Causally symmetric Bohm models / Probability time-neutral models of QM

0:00 The advantages dropped out as well, and one of the obvious ones was that if you switch to this alternative theory with some algebraic modality in it, you can then reduce the formalism down to working in the three dimensions of physical space rather than in three-intent configuration space, and yet still remain completely... What we have here is basically two different perspectives you look at. One is working with both the initial and the final conditions, which is what we normally wouldn't do, but if you were given both of those, you suddenly find that the mathematics and the picture becomes a lot simpler. You can give the explanation of God's theorem and get back to three-dimensional formalism. The other perspective, of course, is the one we're always usually locked into, which is that we can only know the past, we can't know the future. So the most we can do is average over the possible future conditions. When you do that, it goes back to giving you the normal quantum mechanical predictions, but of course you get back some of the complexity and it's less understandable. So that's the general scheme of what I'm aiming to do. So, I'll start off with the usual structure of David Bohm's model, which I assume people are fairly aware of, basically bringing in a particle ontology and having a particle wander along with a particular velocity function. The addition, of course, is that normally we just have a wave function which is prepared for some sort of initial state preparation, but that's the initial conditions, and so we effectively know the past. And that's all you have in the usual Bohm model. But here we're going to bring in some retrocausality, and that is to say that the state of the particle at some future time is also going to have an effect, and we'll bring this in as well. So we have to bring in some effect of the particle's future experiences and other possible factors that you might want to take into account in deciding how the future might have some relevance, the type of the next measurement or the type of the next interaction.

2:30 But of course there's lots of things coming up in the future that we put them all in. At first sight that seems not so easy to take encounter with all. But in fact the principle I work on here all the time is to work with a complete symmetry between past and future. In other words I'm using this phrase causal symmetry. Each time I'm worried about how to bring in the future, I just look at how we deal with past. And by symmetry I'll do exactly the same thing. So what do we normally do? Well we have a wave function, we have an initial state of preparation, formally the wave function simply summarises the initial boundary conditions. So what we normally just call the wave function, I'll now start calling the initial wave function, summarising our initial knowledge, our initial boundary conditions. And I'm going to supplement that with another wave function which just simply summarises the final boundary conditions. If we pick the spirit of that symmetry, both of these two wave functions will be solutions of Schrodinger's equation, and so now it's going to be a matter of building a formalism with both these wave functions in it, psi i and psi f. So I have certainly brought in an extra degree of freedom here in order to achieve this aim. I'm sorry, does psi f solve the time reverse Schrodinger equation with the common conjugate No, it just solves the normal Schrodinger equation. However, it does turn out in the formalism I'm about to write down, it's always psi f star that appears in conjunction with psi i. So that psi f star would be solving the conjugate Schrodinger equation. It's important to understand that we're dealing with two completely distinct wave functions here. One is not simply the other one evolved into the future. The first one summarises our initial boundary conditions. If you like you can think of that as a measurement rather than anything else. And it summarises the result of the last measurement and you can then mathematically evolve it forward to the time you're interested in. Likewise, this PSYF final one simply summarises whatever final conditions are relevant, and you can mathematically evolve that backwards at the same time that you entered it in.

5:00 You'd have two wave functions there containing two quite independent amounts of information. The normal Bohm model is just deterministic with the original wave function alone. This model, of course, will require both of these wave functions before it goes back to being deterministic again. I don't know if that's semi-deterministic or something, but at least there is determinism there, but of course that will go away if you don't know the final business if you have to average over it. The aim here is to make it as similar as possible to the well-known Bohm model. For example, it will be a no-collapse model. I have built a theory of measurement to go with this, which is just analogous to the one of the original model, involving the measurement spatially separating the various possible eigenstates in the spirit of what Bohm did. So it's a no-collapse model because we've got a particle that will just go into one of the possible wave packets and delete by choice the other ones because there's no particle in them so they won't be relevant in the future. Likewise, the intention is to be like the normal bone model in not giving any preferred status to measurements compared with other interactions. Now these two wave functions... At first you might say, well I just brought in two wave functions and it's really just a two wave function model and there's no backwards or forwards in time involved, but in fact they will behave in quite different ways. One obvious one, just think of, say, a position measurement as our initial psi i, the initial wave function, will spread out forwards in time as it propagates the wave, so eventually it might, say, hit a... In this situation, you use the model to work out what happens in between. And the final state, then, would be the spot on the photographic plate, be the source of our final wave function, which would then spread out backwards in time. So from our human point of view, CyET would be seen to be collapsing down quickly all to one point. It evolves continuously, but certainly not in the regular way we'd expect. So there's one clear example of how the behaviour is different from a different boundary condition. The latent factor would be, if you think of what normally happens with unusual wave function,

