11th UK Foundations of Physics Conference — Simultaneity & the Concept of a Particle

0:00 I'm going to introduce my biologist to the law of the United States. I suppose they are very old and old. We arrived here in the sky. So they are still in the lab in the spaces. At the spaces we were most fantastic. Thank you. Well, good afternoon all of you to the last session of today. This is another string of local heroes I see, as they are called people from Oxford. I assure you it's prettiest to believe that you are a hero if you are born in Oxford. but her speaker is from the theoretical physics in Oxford, Carl Dalby, simultaneously on the concept of partiality. Thanks. And let me start thanking Peter and Harvey for half an hour quite worth it. Overall, we are, to some extent, of a certain conceptual tension that exists between the role of time as it appears in quantum mechanics, which is effectively absolute time, and the role of time as it appears in something like general activity as just one coordinate in a covariant theory. Well, I'm not going to spend half an hour addressing that. Indeed, I'm going to address what seems to be a completely unrelated topic, the topic of particle creation and generation backgrounds, and particle creation as seen by non-inertial observance. But we'll see that addressing those problems really brings us to the heart of this conceptual tension regarding the role of time in the two theories. And so perhaps by tackling particle creation,

2:30 we can bring a little bit of light on this conceptual tension that exists between a different role of time played in the two theories. Of course I'm also doing, I will try to explain what I think is quite a deep connection between our concept of particle and concept of vacuum and our concept of time in simultanity. So I'll start with a brief description of particle and a brief historical of it. Just laying out the base of the task is particle creation and gravitational backgrounds, and the problem of polliation dependence with a very different node background. I'll explain how radar time can be used to relate this problem of polliation dependence with the known phenomena, but not well-explained phenomena, of observer dependence, and then I'll start talking about examples of particle creation and our electromagnetic backgrounds and things like that. So, the first prediction of particle creation and gravitational backgrounds was in a rather remarkable paper by Schrodinger in 1939. This was well before we knew whether or not the universe was expanding, and he wrote in a rather impressive paper, if it's expanding, it will mean the creation of matter merely due to its expansion, and the background is here somewhere. That wasn't picked up on really until the late 60s, when Parker and a series of papers addressed again particle creation and expanding universes. Even then, the subject really didn't hit the headlines until 1975 with the prediction of Hawking radiation from black holes. That was certainly an exciting discovery, but at least for me a much more intriguing discovery later that year by Andrew and independently by Pulling and by Davies that an observer who accelerates uniformly in flat, empty space will observe a thermal bath of particles, even in the state that all inertial observers claim to be. So it forces you to recognise that particle creation, that this phenomena is not just a peculiar property of black holes, that it has to have an element of observer dependence. This is a state that all inertia observers agree contains no particles, and an accelerating observer,

5:00 merely due to their acceleration, sees particles in it. So at that point, the race was on to try to characterise the observer dependence of this notion of particle and this notion of vacuum. And I think it's fair to say that even 25 years after the discovery, no systematic, consistent, observer-dependent definition of particle existed that could be applied to any given observer. Anyway, to explain how this observer dependence comes about and the problems that I've been describing it, I've been first of all to the basic task of describing particle creation in a gravitational background. This is the only piece of hardcore maths, if you want to call it that. governing equations describing some sort of field operator, and any time I get a concrete example I will talk about direct fermions, that's just my habit. Because it's in a background point by definition that means we're ignoring electron-electron interactions, and we're just looking at what this background does to this sea of otherwise free particles. So we can still expand the field operator in terms of modes and annihilation operators, but the only problem is now our modes are not So there's no obvious prescription as to which modes we just put next to the A's and think of as representing the particles, and which modes we just put next to the B-deggers and think of as representing the absence of antiparticles. So the general trick is to, by whatever means possible, assign two such choices. One choice, which seems natural at early times, and defines what you mean by N particles in the N vacuum, choice of which seems most natural at late times, and defines what you mean by out particles in the out vacuum. And if your two choices differ, then the overlap between negative energy in states and positive energy out states defines particle creation. But that of course brings us to the question of how do we choose these in and out modes. Well there are various approaches to choosing in-and-out modes, and it's perhaps a bit simplistic to try to categorise them in these terms, but very roughly speaking they can be categorised into two main types.

7:30 Those that rely on symmetries that are present in the space-time, or those that rely on an arbitrary choice of foliation of the space-time into space and time. the methods that rely on the symmetries that are present in the space time are obviously limited by the fact that you need enough symmetries in your space time otherwise the method doesn't work the methods that rely on a choice of foliation, well once you've made your choice of foliation particularly Hamiltonian diagonalisation allows you to say effectively whatever you would like to say, you can say how many they were created to a certain extent. Sorry, you can say when they were created, to a certain extent you can say where they are created. But everything you say depends on the foliation you chose. So as long as that foliation was chosen arbitrarily, you have to conclude that everything you said was meaningless. Meanwhile, although the practitioners of each of the approaches will often mention a certain observer when justifying a certain choice of coordinates or a certain choice of pollination, there is no systematic way in which the choice of observer is incorporated into the maths of any of these approaches. A more systematic approach to understanding the observer dependence of the notion of a particle is to use particle detectors, which provide a more operational particle concept. However, you can't use them to define particle and antiparticle modes, firstly because all it can actually say is whether or not a detected one mean for none to be there. But also for the rather important reason that it would be circular. So long as a particle detector is anything that successfully detects particles, you can't also say that a particle is anything detected by a particle detector. You run into the problem, for instance, that I can say that my figure packing on this table is a particle detector and every time it packs it's detecting a particle and I could call it a thing on and we can discuss the profits of that. And you would all agree that that's a stupid thing to do. is by definition, meaning you can detect by a particle of detection, you have no way of explaining why it is. a more complete treatment of the observer dependence of the particle interpretation would be to try to take something like this, this foliation-dependent approach,

10:00 but try to find some unique prescription to assign a choice of foliation to any given observer. So if you could for any given observer then you could use Hamiltonian diagnosis with it and you'd have a satisfactory concept of possible. brings us to the concept of radar time although not particularly well known there has been for about 50 years a perfectly consistent way of unically assigning a choice of polliation to a choice of observer and it's really rather straightforward Bondi's in the 50s, he introduced it in his work on K-calculus, however he himself warned against applying it to anyone other than an inertial observer in flat space, and he warned against it effectively because at the time he didn't trust proper time. We've since done the experiments to check that clocks agree even when they're accelerated, etc. So we no longer have any reason to distrust proper time like he did, so we can in fact take his definition wholesale. Let me say exactly what it is. We want to assign some time to some event that is distant from us. So we simply send a ray of light from ourselves to the event, making note of the proper time at which we sent the ray of light. We receive a ray of light back from the event, making note the proper time at which we received the ray of light back. We average the two, and that's the time we assign to that event. So obviously if you're an inertial observer in flat empty space, that becomes Einstein's synchronicity and it simply reproduces your inertial frame. The important thing to note is that all you need to do that is a well-defined proper time. Once you've got a well-defined proper time, you can do that. Of course, it won't cover all of space-time in general. If there are any particle horizons in the hyper-services of simultanity, so defined, will converge at the particle horizon. But of course, that's exactly what we need to describe such effects as the under-effect in Hawking radiation. undesirable feature. We would also consider it fairly unnatural if a person's concept of simultaneity was able to be applied to places where they clearly couldn't see. So it's independent of the choice of coordinates, because I didn't have to mention a choice of coordinates to introduce it. It's single valued in the causal ontology of the observer, that is in the history of his death and the future of his past.

