discussion (contd.) / Thomas Filk: Quantum mecahanics, relational spacetime

0:00 ...in the background, or if you include everything, then the only Hilbert space you want to use is the relational Hilbert space, and you should get rid of those parts of Hilbert space that don't describe relational degrees of freedom. So I'm just trying to draw the analogy between the different possibilities of how you can interpret things. Direct connection to that? Oh, I'm in. You want the hand or you want the finger? You want the fingers? If you have the hand, then good on others. I have actually two comments on Klaus Myrna's contribution. I think Klaus Myrna once was arguing that we learned from Maxwell theory that all wave phenomena are essentially the same. But then Klaus Myrna would argue that you have to consider the sources of these waves. And there are, of course, classical sources like for our kilometer and shortwave transmitters where you have really macroscopic comments possibly that can produce really worse. And then we have these quantum sources like monoclonal atoms, which is the liquidation, and then you have this entanglement problem. So I think there's also this question of classical and quantum limit involved in this whole debate. The second comment would be that Klaus-Mörner's incoherence related to the Fox space But of course in all these quantum optical experiments you need the coherence of different modes. And this is non-touched. Also in any kind of double-spit experiment or in your whole bag, you have the superposition of paths. And with respect to the different paths, you need and have coherence. And otherwise you wouldn't see, say, the coherence on the screen behind the double-spit experiment with an ingredient this is also I mean if this was meant to be I think this was not so you know if you talk to to experimentalists you would be killed if you say that there's no opinions you would say maybe I had green every day that we have careers in this box space one I think the number of photons within one moment but not okay so then we address the two parts of your question The first part of your question was about whether there's a fundamental distinction between optical coherence and say coherence

2:30 in the radiofrequency regime. And so there was a time when I thought that was true, but I think that's a false dichotomy because the arguments you can make at the optical level, you can make equally well at the level of radiofrequency. So you could say, well, how do we generate radiofrequency? We take some electrons, we oscillate them up and down, and we get electromagnetic radiation. Now, if I treat those electrons classically as a source, then yes, I can have a coherent state for my life. But let's say I choose to quantize those electrons. Then all I get is entanglement between the electrons and the fields. And if I look at the reduced density of those radiofrequency fields, I find there's no coherence. So I don't think there's any distinction between optical frequency and radiofrequency. The only distinction is one of what we're used to doing. So basically, we're used to treating atoms quantum mechanically, to treating classically and it seems to me it's the same thing as super selection rules the places where we use super selection rules are places where we're just not used to treating the systems classically like we're not used to treating decs classically and so we have a super selection rule around and over so it's just a line an arbitrary line between what we're accustomed to and what we're not but it's not a fundamental distinction the second part of your question involved uh you know whether there's always coherence in your experiment i i agree that that the two views just say that the coherence is in different places. So one view says there's coherence for a single mode, and the other view says, no, there's only coherence between different ways of distributing n photons across two modes. And what I want to say is that that mathematical difference is really just the difference of how we choose to describe things. Physically, they're the same thing. Those two kinds of coherences are both describing a well-defined relationship, a phased relationship, between a system and a phased reference. So one, maybe fourth question, please. I can work out what happens for an electron and proton, and then take the partial trace and I get the image of the electron. That's not the way it's usually done, because there's a much better way of doing it.

5:00 You go to the center of mass, reference frames of the original one, and now it's a pure tensor product, and therefore you get a superposition for the electron. But the final result is exactly the same, whether you take it to be a partial trace and work it out as a mixture of the electron in the first case, or you take a superposition in the center of mass reference frame and work it out that way. So again, here is a question of convenience of what the reference frame is. And of course, you're not talking about two systems, you're talking about three. You know, the old Cal theorem, which says that pi, if I take a partial trace of a partial trace, it's the same mistake, a single partial trace of the two systems versus the one studied. Kelsey is the same thing. So I'm just making a comment that this period thing is already telling you that the way you look at it doesn't really matter. I mean, the final result is the same. I agree with what you say. one comment which is that the case where you do a change of factorization from proton electron to center mass, sort of fictitious particle which is really the relation between electron and proton, that's a relatively easy way of finding a virtual subsystem. What you need the modern apparatus of quantum information theory for, it seems to me, is these more sophisticated cases where you actually have a direct sum of tensor products like the one I showed, where your factor spaces of the fold over space but factor spaces of subspaces and it seems to me only recently that people have developed the mathematics to do that properly but yeah I agree. So thank you very much once more and the next speaker is probably just setting up

