Quantum Interference in Belnap's Branching Spacetimes

0:00 Thank you very much for inviting me to do that, and as Derek said, I'll be talking about a branching analysis of the double-slip experiment, and that talk is the result of a challenge I received a year ago. So, the challenge roughly was that branching was quite successful in analyzing bell-type inequalities. However, two branching theories have anything reasonable to say about interference phenomena, which are a distinctive feature of quantum mechanics. So I need to take another report on the ongoing project rather than the final work. And before I meet the challenge, let me paint the spectrum. So first, what branching spacetimes is. It's a possible word theory, in the theory of David Lewis or Sal Kripke. It's supposed to be mathematically rigorous, and it combines indeterminates with with some rudiments of special relative. Like in other possible world theories, it has double tasks. The first task is to provide semantics for languages with tenses and modalities, so languages containing sentences like, for instance, in yesterday's experiment the result plus was observed, but the result minus might have occurred as well. And the other task is to give the general metaphysical picture for the work. Now, there are a few things that recommend this theory over its rivals. One is, for the imagination, mathematical recall, in the terminism rudiments of special relativity.

2:30 The other advantage is that it works in terms of little structures, like events or outcomes of events, rather than large structures like possible worlds or even sets of possible worlds. Next, it has a mathematically well-defined block enough for probabilities, and these probabilities are interpreted as ways of possibilities or chances, and these probabilities are assigned to outcomes of events rather than to possible rules. So, given these advantages, a number of people applied the theory to physics or the physical phenomena. And so the first was a series of papers on the analysis of Beldbeck theorems. of the papers of Dernab, Sabo, and Lekovask, and myself. Quite recently, we ventured into the traditional task, namely Thomas Miller gave a branching reading of quantum mechanics as in the consistent history of the problem. Now, what was missing in all this application was the notion of the object, of Pashko, the Pashko moving in this space frame and the big question, where the probabilities come from, where the inference patterns of Pashko come from. So, that's the end of my background. Here's the overview. I begin with a fast sketch of the branching spacetimes. Then I will introduce the notion of locations of particles in histories. I will illustrate this on an example and location of particles in histories in double-slip experiment. Then I will call five months some overall histories approach, which will be a technical tool to provide interference patterns to managing structures.

5:00 And finally, I'll apply the machinery to the Radu's new experiment with and without detectives. So, that's the plan. And the first item is the branching space by DOA. It's a misleading name, I'll come to that in a moment. So, begin with the partial order set W. The elements of W are understood as concrete point-like possible events. The ordering means that X is in the past of Y, or equivalently, Y is in that possible future of X. The ordering is partial because some events are incomparable. Now, we are also backward branching, going this way, which means that we will have downward force like that. And if you think for a while what this downward force can mean, the only sensible answer is two causally unconnected events are in the past of the third event, or if you like two SLR events are in the past of the third event. So the immediate move from the interpretation is that whenever you see a diagram like that, you know that it is in a history or in a scenario. History is a technical term here for the notion of a possible world. So, going further, if you recall the name of upward directed set, Namely, any two elements of an upward directed set have an element about the truth.

7:30 So upward directed substances of W are also part of history. And finally, applying the famous Leibnizian intuition that whatever is compatible with the world should be a part of the world, we define history as a maximal upward directed subsecretary. Now, where we are? We card from the master set W histories. Once we have histories, we define S and R events, namely two events, R and S and R, and they belong to one history, but are incomparable by the orderly. Next, the important relation is that of two histories being undivided at them. So if I use for one explanation that aligns with history, we might say that history one and history two are undivided at E. On the other hand, history one and three are divided by E. The postulates of the theory guarantee that this relation, undividedness at E, is an equivalent relation on the set of histories passing through E. And this means that this relation generates the partition of the set of histories passing through E. So the partition is, in this case, here is one element of the partition, here is the other. And the elements of this partition of histories, H, E, are called elementary possibilities open at T. So in our case, the set consisting of two histories one and two is one elementary possibility open at T. The single of the history tree is the other elementary possibility open at T. So at no expense, we get next a Boolean algebra of possibilities open at E, and immediately we have a mathematical loss for probabilities, namely Boolean algebra.