12:30 it's covariant under affine reframatisations and time reversal that is if you use a class that takes a different rate but still a steady rate or even if it takes backwards then you'll still use the same hyperservices in simultaneity, you'll just label them differently it agrees with proper time on the trajectory the naturally incorporates particle horizons and the large-scale structure of the coordinate is not sensitive to the small-scale details in a way that explained in a second. So having defined a foliation that relies only on the observer it's extremely straightforward to write down the particle definition that relies only on the observer. Basically we've just taken this Hamiltonian diagonalisation prescription, but now we can say, given our observer the Hamiltonian and time tau is just the diagonalisation of this t mu where k mu is now the time translation vector field which I didn't mention, just briefly the time translation vector field is defined such that it's everywhere orthogonal to the hyperservice in question and its length is proportional to how far you are from the next hyperservice so it takes you from one moment in time to the next if you like so now we just do Hamiltonian diagonalisation where this is our k vector, this is our hyperversive simultanity and we've now got a well defined prescription that applies to any observer and any gravitational background at any time so it's independent of the choice of coordinates or the gauge it generalises Gibbons' definition to non-stationary space times Gibbons has effectively said if your space time has got a time like Killing-Vector field then that's really useful because that gives you modes that look like plane weight modes they've got an e to the i omega t and an e to the minus i omega t so Gibbons says if you've got a time like Killing-Vector field use that for your k and then it doesn't matter which hyposemples you use It leads to a concept that particle is non-local on small scales but is effectively local on scales larger than the constant length of the particle concerned. The fact that it's not particularly well known and should be more well known is that that is true even in ordinary non-interacting field theory in flat Minkowski's face for an inertial observer. Anyone who's done quantum field theory will have seen the derivation of the Hamiltonian in terms of creation and annihilation

15:00 operators, starting from the Hamiltonian written in terms of the field operator, for instance, and it's a local function. After they've shown that, the next step in the textbook is normally to show how you get the charge operator in terms of creation and annihilation operators from the charge operator written in terms of the field operator. But this one's always just written down. The derivation is unique, so you can do it backwards just as easily I can assure you that that is the operator, the number operator written in terms of the field operator, and this is a non-local kernel, these are vessel functions, and so this is non-local on a small scale scale, as I said, effectively local on scale flight control than it, which is about what you would expect for the other thing in quantum field theory, it's consistent with the belief that particles are either about a constant wavelength across or shielded by stuff that spreads out across a constant wavelength. It also places no asymptotic requirement on the behaviour of the background, so it allows finite times to be considered, that is, it allows you to say when the particle creation occurs. Also we can write down a finite volume number operator which has controllable fluctuations, by controllable I mean make a bigger volume, you'll get smaller fluctuations, so if you try to be too fussy you'll get fluctuations that draw out your results, but at least you you can say, to a certain extent, we are the particles I created. Now, before going into genuine particle creation, let's just have a quick look at some examples of radar time. First one, of course, the uniformly accelerating observer in flat space. Radar time is granted at time. It reproduces the killing vector that's used in all derivations of the under-effect and effectively reproduces the under-effect wholesale. So we can breathe a sigh of relief on that one. Another couple of similar examples. Now, what I presented with Radar Time is effectively a concept of simultanity that applies to any observer. In flat space there is another possibility that we could use as a concept of simultanity, namely the instantaneous rest frame. So I decided to do a quick comparison in this overhead to show some of the problems with the instantaneous rest frame which would make it quite unsatisfactory for constructing a number operator. in line of being quite unsatisfactory generally. This is a diagram that appears in a lot of textbooks on the twin paradox, for instance, failure of hypersurfaces of simultaneity of the traveling twin. And they have this obvious problem that they're not single-valued here,

17:30 and they don't apply at all over here. So even though Barbara can see these events perfectly well, when she tries to write in her logbook when they haven't, her prescription simply doesn't give her an answer. whereas over here, even though she only saw it once, she had to write it in her log book twice. Whereas if you simply step to the definition, send your array of light, receive it back, no risk for two, then if you're this observer when you see it and you're that observer when you receive it back, then you end up with hyperservice and you can either just do that, and the separation there is a doctorship rather than the separation there. Similarly, you can look at the gradual turnaround case, as it's often said in the textbooks, fix this problem by taking note of the fact that you actually have to turn around during some period of time with finite acceleration. Of course that gets rid of the gap, but now you're assigning three times square root event over here. I can also explain briefly what I meant by the fact that the large scale structure is insensitive to small scale details by imagining what would happen if Barbara, during her turn around was to go to the bathroom, for instance, in the room next door, and then quickly return to her position. Obviously, if you were using instantaneous rest frame, then she would now have another whole set of hypersurfaces that are going into something like that, and, well, they're messy. So now she's assigned three times to every event over here, five times to every event over here, and it's all kind of a fair shame. Whereas if she goes to the do and is using radar time, this leads to a very small change in the nature of her hypersurfaces of simultanity, just here and here and similarly down here and out here and you get the vector. Small changes in her trajectory, small changes in her radar time coordinate which is desirable. A couple of quick cosmological examples. Decider space is another one where we feel we know what we're doing in the pineapple creation and so it's another one where we better check that we agree. Decider space, sorry I didn't actually write the metric down but you know what an FIW metric looks like and this is just an exponentially increasing scale factor. Your time translation vector field is simply the standard killing vector that's

20:00 used in Gibbons' definition of the derivation of the Gibbons' temperature, for instance. Your radar time and radar distance lead you into static coordinates. And so again, the standard derivation of the distance of space temperature comes through effectively unchanged. The Milne universe is rather an interesting one, the 1 plus 1 dimension of the Milne universe is an FRW universe with a scale factor proportional to T. Now if you're a cosmologist and you pick one of your particle creation formidisms from your textbook that's designed for cosmology, so you'll generally use, unless you're in the city space curiously, you'll generally use cosmic time or conformal time or something like that to decompose your moments. particle creation in this kind of a universe, which is qualitatively much the same as you'd get in any other kind of universe. However, all the time, knowing that all you wrote down was flat space and a strange set of coordinates. Indeed, unlike the Unruh case, where you wrote down flat space and a strange set of coordinates that corresponded to a non-inertial observer, this time, the observer you're talking about is an inertial observer in flat empty space. so if your coordinate system is going to trick you into describing particle creation according to that observer I think it's better to say that's a slight embarrassment amongst cosmological models and it's convenient to notice that if you transform back into radar distance and radar time you find yourself back in the underlying flat space so the definition is not so easily tricked How much time do I have? Five minutes Well, very quickly, we've said a little bit about, well, quite a lot about radar time, but not really very much about particle creation. In order to get some sort of intuition for quite how much you can say about when particles are created and where they are created, it's convenient for the moment to have a quick look at particle creation and electromagnetic backgrounds. Even in this case, there has been some subtleties and mistakes made in trying to get the appropriate definition of particle. It's common, and almost entirely everyone puts the Ea0 on the right hand side. Hamiltonian diagonalisation quite naturally requires that the Ea0 go on the left hand side with the DLT, and the Hamiltonian defines particles and antiparticles as the