7:30 Okay, first of all, I'd like to thank you. the organizers for giving me the opportunity to talk about some ideas which well actually are quite closely related I think to what we just heard in the previous talk, particularly to the previous talk. And I have the feeling that somehow I come from the other end and you will see in what sentence it's going on. So let me start with a citation. It's always good to have a citation of Albert Einstein when you do something outside. I think most of you know that, and I don't have to read it. So what I'm going to do is put one concept at this position, which I think is used in physics most of the time in a very special way. And I'd like to consider that concept from a different perspective. And the general idea, to give in a certain sense the conclusion first, is I'd like to talk about a relational interpretation of what the position is. That is, I'd like to replace the notion of that by a notion of to have relations to. And so I think if one does that, and if one goes to their relational interpretation or position, then many aspects, important theory, which some people at least are considered as weird aspects, they become almost natural, as you can see. Some of these aspects have been mentioned here, part of the wave dualities, a bunch of paths, and so on and so on. I think if you look at this concept of position from this relation perspective, then these are not so weird anymore. And finally, Secondly, I have a kind of idea that maybe quantization in general means that we replace absolute properties for relational properties, and that becomes a very close call we just heard.

10:00 And I would like to give that also a more definite meaning towards the end of the talk. before I start I would like to discuss why do I consider position what is special about space why do I not talk at least at the beginning about properties in general and I would like to ask this question what is special about space in the perspective of Heisenberg's critics against the Bohm's model of quantum mechanics was not that it was more loaded. Heisenberg's critics was more that the model doesn't have the symmetry of quantum mechanics. In particular, the symmetry to exchange position x and p momentum, which, of course, in quantum mechanics is quite obvious, or But more general, in quantum mechanics, we have the freedom to choose any base we like. We can choose positions of base, momentum base, energy, or angular momentum as the base of Hilbert's base. And quantum mechanics remain somehow symmetric. But at least in the old version of Bohm's model, the symmetry was broken. So space and position in space have a special property in that model. It's much more difficult to formulate in momentum space, and it becomes much more unnatural when it's formulated in momentum space. So what is special about space? I think there is something special about space, which is hidden in the way in the symmetry that quantum mechanics puts to the space and momentum for instance, we usually treat space more than just potential positions when you think about momentum for instance, and suppose we take out all the more particles in the universe, suppose we could do that then the question is, is there a momentum space left and what is that space is it still an entity is it still substantial or is it just a space of potentialities of possible momenta. With space, we have the feeling that at least as far as we can

12:30 take matter out of the universe, something is left. And so that's one thing which makes space different for momentum. And another thing, I think in general relativity, it's trivial. Space is treated as manifold, while P refers more or less to the tension space, which is manifold. So there's also a difference there. But I think the most prominent difference between space and all other properties is that we require locality. Locality is something which we only require with respect to space. We never wonder how can a particle with low momentum and a particle with high momentum interact directly. But we wonder somehow how can a particle which is somewhere here and a particle which is somewhere at the other end of the universe, interact directly. And as I said, space is the only property in that sense, with respect to which we require this locality. Whenever we transform quantum field theory into a different basis, we get this non-local terms in the interactions, and only with respect to space or space-time we require locality. So some people may say, maybe it's just the other way around. There is one special basis with respect to which nature appears to its local. This is the one which we call space. But okay, that's a question which I'll leave to the philosophers. Two remarks before I start. I will mostly talk about spatial localization of objects and relation to space. And only towards the end of the talk, I will talk about particleization of events and relational space-time. And the second remark is, I don't know, has it arrived yet? No, not yet. Because the expression relational quantum mechanics exists already, and it's not really the same, I think, as what I'm about to do, so I will not use this expression relational quantum mechanics, but again, at the end, and I think you will see that in a certain way I'm just coming from a different end. Maybe we approach and we have the same ideas. Okay, so what am I going to talk about?

