 Okay so it's the first session, welcome everybody, such a such a big number this today, of the Aalofa seminar, it's an annual seminar and this year the Aalofa seminar is without a team, without a team, we are only the Aalofa it's ontological framework of science, yeah and usually we have a very narrow team, but this year no, to open like the first time we open it and there will be many, all the Aalofa seminars, I hope, will be around Belgium, so already we're scheduled to go to Leuven, we're scheduled to go to Liège, hopefully soon Namur will say yes and we will have a a wandering seminar around Belgium and of course part of your traveling will be paid by the FNS for that, but it's not that expensive, so traditionally the Aalofa seminar, I'm saying that to you in fact, are about ontology in science but without any dogmatism, so we're not realist necessarily or anteriorly, it's just when you pay attention to ontological commitment in in the language, in especially in the theory and the representation, that's part of the Aalofa seminar, you can be realist, you can be Daialist, we don't care, usually we try to avoid realism and we try to have a discussion more about the kind of commitment inside the practice, the tradition, in theory, in the way people speak, so it's why there's the part about language ontological, with onto, with separated from the logical, so we have a very nice bizarre French way to kind of word it, because it's more about language than about, you know, as electronics is, I don't care much those body, but do you commit to electrons when you build such such such such so today it will be exactly in that tradition and like I said before, it's again one of my bizarre ideas, I have an idea that something has not been made I think I look for literature, I find nothing and I say but it's a great subject, it must be done I must do it and I discover why people do not did not do it because it's so complicated, so today I will present more project, not a paper possibilities, ways to go somewhere and after that Kevin will come up to start the discussion and I will try to give you the flavor and be as less technical as possible because it's quite a technical subject when I'll try so don't hesitate where our small number you can cut me and ask questions if something is really obscure and it would be okay so just to introduce the subject so when we think about modality and physics in particular all the debate and I say all the debates are about loss, disposition, they are about the part of modality that is necessities what are the natural necessities what should we commit as natural necessities what could they be and they are never and I say never about possibilities ever you would think it's very strange there's nothing published on natural possibilities and physics except to discuss probabilities that's all and you would think you know if you have necessity necessarily you discuss the dual concept no so when you discuss about natural possibilities we have to turn to metaphysical metaphysics literature and it's very interesting the way metaphysics most of metaphysics literature describe possibilities natural possibilities here I put a very difficult quote of Williamson and I will I will read it because it shows exactly how metaphysician understand natural possibilities and it's quite weird for me but understandable in the metaphysical literature like I said physical possibilities usually understood as nomological possibilities so already they push towards the necessity again and this is the quote typical definition of numinical impossible okay is a proposition is numinical impossible so it's a possibility of natural possibilities if and only if it is metaphysically impossible with what in those circumstances are the laws of nature their congestion is metaphysically possible so for the metaphysician a natural possibility is a metaphysical possibility that is selected by laws so all the work about possibilities is done when you define metaphysical possibilities but not when you never directly treat natural possibilities you treat natural laws and you see the natural laws select in the metaphysical possibilities and if you look at the literature about metaphysical possibilities there's nothing about nature it's always it's a kind of objective possibility that you contrast with epistemological possibilities or normative possibilities so the debate is about the difference between metaphysics and something else but it's not about not nature so i was dissatisfied interested it's very elegant it's a very nice definition i think it's very clean it's very clear but it does not help me to understand natural possibilities without passing by laws okay so my plan was let's let's try a bottom up approach let's try to look in physics directly where scientists talk about possible possibilities and that that's that's the plan and that's the plan that i will explain i mean a difficult position to achieve the plan so when you look directly at how possibilities are used in the physical discourse you automatically see two big families there's the experimental possibilities empirical possibilities and theoretical possibilities in the discourse i'm always talking about the discourse so experimental possibilities is systems and their behavior because in physics it's always systems and their behaviors that's the basic ontology of physics that could be empirically produced and the debate should be about the difference between pen and code should it be defined in principle if you had the technology or should it be defined with the technology you can really use and there's an interesting debate and a big part of the dissertation of my student can't remember it's about that and it's very good and this book will be available or if not already given very soon