Pilot Wave Theories

0:00 On the Pirate Way Theory, and I've had many opportunities of interacting with you and appreciating the level of your mind, your work, your hospitality. I'm very glad that you've accepted to come and give a series of three talks which this is the first partway theory of fields thank you very much thank you for the invitation does this work first of all I should apologise that the talk I'm going to give probably doesn't have much in it that I've not said I wasn't sure what sort of audience I was going to have quite a few things probably, in fact I see there are a couple of people from the states that I gave five talks there last autumn I assume that well ok, we'll see how it goes things, but I'll sort of begin with an overview. I suppose there's actually no need at all for that. Just a quick... I don't know if this is all things that everyone knows. Okay, I'll be quick anyway, okay, so, well, where should I begin? I mean, illustrating the theory for, can people see this problem? Can people see that? I'll bring it up a little bit. Oh, this is what? Top of the mirror. Okay, well, so you know the theory for n particles being guided by a field-on-configuration space. These are the fundamental laws of motion.

2:30 This theory was actually proposed by, this dynamics was proposed by de Broglie in 1927 not many people are aware of that, he has a full dynamics in configuration space in the paper he presented at the 5th Solvay Congress it's a radically non-classical dynamic the main feature seemed to me to be that it's an Aristotelian dynamics which entails an Aristotelian kinematic I'll be talking about that tomorrow It really takes place on an Aristotelian space-time, this is my viewing rate. The Psi field is utterly unlike ordinary fields. Is that the right time? I mean, one particular feature is that usually when the field, you imagine that you have a notion of a test particle. I can imagine some infinitesimally small probe that I can stick in there to see what the field is, whether it's a gravitational field or an electric field. I can imagine I have an infinitesimal test particle probe the field. There's nothing like that for a psi field. If you introduce an extra body, it doesn't matter how small it is, how physically insignificant it is, you actually increase the dimension of the configuration space that the thing is defined on. So it's a radically different sort of causal agent, much more abstract in all these fields. And, of course, the basic dynamics takes place in configuration space. And when you slice this down and project it down into three space, you get these extraordinary non-local effects. But I don't want to just... Okay, of course, I mean, that is... Fundamentally, that is the theory. you just have this dynamics and these particles moving that is the theory if you want to recover quantum theory you need to assume that there's a probability distribution of psi squared as Bohm did in 52 you can ask how you justify that and various arguments you can build up a sort of analogue of classical statistical mechanics can we just ask for history if that condition wasn't occurring was that why it was shot down by family? ah, that's a long story De Broglie did, he noted that psi squared probability is preserved by the evolution, so he says, let's take that as the probability, he has that what De Broglie didn't do is he

5:00 well, I mean, the quantum theory of measurement didn't really exist in 1927 that was the sort of abstract theory of measurement, how this dynamics accounts for the full quantum theory of measurement was done by Bohm later on but that story about Pauli is actually going to translate that volume and there are a lot of misconceptions about basically de Broglie abandoned the theory partly because he didn't quite understand how to do what we call a contextual measurement but partly he just thought that the dynamics in configuration space was physically unacceptable you have this real wave physical wave in configuration space which in three space you get this non-locality and so on. In fact, when Bohm revived the theory, de Broglie still rejected it, essentially for that reason. But anyway, I won't go too much about this. So, of course, once you have equilibrium, not only do you recover quantum theory, you also recover locality and uncertainty. I think people are probably familiar with all these things, so I'll just go on. Is everyone familiar with this? Ah, right, okay. Well, for example, if I had two boxes that are entangled, that the total wave function is entangled, and I have a particle in each box, if I do something at box B, such as I move the walls or change the Hamiltonian, in this theory, the position of the distant particle instantaneously moves, starts to move. But if I had an ensemble of these systems with a distribution given by psi squared, then the partial distribution over here is not actually effective. The individual particles do respond to the distant action, but the partial probability distribution at A doesn't change. It changes if and only if you have a deviation from equilibrium. and you can show A and B are factors that depend on the wave function and so on you can show that you get a small change in the probability distribution over here if you do something here and the change is proportional to the difference between P and psi squared if P is psi squared there's no change

7:30 so you have instantaneous signaling out of equilibrium but not in equilibrium And this, I mean, what I think is an important point to stress is that in this theory, what people usually call pilot wave theory is actually a severe restriction of the theory to a special domain of equilibrium. People usually call that pilot wave theory. That is actually equivalent to talking about classical mechanics in a state of thermal equilibrium. And there is an interesting analogy here that I've talked about I'd just like to emphasize this point that I think still a lot of people it hasn't really sunk in that if you're asking fundamental questions about this theory you must address them to the theory at the fundamental level you shouldn't look at this theory in this special state of equilibrium you should look at it at the fundamental level so for example In some people's minds, it seems odd that in the theory, or actually in the equilibrium theory, the trajectories seem to play a very minor role. And they do. In a level of equilibrium, you don't see the details of the trajectories. All they seem to do is single out which branch of the wave function is realising. And you think, well, they're playing such a minor role. Are they really there? but that is just a peculiarity of equilibrium if you looked at classical mechanics in thermal equilibrium if the whole universe was at a single temperature you would find that there were things you couldn't do you wouldn't be able to do hardly anything but that's just a peculiarity of this equilibrium state that has special properties and restrictions we are very restricted because we happen to be stuck in this equilibrium. But let me go on then, and just a quick... I talked about the particle theory. What I'd like to argue... In my view, the actual pilot wave theory of particles is actually wrong, as a theory, even as an approximate low-energy theory. And the correct theory

10:00 can only be a fuel theory. I'll use some examples of what there are people who are trying to do a high energy theory of let's say quantum electrodynamics with particle trajectories maybe at that level there are a lot of things you can do such as you could account for pair creation by having trajectories that come backwards in time and then move forward in time again and as you go up in time you've suddenly got two particles appearing and so on but it seems to me that there are well there's this point that even at the quantum level there are serious there are serious ambiguities with the notion of particle even at the quantum level and you could ask well if that's the case then how would a theory based on particle trajectories if it reproduces quantum theory in equilibrium at the quantum level in particular the notion of particle number is very ambiguous for instance in the high energy domain usually people do scattering theory you have in states and out states that you essentially have free particles coming in and free particles going out and the particle number is well defined at t equals plus or minus infinity but in high energy physics during a collision there's no well defined distinction between real and virtual particles how many particles are present during the collision there's no clear answer it seems you'd have to have some sort of theory in which the number of particles present can vary with time or possibly be a contextual variable or something like that similarly there's a position operator, in relativistic quantum theory you can show, in very general, Hegefell has a few papers where he shows if you assume I have some sort of definition of localization for a relativistic particle, then the probability is spread faster than the speed of light. This is at the quantum level, so there are problems there. And basically it seems that when you try and localize a high energy particle, where the problem the root of the problem is probably that any localization entails some sort of amplitude