15:00 I just mentioned some of those aspects which at least in my opinion are weird about quantum theory. And then I will introduce what I mean by relational space and relational positions. Then I will speculate, and you will see what I mean by levels of speculations on the nature of these relations. Then, as I mentioned before, I will talk about relational space-time. At least I will make a few remarks. It's not even much to say about that. And finally, also mentioned before, I'd like to put the question that quantization is a step the properties in relation to properties. In what sense can we view quantization in that form? Okay, so let me start with these aspects. We are in aspects of quant theory. We have particle wave duality, or sometimes the question is raised, how can a particle be at two places at the same time? Double-slit experiments on theta in the parameters. Well, the standard answer to that, of course, is because it's not a particle. Because it's a wave. That's how I treat it and what's the theory. Now the standard counter argument then is, but why do we always detect particles on the waves? Or integer number of particles and not half integer number of particles. And then the standard answer, well, because it's not a substance field, but a probability amplitude. The absolute value of this field is the probability is measured, and this is where at least my concept of feel slowly breaks down, and where would I say, well, I don't really understand anymore what ontate level I should attribute to this kind of feel. Second weird aspect, spooky action at a distance, how can a non-local state change globally and instantaneously as a result of a measurement performed with respect to space? and one side and the standard argument here is that well it's a state it's a ray in Hilbert space and it gets reduced as a result when measurement like any other ray so nothing is special it's just that one ray changes into a different ray

17:30 but again there is a counter argument the state has special properties with respect to observables which are elected to position it. And that's why we call this state non-local. And if we attribute a multi-elemental state, that is, if we consider the state not only as our knowledge about the universe, but maybe something more, something which is there even without us knowing it, then this non-local reduction would define a non-local smootenating. Now, it doesn't contradict relativity because there is no energy flow, there is no flow of information there, but at least it would define such a simultaneity, even though we cannot measure it. Finally, we sometimes use quantization by summing over histories, and the question here, can we somehow imagine how a particle follows different paths and spacetime simultaneously? And all these weird aspects of quantum are somehow related to this property of position and these things which we all mean by locality. to be at two places, to have distance, to be on local, on space-time, et cetera. So the argument in a certain sense is that, on the one hand, we treat particles on a quantum level, we talk about interactions, we talk about entanglement, that it's all treated on a quantum level, but then we put all these things into a classical space-time and the question is, how do we put one quantum level into the classical level? And usually we do that by kind of embedding, by attributing the special position to objects or to fields. And the question is, that embedding is not where the mysteries come from. Okay, so let me come to relational space and relational positions in the sense I mean it. I will talk about it. I think I don't have to go over this list. Aristotle already raised the question if a position is not related to the surface of a body.

20:00 I think the clearest example of a relational space-time and relational position is given by Descartes in his Principles of Philosophy, where he really says if we could take, or if not we, he says God, if God could take out all the substance from a vessel, what would happen? And the argument is the vessel, the walls of the vessel meet and touch each other. And he describes clearly or change, it's not movement in some space, it's just changing the relations between the origins. There's this famous exchange of letters between Leibniz and Samuel Clarke. There is the famous criticism of Mach, in the mechanics of absolute space and absolute time, Newton. And there are more recent models, some of them already mentioned, or in some way or another they all consider space as relational and the question is what is positioned there in this relational space. So I'm looking at relational space in the way that there are certain elements which I'm not specifying. I've drawn them as dots but that's completely irrelevant there are certain elements and there are relations between these elements and the only thing which is relevant is the adjacent matrix after computations that is relabeling of the points nothing else there's no dimension on that level everything which we know about space is somehow a large-scale picture so on a very large scale this relational matrix looks like a smooth manifold with a certain dimension. Now, then the question is, what is position in space? And usually we think of position as to be at some point. That's usually what we say. Physically, the particle is something. So we treat it as being at the point. and movement is somehow there's a topic from one point to the other.