7:30 It starts out, say, as a normal single particle wave function, just in three-dimensional physical space, but then as that particle interacts with other particles, you get correlated states. Suddenly the wave function is now defined in configuration space, and with each new interaction with a new particle, it becomes excessively more complicated. Whereas, if we go to the final wave function, you'd like to think of it starting at that point in time. On the previous slide, it will evolve initially backwards in time as a separate wave function, but then it will start to interact with other particles going in a backwards time direction, so it will get progressively more correlated and complicated as we go in the backwards time direction. So again, we're getting different sort of behaviours because of the different boundary conditions. At this point, I'm not saying we've actually got retrocausality, because I haven't actually discussed the full ontology yet of the particle. But once I've brought in the basic formulas, it will be obvious that we do actually have retrocausal effects going on as well. I'll just write down the usual equation with the foam model, simply so I can compare them with what I'm adapting it up. I want to keep the equations out of this as much as possible, but these may well be fairly committed to people anyway. The foam basically postulates that we're dealing with a particle, that we have the usual probability distribution. I'm going to discuss the nominal logistic case here, even though it would be more appropriate to do a relativistic version. Because the discussion will become rather relativistic as we go along, this has been written up in a paper that I posted in the first slide, and I've done the direct translation case there to show that it's been closed smoothly and there's no problem. But my purpose here is to compare the two models as closely as possible. Since it's the non-relativistic version of Bohm's model that's best known, I'll stick with the non-relativistic version of what I'm doing so they can be closely compared. So I'll come back to that slide to...

10:00 Compare those equations with the ones I'm going to get short on. Just to mention in passing that the usual way of writing those equations that involve splitting up the wave function, you do R and F, modulus and phase of the wave function, and that might be more familiar to you, but in fact this is only something that works in the special case of non-relativistic quantum mechanics without spin. As soon as you bring in particles that spin, so going to the Dirac equation, that sort of break-up doesn't work well anyway, and so I won't explore it either, because I want to do it as generally as possible. So the equations I showed on the previous slide are the ones that we'll be comparing with the alternative model I've used before. Now, there's various ways of deriving those basic equations of Bohm. The one most convenient here is to look at the usual. The equation of continuity comes from the Schrodinger equation, the first equation there, but the general Schrodinger equation is the first equation, without the usual Schrodinger formula for the equation, the second one, and then just by doing a straight comparison of the equations, identify what rho the density is, and identify what v the velocity is, and you'll get those usual Bohm equations that happen two sides together. I want to do something similar here to get the alternative model. The key way forward here is to note that although it's not usually done in any of the textbooks, that derivation of the Schrodinger equation of continuity works just as well if the science by start that you're using not just completes conjugatively the answer, but pursues a pretty different function, the derivation just goes through quite naturally regardless, which usually is not done because people have no need to do it. But if you do that you still get Similar sort of equation of continuity. And to show that they're quite different wave functions, I've put an i on one and an f on the other. The complex conjugate one, the star one is getting the f, and that's what we have here on too. And so now I have another equation of continuity which will have a conserved quantity, but now this is obviously designed... There are a number of ways you can use these terms, and I think it would be useful for me to disrupt the model because it's got both of these two wave functions in it. The initial one summarising our initial knowledge of the past, and the final one summarising the knowledge that we'd like to have about the future that we're going to have to have read over, because it's obviously not normally available to us.