and there's very nice things to say about what is an empirical possibilities and the other possibility that i will the other kind that i will discuss today is theoretical possibilities so systems and behaviors that could be represented that are at work in our best theoretical families so today i will concentrate on this one but of course a bottom on project should include this one too and the question of the relation should be discussed but i want to today so when you look for possibilities discourse of possibilities you have to look in certain formalism where you have to discuss okay i vary the situation we could have done something else etc that's the way we go into theory to see what is about the theoretical possibilities but first there's the problem of what is a system and you would think that after hundreds of years of using this word it would be clear absolutely not here i put four defendable definition and there's other one about what is a physical system and of course of the ideological systems it's even worse because the individuality of biology is more complicated than physics so first definition a system is a collection of entities here where i use the word entities in a very loose way so it's the for me it's the more general you know it's more general than object individuals etc so a system is a collection of identities forming a whole in a certain sense system is a connected portion of space time and everything in it or the system is an entity for which we know what happens on the frontiers whatever you mean by frontiers spatial or not you know the system of a quantum system the frontier will not be defined by space time or and that's that's the Aristotelian strategy it's the subject of dynamics so if anything that has a dynamic is a system so in this talk really i don't want to enter in a discussion about system because it would be another paper but in this talk i will for practical reason use the the intersection between these two definitions so the system we know what happened on the frontiers and a system that is subject to dynamics so i will really concentrate when physics talk about behavior spot about change talk about stuff happening and not when physics talks about structure crystals things like that won't be discussed here okay so for me for the rest of the talk system is in terms of intersection of these two definitions whatever it is okay if we look to classical physics so for those of you that do not know what classical physics is when it's not quantum every part of physics that is not quantum is called classical question if you go to classical physics and you look when scientists when physicists invoke explicitly possibilities there's there's the main place to see that it's in when they invoke a variational principle so they try to get to an equation by varying certain conditions so mathematically variational principles are at the center of physics they are extremely important there's many ways to use them there's many of them and there it's the clearer use it's not the only use of possibilities but there's a clear quantifier on possibilities when they say i i vary blah blah blah and the good solution will be blah blah blah but problem they don't seems to be coherent at least in no way they use that it's pretty free in certain case the system you're trying to describe keeps its identity and you vary the possibilities the dynamics you vary the dynamics of course Aristotelian people will say this this is wrong a system cannot keep its identity if you vary the dynamics but it's what they do at least in the formalism and there's some formalism that correspond to this strategy but you can also and this definition i took in butterfielder i will quote it quote in next slides you conserve the identity of the stem and the dynamics but you do you you play with the frontiers or everything that is contingent so you vary the contingent you keep the identity of the stem and the dynamics or you keep the dynamics but you vary systems and this is some generalization of the Lagrangian formalism and the Hamiltonian formalism is what you do so there's a lot of ways to get to the dynamics to the physics to use our general principle there's no general theory of very traditional principles in physics there's some relation between them if they are empirically coherent or not but it's it's it's an art it's techniques that were developed along for a long time in this talk i will only focus on one of them the Lagrangian formalism standard use so you keep the identity of the systems and you vary the dynamics okay because it's a short talk and because i have good reason to believe that the Lagrangian formalism is central to physics more than the other why two reasons that only interest in philosophy are physics but i'll probably explain it to you there's a problem in physics called the problem of time so time does not behave well in many formalization of physics so it's called a problem of time so sometimes for example general relativity you could you could show that time there's a strong reason that there's a there's a the time is not a real variable it's a gauge variable so so it's arbitrary so it looks like conventional it's not conventional it's for certain because if you believe time it says so there's some pathology in many form many theory physical theory related to time but Lagrangian is extremely robust the Lagrangian formalism to the problem of time it's the more robust so if we we think and most theoretical physicists that i know believe that we will have to get beyond the problem of time to get to the quantum gravity the next big theory the problem of time is a real problem it's not just an artifact it's good to use a formalism that is robust that is not affected by the problem of time for example the Hamiltonian formalism