22:30 That's what we usually have said, the thing of positions. And what I would like to replace it by is this relational picture which has already been described by Descartes. position as being related to these elements which make up space structure. And then movement is just a change of these relations and then you see that in the end the relationship can be very well in two places at the same time there's no problem just has relations to these so this is just a different picture a simple picture to draw the same situation so uh with respect to the concept position. Particle can be at two places at the same time. Or, to give you a difference it is, can you go back and just define for me what the relational particle is in your picture? Relational particle is maybe not a good concept or a good expression. What is your definition of a particle such that you state that a particle can be a different mean another element which is not considered as an element of space-time. But what is the movement of the relationship position? Movement is just the change of the relations. Yeah, but you could also describe it as the moving part of it as part of it. You also describe it in that way. But you choose exactly that. Somehow you keep it in the middle. Yes, because the place where I've painted is completely irrelevant. I'm only using the relations. The relations among these elements, whatever they are, which make up space. And this one extra element, which I call particle, but which can be any other object, elementary object, which you like to think of. There are certain relations between this and the spatial elements, and these relations can change. But you also define the moving particle

25:00 as in your first hopping. Right? And then you also have different relations. But then I have a very special kind of relation, because the particle has only relation to one point at each moment. So that's in the sense an absolute position. that the particle has this property to be at that point x, and not to have relations to x1, x2, x3, and x4 at the same time. Thomas, wouldn't it be a kind of attempt to answer the question just to refer to the adjacent matrix? Yes, I could have drawn, I mean, I was wondering, right down, for instance, all the relations for a cube, so there are how many 12 relations I just write down eight elements with 12 relations and that's all and I think it's very difficult at first sight when you look at only these relations to figure out that it's cute but in the end that isn't this relation I think it's just a different way of looking at it it's just the same and changing the adjacency matrix, changing the end adjacency matrix is that movement. So these positions don't have an independent identification? What do you mean by that? They don't have an independent identity. You know, you're like number one, number two, number one. No, no, no, no, no, no, no. They don't have, it's just, that would be just a relabeling. Why do you draw lines just between the red point and those four black points? In principle, there would be relations with everything, that would be the general picture, but some of the relations maybe have weight zero. So I wouldn't draw those which have weight zero. Up to now, the relation is only there or it's not there at this point. Later, when it comes to the interpretation of the wave function, I say that these relations are represented by complex numbers. And then, of course, it's a relation to everything, but some of the numbers are zero. and then it's just the weights in a certain way I would say

27:30 I'm not changing quantum mechanics it's nothing changed there it's just changing how do I talk about the wave function not the wave function itself quantum mechanics remains the formalism of quantum mechanics is untouched so another thing is that objects which are miles apart with respect to the spatial properties could still be related in this relation of space. So if we define locality by the relations, that might be a different concept of locality compared to spatial distance. And that may be a possible way to circumvent those theories. If you are up for a theory with hidden variables, I'm not up to that, So if you're after a theory within variables, then such a relation of theory could circumvent valid theory. You can have locality at the same time in reproducing quantum mechanics. Of course, the question arises, what is spatial distance? So is it just the number of steps down here from one to the other? that would be the picture, something of the order of 12 to 14, and maybe in reality, we take this average distance or something. If we attribute a distance to that in the order of Planck length, that would be something of the order, let's say, 10 to the 33 or so. So what is the distance between these two particles? And there are two answers. It's the one who wants to treat things in a very simple way and say, well, the distance and flow of energy is only determined by those relations between spatial points. So even though they are related in this relational sense, they have spatial distance of the order of centimeters or whatever you like. But in the end, I would like to have all these relations somehow of the same nature. That's now another level of speculation. If you keep these kinds of relations as different, then I have nothing to change. But if I say these relations may have the same nature, then there is no reason why this party

30:00 and this particle will have distance one. Then, of course, there's a problem. So the question is, what is the distance on a graph? What would be the distance between, now I take these two elements? There are two definitions which are used in graph theory. The one definition, which is mostly used, is to take the shortest of these two points. That would be three in the picture here. But that's not what we do when we measure distances. Measure distances, we let particles propagate. So what we do is when we measure distances, we take how we somehow average all possible functions from A to B measured in a certain way, for instance, to the lines, something which is related to the mass of the particle, then we come to a propagator, and that may relate to final summation of the parts. I will come back to this later. In that sense, if there is one path, which has only length one, but if there are billions of paths which have length 10 to the 33, then one path wouldn't matter. So that would be a way out if one doesn't subscribe to the first simple solution, that distance is only defined with respect to relation to space. So let me now discuss about the nature of the relations. I have drawn up to now three different types of relations, the relations between particles, the relations between particles and spatial points, and relations among the spatial points. And my interpretation would be that the relations between particles and spatial points, that they are expressed in the wave function. And that wave function, in principle, is nothing else but to specify which kind of relations a particle has to the spatial point. Now, the relations among spatial points, I don't know. That would be up to a theory of quantum gravity. But what I know is that on large scales, something survives with these relations, and that's the metric. metric, we don't know where the metric comes from. It should come from some structure, and point of gravity and local structure.