22:30 rest. Effectively, an antiparticle or a particle with a negative kinetic energy, not a negative total energy. If you put this on the other side, for instance, you could add a large constant a-nought that stops up to a differential. So having written it in that form, you can now see, remember that particle creation is caused any time a negative energy in state evolves to pick up a positive energy component. And there's two ways in which that could happen here. Either a-nought could be non-zero so that it acts as a potential in which particles could tunnel Or the spatial part of A could be time-dependent, which will mean that something that started as a negative energy eigenstate won't stay a negative energy eigenstate. If neither of those are true, if you can find a gauge in which this is zero and this is time-independent, then obviously this equation takes the form of a time-independent. So your equation, eigenstates remain eigenstates and no particle creation occurs. That is, time-independent magnetic fields don't create particles. Actually, another thing I could briefly mention, approaches that put this to zero and this not to zero rely on something called the tunneling approach, which works perfectly well in most cases, but gets the wrong answers in any other case. Approaches that assume that anual's going to be zero and this is going to be time-dependent rely on something called the boggle-youbop approach, and they get the right answers in that approach, but the wrong answers in any other time. But if you just put the annual on the appropriate side, then the two approaches are kind of combined into this. You've got a tunnel in and you've got a tunnel in. So how much does that allow us to say? Just one very quick over it. Particle creation in an electric field that looks like that, it's spatially uniform where it's slowly turned on and slowly turned off. The reason for using one that's slowly turned on and slowly turned off is so that I can compare what this particle definition would say to what other definitions asymptotically well-behaved backgrounds give the asymptotic answer which is that a time-dependent concept of particle analogy to say not just how many were created but when they were created and you can see that at early times all you've got is this peak around the origin saying that particles that are not moving are easier to create than particles that aren't moving. Once the particles are created they get accelerated by the fact that they're in a left field

25:00 you know, entirely classically they behave like a classical particle, so the momentum increases a little bit. So the height of this peak is proportional to the current height of the electric field, while this bulge is slowly being filled out due to all the stuff that has been created up until that point, until you eventually end up with the standard result. So it all seems to be oversensible. another very brief example you can do consider a potential barrier and for starters let's just consider a potential barrier a potential barrier with V less than 2 m's the time paradox would certainly predict there's no particle creation here and in the conventional sense there certainly isn't particle creation here But what there certainly should be is vacuum polarisation around this barrier here and vacuum polarisation around this point here. We would expect that this sudden, strong, spiked electric field that's on this line would cause the vacuum fluctuations to be distorted in some way, given vacuum polarisation as described in the graduate synchronic field theory. but if you've got a final point number operator with controllable fluctuations then you can actually say where the so called created particles is that are in this case and you get a little bit of antiparticles concentrated just inside the line a little bit of particles concentrated just outside of the line and I should mention that if you measure the fluctuations in those measurements The fluctuations are always bigger than the measurements to be best in 2M. So it's, you know, you can understand why they don't call it particle creation and why they do call it vacuum polarisation. It is just a slight distortion in the vacuum fluctuations. And if you turn the potential up above 2M, then as you might expect would happen, antiparticles start appearing inside for a while, while the particles start getting created and being spat out. Taking the intuition back to the uniformly accelerating case, I already told you there was a thermal spectrum created, we can say where those particles are created and roughly

27:30 speak, that's the total particle distribution there and within a certain frequency, you can say that's the spatial distribution of particles at a certain frequency, the variable distance. It's not this distance which goes to zero here, radar distance goes to negative infinity gap. And you can see this particle operation is effectively due to the mass gap being squeezed rather than the mass gap being higher or lowered, which is why particles do this when there's the antiparticles rather than the opposite. I'll add that Okay, radar time provides an observant in an exfoliation of space time that is independent of the choice of coordinates agreed to prop time on the trajectory a single value can cause a height of the surface and you can use it to define an observant definition of particle and antiparticle modes which applies to an arbitrary observer in any of the mathematical gravitational backgrounds. It's consistent with detector models, but allows you to say what it is that the detector is detect. It's independent of the choice of coordinates or gauge. It generalises givens as definitions non-stationary spacetimes. It's non-local on small scales, but effectively local on scales large in the complement. It allows finite times to be considered and allows you to say with definable precision when and where the particles are created. And a slightly bold final play, which really just relies on the fact our time at our disposal, is that there needn't be any inconsistency between the foliation dependence of quantum mechanics and the coordinate covariance of general relativity, provided we correctly take into account the role, the important role played in both of those there is by the objective. Thank you. Anthony. The class becomes the definition of radar time. What happens in the Frieden model, the very early universe, near the singularity? You've got a tiny region where you can have this signal going backwards and forth. There is an initial singularity. Actually, I've got the over here, but I told you that because I think I was going to run over time anyway. Again, you've got a hyperservice of simultaneity that doesn't go all the way across, but you condition at the edge. In the case of, like, Unruh, etc., where your radar time doesn't

30:00 cover the whole space-time, your k-vec that goes to zero at the edge, which applies a certain boundary condition so that your eigenvalue problem is still well-defined. But it's going to cover just as a causal horizon. Yeah, it's going to cover, according to that observer, the day after the fifth bank is the late day on. Which is a vanishing, as the whole part of the space-time, you were purchasing the bank. Yeah, but that's all that an observer who was there could possibly discuss. doesn't cause any problem with using it to the same particle mode? No, obviously there's an interesting question which I have not addressed at all and which cosmologists have to address in whichever fashion they can which is what state you would expect the universe to be in and that question has nothing to do with which observer is trying to look at it you know in the case of the set of space they generally use quite a state of its vacuum or they use the conformal vacuum or whatever I certainly have not said anything about what state you should have expected the universe to be in. But given a state, and given an observer, I can tell you what the observer sees in the state. And obviously given... No, no. Yes, Simon. Sorry. Simon. I mean, I think the obvious question is, given observer dependence, or world-land dependence, what, if any, conditions of consistency would you require? Is it okay for two entirely different world lines to disagree, systematically disagree? Obviously in flat space we had the rather convenient fact that all inertial observers agree with all other inertial observers. And if we want to, well first of all let me point out the number operated doesn't appear in the governing equation. If it did, this would be a complete disaster. the energy momentum tensor if you were going to try to find something to put on the right hand side of some sort of semi-classical back reaction problem then you'd better make sure that the things that appear in the equation don't become which observer put them in. But that's not the case with the number operas. There's nothing wrong with that being observed in energy. But if you wanted to make some systematic definition of what you thought the energy momentum tensor was in an observer independent fashion and to link that to what particles are there then obviously you need some sort of consistency condition. And it would be nice if we could show that to at least within the uncertainty that is inherent in measures of fluctuations and things like that, free-falling service through the same event