12:30 It's more or less symmetric with respect to the i and the f there, which is not what we want. It'll get a little more symmetric in a moment. The conserved quantity here, which I'll mention here, I don't want to put too many equations up, but this A quantity, which is the conserved quantity, are going to be appearing in the later equations, so I don't need to mention it. But the usual way of integrating over space to find the conserved quantity associated with that equation of continuity gives you a quantity that's just a change with time, and it's obviously something that we can identify as a possible total probability. In the equation of continuity, I just compare it to the old general form and again just read off an expression for rho, the density, probability density, and an expression for v, the velocity. Before I do that, I have an extra step I need to do just to get it into a form so it'll work. By taking that extra step of going to a new equation of continuity, it's no longer normalised. Normalisation was designed just for psi i alone. So I do need to bring in a normalisation factor here just to make sure it works, and that just means dividing through by the quantity a that I've already mentioned, just to ensure the total probability is equal to one, so it's a new normalisation to allow for this generalisation. The other obvious thing is that the equation wasn't real, but I'll just take the real part of it. That may sound a little bit arbitrary, but there's a good reason to justify it, and that is that the equation isn't fully symmetric with respect to the initial and final space until I do it. Once I do take that real part, then I do have complete symmetry between psi i and psi x. So I think we justify it on that basis, and I'll name it as complete. So having done that, the equation got a little more complicated, and that's our equation of continuity that I'm going to compare in order to just identify.

15:00 New probability distribution for the particles, if I compare them, I get these equations. So these are the basic equations of the new model, if not rather more equations than I would have hoped at this point, so these are not here on, but I needed to get to that point of introducing the two basic equations on which the model would be based. If you can hold that in your mind for a moment, I'll go back to the Bohmian ones. If you compare these, this one, the first one doesn't have a... The new version looks slightly more complicated, not disastrous, we say, but will serve a purpose for what? To have a model that has this metric coordinate built into it. Well, you get a minus I instead of a plus, so you haven't quite restored the symmetry because interchanging I and F gives you minus. But in any case, the other problem, the easy way out for me to say is the model doesn't work very well if you try this method at heart. I can't really give you the full details here, but it's very obvious by taking the real part. If you go back to, that's the point, it needs to reduce back to the normal model, psi i and psi f in the same function, you can just drop the f and i off and it should drop back to the boning model and it won't do that if you have the imaginary part, it's just zero. This is the one that reduces back to the boning model in the first place.

17:30 There is also a need to make a statistical assumption which basically postulates the Bourne rule. I guess all interpretations of quantum mechanics have to bring this in at some point, and I'm just bringing it in as an assumption. I don't think too many of the viable interpretations would be able to actually derive this rule. There have been suggestions that it's derivable in some cases, but as far as I understand it, there's no unanimous opinion that that's been successful. So in any case, here I'll just postulate the rule. Which is basically saying that given an initial component function psi i, the probability of a particular final result, which is summed up by psi x, is just the usual square probability function. And this will just ensure that we get all the usual kind of quantum predictions. And so we come to the first obvious projection of this plan. The two probabilities that we get, the first equation there is... But the remarkable thing that arises when you're dealing with vector causality is that it gives you an immediate way out of this problem. This would normally be fatal for any model that isn't involved with liquid fidelity, it can have negative probabilities. However, as I'm going to demonstrate as we go along, there is quite a natural explanation in the case where you're allowing factors of time effect. Indeed, it's almost something that you would expect once you bring in this extra degree of freedom of allowing motion factors of time. So it is quite easy to, in limited circumstances, give a meaning to a negative probability, and that's what I'm going to do as we go along. I'm not going to do that first. There's a collection of things to do, and they're the four things which I'll be mainly working my way through for the rest of the talk. First, I want to just demonstrate that we really are having factors in time effects in the model. And secondly, obviously, I want to try to prove that the model is consistent with observation. Then I'll come to demonstrate if the negative probabilities are okay, but then also go finally to the motivations of the whole thing, which is to show that it does give a rather natural looking explanation of the non-locality, of the apparent non-locality, of the rise and the fall of students.

20:00 In showing that it's consistent with observation, I'll have again this usual dual perspective where if you look, if you work with... Both the initial and final boundary conditions, initial and final knowledge, are known, then at first sight it doesn't appear to be agreeing, but then once you average over the unknown final state, which we can never know in advance, we can't know the future, when you do that, it drops back to the standard predictions of quantum mechanics, just to the perspective of any known part. The first item is just to demonstrate that we really do have a retro-causal effect here, so we'll just consider two separate particles and begin to see that they will behave differently after the initial state, after the initial circumstances, depending on what we do differently in the future. So a choice we make somewhere in the future will affect how one particle behaves compared to the other one at earlier times. So we've simply prepared them both with the same initial wave function, so it's nothing in the past that's going to make the difference, but then we have a choice of measuring two different observables at some time in the future, where we measure one on one particle and a different observable on the other particle, and we'll make them run commuting observables so that the wave function going backwards in time to summarise this are different and compatible with each other. Since the final wave functions coming back from that final measurement to the in-between time are quite different wave functions, and since we have both the initial and the final wave functions appearing in this equation for the velocity particle, we will clearly get different velocities for the two particles at the in-between times, depending on what final measurement we do.