32:30 And it could be that, well, no. We only know that on a large scale, this metric just expresses these relations between spatial points. And now comes the essential point here, the highest level of speculation in a certain sense, namely the relation between particles, may be expressed in terms of entanglement. So the question is, whenever two systems are entangled, in this picture, they are immediately related. So that would be the concept of these relations here. The question is then, suppose the relations among particles But the question is, are these the same relations here on this level, and are they the same on this level? Of course, that would be an interesting theory if one could say, well, the wave function expresses just to relate the entanglement between a particle and the spatial degrees of freedom. That would be, as I said, a certain speculative level, but a principal possibility. So in a way, how to calculate this wave function would be you take all the total entangled system and you trace out all the degrees of freedom except the particle and one of these points. And that should give you a complex number in this psi of x. That would be a possibility. Now I should make another remark entanglement is not a binary relation. Yes. Why does that give you a complex number? Pardon? Why? Yeah. I mean, this looks like you could have said all these same things about classical physics. I wonder where the complex numbers actually come in. Well, if you have entanglement and let's say you integrate that out only between two degrees of freedom left, then in principle you can have complex numbers entering there. when you start importing systems. And if you are up to a model of hidden variables, I don't know how to introduce complex numbers. One vision would be these lines express channels of information flow. That's maybe one view.

35:00 Entanglement could also be used in that sense to express channel of flow of information where quantum information flow is possible. And now to express what kind of channel that is, I could very well imagine public's numbers, likely I also used it in education hearings. I don't want to specify this anymore because as I said, I'm not up to a hidden variable model. Then you can specify, then you can say, well, maybe certain currents or I don't know of the whole party, but that's not what I want to do. Okay, let me introduce a new principle in a certain sense of locality, that is how can these relations propagate? The locality principle would be E1 and E3, so let's say two elements, whatever they are, particles, spatial elements, whatever, they can only become related if there exists already and element D2, such that D1 and D2 and D2 and D3 are operating related to it. That would be the simplest assumption, how changes in the adjacency matrix can occur. If these changes in adjacency matrix can occur arbitrarily, then again, I have to face the problem of non-eccality. So what happens is that whenever certain relations exist, that the relations can propagate between two elements which are already connected. They can be a new relation. Of course, relations can also vanish again. I'm not sure if I understand what they can do. By E, I just mean some elements as I said, which I don't want to specify further. For instance, if you look at quantum gravity, blue gravity. These can be, for instance, also some knots or so in these pictures. Okay, so consciousness, okay, there is something like... There is something which I represent by points. I wouldn't say they are points because the notion of a point is meaningless. Okay, mathematically. Okay, let's forget about this. Okay. Okay. So, okay, I understand that this black thing, right? These. What?

37:30 Then you wrote down these things like this sign or that thing. Right? They understand that. But then, on the road before that, you said you wrote articles. And you don't want to specify what is the math and math representation of that thing that you call . So, I'm not... Something when it is detected looks to us like a particle. So when you write down the mathematics you want to, what is, what is? Mathematics on this level, particles are also just an element. Just an element of, just graph theory. Let's say, but an element which has a different, let's say, label. So when I write down, you can write down, well you can write down an adjacency matrix for all these spatial points. And now we can add one more entry in your adjacency matrix, and this entry refers to this. So you just have a larger adjacency matrix. Well, the Schrodinger equation, I mean, of course, we can also write down the Schrodinger equation for discrete spaces. That's all. Right, never mind. I think on that, could one say that it maybe more distinguishes particle as opposed to a spatial time form and PA design, a particular dynamical behavior? It could be that it has a different dynamical behavior, it could be that it has a different property, like charge, which can be measured in a certain experiment, or spin, or whatever. At this level, we just have adjacent to the matrix, or chamber of adjacent to the matrix. and I guess you want the possibility also of space being dynamical, but right now, for instance, it's only particles that have a dynamic set of that space. No, space should also have a dynamic set of permanently changing. Space might also have a dynamic, but maybe the particles have different kind of dynamics than the space, and that will be something that will just distinguish what the particle is at this abstract class. I mean, the particles, of course, that I have suppressed,