32:30 would hopefully agree on the particle content at that event. If that were true, you could to a certain extent say this is the piece of the creation that's due to the background It's just due to the observer. It's the one where that remains a conjecture and one that I'm certainly interested in trying to show you. But it's not the straightforward one. Okay. Next speaker from the philosophy faculty in Oxford, Oliver Pooley, The Philosophical Significance of Herity Violation. The floor is yours. okay well first I'd like there's another person who had nothing to do with the organization of this week to add my thanks to everyone else's and thank Peter Harvey for organizing it okay Okay, while preparing this talk, I became slightly embarrassed about the title. It just started to seem a little bit grandiose. I mean, it would be much better to call it the significance of parity violation for some questions in philosophy. Or something like that. So you're definitely about to experience a change of gear down here. But this paper is sort of talking about some similar things. Okay, so, and these four papers that I mentioned here are ones which sort of got me interested in this topic, but references to those here and there. Okay, so there are two questions in particular that I want to raise and say something about an answer to, and these are the philosophical questions that you might ask concerning parity violation. First of all, is it an example of this sort of thing, that the failure of the space-time symmetry implies the existence of some sort of absolute symbol? And the obvious analogy I have in mind there is Newtonian mechanics, so I'll just say something about that in a second. The second question is, does parity violation show that being of a particular handedness is an intrinsic property of the handed object. Now that might seem a peculiar

35:00 question to ask. The point is that the account according to which handedness is not an intrinsic property is by far the most attractive one philosophically and it may seem the obvious one to all of you, in which case you'll be able to close your eyes for a bit. But some people, well, you can set things up in such a way that the fact that nature distinguishes left and right, suggest that this perhaps is untenable. I want to answer that it isn't, so that's a question I'll be looking at. And then, finally, in answering these two, I want to just make some very vague remarks about the link between explanation, ontology, and things like that. Excuse me, do you mean you will say no to question two? I would say yes. I would say parity violation... No, I will say no. Right, so that's some very general things to set the scene and make sure we're all talking about the same thing. Okay, so the parity transformation is just spatial reflection through the origin and in spaces with a non-number of spatial dimensions this maps objects of one hand in a sense of their incongruent counterparts so for example left hands get mapped to right hands and the next question, well what does it mean physically for this transformation not to be a symmetry of physics well one claim, in fact while I was preparing this I realised that this was falsified by the example that Nick Havitt discusses But if you're considering realistic theories, this is going to have to mean, if it's not a symmetry, that for some sort of handed processes, the probability of a process of one-handedness differs from the probability of the process of the other-handedness. if the probabilities were the same, in the deterministic case, if they were either always possible, always happened or always didn't happen, then parity would just be mapping one physical state of affairs to a physical state of affairs. So for it to map a physical state of affairs to something which is unphysical, this has to be the case. Now, a different

37:30 way of putting things is that the laws do not take the same form in coordinate systems related by parity and this is meant to make you think Weinstein's statement of relativity principle where the fact that you do have the symmetry means the laws do take the same form in coordinate systems moving with uniform velocity relative to each other but it's not a symmetry means that the laws written with respect to a left-handed coordinate system they're just going to be different in forms that the ones when written with respect to right-handed coordinate system precisely. The differences are rather trivial, but we'll see what those are later. Perhaps we should forget three, because I need to speed up at four. Well, this is couched in terms of the form of the laws with respect to coordinate systems, and in terms of quantum mechanics, that might seem a bit unsatisfactory. Perhaps what I should be saying is that the representation of parity on the Hilbert space sends physical states into unphysical states or something like that but I'm not really sure about that so if anyone has any comments of that sort afterwards I'll be grateful to hear them OK, so now turning to the first question I mentioned the analogy or the example that makes us ask the question is Newtonian mechanics and what we say about absolute space, the reality of inertial structure and that sort of thing. And a sort of standard line is that the fact that the laws of classical mechanics are invariant under boosts in addition to being invariant under time-independent translations and rotations means that there is no absolute standard of rest and therefore Newton's concept of absolute space in a preferred frame is undermined. However, that the laws are not invariant under time-dependent rotations and arbitrary time-dependent translations indicates that there are dynamically preferred ways of matching up the points of space at different times that are independent of matter and its relative motion. In particular, we have preferred coordinate systems, the inertial frames, and if we do write the physics in a coordinate general way, the inertial structure represented by any fine connection you know becomes explicit and you know

40:00 this is naturally given a realistic interpretation I mean obviously that's a contentious claim and I personally would disagree with it but I think that the reason that where you have room to disagree with it is the fact that the structures in question are non-dynamical and so if you consider the case of general relativity, it is generally covariant, but that's because all the structure fields are in there already, and they're also dynamical, and it's the fact that they're dynamical which means that you don't have any preferred coordinates. That's just my soundbite view of the general covariance of GR, that it in no way supports the sort of anti-realism about space-time structure. Okay, so can we say similar things in the case of parity? Well, are there coordinate systems? The answer, I mean, I want to say yes and no. It's true that the two otherwise equivalent coordinate systems, the laws, will look different right-handed, with respect to a right-handed coordinate system than when driven with respect to a left-handed coordinate system, or there is the form of the laws for which that would be true, but there's no sense in which one or the other is preferred, and that's different from the case of inertial frames, where obviously the inertial frames are preferred, the laws take a simple form in those. So, you know, there's a disanalogy there with the Newtonian case, and is there an associated yes I mean if you want to write the physics in a coordinate independent way then you're going to have to introduce some orientation fields such that the physics does take the same form in both right-hand and left-hand coordinate systems and Huggier for example suggests that we should take that structure field seriously as representing something real in the world so this is his paraphrasing was talking about d8 my connection and a natural structure so target says I mean how it's actually worrying about the implications of this for the reality of space-time that an intermediate step is to take the orientation field

42:30 seriously is a real field okay so I want to come back to the question of whether But doing these things, taking that line is a good thing to do when there are these differences with the inertial case. Okay, so I'll be coming back to those questions, but now it's the question of handedness. Right. Okay, so consider an object lacking any plane of mirror symmetry and its mirror image. two such objects are incongruent in the following sense you can't through a continuous transformation that doesn't alter the metrical relations internal to the object map one of them onto the other and the sort of nice standard example that gets trotted out to illustrate that is that you can't fit a left-handed glove on a right hand or a left hand in a right cubby but they are counterparts which is just to say that they're identical in terms of their relations. Something that I realise is blindingly obvious as I have the picture. So left and right hand, but you can put the points to one and one correspondence so that the distances and angles between, you know, the corresponding points of the state. Anyway, so why is this interesting? Well, it may be a sort of historical accident, but Can certainly thought it was equivalences and reductive account of space. The point being that if all spatial facts are supposed to supervise on facts about the relative distances between bodies, and if these facts are the same for left and right hands, how is the relationist supposed to be able to, one, explain the incongruence of left and right hands, and two, in fact Kant eventually said that that's something that you can't understand or explain, it's just something that we recognise in perception. And secondly, how can the relationist explain what it is to be the one-handedness rather than the other? That was the question that I raised at the beginning. And Kant said, well, consider the possibility where the first creative thing is a hand. Surely it's either a left or a right hand, but according to relationism it can't be either. And he thought that was a patent of absurdity. Of course it's not either a left or a right hand we should reject the premise but that was Kant's