10:00 Next, if the set of possibilities open at E contains more than one element, we call E a choice point for histories. And it can be proved that a choice point is always the maximal point of the intersection of some histories from the set of histories passing points. So, here we come to the point where it's clear that the name branching spacetime is not correct. Namely, it is at this point where we introduce something similar to spacetime. Namely, we postulate a relation, say spatiotemporal location x. And this is an equivalent relation, we introduce instants as equivalent classes over this relation. Now again, this is somewhat unfortunate terminology, but by saying that two events, x and y, happen at the same instant, we need that they have the same spatiotemporal location. There's no way to define the same spatial location or the same temporal location, otherwise the two together. Yes, but this specific relation is for us to say that these two events, here and there, for instance, they occur exactly at the same spatial temporal location. However, no way to define a notion that this then happens at exactly the same time as this one. So always work in terms of spatial temporal location, never in terms of space and time separation.

12:30 Now, as you see, the theory is quite general. You were using already in the first remark you made, the first definition, the notion of causality. Yeah, that was . But you don't need it to be a notion which has to be defined in terms of space time or capillary. Well, this relation here, in order somehow to convey my intended meaning, I call it causally connected or whatever. Well, once I've managed to convey the meaning, later on I could define causation, something causing something other. Well, I just refer you to Ben Lapp's paper in BJP S2024. So, that was all. of the non-spacetype separatists. Yeah, sure. Now, as you see, the models of branching space types could be very general, but what seems to be physically significant are Minkowski structures. These are roughly the structures from which the set of instants, that is the set of same special temporal location is Minkowski's facetime. So to visualize the structures, we might think of copies of Minkowski's facetimes being pasted Here is the picture of how they are pasted. So just think of a single choice point of two histories, H and G. The shared region can be open where G shares a region with H. So the version of the image is in the outward background.

15:00 It's getting more complicated if we have two choice points. The two choice points are separated from the picture, And again, the conversion is that the shaded region indicates where the human history shares its region with the reference history. So, it turned out very fruitful to develop the theory, not in terms of point-like events, but rather in terms of transitions. We do not subscribe to the general philosophy that the world is built out of transitions rather than points, it's quite heavy I'm thinking, but it's just a mathematical philosophy of prudefulness of that approach. So, the first notion is that of basic transitions, and to have a basic transition, you take a choice point, each, and some possibility open it. So to give you an illustration, in the first example we've got two transitions, one is C and the single knot H, the other is C and the single knot G. Here is the more complicated story, namely, we have here a transition consisting of C and the set of history first and third. First and third because the two are not divided.

17:30 Does the transition have to be to an elementary possibility? Yes, that's why it's called bad, basic. Your pi e is actually the elementary possibility. No, my pi e is the partition. It's the set of elementary possibilities. Sorry. The H, the capital H, is the element. Thank you very much. So, we defined a platophora of various transitions, which is a point, so I will not go into that. Apart from one distinction, namely, we need a distinction between a normal event, so to speak, and a disjunctive event. That corresponds, for instance, to the distinction between fragile and non-fragile event in the Jewish system. So the idea is that if non-disjunctive then occurs in a history, then all its parts occur in a history. As for disjunctive then, any two parts of it must occur in different histories. And this distinction is important because of the mathematical results. So first, if I draw your attention to Miller's paper in the most recent D.J. Pierce, it's And the result that he explained that is that probabilities are defined from basic transitions. And if there is no EPR correlations, probabilities of all other transitions, superhuman probabilities of basic transitions. The result important for the present talk is this, the probabilities of a transition to a disjunctive outcome equal some probabilities of transition to a contributing non-disjunctive outcome, scattered, therefore, non-disjunctive outcome.

20:00 At this moment, I finished a first sketch of branching spacetimes, and I'm starting to develop the theory first by assigning particles to branching histories. As we covered in monsters, here is quite a problem, just a geometric, geolactical theory, without any oceans. So here is the chart. Let capital theta be a finite set of systems and particles, and each particle has an association with Lagrange. Capital C is the finite set of choice parts in the DSD model, and capital T is the finite or not set of non-trivial-like basic transitions. So the first notion that I'm going to introduce is transitions that a particle side undergoes. these particles merely form, these transitions merely form a subset of the set of all transitions, and generally I'm postulating a mapping X from the set of particles to the power set of transitions. Now, what does it mean to say that a particle undergoes a second transition? it means that the particle, say, psi, is at the initial of the transition, and then, at least for some time, it is in every history, from the elementary possibility, we don't know about it. Death is not a transition.