40:00 the particles, there's also a problem in changing these places to make it to a space. But it should be somehow self-consistent. So the time evolution should reproduce, in principle, in the average, the same state. but the advantage is that you have a dynamical space picture and of course you can introduce a metric it's no problem to use a metric on the space you have this dynamics and well if you want to become speculative again when you enter additional particles for instance or matter with certain properties the distance with respect to space also changes because there is now this an extra relationship. So that makes it more or less natural that if one matters included the geometry of the somatic space changes, but that's again in a certain way we're speculating. So this is just an example of how these propagation of relations can be, you have an EPR state, you have an external measurement apparatus in state zero, you make a measurement of particle two which will make these two entangled because there is already entangled between two and one in the end you get a state which all three systems are intact and that's the state which we have before now the reduction process takes place which signals are only one of these two but before the reduction process process if the measuring So, again, only one half particle or so, I can end up with such an entangled space. Now, this is, as I said before, I've come to find some of the histories. The standard interpretation, or when people talk about the summation over histories, is that your particle propagates along part one, and along part two, and along part three, et cetera, et cetera. But in this relational interpretation, it only says relation one, which is between particle and spatial point, propagates log path one, and relation two propagates log path two, and relation three, et cetera, et cetera. So in this sense, I find the final sum of our histories much more natural to say the propagation of relations which can exist in parallel than to say it's the sum of this part plus that one plus that.

42:30 Okay, let me make a few remarks about relational space-time. The question is, what are elementary events? Because when it comes to relational space-time, it's now not objects which relate to space, but it's events which relate to space-time. So I have to say, in principle, what are elementary events? Now, this is, as you may know, a very difficult question, which I cannot answer, but it has been, for instance, addressed in these two articles by Rudolf Haag. So if you look at elementary events in quantum field theory, where you, for instance, envision the emission of quotient by an electron and a cumulative biomegraph as an elementary event, and these are events are usually treated as virtual or as possibilities, not as real events. But when you now calculate the contribution of the finding graph to the total process, what you essentially do is you place this event of the emission of the photon by an electron everywhere in space-time. You integrate over that point where this emission takes place. And for each position where this event would be, you have a certain complex weight again which now is defined by the product of the Green's functions, the Green's functions of the electron, and the Green's function of the photon, oh, the photon, sorry. So, in a sense, you can say, it's not that you have one event and you sum over all possibilities where this event can be, but you have one event and this event has relations to all the possibilities in space-time. So in this sense, this event is spread over space-time, but not in the sense of position, but in the sense of relation over conversation. So let me come to this final part. Could we visualize quantization as a step from absolute properties to relational space? The question, for me at least, arises in the context, what is a quantum theory anyhow? You give me a mathematical structure or a mathematical model and I should say, well this is a quantum theory

45:00 or this is a classical theory. what defines the point of theory. Now some people may say, well, if observations don't commute, there are non-commutative observables. But then I have a problem already with classical physics. In classical physics we distinguish between observables, which do not change the state of the system, and actions or interactions which can change the state of the system. And when the state of the system can change, Already in classical physics we have non-commutativity. I take this pointer and I rotate it first 90 degrees that direction and then 90 degrees that. Or I do it the other way around, 90 degrees that and then I get the different positions. So actions already in classical physics don't commute. It's only that we then have somehow the distinction between observables and actions. On the point of theory, somehow this distinction seems to be lost. everything is in a certain way in action and thereby can change the state so the question what is quantization for me to a certain extent remains open there is a mathematical answer saying well you have one parameter family of c star algebra and if this one parameter which we may call h bar is zero then the c star algebra is commutative and otherwise it's usually not commutative and that is what we call a quantization. This is not something which I can understand from a physical point of view. Let me look for the arguments that quantization may be described as the replacement of absolute properties to relational properties. And now I should say I make another step. Up to now I have considered relational properties only with respect to space. Now, let's assume for a moment that this relational picture can be taken for all properties. So, say A is related, or taking the scalar product of A and B, which we usually interpret as the transition amplitude going from A to B. Let us interpret this as A is related to B. So then, these properties, in classical, we have fixed properties, and we know it, on theory, we replace them by transition properties between states, so there's already two entities entering here.