45:00 Kant's line so with that sort of historical that's the historical origins of philosophers' interest in these questions, I mean I would like to put it like this that more generally there are two basic options you could either have some story according to which incongruent counterparts do different intrinsically, being left handed hands. And, I mean, okay, that already explains what it is to be of a particular handedness once you've said what such intrinsic differences are, or intrinsic properties are. But then you go on to exploit such properties in explaining the incongruence. So either you adopt that position, or you say that left and right hands are intrinsically identical, and then you've got to explain not only the incongruence, but then you have to explain or have some story about what it is to be of one handedness rather than the other, which doesn't really arise there. Now, why this is the obviously preferred option, I would say, is that there are these various problems with the first. One and two are related, and the basic point is, for example, that if you, I mean, take Fs, which is the standard example, these are encumbering counterparts in two dimensions, but if you can rotate the F in the plane, you can map the left-handed version onto the right-handed version and simply for all handed objects and also if you're in a non-orientable space then you can sort of continuously move one round into the other. Now John Ehrman sort of responded to this by saying well actually this isn't so so someone who holds this account at least has to say something like well whether or not these intrinsic properties instantiated depends on the dimensionality of space, or whether these intrinsic properties are always instantiated, but whether or not they ground in congruence depends on the dimensionality of space. I mean, that's, you know, clearly the logical room to say that, but of course what that amounts to is entirely mystical. Now, Erwin says, well, it's not at all mystical that certain properties can depend on the dimensionality of space. For example, the fact that a set of vectors is maximal in one space it won't be in a higher dimensional space but of course the disanalogy is we can completely understand why it is that whether or not a set of vectors is maximum depends on the dimensionality of space but we haven't

47:30 even been told what these intrinsic properties are to be able to evaluate the claim that their possession or non-possession depends on the dimensionality of space and also I mean there is no such account but you would have to ask well how does that fit in with our ability to recognise them as left and that sort of thing. So clearly this is beginning to seem the obvious account of what it is to be had in this. So a brief summary of the account. You say incongruent counterparts are intrinsically identical and then you say contra-count that the incompetence can be understood in terms of the spatial relations that hold between them so for example the obvious point to make is that let's just consider a euclidean distances if the distances between the hands are constrained to remain euclidean you can understand that it's a sort of mathematical theorem that for given sets of distances that are instantiated between the left hand and the right hand it's impossible to alter them continuously keep them euclidean keep the internal distances of the hand unaltered and yet send all the distances between the parts of each hand to zero so that's the relation's basic explanation of incongruence of course he must have a different story about well what constrains the distances to be euclidean or whatever but that's just a different question and then given incongruence comes first and then you explain what it is to be left and right in terms of incongruence congruence, the relation of congruence for a particular sort of object partitions a set of a particular sort into two, and then left and right are just like arbitrary labels and we recognise a particular hand is left by recognising that it's congruent to one that we've learned by abstention to call left. So there's nothing intrinsic to being left-handed that's all to do with being congruent to the hands that other people call left. And this is very constant without there's a sort of thought experiment how would you explain to an alien galaxy what we meant by left if you can point to some asymmetrical object in common, putting aside parity violation which would enable you to do it and so canceling hands neither left nor right and this collection of people have discussed such an account and basically these are on the side of people who speak the truth

50:00 Okay, so there are two questions, and now I'm going to review rather quickly just some facts about how we actually, some details of our parity violating theory, the electroweak theory. So you've got this four-component object Dirac spinner, which, I mean, just considering master's fields, the Dirac equation and the Lagrangian is invariant under parity, which turns out to send psi to this. So you not only, x doesn't only get sent to minus x, but you pick up this gamma nought factor. Now, sometimes you see this justified in terms of keeping this invariable. It seems to be much more preferable to actually work the other way around. And actually moving on to the next slide, if you start with your expansion of the 3 field in flat space, after the last talk I should say things like that and interpret these as annihilation and creation operators for the different sorts of particle and then you say parity should send a particle of spin lambda momentum p to a particle of spin lambda momentum minus p and work out how these have to transform that's where you get the gamma naut in front of there and then it turns out that the equation is going to be a very important parity that seems to be a conceptually preferable room to go but ok so that's the parity symmetric general situation but now you need to find these you split the field into these two bits the left handed and right handed bit where you've got this 1 minus gamma 5 or 1 plus gamma 5 projector where gamma 5 is that these I mean to just motivate the left and right parity now sends the left one into the right one, roughly, and if you consider this, it turns out that in the Masters case these are states of the left corresponds to a state of negative velocity and the right to positive velocity. So a great picture that I know some of you will object to because these are not classical objects, you've got a spin like that and the direction of motion like that and the thought is that these are intrinsically identical right

52:30 there's no intrinsic description that picks out a left-handed one sorry a right-handed one rather than a left-handed one it's only the convention that we associate a particular vector with a certain direction which we have to get a hold of by saying what we mean by clockwise or something like that, that allows us to say, allows us to pick one of these out in terms of its relations to us. So, the basic claim I'm making is that these chiral components, although more heterical hands, are pretty much the same, they're intrinsically identical, certainly in the non-interacting case, and this is just choosing a particular representation you've got. I mean, this is just what we have before, but now choosing a certain representation of gamma matrices. So you can see now gamma-naught is sending, phi-r now corresponds to the top two components, phi-r, the bottom two components in the spinner, and gamma-naught's just interchanging them. And in this representation, you can see explicitly that these two spinners transform under incompatible, sorry, under inequivalent representations of the Lorentz group. And And that, you might think, well, doesn't that mean they're sort of somehow differing intrinsically? But of course, this is relating the spin to the coordinate system. And in particular, if we switch coordinate system by parity and choose a left-handed coordinate system, then the sign of beta will change and phi r turns out to transform, as you can see, just as phi l does under the old coordinate system. So, my claim is that this is all consistent with there being no intrinsic difference between the left-handed and right-handed spinners. And that the mathematical difference between R relates them to our forward systems and conventions and that sort of thing. Okay, but of course we do introduce a difference when we introduce interactions. and we take this parity-symmetric Lagrangian and now just reorder it by grouping the left-handed electron and neutrino fields together, I mean this obviously no left-handed neutrino I think or right-handed neutrino if I put it in I think it would make my story better