22:30 Death is not a transition. Death is not a transition. We're sorry. Death is a manipulation. So now, in terms of transitions, I will look at a picture of how an object, a particle, So it's a branching structure. And these clauses are very similar to those of the miller proposed . That's why I call them miller-style conditions. So the meaning of the first clause is that no transition without the particle attack. So whenever there is some transition, that there is a transition of some particle. The second is more controversial. Namely, it says that in the logic structure, each particle enters at a minimal node. If we unpacking it, it's actually two claims. One is that the set of transitions can be partially offered, and that's provable. The second is just the postulation that in this partial order of the second condition, the meaning of Adam. And the meaning of that clause is that there is no creation. So everything is from the beginning. The meaning of the third clause is that no particle can be at two places at once. So if we extend somehow the notion of space-like separation from point-to-best to transition, meaning if initials are SLR, the transitions are SLR, we formulate this. If the two are SLR, then there is no particle that is assigned to these two transitions. Finally, in other clause 2, clause 2, it requires that if a particle is assigned to some transition,

25:00 then it must be assigned to a transition. Note that there is no symmetry here. Namely, it is not postulated that if a partial is assigned to a transition, then there must be some transition about it to which it is assigned. So, in other words, we allow for annihilation, but we don't allow for creation. Well, in this picture is the idea that a particle is also a branching object, or at least it has a branching line. So, there's no way to define simply a location of a particle. We'd rather define a notion, location of a particle site in an eastern edge. And before I do that, I postulate as well some special objects in the branch of structures, namely detections of the particle side. These are point-like events. So here is the definition of the location of the particle site in the history page. We say that it belongs to such a location. First, if there is a transition to which side is a sign, but second, there is no red transition between this transition and the point x. that the red transition does not belong to X, Z. So that's the meaning of the second clause. And the third clause says the particle is not detected in the wings of X.

27:30 Here's a picture of some history and the assumption is that the two transitions, black and black and red are involved in this position, meaning H is an element of the elementary possibility of black and the elementary possibility of red. So that's the cultural history from which perspective to look at this transition. And now we're saying, well, X is in the location of XI and H, provided there is a transition involved in this history to which XI was assigned, and there is no transition between this transition and XI that is not assigned to Let me show you the pictures there. Again, we have the same conversion. We are looking from the perspective of history-age at three transitions, U, T, and V. Pachku Alpha is assigned to U and to P, it's not assigned to P. Where is the location of the Pachku Alpha? Here in history H, the shadow of traditional existence. Here is a somewhat more complicated picture to postulate a detection event somewhere powder and it means then the need to remove the wings of the presentation. There's no

30:00 touch on the surface. So is that the same as the intersection of all the forward light cones of the transitions at which the particle is located? Say it again? Is it the same as the intersection of all the forward light cones at which you have Well, So, let us move with this machinery to the double split experiment. And let us consider first an experiment with a detector at once in the present. So, we consider three scenarios with different locations of the second detector on the screen. The pictures of the location of the histories are spotted. Now, if we change the location of the ductus at the slit, that is that the ductus is now on the right hand side of the slit, these three pictures result. And for double-sleep experiment, we don't detect those, it's efficient to explore. Now, if we return to the double-sleep detector, we ask the question, what's the probability of finding the election on the street just there, here.

32:30 We must be thinking of two different events, the and the start. Moreover, these two implants, D and D-star, although they belong to the same spatial temporal location, they cannot belong to the same issues, H1 and H2. So in the right question, in the context of those with electrons in the screen, we would then the question, what's the probability of finding an electron on the screen, on this particular location? We need to consider a disjointed event that consists of these two events in the question. then by the result, by the minimum result that I already mentioned, the probability is the sum of probabilities. So it seems that as in probability cultures, probability cultures with branch gives you the prescription. And you have states, you have the back of the states go ahead and out to the Philippines. There is nothing that enforces the summing up for the area that we see. So, where does the influence pattern come from, according to the present? Here, the idea, the next show idea, where branches take time to Heinemann's some of the history's approach. Feynman, when we ask, consider a particle at the location x and then at the location e,