12:30 for multi-particle states, pair creation and so on so the sort of consistency of the whole thing becomes very tricky there also this problem in curved quantum field theory, in curved space-time there is an ambiguity in the notion of a vacuum In flat space-time, you've got a preferred set of modes, plane waves, and there is a preferred notion of a no-particle state. In curved space-time, there are different choices that you can have for the vacuum. In fact, you have a state that's empty with respect to one choice of mode functions, but full of particles with respect to another choice. I wouldn't want to say that these are anything like impossibility proofs. So I'm sure if you put your mind to it, you could maybe do a pilot wave theory of particle to maybe get around these things. But there's certainly challenges, I think, for such a theory. It seems to me that a theory based on particles is also very limited. If you were just going to do quantum electrodynamics, maybe you can do it. But nowadays we have theories based on spontaneous symmetry breaking. For instance, in the early universe, we believe there were various phase transitions and breakings of various symmetries. And what happens is that, in effect, the masses and couplings of particles change with time. And in quantum field terms, you've got the Higgs field that is oscillating around a minimum. If the minimum changes, then you have different... In effect, you have different sorts of particles present. I don't see how you could do that sort of thing in a pure particle theory. Also, something like a weak interaction decay in the Feynman diagram, and here for the Nuon decay, you have an electron created without a positron. Okay, so if you're just in QED, you have electrons created with a positron, so you could say, well, either you say the electron has jumped out of the negative energy C, there is in Bohm's theory, for instance, or... but with this sort of process I don't see how a theory based on trajectories is going to give you this it would have to be a very artificial sort of theory so I think field theory is really the way to go

15:00 and there's a natural simple generalization the dynamics is the same You just extend this to a continuous system, to value a discrete number of particle positions. I've got a continuous field. If you like, the field value at each point in space takes the place of a particle position. That field value is there at each time. It's having a function of each position that has a function of the whole function. It's a function. And the growing guidance condition becomes, you know, if anyone's not familiar with functional derivatives, it's exactly the same with an ordinary derivative. You're differentiating with respect to the field value of the point. It's just a sort of normalization. If you imagine you've divided space into little cells, the volume, x, i, and q, then the function, then if you take the northern derivative and divide by a silent view, that's the function of the derivative. It's proportional to the northern derivative. And your Schrodinger equation becomes a functional Schrodinger equation. So this is just a Schrodinger equation that you have for quantum field theory in the Schrodinger picture. Quantum field theory is usually done in the Heisenberg picture or interaction picture. But the Schrodinger picture has also been found to be useful. So that's the basic dynamics. Now, this again is something I'll be talking more about tomorrow, that this is really taking place on an Aristotelian space-time. For the moment, just imagine that we have this mon-locality, so the mon-locality is physically associated with these definite slicings of this space. So the rate of change of the field at one point usually depends instantaneously on the value of the field at distant points. And fundamentally, all you have are the symmetries of this space, this Aristotelian space-time, translations and rotations. but in equilibrium when you recover the quantum theory or here quantum field theory in the usual way you can no longer see the actual detailed motion

17:30 of the field and you drop reference to this Droy equation and you're left with quantum field theory just as you're left with quantum theory in the particle theory and in the Heisenberg picture it's clear in the Heisenberg picture you end up with symmetries that were not there before. You have an effective Lorentz-Embarance. You get field equations that are Lorentz-Embarance. Even though fundamentally there is no Lorentz-Embarance. So you get an... In this equilibrium state, it actually has more symmetry. Okay, it's an interesting feature here. That fundamentally you have just the symmetries of Aristotelian spacetime. that the equilibrium state has more symmetries than the underlying theorem. And it's sort of the opposite of spontaneous symmetry breaking, where spontaneous symmetry breaking has an underlying Lagrangian, but the vacuum state may violate some of the symmetries of that Lagrangian. Here it's the opposite. It has more symmetry. And there is a question here. Why is it that all different fields and different interactions give you the same symmetry? I mean the fact that you get an extra symmetry in equilibrium is fair enough but why do you always get more x-symmetry and that's a question that I'll be looking at tomorrow here again is something probably most people have seen this is everyone sorry is this actually I hope some people are seeing something that they haven't seen before. One question then arises, well, if you say, well, if fundamentally you have a field evolving, how do you account for particles, what we see as particles? Now, what is it? This question here actually has nothing to do with pilot wave theory. You could ask the same question in quantum field theory. just ordinary quantum field theory you should take it as a field theory it's about fields this is something I've never seen discussed in any textbook I think it should be for instance if you look at a textbook on ordinary quantum theory there's always a chapter on the classical limit and it tells you how you get a Newtonian trajectory from this theory if you turn to a book on quantum field theory

20:00 you would expect it's going to tell you get non-relativistic quantum theory? How do I get a little wave packet moving in space representing approximately a particle via a fair signal? And it's never done anywhere. If you look at what will be called a single particle state in quantum field theory, it's just that you have these momentum states, you just have a creation operator acting on the back of it. So I've got single particle states, and I've got a superposition of different momentum. If you look at the wave functional, you can calculate the wave function in a low energy approximation. Low energy meaning you assume that these coefficients, C, are negligible for energies much greater than the rest mass. It's sort of low energy approximation. This, you calculate this is what the wave functional at this stage looks like. This is in the basis of field Okay, that state in the basis of field configuration looks like this. This factor here is the well-known ground state, the vacuum state wave function, which is a sort of dousin. Okay, and this is just vacuum fluctuation. You have a term multiplying it that depends on this psi is just the Fourier transform of those coefficients. That psi obeys the non-relativistic Schrodinger equation. That entity is what we call a non-relativistic wave function. Of course, fundamentally here, there are no non-relativistic waves, but fundamentally there's a wave functional guiding field. But mathematically, there is this psi that is the Fourier transform of that. So, in equilibrium, the square of the modulus of this gives you the probability you. If you ask what field configuration maximizes this probability, you can quite easily show that it has to satisfy this equation. For example, if this little is psi, this non-existent equation, happens to be real, the solution is just plus or minus this little psi. It's just basically proportional to what we call the non-relativistic wave function. Can you see that?

