaking, spontaneous symmetry breaking, you could say. But what sparked this symmetry breaking? Well, if you have a completely deterministic theory, it must be that somewhere along the line there was an equation that it didn't have that symmetry. So ultimately, I think if you have an outer theory of the world, it's quite different from present theories where you always assume things are known and are attainable, like we don't know the initial state. But in an outer theory of nature, you should also include the initial state.

1:17:30 That obviously makes worse events. So, yes, there is some great down-lourced events, although minute and possibly not within experimental observation for various ideas, but who knows? Eventually, not having the events is very kind that we see to be approximately valid in this world. I think that we maybe should discuss further over coffee and be back at 11.40 so let's thank the speaker again the times have changed for the other talks I'll just maybe quickly announce them we have two blackboard seminars at 2.30 and then we have We'll talk here at 4, and then there will be a reception at 5. Jonathan, what are the authors here that want to? Louise Clarkman is talking about knots. I don't know the exact title. The titles are all out there if you want to see them. And 3 o'clock is on information loss. I'm also supposed to come down like a ton of bricks on those people there, but since I'm one of them, I won't. And our next speaker is Roger Penrose, who is going to speak on the limits to quantum mechanics from general activity. Thank you very much. I want to address the issue of quantum gravity, which I think to most people means the appropriate application of quantum field neurotic procedures to Einstein's general relativity, or possibly to some modification of Einstein's general relativity. But should we mean some more even-handed marriage between quantum theory and general relativity with some give on both sides? That is to say, does quantum gravity mean standard quantum mechanics, or does this union involve some change in the structure,

1:20:00 or should the union involve some change in the structure of quantum mechanics? In fact, what's nature's idea about it as opposed to what we might try and do. And I want to, the reason I'm bringing this up, of course, is that, in my view, there should be some change in the structure of quantum mechanics. And there are various reasons, I think, for believing this. I guess I could use all these other machines. I believe there are some reasons there is nature's choice of quantum gravity should involve some non-standard quantum theory and I want to give a list of these I'm not going to address most of them in detail here but I'll just mention them I'm going to say something about this. Quantum theory does not provide a coherent picture, but it's a coherent ontology of the physical world. And this is connected with the notion of paradox. I'll say something about that shortly. And if a change in quantum theory is to be made, and some people, including myself, believe that this is a strong enough argument, that at some level there should be a change in the structure of quantum mechanics, If the change is to be made, then general relativity is the most natural place for new ingredients. It's a place where we have, in fact, different principles from other physical fields, and very structured space-time is involved, where that does not apply to other physical fields. As it's today, the structure of space-time is what we're talking about. That's the field of gravity, and if quantum mechanics is to be applied to that, then it's to be applied to the structure of space-time, which is a serious thing. So, we do have to, it is a place where we expect big changes to take place. So, it's natural, if we are going to change quantum mechanics, that this should be a place where it is. Again, not a very strong argument, but it's a, I'm going to say, yes, this is a strong argument. This is not such a strong argument. Then there's the Hawking Black Hole Information Loss Paradox, which I personally think is

1:22:30 a strong argument. deal about that just mention it uh space-time singularities we know there has been a standard argument that one of the reasons one wants to do quantum gravity at all is that you have this problem that classical theory has these singularities and this means that that's a place where we should actually look to quantum mechanics to see what we have to do about the classical theory the classical theory evidently has to be changed in order that the space-time singularities could be handled in a physical way and this seemed to be a role for quantum gravity but there is something very strange about the singularities that we see in the universe particularly the time asymmetry and its relation to the second law of thermodynamics and finally is this issue, which the title of this talk refers to, is what I regard as a clash of basic principles. And I put these principles here on the two sides. On the left-hand side, we have the principle of general covariance and the principle of equivalence. People worry quite a bit in these many approaches to quantum gravity, particularly the loop variable approach, worry about the issue of general covariance and try to make the quantum gravity theory, in some sense, invariant the principle of equivalence if you like is the more basic thing to look at and I regard these principles as important principles which are very hard to fit in with the principles of quantum mechanics and when I say the quantum mechanics principles I mean particularly the super position and so in this clash of principles do we expect to see some give either on this side or on this side and I'm really trying to argue that there should be give on the side in order to fit in with the principles over here. Other people might try and modify what's going on this side. In any case, although the principle of superposition in quantum mechanics is a very beautiful principle, it certainly is. It's a linear principle, and certainly our experience in physics is that when you see linearity, you're very pleased. On the On the other hand, there's perhaps a suspicion that that linearity is something which is

1:25:00 an approximation to something which is a more profound level, or is a level which is more universal. One might find that the approximation to something non-linear. So, is the superposition principle, the linear superposition principle of quantum mechanics something that will survive in this linear general relativity of quantum mechanics? So since I'm using these things, why don't I put this on this side too? I don't know how to turn this one on. Okay. Well, just a remark or two about singularities in a second, though I won't say a great deal about it. I waffled on about these things endlessly in other places. but let me just mention that this is the sort of standard pictures that one used to have of the various cosmological models. Nowadays, it doesn't have these pictures anymore, partly because there seems to be a technological constant, so they all look rather similar to each other now. We just go on expanding exponentially. But the other remark I want to make is that if you put irregularities in, then you have a singularity not only here, which is the Big Bang, but also all the way through where you have collapses to black holes and the singularities in black holes. So any theory which is to deal with the Big Bang singularity should equally deal with these other singularities. Now the fact is that what we expect to see in the universe is something extremely different in the detailed structure between the big bang and the others big bang seems to be extraordinarily uniform corresponding to a very low entropy which is the origin of the second law and one can at least try and guess what the difference in the structure is here i've got a picture this is more like a sort of conformal diagram where the causal structure of the Big Bang is like a nice smooth space-like surface whereas the causal structure of the singularities in black holes is some great mess and one can think of that as the vial curvature as being either zero or something very small at the beginning and wildly diverging to infinity when you approach the singularities of black holes