35:00 what's the probability that human covers from x and e? And the answer that is kernel SD squared, where this kernel SD is the sum, or generalized sum, of amplitudes along paths from SD. While unpacking it a bit, we will write kernel is the generalized integration with the option where the action is the familiar integral over the Lagrangian, if we assume a standard the result is following. The integration and product here is what I'm supposed to convey this formula here. Now, one tragic thing of this formulation is that if this formula at the first appearance is correct, then we will have interference all over the place. However, the mathematical path is the so-called dominance of classical paths, that is, paths along which the variation of the action vanishes. And roughly, the approximation is that the kernel is the sum over these exponents, over classical pathology. In the illustration here, although there are many parts born, there's only one plastic car, so the probability is just the kernel squirm and the stomach appearance.

37:30 Now, for calculating the altitude of the kernel KST, we consider only paths that go to regional locations in SMT, and there are some problems, so returning finally to the double split, without detectors and splints. We observe first that there are only two classical paths. The kernel is roughly the sum of these two exponents, which, given the usual formula with the kernel square, So, to the morals and conclusions finally, so the first question may be, to some of the probabilities or not, gets an answer, namely, by the causal probabilities of Miller, there disappears some of the probabilities in the context of the experiment with the tectos and the stits, but don't enforce something in the experiment without the tectos and the stits. The second rule is the importance of the spread locations, namely if we did not have spread locations and worked with classical trajectories, then we will not get interference terms. And finally, it's about the observation that the interference that our believer here will find the issue. Thank you very much.

40:00 Thank you. Oh, that was about the, the, the, the classical, uh, dominant, dominant approximation? I see. I see. I was, okay. I was happy with this approximation. That's the last thing here. about buttons that I misunderstood, because actually there is an approximation, so I mean if you are doing an exact calculation with Herman Pax, you have the same result as if if you make the foundation with a time-dependent shooting and recreation, and last, considering the precise boundary conditions in the exercise. And what is important, that this is actually a common mistake, that we are just adding the amplitudes, so to say, saying that we have a disjunction of two possibilities, blah, blah, blah, which is, of course, absolutely not true. This is, even from the Schrodinger equation, what we have, it's just a perfect, but this This is too only an approximation if the holes are very small relative to the distance of them. But the clarity of the extreme education does not follow the kind of linearity of the boundary conditions.

42:30 That's the point. Not to mention that it is an absolutely stupid categorical mistake to talk about the disjunction of the possibilities. I think that the, it's unfortunate that you haven't dealt a more than a partial derivative, but what happens is that when h bar is small, it's the functional derivative of s with respect of the parts, the zero of the classical parts. This is the stationary phase of approximation So it's not really an issue about single slit experiment, it's an issue about age value being small that makes this approximate classification. We had a similar discussion before, I'm a little bit unsure that I'd like you to tell me a little bit more about or answer the question. At the beginning you said that the branching spacetime theory was a theory in synaptics and physics, and then you started talking about physics, more or less the rest of the talk almost. I would like to know a little bit more about what's the physical status of these branching spacetimes. So consider, for instance, the following problems. Yesterday, we made an experiment that the experiment might have two results, plus or minus, I think we've got plus. So the question is, what's the status of the possible result, minus? I think, is this regulation addressing your And what's the status of one of the possibilities of the moving leonards?

45:00 Okay, so that would then mean that these private spaces don't really have physical existence, it's more sort of a modal existence. Yeah, so then the branching space used as a semantic for language moving modalities and tendencies will deliver as a true disstatement yesterday the result was possible But now, it's not possible any longer. Okay. So, if you make an equivalent, not possible any longer with unreal, then you can safely say that yesterday's possible result that did not occur is not real. Okay, so you're not thinking of branching spacetimes as a sort of having a physical existence in the sense of a trans-spacetime or something like this? Unlike Belmont. No, Belmont. Okay. Yes, of course, for Belmont, there is no ontological... Well, if you want to see what you're talking about... There is a second point of the dilemma, namely, for a logician, the whole thing should provide evaluation of sentences. So if you have a sentence like, yesterday, I might have had a camera, but I decided not. So, in order this sentence to be evaluated as true, there must be, in the modern, this unfortunate sentence, with me possibly eating that heaven. And you cannot remove it from the logical point of view, because you will not get the proper evaluation sentence. why a logician like Bernhardt is insisting that he have a history, as I call it, is still there.