22:30 psi was not real, you have a sort of psi plus psi star in it, but it's basically linearly dependent on what we call a non-relativistic wave function. In other words, if I have, let's say, I mean, we're talking about stimulus particles in the scalar field. Imagine I had a spinless electron in the hydrogen atom. The ground state non-relativistic wave function, I have this little The most probable field configuration is a little lump, which has to be spread over a bore radius. This is the picture of the atom in the quantum field here, even though it never seems to be discussed in textbooks. In pilot wave theory, of course, there is actually a field configuration there, evolving, and it is most likely to be approximately a sort of lump, with the size of around the polar radius. So, an interesting conclusion here, that pilot wave field theory, it's true that the actual field lies somewhere inside the wave functional, if you like. If the wave-functional vanished in a certain region of configurations, where the configuration creates a field, then the field can't be there. But the particle is not, there is no, this is a low-energy limit. You don't get a point-like object sitting somewhere inside this non-relativistic little sign. So even in the low-energy limit, sort of the dynamics I wrote down at the beginning non-rhythmistic wave function is part of the trajectory. You might have expected that to be true as a low energy limit of the high energy theory. It is actually wrong. It is ontologically wrong. There is no point of arc of the city. It is very important to you. What does happen in the classical limit, where this psi, this psi would be a sort of narrow lump moving on, a little Gaussian moving around, then you could associate that with a trajectory that obeys Newton's law so you recover particle trajectories only in the classical there are no you just mentioned some advantages of pilot wave field theory ordinary quanta yeah maybe I should say

25:00 I think a lot of people worry that this pilot as attractive as ordinary quantum field theory. It seems to me that there are actually distinct advantages. One, for instance, you do not have this tension between special relativity and wave-packet collapse. You do have, you have Lorentz invariance, it's supposed to be fundamental, and then the question is, along what hypersurface do wave-packets collapse? In this theory, there is built into the theory a preferred state of rest. So you don't get that sort of problem. Another thing that in gauge theories, I'll be looking at some of this. In gauge theories, such as quantum electrodynamics or chromodynamics, you have gauge fields that are four-vector fields. They have a time component. and what you get is you always have particle states in a gauge that is covariant in the sense that that choice of gauge is not upset by doing a Lorentz transformation you always find that there are particle states with negative probability the actual norm, you have to define the norm in Hilbert's space has to actually be negative to a certain state and there are theorems that show that any Lorentz invariant choice of gauge will always give you particle states that have negative norm. And of course people just say, well, in the end, the actual predictions are not, you still get sensible predictions in this theory, but you have to say that these particles, these states are sort of fictitious. but there are what has been very popular is to work with a non-covariant gauge, such as a Coulomb gauge or the axial gauge or the temporal gauge, not so much the temporal gauge says that the time component of the field is zero you can always, that will be much in those gauges you don't get these particle states with negative probabilities it's sort of interesting it makes me think that well If you insist on a Lorentz-covarian gauge and it gives you this horrible stuff that you've then got to sweep under the carpet, it gives me the distinct impression that you're doing something you shouldn't be doing.

27:30 You're imposing this sort of symmetry and you're having to introduce some fictitious state in order to get away with doing that. But in this theory, it's actually perfectly natural to say that gauge fields are just three vector fields evolving on Aristotelian space-time. That is the natural thing. again is an advantage. And having this underlying preferred slicing also, I think, opens up an interesting approach. Can I ask you a question? So that your gauge principle will be three-dimensional? Yes, it's the function you say, for instance, vector potential A goes into A plus grad theta. That theta only depends on position, not on time. But I'll be showing these for the details. Maybe. Well, I've got a question, but maybe it's better for me to wait. Okay. Yeah, I think it opens up also a new approach to quantum gravity. But anyway, I think there's actually a better formulation of field theories. Just briefly, I'd like to judge people who might also think, well, there is a well-established theory of particle physics How are you going to do all this with this approach? I actually think that this is almost trivial. Let me just give a brief survey of what you might call pilot-wave particle physics. I'll just show you for instance. If I have Q, quantum electrodynamics. So I have a free field, then I have a free vector. These A's, these are three vectors. you have sort of three-gauge transformations, you know, like the magnetic field. These are two equations, these are just, well, probably not many quantum field theorists are very familiar with the temporal gauge, but there are people who have used it for particular purposes. These two equations are just, in the Schrodinger picture, Q-E-D in the temporal gauge, okay. This, you'd probably be more used to seeing that in the Heisenberg picture, you have a sort of field equation to operate A. You have a constraint here, basically, if you impose the condition

30:00 that the way functional, you write it as, you write it as a functional of A, of this field A, But you don't want it to actually depend on the gauge degrees of freedom. So if you impose the condition that when I change the free vector potential, I do a gauge transformation, the psi doesn't change. In other words, psi of a plus grad theta is equal to psi of a. If you impose that condition, then for infinitesimal theta, you get out this constraint here. It's basically saying that psi is not a function on the space of gauge-dependent fields, it's a function on the space of equivalence classes of fields. And of course here we have the de Broglie guidance equation for the field. In equilibrium, this equation here gives you basically what is called Gauss's law, okay, which is a sort of condition on the state base. And you have, and from here, this is QED and Maxwell's equation in temporal gauge. You'll just note at the bottom there, given any four vector field, the noise through a four-gauge calculation sets the time component equal to zero. The color QED, but it doesn't have electrons in there. Sorry, yeah, this is for the free, this is for the free, free electromagnetic field. The next transparent thing I'll show, if you do, say, interaction with a charged scalar field, it looks like this. I have a charge scalar field, which is a complex field phi, and I have my A, and I have now local three-gauge transformations. Sorry, before it... Yeah. Yes, sorry, what I mean is, if I just had the phi, the complex scalar field, you have an invariant on the global gauge transformations. for the electromagnetic field is theta.

32:30 Now, it depends on that. It's quite similar to what you do in the homilatavistic Schurling equation coupling is an external vector potential. It's the same sort of idea. And you have to introduce a gauge for a varying derivative. And what you basically get here is what's called scalar QED written in the temporal gauge. And you may say, well, What about if I have fermions? Well, there's no problem with that either. You just use Grassmann fields. It turns out you have to use the Van der Werden field, not the Dirac field. Again, it's a peculiar thing. If you try to use a Dirac field, the Lagrangian is linear in the time derivatives of the field. So the canonical momentum of the Dirac field is just the Dirac field itself, or actually the conjugate thereof. So your sort of guidance condition, the guidance condition is always canonical momentum equals gradient of the phase of the wave function. Canonical momentum is just the field itself. You'd have the guidance condition, which would just say the conjugate of the field equals the gradient. It wouldn't be a dynamical equation. But the Dirac field can be written as a linear combination of the first space and time derivatives of what's called the van der Werden field. The van der Werden field obeys a second-order wave equation. I've not written down here. This is the Lagrangian. It obeys a second-order wave equation. It's really for historical reasons. Dirac thought that he would... way wave mechanics developed Dirac was looking for a generalization of the Schrodinger equation. He thought, well, it has to be first order in time, and he thought that the field he'd found was a wave function. There's a sort of torturous history, but you can use the van der Werden field just as well. In the 50s, Feynman and Brown and various people published some papers showing you can do QED with you, you don't have to use a Dirac field, you can use the band of everything. So you can do a spin-half, and just to say there's no problem with, say, a non-Abenian gauge theory, if you're looking at the free, case of a free gluon field, it's just like the case of electrodynamics, except I have eight three-vector fields, okay, with three-gauge