22:30 So therefore the type of measurement done sometime in the future, having a bearing on the physical reality existing at the earlier time. So that's what we mean by retrocausality. There is an assumption being made here of naive view of free will, that you can choose to perform whatever measurement you like. In fact, just make a decision later on as to which measurement you feel like doing. And by doing so, exercising that free will, you can change the things at an earlier time. I have formulated an alternative version of this that avoids mentioning free will and simply works by a more mechanistic method of choosing the measurements that I'll leave it. The way it is here, just the free choice of these, forgetting the causality of the plague. I will at this point just mention an alternative interpretation one could try to do to avoid causality. One could just assume that we're dealing with two wavefunctions and they arise quite differently in the past and go towards the future, and because they're different, because the two psi-efs are different from the two particles, you might get the causality of the rule here. However, this is really not going to make sense in the sense that, if that were the case, the psi-efs that arise in the past would almost just happen to be... An appropriate eigenfunction of the particular observable is going to be chosen freely at some later stage. At this stage the observer hasn't even made it in the past. The thing that's arising is an eigenfunction of it. It's hard to see how you could do that. Alright, the second item I want to deal with is just demonstrating that it's consistent. This does require some calculation. The first one is that this is the new... But the reason for this is that we're actually dealing with two different probability distributions.

25:00 The first one there is the probability given both given knowledge of both the initial and the final states. Whereas the thing we always measure in quantum mechanics because we're So in order to prove that we're consistently able to paint that first equation and convert across by averaging over the future states, it's not difficult to show, which we write this in properly, showing conditional probability of what we're placing it on, i and psi f, take that expression and then convert back to the language of conditional probability, given only psi i, the conditional state, is implying that that expression just drops back to the one that we're familiar with. In any case, it should be noted that the probability distributions we're dealing with in models like Bohm's models are basically talking about the probabilities of times in between measurements, which are times we can't see anyway. So there's actually quite a bit of freedom in building models. You can make it be anything you'd like at those times. The only real need is that it be an experimental experiment just to find the time. Here it does work out. In the case of the position distribution data is in agreement at all times, not just at the end, but there is considerable freedom in this sort of model anyway. Indeed, in Bohm's original model, the distribution for variables other than position do not agree with the experimental results until you actually get to the measure of changes. The other consistency issue I want to mention quickly is that in the case where the final measurement is one of position, the final wave constant psi f, which is summarising our knowledge of that final result, will just be a delta function, as I've shown there.

27:30 But of course, the thing that we're really dealing with in this model is the probability distribution rho, strictly speaking, I need to show that rho also reduces to a similar sort of delta function, just so that the model is self-consistent. It's not difficult to do a short calculation and say that's the case, which obviously I'll leave in the paper. But the point I want to make about this, the conclusion I want to draw from it, is that this means that as you approach that point of the... What you're finding is that your probability distribution just gradually reduces to a point and in particular it becomes completely positive, which is another delta function. And the significance of this is that as we approach the time of measurement, any negative probabilities that were in the original expression just gradually go away and you've just got positive probabilities for the measurement itself. This will be useful as we go along because we need some self-consistency. It really doesn't matter what it's doing in between as long as I can give a meaning to it, and I will do that, the meaning will be different but it's all quite easily interpretable. But it all goes away anyway as you approach the time of the measurement because this final wave function has an influence backwards in time and basically pulls things in line as time approaches. And this is very convenient, as well as giving full-time symmetry. It avoids a lot of complications, we'll see. Alright, so of course it stands and falls, or stands or falls on whether you feel comfortable with the idea of probability. So I'll go through the interpretation of what that means. But it doesn't work that well unless you also have... To get the results, I'll just compare the usual way of writing the plane of continuity with the relativistic notation. Going across, instead of just having a probability density, now we need to have a density in the rest frame, rho zero, and work with a rest density.