47:30 It's still there in some logical or semantical sense, but there is no need that exists to I mean, this fan of the paper about no red line. So I mean, it is difficult to explain. I'm not that person who is able to explain this idea, but it's far from me. but in a certain sense they believe or explain that finally in some sense we are not able to make any difference between the ontological stages of any possible history. The worry that the relativist has, of course, that if you take it as a physical plunge example, that you will have to deal with Gerard's theater in sounds like this, which brings autology change. Autology change. Did I say autology? Autology change. Autology change. Autology change. I had a technical question. In your definition of the particle, you restrict yourself in your final particle. You restrict yourself to the particles which are subluminous. But usually you have to integrate your whole particle. So you get something that is different from the chemical. Yeah, these are really muddy waters, because there is the basic inconsistencies, I am writing, non-relativistic formulation of Ayman approach to rudimentary relativistic So that's true, and usually what needs to be done is to use the relativistic version of

50:00 And then, there might be this difference in the approximation produced just by the restriction of the sub-Lenin rule. But, I'm not so sure. Is it true that in relativistic quantum theories you will, in fact, have a fine molecular role that involves superluminal parts? Well, yeah, usually you have, in the relativistic theory, you use a final propagator. A final propagator is not causal at fault. So there is a real dismatch between your kind of chain of little diamonds, because the natural interpretation of your grey diamonds is that they are the support of the parts that will contribute to your final digital. There are two small ones, but you can use the branching space-time description, just you should open the white box. of a certain point appears along the life of, I mean, all relevance or all influence or something, how to say it, is propagated with your life. And it's not necessarily true. For instance, the letters are delivered by the Hungarian folks of this much slower.

52:30 I mean, you said in the very first transparency that it's kind of, because of the world, like a possible rules model. And of course, possible rules in the Lewis dialogue, because it's not better than I do, can satisfy the logician worries about sentences, propositions like these ones, you know, and all that. And Lewis could also satisfy worries about that's a far richer and broader structure, I mean for Lewis, one of the, what we're talking about, would be one possible world, one could have well put as well, one history in itself as one possible world, and all of them as possible worlds where there is no literal branch in one's place, but still there is this neat, this duels for, you know, giving in a model of modality. So I wonder in which sense this branch in space are meant superior to it, because it's possible. Because you can put that axioms on data, and you can do theorems, and in Lewis-style cosmologists, you can place it in anyway. I haven't seen a single derivation between Lewis-style and cosmological theory. I mean, you can use words just by fear, I would say, miracles, strange special temple pictures, and the walls, Santa Claus, do you remember that? But there is no miracle. Can I follow up? I mean, I think that there's three different things. One is the traditional idea, which is somewhat familiar to a space-time theorist who is never worried about modality,

55:00 what they sometimes call the trousers world, the space-time that gets a topological rupture. But now that you have been talking about modality, there's two ways. There's fellow nationalism. Lewis. Lewis says that indeterminism is a matter of two total possible histories which match exactly up until a certain stage after which they diverge. But they're distinct. There's no mutual overlap. Belknap says there's a single reality and then a divergence. Now, So, mathematicians will say, big deal, can't I make my theory much the same? Metaphysicians will say, literal overlap is not the same as duplicateness in Nyman's space of mobile reality. and so we can fight about that in metaphysics. But Holger's point is, surely you can do most of the discussion with full rigor of Bell-Nap-Clap's expanded of rigor if instead of your W and then defining histories as maximal paths in W, you start with a curly L for Lewis, which is a set of possible histories, And then, with these as your primitive items, you can probably recover something like Right. That's the kind of... Well, that's the management there, really, whether you start with histories and make them match up until a time and then diverge, or whether you start with points and assemble chains. That's good. But in a simple group, it will not have a real indeterminate, not necessary. They do, they do. I mean, I'm not completely sure, but there are those options in Merlach's branching statements, for instance, axios that deliver exactly that kind of splitting, and these are axios about branching.