1:27:30 or the big crunch if there had been one but that seems out of date now out of date in the sense that we have a cosmological constant which seems to be large enough to stop the collapse of the universe vile curvature which as I say seems to be pretty small at the beginning and wildly diverging at the end describes the gravitational degrees of freedom In Maxwell theory, you have two tensors which play a role, the Maxwell tensor, which describes the field degrees of freedom, and the, uh, charge curve vector, which describes the source. In general relativity, unlike in electromagnetism, one has these two quantities at the same order of differentiation. In, in Maxwell theory, there's a slightly different order of differentiation, but that's just to do with the spin, uh, being two in the case of gravity and one in the case of electromagnetism um the the two tensors that one's concerned with in general relativity are the vial tensor which is the part of the curvature with the richie part extracted from it and that describes the gravitational degrees of freedom as the maxwell field cancer would and the richie tensor which describes the uh the sources in the same way that the charge current vector described sources in electromagnetic theory. And it seems that the gravitational degrees of freedom are set to zero by, well, either it's an act of God, if you like that way of thinking about things, or it should be part of physics. If it's part of physics, it should be apparently the quantum gravity theory we're seeking, because after all, as I said before, that's what one of the jobs that quantum gravity is supposed to do for that job is to produce singularities or to explain why these singularities have the structure that they have. It seems that there's something gross in time asymetrical involved in this. Now, not everybody looks at it in the same way, but it does seem to me that there is at least a strong argument that there is something time asymetrical involved in quantum gravity, or that nature's quantum gravity is. And it's hard to see how that can come about if we're just thinking in terms of classical called general relativity in some sense quantized in a standard way. So that is an argument that at least something should be different.

1:30:00 What the difference is, of course, isn't said by this, but at least it's an indication that there should be some difference. Then you make a quick remark about the Hawking black hole information loss paradox. As Bill Andrews said last time, we call it a paradox if you come from particle physics and quantum field theory, you just say, oh hum, it's come from general relativity. Since I come from general relativity, that's more my reaction. Oh hum, perhaps isn't quite the right response. At least it's an indication that maybe unitarity is not something which applies to all levels when you have black holes, that there is some deviation from unitarity because things are extreme enough, something which is there all the time, and if one believes that quantum mechanics has to be modified, this is to say, unitarity has to be modified, and so the argument is that you're seeing it in a more extreme form, black hole collapse even if it's there all the time. Problem is, at least one of the problems, is that you've got this information on past null infinity which somehow is spread between the singularity and future null infinity. In fact, this was the original Hawking argument of why we have black hole radiation in any case that you only have partial information if you have the future null infinity. But if you allow your black hole to evaporate and finally disappear then the question is what happens to all the information that's producing the specific black hole that you have. It seems to get ironed out. There are many arguments that somehow it's got to come out again in this final explosion. One problem with that, as far as I see it, is that the final explosion doesn't seem to know anything about how big the black hole was that you started with. It could have been an enormous galactic scale black hole, or it could have been an order of a solar mass one, or what have you. And the amount of information that's been swallowed up by the black hole could be enormously different And if everything is happening at the last moment here, how is it that it's remembered that, of course, the big one or the little one, of course, it could have been coming out all the time, but then how is this part of the space-time know what's going on here? Because the destruction of the information doesn't occur until you get near the singularity

1:32:30 where you have flat-scale curvatures arising only in the neighborhood of here. And so how is it that somehow out here that information is being spewed out? very hard to believe that somehow the information should come back out again. I don't want to dwell on that particular argument here, but if you believe that unitarity is going to go wrong at some level, well, then you're not so surprised, that's all I'm saying. So, okay, it's an interesting question, and how do we deal with it? But it doesn't, it's not such a puzzle because we're not wedded to the unitarities at all Okay, well now let's say something about the last point, which is up here, well not the last point, it can be the principles, the last point up here, and I want to relate it also to the issues here of the measurement paradox, and then ultimately to this green one here. So let me say something about the superposition principle. Some of these transparities are ones that I would use in popular talks. I don't see that that's any bar to using them here. What is quantum linearity? Well, it manifests itself, for example, in this form that one might have a source of, say, a photon, which goes along and hits a green thing. That produces a whole lot of junk. This can be in any kind of scale of things. or you can have a mirror in between, and it's the brown thing and produces a whole lot of different junk, and because we have linearity, you could have superposition of two by putting a green splitter here, and the green splitter puts the photon into a linear superposition of the two alternatives, and then it looks like quantum linearity, this must extend itself right up to all scales and this means that you're left with the superposition of these two green-brown things. Well that may be your right, certainly if there's still quantum level activities you wouldn't worry about it. of course rather boring experiment the source going along here and a detector it clicks if