55:00 but you'll notice it's absent at the moment but you now, you first of all To take this sort of freely grinding and turn it into a gauge theory where left and right behave differently, we choose a global transformation where the left-handed field transforms differently to the right, in particular under SU2, we've got this non-trivial transformation on this SU2 doublet of the left-handed component of the neutrino and electron, but the electron right-handed field is a scalar. And then for the U1 group, you've got different transformations of left and right. And of course, when you turn that into a gauge theory and introduce counteracting interaction fields to make the whole thing invariant, you start getting an interaction between certain fields and the left-handed fields, but no corresponding interaction between the same interaction field and the right-handed fields. just the same thing again but in the physical where I've chosen the physical the mass eigenstates of the gauge field so that you've got you can see that the left-handed fields are coupling to the W bosons but no right-handed field does and it's actually only the coupling to the photon that's parity-symmetric OK, so that's the basic theory and now at the end we just have to ask the questions Does this theory suggest that left and right-handed particles differ intrinsically? Well, I mean, what we had before we introduced interactions was clearly the spin of the particle is an intrinsic property. I mean, it's intrinsic to the fact that we're representing it by this spinner, that it's got this property. but in in terms of what's differentiating the the left-handed and right-handed particles it's just their interactions and in the theory those interactions aren't explained or grounded in any particular intrinsic properties unless you're suggesting something like you know the hypercharge the value of hypercharge in a particular particle has is the categorical ground or it's interacting with the field in the strength that it does so that could be one thing you would say that left on our right-handed fields do different intrinsically, but it's not, it doesn't mean that being left-handed

57:30 or in particular being a left-handed field is an intrinsic matter. It's just a brute law-like fact that all left-handed fields have this property, and it's because they have this property that they interact in the way that they do. So the claim is that the law gives us no reason to suppose that handedness is an intrinsic matter. Although we don't actually have to explain it in terms of um uh attributing intrinsic properties to left and right hand fields we we can introduce this orientation field so okay the fact that the the way we distinguish left and right really related the spinner um the different components of the spinner to our coordinate system means that if we wanted to call it free expression we would have to introduce an orientation field explicitly you don't I mean you could actually make sense of the theory without taking that field seriously or suggesting that there are these intrinsic properties you could just say that the basic fact is that particles that interact in a certain way are handled in the same way it's not grounded in anything it's just a law-like fact the problem with taking that line is that this is a highly non-local fact right you've got particles here and over the other side of the universe coupling to W bosons say an electron and it so turns out that they're handed in the same way and no matter where you go in the universe you won't find a right-handed electron coupling to W boson so at least if you take the orientation field seriously you've got some sort of level explanation of this correlation I mean it's not just a long locality you even have indeterminism at the very first decade but there are equally problems with regarding this field as physical I mean is it really giving an explanation of why only left handed rather than right handed fields are interacting in this way or is it just encoding the fact that they do and I think this is related to the fact well you might think that this is related to the fact but actually I'm not sure it is because in GR you've got a dynamical metric which you want to regard as a real field but it's certainly not explaining why Robson-Clox behaviour say to you in any cause of work ok so maybe I'll stop there come up please my hand applause applause

1:00:00 applause A few questions. Could I just make a light, because this is correct, and I just wonder whether, at perhaps a much lower level, it seems to me that there are two problems, and maybe this is what you're saying, there are two things that happen. There is the appearance of objects of different parities, such as our hands, which, on a somewhat more naive theoretical business point of view, I describe by saying that you get equal numbers of rights and lefts because they're degenerate say it's in some Hamiltonian, which does not itself, but it's in it. And then there is the problem, or then there is the question as to whether some Hamiltonians create symmetry and create particles which are preferentially what more one is looking at. Do you have problems with, do you have, I was going to say problems with both these problems, or do you address both these problems as being interesting questions, or just a separate one? Well, I certainly, I'm not sure what the, I think, I think the, I think, I think what my position is, is that the, at first glance, the first problem is an interesting problem. There's a sort of very attractive philosophical story to be told about it, and it then becomes a question of whether that story can be upheld, whether that's compatible with explained at the second stage. The question is, could a classical, at least one question is, a classical universe, where the laws were not paradigms and produce paradigms, a function of the universe can. Right. Could a classical universe ever produce paradigms, and it's an awesome thing to treat it to the physical laws? i mean just i mean you know i mean most solutions of you know

1:02:30 involve asymmetric It has the difference about the difference, if we have this orientation field, does that mean the difference could be another universe might have the particles oppositely oriented with respect to the orientation field? Exactly. And it seems that if you're taking the film seriously or you think there's some sort of asymmetric structure of space-time itself which, you know, and it's the particles' relation to that which explains the ability to interact one way or the other, it seems that you're always going to have the option of the world where things with exactly the opposite relation behave in the way that the opposite So if you had, say, empty space-time with this orientation and then the mirror image of those, those leading for the same worlds, could they have to be distinct? Do we start to be distinct, or when we start saying one world that a particle is in this way in perspective, and that world hasn't made, even though we can't detect that? at the observable level the matter fields in the two models are going to be identical the only difference is that the congruence of the matter fields to the orientation field which we're treating as a real field and it seems that you can't just treat the field as real and at the same time these two are different states that was the last question thank you all Next speaker is from Alexander Atria altering the remote past and we're all hoping you're going through something radical A couple words Well, by remote, I, um, I mean, um, either temporally or spatially remote.

1:05:00 Anyway, basically it's little more than a semantic trick. My approach here is to have a very abstract approach both to the Bell formalism and to the relevant bits of quantum mechanics. So I begin without any, I don't have any reference to a particular ontology at first. So we're used to an ontology, sort of equality ontology, referring to proton pairs, angles, directions and so on, polarizers or spin meters or something along those lines. So I begin with this abstract scheme, both, as I say, developing quantum mechanics and the Bell Formanism, and in that abstract context, I define a, you might want to call it a locality condition, but I'm not sure that's exactly the best term. I use the term parameter independence, which is like misleading, because the term, of course, already exists, and it has a very well-defined meaning, which isn't exactly the one that I have in mind, which is slightly different, but it's basically the same idea. Um, and, um, anyway, depending on the particular semantics one adopts, the violation of that, uh, parameter independence can take on various different meanings, and, of course, um, in, In the case we're familiar with, in which the semantics is about angles and so on, the violation of the locality condition means, well, the locality condition itself, this parameter independence means that says that the rotation of an apparatus on, say, the

1:07:30 right side, can't change the value on the other side, on the left side, such a violation suggests that it can. That's in one semantics. In another semantics, which I would consider, in which the parameters in question would be times rather than angles, well, it's no longer a matter of rotating an apparatus on the right, so it's no longer a matter of choosing between two directions on the right, it's a matter of choosing between making a measurement at one time rather than another time. And so if that kind of parameter independence is violated, it means that by weighting and making a given measurement, exactly the same measurement. At one time rather than another, the value on the other side is changed. And as far as I know, well, put it this way, in the framework I consider, there don't seem to be any particularly significant restrictions on the time ordering. So the two times at could lie in the absolute past of the time in which the value is considered on the left, or in the absolute future, or they could be space-like separated. So that's why I called it, I called the talk of the remote past. By the way, what time did you get exactly? You have 20 minutes from now. Including the platform. Well, usual framework source produces these pairs. This is a slight difference. So I'm assuming that each object has these dichotomous properties, which depends on two parameters, which are called M and N.