57:30 I am not so sure whether they could be simply rewritten as axios about publication. I think that much it belongs, because it's a nice axiom, a single axiom, that they use the W-like shape, says, if you have an event, E, that belongs to one history, but does not belong to another history, then there is a choice point of these two histories that is below the question. And that's enough for the legal in the W shapes. I'm not sure what would be the meaning of all that translated into the duplicate term. Well, another point is the difference in the notion of tenses and allegedly necessity of referring to your point of appearance, which is very emphasized in Lewis's problem. So that's completely absent from the standard of the U.S. So the answer that I gave to Witschich, I couldn't do it. I couldn't give it in the standard of the U.S. because there are instances in the U.S. My efforts are now for now. OK, so one last question. and I'm glad that the country has impressed me to this Hungarian conference the author. What is Garofsky's theorem? Well, you're not allowed to have a topology change or a construction like what Jeremy called the trouser world that you have a if you cut it crotch, as it were, you have topology of whatever, some connected topology anyway, and then you make a later cut after the crotch up here and you have sort of a disconnected two connected

1:00:00 components, and that's not allowed, given certain conditions of course, which however all seem more or less intuitive, such as Hausdorff quality of space. Okay, we can discuss about, of course, the conditions but then if you want to take this literal then you would have to deny at least one of the conditions of of the theorem and that's just of course the structure of the dialectic Thank you so much. the spatio-adaptive areas of this achievement. I know this is a question. OK, before I ask you to thank Thomas, do I just say that we're going to have concluding remarks from . So he's going to invite your . So thank you very much, Thomas. Thank you. I would look back a little bit and take a look at what this network has done in the past two and a half years. Not only is this conference over, but unfortunately perhaps the whole network is actually going to be worked by the end of this week. So I think it's time to take a look at that and look back at what we have done. And at the end of a little review of this little report which I'm going to present to you, I'd like to also ask you to comment on what we should do perhaps in the future that would be beneficial for this professional philosophy of physics.

1:02:30 I'd like to begin by some comments concerning the history of this matter. This is the logo of the... of the matter, as you may already know. Anyway, so the structure of this little report is that I'd like to see a few words about the history of this matter and then summarize the activities which we have organized, and in particular I'd like to show you some numbers and some statistics as to who got involved in this activity and how many of them are. And finally, as I indicated, I'd like to discuss with you together as to how we should perceive in the future. What is it that our production needs? The idea of establishing a network came up in the discussion, which in all of the project in February 2002, and we thought it would be a good idea to apply for a PSNAP scientific method project. It formed an eight-member screening committee. The next slide you can see in the names of these three. So that was in March 2002, and when the screening point

1:05:00 was formed, then we contacted PSNAP's headquarter, which is the start board, and asked them that to support driving activity and the feedback was so positive that we decided to make the move and to start with a formal application which was done in May of 2002 and the proposal was approved in December 2002 and the first feeling committee to place the structure into the city of Venice. Well, there, and then we, uh, started. Here is, uh, the list of the members of the feeling committee, and I'd like to take the opportunity to thank the feeling committee for all their heritage. without this enthusiasm, you must be here and you should not be able to do what you have. One comment. I'd like to make one point which is perhaps important because there is a representative view of ESF. She's sitting in the back room. You might have seen her during lunch. She's a contact officer for ESF. And I'd like her to convey a common comment to ESF headquarters, namely that in contrast to the Egan application procedures, the application for the scientific network, PSF was extremely scholarly, extremely transparent, extremely easy, I mean, in comparison with the EU. With EU, the procedure has become so crazy and so complicated that I know that some scholars have to purchase the services of legal, of private companies to help them to care the application, because data and stuff are unlimited to me. Now, I would not like to overestimate the intelligence of the research community, but the application procedure is so complicated that even scholars can do,