which is a very popular formalism for mechanics and for classical physics is you have to twist it to add constraint to do something quite complicated to make it survive the problem of time to be able to do some physics second good advantage of the Lagrangian formalism it's one of the formalism not the only one but it's one of the formalism where the passage from classical to quantum physics inside of using the formalism is elegant it's direct it's a nice transition so it's under control mathematically compared to other formalism so it's a formalism that is robust for the main problem today of the problem of time theoretical physics and it's a formalism that could be used in a certain way for classical and quantum so you can compare you can discuss transition from one to the other so it's a very nice formalism that's the main thing you should keep in your mind it's a nice formalism and i have to say i'm not sure i should say that recorded that most paper in philosophy of physics stopped there so it said i describe my new formalism i really like my formalism i don't solve any philosophical problem because i don't care but look at my formalism it's better than yours or it's nicer so that's typical philosophy of physics i'm just saying that for a philosopher would be a biology that aren't real philosophers oh man that line it would be bad okay let's discuss now a little bit of the idea of possibilities in the Lagrangian mechanics because i presume that you don't you accept Kevin or you're oh and and Matthew you're not familiar with it so the basic unit of possibilities in the Lagrangian mechanic is called kinematic possible things it's a mystery what is a mystery it's something like that it starts somewhere it finished somewhere it's a mystery it's not necessarily a trajectory it could be anything time is inside so it's not even clear that it's a passive it's not a mystery a story like a passage of of state true time no it's a block you don't think Aristotle thinking history it's a thing okay and that's what a kinematic kinematical possibility the set of possible histories of a system make the set of possibilities of course now i i did not define it and and it's almost never defined in physics it's presumed that it exists i will in the next slide discuss a little bit what these kinematic kinematical possibilities could be okay just this i have a set of possible mysteries of the system the dynamical possibilities are a subset of this set and they are the set of possibilities that could actually happen according to laws to what to the necessities so you have kinematical possibilities dynamical possibilities or or a subset of the kinematical possibilities and i have to say that the distinction of between kinematics description of movement dynamics you know why the movement happened is a very canonical distinction in physics certain would say since ganileo there's description of movement compared to description description of why and if you look even in you know and scopedia britannica 1911 you see clearly in the Boltzmann article about physical science physics is divided between analytics and dynamics and among the analytics there blah blah blah blah blah so it's it's strange but you know it's our discipline aside okay now whatever these kinematical possibilities that are rarely explicitly defined oh no next slide first if a history is not a succession of state it's a block how could we define change in Lagrangian mechanics because we don't have change we have whole history possible history of the system so here i have to say that there's a a pirouette in french there's no good term to say that in english there's a technical way to define change in a basic ontology where there's no change up so change is the absence of non change so change is the absence of changelessness and what is changelessness the invariance of history under the time translation of a group under spacetime blah blah so there when you take a history it's not a succession of states so you don't have a natural notion of time of change but you can say sorry to history have this property when we do some translation group blah blah blah transformation that allow us to think that these are describing change and not about it okay it's not important for the rest of my discussion but it's just if you worry about the fact that there's no change in my basic ontology of Lagrangian mechanic you're right and it's why Lagrangian mechanic resists to the problem of time because there's no time outside those necessary there's not a general clock for all these change okay so the atoms of possibility in Lagrangian mechanics histories and histories are not succession of states index by time okay come back to kinematical possibilities so i propose i propose that there's such a set but what could it be how do i define the set of kinematical histories and there's not much literature about that in fact even Butterfield does not discuss that in details and Butterfield 2003 is the only paper i found on modality possibilities in physics serious paper philosophical paper there's there's maybe others but i didn't find any but if you look at the way it's defined so of course dynamical symmetry possibilities are subset of the kinematical but when you look it's the dynamical we're interested in because we want to know what happened in the actual world you see that the kinematical that are first because they didn't let go are subset but in fact since we aim for the dynamical the natural way to understand the kinematical is that what would have happened to the system under different laws so the kinematical possibilities according to my interpretation of the Lagrangian natural that i find natural of the Lagrangian mechanics is necessarily nomological so there's no possibility the kinematical of something