1:35:00 it sees the photon too boring so pick it up a little bit you attach a murderous weapon which You can save the cat by putting a little mirror in between instead. The cat's fine. But then, of course, why not a bean's bitter? And you end up by superstition, a dead and alive cat. But then a few people will say, well, that's all very well, but you've forgotten all sorts of things like taking into account the environment. So then, as I say, I would do this in a popular talk, so, let's say, you have the dead cat, and the environment, well, there's a thing like that, or you could have the live cat, and, uh, there's a thing like that. Sorry? It's hard to see environments, that's the whole point about it. There's this environment. So that's fine. And then of course you have to see position. Here's the environments, and there they both are. And it's so... Hard to see what that's done for me. Well, of course, the thing is that, I think it's because sometimes I use American sizes of transgressions and sometimes English ones in little different shapes. It's a little dark, but never mind, it's just, the more of these you lay on, the more obscure things are. Now, let me just say a comment about environmental decoherence and how it tends to be used in ordinary arguments. Well, the point I'm trying to make is that the normal argument, the problem, it involves what I would call a double ontology shift, and if you try to keep your mind on what you're

1:37:30 actually doing, I find it very unclear, and the problem is that there's no unique interpretation of a density matrix as a probability mixture of states and let me do it in a particular case of two-dimensional hilbert space where we have the block sphere so this is a ordinary sphere in three space point in the middle represents the unit density matrix and the points around the outside are what's referred to as pure states states, and if you take any point in the Bloch sphere, let's say this point here, then there are lots of ways of representing that as a linear combination of, or a probability mixture, I should say, of two different states. You just draw any line through that point, and then the two pure states that you have on the outside, this thing can be right, written as a probability of inverse two. So there's no unique representation. Somebody might say, ones here are not orthogonal. There's no reason why they should be orthogonal. It's very easy to produce examples using examples where the probability mixture comes out as something where they're not orthogonal. So there's absolutely no reason why they should be orthogonal. There's also absolutely no reason why the number of them should be the same as the dimension of the Hilbert space. You might have a whole lot of states which you're thinking a probability mixture of. And then of course there's a line to all you could represent was the sort of weighted sum of three points on the boundary or any number you like. They're just endless different ways of reinterpreting your density metrics. So the problem I try to bring up here is what do you think is really going on? I mean, this sort of argument seems to be something like this, or usually not stated very specifically, but somehow you've got a state, which is supposed to be what the real thing is. That could be your cat, for example, in this human position, and then you say, okay, you should bring in the environment, and since you have no control over that, you don't know, you can't get that information out, you say it's all lost in that environment, and then you say, well, let's trace over those states, and then you go to density matrix, and then somehow the density matrix is, you change your attitude as to what's real, and you think, oh, well, the density matrix is how you should be describing things in nature, and then you, then, sort of,

1:40:00 reproduced it, re-express this in a different way, as a different probability mixture from the one you had before, because originally it was dead or alive cat, but then you, so originally it wasn't dead, it was some combination, which your photon was in some state originally produced as some linear combination. And then, you reinterpret your density matrix, you say, well, it's a probability mixture of dead and alive cat, well, you may be entitled to do that if you want to, together with some company environments. But then, you shift it back to a state. So you start with a state, and then you say, okay, this is real. And then you say, well, if that's real, then I'm allowed to reinterpret a different probability mixture. And then you say, let's choose one of them, because it's a probability mixture, it might be one, it might be the other. So you see, there's at least two shifts in your ontological viewpoint involved in this. So as John Bell would say, it's a fact point of view. It's if you like, it's telling you that the two principles that you use in quantum mechanics, unitary evolution on the one hand, and the reduction of the state on the other hand, although they're inconsistent with each other logically, they can sort of peacefully coexist. That's a sort of peaceful coexistence principle. If you really have no way of getting hold of the environment, then, okay, it doesn't give you a consistent picture of the world, but you're not in the lines of trouble, is it the other? So long as you never actually can measure the environment state. I find this a very uncomfortable position to take. It's all right for the moment, perhaps, but you say, well, maybe later technology will have ways of keeping track of environments and so on, and where are you going to push this? It's a very unsatisfactory viewpoint, in my view, for an ultimate standpoint with regard to quantum mechanics. So, it'll do for a while, but can we survive with that viewpoint for a long time, and what's going to happen in the future? If we want a better theory, it seems to me we've got to taste after this. Now, this is of relevance to what Bill Andrew was saying yesterday, because I think his point of view was rather different from mine, and I'll come to that shortly, it was basically he kept saying that somehow a form of decoherence is supplied by the gravitational field.

1:42:30 Now, that might be a way of looking at it, but it's certainly not my point of view. my point of view is that we need to change quantum mechanics it's not that decoherence there's some form of decoherence we can't get rid of because decoherence if you haven't got around this point here you still have this ontological problem which is unresolved so I want just briefly to go back to the cat and so on, just because many people have a different view on this, which is not so much the environment. I can put the environment in there too, but it just makes the transgressions get very cloudy. So let me just remove it. You can put them in if you want to. On the other hand, I'll take the dead cat first, that was how I started it. On the other hand, this way, they say here is the observer comes along, looks at the dead cat, and it led to some sort of limited world's point of view, and this really amounts doing that, or doing this, the mirror there, then that's the other situation. Of course, then if you have a bead splitter, you've got this. Of course, I've put the mental state of the observer here. You might say, how do you describe that one mechanically? It doesn't matter so much, because you can look at the person's expression, and that's a happy expression So, the question is, why is this superposition not committed? And then you have to be led. Okay, you're somehow led into many worlds if you want to preserve unitarity at all levels. But it's not resolved, doesn't resolve the problem. Because, let's say, why is a conscious being only allowed to see one or the other, rather than the superposition of two? That needs a theory, consciousness, and so on and so forth, which seems to me to be taking a problem which is really a physics problem in a direction which is very hard to see how it's going to get nice probability laws and so on out of it, at least with our present