1:10:00 So the S is just the subsystem. S is one or two. K is the parent. K is one to N. And so these are the, what I'm calling the parameters, and the independence will refer to the second one. Anyway, so until I've defined that independence, this quantity would in principle depend, aside from what is the obvious dependence on k and on s, it will depend on both these subscripts. Anyway, having defined that, for the k-th pair, by the way, quantum mechanics has yet to end of the picture. These are objects of any kind. They could be just about any one. So I define this quantity for the k-th pair. And until I've said anything about the dependence of the second index, it could be as large as 4 or as small as 4 or minus 4. And when I've written it, the second index of the first factor of every term is the same as the first index of the second factor. Anyway, now I introduce the assumption. I say that there's no dependence. I don't justify it physically. I say that there's no dependence on the second index. So once I've done that, I can rewrite the same expression in this form. This is something one finds in, well, without the second index, but Mermin and Redhead's book, Celery has something similar. There's nothing terribly new about this. Oh, by the way, before I continue, the idea of doing Bell and Pauli's with times rather than angles, let me see, Tony Leggett gave a talk in Utrecht, about a year ago, I suppose, in which he did Bell and Pauli with times, but that just referred to a single system. Ghirardi, Grassi, and Weber worked on it six or seven years ago, maybe.

1:12:30 There was another talent, Tommaso Calarco, he was in Intervalle at the time, I think it was about seven years ago, who did something similar to Tony Leggett. And, of course, celery as well. Anyway, so once this expression is rewritten in this form, we can have the bound of the modulus from 4 to 2. Well, then I just sum over k, y by n, and that average, the modulus of that average can exceed 2. And that's why my bell inequality, which I presume it in this form, where these correlation functions have that form. So, again, so far, nothing to do with quantum mechanics. Now, this is the relevant part of quantum mechanical formalism, which I will use. There must be a better term for these objects. I call them unitary self-adjoined zero-trace operators acting on C squared. There's probably a word for them, but... Well, as I say, I call them generalized Pauli operators, because, of course, the Pauli operators of matrices refer to three particular directions, and these are just generalizations. Maybe sigma dot n, maybe that's the best thing we're called. Anyway, they're characterized by a pair of angles where we just need one. So, this is the thing that I'm referring to, where this and this are orthogonal and normal. Anyway, in C squared times C squared, I define this average value where the B is this linear combination of products of things of this form, where the superscript, of course, represents the subsystem, and this is this vector sigma, this vector in the average value.

1:15:00 And, well, for instance, with this choice of angles, this will reach a maximum of 2 root 2. Anyway, so how am I going to replace angles by times? Well, take the angular version of the parameter dependence. It says, as I said before, by rotating an apparatus on the right, you can't change the value on the left. Well, the rotation of the apparatus involves an initial angle and a final angle. To both angles will correspond one of these generalized powering things. And so physically that's what's happening. Mathematically, corresponding rotation is carried out by a unitary operator. So, u times sigma sub alpha, and then the conjugate of u, the original unitary operator. So, in fact, for any angular difference, there will exist a unitary operator which will get you from the initial angle to the final angle. So that rotation, which figures in the permanent defense condition, is represented by a unitary operator, and there will be a cross-bonding group of unitary operators. Well, suppose that group happens to be the time evolution group. So, well, I've written spectral representation, spectral expansion of the unitary operator, which rotates this angle of difference. Suppose these happen to be the eigenvectors of a time-dependent Hamiltonian, where the important thing to get the right kind of time evolution, or to get a time evolution, because usually one considers the triple time evolution. The important thing is that these E's be different. So basically I'm, well anyway, I end up taking an operator like this on the left, another one on the right, so it's a product evolution. And the time evolution generates beats, oscillations

1:17:30 like two tuning forks. You get beats whose frequency is equal to the difference of the frequencies of the two tuning forks. And the beats, of course, in this case, are in configuration space. And so the effect in question is a measure of those beats. The violation of belting equality will be an indication of the expression of those beats. So this is basically the same operator I had on a previous page times as a substitute for other angles. And, well, I've rewritten it in terms of this is the average value which has a maximum of 2.2. This is all the same as I had on the previous slide. So the correlation functions, these average values assume that form. That's again the difference between the energy eigenvalues, and this is the time difference, of course. So those are times that will give you a maximum violation. Now, again, first I didn't make any reference for quantum mechanics. This now is the relevant part of the quantum mechanics of womanism. So here, I compress a number of very delicate issues into a paragraph. Well, these are not really the issues that I want to talk about. I know I'm sort of vulnerable, all kinds of objections, and... But now I try to draw a connection between the two things I've been talking about. And I assume that the pairs that I was talking about in the first part are accurately described by this vector, which has been at issue in the second part. Furthermore, that these generalized power operators faithfully reveal the corresponding properties, the properties that I was talking about, plus or minus bondings, that I was talking about in the first part. So if I make all those assumptions, then the observables represented by V or V tilde, so the tilde just means the time version of V, would violate the parameter independence that I mentioned.

1:20:00 Well, anyway, so, for the past while, we just had one substitute, president, too. but now since proper independence is again at issue it'll be best to reintroduce well at least the possibility of having a second subscript, so occasionally the second subscript will reappear where there is well notation becomes a bit of a problem at this point, but where I do write just one subscript, that doesn't necessarily mean that there's no dependence, because again the second subscript remember, is always The second subscript of the first factor is always the same as the first subscript of the second factor. So, for the modulus of this to exceed 2, the modulus of... There will be at least one term in the expression, so one pair, possibly one, which does not, which is not equal to 2 or minus 2. So, suppose the k0 pair is to blame, there must be at least a time h, such that there's a dependence on the second parameter, so where j is not equal to j prime, where these are times suppose that in fact we're talking about so these are what the last two terms so I'm supposing that this will depend on whether we've got u or u prime well if you think about the meanings that we've assigned to their symbols it looks very strange I mean how can that possibly the semantics in question. And I agree that there's something extremely strange going on, and I'm not really sure how to interpret it. But just for the sake of discussion, I'm just exploring the implications of this temporal semantics.

1:22:30 Again, it's not entirely clear to me what they are exactly, but let's try to explore the implications. And suppose that, for the time being, that quantum mechanics is not at fault, and that the assumption of realism remains valid and sort of play tricks with time. So we have to wonder how it is that... So this is the problem we're trying to understand. How it is that this is equal to, say, minus 1 and this is equal to plus 1. So, well, one possibility, a pretty absurd one, is, but I think the alternative is just as absurd, so don't be too surprised that I'm mentioning this possibility, is that it's just a kind of conceptual or notational fact, that it's just by considering this symbol beside the first one, somehow that influences the first value. So it's just by association that this is equal to whatever it was, say, plus one, and this is equal to minus one. But how can that be? I mean, notation doesn't have that effect. There must be something more physical at this point. there, surely just ink on a page doesn't change, or just the fact that one expresses more of an interest in one angle, one time, rather than another, in one term of expression, surely that can't change the value. So it must be something more concrete, must be this, like measurement. But measurement, of course, was assumed to do no more than faithfully reveal the underlying value. Of course, that's the assumption of the question, but here I'm not. So measurement refers to... So maybe those two terms in which the second factor is different. So, they refer to two different experimental situations, in which, on the one hand, so