that is not there's no laws there's no necessity in any modality of any kind of a certain set okay so it's the set of history generated if the system could be governed by different laws so it's a very structured set much more structured than the metaphysical possibilities but of course it's more structured it's it's it has been defined for other use for use to do that discuss dynamics and solve physical problems so it's normal it's it's much more structured but it's not just a little bit it enormously more structured than metaphysical so the according to this formalism the space of possibilities is much more structured than the general space of metaphysical okay how do we know which which kinematical histories or are dynamical histories so how do we work this variational principle i was talking about a few slides so this is the principle this is the way it's done so you say that the action the action is yeah the action is a functional of histories so for each history it gives you a number each possible histories gives you a number all the laws of all the dynamics is coded in l in the function l so it's a functional of histories so for each histories it gives you a number and the idea is that the actual world dynamical is an extremum of this function the action function so it's a minimum or a minimum or a maximum local so among all these stories i have this function called the action that gives that gives me a number for each histories and the one that is physical are the extremum of this this function a two remark there could be one more than one extremum in the space of possibilities because the extremum is defined locally it's locally a maximum or minimum so the status of actual what is actuality it's not that clear it's that because there could be at least in principle more than one actual situation for identical loves identical situation second remark you see now that the kinematical possibility is even more structured than we thought because it's defined in a way that you can define this function this number on each possibilities and this number and that's that's explained in the in the battlefield paper could be built as a as a as a metric so you could be you could have a metric between histories histories with closed action or closer in the space of possibilities than history with big difference of action so you're not you're not in your typical semantic of possible worlds here maybe you could accommodate this semantic of possible world but but it's not obvious because you have a natural metric a generous metric okay now a warrior philosopher not a warrior for scientists a warrior philosopher i explained the kind of possibilities blah blah blah a warrior philosopher is the actual history extremum because of the Hamilton principle dependent of possible numerical possibilities and you have you have your mathematical expression that says if you have a local extremum of that it's when you have a local extremum of that and this depends possibly on other histories than the one that is selected so is there is there here a necessity to comment if you say that this formalism is committing to possible histories beyond the dynamical world beyond the actual you could also find that in term of truth maker is the truth makers of this sentence beyond the actual world if it was the case it would be extremely weird okay because usually in in classical model language we're discussing about the model property of the actual world we prefer to possible world as tools to understand the model property of the actual world we don't commit to the existence of these possible worlds to explain the actual world we can commit to the possible world for other reasons like Lewis but not because you need absolutely to use them to model the truth maker of sentence scientific sentence in the actual world this is a real worry and i i say that that no there's a way to get together and it's well explaining it's a strategy that Lewis developed for another problem that Butterfield used for this one and i think it works so i will just resume this thing is that you know the minimum here you have to find the minimum s to have the actual world the actual what happened and you can say that the possible world that you need to the possible histories that you need to compare or in fact very close possibilities so in fact you're just discussing a variation of your world little variation not too far from this world so these the truth maker here that seems to require to discuss possibilities that will never happen could be reinterpreted and that's the Lewis strategy as just discussing variations of our world so model properties of our of our the actual and there's nothing in this equation that forced you to go beyond because each history each action only this is the properties of that's history and there's nowhere you discuss a real relation between a thick relation between possibilities you just compare possibilities this one has a bigger action than this one you never have a thick relation that would force you to discuss the status of each so you have only intrinsic only a relation that refer to intrinsic properties of each possibility so no danger no possibility of truth maker difficulties okay so for the non-philosophery physics and even for philosophy physics the very condensed it's called the condensed foundation so here you have a amplitude of transition so here you have something that says that that will be if you do the square of that you get the probability that with a certain state you will get another state a state in a state out so this is a model property of the actual world say after that some interpretation of quantum mechanics interpret the probability in a sense or another sense but that put aside but at least everybody's talking about the probability here how