1:45:00 level of understanding. Okay, well, bringing the cat in is a complicated thing to do. Schrodinger just did that because he wanted to make it dramatic, but there's no reason why we feed a cat, it just makes it a lot complicated, here we have the two superposition of these two alternatives, one of them causes a lump of material to be moved from one location to the other, and the other possibility it leaves that lump of material in its original Now, what I'm going to try and argue is that if we try to bring general relativity into this, we are led to believe that this superposition, in fact, that the spot of linearity is somehow not preserved at all levels, and that this superposition is unstable, reducing to one location or the other in a time scale of the order of H bar over EG, where EG is the gravitational self-energy of the difference between the two mass distributions. So you take this mass distribution and that one, subtract one from the other, and work out the gravitational self-energy of that, which is roughly the energy of displacement from one, if you imagine a lump sort of on top of each other, two lumps on top of each the other and calculate the energy that's involved in the gravitational field of separating one from the other. So, there's a slight attraction between these two, and that energy is EG in the case of a rigid displacement. Of course, it might not be a rigid displacement, but if it is, then the expressions come out the same. So, this is the proposal, and I want to say something about why I think it's a reasonable what we can do, and why, how one can perhaps see if it's true of nature. This is just a little qualitative picture, where this is the space-time diagram. You start off with the lump in one location, and then you displace one, or done, to this linear superposition of these two alternatives. And this is the argument that somehow this is unstable. The The basic argument is that this thing, e.g., represents some fundamental uncertainty in the energy of the superposition, that that is related by the Heisenberg time and time

1:47:30 energy uncertainty. Well, as one would use this thing for an unstable nucleus, you see an unstable nucleus has a certain lifetime, and that lifetime is reciprocally related to a fundamental uncertainty in its energy. I'm just using the same formula here, so I build, you guys, this is legitimate use of the time and energy uncertainty, so that's fine. It's certainly part of the staff of physics, but I'm using it sort of in the reverse way here. Usually one says, you know the lifetime, and therefore there's an uncertainty in the energy. I'm saying, if we believe there's fundamental uncertainty in the energy, this leads us to at least speculate that there might be a time scale in that same position. And that's what I'm going to try and persuade you that it's reasonable that there should be such a time uncertainty. I'll take this up here. I don't think I need all that for the moment. I'll give you the sort of argument that I've tended to give in the past. you see I'm just considering a situation in which each of these individually is stationary and I want to ask whether this superposition is stationary in ordinary quantum mechanics that would be the case let's suppose that the energies of the two are the same and you can just add them and each is each in an eigenstate of energy and so is the superposition in an eigenstate with the same energy and if you start to take into account general relativity have to worry about is how do you write down the Schrodinger equation, where you see normally you'd have a killing vector, and say that represents the d by dt in the Schrodinger equation, but then if you're considering something which is a superposition like this, how do you write down your Schrodinger equation, because in some sense you've got two different killing vectors, which are your d by dt's, and in what sense could you say these two Killingvectors are the same. And I've drawn it in such a way that they don't look the same. Well, it's worse than that because, now here's where the general principles of general relativity start coming in. We worry about the principle of general covariance. And the principle of general covariance will tell us if we've got two different space times,

1:50:00 we shouldn't really be identifying them at all. It's not just that the Killingvectors are different, But the space-times are different, and to identify the killing vectors, I would have to identify a point in one space with a point in the other space, and that's not fair according to the principle of general covariance. There's no label on one space-time that you're supposed to say is the same as the other one. Well, you might say just give up at that point, or you go into some fancy things, you use and this and that, and it doesn't still quite seem to resolve this issue, but what I want to do is say, well, let's not be that ambitious. Let's, first of all, consider the limit when the speed of light is taken infinite, so whereas problems about causality are removed, it's the Galilean limit, which means, in a sense, we're looking at Einstein-Cartan theory. You times are not the same, but the d by dt's are not the same, just because the times are the same, that's the standard of what Nick Wood has called the second fundamental confusion of calculus. Just because the t's are the same, of course, the d by dt's are not the same, because they depend on the spatial variables, and so one has to worry about how you identify the spatial variables, and that's the crucial element here. So, I'm going to say, well, So I am going to cheat, I'm going to identify them, but I'm going to take note of the fact that I'm cheating. And what I'm led to, this is an argument I've given many times before, is a calculation rather like this, where you say, I don't know really how to identify these things, but I can say, let's locally at least try and identify them. And what would you try and do? Well, you'd say, this is where the principle of equivalence comes in. I will say a bit more about that in a minute. The argument is that I try to identify them and then estimate the error by looking at how the free falls in the two cases differ from each other, and regard this as a measure of the error. Now, I'm going to give you a different argument shortly, which I think is much more powerful than the argument I've given here, but if, let's say, the free falls are different, and I try to measure the error involved in making this identification, estimating that error by taking the square of that difference and integrating that over space and then integrating my parts and so on. That's where I end up by getting gravitational self-energy, the