35:00 This, this, this, all this, again, is just QCD, for the pre-drilled field, in the temporal gauge, okay, in the functional Schrodinger picture in the temporal gauge, adding in the Freud guidance equation for the actual drone field. And it's the same in electro-weak theory, you can just, you've got these three vector fields W and B that are related to the usual W and Z and A by a sort of transformation you know people do do electroweak theory in the temporal gauge as you sometimes, all you have to do is transcribe that, put it in the Schrodinger picture and add in it's quite trivial we just say that at the quantum level you can easily reproduce the standard model of particle temporal gauge, where all gauge fields, like your magnetic field, WZ, boson, gluon, they all have vanishing time component. That's all the, uh... Can I ask, in a very interesting discussion, but, I mean, what's this, is this reproducing? You really, you are starting off, you're sharing this. Yeah. I've thought this, I mean, in public experience. Yeah. You're adding in the guidance of creation, and you're pushing a certain choice of gauge, but other than that, that's not reproducing, that's just, you're taking particle physics, you're adding on the guy that's a quick question, that's it, that's the Birmingham particle physics. Well, I'm recovering it as a phenomenology. I'm saying that the fundamental theory is a field theory on Aristotelian space-time, And these are the equations. It's a non-local dynamics. It looks nothing like classical or quantum physics, fundamentally. In equilibrium, at the quantum level, where you have... Actually, as you get the quantum level, you have to assume that it's experimental. You basically function at the classical level. At the quantum level, you don't see the details of that field evolution. You just recover this, and in equilibrium, you recover the statistical predictions of quantum field theory.

37:30 You recover in that sense that they are a consequence, phenomenologically. I guess that's the positive that we're not seeing, because, you know, try and take the standard, try and write down the data score. Right, maybe what they're saying is, how do I get, usually one might start off with a Lagrangian. No, that's not my worry. You're worried that I just use the Schrodinger equation. No, no, no. In all of these theories there are problems with actually, you know, like And you can write down the guidance, if that's okay too, but to say, you know, thereby you've recovered the standard theory, I mean, a better way of putting it, perhaps, is you're beginning with the standard theory, you're adding to it the guidance condition, and then the further thing that one would expect to be done, to show that you've got a satisfactory value of the theory, is to actually compute the trajectory, is to actually show how... And it seems to me that part of the discussion then becomes one of those things of who came first, right? Because quantum field theory was there first. It looks as if, well, I'm just adding some... I'm beginning with that and adding some things. I'm using your theory. I mean, it seems to me if you look... I mean, maybe getting away from quantum field theory, but quantum theory generally, if you look at history, you'll find that the trajectories were never added in. Nobody ever completed. theory is often presented now as a completion of quantum theory. Historically, this is complete nonsense. De Broglie, in 1923, had phase waves guiding particles and was discussing interference effects that nobody had dreamed of that they would exist. Before quantum theory existed, Schrodinger took De Broglie's theory, where he had these actually relativistic phase waves, guiding these trajectories. He took that dynamics, and he used de Broglie's picture to, he found the wave equation for those waves, but ignored the existence of the trajectory. What happened in reality is that the trajectories were cut out, they were added in. I mean,

40:00 the physics, if you ask where did the Schrödinger equation come from originally, it came from de Broglie, looking at the principles of Maupetui and Fermat, seeing that they were similar, and thinking, ah, a particle must have a phase wave guiding it. That was his dynamic. And that is where we got the Schrodinger equation from historically. And so, it seems to me that in reality, the people who use the Schrodinger equation have just been ignoring the trajectory all these years, because in equilibrium, it so happens you don't need the trajectory. but that's not quite my complaint I tell you what, let's come back to do this okay, right, sorry if I went on and offered attention can I ask you a quick question which may be part of what Simon said you said a while ago some four slides ago that one could show how in quantum equilibrium you get phenomenological Lorentz covariance claim apply equally to the to the particle physics slides we've just been having like this that you recover phenomenologically the whole of particle physics yeah well absolutely i mean you recover the same so if you like if you like all you do here look if i just do that okay and say well in equilibrium i don't see the trajectory and i've got equal called psi squared. Those equations up there are just quantum field theory for a free gluon field in a temporal gauge. If you want, you can transform to the Heidenberg picture, which is what is used more usually. You could then introduce a time component and introduce four gauge transformations, if you like, to make it look the rents per variant and so on. And you, as in, just as in the particle theory, you recover ordinary quantum theory. You recover Isn't Lorentz invariant usually used in the particle theory to help restrict the visualization? Yes, yes, yes. Now that is an interesting point which I'll be talking about tomorrow. It is essential in ordinary quantum field theory that you start off with a Lorentz invariant Lagrangian. that guarantees that you will get Lorentz invariant in the field theory. Not only does the field equations look Lorentz invariant,

42:30 but it actually guarantees the existence of generators, operators satisfying the Poincaré commutator algebra and so on, which you need in order to be sure you've got a Lorentz invariant theory. But, uh, the question, basically your question is, why, this, the Hamill, the form of the Hamiltonian in the Schrodinger equation, if this Hamiltonian was different, if there was a minus here or something like that, then I would not get Lorentz invariance in equilibrium. So your question is, how do I restrict that Hamiltonian to make sure I'm going to get Lorentz invariance? So that's a question I'll be discussing tomorrow. So, just a quick question about, if you start with this non-Dirac particle field, and you... Van der Verden field. Van der Verden field. Yeah. And suppose that you impose local gauge invariants in your form. Yes, right. Then you're not going to be able to recover natural equations in the usual Yang-Mill sense? Well, the van der Wieden field is an electron-positron field. If you impose local gauge invariance on it, you would couple it to a three-vector potential, which would represent the electromagnetic field. It would... yes. Sorry? It would represent magnetic the electromagnetic field it's actually similar this theory I wrote down before for sort of scalar QED this phi would be a two-component van der Werden field you do the same sort of thing this fire would have an index alpha as values 1 and 2 you do the same sort of thing you have this A E is just minus the time derivative of A it's the electric field the magnetic field is just the curl of A this is just electrodynamics in the temporal gauge usually you have E is minus grad A0 sorry but there is no A nought here

45:00 E is minus the time derivative of A and B is the curl of A you don't need A nought I mean it may sort of sound weird but look at this chart so you can always choose a gauge where A nought vanishes what I'm saying is I'm not taking the view I pick a gauge where A nought vanishes I'm saying there never is and there never was an A an A nought it doesn't exist it never did exist in reality you have a three-vector field. And it's just in equilibrium. You've introduced an A-naught to make it look Lorentz covariant, because in equilibrium you get this phenomenological... It's just surprising to me. It's remarkable that taking this view when you're playing just a local gauge symmetry, you end up getting... you end up getting Maxwell's equations in the unilateral sense. Yes, but it's a three-gauge symmetry. The gauge function doesn't depend on time. And you, yeah, I was surprised myself, actually, when I first looked in. You don't need anyone. Well, I think I... You're doing electromagnetism in a stamp, okay? That's right, yeah. I mean, I think what I found... No, I'm not saying... One thing is to take electromagnetism and do it in a certain gauge, fine. The other thing is to play what's essentially a game that's often played in quantum field theory, generate the field by a lot of change. Yeah, in the Yang-Mills trick. But given that you can do that, then it must sort of go back to a certain gauge and get out the same equation with that gauge. Is that obvious? Well, all you've done, yeah, you've you do, apply the same principle but it's local gauge transformation in space, not in space-time. They're not the time-independent. And so you get out a three-vector field rather than a four-vector field. And I found it surprising at first, because it's often said that A0 is somehow, you need it to account for Coulomb interactions. A lot of textbooks say this sort of thing. But actually what happens here in this gauge, it's just the longitudinal part of this three-vector field that Darwin was on. I'd better rush on, because I've... Oh, you've been interrupted, and so... Sorry, I have an excuse for an extra 10 minutes. Just a quick thing about gravity. It seems to me that the way to go, or at least the way I've been trying to go,