30:00 Likewise, instead of just working with a normal three velocity, now it's having to use four velocity. But if you compare those two equations, you just find that the connection between the usual density and the rest density, the equation there, involving mu zero, which is just at the four velocity. Now since the right-hand side of that equation is made up of invariants, the time component, it basically means that the left-hand side, our standard probability density, we need to keep in mind that it is in fact the time component of the four vector once we go to the relative, we tend to just neglect dealing not relativistically, but it's important and we need to keep in mind that we're dealing with. This of course means that now we have an immediate interpretation for what the negative value means. I'll go back again. The negative value is not going to come from the rest density of O0, which will always just be positive, that's giving the probability of the rest frame. The negative value will simply come from this point, that's showing which way the particle world line is directed in space-time, and in particular it just means that it's pointing backwards in time. So, the negative value will simply mean that we're dealing with the current density going backwards in time, which is, like I say, not a interpretation that I've invented. I'll just draw a space-time diagram there of the current density vector, and you can see that the actual magnitude of the vector is rho zero, the diagonal line, but pointing backwards in time, the vertical dotted line is our probability density. And it's pointed backwards simply because U0, so U0 of the four velocity component is negative in this case.

32:30 So what will that mean in a real physical situation? Let's have a look at a diagram, a space-time diagram of a typical flow of current that would produce this effect. Obviously the point P on this curve is a point where our world-wide has turned temporarily backwards in time. I should say our flow line, because at this point we should be talking about current cancer. Now, of course, such a path would normally be considered to be not possible. That's not the sort of thing you see happening every day in relativity. But in this particular model, you'll remember that the effect of a measurement is to make things straighten out. And so your measurements, say, points one and four, will just see normal world lines. This would be what would exist at times in between. And as long as we know that any attempt to do a measurement is straightened out so it's not there anymore, it means that such a behaviour is quite acceptable and there's no real reason why we can't use it if it's going to be useful. Where do the arrows come from? Why is that? Why is two and three backwards? Okay, what I'm showing here, well, let's look at the arrow between one and two first. That's just a normal, say, electron, for example. Thank you very much for your attention. I'm going to discuss that in a moment, because that would be called a producer quantum field theory when I'm looking at it, but it's not quite as easy to work with, even though it's equivalent, so I'm treating this thing as a single particle that flows forward in time, or if the world line is forward in time, this world line just smoothly turns back for a while and then turns forward again. I'm asserting that there doesn't seem to be any reason why such a thing would be impossible, it just simply hasn't been observed.

35:00 Indeed, you can follow this with a rest frame if you like, as you go along the rest frame itself. The particle would have to turn backwards in time, but it's not difficult to define such a frame. Indeed, if you study a tachyon literature, faster than light, different frames are routinely introduced. And since by switching to another frame, faster than light automatically becomes backwards in time. I suppose you can think of large numbers of reasons you might want to put forward as to why this wouldn't be acceptable. The discussion now, we'll imagine, since we're dealing with a probability flow that followed that path I showed a moment ago, We would have to interpret this as being made up of a lot of particles, an ensemble of particles, so our probability flow consists of a lot of separate world lines, some of which would be of the shape I just showed. So we'll take that S-shaped curve as being, doubling that curve as being the world line of an individual particle, and see why you might object to it. Well there's a list of five possibilities there, and you may be able to think more. You might say particles are not allowed to go faster than light, they're not allowed to go backwards in time, they're not allowed to exist without causality paradoxes. You also have to actually go through the light barrier and pass through the speed of light to get to that point. Again, you might say that's not something that's allowed by the classical laws of physics. But indeed, all of these subjections can very easily be overcome. I've listed a collection of individual responses there, but firstly, keep in mind that this is going on between measurements, and as long as it goes back to behaving in the normal way at the time of the measurement, there really isn't any problem. And although I haven't gone into any detail here, that's one of the things that is necessarily true in my paper, that indeed you do.