1:52:30 difference. So this is why I'm saying this is an appropriate thing to look at. So let What I'm really doing is not quite what I've said here, because the problem is not so much in the killing vectors, the problem is identifying spaces before I try and think about the killing equation. So, what's really the trouble? The trouble comes about, and I have a different picture here, and what I've drawn on this picture, not so much the killing vectors, but the notion of free-fall. So, you see, that's what I'm saying, how the free-falls differ in the two pictures, and I'm regarding the difference between them, if you like, the gravitational force. That's what the F is. It's the Newtonian gravitational force, and I take the difference, square it, integrate it over the space. So, what I'm saying is, okay, now I just space one of these with respect to the other, and you see that these free-falls, if you like the curvature that I have here, which is the representing three-fold, are different, and it's this difference which is the thing that I'm regarding this. I try, shouldn't you see, really be trying to identify them. Nature would be saying, well, that's, this three-fold should be identified, but I can't do that globally, so what I do is I do identify them and then try to estimate the error I've made, and the EG is calculated from that procedure. So I'm not trying to work out, if you like, gravitational decoherence, because my view is that that doesn't help you anyway. That might be a way of looking at it, but it's not clear that it is, and in fact, I had a look at Bill Hunter's example, because he was talking about that last time. let me put this up here. This is the example with the different accelerations. I'll come back to this wire to regard that as important in a moment, but let me go around this example. Here one has two shells of matter. Time is going up the picture as always. And And inside, you have no acceleration, the field that you turn into, you disappear, but outside, you have an acceleration field, and there's this other cylinder, mass distributed further out, and you're thinking of the superposition of those two, so I'm not displacing it like this, I'm just putting them on top of each other, and you'll see that, indeed, in the middle or on the outside,

1:55:00 things agree, the only problem is that they don't agree between the two, and so there would indeed be a contribution, according to my calculation, which gravitation of self-energy, as Bill said, could be in different cases. And the thing is, it's okay, it's just what is nature doing? I mean, we get different answers, but okay, that's why it's useful to do experiments. We want to know what the truth is, what does nature actually say? And my claim is that we would get different answers in this case. say that this superposition would be unstable, and you could calculate the length of time it would take to decay by doing the integral that I just mentioned over this region here. And it's not the same as what Bill was doing. And, okay, he has his reasons for doing it his way. He says he doesn't get a gravitational decoengineering. In fact, that's good from my point of view, because I've always worried that if everything went through and the things I'm saying, suppose they were experimentally confirmed, I'll come of that at the moment, then some people would say, well, that's just another form of decoherence, gravitation of decoherence. But if in fact they're different, that's very interesting. And so, thank you for your example. But it certainly, as far as I can see, it's not an objection to my point of view, it's just pointing out that there are differences. But this point of view is different from the ones that they always be telling you about. let me now try and provide a different reason from the one that I've been giving you for thinking that one might have one might worry about the suppositions when you have different three forms and here he built up my name in this book so I'm going to take his name in there Now, by thinking about what you might call as the Galilean limit of the Unreal effect. Now, I think this is really the way of looking at it.

1:57:30 But let me first just think about the principle of equivalence and quantum mechanics, which is something people have worried about for a while. Now, you could think of doing your quantum mechanics with a system just sitting on the table and taking the gravitational force as giving you a term in the Hamiltonian of the conventional type, so you've got an extra term which comes from the gravitational potential. That's fine. Or, you could think of your system in free fall, and then there isn't any gravitational The gravitational field is just falling freely, the gravitational field disappeared. Do you get the same quantum mechanics? Well, there's certainly experiments, this thing called the Cowell experiment, Colella, Overhauser, Werner, this was some years ago, was done to show that in certain situations you get the same answer, gravitational field can be thought of one way or the other. Well, in fact, this is also theoretically the case, because there is a transformation from one system to the other. I've used the capital letters for the free-fall system and small letters for the system with reference to the fixed table sitting there. And the capital of size, the free-fall one, and so on. I won't go through the calculations here, but it's a straightforward calculation. So I'm going to take the moment on top. But what one finds is that the two, this is just for a single particle for the moment, The two are completely equivalent, provided that one side, when you go from one side to the other, you introduce a phase, which is this term here. Now there are two terms in here. This term here is just a sort of energy effect. It's just the potential energy of a gravitational field, and it's a straightforward thing. The other term is not so straightforward. It involves the time cubed. Now, when I say this is sort of, well, let's come to the Unruh effect in a minute. This is just a transformation. There's no general relativity involved here. I'm just using Galilean physics. I'm just going from a non-accelerating frame to an accelerating frame. And, in fact, you can go to a general system with many particles, and that's how it works.

2:00:00 the term in here is just the potential energy term again, but then you have this term with the t cubed, that's the time cubed, times the square of the gravitation acceleration, that's little g, which I've got sitting in. Now, let's imagine we are applying this now Now, to the situation which I've been talking about. So this is, this is straight forward. You turn in. As you call it. Straight forward Schroding calculation. But now suppose we have a superposition of two gravitational fields. You have to imagine that you're an amoeba or something sitting here. and I've now displaced these bodies that say it's a superposition of being here and being here is one body in a superposition of two locations and I've now got this transformation but if I want to go from let me just rephrase this the idea is to take Einstein seriously to say that in some sense the gravitational field in the sense of a gravitational Newtonian force is a secondary thing, and that free fall is the natural thing. So this is a sort of philosophical standpoint. You say that you should be doing your quantum mechanics in a free fall frame. You can transfer back to any other frame if you like, and then you have to introduce this funny little term. And then it looks as though you've got a force there. But the correct thing to do, according to the Einsteinian view, is to think of the free fall as the natural frame. Now, you can't do that here because you've got two different free forms. You've got this one and that one, the G1 and the G2. And the point that I'm trying to emphasize here, although I haven't done it yet, is that because we've got this C cubed in here, you actually have different pachyon. Now, I say this is the sort of Galilean limit of the Unruh effect. The Unruh effect, you can think of the Hawking temperature in two different ways. I think somebody's sitting out at infinity or somebody using a frame which is fixed and then you see a temperature or you can fall freely into the hole and you don't feel the temperature.