47:30 is to say that you've got this Aristotelian space-time, and the third slicing, this non-locality, and it's the third quarter dynamic. And what you should do is imagine that the three-space becomes curved. You now have a three-geometry. and that pre-geometry evolves in time but I've always got a preferred and absolute time to have a theory of this three-space whose geometry changes with time I'm trying to find the dynamics of it and this theory is not complete in some attempts and suggestions there is another school of thought well, school of thought I'm the only member of this school of thought there's another much larger school of thought that I think began with Vink in 1992 a lot of papers have appeared on this in recent years, published in all sorts of journals what they do is they take sorry, I should have mentioned that in this theory I've got I say that the three geometry evolves with time before I had a field evolving in time I had a wave functional guiding the field the wave functional was time dependent it's got a Schrodinger equation and what I envisage is a similar sort of theory wave-functional obeying a time-dependent Schrodinger equation. It will be a functional of the three-geometry in absolute time. And we need equations governing the evolution of this three-geometry. What other people do is they take the Wheeler-DeWitt equation and this peculiar time-independent version of the Schrodinger station. The wave-functional is just the functional of the three-metric. and what they do is insert the de Broglie trajectory for the three metric and you just say the gradient of the phase of this wave function gives me proportional to the canonical momentum which is proportional to the time derivative of the three metric I get out the guidance equation saying that the time derivative of the three metric equals proportional to the gradient of the phase of this time independent side so you get a moving three matrix and a lot of people seem to think that this solves the problem of time and quantum gravity and so on I find I don't understand this it seems to me that if you look at this theory in the quantum or classical limit you don't see the details of the trajectory what you do see is the statistics given you

50:00 squared, and this psi is time independent, you're stuck with the same problem, that there is no change. There is change going on at the sort of sub-uncertainty level, fine. See what I mean, let's say for instance how you would try and arrive at the classical limit. Let's think about the simple theory, low energy theory of one particle. Okay, I've got this wave function guiding these particles into Breuven theory. How does a classical limit emerge? How it emerges is that the little non-relativistic wave function may have some little Gaussian moving along in space. The particle is sitting somewhere inside it. We don't care exactly where, as long as it's somewhere near the voltage packing. The motion of the centroid follows Earth. It's very Newton's law, approximately. That is how you get the classical limit. it's not true well some people think that it's putting the quantum potential equal to nought is the point, but if I had a, say, a very large, broad almost approximate plane wave, quantum potential is negligible and the particle moves in straight lines, but it's not a classical system, because if I open the window and make that wave pass through it you'll get diffraction and over there on the walls of that college you won't get you will get an interference and it's not if you do something to it on an everyday classical laboratory level you don't get classical results it's not a classical system to get to have a system actually classical behaving classically under experimental operations of the classical you have to have this little localized wave packet moving around okay so you have this sort of thing with a classical trajectory. If I had a psi that's very broad in this sub-quantum trajectory, that can never be a classical. In fact, my point here is that because psi here is static, there's no way you can build up a moving localized packet in configuration space. If you could build up a localized packet, fine, but it'll just be sitting there at the point in configuration space. what people are actually doing they've got a static function you've got this sub-constant trajectory

52:30 which is moving they're assuming that we can somehow see that and that that accounts for the change that we think the universe is expanding because this thing is moving what you're doing there you're assuming that we can see actually this trajectory is defined to an accuracy that is much smaller than the uncertainty width of this packet sign we can actually see the trajectory inside the wave function. If we could, you would see non-locality, you would see all sorts of crazy things. Our senses are not receptive to that level. So I really think that this... By the way, the same mistake is made in what's called the WKB approach in canonical quantum gravity. They have a sort of WKB wave function, and they associate trajectories to the metric. but it is actually a form of pilot wave theory a simple form of pilot wave theory and in fact most papers on quantum cosmology have their predictions based on that theory and it's assuming actually that you can see inside the wave function the trajectory is defined to an accuracy much smaller than the uncertainty principle allows but uncertainty can be psi broad like in your picture rather than yeah, well they are approximately plain waves The amplitude varies much more slowly, and they are broad. In some papers you see this problem discussed, they call it the sort of Schrodinger cat paradox with large or something like this, but I don't think it quite realises that they're assuming that you're seeing inside the wave function. How long do I have? Ten minutes? A quarter of an hour? I do? Right, well, so I'm going to get on to now discuss the theory of measurement. Theory of measurement. I haven't discussed theory of measurement I'm going to discuss theory of measurement eventually it will be for field theory in particular but for the moment I'd like to just discuss this in general terms now not necessarily field theory but what are quantum measurements

55:00 I think it is well, for a start at the fundamental level in this theory I've got this evolving, this trajectory whether it's particle positions or field configuration, that is the theory fundamentally it's non-local if I could see exactly what this particle is doing I could deduce that someone over there is moving something because there would be non-local action and so on and I could, if I were a sub-quantum demon that is, if my senses were receptive to the details of the trajectories the way I would do a measurement would be like this I would have this particle here and there's a particle over there and they're entangled the velocity of this particle depends on the position of that particle if I look at the velocity of this particle of that one. Just the same way Newtonian gravity, if this particle is accelerating because there's a distant mass, I can deduce the position of the mass. So that is true measurement in this theory, which we cannot perform. But they are, fundamentally, they are measurements. what are called quantum measurements are just are really very distantly related to they're not well, they're not really measurements they're called measurements for historical reasons and I think the historical reason is this that in the early discussions with Bohr and Heisenberg if you look at the early papers they have you'll see a mass on a spring and a diaphragm and a shutter and they are, say, measuring the momentum let's say, how do you measure the momentum of a particle? And in one way, if I have the particle it's in this little box, okay I want to measure its momentum now how do I measure its momentum? If I open the box and the particle, say, flies out that way and the long way away goes click I found the particle here and I long it took. And I divide the distance by the time, I get a velocity. I multiply by the mass, I get a momentum. And I say, ah, that's the momentum that the particle has. I've measured the momentum. Because all I did was free it. I just switched off a confining potential. And all the early papers just assume as a matter of course that this is