do you compute this probability you do a summation and integral on the possible classical histories of this function of the action so to get a probability a quantum probability an hour ago you need this formalism to do a summation of a functional on possible classical mysteries so you have to use the k possibilities of classical mechanics to calculate something about the quantum world and this function this this it's not a function this this element of the equation is the volume density of history so your history is even more structured because you need there could be more or less dense histories depend in the space of possible histories and you have to know how dense it is to do this calculation you see that even before interpreted that cementically okay that's the goal to talk about possibilities in possible world is to interpret this equation semantically this does not look good for standard model thought because here you have something like a density of histories it will i don't know how to get rid of the relation between histories if you have explicitly a density at play in the in the equation second it's quite strange that here you have quantum information and here you require any possibilities which are classical which are false according to most people defending quantum mechanics the world is not classical how to interpret these possibilities cementically so i see two questions and i will just catch the way to answer them and we'll be able to answer it i see two big philosophical questions first one how do we interpret this dependence this is you know syntactic stuff where you have actual here classical possible here but in which you know semantic of modality this makes sense secondly before we have just comparison we just have comparison possibilities here we have a sum of phase so some possibilities we constructively interact other word destructively interact what is the status of a sum of possibilities i could say what is the status of the sum of possibilities of this six phase dice but i just add them i don't know if there's no meaning interesting here it's quite important you need the sum to get the possible thing about the actual what is the status of the sum here so first question three strategies first you explain that in fact there's no problem it looks like a problem but we have good reason to say it's not exactly what i did with classical physics play before it looks bad but it's not first strategy second strategy get rid of the candidate the kinematician find a way to say it's redundant third and more pragmatic considerations yeah it looks bad but for cognitive you know social blah blah blah reason we cannot do otherwise three different strategies that are not not necessarily exclusive but to make sense of the first question so let's maybe it's not a real problem because in fact these classical possibilities using this formalism aren't really classical possibilities they are some kind of quantum possibilities written another way you know yeah in a certain sense a classical possibilities is a quasi limit of quantum stuff which would need to be very discussive details to make sure it works but something like that and maybe if we adopt the consistent histories interpretation of quantum mechanics where you don't have classical histories but you have the coherent history so almost classical history almost in the mind of physicists of course not in my philosophy so that would be a strategy to say there's no problem second strategy to say there's no problem okay classical possibilities are false and impossible because we know that the world is quantum or something like one so they are impossible in our so let's use you know that those impossible worlds formalism i have no idea how to do that but why not let's try impossibilities generating stuff about the actual world will be typical of that kind of metaphysicist on metaphysicist okay it's been it's been a long time i'm talking english you know one year at home okay so this i'm just putting that there i have no idea how to do it but i know that some people said to me maybe you should try that why not it's not that was the first strategy you see that not easy not easy i don't know how to do it in details just except waving my hand saying yeah there's some kind of second strategy get rid of the kinematical possibilities nobody to my knowledge know how to do that it seems that we always need something of classical physics when we build a quantum theory so maybe it's not necessarily a proof it's not necessary but we don't know how to get rid of it so this strategy for now is not very strategic and i use one of these strategies in my another paper another subject yeah you know we have cognitive difficulties to understand quantum mechanics so when we formulate quantum mechanics to equation we need to rely on classical physics for all commutative mathematical formalism we're just on it's just a good trick since we do not have a consensual solution to the measurement problems we don't really know how classical in quantum connect quantum physics and classical behavior empirical behavior connect in the real world we don't really know how to get rid of it and it's because there's another deeper problem in quantum mechanics that we have to solve first so as you can see i'm not that impressed by these possibilities but they seems plausible someone could try to to do second question and i will that will be the last part what about the sum what the sum what is the status of the sum here the sum over classical possibilities to get to quantum stuff and i've thought about that for a long time until i discovered that i had a solution in another paper that i that i wrote not a long time ago and i forgot that it was a solution to this problem so in a paper with the published in 2018, Vincent