2:02:30 So, the Anru way of looking at it is to think of the, like looking at the, like a Rindler coordinates locally. And I'm trying to do the same thing here. Now, it's not quite the same as the Anru effect, because in the Anru effect, if you take the Galilean limit, the temperature actually goes to zero. So, you'd think there wouldn't be a problem, if you like. Because although the vacuum are different, when the velocity of light is finite, if you have a thermal vacuum in one case and not in the other case, let the speed of light go to infinity, that temperature goes to zero. And so you don't have that particular problem. But the thing I'm pointing out is that you have a residual, which is this phase factor. It's not a thermal vacuum, but it's a different vacuum. So what I'm saying is that you, in fact, have two different vacuos here and here. And in forming this superposition, so you think of your amoeba, which is trying to make sense here, and that poor amoeba thinks that it's got one vacuum because of this thing here, and a slightly different vacuum because of that one. And it then says, well, when I learned about quantum field theory, I learned that you're not allowed to form superpositions between two different vacuums. So I'm cheating. So the claim here is that yes, you're not allowed to, but you'll get away with it for a while. Now the idea is it's a bit like what you do, say, in superconductors or something, where, in fact, you treat superconductors as though you have a different vacuum, but then how do you ever get there? How do you build a superconductor in the lab? Because you shouldn't be able to get from one vacuum to another just by building a superconductor. So the thing is that, okay, you have to look at it properly and say, well, no, there's some effect which you go out so far, and it's not exactly in this and that and so on. So you have to do some estimate of the errors involved and so on, and to what extent is So I'm saying that the same thing is applying here, and I have to go off and do my homework, and I haven't had time to do it, maybe not for another year or so, which is to find out what the right way people do that sort of thing is. You go and you actually try and do something which looks as though you're cheating by going from one vacuum to another, and you're not really cheating because you're seeing how far up you go, how long you've got to wait,

2:05:00 and so on and so forth. So, this is just a guess at the moment. I don't know if what I'm saying is right, but the guess is that because the terms here, or this term here, which is the t cube, which is what's causing the problem, is exactly the same thing as that one has in one's calculation here. It's the difference between these accelerations. Is it right to say that, okay, I could preserve this superposition for a while, but after a while I'm in a trouble? Because it's not really. They're not really different vacuoles for a while, but after a while, I'm going to run into trouble with that. And the suggestion is that I'm going to get the time scale which involves integrating this square of G1 minus G2 over space. Okay, that's just something for the future. I don't know if that's what we get, but at least there's a reasonable plausibility there. There's something coming out of this which says, okay, they're different vacuoles, and and trying to superpose them is all right for a while, but to sit there forever could easily land me into some contradiction. So when I say there's a clash of principles, that's exactly what's going on here. There's a clash between the principle of quantum linear superposition, on the one hand, and not just so much the principle of equivalence, but this Weinsteinian point of view with regard to principle of equivalence, to regard the free fall as the natural inertial frame, and that to take some, you know, take some other point of view as, as, as, as the normal Einstein angle, so we say to take the free fall as natural, and that there's some problem with the superposition. So that's the clash of principles I'm, primarily talking about. Let me now just say a little bit about, uh, other things here. people might argue, they'd say, surely, quantum gravitational effects are far too tiny to have any relevance at the ordinary scale of the considerations, such as stats and so on. And you worry about the Planck length, which is ridiculously different from things in particle physics, let alone ordinary scales, or the Planck time. Likewise, some 20 orders of magnitude below the tiniest particle physics processes. But the thing is, these come about because as we multiply together two quantities which on ordinary scales are small, Newton's constant and Mach's constant, each of which is tiny on ordinary scales. And so when you multiply

2:07:30 them together, you suddenly get something ridiculously tiny. Okay, that's right. But in this case, you're dividing one by the other. And then you have to look carefully to see is it small or not. It's not obvious that it's going to be small. So one has to examine the situation in detail to see if this is significant in any particular situation. So that's the first point, is the, it's something you may have to take seriously. The second point is a little bit about, you know, what you might do here, well, I don't have a theory. All I have is a sort of what I call a minimalist proposal, which is concerned with quantum super of two states, each of which on its own would be stationary. And the idea is, if it's stationary, to be stationary, you have to solve the Schrodinger equation with an additional gravitational potential term, whose source is the expectation value of the mass distribution. And this is what I call the Schrodinger-Newton equation. And then you look for stationary states, which are meant to be solutions of this. And it looks as though you've got to do reasonable things here. And then you take the EG, which is the gravitational self-energy of the difference between them. I should say you're only using this equation for determining the stationary states. Usually the Newtonian term in practical situations is something you can completely ignore. Or if you like, it just fixes the mass center. It does something very minimal. And then you, the gravitational self-energy of the difference between these mass entities of the two things in superposition, and you get this decay time. I should say it's very close to ideas of Diocese, and stimulated also by work of other people, Poe, Girardi, Rimini, Weber, Kerala Haase, and Um, now, I say this is something that you might not be able to ignore, so let me say a little bit about the experimental prospects of measuring this. Now, this is something I've talked about many times before, but let me just say it again.