37:30 So, you can find without having to force it or anything that the behaviour of the thing automatically goes back to moving like a normal particle due to the backwards in time effect as you approach the measurement. So, this is all just what goes on in between measurements. Obviously faster than light particles and backwards in time behaviour is considered by a lot of people to be perfectly plausible, just not experimentally sound. Classical laws, and they certainly would have learned such a motion, but then we're dealing with quantum mechanics here, we're not dealing with classical laws, and the law I've written down, the velocity of grade and the rate down, essentially replaces those laws, and once you do that, the law just allows the motion to vary without any problem. If you want to worry about conserving energy and momentum at the same time, in fact that can be done too, a version of this, a version of Bohm's model done by de Broglie, I think in 1960, just by bringing in some variation in the particle's rest mass, was able to run it smoothly through the white cones and other cohomons of conservation and energy. The point is that if you're going to bring in retrocausal effects, I'm treating this as an essential part of the model but also perhaps a natural part and you mentioned I will go I will look at this question of whether you should interpret that s-shaped curve as the creation of a pair creation of the particle antiparticle and the other the other point of being an annihilation. The point is though When you normally deal with particles and antiparticles, these points here are sharp, and so they're the same in all reference states, but if you have smooth turning backwards in time here, we're assuming that that's a line of simultaneous events, but if you switch to another frame of reference, your line of simultaneous events will run this way, and so the point where it actually turns backwards again moves up the line here, so you find if you attempt a particle antiparticle,

40:00 The second thing is that it's convenient to have a proper time variable increasing along the curve, there's three particles in this region here, then you're going to have to have three separate proper time variables to do the calculation. The third point, since we're dealing with a non-observable thing here, is what's going on between measurements. Unlike quantum field theory, you don't have to think about what would actually be observed by a human observer moving forwards in time. That perspective is unnecessary, so it's quite permissible just to draw up a single line. I need now to just discuss the final point of how this will help with Bell's theorem, and so to do that I'll look at the standard picture of the spacetime diagram of Bell's situation, so we've got an initial part of, you know, the decaying student perceptive particles on which measurements have been performed. For convenience, I'll push measurement M2 a bit further in the future, just to durate the discussion. I'm assuming there's a space-like set of names, so that's depending on what kind of reference you choose anyway. So I just want to compare how the two models will deal with the situation. So in the standard Bohr model, you have to have a space-like influence being exerted

42:30 when the measurement is performed on the first particle. The Bell's theorem tells you that this has to have some effect, cause some change on the other particle in order to conform with the quantum mechanical predictions. The reason for this is that we start off with a standard single wave function describing both particles, this psi i, which is here in six dimensions, and as a result the second particle's velocity is depending on this wave function, and so therefore is indirectly depending on the other particles. Once you actually do a measurement on the first particle, though, it basically factorises the wave function into two separate terms. And from then on, you can treat the second particle as being independent, and you have a separate velocity expression for that particle that, depending only on that particle, no longer has any connection with the other particle. You get this sudden treating up, well after the initial decay took place. It's already well separated. That's the thing we're trying to avoid. In order to look at what just happens here, after that measurement... We start using a new wave function for the second particle. From that point on, the result of the first particle is measuring the idea that you feed in the fact that you've done the first measurement, like the scalar product, and you get the wave function for the other particle. But this is suddenly arising at some event, sometime later, not entirely desirable. And now we go to the new model and how it deals with the situation. Obviously we don't want any of these space-like influences. The aim is for the whole description to be local. What does all this new approach achieve the aim? Well, in order for it to achieve it, the new wave function that is already widely separated will need to have it already there right from the word go from the time when the decay occurs from one particle to two.

45:00 So this reduced wave function we've got must be the right one all the way back to the decay. So that means we're describing the second particle at all times via a three-dimensional wave function. All of this in accordance with the usual zigzag picture which has been The results of this measurement produces the final wave function that comes down this way, and just by simply taking the scalar product of those two wave functions, we generate this wave function up the other way, which is the one we want all the way through the case, to give the right statistical result for the measurement in the second part of the data that we were thinking about. So the model is giving a local description of Bell's result. For doing something more, too, that was only two particles in the Bell case, but I wanted to do a general case and follow up in detail, but the point I wanted to make was that by the same mechanism, you can now, for any particle, generate a three-dimensional wave function rather than a configuration space one, and use that to describe the particle. It will be what determines.