1:07:30 that I think it's very bad. And on top of that, there is also the opportunity to apply for funds that can be used to pay those private companies to help to apply. So this is a kind of danger here, this is a Zenonian kind of danger here. The men are actually scarred. Anyway, ESF is very different, very transparent, and very easy. Let me tell you, the only thing we had to do was to prepare a 12 page project proposal. No force to be fielded, no nonsense to be able to be fielded, and it was, that was the only thing we had to do, we had to say what we wanted to do, how we wanted to do it, why we wanted to do it, and that was all. It should remain so that it is placed. Try to do your best. Thanks to Antonio Lamara and Elizabeth Westergaard, they were the scientific secretaries at the time, and William Shea was the chair of the Senate Committee for Humanities. He had a great say in his approval. What have you done? We have organized three conferences of which this one is the last. The first conference was organized by Professor Deeks in Lutrecht with the help from Eosupti on the philosophical conditions of statistical mechanics. The second one was in Oxford, out from Oliver Cooley, and this one has been organized by me and by my friend and for the class to support. We have also planned to organize four workshops. Always in the philosophy of physics is also what you must have seen here. The area of time and thermodynamic irreversibility in La Nude in Belgium by Michel Ginz is not here unfortunately. And there is going to be one more conference on the very topic we have heard the talk about in the last of unbranching space-time.

1:10:00 This is going to take place in Draco in about two months. Other activities which we have planned and which we have done, we created the webpage of the conference, you might actually have seen it. The webpage is maintained by Michael Seving. Thank you very much on behalf of the network. And we also have established Filthy's mailing list. I assume that all of you are subscribers to this mailing list. If you're not, shame on you, and you should be subscribing. Please. This was done by last of several. At this point, out of 2005, it got 469 subscribers. If you have events, jobs, job awards events, please don't forget to start getting used to this page. I think it's a good piece of communication. Some numbers. The total number of talks, including the talks of this conference, I was doing before the talks of the conference, 107, total number of speakers 88, some speakers have been in trouble doing more than 1,000 in these three years, we had two very distinguished speakers here, and the total number of participants including the ones who are just traditional participants are 250. This is the national distribution of speakers, just don't want to work with the numbers, with the media numbers. You will see two anomalies. I will comment on these anomalies. But here is the border of these countries, Austria, Belgium, Switzerland, Germany, Spain, France, Hungary, Italy, the Netherlands, Poland, Sweden, Finland, UK, and USA.

1:12:30 I'm not going to be here, but let me just make a couple of comments on what you can read from these statistics. There have been 13 ESF Congress states that provided the speakers, and this is very much something we have to keep in mind, namely ESF requires a certain geographic diversity of speakers, and that has been done. We have eight speakers from the U.S.A. who could not support more the ESF rules for giving spending more than roughly 100% of the budget for U.S. speakers. I would like to mention here that we should have obtained some MSS support. We failed to do that for reasons which I did not want to discuss here, but which should be perhaps secured. Italy is very strong. One of the anomalies was Italy. This is sort of what we expected because Italy is very strong in quantum information, quantum communication, which is also shown here by Professor John Kaney. In any case, Marisa did a wonderful job in organizing the climate control, corporate control conference. The UK is very strong, of course, especially in philosophy of space and time. This was expected and we should not be surprised, and at last, thanks, Jeremy. Other comments I think have been represented proportionally to their extent, except for perhaps the surge of interest in the direction of time and to the bank. I can't explain this, and I don't know how he managed to get 60 registered participants in the error of time workshop, but I thought that was somewhat surprising. One thing I'd like to emphasize is that it's shown here by affecting young scholars. By young, I mean, I don't mean younger, me, which is really easy. But ones who are PhD students, they are within five years of their PhD degree. In this conference, we have had six speakers who are in that category, we have seven speakers who are in that category, 13 people in the size of a proportion of publications.

1:15:00 with the relatively convenient decision not to publish proceedings after these conferences. However, there are a number of slack papers that have been published in the leading journals . Here are the data . to this detail, discussions will rely as to how do you see it in the branched-based literature and reading literature in the perspective of possible inviting publications in the study of history and philosophy in some. I think the network project is successfully realized. I think the community of philosophers of physics in Europe became a bit better. We got to know each other a little bit better. I certainly had made contact with people who I otherwise would not have made contact. And I told this with a clear statement. I think also that it's fair to say that, if you remember, there were roughly 260 people who got involved in this antiquity. This is, I think, the size of the country is not why the boundaries are completely elusive, but 260 people who are contributing for this is a sizable version of the country. I also think that we have been able to create opportunities during this conference for a libel between what I would call philosophers and non-philosophers, scientists, which are I will come back to this point a little bit later, but just as a summary, I think we made a deliberate attempt to attract and invite scholars, researchers, who do not consider themselves as philosophers, but nonetheless, who do things which have conditions or results, and who are unsympathetic from how to look at them.