2:10:00 Um, various people have often tried to formulate an appropriate experiment. This is a kind of simplified picture, just a general idea. Here we have a source and a beam splitter, and you have to keep both parts of the beam. This one, you just, it marks time for a while, you just keep it there. The other one, it does its marking time as well, but by bouncing backwards and forwards on a little mirror. think of as being about, I should say, this is an experiment which is actually being, rather being done, it's being worked towards, I should say, in Santa Barbara, by Dick Barmeister and his group, the collaborators are now different from the ones I wrote here, but never mind, they keep changing, but Dick is the same person. And the idea is to try and do an experiment like this. And what they're proposing is that this object here is a little mirror, which is about 10 micron cubed. So it's about a tenth of the thickness of human hair. It's about seeing. So generally macroscopic in that sense. And this photon is a visible light photon. In order to give it enough impact, it has to bounce backwards and forwards. It's on jumping up and down on it, and it gives it, if it has something like a million reflections, it can give it enough impact that this object will displace the nuclei by an amount, and I've sort of indicated it here, which will be significant, so that the decay time, according to my proposal, will be something of the order of a second, something about like that. So you'll have to keep this thing going for something like a second, but that's a bit beyond what they can do at the moment you have to get all sorts of things working like a very very good mirror probably more than a million reflections i'm not sure what they're aiming for now it has to be cooled down pyogenics are involved the absolute zero vacuum all this sort of thing so it's a difficult experiment but they are working towards this i have some

2:12:30 The problem of getting funding, I think, is one of the issues which is holding them up. But nevertheless, they have some temporary funding, which is working for the moment. I should finish by saying what's supposed to happen here. You see, you have this superposition of these two things here, and gradually this thing gets displaced as the photon bounces up and down on it. And so it's now in a superposition of two different locations. My proposal says that won't last forever. Something of the general order of a second, it will become one or the other. When it becomes one or the other, it's entangled with a photon, so the photon becomes one or the other too. So that means the photon is now either in this or in this, depending on which way it reduces to. And when it comes back again, instead of being in a nice little position, which ideally would mean that it goes back into the laser and the detector here would see nothing, instead you'll get 50% chance of this detector seeing. Of course, this is a simplified version, and in detail, what they're trying to do is a lot more detail on this, but this is more the official picture, which is in paper, so you can learn on this. I won't explain what all these things are I'm no expert on this sort of thing it's all explained now the idea is that you would then have to, if you do see that this thing reduces spontaneously because it might be the environment of decoherence of any number of different kinds. So we're asked to try and pick out the effect that one's looking for here from all kinds of other forms of decoherence. Well, you want to reduce them to as small as possible anyway. But having done so, you can do things like vary the, well, you can certainly vary the mass in each nucleus you can vary the number of nuclei this is a more important one in the sense the spread of the nucleus in the wave function so you have to know how this thing is the wave function is spread out the effect depends rather critically on that so you have to have a good estimate of this here you for instance if the nuclei are much more localized you would have a bigger effect than if they spread out so this would be another thing you could try and vary and then the idea

2:15:00 see whether the reduction is something which is consistent with the proposal I've been putting forward, or is it inconsistent with that. So at least it's something testable, at least in principle. I should say that where they've got to at the moment is something which, if successful, would fall short of the level that I need by a few orders of magnitude. And the hope is that the experience that they would gain on this would tell them how to pick up a few more orders of magnitude. However, even at this level, it's something very interesting because it would give you a superposition which is, ah, I forgot them again, I always forget to say, I think it's nine orders of magnitude more massive than the present record. That was the 12. That's my guess. Anyway, it's a lot. The present record being the buckyballs that Anton Zeilinger and his group have superposed and shown that you do, in fact, get quantum tube positions for these things. But this is far larger. You don't move it as much as the buckyballs move. It's only a diameter of a nucleus, so you couldn't see the displacement. But nevertheless, as far as mass is concerned, it's far huger. Well, it's interesting, there may be other experiments that one could do, and I only mentioned one other possibility that I'm aware of, which would be to use a squid, and a squid one has a superposition of currents going in different directions. The trouble with this is that the mass displacement is virtually zero, for two reasons. Well, it's very small because, in any case, the mass in the electrons in these currents is very small. It's only a surface effect, and there's not much mass. But the second thing is that there's not much mass displacement because it's the electrons going one way or the other way, and it's just a momentum difference. It's not a mass displacement. So, as it stands, this isn't very good as a test, except that you can confirm quantum mechanics, according to my point of view, they shouldn't give any deviation but what you might do is introduce some little magnet somewhere and this magnet would be sensitive to the way the current is going so okay maybe that's an alternative version that's not the route

2:17:30 that Barmester is really mainly because their expertise lies more in that area than this but maybe some other people might take this idea up see whether it's It's feasible to do an experiment of just nature, which would test the proposal I'm putting forward. Either way, it would be very interesting, because either it shows quantum mechanics still survives in its standard form at a level far beyond any experiment up to this point, or it would indicate that something new has to come in, where it might be limitations to what kind of proposals one might go forward has changed the front of the next. So I think it's very exciting, and I certainly hope that this experiment continues and can be performed in not too distant future. Thank you very much. Thank you. Because of most of the effects you're talking about, we get deviations from standard probability. Is it the first order at a neutron constant? That's right. At least in principle, we have a thing called perturbative probability, where you can expand to any finite order, a neutron constant to the sixth power order, and get completely consistent results. It doesn't mean the theory is right. I mean, this is the point, you see. It's a bit like Bill Andrews' objection, but in a different form. You say, yes, well, look, you say, well, we could do a calculation in quantum gravity, what we think is quantum gravity, which doesn't give effects that I'm claiming. But the thing is that I would also claim that in some sense those perturbative calculations