47:30 In the case of a bone model, for example, it will be what determines the particle's velocity, not the configuration space version, and yet you can still get the correct statistics, because when you're dealing with these sort of wave functions, that's when you know both the initial and the final boundary conditions that humans never know, so we can't know the future, so we can't mix that out, and when we do so, we come back to the usual configuration space description and recover the usual quantum probabilities, but at the expense of getting... These are some of the things that seem to be strange about the three-dimension. Obviously the achievements that we are getting here, the three-dimensional description of Bell's result, and yet still to keep the correct controls and climates here. Your own opinion on whether it's all worth it. The advantages are obvious. It restores Lorentz invariance while at the same time giving a local description of Bell's result. It certainly avoids the lack of Lorentz invariance in the standard plane model. It also allows you to go to the three-dimensional description, two things I've been mentioning repeatedly. Well, they're pretty obvious too. By bringing in the final conditions, we've lost the determinism to the original model. It's true it's deterministic once we put the knowledge of the final state in, but of course we never have that knowledge, so we're having to average over it in any real situation. Secondly, although I can give quite a straightforward explanation of negative probabilities,

50:00 The rest may not be to everyone's taste, but it's very difficult to build a model of this sort without allowing such world-wide turn-backwards in time. So that's been put under the heading of discipline. Finally, just comparing the equations of the two models, the equations of the new version are not quite as simple as the old one. I guess that's only natural because I've brought in an extra degree of freedom, final weight function summarising. Knowledge of the unknown future of interactions, which wouldn't have been there normally in, say, the equations, they would have gotten a little more complicated. Alright, I'll see you in the next one. The fundamental story of what's going on in this role, as opposed to some story that I know is going to be causationally expedient and acceptably accurate on certain surfaces. Am I going to be working with weight functions that are defined on the configuration space of the universe, and I'll have just two weight functions initial to final? Or am I going to be working with lots and lots and lots of weight functions on those three pieces? What's the point of that? It's true that you could just take an initial and final configuration space wave function, so you will just have the first of the two possibilities you said is the right one. However, when it comes to axial governance, you'll just have an initial and a final configuration space wave function for the universe. However, with the usual... In the measurement theory, which I haven't gone to here because it's in my favour, what you assume is that when you do a measurement, you get the spatial separation of the possible outcomes of the measurement, and so you're effectively deleting some parts and getting back to a single branch, and so that combined with one coming from the future does take the perspective of the three-dimensional description, which is what actually determines the velocity of the particle. So the velocity of the particle is determined.

52:30 All purely by the three-dimensional plane. Well, presumably that's a concern of the velocity of the classical from the fundamental of a classical rather than the effect of one of the ones. I mean, the whole reason why we call the effect of one of the ones is that it gives the same predictions for the velocity of the classical. Yeah, but in this case it might give the same predictions, and if you use the configuration space function, it's all on its own. So if you're actually working out the velocities, you're just working through the... That is what you're talking about in terms of... So I'm defining it differently here, and three-dimensional models are different. So here, I guess, so here at Key you can't say the configuration space wave functions are the fundamental ones and we define up the effective ones from that because we actually give different predictions. Does this mean we need to plug in separately the configuration space wave function and sometimes there's lots of 3D ones that we need to run with that? No, no. Just starting from the configuration space ones, that's got all the information, including information as to how to recover the three-dimensional function. So the information is all there in your initials. The reduction down is pretty useful. It's an extra step, it's not more than a new sort of file, but I understand that it's necessary in order to get the simplification, to get rid of the non-mycology and also get rid of the straight information description. So it's probably interactions that I can use, but I don't know what's going on at the moment. So I suppose what's worrying me, I don't know if this does turn out to happen or not in your class, I had some worry that if I want to represent interactions between two classes, I'm not going to be writing down the dynamics for that, I'm rather going to be plugging in the effects of the interactions when I plug in aspects of the final weight functions of the various classes. So that's going to be my favorite part. I was worried at one point, and I'm now not sure whether I still am or not, that if I've got two particles and I'm going to add a small one, I'm not going to be able to replicate that interaction just by writing down an interaction with Hamiltonian.