1:25:00 on the left, suppose on the left, the measurement is made at time t, and on the right, in both cases, and on the right, it's made at t prime on one hand and t double prime on the other hand. So, whether the measurement on the right is made at t prime or t double prime, if measurement seems to affect the outcome on on the left but first of all well there are no problems with that with that possibility for one thing in the case in which the problem was an angle we did something far more spectacular and physically obvious we actually turned it up right in this case we just wait we do exactly the same thing at one time rather than another so why is it that that should have an effect on the value on the other side. And furthermore, what value is the other side supposed to have before the measurement is made? So if there is this dependence on measurement itself and not on something a bit more obscure, which I don't really know how to characterize, well then what kind of value is it to be assigned before the measurement? So, anyway, there are a number of problems, I think, almost as many, associated with second to the measurement interpretation I've discussed. Anyway, to make the effect more spectacular, the values can, of course, be linked to larger circumstances. So, they can be linked, for instance, to railway tracks or something. And so, in fact, I'm saying that, well, at 12 o'clock, January 1st, 2000, two trains pass each other without incident at the central station of Tokyo, if we make a measurement today at 5 o'clock in Oxford. Suppose we wait an hour and do exactly the same thing we would have done at 5 o'clock, but at 6 o'clock instead. Well, in that case, same time, so 12 o'clock, January 1st, 2000 in Tokyo, the trains collided instead. I think I've...

1:27:30 That sounds like a spectacular ending of your book. Do you want to end here? If I run out of time. You have a few minutes. Well, should I leave a few more minutes for questions, or shall I go on? I'll leave a few more minutes for questions. at the very beginning of Bell analysis one considers anti-correlated or correlated pairs the one word you didn't use in the whole story was correlation you didn't tell us that these two D's whatever they are, are correlated or uncorrelated and how they're correlated did I have to? if you're doing Bell analysis I would think so I don't think I have to. You don't think correlation plays any role? That's not what I said. I said that I don't think I have to derive that inequality. All I need is the fact that they have values of plus and minus 1. So that kth term in the average, well, in what becomes an average later, will be equal once I've made the assumption. So, before I make the assumption, it's equal to, it is bounded by plus or minus 4. Once I've made the assumption of parameter independence, it's equal to plus or minus 2. Regardless of correlations, it's just not... Perhaps, well, in that case, you're just playing with a fact that dichotomic arithmetic trivially and tautologically satisfies Bell inequalities and has no significance. Oh, no, no, no, no. But then I connect quantum mechanics to the arithmetic I was playing around with in the first part. But then you're doing something that's entirely irrelevant to Bell analysis because Bell's point was by assuming, by trying to reinstate locality and reality into a greater theory, that he could then do two things. He could average it down back to quantum mechanics, but have reality and locality in the bigger theory. So, his whole point was that locality and reality impose certain limits on this bigger theory. And his question was, what limits do they impose? And those limits are supposed to be a Bell inequality. So, everything from the start of the derivation to the end of the derivation of a Bell inequality quality is supposed to be in a classical realm. And then you take the results and go to the

1:30:00 lab and see whether nature satisfies that or satisfies quantum mechanics, which runs entirely independent of any Bell analysis. Ah yes, but I haven't really talked about nature itself. I've talked about the relationship between quantum mechanical, the quantum mechanical formalism on one hand and my arithmetic for the first part. Any of this question? Thomas. My remark goes a little bit in the same sense that if you take this experiment with trains and collisions in Tokyo, to establish a correlation that will violate causality, then you need quantum mechanics, you need quantum correlations, and if you do this experiment every day during one month that you make the statistics, in average there will be no correlations. locality for macroscopic observable. Sorry, there will be no correlation? There will be no correlation. If you make an average, the correlation disappears. Between the collision in Tokyo and the fact that every day you choose to make an experiment at 5 o'clock or 6 o'clock. Because the train is macroscopic. If you do it many times, then there is no correlation anymore. Because the train is macroscopic? Yes, and because it is weak locality. Well, could be, but, no, I agree that it's very difficult to take advantage of this sort of thing in any controlled way, but I think in a single instance, there does seem to be this dependence on the, well, I don't mean that it does seem to be, if one makes a number of assumptions one seems to be able to conclude that the assumption parameter independence is violated and I think that that directly leads to the train scenario okay Anthony and then Jeremy and then I'd just like to ask, in the usual EPR-type thing, where you have space-like separated events, you conclude that there has to be some sort of non-locality, but it can be just one way. It can be just one in one direction. If I have this non-local influence, it can just be in one direction.

1:32:30 So, presumably, in an analogous situation where the events are timelines separated, this influence can be in just one direction. It could just be forward in time. Yeah. Now, I singled out the time choice as being the cause rather than the effect. by an appeal, for instance, to free will or to a random number generator which uses something that can be shielded in an appropriate way from the effect of the other measurement which could lie in the past. Now, of course, collapse represents a problem and there are a number of ways of dealing with that, I suppose. But I can introduce an arrow by an appeal to things like that. I think I was very confused and now I want to make a comment and I congratulate you on the imaginative construction but I'm going to make a comment that sounds a bit deflationary. The only way I can avoid being confused about my goodness could the passage of time be a cause of a distant and so on, or marks on a paper or consideration, is to hold on tight in my mind to your equation that for a single wing, a single sigma matrix, said that sigma T dashed is a kind of Heisenberg evolute of sigma T. So when I fix on that, I think, ah, so we are now concerned with of the four observables, two in each wing, in which they, within a wing, they're related by this Heisenberg evolution. Sigma t dash is a certain Heisenberg evolution of sigma t. Now when I do that, I think, well that's fine, one could consider what the quantum correlations are for a pair of observables in each wing related by this unitary transformation and you may or may not get a Bell inequality violating quantum prediction depending on the choice and you could label

1:35:00 helpfully sigma with t and t dash but that's got nothing to do with the passage of time or waiting through time being a cause experiment and its quantum predictions and its local realistic predictions would proceed with the usual requirements that there has to be a free choice of whether you measure sigma t or sigma t dashed and you don't on any single particle measure both. And instruction sets in the local realistic model must be the same. Whatever the freely choosing experimenters choose to measure of a pair, you know, the instructions that a pair carries is independent of what the two parts of it are later destined to be measured for. So, in a sense, I don't see how you get the verbal argument for the train scenario, because I think you've just labelled what we normally call kind of sigma A and sigma B as sigma T and sigma T-dash. and if they're just non-commuting spin components you've got to proceed in the ordinary discussion of the experiment you can't measure both etc etc on a single component they certainly don't commute in how they're in a sense that how they're in a sense in which the angular ones don't commute that's got so much good That sounds very reasonable, but still, how does one encounter a dependence? Well, I mean, one thing is, you were saying we're going to get an argument for parameter dependence. Well, a quantum person would say, no, there's only out there for dependence. Well, actually, no, the kind of parameter dependence that I use is very different from the... terminology that's not the standard i i'm i'm just saying that there's no dependent the assumption of primary independence just says that there's only dependence on the on the first subscript not on the second one so i'm trying to account in some way

1:37:30 for the dependence on the second parameter which seems to emerge from the violation before we thank the speaker i want to point out on the program there is sort of a brainstorm session six o'clock about the conference next year well thank you all the time