47:30 We have seen this location or position in absolute space or as an absolute position and as a relational position. This difference I have discussed already. But finally, I think the most convincing argument for me that quantization is related to the transition from absolute properties to relational properties is that in classical physics, the same measurement, the same pure state, is always the same result. That is, we can express it by a function, an absolute concept. While in quantum theory, the same measurement or the same action right in the same pure state does not always mean the same result. But this is the relation between the initial state and the final state. It's just expressing the previous idea in a similar, in a different way. Now, I should say that we consider this relation picture in a more general context, and this is worked together with our written work, and the idea is here that we have a set of classical concepts. For instance, when we talk about properties, objects, these objects either have a property or they don't have a property. So we talk about, and we use this . But when we replace that by quantum properties, we say no, a particle or an object-informed system can have property A and property non-A in a certain sense. So it has property E1 and E2 and E3 as a, for instance, energy. So for properties of objects, we have the superposition principle in quantum mechanics, which I interpreted as a relational principle the expression-parataptic principle. For events, that is, a sharp-sequent point-like elementary events, which we have classical theory, these become events which are related to space and time, in particular, also related to time. And that means that the spread of an event

50:00 is not localized by a single point in time, but it's spread, in principle, also over time. So the present for this event is not a sharp fixed point, but an extended present. Now comes the concept which maybe comes most closely to relational quantum theory in the sense of Cardinal Valley, namely the separability of observer and observed, which we have in classical theory, is lost, and observer and observed are non-separable, or we usually that they are tangled after measurement. And that leads now to the concept of relational quantum mechanics. And finally, strict determinism in classical theory becomes replaced by some non-deterministic but in general non-determinism, some non-deterministic deduction processes. We use in that context the expression autogenisms. So the idea is that classical physics represented by these categories, which we use when we describe the classical physics, while a quantum theory uses these categories when we describe it as we describe. What we use when we say we quantize the system is the transition from these properties to these properties. Okay, let me come to the conclusions. And I think that one should consider in particular positions, but maybe in general any property, not as an either-or property, so a particle is either there or is not there, but rather like a relation between this particle and spatial elements. Then relational position may be, as I said, only a special case of relational properties in general. So up to that point, this relational picture does not change the formulas or quantum mechanics in any way, it's just a different way to talk about quantum mechanics, but at least in some concepts, I think the final summation of the histories, in my opinion, as a good example, the computation becomes more natural. But on the other hand, if you want to find a model with hidden variables, then this relational picture allows to circumvent Bell's constraints given by Bell's theory, that is you can have

52:30 a theory which is local with respect to this relation and still reproduces, has an effect of realism and still reproduces the result of what happens. Okay, thank you very much for your attention. Thank you very much, Thomas, for this presentation. I see a number of questions. Let me start there. Yes, you. Can you just, there seems to be a little bit of a problem with defining the particle. But it seems like what you just could say to everybody really simply is that, well, there are no objects. That the object itself is just more relations. And recall his comment that you just simply enlarge what you call the adjacency matrix by just one element. Yes, but this element, as I said, may have properties like charge, which the other elements do not have. But with respect to these relations, you're right. It's just on the same level. Just we're deleting the notion of object. I have five fingers. You have to direct me to that? This was also my question. Well, I can, of course, I can abstract and say there is no object. I have an abstract entity as a particle. I have similar problems I think. But when I start with your picture, I think it's a synthetic visualization of the picture, but at the beginning, the definition, I have a problem with the definition in a way. When you started from the neutral space picture and you showed the moving part in space, yeah? So I could also say, take that out, and let a whole move, and just take the net which surrounds the whole. It's a similar way, and then you have relations between these different nets. I do not see your first definition of this adjacent matrix, actually. Because you can have, if you are always relating to space and points. I can relate it to every state's point. So I have a totally, I cannot see how this really applies. Well, I would say the absolute picture of position is that you have a set