55:00 I have to say the result of the interaction is that this particle has this final wave function, that particle has that final wave function, and I'm going to tally back the interaction happened by just plugging in by hand the effects of the interaction. No, you could go ahead with your two big configuration space wave functions and your Hamiltonian and do the usual calculation and you'll get the whole thing, but there's this extra step which from those two wave functions you take an extra scalar product before you evaluate the velocity. You don't jump immediately to what the normal value would say is the velocity if you do a scalar product that reduces it down. So, I mean, it's all coming from the initial waveforms, as you said, depending on the perception. I just want to follow up on that. It's related to what I'm trying to understand. It seems like you need the future waveforms to figure out what's going to happen, but you don't know the future waveforms unless you have the result of the interaction. The way you presented it, I mean, the measurements are kind of put in as primitive, right, so you're... If you're describing a certain type of interaction in the future, it's an addition question, but if there's a certain form of interaction, then there are differing results in the past. This is a different question. Hillary's question, which you're effectively doing, I think, is you're trying to model the interaction itself. It's hard to see. So how do you model? Maybe the question is, how do you model the interaction? Well, the intention was... You have to go further ahead. I'm trying to do it so it's identical to what you do in the past wave functions, so whatever you did there to prepare the initial wave function or whatever, and however you view the vision in the past, it's exactly the same thing in the future as what we had to do, I think. Yeah, what I'm worried about is that this also touches on just the general question about how do you do state preparation, which is what you would call a measurement of the past. Yeah, I am just assuming the usual picture is going to be the time you're working with the kids, but maybe you're working with the kids as well.

57:30 The question that I had was I don't quite understand the motivation for... This, because usually the new, the whole theory itself is sufficient to what is known and counts for the results prior and so on and so on and so on. So it's also known that the only derives of that development you do know, that you assume statistical independence would be assumed. There's no, one way to talk about this is to use an electron causation. If you allow that kind of model, and I think this is actually one of the reasons. If you allow a retrocausal model, then there's no real reason to be using quantum mechanics as a model. Right. If you allow retrocausal models, I'm just wondering why you would want to use quantum mechanics on top of that. Arguably, you can get non-locality from a quasi-classical special cosmology. But I'm trying to get all the statistics as well. I mean, I'm trying to reproduce the full quantum mechanics. It's not that I'm trying to... Well, but the whole theory reproduces the full quantum mechanics. Yes, at the expense of the lack of variance and variance, and at the expense of having no good understanding of the flow. It's really non-local. It's producing effects across a space-like distance, and it's really non-local. Whereas you can view this model as a thing trundling down one world line and up the other. It's as local as it can be. It's like touching. If we're going too wide, do we have to be quick? Yes, so two quick things about the three-dimensionality of the effective wave function. First of all, you showed us with one measurement first, then the other one, and one wave function coming back and then constructing the other one going up.

1:00:00 Yeah, I mean, I was space-like separated, so I mean, that was just convenient. Switch to a different frame and I'll change the order. Yeah, but I mean, each part was going to have a final wave function and an initial wave function. This was a trick to calculate one and then the other, but those would be the same if you switch frames. Yeah, I mean, I didn't say it here, but of course, it's symmetric, isn't it? I can do those two and get the wave function for that, but I can equally well take these two and get the wave function for that. So there's got to be symmetric between particles one and two as well. So I just did that to try and create a discussion for the moment. You just mentally shift them the other way and you can do the whole thing. Okay, and combining those two completions you get two initial and two final wave functions. That's right. And those are all. Okay. You get completely symmetric and you get all the predictions for both of those. But I didn't have time to go through them. And the other quick thing is, in one of the slides you have, provided the final weight from two parts to j is disentangled, that should depend on whether the measurement you're making is a disentangling measurement. You can call that some measurements which you make, in which case you would still have some entanglements in the final wave function, so is it correct that depending on which measurements are made, sometimes it would not be possible to have a completely 3D... And if that's the case, does one have some remaining problems or things? So, the answer to that is that, yes, there was that extra assumption that that particle had its own separate wave function. In order to get, in order to do the general case for all wave functions reduced to 3D, if you don't have that...

1:02:30 Then, although you won't get a wave function reduced to a 3D description, you'll still get a fully three-dimensional description of the velocity. It always comes down to physical space description and not innovation space one, regardless of that assumption. So that assumption only determines whether you can get its own separate wave function. But when you come to velocity expression, you avoid the problem. So even if it's only a partial measurement, as you said, you still get a pretty precise result on the modality. Thank you. Time off. Time to work. Okay. Let's go ahead and take a little bit of a step back and look at the scientific models in general.