Durair, we developed another new theory of quantum causality and we had an interpretation of the sum puzzle so in fact it's an interpretation a semantic interpretation of the syntax of the sum and i will just give you a flavor because it's quite technical maybe Kevin will discuss that because he read the paper yesterday or today but i will just give you a flavor of this theory and you will see how it connected possibilities and sum of possibilities give a semantic interpretation of the sum of possibilities so here imagine classical process they are classical so there's the process one you give him a zero give it the zero it gives you zero process two you give it a zero let's imagine they are deterministic process okay so you can be understand as causal process in a down you know classical process rule conception of causality and you have here you know these same input these two processes something i have a process of interaction some kind of interaction that makes the process and i have a result so you see here everything is actual it's just two classical process interact it's a typical causal interaction okay okay now imagine that you have the same process but this process could sometimes be zero or one okay so along this process is a classical process giving sometimes zero stochastic or sometimes one okay but you say these two histories the one in which the process gives zero in the one they in fact interact causally in the quantum world so these two classical stochastic histories combine in the quantum process like they were happening at the same time but not cool they are not happening they are possible stories that interact in a certain way and that's what this quantum process rule goes out so we can generalize that do a lot of math and diagram engine for it to work but it's the basic idea is that possible classical history so possible classical process a quantum process is a combination of classical incompatible stories like they were happening at the same time but of course they don't i'm not realistic about that it's a black box it's just a way to represent the difference between classical process and quantum process so one of the conclusions in the paper in our account of causation a quantum causal process is a model functional addition of classical causal process in consequence quantum causation is radically different from classical causation however there's a strong continuity between classical and quantum causation for example possible histories that are close to the actual classical one contribute more to the quantum process than the one that are far there's a relation between two to the transition and pletur and that's a way to interpret causally this this sum but of course there must be other semantic interpretation around that i didn't find so the conclusion i was pretty sure that's cool this short exploration shows that when you start from practice you can get to very strange stuff that will be difficult to fit in the very elegant model of metaphysician i'm not saying that the model of metaphysician is wrong it's not a falsification but at least it gives you an an instation to go deeper in you know what what are the possibilities used to maybe enrich the metaphysical the metaphysics pure metaphysics for medicine but of course we cannot just say they are doing that and that because maybe it's inquiry so at one point we will have to connect with food makers semantics semantic of possible a formal tool developed by metaphysician logistic or logistic to to come back to physics and give a good semantic interpretation in a nice formalism that guaranteed coherence and not obscure not to be obscured so so here i see that the the notion of Lagrangian possibilities that they are used in in in in physics and classical physics and use also in in metaphysics it's much more structured and much more uh structure than metaphysical possibilities and that this kind of structure at least give us a certain flavor or possibilities that we can maybe define natural possibilities not just as what is selected by laws but something something richer something more interesting and how to represent this richness in a nice you know model formalism for me is uh i don't know i i tried then i didn't find i think possible worlds are not perfect for classical physics but i still do seem to do the job but clearly they are completely useless because there's some kind of density and some stuff that would make possible a little bit difficult to understand thank you and here are comment of Kevin should we turn that or maybe you should yeah that's the easiest way finger distance yes okay thank you for this talk i think i want to start with a few general comments a couple of things that i think is really nice in your talk one is the fact that you're talking but like rungent but the history is not drag to this it's very nice to have research orization with general coordinates and we are not just talking about movement but i think about change your mass often no yeah i'm i'm a root no i don't know what's the root okay uh so yeah i think this emphasis on histories in the dynamics rather than treachery is a really nice thing because of this extension to quantum stuff in quantum stuff when you do Feynman diagrams a lot of people tend to have this wrong interpretation of Feynman diagrams as treachery of particles which is not true and it's nice that we insist on histories of our treacheries another nice thing with that is that uh movement doesn't have uh movement is not like a specific stuff it's just one of the change and i think metaphysics is a nice way to see stuff rather than just think that movement is a specific stuff that physics should put in another special uh place um another thing is uh with this uh quantum and classical relation that you should show