57:30 how you measure momentum. Now, why is that a measurement of momentum? You're assuming, Newton's first law. I mean, that would be a measurement of momentum in the Atomian mechanic. It's not a measurement of momentum in pilot wave theory, in fact. You know, if that was the ground state of a box with a real wave function, the particle could have been at rest. When you open the box, the wave function starts to change and spread and drags the particle along with it, such that at large distances, the distance shall we divide by the time is multiplied by the mass is equal to one of the momentum components that his wave function had, but you haven't measured the momentum. So, what I'm saying is that they're called measurements because quantum measurements are actually just formal analogs of classical measurements. It began in a simple-minded way with people talking about masses and springs and diaphragms, and this was then generalized to a fully-fledged abstract mathematical theory that you create formal analog of a classical measurement. This is a case of an ideal von Neumann measurement, okay. let's say I have well, classically let's say I want to measure some observable q, it could be an energy or angular or something writing in terms of Hamiltonian mechanics The mathematical analogy is very clear. If I have this interaction Hamiltonian, where PY is a momentum conjugate to my apparatus variable Y, I've got these initial positions. Hamilton's equation gives you this evolution, that the final point of position Y depends on the initial value of Q. If you look at the point of position Y, you can deduce the value of Q. This is an ideal measurement classically. Neumann says, well look, just replace everything by, turn everything into an operator initially I've got this sort of way, but here's a superposition, and I assume that I say

1:00:00 there is some attribute Q, represented by an operator, big Q, I'm trying to measure it, see I'm going to measure it, and this is how you measure it, you have this interaction Hamiltonian, if you ask, well why is this how you measure it? The reason, actually, is because it you get this separation of branches and looking at the point of position singles out one branch which is associated with one value of Q what is a measure is it's actually a formal copy of an ideal classical measurement and the reason you think you're measuring something Q correctly is because it looks like the sort of operation you would do if you were going to measure Q for a classical system See, and Bohr and Heisenberg believed that classical language was fundamental, and that you had to discuss experiments using the language of Newton and Maxwell. And that made this thing seem so plausible. Now, what happens, because you believe that you have measured Q, you believe you've measured Q because this would be a correct measurement of Q if it were classical, and you believe classical physics is somehow fundamental to discussing measurements, you say, this is a correct measurement of Q. So what conclusion do you draw? this fatal conclusion that a system with wave function psi q possesses an attribute whose value is little q. Right? You could call this eigenvalue realism. Okay? This is the fatal conclusion. Okay? And this is the root of the whole problem in quantum theory. A system with wave function q possesses an attribute whose value is q. Now, what has made you think that? What has made you think that And I would say that this sort of argument I'm giving here doesn't really depend on pilot wave theory. Pilot wave theory is a good example to show, or a counterexample. But it's a general point. What makes you think, okay, that you have seen or prepared a system with an attribute whose value is Q? What makes you think that? You think you've done it because the operations that you perform would correctly measure Q for a classical system. with this peculiar philosophy of Bohr and Heisman which has carried on appealing to those same operations or formal analogs there are now the point is I'm sure everyone here knows

1:02:30 that observation is theory laden if I'm a chemist before Lavoisier I believe that when something burns it releases phlogiston and I go about measuring the release of phlogiston has a negative weight. Again, I've measured, I've shown that progestin has a negative weight. Okay, but you're not measuring the release, you think you're measuring the release of progestin, you're actually measuring the absorption of oxygen. You're theory. And it's a similar thing of course, another good example is if you discussed general relativity using ideas from Newtonian mechanics, you can get into all sorts of trouble. if you assume Newtonian gravity in a general relativistic context, you think you're measuring something, really you're not, and you get all sorts of odd, spurious results. So the point is that the theory used to interpret an observation makes you believe that you've measured this or you've done that. Now, if an observation is interpreted using the wrong theory, then you get havoc. You do get havoc. I've written havoc. And you get havoc with an exclamation mark. I mean, maybe, I mean, if I've got time, I'll just give this example that I think is quite nice. Well, I mean, maybe I won't. Maybe I won't. I mean, there are some examples you can give in general relativity, that if you use ordinary turning gravity intuitively to think you're measuring something, you come out with nonsense. so I think that's pretty clear the consequences of course because you think you think that the system with wave function is eigenvalue realism possesses an attribute which values cube because you think that well then you get in trouble because if I have this side Q it's not an eigenfunction of another operator and so this variable this other variable seems to have no definite value and you get all this sort of schizophrenia and you don't know where they're coming or going so what I think sequence here conceptually is that the reliance on classical operations led to this eigenvalue realism, which in turn leads to the quantum schizophrenia. So quantum measurements are usually not true measurements. True measurements really take place at the sub-quantum level. We can't perform that. They are just a particular

1:05:00 kind of evolution that formally resemble a classical measurement. What you're doing here Quantum theory says, I'm measuring the observable Q. Pilot wave theory, you're just causing the wave function guiding the system to evolve into Psi Q. In general, you're not measuring anything. You're just creating a certain sort of state. Quantum theory says, oh, the observable Q has value little Q. No, in general, the wave function guiding the system is simply an eigenfunction we operate. So, really, this quantum theory of measurement is really just, it shouldn't really even be called measurement. I mean, they're always quite right to emphasize that. It's a certain type of experiment. Now, one point, a crucial point, is that the system ends up being guided by this little packet side view because there's a separation of packets in configuration space. now, and that gives you a sort of effective wave packet collapse because the actual configuration can only be in one place it can only be in one packet or another there seems to be an impression, there's sort of misunderstanding going around this depends a lot on the fact that it's a particle theory and that I've got a particle trajectory that particle positions Yeah, the particle positions are, as it were, the basis for different experimental results. You can always boil observations down to particle positions. I think Bell overemphasized this point, because in reality, the fundamental mechanism that, as it were, solves the measurement problem is simply the separation mechanism in configuration space. each point of configuration space represents a distinct physical state but the actual physical system it could be anything particles, fields, the geometry of free space colours any abstract space you wanted as long as the wave function in certain conditions that we call measures it separates into two non-overlapping branches

1:07:30 And the other packet, effectively, is no longer dynamically important. There is a separation mechanism. That is, it doesn't matter what sort of configuration space it is. In field theory, in fact, what you would have distinct points here must represent physically distinct field configurations, which, for instance, in electrodynamics, you can use point would be an equivalence class modulo-gauge transformation the fields themselves are not real it's the equivalence class of fields under gauge transformations corresponds to a single point two configurations particle positions for the apparatus are not required let me discuss seems to me the sort of general von Neumann so-called measurement. We're trying to have two interacting scalar fields, little phi and big phi. Well, one you can call it the system, and the other the apparatus. Of course, it works. The initial wave function here, the system, is a superposition. I have a superposition of different eigenfunctions of this operating omega. And the apparatus, this is a product state with an appropriate Hamiltonian and to sort of form von Neumann and use it as a result. This will evolve, at least just be the continuous generalization of Hamiltonian, this will evolve into a superposition where now these packages, this could be, if you like, the zero state of the apparatus, and I have these different states for this field, the wave functionals for this field, negligible overlap in the space of the big five. It's just analogous to the X's and Y's of the ordinary, this is sort of the, in a sense, the pointer, I suppose you want to call it that. Now the point is that the wave functional, the little five things are guided by this wave function, but the motion of my system field, if you want to call it that, will at the end be guided by just one of these packets because these don't overlap. I mean, if you've actually done what a quantum measurement is supposed to be and it generates this, these don't overlap, it will be guided by just one.