2:20:00 are not consistent with the principle of equivalence in the sense I'm making that one. But there are many other examples. For instance, in there are other kinds of principles of the sort. is very similar you can also do these things. In that case, the claim is different. The claim is that it's different. That's right. People often say, well, you know, gravity, what about electromagnetism, you see, isn't the, shouldn't I again take that force into consideration? Of course, there's two reasons why I don't, or shouldn't. One is that I'd get an answer which is probably grossly in contradiction with observation, but that's not a good reason, if you like, because I want a theoretical reason. Theoretical reason is that you don't have a principle of equivalence. So none of these other theories do you have the guiding principle which I'm depending upon. It is similar in many respects, but it doesn't affect, say, the causal structure of space-time. You've got a background space-time in which you do it. But don't you call such space only infinitesimally affect? You know, the light is wriggling a little bit. Well, no, that's not the point of view. Regarding it is a more serious thing. But in effect, if you like, it's a bit like saying the point I was making before. You know, surely these quantum gravity effects are so small that why do we worry about them? And I'm saying, okay, they are normally because we're thinking about it the other way around. You're thinking about how gravity as a force might come in and affect calculations that we do otherwise. But what I'm saying here is, I'm looking at it the other way around, might the principles of general relativity affect the structure of quantum mechanics? And I think there are, as I mentioned, the other reasons too, other good reasons, I think, we're thinking that the principles of quantum mechanics are going to have to change in some way. And I think the measurement paradox, to my way of thinking, is the major one. But certainly the singularity issue is almost as strong. So I think there are good reasons for believing that quantum mechanics will have to change. And so my point of view is, we look for clues as to where there might be input into how to change those goals. It doesn't say, as you rightly point out, that we can't get away with our present understanding combine that with generative producer theory, which at this level is still consistent, which is what you're saying. I think it's a perfectly valid point, but I'm taking a different viewpoint

2:22:30 on this and say that that's, in a sense, not what we should be doing. We should be doing something which seeks to look for actual differences in quantum mechanics. So, yeah. So, in your experiment, you imagine this ball, which may be in a superposition of being or displaced and then a little test particle doesn't really know in which space-time it is. But imagine that the observer is a little amoeba that lives on the board. So, originally, before the board was displaced, the observer is a superposition. But then this amoeba would just describe a normal board, a normal gravitational field, only that the test particle is now in a superposition of things in two locations, and everything would work perfectly fine. Yes, but that's not the situation I'm considering, yeah. No, no, but it's exactly the same situation, only described from a different point of view. From that of the area, I mean, I mean, it's all right. Which, by the way, cannot be done in the case of this experiment. That would be done? cannot be that in the case of because there is not just a question well you could think of I thought it was actually I mean he was talking about a supposition to mass distributions but you've got to get them there somehow haven't you in some sense you put the amoeba could be just sitting on one of the particles of the material well it would see that the bigger channel is smaller well I think one raises the issue of whether an amoeba And, I mean, how are you allowed to be in a superposition? See, it goes back to the many worlds problem. Can you perceive a world which is... See, many worldsists would say, that in me, though, if it's allowed to be conscious, or I don't know even whether that's supposed to come into it, would only perceive one world anyway, you see. It wouldn't see the superposition. It would only be perceiving the thing in one place or the other place. But I understood that your point was that gravity makes a difference. Yes, but your amoeba is to be the observer, isn't it? And you will see just the one well-defined gravitational field? It's only one field, that's it.

2:25:00 No, I don't... You see, that's a different situation. You're trying to do quantum mechanics in a situation where... I mean, the situation you're pointing here is driving you into the many-worlds viewpoint. Yes, because you're saying there's two perceiving beings, if you like, in superposition. One is perceiving the lump over here, and the other perceiving the lump over there, and somehow it's that superposition of those two perceptions, which is... Most of them in this case will perceive the same thing, the lump under the tree. But what is it, does it see one lump, or does it see a superposition? What would your answer be to this experiment, you see? You say it's in a superposition, it's being held there, you know, for a second. And as you sit there contemplating it for a second, are you, I can't look at it all, you're disturbing, but are you, is your world, has it got the lamp only in one position or in the other position, or is it in a superposition? If I'm sitting on the lamp, on the big wall, the big wall is just under one piece of depression. Only the test particle is in two different places in this well-defined gravitational field. And then I do ordinary quantum mechanics for the test particle. Yes, but ordinary quantum mechanics, it is because you run into the many words. Ordinary quantum mechanics doesn't treat this. Ordinary quantum mechanics treats this position of this. there's one thing at what point are you saying that one or the other happens? I possibly shouldn't do this because it's in the question of how does one treat it? You run up against a problem that's just that hydrological reduction. He's doing the equivalence principle in the other way in other words, do a coordinate transformation where you identify the two balls so the balls are not in a superposition Yeah, the rest of the world is, and that's worse, yes. The rest of the world involves a much larger mass distribution, yes. I mean, if you're going to take general covariance seriously, then that should be a valid point of view. I agree. And this is, of course, this is a problem with any quantum gravity theory. If you try and move something from here to here, have you done anything? Because you say the general, the principal general professor says they're the same. But you can't adopt that in quantum mechanics, so you get nonsense. because you say, okay, how do you form superpositions of, how do you form a momentum state, a position

2:27:30 state, where you superpose all the different locations of the thing you have. If all those different locations are the same, then the superposition is just one thing, it's a position state. You can't do quantum mechanics, doesn't it? But I understand the problem, I mean, as Bill was saying, this is your problem. No, I understand the problem, and of course, one has to address that. And my point of view is that you do have to take, I mean, it has to be some average. You look at different ways you do it, and you take the one where this mass displacement is the smallest. That's what I would do. So I'd say, I'll even move the whole Earth. And then the gravitational same energy effect is huge. So you have to Yeah, there's more things to say, but I started to tell you a point, I hadn't realized that's what you were saying, but that's, no, no, no, you have to take that on board. I do discuss this in the first half. So maybe we can do the rest of our lunch. Let's thank Roger again. Thank you.