it is uh it's uh links back to a problem that we had that was in the start of quantum mechanics with Bohr's principle of necessity of classical conceptions to use to describe metaphysics because quantum physics because as Bohr said at the time when you're doing experiments you're doing everything classically and so to link to quantum stuff you are forced to think classically so you have here i think another instance of this kind of issues when you talk about quantum stuff what are you talking about because why every efficient we have it every thinking we have is about classical stuff so here we have another kind of this issue with how to understand quantum mechanics after a while i have a few other comments that i'm not so sure about because um you were saying that you probably want to do this stuff to avoid having the selecting by laws possibility selected by laws but uh when you're talking about physical uh possibility in physics my understanding of it is uh it's the possibilities that are selected by the equations of your system that your system follows so in that way how is different from selecting by laws i'm not so sure about that so can comment that out uh you want me to uh comment that i know i can say nothing but uh nothing that i know i can wait at the end okay okay no it's really okay no i can have other questions i could just specific question that issue want to i can flow okay uh another thing yeah i know i think i had a point of question with is uh with this possibility of having uh the fact that you're talking about having more than one experiment for the histories uh because you say it's because of the locality of it but there is another possibility uh with linked points if you have linked points you can have different uh trajectories and you can't select just up here on which history is the actual one because you have uh continuum and we've all the actual extreme of action without all these infections um and after what it would be a more general more precise question on the extension to your dog so you want to install no on that okay okay thank you for this already too good question so i i used the word i used the world the word um variation a kinematic history is what blah blah blah the history could be if there were other laws of course i used the word laws to make to be to become principal but it's true that it's it's a bad word because laws means something else in metaphysics of science so means could be could be disposition could be and no i should have been chosen by the dynamics and a kind of dynamics in physics is a not say primitive object but it's considered a primitive object in the way people talk and after that people like us metaphysics try to understand could we understand what is a dynamic through a concept of laws okay but you're right that i was claiming that i was bottom up starting from possibility to get to a different thing but at the end i i was saying that in fact they in fact these kinematical possibilities depend of what dynamics possible dynamics so someone could say in other words laws yes so so that was not the goal i don't think but it's the conclusion on the other hand i still think it's a bottom-up approach because it starts from the practice and not from the metaphysics so it's not bottom up starting from possibility to get to laws like i announced but still it's starting from the practice but you're right that i should have been maybe i should not use the word laws it's only later in the project when we try to interpret what is this selecting dynamics or this structuring dynamics and could it be explained by a theory of laws i'm strong like a like the lewis et cetera sorry that you're absolutely right what was the second one yes you're absolutely right that certain case of multiple extremum are not problematic they could be the produce of a surplus of structure in the formalism they could be in the way we built the we built the coordinate system there could be all kind of example that are just non-problematic they are but still there's the possibility that we can meet problematic one it's not forbidden in the formalism to my knowledge in the lagrangian formalism that there could be more than one genuine extremum that we would have to discuss but you're right that many case of multiple extremums are easily dissolved so again if i can follow on that so we have these cases with where the set of dynamic possibilities are not just a single element and you have several of them like if you have a coging variance something so in terms of this modernity interpretation of it how do you interpret picking a cage to resolve your system but it's actually doing practical physics okay and that that's just an asti question because you know no no it's not nasty you know you know that it's a technical question that i could not answer because it will depend of how you interpret gauge gauge gauge gauge degrees of freedom uh i would say for pedagogical give reason that many of our best actual theories are what we call gauge theory so they have this symmetry that makes that that says that there's too too many solution for the real world and so there's this end determinism in the solution and you have many solution and you have to to select one to get to the to the prediction and i have to say that this is not rare all the best theories that we have standard model generalities all have this flaws should we say flaws for now but depending of your interpretation what is what is that play i think it could be a problem or not so if you see you say that it's a surplus of structure that the standards interpretation it's a technical problem to get rid of it okay it's a technical problem how to get to the to the to the real histories the real mathematical objects and dependent of the coordinates because this is why