1:10:00 I mean, this process is by definition. It causes the system field to end up being guided by just this, which is an eigenfunction of this, of greater omega. And by definition, we call that a quantum measurement of omega, with a result of omega n. Of course, it's not really a measurement, it's just that. This is just a field theory generalization. Now, in order for you to get what you call an outcome, in this theory, you have a well-defined evolution all the time. If you're worried that I'm sure this, you only end up being guided by one packet. it, if you look at it, you'll see that the necessary and sufficient condition is that the functionals for this big phi, they have negligible overlap with respect to the field values in at least one small region of free space. And one way of thinking about that, if you looked at the particle theory, say the apparatus is made up of thousands of particles, I want the different apparatus wave functions to not overlap all you need is that with respect to one particle making up the apparatus the apparatus wave functions don't overlap and that's it it's similar here, all I need actually is just one small region of three space where say if I've got a chi 1 and a chi 2 chi 1 I don't know, let's say chi 1 square, mod square that the probability for the field to be non-zero in this small region is zero. The other one says it must be non-zero. That would be an example. It has to be in at least one small region of three space, but there is no overlap in the configuration space of this big find. Is that fairly clear? Can I just say a couple things? First of all, am I right in saying that what you have just said is roughly orthogonality in a tensor product space, i.e. zero in a product. It's sufficient for that, that you have zero in one of the factor spaces, because the inner product in the product, because that's essentially what you're doing. You're securing a zero for a single particle out of the thousand,

1:12:30 or for a single little region, when you analyze the field case in terms of... Yeah, but the other thing, a more general comment that I wanted to make was that I completely agree with all this, of course, about it not being measurement. You said it's a particular kind of experiment, but there is a traditional word that you might endorse for it, which is preparation. yes well that then you could well if in the ideal case where at the end it is actually guided by the little side q you could call it preparation of a system being guided by it but there are of course non-ideal measurements where you don't even you're not left with an eigenstate so it depends on the you're establishing loosely speaking a correlation between the final state of what you call the instrument and the initial pre-interaction state of what would be objects. That you do, the interaction in one time gives you that correlation. So that's why you call it that. I mean, you're doing some sort of correlation, right, okay, but what, I mean, just a simple correlation doesn't justify you calling it, say, I've measured momentum. Call it what you will do. But you may have actually created the value, you generate the value so it's not you're not seeing what you think you're seeing just my final discussion about that just final thing, that's sort of saying what I just said for the case where you think you're measuring particle position what you would have and maybe I should I have this here, okay, a superposition of different functionals with this apparatus. What you would have here, you've got the apparatus variable Y, which is built out of this field big 5 that I had. And the apparatus is built out of fields. And let's say I've got some apparatus variable Y that's really built out of this field. We saw before, if you remember, that the wave function for a low-energy particle state is just psi-nought, the vacuum. This is here, the vacuum wave function multiplied by a term that seems to be by a time this is a non-relativistic wave function. If I had a superposition of these,

1:15:00 this is a low-energy state with non-relativistic wave function psi-1 that may be peaked here. essentially state with non-existent wave on the Psi2 that we picked over here. The likely field here is spread over both. Remember we saw it's sort of essentially a linear combination of Psi, a little Psi, which is sort of Psi1 plus Psi2. What happens during a so-called measurement of particle position by definition makes the system field end up being guided by just one of these functionals. telling you what will happen is that that will evolve into this, where now these two apparatus packets don't overlap, have negligible overlap. And the field level 5 is now just guided by one of these. And now the probable field is sort of just peaked around psi 1. So what actually happens, I mean, the field is sort of constrained to evolve towards one of these packets. It's a bit like the momentum that you're creating. Particle position is actually a sort of contextual variable. It wasn't there before. It's just created. You've made the field concentrate in a certain region. That's it. I'm sorry. Thank you. Right. I do have a lot of strongly held views that this isn't a problem of measurement. To pinpoint the issue of mass transparency, you can't say by definition, so long as this is a measurement position, What you've got to show is that by virtue of the dynamics in the field distributions of which the accesses stay localized. And you said nothing whatsoever. Hell no, they don't have to stay localized. Well, if they don't, then in what sense... Well, all you need is that... I mean, looking at the example, the field of the apparatus could be completely delocalized.

1:17:30 Let's say it's the pointer, as it were, might be the value of magnetic flux in this room. So let's say there were two values. It could be that way or that way. Well, not if it's anything that we see. Sorry? Not if it's anything that we see. The pointer has to be seen by us. So Simon wants it to be something like the center of mass of an array. Look, I don't really care what it's made out of, but I want it to be local. Well, hang on. What I see are local events. I mean, this is what's right about that. He's saying, look, we always see local events, and the measurement problem, that bother is to, how is it to recover local events? Well, hang on, I mean, a measurement, the apparatus does not necessarily have to function. I mean, it might be that you've got a pointer, a local eye pointer that moves around. It doesn't have to be there. Electric field intensity or a magnetic flux or... The colour of a wall. Sorry? The colour of a wall. The colour of a wall. If it's anything that we see, as a result of an energy, it's a local thing. That's what we see. Now hang on, when you say what we see, are you talking about you see the apparatus? The apparatus, the actual instrumentation, which is built out of these field configurations. What we actually see, all those are localised objects, local events. what you're asking is how do I account for the fact that say there is a localized piece of equipment at one point in terms of fuel kit why doesn't it spread well I mean one thing let's first get this do you agree that in principle you could do measurements of a completely different type you don't necessarily need localized equipment not fundamentally. It may be that we often do that. Well, look, I don't agree with that, but let me grant you it for now. I don't agree with that. But let's grant it for the few... Right, okay, well... Let's focus on the experiments that we really do. Okay, the experiments we really do. The fact that there exists localised... You're asking me to explain... I've understood you rightly, to explain the fact that there exists localised equipment in space. Well, and in particular, how come at the end of the measurement we see a localised position from the point of a point of place in a particular region of a dial Right, well, hang on will you grant me that it starts off

1:20:00 because if it starts off if it starts off localised so I've got, say, my chi of a field that is concentrated such that the field has to be in a certain region of space probabilistically then just by construction of the Hamiltonian operator it's just a generalization of the von Neumann thing it does make it turn into packets that don't overlap anymore I mean, you could have set it up so I've got my chi-naught which is sort of the zero state and I end up with a superposition, chi-naught plus chi-one chi-one does not overlap with that but if you're asking me to explain how is it at the beginning? Maybe that's what you're asking. How is it that at the beginning it's localized? No, no, hang on. Look, I mean, there's two stages to it. I do indeed want to push you on how is it in the beginning of it. But look, if we can just keep track of this. Granted, it's localized in the beginning of the beginning. Right. It evolves into what we normally say. It evolves into its position of two point positions. If we were going to be using this... Right. But if you've done it properly, the functionals for the pointer, as it were, don't overlap in the field space. I think the field space, I don't think that's correct, because the field space, you're looking at distinct field configurations. That's where the criterion is no overlap. That's right. And it's because the distinct field configurations are, or above, the orthodonality condition at the level of those things. It's not an overlap condition. I know, it is. but they mustn't overlap significantly in the space of field. So if, with respect to the initial functional, the field is inevitably concentrated here, then that field configuration, if I take the other, say the chi1, and insert this value of the field configuration into that functional, I should get essentially zero. with respect to this other branch of the apparatus packets, if you like, this field configuration has vanishing amplitude. To some extent, I think, I mean, to some extent, I think, actually, the answer to your query is surely this,