1:17:30 And I think we also have succeeded in helping young people. One has the impression that they are a generation of philosophers emerging and I think they should be somewhere in the future. future. This is the last slide, so I hope I'm not going to be here. What we should do in the future, I think we end in a large measure from what we see, our professional needs. And on this point, I'm inviting your feedback, your views on this. Let me just mention here what I think is needed and what we should. I think it's crucial that we operate for the obvious reason that this community being relatively small is very stagnant. By recommendation, I mean that people who are interested in philosophy and foundations of physics work in different academics or departments. Some work in mathematics, some are in computer science, or in history of philosophy or science, and I don't know why. So, all sorts of departments are included. And also programmatic in the sense that at any given university, except perhaps for us who are very large, relatively large, that most places the people who are interested in these kinds of issues are below critical mass. It's just not, it's just too few people who can be at a place who are interested in them and have a reasonable activity. So I think that's very much the view that these people consciously seek the opportunities of cooperation. But I would like to amend this idea by saying that I don't think it would be enough to just have conferences like what Steve had. I think we would need more intimate, more regular, more continuous cooperation. What I have in mind is perhaps aim at organizing shorter visits, by shorter I mean a week or two weeks, possibly a month, coupled with a number of talks, or seminar series on a certain topic which can then be very deeply discussed, or workshops, focused on very specific topics, semantic workshops, as I would like to throw them.

1:20:00 And I think that's what we should, this is what by which I think we should enrich the activity we have in this world. And finally, a point at which I alluded to before, I think what we very much need is the effort of constant striving to establish any dialogue between science. This philosophy and foundation of physics profession is a very dangerous profession. It's extremely easy to say things which are either trivial, or not true, or both. And I don't think there is any insurance against it. The best insurance type that you put against this type of danger is to seek out the rules I hope that you can ask them to get them involved, I think this morning has been a prime example of how beneficial this could be for our profession. With this light focus, I'd like now to ask, to give some thoughts, to give some feedback as to what you think is needed and how you're doing these issues. I don't think we should span a whole hour by discussing this. I think we're going moderate on this government, like you said. Well, before somebody comes in, I want to say I'm part of us all because, I'll say this again at the end, but I mean both about this conference, that are part of the network of quality. Although you were alphabetically and modestly lost in that initial list of the steering committee, you know, our hearts go out to you and the gratitude we've lost for you. Thank you very much.

1:22:30 Because there are only three children, two humans and the network. Thank you very much. So, anyway, this question is likely about the future. The network ends by December 31st, this year, and it cannot be extended. This kind of activity is over with ESF, so we can't go on with that, but there are some other opportunities, partly offered by ESF itself. But the question is what you would like to aim at. So the opportunities are there. Also, I said that the EU is terrible in these applications. But nevertheless, we should try whatever hurdles we have to overcome, I think we should try. The question is what we should ask, what activities we should try to support as a humane effort. Or if you have any particular foundation, agency, which you think could be or should be with some sort of an application to cultivate this philosophy of business, then I think that would suit. I mean, I'm in response to what we need. I would like to endorse, especially your reg, that it isn't so much conferences as a week or three months or whatever for young researchers or graduate students to visit or senior researchers. I think that's good. But also to throw out the questions, meaning people either in the physics community or from North America who think of things like foundations of physics for within American physical society, within German physical society, things like that with other societies with which this community is in fact not in touch, but which it could be in touch.

1:25:00 even at funding possibilities in a way we'd like to hear, either from the physical community or transatlantic colleagues, things that the European philosophy of physics community, which is mostly institutionally in philosophy departments, should be impartial. The Finnish Academy of Sciences, whatever it might be. My question was already answered, but I was going to ask if we could continue years before we cannot. Not within this particular framework, that's not possible. But of course, we can continue with the website. Sure. And, well, yeah. I think this is not really answering Jeremy's question, but I think it's an idea which is