i like Lagrangian mechanics it's because it's a the histories it's an object it's a pure mathematical option that could be described in many ways with many coordinate systems but if gauge gauge symmetries is the sign of something else like relational strong relational properties especially among spacetime points or things like that i think you don't have to choose or you have a natural gauge to choose so you have good reason to choose one and you get to the right kinematical possibilities or you have a very messy kinematical set where yeah that's about the case that there's a lot of physical when you're under the learning physics there's a lot of cases when you exercise and you're just asked to pick a gauge and you have like some kind of conditional gauge but they are not necessary so let me explain why you're in MS okay because the notion of histories will be well defined even if it's weird because it's histories that's it but the problem is the Lagrangian the Lagrangian function to get to the action how do you calculate the action of something that is in very complicated and non-local variables so there there will be a real problem possible problem and there's all kind of trick to get rid of them to cut this symmetry or to find a way to get it under control but it's not in the basic notion of history because a history is a history whatever it is whatever it described it's a history you know that's it whatever you call history in your in your physics it's it's on but when you want to do the amilton principle and you want to to do some some work on that then you want to have a derivation and things like that uh if the if the variables is a mess very difficult to define a variation because I didn't say that but here here it's a very compact way to say that there's a derivative of the of the of the different fields that play through the the the index mu so it's a derivative here so you could have difficulties to define a Lagrangian in a in a correct way so the amilton principle will maybe not work but these are over my big rate but I can see how they could be a problem so to think we discussed this morning so with this question of how to define the Lagrangian because the eyes are in the practice of physics there is another thing that we do is using the tertiary m same as we have principles that we want to uh to apply to our physics systems where they can be realistic like energy and conservation for example and this implies something for a Lagrangian so it's constrained with a Lagrangian anyway it should constrain the possibilities of the chemical and the possibilities we have right so as uh what you discussed this morning so maybe if you want to yeah so just just to explain to to the to public if you have other constrained like you say energy must be conserved all kind of reason of course kinematical histories that we not do not conserve energy would be excluded and how do you exclude it because they are not necessarily in the simple dynamics that i'm using or maybe i don't know that my dynamics is conserving energy or not so there's a theorem there's two and a half theorem of neuters so one of them is to say that for a vast a class of system and i won't define it here because technical for a vast a class of systems if you have a conservation principle if and only if you have some kind of invariance in the Lagrangian and it's a if and only if so it goes both ways but like i said to to you this morning it's not because it mathematically both go both ways that it philosophically or metaphysically goes both ways the standard interpretation of Lagrange for example is that the dynamic is first the conservation principle is a derivative so he would say that okay there's a if and only he would not say because the term was published after his death but he would say there's a if and only if mathematically and i agree with that but conceptually or this ground that and not the reverse and like i said for Lange also it's symmetry that ground conservation principle because invariant symmetry or meta laws or potentially meta laws and they constrain dynamics so it's not there okay it's going up here the guy going down here and coming to the conservation but of course these all can all can be discussed semantically what is the commitment because mathematically these are most of it objection if and only if and i would agree one of the difficulties that i had when i began to just to think about physical possibilities is what are the constraints of physical possibilities beyond beyond you know dynamics is their meta principle like continuity of movement it's implicit here in the kinematical that all histories do not are are are continuous is it in time is it in space not that clear but they are continuous in a certain sense this is not where it's coming from this commitment is there other bizarre commitments like that like energy conservation or whatever others that would be not just empirical derivation of dynamics but meta principle in a very strong metaphysical sense and i don't know what they are because this continuity is the only one i found that seems always every classical history is continuous in a certain sense not always in the same one i could be fields it could be particles could be machines they are continuous in a certain sense but not in all sense conservation of energy you can imagine possible physical classical world where energy is not conserved in certain interaction it's does not seems to be a some a strong strong constraint even if in practice in the practice of physicists a very strong constraint but the continuity for classical physics i don't know how to get rid of it determinism you can get rid of it even in classical physics there's there's possible worlds where classical physics is not deterministic but yeah it's a good point