55:00 which you call spatial points, but it's just a set at this stage. And you have maybe a set of relations between these, once again, which allows you to draw this graph and to draw and to talk about distance, Let's say these concepts are given only for the spatial elements. A set of elements and these relations. And you do not specify what the relations are. I don't specify what the relations are at all. Now, I introduce a particle in a classical sense as it sits at some point. So I write down a function, x of an element, t, and this x is always a function of an element in this set. So the particle is at one point. That's the description mathematically. We use this function at each time space. At each time t, the particle is at one point in this set. Well, this I would like to replace by adding a new line and a column to the adjacency matrix and say this now is the extra element, the new element. be a spatial element, but then it's difficult to detect. So I'd like to have it certain properties which can be detected, like charge or so, but it doesn't matter at this level. So I add an extra line and column in the adjacency matrix and now add certain entities there, entities there. And that's a different concept of position. It cannot be reduced to the other one. It cannot be rewritten as a function of being at a space or point and not at the others. maybe more details later because there are three more I see you Joseph first of all can you just tell me why isn't that the topic theory already the content theory I think there are some elements missing furthermore I'm not quite sure there's the element and a distance is already put in there. And I would like to have the element of distance here coming out of this underlying relation of space. But of course, if I say forget about this underlying relation of space, I use already something which has an metric,

57:30 which has a distance, and then refer only to the particles in it. Then I have only the relations between the particles. But then I'm only on the level of where I just said, what is lost is the wave function of the computation. And as I said, I don't want to go away from quantum mechanics, I'd like to keep the wave function as it is, as a function which can be attributed to a system with a particle, and which gives a certain probability of measuring it somewhere. So you're not explaining where the quantum comes from? No, no, no, no, I don't explain where the quantum comes from. I think in some sense, the table is a primitive notion of our approach. Is this level of speculations? No, no, I don't want to explain one. I cannot also, the reduction problem is the same here as in quantum theory. I cannot explain why when there is a measurement made, one of these relations becomes special. So it's not that I can add more to quantum mechanics than it's there. It's only that I like to talk in a slightly different language about quantum mechanics, The language which leads to my sense is more appealing. When you say that position is between particle and special elements, can you say what is your ideal for this relation? What would be the relation? I mean, I understand the relation being x. Now, you have a different idea. Mm-hm. So what does it mean for a particle to be in relation to this place? Well, if I have now some classical notion of this relation, then I would again go to this hidden variable theory, which I would not like to do. But if you have quantum, you didn't want... If I'm purely quantum, then, well, what speculation would be that, let's suppose all relations which we have in nature are only of, let's say, of the type entanglement. Let's suppose that for a moment. Now what you have is a many particles, a many object system of which one object is special, let's say, because it carries a charge and the others don't. Forget about space. It's just a many object system. Now these objects are all entangled. An entanglement is not a binary relation. As I said, it cannot be reduced to lines

1:00:00 as I did it here. but that's not important for the argument, but entanglement is something which is attributed to the whole, and it describes the relations among these objects. Now suppose I would like to have only the entanglement described effectively, which one of these objects has, which has a charge maybe, to the rest. I don't want to describe the entanglement of the rest. So what I do then is I integrate out. I take part of traces leaving only this one object and maybe one element there that gives me a compliment that gives me some number I understand this this is left yes it's the relation so when you say that the Particle is in relation to position element. What's the meaning? What was the one that was entangled before? Do you understand when I say particle A is entangled to particle B? No, I don't understand because I don't understand the relation. Not in my language. I mean in quantum mechanics. Do you understand what it means that two systems are entangled? Okay, so that is the relation. That is what I call the relation, that they are entangled. I'm talking about the ratio of one particle to one space element. Okay, I consider these space elements just as objects like any other object in principle also. Just consider it as a set, let's say, of n objects. One object is the one you concentrate on, and the other n minus 1 are very similar. But then... Yes, but to but with respect to some of them the relation may be zero that is when you integrate it no no not just because it's not there because when I take out the traces then it turns out that what's left zero because the relation between these two well in the sense that it's a separate separable state we have four more questions that I should say that this will be closed after those

1:02:30 locality is connected to the very special culture Thank you.