1:22:30 to say that just as we've been talking about the effective wave packet collapse for the system, which is a result of the separation of packets in configuration space, so that the system will be driven in the way I was talking about preparation. Right, the same thing happens in the apparatus. The very same argument will make the apparatus field configuration, or in a non-relativistic point particle scenario, the point particle that represents a definite outcome of the pointer. The field configuration or the particle pointer will be driven by just one of the two packets as well. I mean, the argument is symmetric about separation or orthogonality pushing the system by just one component. It's not symmetric because the difference in configurations is not a difference between one of the configurations. It's a difference in the configuration of classical fields. But those classical fields don't have to be localized. But... But if it happens to be... No, no, that's right. There's nothing... Well, you see, maybe what you're asking is, why does it start off localized? Maybe you're asking, why is it that at the beginning I have a pointer that is a localized field? I'm not particularly resting the argument on that. But if I can see why it starts off localized, it would always be driven into localized configurations. Then I guess I'd begin to see how come it starts off localized too. Well, okay, maybe saying to show that it is driven to something that is also localized, and that would, what you, I mean, by construction, let's say the two packets mustn't overlap. It might be that in the first packet, the field is localized here. In the second packet, the field is delocalized, but it's all over there, okay, so there's no overlap. So maybe to sort of show that, how do I account for an actual pointer that sort of stays, doesn't break up? Well then that needs some, maybe I should sort of work out some examples. But I think, no, no, no, it's a level of quantum field theory, no, no, no. No, sure, no, no.

1:25:00 That's a good intermediate state because what Jeremy was saying was that we will have one of two possible, one of two or several possible evolutions for the pointer each corresponding to the system having been, as if the system had been in an eigenstate. of the measured quantities to start with so we can reduce the problem to see whether the the the state of the of the operators will remain localized if we assume that the wave function of the of the system was an eigenstates of the of the measured observable to start with. So it can reduce the problem to that situation. And now we have to look to the Hamiltonian of the measurement interaction. And it seems to me there's nothing. The really important point is that at the end you don't have the overlap. Simon is then asking for something more that the field thing remains localized it was localized here now it must be localized over there that doesn't necessarily follow is that a question about measurement at all or simply about that's right I think yeah I think that is a question really about why is it that for certain particular types of measurement I have an apparatus with a pointer and how do I account for a pointer remains localized, which is sort of analogous to the problem of, presumably, you know, the wave packet of this particle here is quite narrow, and the Schrodinger equation says it spreads, okay? My little psi, the sort of phenomenological non-autistic wavefront spreads in time. How do you account for the fact that actually, as a matter of contingency really, of course the universe could have been a uniform blob, right, even in Newtonian physics. I mean, you can't derive the existence of localized equipment. It could have just been a fluid. Do you have a general answer against that whole problem that only simple harmonic oscillators do nicely compacted, the multi-field state, nicely compacted?

1:27:30 Sure, mass. Right. If that answered it, then we wouldn't need the bone theory in order to solve the mission. Which has nothing to do with that. No, what that, I mean, it seems to me that question there is asking how do you explain the maintenance of the classical limit if i have a t equal zero packets are nicely localized i've got this localized equipment so that's fine over time and it could be moving say for short time approximately classically okay one open problem i think still is how do i account for the fact that after a million years we've still got essentially classical equipment. Now that is a problem for the pilot with particles, anything, it's the same here. And I would have thought that it's to do with the, in effect, the packet is continually being in effect collapsed by interactions with other things. In this case, it would be interactions with different fields. A certain interaction, all I need, Simon, there, is that the fields it's interacting with, if the different packets in the branch that forms don't overlap with respect to any small region it doesn't have to be localized field configurations it could be just the value of magnetic flux in the real region interaction with that magnetic field will collapse in effect this packet and I think that but there's a sort of promissory note I'm a bit worried about that because it will collapse the packet in the sense of picking out one of the non-overlap regions in configuration space away the others yeah but the points in that configuration space now represent field quantities in the dimensional configuration space just because you've thrown away all the regions except one doesn't mean that the points in that region are going to correspond to fields representing lumpy classical type things no matter how many collapses of that sort there may be you may still end up with the packets that are left over which have the field configuration in them having almost every field configuration point in that packet representing horribly smeared out the type of things and not the long-term things you need. I don't see how a wave packet will add. Right, you're saying that the actual... Roughly, take a tiny region, keep it tidy by constant decoherence. Nevertheless, Larry's suggesting over time

1:30:00 this selected region, constantly maintained timing, can wander from a region where its members are localized field configuration to a region where its members are very delocalized. Yeah, I mean, whether that happens or not depends on the interaction. I think it's a matter of the field dynamics. Yes, that's right. That's right. I agree. Yes, absolutely. I agree. You've got a horrendous integral differential equation, and you need to show that that equation, by virtue of that dynamics that it encodes, drives these build configurations into local environments. I disagree with that. I disagree with that. As long as, are you saying fuel for the system fuel? because what I've done here I mean all I need if I write down a Hamiltonian that is just a generalization of von Neumann's A Q P Y to be a functional functional operator here the particle the system field is delocalized I've got a Psi 1 and Psi 2 if with an appropriate Hamiltonian as long as these psi 1 and psi 2 for the apparatus field as it were don't overlap then it will have to be I mean otherwise a dynamics just from the fact that the dynamics preserves psi squared will have to be that the field system field goes into one or the other because these two branches don't overlap it has to happen if I have the appropriate Hamiltonian that does this So the system, it's okay, if then you want to ask about the apparatus field, does that remain localized, then okay. May I add something? That's a chance. I want to make sure of it there. All right. Are there any questions about something else? May I just add one point? What the pilot wave theory is, the work the pilot wave theory is doing, is what Durian pointed out, I mean, the separation and the fact that we are going to have two dynamically distinct situations where we've got the system and the operators being guided by one thing.

1:32:30 of the total wave, or the other bit of the total wave, the pathway theory is taking care of the choice between those two. Now, your problem is, if you can give them one of those two, how do we know that the apparatus looks in a way close to what we usually see? That's your work. Especially in five minutes. And now, I mean, Jeremy's point was, really, pathway theory gives us the choice, tells us that it's going to look like one of those two, and that's exactly the same situation as if we had started off in an eigenstage of those to be measured, and that's how that looks. play at the game, is it? So, they placed it, isn't it?